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cellular_activity.c
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cellular_activity.c
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/*
* This file contains the functions to simulate gene expression and
* instantaneous fitness during development.
*
* Authors: Joanna Masel, Alex Lancaster, Kun Xiong
* Copyright (c) 2018 Arizona Board of Regents on behalf of the University of Arizona
* This file is part of network-evolution-simulator.
* network-evolution-simulator is free software: you can redistribute it and/or modify
* it under the terms of the GNU Affero General Public License as published by
* the Free Software Foundation, either version 3 of the License, or
* (at your option) any later version.
* network-evolution-simulator is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
* GNU Affero General Public License for more details.
* You should have received a copy of the GNU Affero General Public License
* along with network-evolution-simulator. If not, see <https://www.gnu.org/licenses/>.
*/
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include "cellular_activity.h"
#include "lib.h"
#include "numerical.h"
#define DO_NOTHING -2
#define INITIALIZATION -1
#define SUDDEN_SIGNAL_CHANGE 1
/*expression rate parameters*/
static const float TRANSCRIPTINIT=6.75;
static const float TRANSLATION_INITIATION_TIME=0.5; //min
static const float TRANSCRIPTION_TERMINATION_TIME=1.0; //min
static const float TRANSCRIPTION_ELONGATION_RATE=600.0; //codon/min
static const float TRANSLATION_ELONGATION_RATE=330.0; //codon/min
static const float MAX_REP_TO_INT_RATE=0.92;
static const float BASAL_REP_TO_INT_RATE=0.15;
static const float MAX_INT_TO_REP_RATE=4.11;
static const float BASAL_INT_TO_REP_RATE=0.67;
static const float MAX_INT_TO_ACT_RATE=3.3;
static const float BASAL_INT_TO_ACT_RATE=0.025;
static const float DEFAULT_UPDATE_INTERVAL=10.0; /*min*/
static const float MAX_TOLERABLE_CHANGE_IN_PROBABILITY_OF_BINDING=0.01;
/*fitness*/
static const float Ne_saturate = 10000.0;
static const float c_transl=2.0e-6;
static const float bmax=1.0;
/******************************************************************************
*
* Private function prototypes
*
*****************************************************************************/
static float calc_tprime(Genotype*, CellState*, float*, float, float, int);
static float calc_integral(Genotype *, CellState *, float *, float, float);
static void calc_fx_dfx(float, int, float, float*, float*, float*, float*, float*);
static void calc_leaping_interval(Genotype*, CellState*, float *, float, int);
static void calc_TF_dist_from_all_BS(Genotype *, CellState*, int);
static int Gillespie_event_mRNA_decay(GillespieRates *, CellState *, Genotype *, RngStream);
static void Gillespie_event_repressed_to_intermediate(GillespieRates *, CellState *, Genotype *, RngStream);
static void Gillespie_event_intermediate_to_repressed(GillespieRates *, CellState *, Genotype *, RngStream);
static void Gillespie_event_intermediate_to_active(GillespieRates *, CellState *, Genotype *, RngStream);
static void Gillespie_event_active_to_intermediate(Genotype *, CellState *, GillespieRates *, RngStream);
static void Gillespie_event_transcription_init(GillespieRates *, CellState *, Genotype *, float, RngStream);
static int fixed_event_end_translation_init(Genotype *, CellState *, GillespieRates *, float *);
static void fixed_event_end_transcription(float *, CellState *, GillespieRates *, Genotype *);
static int does_fixed_event_end(CellState*, float);
static int do_fixed_event(Genotype *, CellState *, GillespieRates *, Environment *, Phenotype *, float *, int);
static float calc_fitness(float *, Genotype *, CellState *, float*, float);
static void update_protein_number_and_fitness(Genotype *, CellState *, GillespieRates *, float);
static int do_Gillespie_event(Genotype*, CellState *, GillespieRates *, float, RngStream);
/******************************************************************************
*
* Global functions
*
*****************************************************************************/
/*
* initialize the cell state with the specified initial protein
* concentration, mean mRNA number and mRNA decay
*/
void initialize_cell( Genotype *genotype,
CellState *state,
Environment *env,
float t_burn_in,
int init_mRNA_number[MAX_GENES],
float init_protein_number[MAX_PROTEINS])
{
int i, j;
state->t=0.0;
state->cumulative_fitness = 0.0;
state->cumulative_fitness_after_burn_in = 0.0;
state->instantaneous_fitness = 0.0;
state->effect_of_effector=env->initial_effect_of_effector;
/* initialize linked tables*/
state->mRNA_transcr_time_end_head = NULL;
state->mRNA_transcr_time_end_tail = NULL;
state->mRNA_transl_init_time_end_head = NULL;
state->mRNA_transl_init_time_end_tail = NULL;
state->signal_off_head = NULL;
state->signal_off_tail = NULL;
state->signal_on_head = NULL;
state->signal_on_tail = NULL;
state->burn_in_growth_rate_head =NULL;
state->burn_in_growth_rate_tail=NULL;
state->sampling_point_end_head=NULL;
state->sampling_point_end_tail=NULL;
state->last_event_t=0.0;
state->change_signal_strength_head=NULL;
state->change_signal_strength_tail=NULL;
state->t_to_update_probability_of_binding=TIME_INFINITY;
state->cell_activated=0;
/*initialize gene state, mRNA number*/
for (i=N_SIGNAL_TF; i < genotype->ngenes; i++)
{
state->transcriptional_state[i]=REPRESSED;
state->mRNA_aft_transl_delay_num[i]=init_mRNA_number[i];
state->mRNA_under_transl_delay_num[i]=0;
state->mRNA_under_transc_num[i]=0;
state->last_P_A[i]=0.0;
state->last_P_R[i]=0.0;
state->last_P_A_no_R[i]=0.0;;
state->last_P_NotA_no_R[i]=0.0;
state->protein_synthesis_index[i]=(float)state->mRNA_aft_transl_delay_num[i]*genotype->translation_rate[i]/genotype->protein_decay_rate[i];
}
/* initiate protein concentration*/
for (i=N_SIGNAL_TF; i < genotype->ngenes; i++)
state->gene_specific_protein_number[i] = init_protein_number[i];
for(i=N_SIGNAL_TF;i<genotype->nproteins;i++)
{
state->protein_number[i]=0.0;
for(j=0;j<genotype->protein_pool[i][0][0];j++)
state->protein_number[i]+=state->gene_specific_protein_number[genotype->protein_pool[i][1][j]];
}
/* deal with the sensor tf*/
for(i=0;i<N_SIGNAL_TF;i++)
{
state->mRNA_aft_transl_delay_num[i]=0;
state->mRNA_under_transc_num[i]=0;
state->mRNA_under_transl_delay_num[i]=0;
state->gene_specific_protein_number[i]=0.0;
}
/*mark when to start calculating average fitness*/
if(t_burn_in!=0.0)
add_fixed_event(-1,t_burn_in,&(state->burn_in_growth_rate_head),&(state->burn_in_growth_rate_tail));
else
add_fixed_event(-1,(float)TIME_INFINITY,&(state->burn_in_growth_rate_head),&(state->burn_in_growth_rate_tail));
/*plot protein concentration and fitness vs time*/
#if PHENOTYPE
float t;
int N_data_points;
t=0.0+TIME_OFFSET;
N_data_points=(int)(env->t_development+t_burn_in);
for(i=0;i<N_data_points;i++)
{
add_fixed_event(-1,t,&(state->sampling_point_end_head),&(state->sampling_point_end_tail)); //get a timepoint each minute
t+=1.0;
}
#endif
}
/*
* Calculate the rates of all Gillespie events
*/
void calc_all_rates(Genotype *genotype,
CellState *state,
GillespieRates *rates,
Environment *env,
Phenotype *phenotype,
float t_burn_in,
int UPDATE_WHAT)
{
int i,cluster_id,gene_id;
int concurrent;
float t_to_update_probability_of_binding,interval_to_update_probability_of_binding;
float diff_PA,diff_PR,diff_PnotAnoR,diff_PAnoR,diff_max;
/* reset rates */
rates->total_mRNA_decay_rate=0.0;
rates->total_active_to_intermediate_rate=0.0;
rates->total_repressed_to_intermediate_rate=0.0;
rates->total_intermediate_to_repressed_rate=0.0;
rates->total_N_gene_transcript_initiated=0;
rates->total_intermediate_to_active_rate=0.0;
rates->total_Gillespie_rate=0.0;
for(i=0;i<genotype->ngenes;i++)
{
rates->repressed_to_intermediate_rate[i]=0.0;
rates->intermediate_to_repressed_rate[i]=0.0;
rates->intermediate_to_active_rate[i]=0.0;
rates->active_to_intermediate_rate[i]=0.0;
rates->mRNA_decay_rate[i]=0.0;
rates->transcript_initiation_state[i]=0;
state->P_A[i]=0.0;
state->P_R[i]=0.0;
state->P_A_no_R[i]=0.0;
state->P_NotA_no_R[i]=0.0;
}
/* update mRNA decay rates*/
for(i=N_SIGNAL_TF;i<genotype->ngenes;i++)
{
rates->mRNA_decay_rate[i] = genotype->mRNA_decay_rate[i] * (state->mRNA_aft_transl_delay_num[i] + state->mRNA_under_transl_delay_num[i]);
rates->total_mRNA_decay_rate += rates->mRNA_decay_rate[i];
}
/*update probability of binding configurations that activates expression
* and use it to update other rates*/
for(i=N_SIGNAL_TF; i < genotype->ngenes; i++)
{
cluster_id=genotype->which_cluster[i];
if(genotype->cisreg_cluster[cluster_id][0]!=i) /*if this gene does not have a unique cis-reg sequence*/
{
state->P_A[i]=state->P_A[genotype->cisreg_cluster[cluster_id][0]]; /* copy TF distribution from elsewhere*/
state->P_R[i]=state->P_R[genotype->cisreg_cluster[cluster_id][0]];
state->P_A_no_R[i]=state->P_A_no_R[genotype->cisreg_cluster[cluster_id][0]];
state->P_NotA_no_R[i]=state->P_NotA_no_R[genotype->cisreg_cluster[cluster_id][0]];
}
else /* otherwise, we need to calc the ratio*/
{
if(genotype->N_act_BS[i]!=0 || genotype->N_rep_BS[i]!=0)
calc_TF_dist_from_all_BS(genotype, state, i);
else
{
state->P_A[i]=0.0;
state->P_R[i]=0.0;
state->P_A_no_R[i] = 0.0;
state->P_NotA_no_R[i]=0.0;
}
}
/* calc other rates*/
switch (state->transcriptional_state[i])
{
case REPRESSED:
rates->repressed_to_intermediate_rate[i]=state->P_A[i]*(MAX_REP_TO_INT_RATE-BASAL_REP_TO_INT_RATE)+BASAL_REP_TO_INT_RATE;
rates->total_repressed_to_intermediate_rate+=rates->repressed_to_intermediate_rate[i];
rates->intermediate_to_repressed_rate[i]=0.0;
rates->intermediate_to_active_rate[i]=0.0;
rates->active_to_intermediate_rate[i]=0.0;
break;
case INTERMEDIATE:
rates->intermediate_to_repressed_rate[i]=state->P_R[i]*(MAX_INT_TO_REP_RATE-BASAL_INT_TO_REP_RATE)+BASAL_INT_TO_REP_RATE;
rates->total_intermediate_to_repressed_rate+=rates->intermediate_to_repressed_rate[i];
rates->intermediate_to_active_rate[i]=MAX_INT_TO_ACT_RATE*state->P_A_no_R[i]+BASAL_INT_TO_ACT_RATE*state->P_NotA_no_R[i];
rates->total_intermediate_to_active_rate+=rates->intermediate_to_active_rate[i];
rates->active_to_intermediate_rate[i]=0.0;
rates->repressed_to_intermediate_rate[i]=0.0;
break;
case ACTIVE:
rates->active_to_intermediate_rate[i]=genotype->active_to_intermediate_rate[i];
rates->total_active_to_intermediate_rate+=rates->active_to_intermediate_rate[i];
rates->transcript_initiation_state[i]= 1;
rates->total_N_gene_transcript_initiated+=1;
rates->intermediate_to_repressed_rate[i]=0.0;
rates->repressed_to_intermediate_rate[i]=0.0;
rates->intermediate_to_active_rate[i]=0.0;
break;
}
}
rates->total_Gillespie_rate+=rates->total_intermediate_to_repressed_rate;
rates->total_Gillespie_rate+=rates->total_intermediate_to_active_rate;
rates->total_Gillespie_rate+=rates->total_repressed_to_intermediate_rate;
rates->total_Gillespie_rate+=rates->total_mRNA_decay_rate;
rates->total_Gillespie_rate+=rates->total_active_to_intermediate_rate;
rates->total_Gillespie_rate+=(float)rates->total_N_gene_transcript_initiated*TRANSCRIPTINIT;
/*Check if Pact needs to be updated more or less often*/
if(UPDATE_WHAT!=INITIALIZATION && state->cell_activated==1)
{
diff_max=0.0;
cluster_id=1;
while(genotype->cisreg_cluster[cluster_id][0]!=NA) //check if Pact changes too much
{
gene_id=genotype->cisreg_cluster[cluster_id][0];
diff_PA=fabs(state->P_A[gene_id]-state->last_P_A[gene_id]);
diff_PAnoR=fabs(state->P_A_no_R[gene_id]-state->last_P_A_no_R[gene_id]);
diff_PnotAnoR=fabs(state->P_NotA_no_R[gene_id]-state->last_P_NotA_no_R[gene_id]);
diff_PR=fabs(state->P_R[gene_id]-state->last_P_R[gene_id]);
diff_max=(diff_max>diff_PA)?diff_max:diff_PA;
diff_max=(diff_max>diff_PR)?diff_max:diff_PR;
diff_max=(diff_max>diff_PAnoR)?diff_max:diff_PAnoR;
diff_max=(diff_max>diff_PnotAnoR)?diff_max:diff_PnotAnoR;
cluster_id++;
}
if(diff_max<EPSILON)
interval_to_update_probability_of_binding=DEFAULT_UPDATE_INTERVAL;
else
interval_to_update_probability_of_binding=MAX_TOLERABLE_CHANGE_IN_PROBABILITY_OF_BINDING/diff_max*(state->t-state->last_event_t);
#if PHENOTYPE
/*record the maximum change in probability of binding except when it is a sudden change in the signal*/
if(UPDATE_WHAT!=SUDDEN_SIGNAL_CHANGE)
phenotype->max_change_in_probability_of_binding=(diff_max>phenotype->max_change_in_probability_of_binding)?diff_max:phenotype->max_change_in_probability_of_binding;
#endif
if(UPDATE_WHAT!=DO_NOTHING)
calc_leaping_interval(genotype,state,&interval_to_update_probability_of_binding,env->t_development+t_burn_in,UPDATE_WHAT);
/*Update the next time that Pact will be updated mandatorily*/
t_to_update_probability_of_binding=state->t+interval_to_update_probability_of_binding;
concurrent=check_concurrence(state, t_to_update_probability_of_binding);
while(concurrent)//if the time to update overlaps with existing events, add a tiny offset
{
t_to_update_probability_of_binding+=TIME_OFFSET;
concurrent=check_concurrence(state, t_to_update_probability_of_binding);
}
state->t_to_update_probability_of_binding=t_to_update_probability_of_binding;
}
/*Keep a copy of Pact and time for comparison at next time Pact is updated*/
for(i=N_SIGNAL_TF;i<genotype->ngenes;i++)
{
state->last_P_A[i]=state->P_A[i];
state->last_P_R[i]=state->P_R[i];
state->last_P_A_no_R[i] = state->P_A_no_R[i];
state->last_P_NotA_no_R[i]=state->P_NotA_no_R[i];
}
state->last_event_t=state->t;
}
/*
* run the model for a specified cell for a single timestep:
*/
void do_single_timestep(Genotype *genotype,
CellState *state,
GillespieRates *rates,
Environment *env,
float t_burn_in,
Phenotype *timecourse,
RngStream RS)
{
int event, UPDATE_WHAT;
float fixed_time;
float dt;
float x;
float developmental_time=env->t_development+t_burn_in;
/* draw random number */
x = expdev(RS);
dt = x/rates->total_Gillespie_rate;
/* check if a fixed event occurs during dt, or in tdevelopment if running for a fixed development time */
fixed_time = (state->t+dt<developmental_time)?(state->t+dt):developmental_time;
event = does_fixed_event_end(state, fixed_time);
while(event!=0)
{
/*after doing fixed event, return a flag to indicate whether mandatorily update Pact or Prep*/
UPDATE_WHAT=do_fixed_event(genotype, state, rates, env, timecourse, &dt, event);
/* advance time by the dt */
state->t += dt;
/* we've been running with rates->total_Gillespie_rate for dt, so substract it from x*/
x -= dt*rates->total_Gillespie_rate;
/* update rates->total_Gillespie_rate and compute a new dt */
calc_all_rates(genotype, state, rates, env, timecourse, t_burn_in, UPDATE_WHAT);
dt = x/rates->total_Gillespie_rate;
/*deal with rounding error*/
if(dt<0.0)
{
#if MAKE_LOG // if enabled, error file can be huge, because this rounding error can happen very often
LOG("Negative dt!\n");
#endif
dt=TIME_OFFSET;
}
fixed_time = (state->t+dt<developmental_time)?(state->t+dt):developmental_time;
/* check to see there aren't more fixed events to do */
event = does_fixed_event_end(state, fixed_time);
}
/* no remaining fixed events to do in dt, now do stochastic events */
/* if we haven't already reached end of development with last delta-t*/
if (state->t+dt < developmental_time)
{
/*update protein concentration and fitness after dt*/
update_protein_number_and_fitness(genotype, state, rates, dt);
/*do Gillespie event*/
UPDATE_WHAT=do_Gillespie_event(genotype, state, rates, dt, RS);
/* Gillespie step: advance time to next event at dt */
state->t += dt;
calc_all_rates(genotype,state,rates,env, timecourse, t_burn_in, UPDATE_WHAT);
}
else
{
/* do remaining dt */
dt = developmental_time - state->t;
/* the final update of protein concentration */
update_protein_number_and_fitness(genotype, state, rates, dt);
/* advance to end of development (this exits the outer while loop) */
state->t = developmental_time;
}
}
/*****************************************************************************
*
* Private functions
*
*****************************************************************************/
/*
* compute t' factor used in the integration of fitness
* t' is the time the effector protein increases or decreases to a given amount
*/
static float calc_tprime(Genotype *genotype, CellState* state, float *number_of_selection_protein_bf_dt, float dt, float given_amount, int protein_id)
{
int n_copies;
int i;
n_copies=genotype->protein_pool[protein_id][0][0];
float protein_synthesis_rate[n_copies],protein_decay_rate[n_copies];
for(i=0;i<n_copies;i++)
{
protein_decay_rate[i]=genotype->protein_decay_rate[genotype->protein_pool[protein_id][1][i]];
protein_synthesis_rate[i]=state->protein_synthesis_index[genotype->protein_pool[protein_id][1][i]]*protein_decay_rate[i];
}
return rtsafe(&calc_fx_dfx, n_copies, given_amount, number_of_selection_protein_bf_dt, protein_synthesis_rate, protein_decay_rate, 0.0, dt);
}
/*
* calculate f(x)-Pp_s and f'(x),
* f(x) is the number of effector protein molecules at time x
*/
static void calc_fx_dfx(float x, int n_copies, float given_amount, float *intial_protein_number, float *protein_synthesis_rate, float *protein_decay_rate,float *fx, float *dfx)
{
int i;
*fx=0;
*dfx=0;
for(i=0;i<n_copies;i++)
{
*fx+=(intial_protein_number[i]-protein_synthesis_rate[i]/protein_decay_rate[i])*exp(-protein_decay_rate[i]*x)+protein_synthesis_rate[i]/protein_decay_rate[i];
*dfx+=(protein_synthesis_rate[i]-protein_decay_rate[i]*intial_protein_number[i])*exp(-protein_decay_rate[i]*x);
}
*fx-=given_amount;
}
/*
* calculate F(delta_t)/Ne_sat. F(x) is the integral of f(x) over delta_t.
* f(x) is the number of effector protein molecules at time x
*/
static float calc_integral(Genotype *genotype, CellState *state, float *initial_protein_number, float dt, float saturate_protein_number)
{
int i,n_copies,gene_ids[MAX_PROTEINS];
float integral=0.0,ect_minus_one;
n_copies=genotype->protein_pool[genotype->nproteins-1][0][0];
for(i=0;i<n_copies;i++)
gene_ids[i]=genotype->protein_pool[genotype->nproteins-1][1][i];
for(i=0;i<n_copies;i++)
{
ect_minus_one=exp(-genotype->protein_decay_rate[gene_ids[i]]*dt)-1.0;
integral+=(state->protein_synthesis_index[gene_ids[i]]*ect_minus_one/genotype->protein_decay_rate[gene_ids[i]]-
initial_protein_number[i]*ect_minus_one/genotype->protein_decay_rate[gene_ids[i]]+
state->protein_synthesis_index[gene_ids[i]]*dt);
}
return integral/saturate_protein_number;
}
/*
* return the instantaneous fitness given the current cell state and environment,
* also return the integrated fitness
*/
static float calc_fitness(float *integrated_fitness,
Genotype *genotype,
CellState *state,
float* number_of_selection_protein_bf_dt,
float dt)
{
int i;
float instantaneous_fitness=0.0; /* this is returned from the function */
float total_translation_rate = 0.0;
float dt_prime;
float cost_of_expression;
float Ne_next=state->protein_number[genotype->nproteins-1];
float Ne=0.0;
for(i=0;i<genotype->protein_pool[genotype->nproteins-1][0][0];i++)
Ne+=number_of_selection_protein_bf_dt[i];
/* compute the total cost of translation across all genes */
for(i=N_SIGNAL_TF; i < genotype->ngenes; i++)
{
total_translation_rate += (genotype->translation_rate[i]*(float)state->mRNA_aft_transl_delay_num[i]+
0.5*genotype->translation_rate[i]*(float)state->mRNA_under_transl_delay_num[i])*(float)genotype->locus_length[i]/236.0; //236 codon is the average length of yeast protein
}
cost_of_expression=total_translation_rate*c_transl;
switch (state->effect_of_effector)
{
case 'b': /* effector is beneficial!*/
if(Ne>Ne_next)//decrease in effector protein
{
if(Ne_next>=Ne_saturate) //too many effector throughout
{
*integrated_fitness =dt*(bmax-cost_of_expression);
}
else if(Ne<=Ne_saturate) // not enough effector throughout
{
*integrated_fitness = bmax*calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt, Ne_saturate)
-cost_of_expression*dt;
}
else // bf dt_prime, the benefit saturates
{
dt_prime=calc_tprime(genotype,state,number_of_selection_protein_bf_dt,dt,Ne_saturate,genotype->nproteins-1);
*integrated_fitness = bmax*dt_prime+bmax*(calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt, Ne_saturate)-
calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt_prime, Ne_saturate))-
cost_of_expression*dt;
}
}
else // increase in effector protein
{
if(Ne>=Ne_saturate) //too many effector throughout
{
*integrated_fitness =dt*(bmax-cost_of_expression);
}
else if(Ne_next<=Ne_saturate)// not enough effector throughout
{
*integrated_fitness = bmax*calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt, Ne_saturate)
-cost_of_expression*dt;
}
else //Aft dt_prime, the benefit saturates
{
dt_prime=calc_tprime(genotype,state,number_of_selection_protein_bf_dt,dt,Ne_saturate,genotype->nproteins-1);
*integrated_fitness = bmax*(dt-dt_prime)+bmax*calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt_prime, Ne_saturate)-
cost_of_expression*dt;
}
}
/* compute instantaneous fitness at t */
if (Ne_next < Ne_saturate)
instantaneous_fitness = bmax*Ne_next/Ne_saturate;
else
instantaneous_fitness = bmax;
break;
case 'd': /* effector is deleterious! */
if(Ne>Ne_next)//decrease in effector protein
{
if(Ne_next>=Ne_saturate) //too many effector throughout
{
*integrated_fitness =0.0-dt*cost_of_expression;
}
else if(Ne<=Ne_saturate) // not enough effector throughout
{
*integrated_fitness = bmax*dt-bmax*calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt, Ne_saturate)
-cost_of_expression*dt;
}
else // aft dt_prime, the benefit becomes positive
{
dt_prime=calc_tprime(genotype,state,number_of_selection_protein_bf_dt,dt,Ne_saturate,genotype->nproteins-1);
*integrated_fitness = bmax*(dt-dt_prime)-bmax*(calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt, Ne_saturate)-
calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt_prime, Ne_saturate))-
cost_of_expression*dt;
}
}
else // increase in effector protein
{
if(Ne>=Ne_saturate) //too many effector throughout
{
*integrated_fitness =0.0-dt*cost_of_expression;
}
else if(Ne_next<=Ne_saturate)// not enough effector throughout
{
*integrated_fitness = bmax*dt-bmax*calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt, Ne_saturate)
-cost_of_expression*dt;
}
else //Aft dt_prime, the benefit becomes zero
{
dt_prime=calc_tprime(genotype,state,number_of_selection_protein_bf_dt,dt,Ne_saturate,genotype->nproteins-1);
*integrated_fitness = bmax*dt_prime-bmax*calc_integral(genotype, state, number_of_selection_protein_bf_dt, dt_prime, Ne_saturate)-
cost_of_expression*dt;
}
}
if(Ne_next<Ne_saturate)
instantaneous_fitness = bmax - bmax/Ne_saturate*Ne_next;
else
instantaneous_fitness = 0.0;
break;
case 'l':
*integrated_fitness=(bmax-cost_of_expression)*dt;
instantaneous_fitness=bmax;
}
/* and instantaneous integrated rate */
instantaneous_fitness -= cost_of_expression;
/* return the instantaneous fitness */
return instantaneous_fitness;
}
/*Calculate probability of binding configurations*/
static void calc_TF_dist_from_all_BS(Genotype *genotype, CellState *state, int gene_id)
{
int max_N_binding_act=genotype->max_unhindered_sites[gene_id][1]+1; //Binding configurations can contain at most x activators, plus 1 type of configurations that don't have activators at all.
int max_N_binding_rep=genotype->max_unhindered_sites[gene_id][2]+1; //Binding configurations can contain at most y repressors, plus 1 type of configurations that don't have repressors at all.
double ratio_matrices[genotype->binding_sites_num[gene_id]+1][max_N_binding_rep][max_N_binding_act];
double sum;
register double product_of_freq;
register float cache_Kd;
int pos_of_last_record;
int pos_of_mat_nH;
int pos_next_record;
int i,j,m,n;
double temp;
AllTFBindingSites *BS_info;
float *protein_number;
protein_number=&(state->protein_number[0]);
BS_info=genotype->all_binding_sites[gene_id];
/* initializing matrices to all zeros */
for(i=0;i<max_N_binding_rep;i++)
{
for(j=0;j<max_N_binding_act;j++)
ratio_matrices[0][i][j]=0.0;
}
/* body of the forward algorithm*/
pos_next_record=0; //where in the ratio_matrices to put the next record
ratio_matrices[pos_next_record][0][0]=BS_info[0].Kd;
/*calculate distribution based on the first BS*/
if(genotype->protein_identity[BS_info[0].tf_id]==1) // if a activator binds to BS 0
ratio_matrices[pos_next_record][0][1]=protein_number[BS_info[0].tf_id];
else
ratio_matrices[pos_next_record][1][0]=protein_number[BS_info[0].tf_id];
/*keep calculating distribution from the remaining BS*/
for(m=1;m<genotype->binding_sites_num[gene_id];m++)
{
pos_next_record++;
/*If binding of site m blocks other binding sites*/
product_of_freq = protein_number[BS_info[m].tf_id];
if(BS_info[m].N_hindered!=0)
{
for(n=m-BS_info[m].N_hindered;n<=m-1;n++)
product_of_freq*=BS_info[n].Kd;
}
cache_Kd=BS_info[m].Kd;
/*Check whether m is a site of activator or repressor*/
switch(genotype->protein_identity[BS_info[m].tf_id])
{
case ACTIVATOR: // a BS of activators
if(m-BS_info[m].N_hindered!=0)//if binding of m does not block all of the BS evaluated before
{
/*find matrix(n-H)*/
pos_of_mat_nH=pos_next_record-BS_info[m].N_hindered-1;
/*find matrix(n)*/
pos_of_last_record=pos_next_record-1;
for(i=0;i<max_N_binding_rep;i++)
for(j=1;j<max_N_binding_act;j++)
ratio_matrices[pos_next_record][i][j]=cache_Kd*ratio_matrices[pos_of_last_record][i][j]+product_of_freq*ratio_matrices[pos_of_mat_nH][i][j-1];
for(i=0;i<max_N_binding_rep;i++)
ratio_matrices[pos_next_record][i][0]=cache_Kd*ratio_matrices[pos_of_last_record][i][0];
}
else
{
/*find matrix(n)*/
pos_of_last_record=pos_next_record-1; //find last record
for(i=0;i<max_N_binding_rep;i++)
for(j=0;j<max_N_binding_act;j++)
ratio_matrices[pos_next_record][i][j]=cache_Kd*ratio_matrices[pos_of_last_record][i][j];
ratio_matrices[pos_next_record][0][1]+=product_of_freq;
}
break;
case REPRESSOR: // a BS of repressors
if(m-BS_info[m].N_hindered!=0)
{
/*find matrix(n-H)*/
pos_of_mat_nH=pos_next_record-BS_info[m].N_hindered-1;
/*find matrix(n)*/
pos_of_last_record=pos_next_record-1;
/*Similar problem when pos_of_mat_nH=pos_next_record*/
for(i=1;i<max_N_binding_rep;i++)
for(j=0;j<max_N_binding_act;j++)
ratio_matrices[pos_next_record][i][j]=cache_Kd*ratio_matrices[pos_of_last_record][i][j]+product_of_freq*ratio_matrices[pos_of_mat_nH][i-1][j];
for(j=0;j<max_N_binding_act;j++)
ratio_matrices[pos_next_record][0][j]=cache_Kd*ratio_matrices[pos_of_last_record][0][j];
}
else
{
/*find matrix(n)*/
pos_of_last_record=pos_next_record-1;
for(i=0;i<max_N_binding_rep;i++)
for(j=0;j<max_N_binding_act;j++)
ratio_matrices[pos_next_record][i][j]=cache_Kd*ratio_matrices[pos_of_last_record][i][j];
ratio_matrices[pos_next_record][1][0]+=product_of_freq;
}
break;
}
}
sum=0.0;
for(i=0;i<max_N_binding_rep;i++)
for(j=0;j<max_N_binding_act;j++)
sum+=ratio_matrices[pos_next_record][i][j];
temp=0.0;
for(i=0;i<max_N_binding_rep;i++)
for(j=genotype->min_N_activator_to_transc[gene_id];j<max_N_binding_act;j++)
temp+=ratio_matrices[pos_next_record][i][j];
state->P_A[gene_id]=(float)(temp/sum);
temp=0.0;
for(i=1;i<max_N_binding_rep;i++)
for(j=0;j<max_N_binding_act;j++)
temp+=ratio_matrices[pos_next_record][i][j];
state->P_R[gene_id]=(float)(temp/sum);
temp=0.0;
for(j=genotype->min_N_activator_to_transc[gene_id];j<max_N_binding_act;j++)
temp+=ratio_matrices[pos_next_record][0][j];
state->P_A_no_R[gene_id]=(float)(temp / sum);
temp=0.0;
for(j=0;j<genotype->min_N_activator_to_transc[gene_id];j++)
temp+=ratio_matrices[pos_next_record][0][j];
state->P_NotA_no_R[gene_id]=(float)(temp/sum);
}
/*
* update both the protein concentration and current cell size *
*
*/
static void update_protein_number_and_fitness( Genotype *genotype,
CellState *state,
GillespieRates *rates,
float dt)
{
int i,j;
float ct, ect, one_minus_ect;
float N_effector_molecules_bf_dt[genotype->protein_pool[genotype->nproteins-1][0][0]];
float instantaneous_fitness = 0.0;
float integrated_fitness = 0.0;
/* store the numbers of the effector proteins encoded by each copy of gene before updating*/
for(i=0;i<genotype->protein_pool[genotype->nproteins-1][0][0];i++)
N_effector_molecules_bf_dt[i]=state->gene_specific_protein_number[genotype->protein_pool[genotype->nproteins-1][1][i]];
/* update protein numbers*/
for (i=N_SIGNAL_TF; i < genotype->ngenes; i++)
{
ct=genotype->protein_decay_rate[i]*dt;
ect = exp(-ct);
if (fabs(ct)<EPSILON) one_minus_ect=ct;
else one_minus_ect = 1.0-ect;
/* get the new protein concentration for this gene */
state->gene_specific_protein_number[i]=ect*state->gene_specific_protein_number[i]+state->protein_synthesis_index[i]*one_minus_ect;
}
/* now, use protein_pool to pool gene specific protein number*/
for(i=N_SIGNAL_TF;i<genotype->nproteins;i++)
{
state->protein_number[i]=0.0;
for(j=0;j<genotype->protein_pool[i][0][0];j++)
state->protein_number[i]+=state->gene_specific_protein_number[genotype->protein_pool[i][1][j]];
}
/* now find out the protein numbers at end of dt interval and compute instantaneous and cumulative fitness */
instantaneous_fitness = calc_fitness(&integrated_fitness,
genotype,
state,
N_effector_molecules_bf_dt,
dt);
/* update cumulative fitness at the end of dt*/
state->cumulative_fitness += integrated_fitness;
/* update the instantaneous fitness at the end of dt */
state->instantaneous_fitness = instantaneous_fitness;
}
/*
*
* Functions that handle each possible Gillespie event
*
*/
static int Gillespie_event_mRNA_decay(GillespieRates *rates, CellState *state, Genotype *genotype, RngStream RS)
{
int gene_id;
float x;
int mRNA_id;
while(1)/*in case of numerical error*/
{
x=RngStream_RandU01(RS)*rates->total_mRNA_decay_rate;
gene_id=N_SIGNAL_TF-1;
/* loop through mRNA products, to choose the mRNA with the
proportionally higher decay rate */
while (gene_id < genotype->ngenes-1 && x > 0.0)
{
gene_id++;
x-= rates->mRNA_decay_rate[gene_id];
}
/*rarely, numerical error picks up a gene that has no mRNA at all*/
if((state->mRNA_aft_transl_delay_num[gene_id]+state->mRNA_under_transl_delay_num[gene_id])>=1)
break;
}
/* assume mRNAs are equally likely to be degraded */
x = RngStream_RandInt(RS,1,state->mRNA_aft_transl_delay_num[gene_id] + state->mRNA_under_transl_delay_num[gene_id]);
/* decay mRNA in cytoplasm */
if (x <= state->mRNA_aft_transl_delay_num[gene_id])
{
/* remove the mRNA from the cytoplasm count */
(state->mRNA_aft_transl_delay_num[gene_id])--;
/*update protein synthesis rate*/
state->protein_synthesis_index[gene_id] = (float)state->mRNA_aft_transl_delay_num[gene_id]*genotype->translation_rate[gene_id]/genotype->protein_decay_rate[gene_id];
if(genotype->which_protein[gene_id]==genotype->nproteins-1)
return DO_NOTHING;
else // an mRNA of transcription factor is degraded, which can cause fluctuation in transcription factor concentrations.
return gene_id;
}
else
{
/* decay mRNA in process of translation initialization */
mRNA_id = RngStream_RandInt(RS,0,state->mRNA_under_transl_delay_num[gene_id]-1);
/* delete this fixed event: this mRNA will never be translated */
delete_fixed_event(gene_id, mRNA_id, &(state->mRNA_transl_init_time_end_head), &(state->mRNA_transl_init_time_end_tail));
/* remove the mRNA from the count */
(state->mRNA_under_transl_delay_num[gene_id])--;
return DO_NOTHING;
}
}
static void Gillespie_event_repressed_to_intermediate(GillespieRates *rates, CellState *state, Genotype *genotype, RngStream RS)
{
int gene_id;
float x;
while(1)
{
x= RngStream_RandU01(RS)*rates->total_repressed_to_intermediate_rate;
gene_id=N_SIGNAL_TF-1;
while(gene_id<genotype->ngenes-1 && x>0.0)
{
gene_id++;
x-=rates->repressed_to_intermediate_rate[gene_id];
}
if(rates->repressed_to_intermediate_rate[gene_id]>0.0)
break;
}
/* set state */
state->transcriptional_state[gene_id]=INTERMEDIATE;
}
static void Gillespie_event_intermediate_to_repressed(GillespieRates *rates, CellState *state, Genotype *genotype, RngStream RS)
{
int gene_id;
float x;
while(1)
{
x= RngStream_RandU01(RS)*rates->total_intermediate_to_repressed_rate;
gene_id=N_SIGNAL_TF-1;
/* choose a particular gene copy to change state */
while(gene_id<genotype->ngenes-1 && x>0.0)
{
gene_id++;
x-=rates->intermediate_to_repressed_rate[gene_id];
}
if(rates->intermediate_to_repressed_rate[gene_id]>0.0)
break;
}
/* set state */
state->transcriptional_state[gene_id]=REPRESSED;
}
static void Gillespie_event_intermediate_to_active(GillespieRates *rates, CellState *state, Genotype *genotype, RngStream RS)
{
float x;
int gene_id;
while(1)
{
x= RngStream_RandU01(RS)*rates->total_intermediate_to_active_rate;
gene_id=N_SIGNAL_TF-1;
/* choose a particular gene copy to change state */
while(gene_id<genotype->ngenes-1 && x>0.0)
{
gene_id++;
x-=rates->intermediate_to_active_rate[gene_id];
}
if(rates->intermediate_to_active_rate[gene_id]>0.0)
break;
}
/* set state */
state->transcriptional_state[gene_id] =ACTIVE;
}
static void Gillespie_event_active_to_intermediate(Genotype *genotype, CellState *state,GillespieRates *rates, RngStream RS)
{
int gene_id;
float x;
while(1)
{
x=RngStream_RandU01(RS)*rates->total_active_to_intermediate_rate;
gene_id=N_SIGNAL_TF-1;
while(gene_id < genotype->ngenes-1 && x>0.0)
{
gene_id++;
x -= rates->active_to_intermediate_rate[gene_id];
}
if(rates->active_to_intermediate_rate[gene_id]>0.0)
break;
}
state->transcriptional_state[gene_id]=INTERMEDIATE;
}
static void Gillespie_event_transcription_init(GillespieRates *rates, CellState *state, Genotype *genotype, float dt, RngStream RS)
{
int gene_id;
int x;
float candidate_t;
int concurrent;
gene_id=N_SIGNAL_TF-1;
x=RngStream_RandInt(RS,1,rates->total_N_gene_transcript_initiated);
while(gene_id<genotype->ngenes-1 && x>0)
{
gene_id++;
x-=rates->transcript_initiation_state[gene_id];
}
/* now that transcription of gene has been initiated,
* we add the timepoint at which the transcription ends,
* which is dt+time-of-transcription from now */
candidate_t=state->t+dt+(float)genotype->locus_length[gene_id]/TRANSCRIPTION_ELONGATION_RATE+TRANSCRIPTION_TERMINATION_TIME;
concurrent=check_concurrence(state, candidate_t);
while(concurrent)//if the time to update overlaps with existing events, add a tiny offset
{
candidate_t+=TIME_OFFSET;
concurrent=check_concurrence(state, candidate_t);
}
add_fixed_event(gene_id, candidate_t,&(state->mRNA_transcr_time_end_head), &(state->mRNA_transcr_time_end_tail));
/* increase the number mRNAs being transcribed */
(state->mRNA_under_transc_num[gene_id])++;
}
/*
* END
* Functions that handle each possible Gillespie event
*/
/* do a fixed event that occurs in current t->dt window */
static int do_fixed_event(Genotype *genotype,
CellState *state,
GillespieRates *rates,
Environment *env,
Phenotype *timecourse,
float *dt,
int event)
{
int i, return_value;
return_value=DO_NOTHING;
switch (event)
{
case 1: /* a transcription event ends */
fixed_event_end_transcription(dt, state, rates, genotype);
break;
case 2: /* a translation initialization event ends */
return_value=fixed_event_end_translation_init(genotype, state, rates, dt);
state->cell_activated=1;
break;
case 3: /* turn signal off*/
*dt = state->signal_off_head->time - state->t;
update_protein_number_and_fitness(genotype, state, rates, *dt);
delete_fixed_event_from_head(&(state->signal_off_head),&(state->signal_off_tail));
if(env->fixed_effector_effect)
state->effect_of_effector=env->effect_of_effector_aft_burn_in;
else
state->effect_of_effector='d';
state->protein_number[N_SIGNAL_TF-1]=env->signal_off_strength;
return_value=SUDDEN_SIGNAL_CHANGE;
break;
case 4: /*turn signal on*/
*dt = state->signal_on_head->time - state->t;
update_protein_number_and_fitness(genotype, state, rates, *dt);
delete_fixed_event_from_head(&(state->signal_on_head),&(state->signal_on_tail));
state->protein_number[N_SIGNAL_TF-1]=env->signal_on_strength;
if(env->fixed_effector_effect)
state->effect_of_effector=env->effect_of_effector_aft_burn_in;
else
state->effect_of_effector='b';
return_value=SUDDEN_SIGNAL_CHANGE;
break;
case 5: /* finishing burn-in developmental simulation*/
*dt=state->burn_in_growth_rate_head->time-state->t;
update_protein_number_and_fitness(genotype, state, rates, *dt);
state->cumulative_fitness_after_burn_in=state->cumulative_fitness;
delete_fixed_event_from_head(&(state->burn_in_growth_rate_head),&(state->burn_in_growth_rate_tail));
if(env->signal_on_aft_burn_in==1)
state->protein_number[N_SIGNAL_TF-1]=env->signal_on_strength;
else
state->protein_number[N_SIGNAL_TF-1]=env->signal_off_strength;