fit_sim_data_1.py

"""
The parca, aka parameter calculator.

TODO: establish a controlled language for function behaviors (i.e. create* set* fit*)
TODO: functionalize so that values are not both set and returned from some methods
"""

import binascii
import functools
import itertools
import os
import pickle
import time
import traceback
from typing import Callable

from stochastic_arrow import StochasticSystem
from cvxpy import Variable, Problem, Minimize, norm
import numpy as np
import scipy.optimize
import scipy.sparse

from ecoli.library.initial_conditions import create_bulk_container
from ecoli.library.schema import bulk_name_to_idx, counts
from reconstruction.ecoli.simulation_data import SimulationDataEcoli
from wholecell.utils import filepath, parallelization, units
from wholecell.utils.fitting import normalize, masses_and_counts_for_homeostatic_target


# Fitting parameters
# NOTE: This threshold is arbitrary and was relaxed from 1e-9
# to 1e-8 to fix failure to converge after scipy/scipy#20168
FITNESS_THRESHOLD = 1e-8
MAX_FITTING_ITERATIONS = 150
N_SEEDS = 10

# Parameters used in fitPromoterBoundProbability()
PROMOTER_PDIFF_THRESHOLD = 0.06  # Minimum difference between binding probabilities of a TF in conditions where TF is active and inactive
PROMOTER_REG_COEFF = 1e-3  # Optimization weight on how much probability should stay close to original values
PROMOTER_SCALING = 10  # Multiplied to all matrices for numerical stability
PROMOTER_NORM_TYPE = 1  # Matrix 1-norm
PROMOTER_MAX_ITERATIONS = 100
PROMOTER_CONVERGENCE_THRESHOLD = 1e-9
ECOS_0_TOLERANCE = 1e-10  # Tolerance to adjust solver output to 0

BASAL_EXPRESSION_CONDITION = "M9 Glucose minus AAs"

VERBOSE = 1

COUNTS_UNITS = units.dmol
VOLUME_UNITS = units.L
MASS_UNITS = units.g
TIME_UNITS = units.s

functions_run = []


def fitSimData_1(raw_data, **kwargs):
    """
    Fits parameters necessary for the simulation based on the knowledge base

    Inputs:
            raw_data (KnowledgeBaseEcoli) - knowledge base consisting of the
                    necessary raw data
            cpus (int) - number of processes to use (if > 1, use multiprocessing)
            debug (bool) - if True, fit only one arbitrarily-chosen transcription
                    factor in order to speed up a debug cycle (should not be used for
                    an actual simulation)
            save_intermediates (bool) - if True, save the state (sim_data and cell_specs)
                    to disk in intermediates_directory after each Parca step
            intermediates_directory (str) - path to the directory to save intermediate
                    sim_data and cell_specs files to
            load_intermediate (str) - the function name of the Parca step to load
                    sim_data and cell_specs from; functions prior to and including this
                    will be skipped but all following functions will run
            variable_elongation_transcription (bool) - enable variable elongation
                    for transcription
            variable_elongation_translation (bool) - enable variable elongation for
                    translation
            disable_ribosome_capacity_fitting (bool) - if True, ribosome expression
                    is not fit to protein synthesis demands
            disable_rnapoly_capacity_fitting (bool) - if True, RNA polymerase
                    expression is not fit to protein synthesis demands
    """

    sim_data = SimulationDataEcoli()
    cell_specs = {}

    # Functions to modify sim_data and/or cell_specs
    # Functions defined below should be wrapped by @save_state to allow saving
    # and loading sim_data and cell_specs to skip certain functions while doing
    # development for faster testing and iteration of later functions that
    # might not need earlier functions to be rerun each time.
    sim_data, cell_specs = initialize(sim_data, cell_specs, raw_data=raw_data, **kwargs)
    sim_data, cell_specs = input_adjustments(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = basal_specs(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = tf_condition_specs(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = fit_condition(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = promoter_binding(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = adjust_promoters(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = set_conditions(sim_data, cell_specs, **kwargs)
    sim_data, cell_specs = final_adjustments(sim_data, cell_specs, **kwargs)

    if sim_data is None:
        raise ValueError(
            'sim_data is not specified.  Check that the'
            f' load_intermediate function ({kwargs.get("load_intermediate")})'
            ' is correct and matches a function to be run.'
        )

    return sim_data


def save_state(func):
    """
    Wrapper for functions called in fitSimData_1() to allow saving and loading
    of sim_data and cell_specs at different points in the parameter calculation
    pipeline.  This is useful for development in order to skip time intensive
    steps that are not required to recalculate in order to work with the desired
    stage of parameter calculation.

    This wrapper expects arguments in the kwargs passed into a wrapped function:
            save_intermediates (bool): if True, the state (sim_data and cell_specs)
                    will be saved to disk in intermediates_directory
            intermediates_directory (str): path to the directory to save intermediate
                    sim_data and cell_specs files to
            load_intermediate (str): the name of the function to load sim_data and
                    cell_specs from, functions prior to and including this will be
                    skipped but all following functions will run
    """

    @functools.wraps(func)
    def wrapper(*args, **kwargs):
        func_name = func.__name__
        load_intermediate = kwargs.get("load_intermediate")
        intermediates_dir = kwargs.get("intermediates_directory", "")

        # Files to save to or load from
        sim_data_file = os.path.join(intermediates_dir, f"sim_data_{func_name}.cPickle")
        cell_specs_file = os.path.join(
            intermediates_dir, f"cell_specs_{func_name}.cPickle"
        )

        # Run the wrapped function if the function to load is not specified or was already loaded
        if load_intermediate is None or load_intermediate in functions_run:
            start = time.time()
            sim_data, cell_specs = func(*args, **kwargs)
            end = time.time()
            print(f"Ran {func_name} in {end - start:.0f} s")
        # Load the saved results from the wrapped function if it is set to be loaded
        elif load_intermediate == func_name:
            if not os.path.exists(sim_data_file) or not os.path.exists(cell_specs_file):
                raise IOError(
                    f"Could not find intermediate files ({sim_data_file}"
                    f" or {cell_specs_file}) to load. Make sure to save intermediates"
                    " before trying to load them."
                )
            with open(sim_data_file, "rb") as f:
                sim_data = pickle.load(f)
            with open(cell_specs_file, "rb") as f:
                cell_specs = pickle.load(f)
            print(f"Loaded sim_data and cell_specs for {func_name}")
        # Skip running or loading if a later function will be loaded
        else:
            print(f"Skipped {func_name}")
            sim_data = None
            cell_specs = {}

        # Save the current state of the parameter calculator after the function to disk
        if (
            kwargs.get("save_intermediates", False)
            and intermediates_dir != ""
            and sim_data is not None
        ):
            os.makedirs(intermediates_dir, exist_ok=True)
            with open(sim_data_file, "wb") as f:
                pickle.dump(sim_data, f, protocol=pickle.HIGHEST_PROTOCOL)
            with open(cell_specs_file, "wb") as f:
                pickle.dump(cell_specs, f, protocol=pickle.HIGHEST_PROTOCOL)
            print(f"Saved data for {func_name}")

        # Record which functions have been run to know if the loaded function has run
        functions_run.append(func_name)

        return sim_data, cell_specs

    return wrapper


@save_state
def initialize(sim_data, cell_specs, raw_data=None, **kwargs):
    sim_data.initialize(
        raw_data=raw_data,
        basal_expression_condition=BASAL_EXPRESSION_CONDITION,
    )

    return sim_data, cell_specs


@save_state
def input_adjustments(sim_data, cell_specs, debug=False, **kwargs):
    # Limit the number of conditions that are being fit so that execution time decreases
    if debug:
        print(
            "Warning: Running the Parca in debug mode - not all conditions will be fit"
        )
        key = list(sim_data.tf_to_active_inactive_conditions.keys())[0]
        sim_data.tf_to_active_inactive_conditions = {
            key: sim_data.tf_to_active_inactive_conditions[key]
        }

    # Make adjustments for metabolic enzymes
    setTranslationEfficiencies(sim_data)
    set_balanced_translation_efficiencies(sim_data)
    setRNAExpression(sim_data)
    setRNADegRates(sim_data)
    setProteinDegRates(sim_data)

    return sim_data, cell_specs


@save_state
def basal_specs(
    sim_data,
    cell_specs,
    disable_ribosome_capacity_fitting=False,
    disable_rnapoly_capacity_fitting=False,
    variable_elongation_transcription=True,
    variable_elongation_translation=False,
    **kwargs,
):
    cell_specs = buildBasalCellSpecifications(
        sim_data,
        variable_elongation_transcription,
        variable_elongation_translation,
        disable_ribosome_capacity_fitting,
        disable_rnapoly_capacity_fitting,
    )

    # Set expression based on ppGpp regulation from basal expression
    sim_data.process.transcription.set_ppgpp_expression(sim_data)
    # TODO (Travis): use ppGpp expression in condition fitting

    # Modify other properties
    # Compute Km's
    Km = setKmCooperativeEndoRNonLinearRNAdecay(
        sim_data, cell_specs["basal"]["bulkContainer"]
    )
    n_transcribed_rnas = len(sim_data.process.transcription.rna_data)
    sim_data.process.transcription.rna_data["Km_endoRNase"] = Km[:n_transcribed_rnas]
    sim_data.process.transcription.mature_rna_data["Km_endoRNase"] = Km[
        n_transcribed_rnas:
    ]

    ## Calculate and set maintenance values
    # ----- Growth associated maintenance -----
    fitMaintenanceCosts(sim_data, cell_specs["basal"]["bulkContainer"])

    return sim_data, cell_specs


@save_state
def tf_condition_specs(
    sim_data,
    cell_specs,
    cpus=1,
    disable_ribosome_capacity_fitting=False,
    disable_rnapoly_capacity_fitting=False,
    variable_elongation_transcription=True,
    variable_elongation_translation=False,
    **kwargs,
):
    # Limit the number of CPUs before printing it to stdout.
    cpus = parallelization.cpus(cpus)

    # Apply updates to cell_specs from buildTfConditionCellSpecifications for each TF condition
    conditions = list(sorted(sim_data.tf_to_active_inactive_conditions))
    args = [
        (
            sim_data,
            tf,
            variable_elongation_transcription,
            variable_elongation_translation,
            disable_ribosome_capacity_fitting,
            disable_rnapoly_capacity_fitting,
        )
        for tf in conditions
    ]
    apply_updates(
        buildTfConditionCellSpecifications, args, conditions, cell_specs, cpus
    )

    for conditionKey in cell_specs:
        if conditionKey == "basal":
            continue

        sim_data.process.transcription.rna_expression[conditionKey] = cell_specs[
            conditionKey
        ]["expression"]
        sim_data.process.transcription.rna_synth_prob[conditionKey] = cell_specs[
            conditionKey
        ]["synthProb"]
        sim_data.process.transcription.cistron_expression[conditionKey] = cell_specs[
            conditionKey
        ]["cistron_expression"]
        sim_data.process.transcription.fit_cistron_expression[conditionKey] = (
            cell_specs[conditionKey]["fit_cistron_expression"]
        )

    buildCombinedConditionCellSpecifications(
        sim_data,
        cell_specs,
        variable_elongation_transcription,
        variable_elongation_translation,
        disable_ribosome_capacity_fitting,
        disable_rnapoly_capacity_fitting,
    )

    return sim_data, cell_specs


@save_state
def fit_condition(sim_data, cell_specs, cpus=1, **kwargs):
    # Apply updates from fitCondition to cell_specs for each fit condition
    conditions = list(sorted(cell_specs))
    args = [(sim_data, cell_specs[condition], condition) for condition in conditions]
    apply_updates(fitCondition, args, conditions, cell_specs, cpus)

    for condition_label in sorted(cell_specs):
        nutrients = sim_data.conditions[condition_label]["nutrients"]
        if nutrients not in sim_data.translation_supply_rate:
            sim_data.translation_supply_rate[nutrients] = cell_specs[condition_label][
                "translation_aa_supply"
            ]

    return sim_data, cell_specs


@save_state
def promoter_binding(sim_data, cell_specs, **kwargs):
    if VERBOSE > 0:
        print("Fitting promoter binding")
    # noinspection PyTypeChecker
    fitPromoterBoundProbability(sim_data, cell_specs)

    return sim_data, cell_specs


@save_state
def adjust_promoters(sim_data, cell_specs, **kwargs):
    # noinspection PyTypeChecker
    fitLigandConcentrations(sim_data, cell_specs)
    calculateRnapRecruitment(sim_data, cell_specs)

    return sim_data, cell_specs


@save_state
def set_conditions(sim_data, cell_specs, **kwargs):
    sim_data.process.transcription.rnaSynthProbFraction = {}
    sim_data.process.transcription.rnapFractionActiveDict = {}
    sim_data.process.transcription.rnaSynthProbRProtein = {}
    sim_data.process.transcription.rnaSynthProbRnaPolymerase = {}
    sim_data.process.transcription.rnaPolymeraseElongationRateDict = {}
    sim_data.expectedDryMassIncreaseDict = {}
    sim_data.process.translation.ribosomeElongationRateDict = {}
    sim_data.process.translation.ribosomeFractionActiveDict = {}

    for condition_label in sorted(cell_specs):
        condition = sim_data.conditions[condition_label]
        nutrients = condition["nutrients"]

        if VERBOSE > 0:
            print("Updating mass in condition {}".format(condition_label))
        spec = cell_specs[condition_label]

        concDict = sim_data.process.metabolism.concentration_updates.concentrations_based_on_nutrients(
            media_id=nutrients
        )
        concDict.update(
            sim_data.mass.getBiomassAsConcentrations(
                sim_data.condition_to_doubling_time[condition_label]
            )
        )

        avgCellDryMassInit, fitAvgSolublePoolMass = rescaleMassForSolubleMetabolites(
            sim_data,
            spec["bulkContainer"],
            concDict,
            sim_data.condition_to_doubling_time[condition_label],
        )

        if VERBOSE > 0:
            print("{} to {}".format(spec["avgCellDryMassInit"], avgCellDryMassInit))

        spec["avgCellDryMassInit"] = avgCellDryMassInit
        spec["fitAvgSolublePoolMass"] = fitAvgSolublePoolMass

        mRnaSynthProb = sim_data.process.transcription.rna_synth_prob[condition_label][
            sim_data.process.transcription.rna_data["is_mRNA"]
        ].sum()
        tRnaSynthProb = sim_data.process.transcription.rna_synth_prob[condition_label][
            sim_data.process.transcription.rna_data["is_tRNA"]
        ].sum()
        rRnaSynthProb = sim_data.process.transcription.rna_synth_prob[condition_label][
            sim_data.process.transcription.rna_data["is_rRNA"]
        ].sum()

        if len(condition["perturbations"]) == 0:
            if nutrients not in sim_data.process.transcription.rnaSynthProbFraction:
                sim_data.process.transcription.rnaSynthProbFraction[nutrients] = {
                    "mRna": mRnaSynthProb,
                    "tRna": tRnaSynthProb,
                    "rRna": rRnaSynthProb,
                }

            if nutrients not in sim_data.process.transcription.rnaSynthProbRProtein:
                prob = sim_data.process.transcription.rna_synth_prob[condition_label][
                    sim_data.process.transcription.rna_data[
                        "includes_ribosomal_protein"
                    ]
                ]
                sim_data.process.transcription.rnaSynthProbRProtein[nutrients] = prob

            if (
                nutrients
                not in sim_data.process.transcription.rnaSynthProbRnaPolymerase
            ):
                prob = sim_data.process.transcription.rna_synth_prob[condition_label][
                    sim_data.process.transcription.rna_data["includes_RNAP"]
                ]
                sim_data.process.transcription.rnaSynthProbRnaPolymerase[nutrients] = (
                    prob
                )

            if nutrients not in sim_data.process.transcription.rnapFractionActiveDict:
                frac = sim_data.growth_rate_parameters.get_fraction_active_rnap(
                    spec["doubling_time"]
                )
                sim_data.process.transcription.rnapFractionActiveDict[nutrients] = frac

            if (
                nutrients
                not in sim_data.process.transcription.rnaPolymeraseElongationRateDict
            ):
                rate = sim_data.growth_rate_parameters.get_rnap_elongation_rate(
                    spec["doubling_time"]
                )
                sim_data.process.transcription.rnaPolymeraseElongationRateDict[
                    nutrients
                ] = rate

            if nutrients not in sim_data.expectedDryMassIncreaseDict:
                sim_data.expectedDryMassIncreaseDict[nutrients] = spec[
                    "avgCellDryMassInit"
                ]

            if nutrients not in sim_data.process.translation.ribosomeElongationRateDict:
                rate = sim_data.growth_rate_parameters.get_ribosome_elongation_rate(
                    spec["doubling_time"]
                )
                sim_data.process.translation.ribosomeElongationRateDict[nutrients] = (
                    rate
                )

            if nutrients not in sim_data.process.translation.ribosomeFractionActiveDict:
                frac = sim_data.growth_rate_parameters.get_fraction_active_ribosome(
                    spec["doubling_time"]
                )
                sim_data.process.translation.ribosomeFractionActiveDict[nutrients] = (
                    frac
                )

    return sim_data, cell_specs


@save_state
def final_adjustments(sim_data, cell_specs, **kwargs):
    # Adjust expression for RNA attenuation
    sim_data.process.transcription.calculate_attenuation(sim_data, cell_specs)

    # Adjust ppGpp regulated expression after conditions have been fit for physiological constraints
    sim_data.process.transcription.adjust_polymerizing_ppgpp_expression(sim_data)
    sim_data.process.transcription.adjust_ppgpp_expression_for_tfs(sim_data)

    # Set supply constants for amino acids based on condition supply requirements
    average_basal_container = create_bulk_container(sim_data, n_seeds=5)
    average_with_aa_container = create_bulk_container(
        sim_data, condition="with_aa", n_seeds=5
    )
    sim_data.process.metabolism.set_phenomological_supply_constants(sim_data)
    sim_data.process.metabolism.set_mechanistic_supply_constants(
        sim_data, cell_specs, average_basal_container, average_with_aa_container
    )
    sim_data.process.metabolism.set_mechanistic_export_constants(
        sim_data, cell_specs, average_basal_container
    )
    sim_data.process.metabolism.set_mechanistic_uptake_constants(
        sim_data, cell_specs, average_with_aa_container
    )

    # Set ppGpp reaction parameters
    sim_data.process.transcription.set_ppgpp_kinetics_parameters(
        average_basal_container, sim_data.constants
    )

    return sim_data, cell_specs


def apply_updates(
    func: Callable[..., dict],
    args: list[tuple],
    labels: list[str],
    dest: dict,
    cpus: int,
):
    """
    Use multiprocessing (if cpus > 1) to apply args to a function to get
    dictionary updates for a destination dictionary.

    Args:
            func: function to call with args
            args: list of args to apply to func
            labels: label for each set of args for exception information
            dest: destination dictionary that will be updated with results
                    from each function call
            cpus: number of cpus to use
    """

    if cpus > 1:
        print("Starting {} Parca processes".format(cpus))

        # Apply args to func
        pool = parallelization.pool(cpus)
        results = {label: pool.apply_async(func, a) for label, a in zip(labels, args)}
        pool.close()
        pool.join()

        # Check results from function calls and update dest
        failed = []
        for label, result in results.items():
            if result.successful():
                dest.update(result.get())
            else:
                # noinspection PyBroadException
                try:
                    result.get()
                except Exception:
                    traceback.print_exc()
                    failed.append(label)

        # Cleanup
        if failed:
            raise RuntimeError(
                "Error(s) raised for {} while using multiple processes".format(
                    ", ".join(failed)
                )
            )
        pool = None
        print("End parallel processing")
    else:
        for a in args:
            dest.update(func(*a))


def buildBasalCellSpecifications(
    sim_data,
    variable_elongation_transcription=True,
    variable_elongation_translation=False,
    disable_ribosome_capacity_fitting=False,
    disable_rnapoly_capacity_fitting=False,
):
    """
    Creates cell specifications for the basal condition by fitting expression.
    Relies on expressionConverge() to set the expression and update masses.

    Inputs
    ------
    - disable_ribosome_capacity_fitting (bool) - if True, ribosome expression
    is not fit
    - disable_rnapoly_capacity_fitting (bool) - if True, RNA polymerase
    expression is not fit

    Requires
    --------
    - Metabolite concentrations based on 'minimal' nutrients
    - 'basal' RNA expression
    - 'basal' doubling time

    Modifies
    --------
    - Average mass values of the cell
    - cistron expression
    - RNA expression and synthesis probabilities

    Returns
    --------
    - dict {'basal': dict} with the following keys in the dict from key 'basal':
            'concDict' {metabolite_name (str): concentration (float with units)} -
                    dictionary of concentrations for each metabolite with a concentration
            'fit_cistron_expression' (array of floats) - hypothetical expression for
                    each RNA cistron post-fit, total normalized to 1, if all
                    transcription units were monocistronic
            'expression' (array of floats) - expression for each RNA, total normalized to 1
            'doubling_time' (float with units) - cell doubling time
            'synthProb' (array of floats) - synthesis probability for each RNA,
                    total normalized to 1
            'avgCellDryMassInit' (float with units) - average initial cell dry mass
            'fitAvgSolubleTargetMolMass' (float with units) - the adjusted dry mass
                    of the soluble fraction of a cell
            - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
                    for expected counts based on expression of all bulk molecules

    Notes
    -----
    - TODO - sets sim_data attributes and returns values - change to only return values
    """

    # Create dictionary for basal condition
    cell_specs = {}
    cell_specs["basal"] = {
        "concDict": sim_data.process.metabolism.concentration_updates.concentrations_based_on_nutrients(
            media_id="minimal"
        ),
        "expression": sim_data.process.transcription.rna_expression["basal"].copy(),
        "doubling_time": sim_data.condition_to_doubling_time["basal"],
    }

    # Determine expression and synthesis probabilities
    (
        expression,
        synthProb,
        fit_cistron_expression,
        avgCellDryMassInit,
        fitAvgSolubleTargetMolMass,
        bulkContainer,
        _,
    ) = expressionConverge(
        sim_data,
        cell_specs["basal"]["expression"],
        cell_specs["basal"]["concDict"],
        cell_specs["basal"]["doubling_time"],
        conditionKey="basal",
        variable_elongation_transcription=variable_elongation_transcription,
        variable_elongation_translation=variable_elongation_translation,
        disable_ribosome_capacity_fitting=disable_ribosome_capacity_fitting,
        disable_rnapoly_capacity_fitting=disable_rnapoly_capacity_fitting,
    )

    # Store calculated values
    cell_specs["basal"]["expression"] = expression
    cell_specs["basal"]["synthProb"] = synthProb
    cell_specs["basal"]["fit_cistron_expression"] = fit_cistron_expression
    cell_specs["basal"]["avgCellDryMassInit"] = avgCellDryMassInit
    cell_specs["basal"]["fitAvgSolubleTargetMolMass"] = fitAvgSolubleTargetMolMass
    cell_specs["basal"]["bulkContainer"] = bulkContainer

    # Modify sim_data mass
    sim_data.mass.avg_cell_dry_mass_init = avgCellDryMassInit
    sim_data.mass.avg_cell_dry_mass = (
        sim_data.mass.avg_cell_dry_mass_init
        * sim_data.mass.avg_cell_to_initial_cell_conversion_factor
    )
    sim_data.mass.avg_cell_water_mass_init = (
        sim_data.mass.avg_cell_dry_mass_init
        / sim_data.mass.cell_dry_mass_fraction
        * sim_data.mass.cell_water_mass_fraction
    )
    sim_data.mass.fitAvgSolubleTargetMolMass = fitAvgSolubleTargetMolMass

    # Modify sim_data expression
    sim_data.process.transcription.rna_expression["basal"][:] = cell_specs["basal"][
        "expression"
    ]
    sim_data.process.transcription.rna_synth_prob["basal"][:] = cell_specs["basal"][
        "synthProb"
    ]
    sim_data.process.transcription.fit_cistron_expression["basal"] = cell_specs[
        "basal"
    ]["fit_cistron_expression"]

    return cell_specs


def buildTfConditionCellSpecifications(
    sim_data,
    tf,
    variable_elongation_transcription=True,
    variable_elongation_translation=False,
    disable_ribosome_capacity_fitting=False,
    disable_rnapoly_capacity_fitting=False,
):
    """
    Creates cell specifications for a given transcription factor by
    fitting expression. Will set for the active and inactive TF condition.
    Relies on expressionConverge() to set the expression and masses.
    Uses fold change data relative to the 'basal' condition to determine
    expression for a given TF.

    Inputs
    ------
    - tf (str) - label for the transcription factor to fit (eg. 'CPLX-125')
    - disable_ribosome_capacity_fitting (bool) - if True, ribosome expression
    is not fit
    - disable_rnapoly_capacity_fitting (bool) - if True, RNA polymerase
    expression is not fit

    Requires
    --------
    - Metabolite concentrations based on nutrients for the TF
    - Adjusted 'basal' cistron expression
    - Doubling time for the TF
    - Fold changes in expression for each gene given the TF

    Returns
    --------
    - dict {tf + '__active'/'__inactive': dict} with the following keys in each dict:
            'concDict' {metabolite_name (str): concentration (float with units)} -
                    dictionary of concentrations for each metabolite with a concentration
            'expression' (array of floats) - expression for each RNA, total normalized to 1
            'doubling_time' (float with units) - cell doubling time
            'synthProb' (array of floats) - synthesis probability for each RNA,
                    total normalized to 1
            'cistron_expression' (array of floats) - hypothetical expression for
                    each RNA cistron, calculated from basal cistron expression levels
                    and fold change data
            'fit_cistron_expression' (array of floats) - hypothetical expression for
                    each RNA cistron post-fit, total normalized to 1, if all
                    transcription units were monocistronic
            'avgCellDryMassInit' (float with units) - average initial cell dry mass
            'fitAvgSolubleTargetMolMass' (float with units) - the adjusted dry mass
                    of the soluble fraction of a cell
            - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
                    for expected counts based on expression of all bulk molecules
    """

    cell_specs = {}
    for choice in ["__active", "__inactive"]:
        conditionKey = tf + choice
        conditionValue = sim_data.conditions[conditionKey]

        # Get expression for the condition based on fold changes over 'basal'
        # condition if the condition is not the same as 'basal'
        fcData = {}
        if choice == "__active" and conditionValue != sim_data.conditions["basal"]:
            fcData = sim_data.tf_to_fold_change[tf]
        if choice == "__inactive" and conditionValue != sim_data.conditions["basal"]:
            fcDataTmp = sim_data.tf_to_fold_change[tf].copy()
            for key, value in fcDataTmp.items():
                fcData[key] = 1.0 / value
        expression, cistron_expression = expressionFromConditionAndFoldChange(
            sim_data.process.transcription,
            conditionValue["perturbations"],
            fcData,
        )

        # Get metabolite concentrations for the condition
        concDict = sim_data.process.metabolism.concentration_updates.concentrations_based_on_nutrients(
            media_id=conditionValue["nutrients"]
        )
        concDict.update(
            sim_data.mass.getBiomassAsConcentrations(
                sim_data.condition_to_doubling_time[conditionKey]
            )
        )

        # Create dictionary for the condition
        cell_specs[conditionKey] = {
            "concDict": concDict,
            "expression": expression,
            "doubling_time": sim_data.condition_to_doubling_time.get(
                conditionKey, sim_data.condition_to_doubling_time["basal"]
            ),
        }

        # Determine expression and synthesis probabilities
        (
            expression,
            synthProb,
            fit_cistron_expression,
            avgCellDryMassInit,
            fitAvgSolubleTargetMolMass,
            bulkContainer,
            concDict,
        ) = expressionConverge(
            sim_data,
            cell_specs[conditionKey]["expression"],
            cell_specs[conditionKey]["concDict"],
            cell_specs[conditionKey]["doubling_time"],
            sim_data.process.transcription.rna_data["Km_endoRNase"],
            conditionKey=conditionKey,
            variable_elongation_transcription=variable_elongation_transcription,
            variable_elongation_translation=variable_elongation_translation,
            disable_ribosome_capacity_fitting=disable_ribosome_capacity_fitting,
            disable_rnapoly_capacity_fitting=disable_rnapoly_capacity_fitting,
        )

        # Store calculated values
        cell_specs[conditionKey]["expression"] = expression
        cell_specs[conditionKey]["synthProb"] = synthProb
        cell_specs[conditionKey]["cistron_expression"] = cistron_expression
        cell_specs[conditionKey]["fit_cistron_expression"] = fit_cistron_expression
        cell_specs[conditionKey]["avgCellDryMassInit"] = avgCellDryMassInit
        cell_specs[conditionKey]["fitAvgSolubleTargetMolMass"] = (
            fitAvgSolubleTargetMolMass
        )
        cell_specs[conditionKey]["bulkContainer"] = bulkContainer

    return cell_specs


def buildCombinedConditionCellSpecifications(
    sim_data,
    cell_specs,
    variable_elongation_transcription=True,
    variable_elongation_translation=False,
    disable_ribosome_capacity_fitting=False,
    disable_rnapoly_capacity_fitting=False,
):
    """
    Creates cell specifications for sets of transcription factors being active.
    These sets include conditions like 'with_aa' or 'no_oxygen' where multiple
    transcription factors will be active at the same time.

    Inputs
    ------
    - cell_specs {condition (str): dict} - information about each individual
    transcription factor condition
    - disable_ribosome_capacity_fitting (bool) - if True, ribosome expression
    is not fit
    - disable_rnapoly_capacity_fitting (bool) - if True, RNA polymerase
    expression is not fit

    Requires
    --------
    - Metabolite concentrations based on nutrients for the condition
    - Adjusted 'basal' RNA expression
    - Doubling time for the combined condition
    - Fold changes in expression for each gene given the TF

    Modifies
    --------
    - cell_specs dictionary for each combined condition
    - RNA expression and synthesis probabilities for each combined condition

    Notes
    -----
    - TODO - determine how to handle fold changes when multiple TFs change the
    same gene because multiplying both fold changes together might not be
    appropriate
    """

    for conditionKey in sim_data.condition_active_tfs:
        # Skip adjustments if 'basal' condition
        if conditionKey == "basal":
            continue

        # Get expression from fold changes for each TF in the given condition
        fcData = {}
        conditionValue = sim_data.conditions[conditionKey]
        for tf in sim_data.condition_active_tfs[conditionKey]:
            for gene, fc in sim_data.tf_to_fold_change[tf].items():
                fcData[gene] = fcData.get(gene, 1) * fc
        for tf in sim_data.condition_inactive_tfs[conditionKey]:
            for gene, fc in sim_data.tf_to_fold_change[tf].items():
                fcData[gene] = fcData.get(gene, 1) / fc

        expression, cistron_expression = expressionFromConditionAndFoldChange(
            sim_data.process.transcription,
            conditionValue["perturbations"],
            fcData,
        )

        # Get metabolite concentrations for the condition
        concDict = sim_data.process.metabolism.concentration_updates.concentrations_based_on_nutrients(
            media_id=conditionValue["nutrients"]
        )
        concDict.update(
            sim_data.mass.getBiomassAsConcentrations(
                sim_data.condition_to_doubling_time[conditionKey]
            )
        )

        # Create dictionary for the condition
        cell_specs[conditionKey] = {
            "concDict": concDict,
            "expression": expression,
            "doubling_time": sim_data.condition_to_doubling_time.get(
                conditionKey, sim_data.condition_to_doubling_time["basal"]
            ),
        }

        # Determine expression and synthesis probabilities
        (
            expression,
            synthProb,
            fit_cistron_expression,
            avgCellDryMassInit,
            fitAvgSolubleTargetMolMass,
            bulkContainer,
            concDict,
        ) = expressionConverge(
            sim_data,
            cell_specs[conditionKey]["expression"],
            cell_specs[conditionKey]["concDict"],
            cell_specs[conditionKey]["doubling_time"],
            sim_data.process.transcription.rna_data["Km_endoRNase"],
            conditionKey=conditionKey,
            variable_elongation_transcription=variable_elongation_transcription,
            variable_elongation_translation=variable_elongation_translation,
            disable_ribosome_capacity_fitting=disable_ribosome_capacity_fitting,
            disable_rnapoly_capacity_fitting=disable_rnapoly_capacity_fitting,
        )

        # Modify cell_specs for calculated values
        cell_specs[conditionKey]["expression"] = expression
        cell_specs[conditionKey]["synthProb"] = synthProb
        cell_specs[conditionKey]["cistron_expression"] = cistron_expression
        cell_specs[conditionKey]["fit_cistron_expression"] = fit_cistron_expression
        cell_specs[conditionKey]["avgCellDryMassInit"] = avgCellDryMassInit
        cell_specs[conditionKey]["fitAvgSolubleTargetMolMass"] = (
            fitAvgSolubleTargetMolMass
        )
        cell_specs[conditionKey]["bulkContainer"] = bulkContainer

        # Modify sim_data expression
        sim_data.process.transcription.rna_expression[conditionKey] = cell_specs[
            conditionKey
        ]["expression"]
        sim_data.process.transcription.rna_synth_prob[conditionKey] = cell_specs[
            conditionKey
        ]["synthProb"]
        sim_data.process.transcription.cistron_expression[conditionKey] = cell_specs[
            conditionKey
        ]["cistron_expression"]
        sim_data.process.transcription.fit_cistron_expression[conditionKey] = (
            cell_specs[conditionKey]["fit_cistron_expression"]
        )


def expressionConverge(
    sim_data,
    expression,
    concDict,
    doubling_time,
    Km=None,
    conditionKey=None,
    variable_elongation_transcription=True,
    variable_elongation_translation=False,
    disable_ribosome_capacity_fitting=False,
    disable_rnapoly_capacity_fitting=False,
):
    """
    Iteratively fits synthesis probabilities for RNA. Calculates initial
    expression based on gene expression data and makes adjustments to match
    physiological constraints for ribosome and RNAP counts. Relies on
    fitExpression() to converge

    Inputs
    ------
    - expression (array of floats) - expression for each RNA, normalized to 1
    - concDict {metabolite (str): concentration (float with units of mol/volume)} -
    dictionary for concentrations of each metabolite with location tag
    - doubling_time (float with units of time) - doubling time
    - Km (array of floats with units of mol/volume) - Km for each RNA associated
    with RNases
    - disable_ribosome_capacity_fitting (bool) - if True, ribosome expression
    is not fit
    - disable_rnapoly_capacity_fitting (bool) - if True, RNA polymerase
    expression is not fit

    Requires
    --------
    - MAX_FITTING_ITERATIONS (int) - number of iterations to adjust expression
    before an exception is raised
    - FITNESS_THRESHOLD (float) - acceptable change from one iteration to break
    the fitting loop

    Returns
    --------
    - expression (array of floats) - adjusted expression for each RNA,
    normalized to 1
    - synthProb (array of floats) - synthesis probability for each RNA which
    accounts for expression and degradation rate, normalized to 1
    - avgCellDryMassInit (float with units of mass) - expected initial dry cell mass
    - fitAvgSolubleTargetMolMass (float with units of mass) - the adjusted dry mass
    of the soluble fraction of a cell
    - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for expected counts based on expression of all bulk molecules
    """

    if VERBOSE > 0:
        print(
            f"Fitting RNA synthesis probabilities for condition {conditionKey} ...",
            end="",
        )

    for iteration in range(MAX_FITTING_ITERATIONS):
        if VERBOSE > 1:
            print("Iteration: {}".format(iteration))

        initialExpression = expression.copy()
        expression = setInitialRnaExpression(sim_data, expression, doubling_time)
        bulkContainer = createBulkContainer(sim_data, expression, doubling_time)
        avgCellDryMassInit, fitAvgSolubleTargetMolMass = (
            rescaleMassForSolubleMetabolites(
                sim_data, bulkContainer, concDict, doubling_time
            )
        )

        if not disable_rnapoly_capacity_fitting:
            setRNAPCountsConstrainedByPhysiology(
                sim_data,
                bulkContainer,
                doubling_time,
                avgCellDryMassInit,
                variable_elongation_transcription,
                Km,
            )

        if not disable_ribosome_capacity_fitting:
            setRibosomeCountsConstrainedByPhysiology(
                sim_data, bulkContainer, doubling_time, variable_elongation_translation
            )

        # Normalize expression and write out changes
        expression, synthProb, fit_cistron_expression, cistron_expression_res = (
            fitExpression(
                sim_data, bulkContainer, doubling_time, avgCellDryMassInit, Km
            )
        )

        degreeOfFit = np.sqrt(np.mean(np.square(initialExpression - expression)))

        if VERBOSE > 1:
            print("degree of fit: {}".format(degreeOfFit))
            print(
                f"Average cistron expression residuals: {np.linalg.norm(cistron_expression_res)}"
            )

        if degreeOfFit < FITNESS_THRESHOLD:
            print("! Fitting converged after {} iterations".format(iteration + 1))
            break

    else:
        raise Exception("Fitting did not converge")

    return (
        expression,
        synthProb,
        fit_cistron_expression,
        avgCellDryMassInit,
        fitAvgSolubleTargetMolMass,
        bulkContainer,
        concDict,
    )


def fitCondition(sim_data, spec, condition):
    """
    Takes a given condition and returns the predicted bulk average, bulk deviation,
    protein monomer average, protein monomer deviation, and amino acid supply to
    translation. This relies on calculateBulkDistributions and calculateTranslationSupply.

    Inputs
    ------
    - condition (str) - condition to fit (eg 'CPLX0-7705__active')
    - spec {property (str): property values} - cell specifications for the given condition.
    This function uses the specs "expression", "concDict", "avgCellDryMassInit",
    and "doubling_time"

    Returns
    --------
    - A dictionary {condition (str): spec (dict)} with the updated spec dictionary
    with the following values updated:
            - bulkAverageContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
                    for the mean of the counts of all bulk molecules
            - bulkDeviationContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
                    for the standard deviation of the counts of all bulk molecules
            - proteinMonomerAverageContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
                    for the mean of the counts of all protein monomers
            - proteinMonomerDeviationContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
                    for the standard deviation of the counts of all protein monomers
            - translation_aa_supply (array with units of mol/(mass.time)) - the supply rates
            for each amino acid to translation
    """

    if VERBOSE > 0:
        print("Fitting condition {}".format(condition))

    # Find bulk and protein distributions
    (
        bulkAverageContainer,
        bulkDeviationContainer,
        proteinMonomerAverageContainer,
        proteinMonomerDeviationContainer,
    ) = calculateBulkDistributions(
        sim_data,
        spec["expression"],
        spec["concDict"],
        spec["avgCellDryMassInit"],
        spec["doubling_time"],
    )
    spec["bulkAverageContainer"] = bulkAverageContainer
    spec["bulkDeviationContainer"] = bulkDeviationContainer
    spec["proteinMonomerAverageContainer"] = proteinMonomerAverageContainer
    spec["proteinMonomerDeviationContainer"] = proteinMonomerDeviationContainer

    # Find the supply rates of amino acids to translation given doubling time
    spec["translation_aa_supply"] = calculateTranslationSupply(
        sim_data,
        spec["doubling_time"],
        spec["proteinMonomerAverageContainer"],
        spec["avgCellDryMassInit"],
    )

    return {condition: spec}


def calculateTranslationSupply(
    sim_data, doubling_time, bulkContainer, avgCellDryMassInit
):
    """
    Returns the supply rates of all amino acids to translation given the desired
    doubling time. This creates a limit on the polypeptide elongation process,
    and thus on growth. The amino acid supply rate is found by calculating the
    concentration of amino acids per gram dry cell weight and multiplying by the
    loss to dilution given doubling time.

    Inputs
    ------
    - doubling_time (float with units of time) - measured doubling times given the condition
    - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for count of all bulk molecules
    - avgCellDryMassInit (float with units of mass) - the average initial cell dry mass

    Notes
    -----
    - The supply of amino acids should not be based on a desired doubling time,
    but should come from a more mechanistic basis. This would allow simulations
    of environmental shifts in which the doubling time is unknown.
    """

    aaCounts = sim_data.process.translation.monomer_data[
        "aa_counts"
    ]  # the counts of each amino acid required for each protein
    protein_idx = bulk_name_to_idx(
        sim_data.process.translation.monomer_data["id"], bulkContainer["id"]
    )
    proteinCounts = counts(bulkContainer, protein_idx)  # the counts of all proteins
    nAvogadro = sim_data.constants.n_avogadro

    molAAPerGDCW = units.sum(
        aaCounts * np.tile(proteinCounts.reshape(-1, 1), (1, 21)), axis=0
    ) * ((1 / (units.aa * nAvogadro)) * (1 / avgCellDryMassInit))

    # Calculate required amino acid supply to translation to counter dilution
    translation_aa_supply = molAAPerGDCW * np.log(2) / doubling_time

    return translation_aa_supply


# Sub-fitting functions


def setTranslationEfficiencies(sim_data):
    """
    This function's goal is to set translation efficiencies for a subset of metabolic proteins.
    It first gathers the index of the proteins it wants to modify, then changes the monomer
    translation efficiencies based on the adjustment that is specified.
    These adjustments were made so that the simulation could run.

    Requires
    --------
    - For each protein that needs to be modified, it takes in an adjustment factor.

    Modifies
    --------
    - This function modifies, for a subset of proteins, their translational efficiencies in sim_data.
    It takes their current efficiency and multiplies them by the factor specified in adjustments.
    """

    for protein in sim_data.adjustments.translation_efficiencies_adjustments:
        idx = np.where(sim_data.process.translation.monomer_data["id"] == protein)[0]
        sim_data.process.translation.translation_efficiencies_by_monomer[idx] *= (
            sim_data.adjustments.translation_efficiencies_adjustments[protein]
        )


def set_balanced_translation_efficiencies(sim_data):
    """
    Sets the translation efficiencies of a group of proteins to be equal to the
    mean value of all proteins within the group.

    Requires
    --------
    - List of proteins that should have balanced translation efficiencies.

    Modifies
    --------
    - Translation efficiencies of proteins within each specified group.
    """
    monomer_id_to_index = {
        monomer["id"][:-3]: i
        for (i, monomer) in enumerate(sim_data.process.translation.monomer_data)
    }

    for proteins in sim_data.adjustments.balanced_translation_efficiencies:
        protein_indexes = np.array([monomer_id_to_index[m] for m in proteins])
        mean_trl_eff = sim_data.process.translation.translation_efficiencies_by_monomer[
            protein_indexes
        ].mean()
        sim_data.process.translation.translation_efficiencies_by_monomer[
            protein_indexes
        ] = mean_trl_eff


def setRNAExpression(sim_data):
    """
    This function's goal is to set expression levels for a subset of RNAs.
    It first gathers the index of the RNA's it wants to modify, then changes
    the expression levels of those RNAs, within sim_data, based on the
    specified adjustment factor. If the specified ID is an RNA cistron, the
    expression levels of all RNA molecules containing the cistron are adjusted.

    Requires
    --------
    - For each RNA that needs to be modified, it takes in an adjustment factor.

    Modifies
    --------
    - This function modifies the basal RNA expression levels set in sim_data,
    for the chosen RNAs. It takes their current basal expression and multiplies
    them by the factor specified in adjustments.
    - After updating the basal expression levels for the given RNAs, the
    function normalizes all the basal expression levels.
    """
    cistron_ids = set(sim_data.process.transcription.cistron_data["id"])
    rna_id_to_index = {
        rna_id[:-3]: i
        for (i, rna_id) in enumerate(sim_data.process.transcription.rna_data["id"])
    }

    rna_index_to_adjustment = {}

    for mol_id, adj_factor in sim_data.adjustments.rna_expression_adjustments.items():
        if mol_id in cistron_ids:
            # Find indexes of all RNAs containing the cistron
            rna_indexes = sim_data.process.transcription.cistron_id_to_rna_indexes(
                mol_id
            )
        elif mol_id in rna_id_to_index:
            rna_indexes = rna_id_to_index[mol_id]
        else:
            raise ValueError(
                f"Molecule ID {mol_id} not found in list of cistrons or transcription units."
            )

        # If multiple adjustments are made for the same RNA, take the maximum
        # adjustment factor
        for rna_index in rna_indexes:
            rna_index_to_adjustment[rna_index] = max(
                rna_index_to_adjustment.get(rna_index, 0), adj_factor
            )

    # Multiply all degradation rates with the specified adjustment factor
    for rna_index, adj_factor in rna_index_to_adjustment.items():
        sim_data.process.transcription.rna_expression["basal"][rna_index] *= adj_factor

    sim_data.process.transcription.rna_expression["basal"] /= (
        sim_data.process.transcription.rna_expression["basal"].sum()
    )


def setRNADegRates(sim_data):
    """
    This function's goal is to adjust the degradation rates for a subset of
    metabolic RNA's. It first gathers the index of the RNA's it wants to modify,
    then changes the degradation rates of those RNAs. If the specified ID is
    that of an RNA cistron, the degradation rates of all RNA molecules
    containing the cistron are adjusted. (Note: since RNA concentrations are
    assumed to be in equilibrium, increasing the degradation rate increases the
    synthesis rates of these RNAs)

    Requires
    --------
    - For each RNA that needs to be modified, it takes in an adjustment factor

    Modifies
    --------
    - This function modifies the RNA degradation rates for the chosen RNAs in
    sim_data. It takes their current degradation rate and multiplies them by the
    factor specified in adjustments.
    """
    cistron_id_to_index = {
        cistron_id: i
        for (i, cistron_id) in enumerate(
            sim_data.process.transcription.cistron_data["id"]
        )
    }
    rna_id_to_index = {
        rna_id[:-3]: i
        for (i, rna_id) in enumerate(sim_data.process.transcription.rna_data["id"])
    }

    rna_index_to_adjustment = {}

    for mol_id, adj_factor in sim_data.adjustments.rna_deg_rates_adjustments.items():
        if mol_id in cistron_id_to_index:
            # Multiply the cistron degradation rate with the specified
            # adjustment factor (Note: these rates are not actually used by the
            # simulation but are still adjusted for bookkeeping purposes)
            cistron_index = cistron_id_to_index[mol_id]
            sim_data.process.transcription.cistron_data.struct_array["deg_rate"][
                cistron_index
            ] *= sim_data.adjustments.rna_deg_rates_adjustments[mol_id]

            # Find indexes of all RNAs containing the cistron
            rna_indexes = sim_data.process.transcription.cistron_id_to_rna_indexes(
                mol_id
            )
        elif mol_id in rna_id_to_index:
            rna_indexes = rna_id_to_index[mol_id]
        else:
            raise ValueError(
                f"Molecule ID {mol_id} not found in list of cistrons or transcription units."
            )

        # If multiple adjustments are made for the same RNA, take the maximum
        # adjustment factor
        for rna_index in rna_indexes:
            rna_index_to_adjustment[rna_index] = max(
                rna_index_to_adjustment.get(rna_index, 0), adj_factor
            )

    # Multiply all degradation rates with the specified adjustment factor
    for rna_index, adj_factor in rna_index_to_adjustment.items():
        sim_data.process.transcription.rna_data.struct_array["deg_rate"][rna_index] *= (
            adj_factor
        )


def setProteinDegRates(sim_data):
    """
    This function's goal is to set the degradation rates for a subset of proteins.
    It first gathers the index of the proteins it wants to modify, then changes the degradation
    rates of those proteins. These adjustments were made so that the simulation could run.

    Requires
    --------
    - For each protein that needs to be modified it take in an adjustment factor.

    Modifies
    --------
    - This function modifies the protein degradation rates for the chosen proteins in sim_data.
    It takes their current degradation rate and multiplies them by the factor specified in adjustments.
    """

    for protein in sim_data.adjustments.protein_deg_rates_adjustments:
        idx = np.where(sim_data.process.translation.monomer_data["id"] == protein)[0]
        sim_data.process.translation.monomer_data.struct_array["deg_rate"][idx] *= (
            sim_data.adjustments.protein_deg_rates_adjustments[protein]
        )


def rescaleMassForSolubleMetabolites(sim_data, bulkMolCntr, concDict, doubling_time):
    """
    Adjust the cell's mass to accomodate target small molecule concentrations.

    Inputs
    ------
    - bulkMolCntr (np.ndarray object) - Two columns: 'id' for name and 'count'
            for count of all bulk molecules
    - concDict (dict) - a dictionary of metabolite ID (string) : concentration (unit'd number, dimensions of concentration) pairs
    - doubling_time (float with units of time) - measured doubling times given the condition

    Requires
    --------
    - Cell mass fraction data at a given doubling time.
    - Average cell density.
    - The conversion factor for transforming from the size of an average cell to the size of a cell
      immediately following division.
    - Avogadro's number.
    - Concentrations of small molecules (including both dry mass components and water).

    Modifies
    --------
    - Adds small molecule counts to bulkMolCntr.

    Returns
    -------
    - newAvgCellDryMassInit, the adjusted dry mass of a cell immediately following division.
    - fitAvgSolubleTargetMolMass, the adjusted dry mass of the soluble fraction of a cell
    """

    avgCellFractionMass = sim_data.mass.get_component_masses(doubling_time)

    non_small_molecule_initial_cell_mass = (
        avgCellFractionMass["proteinMass"]
        + avgCellFractionMass["rnaMass"]
        + avgCellFractionMass["dnaMass"]
    ) / sim_data.mass.avg_cell_to_initial_cell_conversion_factor

    molar_units = units.mol / units.L

    targetMoleculeIds = sorted(concDict)
    targetMoleculeConcentrations = molar_units * np.array(
        [concDict[key].asNumber(molar_units) for key in targetMoleculeIds]
    )  # Have to strip and replace units to obtain the proper array data type

    assert np.all(
        targetMoleculeConcentrations.asNumber(molar_units) > 0
    ), "Homeostatic dFBA objective requires non-zero (positive) concentrations"

    molecular_weights = sim_data.getter.get_masses(targetMoleculeIds)

    massesToAdd, countsToAdd = masses_and_counts_for_homeostatic_target(
        non_small_molecule_initial_cell_mass,
        targetMoleculeConcentrations,
        molecular_weights,
        sim_data.constants.cell_density,
        sim_data.constants.n_avogadro,
    )

    target_molecule_idx = bulk_name_to_idx(targetMoleculeIds, bulkMolCntr["id"])
    bulkMolCntr["count"][target_molecule_idx] = countsToAdd

    # Increase avgCellDryMassInit to match these numbers & rescale mass fractions
    smallMoleculetargetMoleculesDryMass = units.hstack(
        (
            massesToAdd[: targetMoleculeIds.index("WATER[c]")],
            massesToAdd[targetMoleculeIds.index("WATER[c]") + 1 :],
        )
    )  # remove water since it's not part of the dry mass

    newAvgCellDryMassInit = non_small_molecule_initial_cell_mass + units.sum(
        smallMoleculetargetMoleculesDryMass
    )
    fitAvgSolubleTargetMolMass = (
        units.sum(smallMoleculetargetMoleculesDryMass)
        * sim_data.mass.avg_cell_to_initial_cell_conversion_factor
    )

    return newAvgCellDryMassInit, fitAvgSolubleTargetMolMass


def setInitialRnaExpression(sim_data, expression, doubling_time):
    """
    Creates a container that with the initial count and ID of each RNA,
    calculated based on the mass fraction, molecular weight, and expression
    distribution of each RNA. For rRNA the counts are set based on mass, while
    for tRNA and mRNA the counts are set based on mass and relative abundance.
    Relies on the math function totalCountFromMassesAndRatios.

    Requires
    --------
    - Needs information from the knowledge base about the mass fraction,
    molecular weight, and distribution of each RNA species.

    Inputs
    ------
    - expression (array of floats) - expression for each RNA, normalized to 1
    - doubling_time (float with units of time) - doubling time for condition

    Returns
    --------
    - expression (array of floats) - contains the adjusted RNA expression,
    normalized to 1

    Notes
    -----
    - Now rnaData["synthProb"] does not match "expression"

    """
    # Load from sim_data
    n_avogadro = sim_data.constants.n_avogadro
    transcription = sim_data.process.transcription
    cistron_data = transcription.cistron_data
    rna_data = transcription.rna_data
    get_average_copy_number = sim_data.process.replication.get_average_copy_number
    rna_mw = rna_data["mw"]
    rna_rRNA_mw = rna_data["rRNA_mw"]
    rna_tRNA_mw = rna_data["tRNA_mw"]
    rna_coord = rna_data["replication_coordinate"]

    # Mask arrays for each RNA type
    is_rRNA = rna_data["is_rRNA"]
    is_tRNA = rna_data["is_tRNA"]
    is_mRNA = rna_data["is_mRNA"]

    # Get list of RNA IDs for each type and tRNA cistron IDs
    all_RNA_ids = rna_data["id"]
    ids_rRNA = all_RNA_ids[is_rRNA]
    ids_mRNA = all_RNA_ids[is_mRNA]
    ids_tRNA = all_RNA_ids[is_tRNA]
    ids_tRNA_cistrons = cistron_data["id"][cistron_data["is_tRNA"]]

    # Get mass fractions of each RNA type for this condition
    initial_rna_mass = (
        sim_data.mass.get_component_masses(doubling_time)["rnaMass"]
        / sim_data.mass.avg_cell_to_initial_cell_conversion_factor
    )
    ppgpp = sim_data.growth_rate_parameters.get_ppGpp_conc(doubling_time)
    rna_fractions = transcription.get_rna_fractions(ppgpp)
    total_mass_rRNA = initial_rna_mass * rna_fractions["rRNA"]
    total_mass_tRNA = initial_rna_mass * rna_fractions["tRNA"]
    total_mass_mRNA = initial_rna_mass * rna_fractions["mRNA"]

    # Get molecular weights of each RNA. For rRNAs/tRNAs, we only account for
    # the masses of the mature rRNAs/tRNAs within each RNA, since these RNAs are
    # almost instantly processed to yield the mature RNAs.
    individual_masses_rRNA = rna_rRNA_mw[is_rRNA] / n_avogadro
    individual_masses_tRNA = rna_tRNA_mw[is_tRNA] / n_avogadro
    individual_masses_mRNA = rna_mw[is_mRNA] / n_avogadro

    # Set rRNA TU expression assuming equal per-copy transcription
    # probabilities. The combined expression levels of each rRNA TU are assumed
    # to be proportional to their expected average copy numbers, which are
    # dependent on the doubling time and the chromosomal position.
    tau = doubling_time.asNumber(units.min)
    coord_rRNA = rna_coord[is_rRNA]
    n_avg_copy_rRNA = get_average_copy_number(tau, coord_rRNA)
    distribution_rRNA = normalize(n_avg_copy_rRNA)

    total_count_rRNA = totalCountFromMassesAndRatios(
        total_mass_rRNA, individual_masses_rRNA, distribution_rRNA
    )
    counts_rRNA = total_count_rRNA * distribution_rRNA

    # Get the total mass of tRNAs that are expressed from rRNA TUs and subtract
    # this mass from the total tRNA mass
    tRNA_masses_in_each_rRNA = rna_tRNA_mw[is_rRNA] / n_avogadro
    total_mass_tRNA_in_rRNAs = units.dot(counts_rRNA, tRNA_masses_in_each_rRNA)
    total_mass_tRNA -= total_mass_tRNA_in_rRNAs

    # Get tRNA cistron distribution (see Dong 1996), while setting values for
    # cistrons that are expressed from rRNAs to zero
    tRNA_distribution = sim_data.mass.get_trna_distribution(doubling_time)
    tRNA_id_to_dist = {
        trna_id: dist
        for (trna_id, dist) in zip(
            tRNA_distribution["id"], tRNA_distribution["molar_ratio_to_16SrRNA"]
        )
    }
    distribution_tRNA_cistrons = np.zeros(len(ids_tRNA_cistrons))
    for i, tRNA_id in enumerate(ids_tRNA_cistrons):
        distribution_tRNA_cistrons[i] = tRNA_id_to_dist[tRNA_id]

    tRNA_expressed_from_rRNA_mask = transcription.cistron_tu_mapping_matrix.dot(
        is_rRNA
    )[cistron_data["is_tRNA"]].astype(bool)
    distribution_tRNA_cistrons[tRNA_expressed_from_rRNA_mask] = 0
    distribution_tRNA_cistrons = normalize(distribution_tRNA_cistrons)

    # Approximate distribution of tRNA-including transcripts from tRNA cistron
    # distribution by using NNLS
    distribution_tRNA_including_transcripts, _ = transcription.fit_trna_expression(
        distribution_tRNA_cistrons
    )

    # Get distribution of tRNA-including transcripts that are not rRNAs
    is_hybrid = rna_data["is_rRNA"][rna_data["includes_tRNA"]]
    distribution_tRNA = distribution_tRNA_including_transcripts[~is_hybrid]
    distribution_tRNA = normalize(distribution_tRNA)

    # Assign tRNA counts based on this distribution
    total_count_tRNA = totalCountFromMassesAndRatios(
        total_mass_tRNA, individual_masses_tRNA, distribution_tRNA
    )
    counts_tRNA = total_count_tRNA * distribution_tRNA

    # Assign mRNA counts based on mass and relative abundances (microarrays)
    distribution_mRNA = normalize(expression[is_mRNA])
    total_count_mRNA = totalCountFromMassesAndRatios(
        total_mass_mRNA, individual_masses_mRNA, distribution_mRNA
    )
    counts_mRNA = total_count_mRNA * distribution_mRNA

    # Set expression counts in container
    rRNA_idx = bulk_name_to_idx(ids_rRNA, all_RNA_ids)
    tRNA_idx = bulk_name_to_idx(ids_tRNA, all_RNA_ids)
    mRNA_idx = bulk_name_to_idx(ids_mRNA, all_RNA_ids)
    rna_expression_container = np.zeros(len(all_RNA_ids), dtype=np.float64)
    rna_expression_container[rRNA_idx] = counts_rRNA
    rna_expression_container[tRNA_idx] = counts_tRNA
    rna_expression_container[mRNA_idx] = counts_mRNA

    expression = normalize(rna_expression_container)

    return expression


def totalCountIdDistributionProtein(sim_data, expression, doubling_time):
    """
    Calculates the total counts of proteins from the relative expression of RNA,
    individual protein mass, and total protein mass. Relies on the math functions
    netLossRateFromDilutionAndDegradationProtein, proteinDistributionFrommRNA,
    totalCountFromMassesAndRatios.

    Inputs
    ------
    - expression (array of floats) - relative frequency distribution of RNA expression
    - doubling_time (float with units of time) - measured doubling time given the condition

    Returns
    --------
    - total_count_protein (float) - total number of proteins
    - ids_protein (array of str) - name of each protein with location tag
    - distribution_protein (array of floats) - distribution for each protein,
    normalized to 1
    """
    ids_protein = sim_data.process.translation.monomer_data["id"]
    total_mass_protein = (
        sim_data.mass.get_component_masses(doubling_time)["proteinMass"]
        / sim_data.mass.avg_cell_to_initial_cell_conversion_factor
    )
    individual_masses_protein = (
        sim_data.process.translation.monomer_data["mw"] / sim_data.constants.n_avogadro
    )

    mRNA_cistron_expression = (
        sim_data.process.transcription.cistron_tu_mapping_matrix.dot(expression)[
            sim_data.process.transcription.cistron_data["is_mRNA"]
        ]
    )
    distribution_transcripts_by_protein = normalize(
        sim_data.relation.monomer_to_mRNA_cistron_mapping().dot(mRNA_cistron_expression)
    )

    translation_efficiencies_by_protein = normalize(
        sim_data.process.translation.translation_efficiencies_by_monomer
    )
    degradationRates = sim_data.process.translation.monomer_data["deg_rate"]

    # Find the net protein loss
    netLossRate_protein = netLossRateFromDilutionAndDegradationProtein(
        doubling_time, degradationRates
    )

    # Find the protein distribution
    distribution_protein = proteinDistributionFrommRNA(
        distribution_transcripts_by_protein,
        translation_efficiencies_by_protein,
        netLossRate_protein,
    )

    # Find total protein counts
    total_count_protein = totalCountFromMassesAndRatios(
        total_mass_protein, individual_masses_protein, distribution_protein
    )

    return total_count_protein, ids_protein, distribution_protein


def totalCountIdDistributionRNA(sim_data, expression, doubling_time):
    """
    Calculates the total counts of RNA from their relative expression,
    individual mass, and total RNA mass. Relies on the math function
    totalCountFromMassesAndRatios.

    Inputs
    ------
    - expression (array of floats) - relative frequency distribution of RNA
            expression
    - doubling_time (float with units of time) - measured doubling time given
            the condition

    Returns
    --------
    - total_count_RNA (float) - total number of RNAs
    - ids_rnas (array of str) - name of each RNA with location tag
    - distribution_RNA (array of floats) - distribution for each RNA,
            normalized to 1
    """
    transcription = sim_data.process.transcription
    ids_rnas = transcription.rna_data["id"]
    total_mass_RNA = (
        sim_data.mass.get_component_masses(doubling_time)["rnaMass"]
        / sim_data.mass.avg_cell_to_initial_cell_conversion_factor
    )
    mws = transcription.rna_data["mw"]
    # Use only the rRNA/tRNA mass for rRNA/tRNA transcription units
    is_rRNA = transcription.rna_data["is_rRNA"]
    is_tRNA = transcription.rna_data["is_tRNA"]
    mws[is_rRNA] = transcription.rna_data["rRNA_mw"][is_rRNA]
    mws[is_tRNA] = transcription.rna_data["tRNA_mw"][is_tRNA]
    individual_masses_RNA = mws / sim_data.constants.n_avogadro

    distribution_RNA = normalize(expression)

    total_count_RNA = totalCountFromMassesAndRatios(
        total_mass_RNA, individual_masses_RNA, distribution_RNA
    )

    return total_count_RNA, ids_rnas, distribution_RNA


def createBulkContainer(sim_data, expression, doubling_time):
    """
    Creates a container that tracks the counts of all bulk molecules. Relies on
    totalCountIdDistributionRNA and totalCountIdDistributionProtein to set the
    counts and IDs of all RNAs and proteins.

    Inputs
    ------
    - expression (array of floats) - relative frequency distribution of RNA expression
    - doubling_time (float with units of time) - measured doubling time given the condition

    Returns
    -------
    - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for count of all bulk molecules
    """

    total_count_RNA, ids_rnas, distribution_RNA = totalCountIdDistributionRNA(
        sim_data, expression, doubling_time
    )
    total_count_protein, ids_protein, distribution_protein = (
        totalCountIdDistributionProtein(sim_data, expression, doubling_time)
    )

    ids_molecules = sim_data.internal_state.bulk_molecules.bulk_data["id"]

    # Construct bulk container
    bulkContainer = np.array(
        [mol_data for mol_data in zip(ids_molecules, np.zeros(len(ids_molecules)))],
        dtype=[("id", ids_molecules.dtype), ("count", np.float64)],
    )

    # Assign RNA counts based on mass and expression distribution
    counts_RNA = total_count_RNA * distribution_RNA
    rna_idx = bulk_name_to_idx(ids_rnas, bulkContainer["id"])
    bulkContainer["count"][rna_idx] = counts_RNA

    # Assign protein counts based on mass and mRNA counts
    counts_protein = total_count_protein * distribution_protein
    protein_idx = bulk_name_to_idx(ids_protein, bulkContainer["id"])
    bulkContainer["count"][protein_idx] = counts_protein

    return bulkContainer


def setRibosomeCountsConstrainedByPhysiology(
    sim_data, bulkContainer, doubling_time, variable_elongation_translation
):
    """
    Set counts of ribosomal protein subunits based on three constraints:
    (1) Expected protein distribution doubles in one cell cycle
    (2) Measured rRNA mass fractions
    (3) Expected ribosomal protein subunit counts based on RNA expression data

    Inputs
    ------
    bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for count of all bulk molecules
    doubling_time (float with units of time) - doubling time given the condition
    variable_elongation_translation (bool) - whether there is variable elongation for translation

    Modifies
    --------
    - counts of ribosomal protein subunits in bulkContainer
    """

    active_fraction = sim_data.growth_rate_parameters.get_fraction_active_ribosome(
        doubling_time
    )

    # Get IDs and stoichiometry of ribosome subunits
    ribosome_30S_subunits = sim_data.process.complexation.get_monomers(
        sim_data.molecule_ids.s30_full_complex
    )["subunitIds"]
    ribosome_50S_subunits = sim_data.process.complexation.get_monomers(
        sim_data.molecule_ids.s50_full_complex
    )["subunitIds"]
    ribosome_30S_stoich = sim_data.process.complexation.get_monomers(
        sim_data.molecule_ids.s30_full_complex
    )["subunitStoich"]
    ribosome_50S_stoich = sim_data.process.complexation.get_monomers(
        sim_data.molecule_ids.s50_full_complex
    )["subunitStoich"]

    # Remove rRNA subunits from each array
    monomer_ids = set(sim_data.process.translation.monomer_data["id"])

    def remove_rRNA(subunit_ids, subunit_stoich):
        is_protein = np.array(
            [(subunit_id in monomer_ids) for subunit_id in subunit_ids]
        )
        return (subunit_ids[is_protein], subunit_stoich[is_protein])

    ribosome_30S_subunits, ribosome_30S_stoich = remove_rRNA(
        ribosome_30S_subunits, ribosome_30S_stoich
    )
    ribosome_50S_subunits, ribosome_50S_stoich = remove_rRNA(
        ribosome_50S_subunits, ribosome_50S_stoich
    )

    # -- CONSTRAINT 1: Expected protein distribution doubling -- #
    ## Calculate minimium number of 30S and 50S subunits required in order to double our expected
    ## protein distribution in one cell cycle
    proteinLengths = units.sum(
        sim_data.process.translation.monomer_data["aa_counts"], axis=1
    )
    proteinDegradationRates = sim_data.process.translation.monomer_data["deg_rate"]
    protein_idx = bulk_name_to_idx(
        sim_data.process.translation.monomer_data["id"], bulkContainer["id"]
    )
    proteinCounts = counts(bulkContainer, protein_idx)

    netLossRate_protein = netLossRateFromDilutionAndDegradationProtein(
        doubling_time,
        proteinDegradationRates,
    )

    elongation_rates = sim_data.process.translation.make_elongation_rates(
        None,
        sim_data.growth_rate_parameters.get_ribosome_elongation_rate(
            doubling_time
        ).asNumber(units.aa / units.s),
        1,
        variable_elongation_translation,
    )

    nRibosomesNeeded = np.ceil(
        calculateMinPolymerizingEnzymeByProductDistribution(
            proteinLengths, elongation_rates, netLossRate_protein, proteinCounts
        ).asNumber(units.aa / units.s)
        / active_fraction
    )

    # Minimum number of ribosomes needed
    constraint1_ribosome30SCounts = nRibosomesNeeded * ribosome_30S_stoich

    constraint1_ribosome50SCounts = nRibosomesNeeded * ribosome_50S_stoich

    # -- CONSTRAINT 2: Measured rRNA mass fraction -- #
    # Get rRNA counts
    rna_data = sim_data.process.transcription.rna_data
    rrna_idx = bulk_name_to_idx(
        rna_data["id"][rna_data["is_rRNA"]], bulkContainer["id"]
    )
    rRNA_tu_counts = counts(bulkContainer, rrna_idx)
    rRNA_cistron_counts = (
        sim_data.process.transcription.rRNA_cistron_tu_mapping_matrix.dot(
            rRNA_tu_counts
        )
    )
    rRNA_cistron_indexes = np.where(
        sim_data.process.transcription.cistron_data["is_rRNA"]
    )[0]
    rRNA_23S_counts = rRNA_cistron_counts[
        sim_data.process.transcription.cistron_data["is_23S_rRNA"][rRNA_cistron_indexes]
    ]
    rRNA_16S_counts = rRNA_cistron_counts[
        sim_data.process.transcription.cistron_data["is_16S_rRNA"][rRNA_cistron_indexes]
    ]
    rRNA_5S_counts = rRNA_cistron_counts[
        sim_data.process.transcription.cistron_data["is_5S_rRNA"][rRNA_cistron_indexes]
    ]

    ## 16S rRNA is in the 30S subunit
    massFracPredicted_30SCount = rRNA_16S_counts.sum()
    ## 23S and 5S rRNA are in the 50S subunit
    massFracPredicted_50SCount = min(rRNA_23S_counts.sum(), rRNA_5S_counts.sum())

    constraint2_ribosome30SCounts = massFracPredicted_30SCount * ribosome_30S_stoich
    constraint2_ribosome50SCounts = massFracPredicted_50SCount * ribosome_50S_stoich

    # -- CONSTRAINT 3: Expected ribosomal subunit counts based expression
    ## Calculate fundamental ribosomal subunit count distribution based on RNA expression data
    ## Already calculated and stored in bulkContainer
    ribosome_30S_idx = bulk_name_to_idx(ribosome_30S_subunits, bulkContainer["id"])
    ribosome30SCounts = counts(bulkContainer, ribosome_30S_idx)
    ribosome_50S_idx = bulk_name_to_idx(ribosome_50S_subunits, bulkContainer["id"])
    ribosome50SCounts = counts(bulkContainer, ribosome_50S_idx)

    # -- SET RIBOSOME FUNDAMENTAL SUBUNIT COUNTS TO MAXIMUM CONSTRAINT -- #
    constraint_names = np.array(
        [
            "Insufficient to double protein counts",
            "Too small for mass fraction",
            "Current level OK",
        ]
    )
    rib30lims = np.array(
        [
            nRibosomesNeeded,
            massFracPredicted_30SCount,
            (ribosome30SCounts / ribosome_30S_stoich).min(),
        ]
    )
    rib50lims = np.array(
        [
            nRibosomesNeeded,
            massFracPredicted_50SCount,
            (ribosome50SCounts / ribosome_50S_stoich).min(),
        ]
    )
    if VERBOSE > 1:
        print(
            "30S limit: {}".format(
                constraint_names[np.where(rib30lims.max() == rib30lims)[0]][-1]
            )
        )
        print(
            "30S actual count: {}".format(
                (ribosome30SCounts / ribosome_30S_stoich).min()
            )
        )
        print(
            "30S count set to: {}".format(
                rib30lims[np.where(rib30lims.max() == rib30lims)[0]][-1]
            )
        )
        print(
            "50S limit: {}".format(
                constraint_names[np.where(rib50lims.max() == rib50lims)[0]][-1]
            )
        )
        print(
            "50S actual count: {}".format(
                (ribosome50SCounts / ribosome_50S_stoich).min()
            )
        )
        print(
            "50S count set to: {}".format(
                rib50lims[np.where(rib50lims.max() == rib50lims)[0]][-1]
            )
        )

    bulkContainer["count"][ribosome_30S_idx] = np.fmax(
        np.fmax(ribosome30SCounts, constraint1_ribosome30SCounts),
        constraint2_ribosome30SCounts,
    )

    bulkContainer["count"][ribosome_50S_idx] = np.fmax(
        np.fmax(ribosome50SCounts, constraint1_ribosome50SCounts),
        constraint2_ribosome50SCounts,
    )


def setRNAPCountsConstrainedByPhysiology(
    sim_data,
    bulkContainer,
    doubling_time,
    avgCellDryMassInit,
    variable_elongation_transcription,
    Km=None,
):
    """
    Set counts of RNA polymerase based on two constraints:
    (1) Number of RNAP subunits required to maintain steady state of mRNAs
    (2) Expected RNAP subunit counts based on (mRNA) distribution recorded in
            bulkContainer

    Inputs
    ------
    - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for count of all bulk molecules
    - doubling_time (float with units of time) - doubling time given the condition
    - avgCellDryMassInit (float with units of mass) - expected initial dry cell mass
    - Km (array of floats with units of mol/volume) - Km for each RNA associated
    with RNases

    Modifies
    --------
    - bulkContainer (np.ndarray object) - the counts of RNA polymerase
            subunits are set according to Constraint 1

    Notes
    -----
    - Constraint 2 is not being used -- see final line of this function.
    """

    # -- CONSTRAINT 1: Expected RNA distribution doubling -- #
    rnaLengths = units.sum(
        sim_data.process.transcription.rna_data["counts_ACGU"], axis=1
    )

    rnaLossRate = None
    rna_idx = bulk_name_to_idx(
        sim_data.process.transcription.rna_data["id"], bulkContainer["id"]
    )

    if Km is None:
        # RNA loss rate is in units of counts/time, and computed by summing the
        # contributions of degradation and dilution.
        rnaLossRate = netLossRateFromDilutionAndDegradationRNALinear(
            doubling_time,
            sim_data.process.transcription.rna_data["deg_rate"],
            counts(bulkContainer, rna_idx),
        )
    else:
        # Get constants to compute countsToMolar factor
        cellDensity = sim_data.constants.cell_density
        cellVolume = (
            avgCellDryMassInit / cellDensity / sim_data.mass.cell_dry_mass_fraction
        )
        countsToMolar = 1 / (sim_data.constants.n_avogadro * cellVolume)

        # Gompute input arguments for netLossRateFromDilutionAndDegradationRNA()
        rnaConc = countsToMolar * counts(bulkContainer, rna_idx)
        endoRNase_idx = bulk_name_to_idx(
            sim_data.process.rna_decay.endoRNase_ids, bulkContainer["id"]
        )
        endoRNaseConc = countsToMolar * counts(bulkContainer, endoRNase_idx)
        kcatEndoRNase = sim_data.process.rna_decay.kcats
        totalEndoRnaseCapacity = units.sum(endoRNaseConc * kcatEndoRNase)

        # RNA loss rate is in units of counts/time, and computed by accounting
        # for the competitive inhibition of RNase by other RNA targets.
        rnaLossRate = netLossRateFromDilutionAndDegradationRNA(
            doubling_time,
            (1 / countsToMolar) * totalEndoRnaseCapacity,
            Km,
            rnaConc,
            countsToMolar,
        )

    # Compute number of RNA polymerases required to maintain steady state of mRNA
    elongation_rates = sim_data.process.transcription.make_elongation_rates(
        None,
        sim_data.growth_rate_parameters.get_rnap_elongation_rate(
            doubling_time
        ).asNumber(units.nt / units.s),
        1,
        variable_elongation_transcription,
    )

    nActiveRnapNeeded = calculateMinPolymerizingEnzymeByProductDistributionRNA(
        rnaLengths, elongation_rates, rnaLossRate
    ).asNumber(units.nt / units.s)

    nRnapsNeeded = np.ceil(
        nActiveRnapNeeded
        / sim_data.growth_rate_parameters.get_fraction_active_rnap(doubling_time)
    )

    # Convert nRnapsNeeded to the number of RNA polymerase subunits required
    rnapIds = sim_data.process.complexation.get_monomers(
        sim_data.molecule_ids.full_RNAP
    )["subunitIds"]
    rnapStoich = sim_data.process.complexation.get_monomers(
        sim_data.molecule_ids.full_RNAP
    )["subunitStoich"]
    minRnapSubunitCounts = nRnapsNeeded * rnapStoich

    # -- CONSTRAINT 2: Expected RNAP subunit counts based on distribution -- #
    rnap_idx = bulk_name_to_idx(rnapIds, bulkContainer["id"])
    rnapCounts = counts(bulkContainer, rnap_idx)

    ## -- SET RNAP COUNTS TO MAXIMUM CONSTRAINTS -- #
    constraint_names = np.array(
        ["Current level OK", "Insufficient to double RNA distribution"]
    )
    rnapLims = np.array(
        [(rnapCounts / rnapStoich).min(), (minRnapSubunitCounts / rnapStoich).min()]
    )
    if VERBOSE > 1:
        print(
            "rnap limit: {}".format(
                constraint_names[np.where(rnapLims.max() == rnapLims)[0]][0]
            )
        )
        print("rnap actual count: {}".format((rnapCounts / rnapStoich).min()))
        print(
            "rnap counts set to: {}".format(
                rnapLims[np.where(rnapLims.max() == rnapLims)[0]][0]
            )
        )

    if np.any(minRnapSubunitCounts < 0):
        raise ValueError("RNAP protein counts must be positive.")

    bulkContainer["count"][rnap_idx] = minRnapSubunitCounts


def fitExpression(sim_data, bulkContainer, doubling_time, avgCellDryMassInit, Km=None):
    """
    Determines expression and synthesis probabilities for RNA molecules to fit
    protein levels and RNA degradation rates. Assumes a steady state analysis
    where the RNA synthesis probability will be the same as the degradation rate.
    If no Km is given, then RNA degradation is assumed to be linear otherwise
    degradation is calculated based on saturation with RNases.

    Inputs
    ------
    - bulkContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for expected count based on expression of all bulk molecules
    - doubling_time (float with units of time) - doubling time
    - avgCellDryMassInit (float with units of mass) - expected initial dry cell mass
    - Km (array of floats with units of mol/volume) - Km for each RNA associated
    with RNases

    Modifies
    --------
    - bulkContainer counts of RNA and proteins

    Returns
    --------
    - expression (array of floats) - adjusted expression for each RNA,
    normalized to 1
    - synth_prob (array of floats) - synthesis probability for each RNA which
    accounts for expression and degradation rate, normalized to 1
    - fit_cistron_expression (array of floats) - target expression levels of
    each cistron (gene) used to calculate RNA expression levels
    - cistron_expression_res (array of floats) - the residuals of the NNLS
    problem solved to calculate RNA expression levels

    Notes
    -----
    - TODO - sets bulkContainer counts and returns values - change to only return values
    """
    # Load required parameters
    transcription = sim_data.process.transcription
    translation = sim_data.process.translation
    translation_efficiencies_by_protein = normalize(
        translation.translation_efficiencies_by_monomer
    )
    degradation_rates_protein = translation.monomer_data["deg_rate"]
    net_loss_rate_protein = netLossRateFromDilutionAndDegradationProtein(
        doubling_time, degradation_rates_protein
    )
    avg_cell_fraction_mass = sim_data.mass.get_component_masses(doubling_time)
    total_mass_RNA = (
        avg_cell_fraction_mass["rnaMass"]
        / sim_data.mass.avg_cell_to_initial_cell_conversion_factor
    )
    cistron_tu_mapping_matrix = transcription.cistron_tu_mapping_matrix

    # Calculate current expression fraction of mRNA transcription units
    rna_idx = bulk_name_to_idx(transcription.rna_data["id"], bulkContainer["id"])
    RNA_counts = counts(bulkContainer, rna_idx)
    rna_expression_container = normalize(RNA_counts)

    mRNA_tu_expression_frac = np.sum(
        rna_expression_container[transcription.rna_data["is_mRNA"]]
    )

    # Calculate current expression levels of each cistron given the RNA
    # expression levels
    fit_cistron_expression = normalize(cistron_tu_mapping_matrix.dot(RNA_counts))
    mRNA_cistron_expression_frac = fit_cistron_expression[
        transcription.cistron_data["is_mRNA"]
    ].sum()

    # Calculate required mRNA expression from monomer counts
    protein_idx = bulk_name_to_idx(translation.monomer_data["id"], bulkContainer["id"])
    counts_protein = counts(bulkContainer, protein_idx)
    mRNA_cistron_distribution_per_protein = mRNADistributionFromProtein(
        normalize(counts_protein),
        translation_efficiencies_by_protein,
        net_loss_rate_protein,
    )

    mRNA_cistron_distribution = normalize(
        sim_data.relation.monomer_to_mRNA_cistron_mapping().T.dot(
            mRNA_cistron_distribution_per_protein
        )
    )

    # Replace mRNA cistron expression with values calculated from monomer counts
    fit_cistron_expression[transcription.cistron_data["is_mRNA"]] = (
        mRNA_cistron_expression_frac * mRNA_cistron_distribution
    )

    # Use least squares to calculate expression of transcription units required
    # to generate the given cistron expression levels and the residuals for
    # the expression of each cistron
    fit_tu_expression, cistron_expression_res = transcription.fit_rna_expression(
        fit_cistron_expression
    )
    fit_mRNA_tu_expression = fit_tu_expression[transcription.rna_data["is_mRNA"]]

    rna_expression_container[transcription.rna_data["is_mRNA"]] = (
        mRNA_tu_expression_frac * normalize(fit_mRNA_tu_expression)
    )
    expression = normalize(rna_expression_container)

    # Set number of RNAs based on expression we just set
    mws = transcription.rna_data["mw"]

    # Use only the rRNA/tRNA mass for rRNA/tRNA transcription units
    is_rRNA = transcription.rna_data["is_rRNA"]
    is_tRNA = transcription.rna_data["is_tRNA"]
    mws[is_rRNA] = transcription.rna_data["rRNA_mw"][is_rRNA]
    mws[is_tRNA] = transcription.rna_data["tRNA_mw"][is_tRNA]

    n_rnas = totalCountFromMassesAndRatios(
        total_mass_RNA, mws / sim_data.constants.n_avogadro, expression
    )
    bulkContainer["count"][rna_idx] = n_rnas * expression

    if Km is None:
        rnaLossRate = netLossRateFromDilutionAndDegradationRNALinear(
            doubling_time,
            transcription.rna_data["deg_rate"],
            counts(bulkContainer, rna_idx),
        )
    else:
        # Get constants to compute countsToMolar factor
        cellDensity = sim_data.constants.cell_density
        dryMassFraction = sim_data.mass.cell_dry_mass_fraction
        cellVolume = avgCellDryMassInit / cellDensity / dryMassFraction
        countsToMolar = 1 / (sim_data.constants.n_avogadro * cellVolume)

        endoRNase_idx = bulk_name_to_idx(
            sim_data.process.rna_decay.endoRNase_ids, bulkContainer["id"]
        )
        endoRNaseConc = countsToMolar * counts(bulkContainer, endoRNase_idx)
        kcatEndoRNase = sim_data.process.rna_decay.kcats
        totalEndoRnaseCapacity = units.sum(endoRNaseConc * kcatEndoRNase)

        rnaLossRate = netLossRateFromDilutionAndDegradationRNA(
            doubling_time,
            (1 / countsToMolar) * totalEndoRnaseCapacity,
            Km,
            countsToMolar * counts(bulkContainer, rna_idx),
            countsToMolar,
        )

    synth_prob = normalize(rnaLossRate.asNumber(1 / units.min))

    return expression, synth_prob, fit_cistron_expression, cistron_expression_res


def fitMaintenanceCosts(sim_data, bulkContainer):
    """
    Fits the growth-associated maintenance (GAM) cost associated with metabolism.

    The energetic costs associated with growth have been estimated utilizing flux-balance analysis
    and are used with FBA to obtain accurate growth predictions.  In the whole-cell model, some of
    these costs are explicitly associated with the energetic costs of translation, a biomass
    assembly process.  Consequently we must estimate the amount of energy utilized by translation
    per unit of biomass (i.e. dry mass) produced, and subtract that quantity from reported GAM to
    acquire the modified GAM that we use in the metabolic submodel.

    Requires
    --------
    - amino acid counts associated with protein monomers
    - average initial dry mass
    - energetic (GTP) cost of translation (per amino acid polymerized)
    - observed growth-associated maintenance (GAM)
    In dimensions of ATP or ATP equivalents consumed per biomass

    Modifies
    --------
    - the "dark" ATP, i.e. the modified GAM

    Notes
    -----
    As more non-metabolic submodels account for energetic costs, this function should be extended
    to subtract those costs off the observed GAM.

    There also exists, in contrast, non-growth-associated-maintenance (NGAM), which is relative to
    total biomass rather than the biomass accumulation rate.  As the name would imply, this
    accounts for the energetic costs of maintaining the existing biomass.  It is also accounted for
    in the metabolic submodel.

    TODO (John): Rewrite as a true function.
    """

    aaCounts = sim_data.process.translation.monomer_data["aa_counts"]
    protein_idx = bulk_name_to_idx(
        sim_data.process.translation.monomer_data["id"], bulkContainer["id"]
    )
    proteinCounts = counts(bulkContainer, protein_idx)
    nAvogadro = sim_data.constants.n_avogadro
    avgCellDryMassInit = sim_data.mass.avg_cell_dry_mass_init
    gtpPerTranslation = sim_data.constants.gtp_per_translation
    atp_per_charge = (
        2  # ATP -> AMP is explicitly used in charging reactions so can remove from GAM
    )

    # GTPs used for translation (recycled, not incorporated into biomass)
    aaMmolPerGDCW = units.sum(
        aaCounts * np.tile(proteinCounts.reshape(-1, 1), (1, 21)), axis=0
    ) * ((1 / (units.aa * nAvogadro)) * (1 / avgCellDryMassInit))

    aasUsedOverCellCycle = units.sum(aaMmolPerGDCW)
    explicit_mmol_maintenance_per_gdcw = (
        atp_per_charge + gtpPerTranslation
    ) * aasUsedOverCellCycle

    darkATP = (  # This has everything we can't account for
        sim_data.constants.growth_associated_maintenance
        - explicit_mmol_maintenance_per_gdcw
    )

    # We do not want to create energy with growth by having a negative darkATP
    # value. GAM measurements have some error so it's possible explicit
    # accounting could be more accurate or the GAM value used is too low which
    # would lead to a negative value. Easy fix is setting darkATP = 0 if this
    # error is raised.
    if darkATP.asNumber() < 0:
        raise ValueError(
            "GAM has been adjusted too low. Explicit energy accounting should not exceed GAM."
            " Consider setting darkATP to 0 if energy corrections are accurate."
        )

    sim_data.constants.darkATP = darkATP


def calculateBulkDistributions(
    sim_data, expression, concDict, avgCellDryMassInit, doubling_time
):
    """
    Finds a distribution of copy numbers for macromolecules. While RNA and protein
    expression can be approximated using well-described statistical	distributions,
    complexes require absolute copy numbers. To get these distributions, this
    function instantiates many cells with a reduced set of molecules, forms complexes,
    and iterates through equilibrium and two-component system processes until
    metabolite counts reach a steady-state. It then computes the resulting
    statistical distributions.

    Requires
    --------
    - N_SEEDS (int) - the number of instantiated cells

    Inputs
    ------
    - expression (array of floats) - expression for each RNA, normalized to 1
    - concDict {metabolite (str): concentration (float with units of mol/volume)} -
    dictionary for concentrations of each metabolite with location tag
    - avgCellDryMassInit (float with units of mass) - initial dry cell mass
    - doubling_time (float with units of time) - doubling time for condition

    Returns
    --------
    - bulkAverageContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for the mean of the counts of all bulk molecules
    - bulkDeviationContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for the standard deviation of the counts of all bulk molecules
    - proteinMonomerAverageContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for the mean of the counts of all protein monomers
    - proteinMonomerDeviationContainer (np.ndarray object) - Two columns: 'id' for name and 'count'
            for the standard deviation of the counts of all protein monomers
    """

    # Ids
    totalCount_RNA, ids_rnas, distribution_RNA = totalCountIdDistributionRNA(
        sim_data, expression, doubling_time
    )
    totalCount_protein, ids_protein, distribution_protein = (
        totalCountIdDistributionProtein(sim_data, expression, doubling_time)
    )
    ids_complex = sim_data.process.complexation.molecule_names
    ids_equilibrium = sim_data.process.equilibrium.molecule_names
    ids_twoComponentSystem = sim_data.process.two_component_system.molecule_names
    ids_metabolites = sorted(concDict)
    conc_metabolites = (units.mol / units.L) * np.array(
        [concDict[key].asNumber(units.mol / units.L) for key in ids_metabolites]
    )
    allMoleculesIDs = sorted(
        set(ids_rnas)
        | set(ids_protein)
        | set(ids_complex)
        | set(ids_equilibrium)
        | set(ids_twoComponentSystem)
        | set(ids_metabolites)
    )

    # Data for complexation
    complexationStoichMatrix = sim_data.process.complexation.stoich_matrix().astype(
        np.int64, order="F"
    )
    # Data for equilibrium binding
    # equilibriumDerivatives = sim_data.process.equilibrium.derivatives
    # equilibriumDerivativesJacobian = sim_data.process.equilibrium.derivativesJacobian

    # Data for metabolites
    cellDensity = sim_data.constants.cell_density
    cellVolume = avgCellDryMassInit / cellDensity / sim_data.mass.cell_dry_mass_fraction

    # Construct bulk container

    # We want to know something about the distribution of the copy numbers of
    # macromolecules in the cell.  While RNA and protein expression can be
    # approximated using well-described statistical distributions, we need
    # absolute copy numbers to form complexes.  To get a distribution, we must
    # instantiate many cells, form complexes, and finally compute the
    # statistics we will use in the fitting operations.

    bulk_ids = sim_data.internal_state.bulk_molecules.bulk_data.struct_array["id"]
    bulkContainer = np.array(
        [mol_data for mol_data in zip(bulk_ids, np.zeros(len(bulk_ids)))],
        dtype=[("id", bulk_ids.dtype), ("count", int)],
    )

    rna_idx = bulk_name_to_idx(ids_rnas, bulkContainer["id"])
    protein_idx = bulk_name_to_idx(ids_protein, bulkContainer["id"])
    complexation_molecules_idx = bulk_name_to_idx(ids_complex, bulkContainer["id"])
    equilibrium_molecules_idx = bulk_name_to_idx(ids_equilibrium, bulkContainer["id"])
    two_component_system_molecules_idx = bulk_name_to_idx(
        ids_twoComponentSystem, bulkContainer["id"]
    )
    metabolites_idx = bulk_name_to_idx(ids_metabolites, bulkContainer["id"])
    all_molecules_idx = bulk_name_to_idx(allMoleculesIDs, bulkContainer["id"])

    allMoleculeCounts = np.empty((N_SEEDS, len(allMoleculesIDs)), np.int64)
    proteinMonomerCounts = np.empty((N_SEEDS, len(ids_protein)), np.int64)

    if VERBOSE > 1:
        print("Bulk distribution seed:")

    # Instantiate cells to find average copy numbers of macromolecules
    for seed in range(N_SEEDS):
        if VERBOSE > 1:
            print("seed = {}".format(seed))

        bulkContainer["count"][all_molecules_idx] = 0

        bulkContainer["count"][rna_idx] = totalCount_RNA * distribution_RNA

        bulkContainer["count"][protein_idx] = totalCount_protein * distribution_protein

        proteinMonomerCounts[seed, :] = counts(bulkContainer, protein_idx)
        complexationMoleculeCounts = counts(bulkContainer, complexation_molecules_idx)

        # Form complexes
        time_step = 2**31  # don't stop until all complexes are formed.
        complexation_rates = sim_data.process.complexation.rates
        system = StochasticSystem(complexationStoichMatrix.T, random_seed=seed)
        complexation_result = system.evolve(
            time_step, complexationMoleculeCounts, complexation_rates
        )

        updatedCompMoleculeCounts = complexation_result["outcome"]
        bulkContainer["count"][complexation_molecules_idx] = updatedCompMoleculeCounts

        metDiffs = np.inf * np.ones_like(counts(bulkContainer, metabolites_idx))
        nIters = 0

        # Iterate processes until metabolites converge to a steady-state
        while np.linalg.norm(metDiffs, np.inf) > 1:
            random_state = np.random.RandomState(seed)
            metCounts = conc_metabolites * cellVolume * sim_data.constants.n_avogadro
            metCounts.normalize()
            metCounts.checkNoUnit()
            bulkContainer["count"][metabolites_idx] = metCounts.asNumber().round()

            # Find reaction fluxes from equilibrium process
            # Do not use jit to avoid compiling time (especially when running
            # in parallel since sim_data needs to be pickled and reconstructed
            # each time)
            rxnFluxes, _ = sim_data.process.equilibrium.fluxes_and_molecules_to_SS(
                bulkContainer["count"][equilibrium_molecules_idx],
                cellVolume.asNumber(units.L),
                sim_data.constants.n_avogadro.asNumber(1 / units.mol),
                random_state,
                jit=False,
            )
            bulkContainer["count"][equilibrium_molecules_idx] += np.dot(
                sim_data.process.equilibrium.stoich_matrix().astype(np.int64),
                rxnFluxes.astype(np.int64),
            )
            assert np.all(bulkContainer["count"][equilibrium_molecules_idx] >= 0)

            # Find changes from two component system
            _, moleculeCountChanges = (
                sim_data.process.two_component_system.molecules_to_ss(
                    bulkContainer["count"][two_component_system_molecules_idx],
                    cellVolume.asNumber(units.L),
                    sim_data.constants.n_avogadro.asNumber(1 / units.mmol),
                )
            )

            bulkContainer["count"][two_component_system_molecules_idx] += (
                moleculeCountChanges.astype(np.int64)
            )

            metDiffs = (
                bulkContainer["count"][metabolites_idx] - metCounts.asNumber().round()
            )

            nIters += 1
            if nIters > 100:
                raise Exception("Equilibrium reactions are not converging!")

        allMoleculeCounts[seed, :] = counts(bulkContainer, all_molecules_idx)

    # Update counts in bulk objects container
    bulkAverageContainer = np.array(
        [mol_data for mol_data in zip(bulk_ids, np.zeros(len(bulk_ids)))],
        dtype=[("id", bulk_ids.dtype), ("count", np.float64)],
    )
    bulkDeviationContainer = np.array(
        [mol_data for mol_data in zip(bulk_ids, np.zeros(len(bulk_ids)))],
        dtype=[("id", bulk_ids.dtype), ("count", np.float64)],
    )
    monomer_ids = sim_data.process.translation.monomer_data["id"]
    proteinMonomerAverageContainer = np.array(
        [mol_data for mol_data in zip(monomer_ids, np.zeros(len(monomer_ids)))],
        dtype=[("id", monomer_ids.dtype), ("count", np.float64)],
    )
    proteinMonomerDeviationContainer = np.array(
        [mol_data for mol_data in zip(monomer_ids, np.zeros(len(monomer_ids)))],
        dtype=[("id", monomer_ids.dtype), ("count", np.float64)],
    )

    bulkAverageContainer["count"][all_molecules_idx] = allMoleculeCounts.mean(0)
    bulkDeviationContainer["count"][all_molecules_idx] = allMoleculeCounts.std(0)
    proteinMonomerAverageContainer["count"] = proteinMonomerCounts.mean(0)
    proteinMonomerDeviationContainer["count"] = proteinMonomerCounts.std(0)

    return (
        bulkAverageContainer,
        bulkDeviationContainer,
        proteinMonomerAverageContainer,
        proteinMonomerDeviationContainer,
    )


# Math functions


def totalCountFromMassesAndRatios(totalMass, individualMasses, distribution):
    """
    Function to determine the expected total counts for a group of molecules
    in order to achieve a total mass with a given distribution of individual
    molecules.

    Math:
            Total mass = dot(mass, count)

            Fraction of i:
            f = count / Total counts

            Substituting:
            Total mass = dot(mass, f * Total counts)
            Total mass = Total counts * dot(mass, f)

            Total counts = Total mass / dot(mass, f)

    Requires
    --------
    - totalMass (float with mass units): total mass of the group of molecules
    - individualMasses (array of floats with mass units): mass for individual
    molecules in the group
    - distribution (array of floats): distribution of individual molecules,
    normalized to 1

    Returns
    --------
    - counts (float): total counts (does not need to be a whole number)
    """

    assert np.allclose(np.sum(distribution), 1)
    counts = 1 / units.dot(individualMasses, distribution) * totalMass
    return units.strip_empty_units(counts)


def proteinDistributionFrommRNA(
    distribution_mRNA, translation_efficiencies, netLossRate
):
    """
    dP_i / dt = k * M_i * e_i - P_i * Loss_i

    At steady state:
    P_i = k * M_i * e_i / Loss_i

    Fraction of mRNA for ith gene is defined as:
    f_i = M_i / M_total

    Substituting in:
    P_i = k * f_i * e_i * M_total / Loss_i

    Normalizing P_i by summing over all i cancels out k and M_total
    assuming constant translation rate.

    Inputs
    ------
    - distribution_mRNA (array of floats) - distribution for each mRNA,
    normalized to 1
    - translation_efficiencies (array of floats) - translational efficiency for each mRNA,
    normalized to 1
    - netLossRate (array of floats with units of 1/time) - rate of loss for each protein

    Returns
    -------
    - array of floats for the distribution of each protein, normalized to 1
    """

    assert np.allclose(np.sum(distribution_mRNA), 1)
    assert np.allclose(np.sum(translation_efficiencies), 1)
    distributionUnnormed = (
        1 / netLossRate * distribution_mRNA * translation_efficiencies
    )
    distributionNormed = distributionUnnormed / units.sum(distributionUnnormed)
    distributionNormed.normalize()
    distributionNormed.checkNoUnit()

    return distributionNormed.asNumber()


def mRNADistributionFromProtein(
    distribution_protein, translation_efficiencies, netLossRate
):
    """
    dP_i / dt = k * M_i * e_i - P_i * Loss_i

    At steady state:
    M_i = Loss_i * P_i / (k * e_i)

    Fraction of protein for ith gene is defined as:
    f_i = P_i / P_total

    Substituting in:
    M_i = Loss_i * f_i * P_total / (k * e_i)

    Normalizing M_i by summing over all i cancels out k and P_total
    assuming a constant translation rate.

    Inputs
    ------
    - distribution_protein (array of floats) - distribution for each protein,
    normalized to 1
    - translation_efficiencies (array of floats) - translational efficiency for each mRNA,
    normalized to 1
    - netLossRate (array of floats with units of 1/time) - rate of loss for each protein

    Returns
    -------
    - array of floats for the distribution of each mRNA, normalized to 1
    """

    assert np.allclose(np.sum(distribution_protein), 1)
    distributionUnnormed = netLossRate * distribution_protein / translation_efficiencies
    distributionNormed = distributionUnnormed / units.sum(distributionUnnormed)
    distributionNormed.normalize()
    distributionNormed.checkNoUnit()

    return distributionNormed.asNumber()


def calculateMinPolymerizingEnzymeByProductDistribution(
    productLengths, elongationRates, netLossRate, productCounts
):
    """
    Compute the number of ribosomes required to maintain steady state.

    dP/dt = production rate - loss rate
    dP/dt = e_r * (1/L) * R - (k_loss * P)

    At steady state: dP/dt = 0
    R = sum over i ((L_i / e_r) * k_loss_i * P_i)

    Multiplying both sides by volume gives an equation in terms of counts.

    P = protein concentration
    e_r = polypeptide elongation rate per ribosome
    L = protein length
    R = ribosome concentration
    k_loss = net protein loss rate
    i = ith protein

    Inputs
    ------
    - productLengths (array of ints with units of amino_acids) - L, protein lengths
    - elongationRates (array of ints with units of amino_acid/time) e_r, polypeptide elongation rate
    - netLossRate (array of floats with units of 1/time) - k_loss, protein loss rate
    - productCounts (array of floats) - P, protein counts

    Returns
    --------
    - float with dimensionless units for the number of ribosomes required to
    maintain steady state
    """

    nPolymerizingEnzymeNeeded = units.sum(
        productLengths / elongationRates * netLossRate * productCounts
    )
    return nPolymerizingEnzymeNeeded


def calculateMinPolymerizingEnzymeByProductDistributionRNA(
    productLengths, elongationRates, netLossRate
):
    """
    Compute the number of RNA polymerases required to maintain steady state of mRNA.

    dR/dt = production rate - loss rate
    dR/dt = e_r * (1/L) * RNAp - k_loss

    At steady state: dR/dt = 0
    RNAp = sum over i ((L_i / e_r) * k_loss_i)

    Multiplying both sides by volume gives an equation in terms of counts.

    R = mRNA transcript concentration
    e_r = transcript elongation rate per RNAp
    L = transcript length
    RNAp = RNAp concentration
    k_loss = net transcript loss rate (unit: concentration / time)
    i = ith transcript

    Inputs
    ------
    - productLengths (array of ints with units of nucleotides) - L, transcript lengths
    - elongationRates (array of ints with units of nucleotide/time) - e_r, transcript elongation rate
    - netLossRate (array of floats with units of 1/time) - k_loss, transcript loss rate

    Returns
    -------
    - float with dimensionless units for the number of RNA polymerases required to
    maintain steady state
    """

    nPolymerizingEnzymeNeeded = units.sum(
        productLengths / elongationRates * netLossRate
    )
    return nPolymerizingEnzymeNeeded


def netLossRateFromDilutionAndDegradationProtein(doublingTime, degradationRates):
    """
    Compute total loss rate (summed contributions of degradation and dilution).

    Inputs
    ------
    - doublingTime (float with units of time) - doubling time of the cell
    - degradationRates (array of floats with units of 1/time) - protein degradation rate

    Returns
    --------
    - array of floats with units of 1/time for the total loss rate for each protein
    """

    return np.log(2) / doublingTime + degradationRates


def netLossRateFromDilutionAndDegradationRNA(
    doublingTime, totalEndoRnaseCountsCapacity, Km, rnaConc, countsToMolar
):
    """
    Compute total loss rate (summed impact of degradation and dilution).
    Returns the loss rate in units of (counts/time) in preparation for use in
    the steady state analysis in fitExpression() and
    setRNAPCountsConstrainedByPhysiology()
    (see calculateMinPolymerizingEnzymeByProductDistributionRNA()).

    Derived from steady state analysis of Michaelis-Menten enzyme kinetics with
    competitive inhibition: for a given RNA, all other RNAs compete for RNase.

    V_i = k_cat * [ES_i]
    v_i = k_cat * [E]0 * ([S_i]/Km_i) / (1 + sum over j genes([S_j] / Km_j))

    Inputs
    ------
    - doublingTime (float with units of time) - doubling time of the cell
    - totalEndoRnaseCountsCapacity (float with units of 1/time) total kinetic
    capacity of all RNases in the cell
    - Km (array of floats with units of mol/volume) - Michaelis-Menten constant
    for each RNA
    - rnaConc (array of floats with units of mol/volume) - concentration for each RNA
    - countsToMolar (float with units of mol/volume) - conversion between counts and molar

    Returns
    --------
    - array of floats with units of 1/time for the total loss rate for each RNA
    """

    fracSaturated = rnaConc / Km / (1 + units.sum(rnaConc / Km))
    rnaCounts = (1 / countsToMolar) * rnaConc

    return (np.log(2) / doublingTime) * rnaCounts + (
        totalEndoRnaseCountsCapacity * fracSaturated
    )


def netLossRateFromDilutionAndDegradationRNALinear(
    doublingTime, degradationRates, rnaCounts
):
    """
    Compute total loss rate (summed contributions of degradation and dilution).
    Returns the loss rate in units of (counts/time) in preparation for use in
    the steady state analysis in fitExpression() and
    setRNAPCountsConstrainedByPhysiology()
    (see calculateMinPolymerizingEnzymeByProductDistributionRNA()).

    Requires
    --------
    - doublingTime (float with units of time) - doubling time of the cell
    - degradationRates (array of floats with units of 1/time) - degradation rate
    for each RNA
    - rnaCounts (array of floats) - counts for each RNA

    Returns
    --------
    - array of floats with units of 1/time for the total loss rate for each RNA
    """

    return (np.log(2) / doublingTime + degradationRates) * rnaCounts


def expressionFromConditionAndFoldChange(transcription, condPerturbations, tfFCs):
    """
    Adjusts expression of RNA based on fold changes from basal for a given
    condition. Since fold changes are reported for individual RNA cistrons, the
    changes are applied to the basal expression levels of each cistron and the
    resulting vector is mapped back to RNA expression through nonnegative least
    squares. For genotype perturbations, the expression of all RNAs that include
    the given cistron are set to the given value.

    Inputs
    ------
    - transcription: Instance of the Transcription class from
            reconstruction.ecoli.dataclasses.process.transcription
    - condPerturbations {cistron ID (str): fold change (float)} -
            dictionary of fold changes for cistrons based on the given condition
    - tfFCs {cistron ID (str): fold change (float)} -
            dictionary of fold changes for cistrons based on transcription factors
            in the given condition

    Returns
    --------
    - expression (array of floats) - adjusted expression for each RNA,
    normalized to 1

    Notes
    -----
    - TODO (Travis) - Might not properly handle if an RNA is adjusted from both a
    perturbation and a transcription factor, currently RNA self regulation is not
    included in tfFCs
    """
    cistron_ids = transcription.cistron_data["id"]
    cistron_expression = transcription.fit_cistron_expression["basal"].copy()

    # Gather indices and fold changes for each cistron that will be adjusted
    cistron_id_to_index = {cistron_id: i for (i, cistron_id) in enumerate(cistron_ids)}
    cistron_indexes = []
    cistron_fcs = []

    # Compile indexes and fold changes of each cistron
    for cistron_id, fc_value in tfFCs.items():
        if cistron_id in condPerturbations:
            continue
        cistron_indexes.append(cistron_id_to_index[cistron_id])
        cistron_fcs.append(fc_value)

    def apply_fcs_to_expression(expression, indexes, fcs):
        """
        Applys the fold-change values to an expression vector while keeping the
        sum of expression values at one.

        Args:
                expression (np.ndarray of floats): Original expression vector of
                        cistrons or RNAs
                indexes (List of floats): Indexes of cistrons/RNAs that the
                        fold-changes should be applied to
                fcs (List of floats): Fold-changes of cistron/RNA expression
        """
        fcs = [fc for (idx, fc) in sorted(zip(indexes, fcs), key=lambda pair: pair[0])]
        indexes = [
            idx for (idx, fc) in sorted(zip(indexes, fcs), key=lambda pair: pair[0])
        ]

        # Adjust expression based on fold change and normalize
        indexes_bool = np.zeros(len(expression), dtype=bool)
        indexes_bool[indexes] = 1
        fcs = np.array(fcs)
        scaleTheRestBy = (1.0 - (expression[indexes] * fcs).sum()) / (
            1.0 - (expression[indexes]).sum()
        )
        expression[indexes_bool] *= fcs
        expression[~indexes_bool] *= scaleTheRestBy

        return expression

    cistron_expression = apply_fcs_to_expression(
        cistron_expression, cistron_indexes, cistron_fcs
    )

    # Use NNLS to map new cistron expression to RNA expression
    expression, _ = transcription.fit_rna_expression(cistron_expression)
    expression = normalize(expression)

    # Apply genotype perturbations to all RNAs that contain each cistron
    rna_indexes = []
    rna_fcs = []
    cistron_perturbation_indexes = []
    cistron_perturbation_values = []

    for cistron_id, perturbation_value in condPerturbations.items():
        rna_indexes_with_cistron = transcription.cistron_id_to_rna_indexes(cistron_id)
        rna_indexes.extend(rna_indexes_with_cistron)
        rna_fcs.extend([perturbation_value] * len(rna_indexes_with_cistron))
        cistron_perturbation_indexes.append(cistron_id_to_index[cistron_id])
        cistron_perturbation_values.append(perturbation_value)

    expression = apply_fcs_to_expression(expression, rna_indexes, rna_fcs)
    # Also apply perturbations to cistrons for bookkeeping purposes
    cistron_expression = apply_fcs_to_expression(
        cistron_expression, cistron_perturbation_indexes, cistron_perturbation_values
    )

    return expression, cistron_expression


def fitPromoterBoundProbability(sim_data, cell_specs):
    r"""
    Calculates the probabilities (P) that each transcription factor will bind
    to its target RNA. This function initially calculates these probabilities
    from the bulk average counts of the TFs and ligands calculated from
    previous steps. Then, values of parameters alpha and r in the equation
    below are fit such that the computed RNA synthesis probabilities converge
    to the measured RNA synthesis probabilities.

    v_{synth, j} = \alpha_j + \sum_{i} P_{T,i}*r_{ij}

    Due to constraints applied in the optimization, both v and P need to
    be shifted from their initial values.

    Requires
    --------
    - Bulk average counts of transcription factors and associated ligands
    for each condition (in cell_specs)

    Inputs
    ------
    - cell_specs {condition (str): dict} - information about each condition

    Modifies
    --------
    - Probabilities of TFs binding to their promoters
    - RNA synthesis probabilities
    - cell_specs['basal']['r_vector']: Fit parameters on how the recruitment of
    a TF affects the expression of a gene. High (positive) values of r indicate
    that the TF binding increases the probability that the gene is expressed.
    - cell_specs['basal']['r_columns']: mapping of column name to index in r

    Notes
    --------
    See supplementary materials on transcription regulation for details on
    the parameters being fit.
    """

    def build_vector_k(sim_data, cell_specs):
        """
        Construct vector k that contains existing fit transcription
        probabilities of RNAs in each relevant condition, normalized by the
        average copy number of the gene encoding the RNA while the cell grows
        in that condition.

        Returns
        --------
        - k: List of RNA synthesis probabilities for each RNA and condition,
        normalized by gene copy number.
        - kInfo: List of dictionaries that hold information on values of k -
        kInfo[i]["condition"] and kInfo[i]["idx"] hold what condition and RNA
        index the probability k[i] refers to, respectively.
        """

        k, kInfo = [], []

        for idx, (rnaId, rnaCoordinate) in enumerate(
            zip(
                sim_data.process.transcription.rna_data["id"],
                sim_data.process.transcription.rna_data["replication_coordinate"],
            )
        ):
            # Get list of TFs that regulate this RNA
            tfs = sim_data.relation.rna_id_to_regulating_tfs.get(rnaId, [])
            conditions = ["basal"]
            tfsWithData = []

            # Take only those TFs with active/inactive conditions data
            # TODO (Gwanggyu): cache this list of conditions for each RNA
            for tf in tfs:
                if tf not in sorted(sim_data.tf_to_active_inactive_conditions):
                    continue

                # Add conditions for selected TFs
                conditions.append(tf + "__active")
                conditions.append(tf + "__inactive")
                tfsWithData.append(tf)

            for condition in conditions:
                # Skip basal conditions, unless the RNA is not regulated by any TFs
                if len(tfsWithData) > 0 and condition == "basal":
                    continue

                # Get specific doubling time for this condition
                tau = cell_specs[condition]["doubling_time"].asNumber(units.min)

                # Calculate average copy number of gene for this condition
                n_avg_copy = sim_data.process.replication.get_average_copy_number(
                    tau, rnaCoordinate
                )

                # Compute synthesis probability per gene copy
                prob_per_copy = (
                    sim_data.process.transcription.rna_synth_prob[condition][idx]
                    / n_avg_copy
                )

                # Gather RNA synthesis probabilities for each RNA per condition
                k.append(prob_per_copy)
                kInfo.append({"condition": condition, "idx": idx})

        k = np.array(k)

        return k, kInfo

    def build_matrix_G(sim_data, pPromoterBound):
        """
        Construct matrix G that contains probabilities of pPromoterBound as
        elements. Each row of the matrix is named "[RNA]__[condition]", where
        there are two conditions [active/inactive] for each TF that regulates
        the expression of the given RNA. For RNAs that are not regulated by
        any TFs, a single row named "[RNA]__basal" represents the RNA. Each
        column is named "[RNA]__[TF]", for each TF that regulates the
        expression of the given RNA. Each element is set to the value in
        pPromoterBound that corresponds to the condition given by the row,
        and the TF given by the column. For each RNA, there is an additional
        column named "[RNA]__alpha", and all elements in this column that
        corresponds to the rows for the RNA are set to 1.

        Inputs
        ------
        - pPromoterBound: Probabilities that a given TF is bound to its
        promoter in a given condition, calculated from bulk average
        concentrations of the TF and its associated ligands.

        Returns
        --------
        - G: Matrix of values in pPromoterBound, rearranged based on each RNA
        - row_name_to_index: Dict[str, int] of row names of G to row index
        - col_name_to_index: Dict[str, int] of column names of G to column index
        """

        gI, gJ, gV = [], [], []
        row_name_to_index, col_name_to_index = {}, {}

        for idx, rnaId in enumerate(sim_data.process.transcription.rna_data["id"]):
            rnaIdNoLoc = rnaId[:-3]  # Remove compartment ID from RNA ID

            # Get list of TFs that regulate this RNA
            tfs = sim_data.relation.rna_id_to_regulating_tfs.get(rnaId, [])
            conditions = ["basal"]
            tfsWithData = []

            # Take only those TFs with active/inactive conditions data
            for tf in tfs:
                if tf not in sorted(sim_data.tf_to_active_inactive_conditions):
                    continue

                # Add conditions for selected TFs
                conditions.append(tf + "__active")
                conditions.append(tf + "__inactive")
                tfsWithData.append(tf)

            for condition in conditions:
                # Skip basal conditions, unless the RNA is not regulated by any TFs
                if len(tfsWithData) > 0 and condition == "basal":
                    continue

                # Add row for each condition specific to each RNA
                row_name = rnaIdNoLoc + "__" + condition
                row_name_to_index[row_name] = len(row_name_to_index)

                for tf in tfsWithData:
                    # Add column for each TF that regulates each RNA
                    col_name = rnaIdNoLoc + "__" + tf

                    # TODO (Gwanggyu): Are these checks necessary?
                    if col_name not in col_name_to_index:
                        col_name_to_index[col_name] = len(col_name_to_index)

                    gI.append(row_name_to_index[row_name])
                    gJ.append(col_name_to_index[col_name])
                    gV.append(
                        pPromoterBound[condition][tf]
                    )  # Probability that TF is bound in given condition

                # Add alpha column for each RNA
                col_name = rnaIdNoLoc + "__alpha"

                if col_name not in col_name_to_index:
                    col_name_to_index[col_name] = len(col_name_to_index)

                gI.append(row_name_to_index[row_name])
                gJ.append(col_name_to_index[col_name])
                gV.append(1.0)

        gI, gJ, gV = np.array(gI), np.array(gJ), np.array(gV)
        G = np.zeros((len(row_name_to_index), len(col_name_to_index)), np.float64)
        G[gI, gJ] = gV

        return G, row_name_to_index, col_name_to_index

    def build_matrix_Z(sim_data, col_name_to_index):
        """
        Construct matrix Z that connects all possible TF combinations with
        each TF. Each row of the matrix corresponds to an RNA-(TF combination)
        pair, and each column corresponds to an RNA-TF pair, with an additional
        RNA-alpha column for each RNA (identical to matrix G). Matrix values
        are set to one if the TF specified by the column is "active" in the
        combination specified by the row or if the column is an RNA-alpha
        column, and zero otherwise.

        Inputs
        ------
        - col_name_to_index: Dict[str, int] of column names of G to column index

        Returns
        --------
        - Z: Matrix of zeros and ones, specifying which TFs in the columns
        correspond to combinations in the rows.
        """

        zI, zJ, zV = [], [], []
        row_idx = 0

        for rna_id in sim_data.process.transcription.rna_data["id"]:
            rna_id_no_loc = rna_id[:-3]  # Remove compartment ID from RNA ID

            # Get list of TFs that regulate this RNA
            tfs = sim_data.relation.rna_id_to_regulating_tfs[rna_id]
            tfs_with_data = []

            # Get column index of the RNA's alpha column
            col_idxs = [col_name_to_index[rna_id_no_loc + "__alpha"]]

            # Take only those TFs with active/inactive conditions data
            for tf in tfs:
                if tf not in sim_data.tf_to_active_inactive_conditions:
                    continue

                tfs_with_data.append(tf)

                # Get column index of the RNA-TF pair
                col_idxs.append(col_name_to_index[rna_id_no_loc + "__" + tf])

            n_tfs = len(tfs_with_data)

            # For all possible combinations of TFs
            for n_combinations in range(n_tfs + 1):
                for combination in itertools.combinations(
                    range(1, n_tfs + 1), n_combinations
                ):
                    # Always include alpha column
                    zI.append(row_idx)
                    zJ.append(col_idxs[0])
                    zV.append(1)

                    # Set matrix value to one if the TF specified by the column is
                    # present in the combination of TFs specified by the row
                    for col_idx in combination:
                        zI.append(row_idx)
                        zJ.append(col_idxs[col_idx])
                        zV.append(1)

                    row_idx += 1

        # Build matrix Z
        zI, zJ, zV = np.array(zI), np.array(zJ), np.array(zV)
        Z = np.zeros((zI.max() + 1, zJ.max() + 1), np.float64)
        Z[zI, zJ] = zV

        return Z

    def build_matrix_T(sim_data, col_name_to_index):
        """
        Construct matrix T that specifies the direction of regulation for each
        RNA-TF pair.

        Inputs
        ------
        - col_name_to_index: Dict[str, int] of column names of G to column index

        Returns
        --------
        - T: Diagonal matrix. Diagonal value is +1 if the direction of
        regulation by the TF-RNA pair specified by the row is positive, -1 if
        this is negative, and 0 if the row is an RNA_alpha row.
        """

        tI, tJ, tV = [], [], []
        row_idx = 0

        for rnaId in sim_data.process.transcription.rna_data["id"]:
            rnaIdNoLoc = rnaId[:-3]  # Remove compartment ID from RNA ID

            # Get list of TFs that regulate this RNA
            tfs = sim_data.relation.rna_id_to_regulating_tfs[rnaId]
            tfsWithData = []

            # Get list of constituent cistron IDs
            constituent_cistron_ids = [
                sim_data.process.transcription.cistron_data["id"][i]
                for i in sim_data.process.transcription.rna_id_to_cistron_indexes(rnaId)
            ]

            # Take only those TFs with active/inactive conditions data
            for tf in tfs:
                if tf not in sim_data.tf_to_active_inactive_conditions:
                    continue

                tfsWithData.append(tf)

            for tf in tfsWithData:
                # Calculate the consensus regulation direction of the TF on the
                # cistrons that constitute this transcription unit
                directions = np.array(
                    [
                        sim_data.tf_to_direction[tf].get(cistron_id, 0)
                        for cistron_id in constituent_cistron_ids
                    ]
                )
                consensus_direction = -1 + 2 * (directions.sum() >= 0)

                # Add row for TF and find column for TF in col_name_to_index
                col_name = rnaIdNoLoc + "__" + tf

                # Set matrix value to regulation direction (+1 or -1)
                tI.append(row_idx)
                tJ.append(col_name_to_index[col_name])
                tV.append(consensus_direction)
                row_idx += 1

            # Add RNA_alpha rows and columns, and set matrix value to zero
            col_name = rnaIdNoLoc + "__alpha"

            tI.append(row_idx)
            tJ.append(col_name_to_index[col_name])
            tV.append(0)
            row_idx += 1

        tI, tJ, tV = np.array(tI), np.array(tJ), np.array(tV)
        T = np.zeros((tI.max() + 1, tJ.max() + 1), np.float64)
        T[tI, tJ] = tV

        return T

    def build_matrix_H(
        sim_data, col_name_to_index, pPromoterBound, r, fixedTFs, cell_specs
    ):
        r"""
        Construct matrix H that contains values of vector r as elements.
        Each row of the matrix is named "[RNA]__[condition]", where
        there are two conditions [active/inactive] for each TF that regulates
        the expression of the given RNA. For RNAs that are not regulated by
        any TFs, a single row named "[RNA]__basal" represents the RNA. Each
        column is named "[TF]__[condition]", for each TF that regulates the
        expression of the given RNA, and each condition given for the RNA.
        Each element is set to the optimized value in r that corresponds to
        the RNA given by the row, and the TF given by the column. For each RNA,
        there is an additional column named "[RNA]__alpha", and all elements in
        this column are set to the value of parameter alpha for the RNA
        optimized in r.

        Inputs
        ------
        - col_name_to_index: Dict[str, int] of column names of G to column index
        - pPromoterBound: Probabilities that a given TF is bound to its
        promoter in a given condition, calculated from bulk average
        concentrations of the TF and its associated ligands.
        - r: Optimized values of \Delta r (the effect of TF on RNAP
        recruitment) and alpha (basal recruitment of RNAP)
        - fixedTFs: List of TFs whose activities do not change with the
        nutrient conditions

        Returns
        --------
        - H: Matrix of values in optimized r, rearranged for each RNA and
        condition
        - pInit: Vector of values in pPromoterBound, rearranged to the ordering
        of the columns of H
        - pAlphaIdxs: Indexes of columns that correspond to alpha's in H and pInit
        - pNotAlphaIdxs: Indexes of columns that correspond to r's in H and pInit
        - fixedTFIdxs: Indexes of columns that correspond to fixed TFs in H and pInit
        - pPromoterBoundIdxs: Dictionary of indexes to pInit.
        - H_col_name_to_index: Dict[str, int] of column names of H to column index
        """

        rDict = dict(
            [(col_name, value) for col_name, value in zip(col_name_to_index, r)]
        )

        pPromoterBoundIdxs = dict([(condition, {}) for condition in pPromoterBound])
        hI, hJ, hV, pInitI, pInitV = [], [], [], [], []
        H_row_name_to_index, H_col_name_to_index = {}, {}

        for idx, rnaId in enumerate(sim_data.process.transcription.rna_data["id"]):
            rnaIdNoLoc = rnaId[:-3]  # Remove compartment ID from RNA ID

            tfs = sim_data.relation.rna_id_to_regulating_tfs[rnaId]
            conditions = ["basal"]
            tfsWithData = []

            # Take only those TFs with active/inactive conditions data
            for tf in tfs:
                if tf not in sorted(sim_data.tf_to_active_inactive_conditions):
                    continue

                # Add conditions for selected TFs
                conditions.append(tf + "__active")
                conditions.append(tf + "__inactive")
                tfsWithData.append(tf)

            for condition in conditions:
                # Skip basal conditions, unless the RNA is not regulated by any TFs
                if len(tfsWithData) > 0 and condition == "basal":
                    continue

                # Add row for each condition specific to each RNA
                row_name = rnaIdNoLoc + "__" + condition
                H_row_name_to_index[row_name] = len(H_row_name_to_index)

                for tf in tfsWithData:
                    # Add column for each TF and condition
                    col_name = tf + "__" + condition

                    if col_name not in H_col_name_to_index:
                        H_col_name_to_index[col_name] = len(H_col_name_to_index)

                    hI.append(H_row_name_to_index[row_name])
                    hJ.append(H_col_name_to_index[col_name])

                    # Handle the case of the TF being knocked out (admittedly not the cleanest solution)
                    tf_idx = bulk_name_to_idx(
                        tf + "[c]", cell_specs[condition]["bulkAverageContainer"]["id"]
                    )
                    if (
                        counts(cell_specs[condition]["bulkAverageContainer"], tf_idx)
                        == 0
                    ):
                        hV.append(0)  # TF is knocked out in the given condition
                    else:
                        hV.append(
                            rDict[rnaIdNoLoc + "__" + tf]
                        )  # Optimized r value for TF-RNA pair

                    # Rearrange values in pPromoterBound in the same order
                    # given by the columns of H
                    pInitI.append(H_col_name_to_index[col_name])
                    pInitV.append(pPromoterBound[condition][tf])
                    pPromoterBoundIdxs[condition][tf] = H_col_name_to_index[col_name]

                # Add alpha column for each RNA
                col_name = rnaIdNoLoc + "__alpha"

                if col_name not in H_col_name_to_index:
                    H_col_name_to_index[col_name] = len(H_col_name_to_index)

                # Add optimized value of alpha in r to H
                hI.append(H_row_name_to_index[row_name])
                hJ.append(H_col_name_to_index[col_name])
                hV.append(rDict[col_name])

                # Set corresponding value in pInit to one
                pInitI.append(H_col_name_to_index[col_name])
                pInitV.append(1.0)

        # Save indices to update promoter binding for active TFs in combined conditions
        for condition, tfs in sim_data.condition_active_tfs.items():
            for tf in tfs:
                col_name = f"{tf}__{tf}__active"
                pPromoterBoundIdxs[condition][tf] = H_col_name_to_index[col_name]

        # Save indices to update promoter binding for inactive TFs in combined conditions
        for condition, tfs in sim_data.condition_inactive_tfs.items():
            for tf in tfs:
                col_name = f"{tf}__{tf}__inactive"
                pPromoterBoundIdxs[condition][tf] = H_col_name_to_index[col_name]

        # Build vector pInit and matrix H
        pInit = np.zeros(len(set(pInitI)))
        pInit[pInitI] = pInitV

        hI, hJ, hV = np.array(hI), np.array(hJ), np.array(hV)
        Hshape = (hI.max() + 1, hJ.max() + 1)
        H = np.zeros(Hshape, np.float64)
        H[hI, hJ] = hV

        # Get indexes of alpha and non-alpha columns in pInit and H
        pAlphaIdxs = np.array(
            [
                idx
                for col_name, idx in H_col_name_to_index.items()
                if col_name.endswith("__alpha")
            ]
        )
        pNotAlphaIdxs = np.array(
            [
                idx
                for col_name, idx in H_col_name_to_index.items()
                if not col_name.endswith("__alpha")
            ]
        )

        # Get indexes of columns that correspond to fixed TFs
        fixedTFIdxs = []
        for col_name, idx in H_col_name_to_index.items():
            secondElem = col_name.split("__")[1]

            if secondElem in fixedTFs:
                fixedTFIdxs.append(idx)

        fixedTFIdxs = np.array(fixedTFIdxs, dtype=int)

        return (
            H,
            pInit,
            pAlphaIdxs,
            pNotAlphaIdxs,
            fixedTFIdxs,
            pPromoterBoundIdxs,
            H_col_name_to_index,
        )

    def build_matrix_pdiff(sim_data, H_col_name_to_index):
        """
        Construct matrix Pdiff that specifies the indexes of corresponding
        TFs and conditions.

        Inputs
        ------
        - H_col_name_to_index: Dict[str, int] of column names of H to column index

        Returns
        --------
        - Pdiff: Matrix with [TF] as rows and [TF]_[condition] as columns.
        Matrix value is set to 1 when the TF of the column matches with the TF
        of the row, and the condition is TF__active. Matrix value is set to -1
        when the TF of the column matches with the TF of the row, and the
        condition is TF__inactive.
        """

        PdiffI, PdiffJ, PdiffV = [], [], []

        for rowIdx, tf in enumerate(sorted(sim_data.tf_to_active_inactive_conditions)):
            # For each TF, find condition [TF]__[TF]__active and set element to 1
            condition = tf + "__active"
            col_name = tf + "__" + condition
            PdiffI.append(rowIdx)
            PdiffJ.append(H_col_name_to_index[col_name])
            PdiffV.append(1)

            # Find condition [TF]__[TF]__inactive and set element to -1
            condition = tf + "__inactive"
            col_name = tf + "__" + condition
            PdiffI.append(rowIdx)
            PdiffJ.append(H_col_name_to_index[col_name])
            PdiffV.append(-1)

        # Build matrix Pdiff
        PdiffI, PdiffJ, PdiffV = np.array(PdiffI), np.array(PdiffJ), np.array(PdiffV)
        Pdiffshape = (PdiffI.max() + 1, len(H_col_name_to_index))
        Pdiff = np.zeros(Pdiffshape, np.float64)
        Pdiff[PdiffI, PdiffJ] = PdiffV

        return Pdiff

    def fromArray(p, pPromoterBound, pPromoterBoundIdxs):
        """
        Updates values in pPromoterBound with fit probabilities.

        Inputs
        ------
        - p: Vector of probabilities optimized in the current step.
        - pPromoterBoundIdxs: Dictionary of indexes to p

        Modifies
        --------
        Values in pPromoterBound - probabilities that each transcription factor
        is bound to its promoter for each growth condition
        """

        for condition in sorted(pPromoterBoundIdxs):
            for tf in sorted(pPromoterBoundIdxs[condition]):
                pPromoterBound[condition][tf] = p[pPromoterBoundIdxs[condition][tf]]

    def updateSynthProb(sim_data, cell_specs, kInfo, k):
        """
        Updates RNA synthesis probabilities with fit values of P and R. The
        expected average copy number of genes for the condition are multiplied
        to the per-copy probabilities.

        Inputs
        ------
        - kInfo: List of dictionaries that hold information on values of k -
        kInfo[i]["condition"] and kInfo[i]["idx"] hold what condition and RNA
        index the probability k[i] refers to, respectively.
        - k: RNA synthesis probabilities computed from fit P and R.

        Modifies
        --------
        - RNA synthesis probabilities

        Notes
        --------
        These values are used to calculate pre-set probabilities for
        pools of mRNA, tRNA, and rRNA, and the genes that encode RNAP and
        ribosome subunits.
        """

        # Get replication coordinates of each RNA
        replication_coordinate = sim_data.process.transcription.rna_data[
            "replication_coordinate"
        ]

        # Update sim_data values with fit values
        for D, k_value in zip(kInfo, k):
            condition = D["condition"]
            rna_idx = D["idx"]

            # Get coordinate of RNA
            rnaCoordinate = replication_coordinate[rna_idx]

            # Get specific doubling time for this condition
            tau = cell_specs[condition]["doubling_time"].asNumber(units.min)

            # Calculate average copy number of gene for this condition
            n_avg_copy = sim_data.process.replication.get_average_copy_number(
                tau, rnaCoordinate
            )

            # Multiply copy number by k_value to get synthesis probability
            # (if k_value is negative clip at zero)
            sim_data.process.transcription.rna_synth_prob[condition][rna_idx] = (
                max(0, k_value) * n_avg_copy
            )

        # Normalize values such that probabilities for each condition sum to one
        for condition in sim_data.process.transcription.rna_synth_prob:
            assert np.all(sim_data.process.transcription.rna_synth_prob[condition] >= 0)
            sim_data.process.transcription.rna_synth_prob[condition] /= (
                sim_data.process.transcription.rna_synth_prob[condition].sum()
            )

    # Initialize pPromoterBound using mean TF and ligand concentrations
    pPromoterBound = calculatePromoterBoundProbability(sim_data, cell_specs)
    pInit0 = None
    lastNorm = np.inf

    fixedTFs = []
    for tf in sim_data.tf_to_active_inactive_conditions:
        if sim_data.process.transcription_regulation.tf_to_tf_type[tf] == "2CS":
            fixedTFs.append(tf)
        if (
            sim_data.process.transcription_regulation.tf_to_tf_type[tf] == "1CS"
            and sim_data.tf_to_active_inactive_conditions[tf]["active nutrients"]
            == sim_data.tf_to_active_inactive_conditions[tf]["inactive nutrients"]
        ):
            fixedTFs.append(tf)

    # Build vector of existing fit transcription probabilities
    k, kInfo = build_vector_k(sim_data, cell_specs)

    # Repeat for a fixed maximum number of iterations
    for i in range(PROMOTER_MAX_ITERATIONS):
        # Build matrices used in optimizing R
        G, G_row_name_to_index, G_col_name_to_index = build_matrix_G(
            sim_data, pPromoterBound
        )
        Z = build_matrix_Z(sim_data, G_col_name_to_index)
        T = build_matrix_T(sim_data, G_col_name_to_index)

        # Optimize R such that transcription initiation probabilities computed
        # from existing values of P in matrix G are close to fit values.
        R = Variable(G.shape[1])  # Vector of r's and alpha's

        # Objective: minimize difference between k and G @ R
        objective_r = Minimize(
            norm(G @ (PROMOTER_SCALING * R) - PROMOTER_SCALING * k, PROMOTER_NORM_TYPE)
        )

        # Optimization constraints
        # 1) 0 <= Z @ R <= 1 : Assuming P = 1 for all TFs, all possible
        # combinations of TFs should yield a valid transcription probability
        # value between zero and one.
        # 2) T @ R >= 0 : Values of r for positive regulation should be positive,
        # and values of r for negative regulation should be negative.
        constraint_r = [
            0 <= Z @ (PROMOTER_SCALING * R),
            Z @ (PROMOTER_SCALING * R) <= PROMOTER_SCALING,
            T @ (PROMOTER_SCALING * R) >= 0,
        ]

        # Solve optimization problem
        prob_r = Problem(objective_r, constraint_r)
        prob_r.solve(solver="ECOS", max_iters=1000)

        if prob_r.status == "optimal_inaccurate":
            raise RuntimeError(
                "Solver found an optimum that is inaccurate."
                " Try increasing max_iters or adjusting tolerances."
            )
        elif prob_r.status != "optimal":
            raise RuntimeError("Solver could not find optimal value")

        # Get optimal value of R
        r = np.array(R.value).reshape(-1)
        r[np.abs(r) < ECOS_0_TOLERANCE] = (
            0  # Adjust to 0 for small values from solver tolerance
        )

        # Use optimal value of R to construct matrix H and vector Pdiff
        (
            H,
            pInit,
            pAlphaIdxs,
            pNotAlphaIdxs,
            fixedTFIdxs,
            pPromoterBoundIdxs,
            H_col_name_to_index,
        ) = build_matrix_H(
            sim_data, G_col_name_to_index, pPromoterBound, r, fixedTFs, cell_specs
        )
        pdiff = build_matrix_pdiff(sim_data, H_col_name_to_index)

        # On first iteration, save the value of the initial p
        if i == 0:
            pInit0 = pInit.copy()

        # Optimize P such that the transcription probabilities computed from
        # current values of R in matrix H are close to fit values.
        P = Variable(H.shape[1])

        # Construct a boolean vector that marks column indexes of H
        # corresponding to alpha's and fixed TFs
        D = np.zeros(H.shape[1])
        D[pAlphaIdxs] = 1
        D[fixedTFIdxs] = 1

        # Mask initial p with boolean vector constructed above
        Drhs = pInit0.copy()
        Drhs[D != 1] = 0

        # Objective: minimize difference between k (fit RNAP initiation
        # probabilities) and H @ P (computed initiation probabilities) while
        # also minimizing deviation of P from the original value calculated
        # from mean TF and ligand concentrations
        objective_p = Minimize(
            norm(H @ (PROMOTER_SCALING * P) - PROMOTER_SCALING * k, PROMOTER_NORM_TYPE)
            + PROMOTER_REG_COEFF * norm(P - pInit0, PROMOTER_NORM_TYPE)
        )

        # Constraints
        # 1) 0 <= P <= 1 : All DNA-bound probabilities should be between zero
        # and one.
        # 2) D @ P == Drhs : Values of P that correspond to alpha's and fixed TFs
        # should not change.
        # 3) pdiff @ P >= PROMOTER_PDIFF_THRESHOLD : There must be at least a
        # certain difference between binding probabilities of a TF in conditions
        # TF__active and TF__inactive
        constraint_p = [
            0 <= PROMOTER_SCALING * P,
            PROMOTER_SCALING * P <= PROMOTER_SCALING,
            np.diag(D) @ (PROMOTER_SCALING * P) == PROMOTER_SCALING * Drhs,
            pdiff @ (PROMOTER_SCALING * P)
            >= PROMOTER_SCALING * PROMOTER_PDIFF_THRESHOLD,
        ]

        # Solve optimization problem
        prob_p = Problem(objective_p, constraint_p)
        prob_p.solve(solver="ECOS")

        if prob_p.status == "optimal_inaccurate":
            raise RuntimeError(
                "Solver found an optimum that is inaccurate."
                " Try increasing max_iters or adjusting tolerances."
            )
        elif prob_p.status != "optimal":
            raise RuntimeError("Solver could not find optimal value")

        # Get optimal value of P
        p = np.array(P.value).reshape(-1)

        # Adjust for solver tolerance over bounds to get proper probabilities
        p[p < ECOS_0_TOLERANCE] = 0
        p[p > (1 - ECOS_0_TOLERANCE)] = 1

        # Update pPromoterBound with fit p
        fromArray(p, pPromoterBound, pPromoterBoundIdxs)

        # Break from loop if parameters have converged
        if (
            np.abs(np.linalg.norm(np.dot(H, p) - k, PROMOTER_NORM_TYPE) - lastNorm)
            < PROMOTER_CONVERGENCE_THRESHOLD
        ):
            break
        else:
            lastNorm = np.linalg.norm(np.dot(H, p) - k, PROMOTER_NORM_TYPE)

    # Update sim_data with fit bound probabilities and RNAP initiation
    # probabilities computed from these bound probabilities
    sim_data.pPromoterBound = pPromoterBound
    updateSynthProb(sim_data, cell_specs, kInfo, np.dot(H, p))

    cell_specs["basal"]["r_vector"] = r
    cell_specs["basal"]["r_columns"] = G_col_name_to_index


def fitLigandConcentrations(sim_data, cell_specs):
    """
    Using the fit values of pPromoterBound, updates the set concentrations of
    ligand metabolites and the kd's of the ligand-TF binding reactions.

    Requires
    --------
    - Fitted pPromoterBound: probabilities that a TF will bind to its promoter,
    fit by function fitPromoterBoundProbability().

    Inputs
    ------
    - cell_specs {condition (str): dict} - information about each condition

    Modifies
    --------
    - Set concentrations of metabolites that are ligands in 1CS
    - kd's of equilibrium reactions in 1CS
    """
    cellDensity = sim_data.constants.cell_density
    pPromoterBound = sim_data.pPromoterBound

    for tf in sorted(sim_data.tf_to_active_inactive_conditions):
        # Skip TFs that are not 1CS or are linked to genotypic perturbations
        if sim_data.process.transcription_regulation.tf_to_tf_type[tf] != "1CS":
            continue
        if (
            len(
                sim_data.tf_to_active_inactive_conditions[tf][
                    "active genotype perturbations"
                ]
            )
            > 0
            or len(
                sim_data.tf_to_active_inactive_conditions[tf][
                    "inactive genotype perturbations"
                ]
            )
            > 0
        ):
            continue

        activeKey = tf + "__active"
        inactiveKey = tf + "__inactive"

        # Determine if metabolite-bound form of the TF is the active form
        boundId = sim_data.process.transcription_regulation.active_to_bound[tf]
        negativeSignal = tf != boundId  # True if unbound form is the active TF

        # Calculate kd of bound TF
        fwdRate = sim_data.process.equilibrium.get_fwd_rate(boundId + "[c]")
        revRate = sim_data.process.equilibrium.get_rev_rate(boundId + "[c]")
        kd = revRate / fwdRate

        # Get the metabolite that binds to the TF and its stoich coefficient
        metabolite = sim_data.process.equilibrium.get_metabolite(boundId + "[c]")
        metaboliteCoeff = sim_data.process.equilibrium.get_metabolite_coeff(
            boundId + "[c]"
        )

        # Calculate the concentrations of the metabolite under conditions where
        # TF is active and inactive
        metabolite_idx = bulk_name_to_idx(
            metabolite, cell_specs[activeKey]["bulkAverageContainer"]["id"]
        )
        activeCellVolume = (
            cell_specs[activeKey]["avgCellDryMassInit"]
            / cellDensity
            / sim_data.mass.cell_dry_mass_fraction
        )
        activeCountsToMolar = 1 / (sim_data.constants.n_avogadro * activeCellVolume)
        activeSignalConc = (
            activeCountsToMolar
            * counts(cell_specs[activeKey]["bulkAverageContainer"], metabolite_idx)
        ).asNumber(units.mol / units.L)
        inactiveCellVolume = (
            cell_specs[inactiveKey]["avgCellDryMassInit"]
            / cellDensity
            / sim_data.mass.cell_dry_mass_fraction
        )
        inactiveCountsToMolar = 1 / (sim_data.constants.n_avogadro * inactiveCellVolume)
        inactiveSignalConc = (
            inactiveCountsToMolar
            * counts(cell_specs[inactiveKey]["bulkAverageContainer"], metabolite_idx)
        ).asNumber(units.mol / units.L)

        # Update kd with fitted values of P and the bulk average concentrations
        # of the metabolite, and use this fitted kd to recalculate the set
        # amounts of the metabolite in metabolism
        p_active = pPromoterBound[activeKey][tf]
        p_inactive = pPromoterBound[inactiveKey][tf]

        if negativeSignal:
            if p_inactive == 0:
                raise ValueError(
                    "Inf ligand concentration from p_inactive = 0."
                    " Check results from fitPromoterBoundProbability and Kd values."
                )
            if 1 - p_active < 1e-9:
                kdNew = kd  # Concentration of metabolite-bound TF is negligible
            else:
                kdNew = (
                    (activeSignalConc**metaboliteCoeff) * p_active / (1 - p_active)
                ) ** (1 / metaboliteCoeff)

            # Reset metabolite concentration with fitted P and kd
            sim_data.process.metabolism.concentration_updates.molecule_set_amounts[
                metabolite
            ] = (kdNew**metaboliteCoeff * (1 - p_inactive) / p_inactive) ** (
                1.0 / metaboliteCoeff
            ) * (units.mol / units.L)

        else:
            if p_active == 1:
                raise ValueError(
                    "Inf ligand concentration from p_active = 1."
                    " Check results from fitPromoterBoundProbability and Kd values."
                )
            if p_inactive < 1e-9:
                kdNew = kd  # Concentration of metabolite-bound TF is negligible
            else:
                kdNew = (
                    (inactiveSignalConc**metaboliteCoeff)
                    * (1 - p_inactive)
                    / p_inactive
                ) ** (1 / metaboliteCoeff)

            # Reset metabolite concentration with fitted P and kd
            sim_data.process.metabolism.concentration_updates.molecule_set_amounts[
                metabolite
            ] = (kdNew**metaboliteCoeff * p_active / (1 - p_active)) ** (
                1.0 / metaboliteCoeff
            ) * (units.mol / units.L)

        # Fit reverse rate in line with fitted kd
        sim_data.process.equilibrium.set_rev_rate(boundId + "[c]", kdNew * fwdRate)


def calculatePromoterBoundProbability(sim_data, cell_specs):
    """
    Calculate the probability that a transcription factor is bound to its
    associated promoter for all simulated growth conditions. The bulk
    average concentrations calculated for TFs and their ligands are used to
    compute the probabilities based on the type (0CS, 1CS, 2CS) of the TF.

    Requires
    --------
    - Bulk average counts of transcription factors and associated ligands
    for each condition (in cell_specs)

    Returns
    --------
    - pPromoterBound: Probability that a transcription factor is bound to
    its promoter, per growth condition and TF. Each probability is indexed by
    pPromoterBound[condition][TF].
    """

    pPromoterBound = {}  # Initialize return value
    cellDensity = sim_data.constants.cell_density
    init_to_average = sim_data.mass.avg_cell_to_initial_cell_conversion_factor

    # Matrix to determine number of promoters each TF can bind to in a given condition
    tf_idx = {tf: i for i, tf in enumerate(sim_data.tf_to_active_inactive_conditions)}
    cistron_id_to_tu_indexes = {
        cistron_id: sim_data.process.transcription.cistron_id_to_rna_indexes(cistron_id)
        for cistron_id in sim_data.process.transcription.cistron_data["id"]
    }
    regulation_i = []
    regulation_j = []
    regulation_v = []
    for tf, cistrons in sim_data.tf_to_fold_change.items():
        if tf not in tf_idx:
            continue

        for cistron in cistrons:
            for tu_index in cistron_id_to_tu_indexes[cistron]:
                regulation_i.append(tf_idx[tf])
                regulation_j.append(tu_index)
                regulation_v.append(1)

    regulation = scipy.sparse.csr_matrix(
        (regulation_v, (regulation_i, regulation_j)),
        shape=(len(tf_idx), len(sim_data.process.transcription.rna_data)),
    )
    rna_coords = sim_data.process.transcription.rna_data["replication_coordinate"]

    for conditionKey in sorted(cell_specs):
        pPromoterBound[conditionKey] = {}
        tau = sim_data.condition_to_doubling_time[conditionKey].asNumber(units.min)
        n_avg_copy = sim_data.process.replication.get_average_copy_number(
            tau, rna_coords
        )
        n_promoter_targets = regulation.dot(n_avg_copy)

        cellVolume = (
            cell_specs[conditionKey]["avgCellDryMassInit"]
            / cellDensity
            / sim_data.mass.cell_dry_mass_fraction
        )
        countsToMolar = 1 / (sim_data.constants.n_avogadro * cellVolume)

        for tf in sorted(sim_data.tf_to_active_inactive_conditions):
            tfType = sim_data.process.transcription_regulation.tf_to_tf_type[tf]
            curr_tf_idx = bulk_name_to_idx(
                tf + "[c]", cell_specs[conditionKey]["bulkAverageContainer"]["id"]
            )
            tf_counts = counts(
                cell_specs[conditionKey]["bulkAverageContainer"], curr_tf_idx
            )
            tf_targets = n_promoter_targets[tf_idx[tf]]
            limited_tf_counts = min(1, tf_counts * init_to_average / tf_targets)
            if tfType == "0CS":
                pPromoterBound[conditionKey][tf] = (
                    limited_tf_counts  # If TF exists, the promoter is always bound to the TF
                )

            elif tfType == "1CS":
                boundId = sim_data.process.transcription_regulation.active_to_bound[
                    tf
                ]  # ID of TF bound to ligand
                kd = sim_data.process.equilibrium.get_rev_rate(
                    boundId + "[c]"
                ) / sim_data.process.equilibrium.get_fwd_rate(boundId + "[c]")

                signal = sim_data.process.equilibrium.get_metabolite(
                    boundId + "[c]"
                )  # ID of ligand that binds to TF
                signalCoeff = sim_data.process.equilibrium.get_metabolite_coeff(
                    boundId + "[c]"
                )  # Stoichiometric coefficient of ligand

                # Get bulk average concentrations of ligand and TF
                signal_idx = bulk_name_to_idx(
                    signal, cell_specs[conditionKey]["bulkAverageContainer"]["id"]
                )
                signalConc = (
                    countsToMolar
                    * counts(
                        cell_specs[conditionKey]["bulkAverageContainer"], signal_idx
                    )
                ).asNumber(units.mol / units.L)
                tfConc = (countsToMolar * tf_counts).asNumber(units.mol / units.L)

                # If TF is active in its bound state
                if tf == boundId:
                    if tfConc > 0:
                        pPromoterBound[conditionKey][tf] = (
                            limited_tf_counts
                            * sim_data.process.transcription_regulation.p_promoter_bound_SKd(
                                signalConc, kd, signalCoeff
                            )
                        )
                    else:
                        pPromoterBound[conditionKey][tf] = 0.0

                # If TF is active in its unbound state
                else:
                    if tfConc > 0:
                        pPromoterBound[conditionKey][tf] = (
                            1.0
                            - limited_tf_counts
                            * sim_data.process.transcription_regulation.p_promoter_bound_SKd(
                                signalConc, kd, signalCoeff
                            )
                        )
                    else:
                        pPromoterBound[conditionKey][tf] = 0.0

            elif tfType == "2CS":
                # Get bulk average concentrations of active and inactive TF
                activeTfConc = (countsToMolar * tf_counts).asNumber(units.mol / units.L)
                inactiveTf = (
                    sim_data.process.two_component_system.active_to_inactive_tf[
                        tf + "[c]"
                    ]
                )
                inactive_tf_idx = bulk_name_to_idx(
                    inactiveTf, cell_specs[conditionKey]["bulkAverageContainer"]["id"]
                )
                inactiveTfConc = (
                    countsToMolar
                    * counts(
                        cell_specs[conditionKey]["bulkAverageContainer"],
                        inactive_tf_idx,
                    )
                ).asNumber(units.mol / units.L)

                if activeTfConc == 0 and inactiveTfConc == 0:
                    pPromoterBound[conditionKey][tf] = 0.0
                else:
                    pPromoterBound[conditionKey][tf] = (
                        limited_tf_counts
                        * activeTfConc
                        / (activeTfConc + inactiveTfConc)
                    )

    # Check for any inconsistencies that could lead to feasbility issues when fitting
    for condition in pPromoterBound:
        if "inactive" in condition:
            tf = condition.split("__")[0]
            active_p = pPromoterBound[f"{tf}__active"][tf]
            inactive_p = pPromoterBound[f"{tf}__inactive"][tf]

            if inactive_p >= active_p:
                print(
                    "Warning: active condition does not have higher binding"
                    f" probability than inactive condition for {tf}"
                    f" ({active_p:.3f} vs {inactive_p:.3f})."
                )

    return pPromoterBound


def calculateRnapRecruitment(sim_data, cell_specs):
    """
    Constructs the basal_prob vector and delta_prob matrix from values of r.
    The basal_prob vector holds the basal transcription probabilities of each
    transcription unit. The delta_prob matrix holds the differences in
    transcription probabilities when transcription factors bind to the
    promoters of each transcription unit. Both values are stored in sim_data.

    Requires
    --------
    - cell_specs['basal']:
            - ['r_vector']: Fit parameters on how the recruitment of a TF affects the expression
            of a gene. High (positive) values of r indicate that the TF binding
            increases the probability that the gene is expressed.
            - ['r_columns']: mapping of column name to index in r

    Modifies
    --------
    - Rescales values in basal_prob such that all values are positive
    - Adds basal_prob and delta_prob arrays to sim_data
    """

    r = cell_specs["basal"]["r_vector"]
    col_names_to_index = cell_specs["basal"]["r_columns"]

    # Get list of transcription units and TF IDs
    transcription = sim_data.process.transcription
    transcription_regulation = sim_data.process.transcription_regulation
    all_TUs = transcription.rna_data["id"]
    all_tfs = transcription_regulation.tf_ids

    # Initialize basal_prob vector and delta_prob sparse matrix
    basal_prob = np.zeros(len(all_TUs))
    deltaI, deltaJ, deltaV = [], [], []

    for rna_idx, rnaId in enumerate(all_TUs):
        rnaIdNoLoc = rnaId[:-3]  # Remove compartment ID from RNA ID

        # Take only those TFs with active/inactive conditions data
        for tf in sim_data.relation.rna_id_to_regulating_tfs.get(rnaId, []):
            if tf not in sorted(sim_data.tf_to_active_inactive_conditions):
                continue

            colName = rnaIdNoLoc + "__" + tf

            # Set element in delta to value in r that corresponds to the
            # transcription unit of the row, and the TF of the column
            deltaI.append(rna_idx)
            deltaJ.append(all_tfs.index(tf))
            deltaV.append(r[col_names_to_index[colName]])

        # Add alpha column for each RNA
        colName = rnaIdNoLoc + "__alpha"

        # Set element in basal_prob to the transcription unit's value for alpha
        basal_prob[rna_idx] = r[col_names_to_index[colName]]

    # Convert to arrays
    deltaI, deltaJ, deltaV = np.array(deltaI), np.array(deltaJ), np.array(deltaV)
    delta_shape = (len(all_TUs), len(all_tfs))

    # Adjust any negative basal probabilities to 0
    basal_prob[basal_prob < 0] = 0

    # Add basal_prob vector and delta_prob matrix to sim_data
    transcription_regulation.basal_prob = basal_prob
    transcription_regulation.delta_prob = {
        "deltaI": deltaI,
        "deltaJ": deltaJ,
        "deltaV": deltaV,
        "shape": delta_shape,
    }


def crc32(*arrays: np.ndarray, initial: int = 0) -> int:
    """Return a CRC32 checksum of the given ndarrays."""

    def crc_next(initial: int, array: np.ndarray) -> int:
        shape = str(array.shape).encode()
        values = array.tobytes()
        return binascii.crc32(values, binascii.crc32(shape, initial))

    return functools.reduce(crc_next, arrays, initial)


def setKmCooperativeEndoRNonLinearRNAdecay(sim_data, bulkContainer):
    """
    Fits the affinities (Michaelis-Menten constants) for RNAs binding to
    endoRNAses.

    EndoRNAses perform the first step of RNA decay by cleaving a whole RNA
    somewhere inside its extent.  This results in RNA fragments, which are then
    digested into monomers by exoRNAses. To model endoRNAse activity, we need to
    determine an affinity (Michaelis-Menten constant) for each RNA that is
    consistent with experimentally observed half-lives.  The Michaelis-Menten
    constants must be determined simultaneously, as the RNAs must compete for
    the active site of the endoRNAse. (See the RnaDegradation Process class for
    more information about the dynamical model.) The parameters are estimated
    using a root solver (scipy.optimize.fsolve).  (See the
    sim_data.process.rna_decay.kmLossFunction method for more information about
    the optimization problem.)

    Requires
    --------
    - cell density, dry mass fraction, and average initial dry mass
            Used to calculate the cell volume, which in turn is used to calculate
            concentrations.
    - observed RNA degradation rates (half-lives)
    - endoRNAse counts
    - endoRNAse catalytic rate constants
    - RNA counts
    - boolean options that enable sensitivity analyses (see Notes below)

    Modifies
    --------
    - Michaelis-Menten constants for first-order decay (initially set to zeros)
    - Several optimization-related values
            Sensitivity analyses (optional, see Notes below)
            Terminal values for optimization-related functions

    Returns
    -------
    - enoRNAse Km values, in units of M

    Notes
    -----
    If certain options are set, a sensitivity analysis will be performed using a
    range of metaparameters. Outputs will be cached and utilized instead of
    running the optimization if possible.
    The function that generates the optimization functions is defined under
    sim_data but has no dependency on sim_data, and therefore could be moved
    here or elsewhere. (TODO)

    TODO (John): Refactor as a pure function.
    TODO (John): Why is this function called 'cooperative'?  It seems to instead
            assume and model competitive binding.
    TODO (John): Determine what part (if any) of the 'linear' parameter fitting
            should be retained.
    """

    def arrays_differ(a: np.ndarray, b: np.ndarray) -> bool:
        return a.shape != b.shape or not np.allclose(a, b, equal_nan=True)

    cellDensity = sim_data.constants.cell_density
    cellVolume = (
        sim_data.mass.avg_cell_dry_mass_init
        / cellDensity
        / sim_data.mass.cell_dry_mass_fraction
    )
    countsToMolar = 1 / (sim_data.constants.n_avogadro * cellVolume)

    degradable_rna_ids = np.concatenate(
        (
            sim_data.process.transcription.rna_data["id"],
            sim_data.process.transcription.mature_rna_data["id"],
        )
    )
    degradation_rates = (1 / units.s) * np.concatenate(
        (
            sim_data.process.transcription.rna_data["deg_rate"].asNumber(1 / units.s),
            sim_data.process.transcription.mature_rna_data["deg_rate"].asNumber(
                1 / units.s
            ),
        )
    )
    endoRNase_idx = bulk_name_to_idx(
        sim_data.process.rna_decay.endoRNase_ids, bulkContainer["id"]
    )
    endoRNaseConc = countsToMolar * counts(bulkContainer, endoRNase_idx)
    kcatEndoRNase = sim_data.process.rna_decay.kcats
    totalEndoRnaseCapacity = units.sum(endoRNaseConc * kcatEndoRNase)

    endoRnaseRnaIds = sim_data.molecule_groups.endoRNase_rnas
    isEndoRnase = np.array([(x in endoRnaseRnaIds) for x in degradable_rna_ids])

    degradable_rna_idx = bulk_name_to_idx(degradable_rna_ids, bulkContainer["id"])
    rna_counts = counts(bulkContainer, degradable_rna_idx)
    rna_conc = countsToMolar * rna_counts
    Km_counts = ((1 / degradation_rates * totalEndoRnaseCapacity) - rna_conc).asNumber()
    sim_data.process.rna_decay.Km_first_order_decay = Km_counts

    # Residuals can be written as follows: Res = f(Km) = 0, then Km = g(Km)
    # Compute derivative g(Km) in counts:
    KmQuadratic = 1 / np.power((1 / countsToMolar * Km_counts).asNumber(), 2)
    denominator = np.power(
        np.sum(rna_counts / (1 / countsToMolar * Km_counts).asNumber()), 2
    )
    numerator = (1 / countsToMolar * totalEndoRnaseCapacity).asNumber() * (
        denominator - (rna_counts / (1 / countsToMolar * Km_counts).asNumber())
    )
    gDerivative = np.abs(KmQuadratic * (1 - (numerator / denominator)))
    if VERBOSE:
        print("Max derivative (counts) = %f" % max(gDerivative))

    # Compute derivative g(Km) in concentrations:
    KmQuadratic = 1 / np.power(Km_counts, 2)
    denominator = np.power(np.sum(rna_conc.asNumber() / Km_counts), 2)
    numerator = totalEndoRnaseCapacity.asNumber() * (
        denominator - (rna_conc.asNumber() / Km_counts)
    )
    gDerivative = np.abs(KmQuadratic * (1 - (numerator / denominator)))
    if VERBOSE:
        print("Max derivative (concentration) = %f" % max(gDerivative))

    # Sensitivity analysis: alpha (regularization term)
    Alphas = []
    if sim_data.constants.sensitivity_analysis_alpha:
        Alphas = [0.0001, 0.001, 0.01, 0.1, 1, 10]

    total_endo_rnase_capacity_mol_l_s = totalEndoRnaseCapacity.asNumber(
        units.mol / units.L / units.s
    )
    rna_conc_mol_l = rna_conc.asNumber(units.mol / units.L)
    degradation_rates_s = degradation_rates.asNumber(1 / units.s)

    for alpha in Alphas:
        if VERBOSE:
            print("Alpha = %f" % alpha)

        LossFunction, Rneg, R, LossFunctionP, R_aux, L_aux, Lp_aux, Jacob, Jacob_aux = (
            sim_data.process.rna_decay.km_loss_function(
                total_endo_rnase_capacity_mol_l_s,
                rna_conc_mol_l,
                degradation_rates_s,
                isEndoRnase,
                alpha,
            )
        )
        Km_cooperative_model = scipy.optimize.fsolve(
            LossFunction, Km_counts, fprime=LossFunctionP
        )
        sim_data.process.rna_decay.sensitivity_analysis_alpha_residual[alpha] = np.sum(
            np.abs(R_aux(Km_cooperative_model))
        )
        sim_data.process.rna_decay.sensitivity_analysis_alpha_regulari_neg[alpha] = (
            np.sum(np.abs(Rneg(Km_cooperative_model)))
        )

    alpha = 0.5

    # Sensitivity analysis: kcatEndoRNase
    kcatEndo = []
    if sim_data.constants.sensitivity_analysis_kcat_endo:
        kcatEndo = [0.0001, 0.001, 0.01, 0.1, 1, 10]

    for kcat in kcatEndo:
        if VERBOSE:
            print("Kcat = %f" % kcat)

        totalEndoRNcap = units.sum(endoRNaseConc * kcat)
        LossFunction, Rneg, R, LossFunctionP, R_aux, L_aux, Lp_aux, Jacob, Jacob_aux = (
            sim_data.process.rna_decay.km_loss_function(
                totalEndoRNcap.asNumber(units.mol / units.L),
                rna_conc_mol_l,
                degradation_rates_s,
                isEndoRnase,
                alpha,
            )
        )
        KmcountsIni = (
            (totalEndoRNcap / degradation_rates.asNumber()) - rna_conc
        ).asNumber()
        Km_cooperative_model = scipy.optimize.fsolve(
            LossFunction, KmcountsIni, fprime=LossFunctionP
        )
        sim_data.process.rna_decay.sensitivity_analysis_kcat[kcat] = (
            Km_cooperative_model
        )
        sim_data.process.rna_decay.sensitivity_analysis_kcat_res_ini[kcat] = np.sum(
            np.abs(R_aux(Km_counts))
        )
        sim_data.process.rna_decay.sensitivity_analysis_kcat_res_opt[kcat] = np.sum(
            np.abs(R_aux(Km_cooperative_model))
        )

    # Loss function, and derivative
    LossFunction, Rneg, R, LossFunctionP, R_aux, L_aux, Lp_aux, Jacob, Jacob_aux = (
        sim_data.process.rna_decay.km_loss_function(
            total_endo_rnase_capacity_mol_l_s,
            rna_conc_mol_l,
            degradation_rates_s,
            isEndoRnase,
            alpha,
        )
    )

    # The checksum in the filename picks independent caches for distinct cases
    # such as different Parca options or Parca code in different git branches.
    # `make clean` will delete the cache files.
    needToUpdate = ""
    cache_dir = filepath.makedirs(filepath.ROOT_PATH, "cache")
    checksum = crc32(Km_counts, isEndoRnase, np.array(alpha))
    km_filepath = os.path.join(cache_dir, f"parca-km-{checksum}.cPickle")

    if os.path.exists(km_filepath):
        with open(km_filepath, "rb") as f:
            Km_cache = pickle.load(f)

        # KmCooperativeModel fits a set of Km values to give the expected degradation rates.
        # It takes 1.5 - 3 minutes to recompute.
        # R_aux calculates the difference of the degradation rate based on these
        # Km values and the expected rate so this sum seems like a good test of
        # whether the cache fits current input data, but cross-check additional
        # inputs to avoid Issue #996.
        Km_cooperative_model = Km_cache["Km_cooperative_model"]
        if (
            Km_counts.shape != Km_cooperative_model.shape
            or np.sum(np.abs(R_aux(Km_cooperative_model))) > 1e-15
            or arrays_differ(
                Km_cache["total_endo_rnase_capacity_mol_l_s"],
                total_endo_rnase_capacity_mol_l_s,
            )
            or arrays_differ(Km_cache["rna_conc_mol_l"], rna_conc_mol_l)
            or arrays_differ(Km_cache["degradation_rates_s"], degradation_rates_s)
        ):
            needToUpdate = "recompute"
    else:
        needToUpdate = "compute"

    if needToUpdate:
        if VERBOSE:
            print(f"Running non-linear optimization to {needToUpdate} {km_filepath}")
        Km_cooperative_model = scipy.optimize.fsolve(
            LossFunction, Km_counts, fprime=LossFunctionP
        )
        Km_cache = dict(
            Km_cooperative_model=Km_cooperative_model,
            total_endo_rnase_capacity_mol_l_s=total_endo_rnase_capacity_mol_l_s,
            rna_conc_mol_l=rna_conc_mol_l,
            degradation_rates_s=degradation_rates_s,
        )

        with open(km_filepath, "wb") as f:
            pickle.dump(Km_cache, f, protocol=pickle.HIGHEST_PROTOCOL)
    else:
        if VERBOSE:
            print(
                "Not running non-linear optimization--using cached result {}".format(
                    km_filepath
                )
            )

    if VERBOSE > 1:
        print(
            "Loss function (Km inital) = %f" % np.sum(np.abs(LossFunction(Km_counts)))
        )
        print(
            "Loss function (optimized Km) = %f"
            % np.sum(np.abs(LossFunction(Km_cooperative_model)))
        )
        print("Negative km ratio = %f" % np.sum(np.abs(Rneg(Km_cooperative_model))))
        print("Residuals (Km initial) = %f" % np.sum(np.abs(R(Km_counts))))
        print("Residuals optimized = %f" % np.sum(np.abs(R(Km_cooperative_model))))
        print(
            "EndoR residuals (Km initial) = %f"
            % np.sum(np.abs(isEndoRnase * R(Km_counts)))
        )
        print(
            "EndoR residuals optimized = %f"
            % np.sum(np.abs(isEndoRnase * R(Km_cooperative_model)))
        )
        print(
            "Residuals (scaled by Kdeg * RNAcounts) Km initial = %f"
            % np.sum(np.abs(R_aux(Km_counts)))
        )
        print(
            "Residuals (scaled by Kdeg * RNAcounts) optimized = %f"
            % np.sum(np.abs(R_aux(Km_cooperative_model)))
        )

    # Evaluate Jacobian around solutions (Kmcounts and KmCooperativeModel)
    JacobDiag = np.diag(Jacob(Km_cooperative_model))
    Jacob_auxDiag = np.diag(Jacob_aux(Km_cooperative_model))

    # Compute convergence of non-linear optimization: g'(Km)
    Gkm = np.abs(1.0 - JacobDiag)
    Gkm_aux = np.abs(1.0 - Jacob_auxDiag)
    sim_data.process.rna_decay.Km_convergence = Gkm_aux

    # Convergence is guaranteed if g'(Km) <= K < 1
    if VERBOSE:
        print(
            "Convergence (Jacobian) = %.0f%% (<K> = %.5f)"
            % (len(Gkm[Gkm < 1.0]) / float(len(Gkm)) * 100.0, np.mean(Gkm))
        )
        print(
            "Convergence (Jacobian_aux) = %.0f%% (<K> = %.5f)"
            % (
                len(Gkm_aux[Gkm_aux < 1.0]) / float(len(Gkm_aux)) * 100.0,
                np.mean(Gkm_aux[Gkm_aux < 1.0]),
            )
        )

    # Save statistics KM optimization
    sim_data.process.rna_decay.stats_fit["LossKm"] = np.sum(
        np.abs(LossFunction(Km_counts))
    )
    sim_data.process.rna_decay.stats_fit["LossKmOpt"] = np.sum(
        np.abs(LossFunction(Km_cooperative_model))
    )
    sim_data.process.rna_decay.stats_fit["RnegKmOpt"] = np.sum(
        np.abs(Rneg(Km_cooperative_model))
    )
    sim_data.process.rna_decay.stats_fit["ResKm"] = np.sum(np.abs(R(Km_counts)))
    sim_data.process.rna_decay.stats_fit["ResKmOpt"] = np.sum(
        np.abs(R(Km_cooperative_model))
    )
    sim_data.process.rna_decay.stats_fit["ResEndoRNKm"] = np.sum(
        np.abs(isEndoRnase * R(Km_counts))
    )
    sim_data.process.rna_decay.stats_fit["ResEndoRNKmOpt"] = np.sum(
        np.abs(isEndoRnase * R(Km_cooperative_model))
    )
    sim_data.process.rna_decay.stats_fit["ResScaledKm"] = np.sum(
        np.abs(R_aux(Km_counts))
    )
    sim_data.process.rna_decay.stats_fit["ResScaledKmOpt"] = np.sum(
        np.abs(R_aux(Km_cooperative_model))
    )

    return units.mol / units.L * Km_cooperative_model