Supporting Information Tom Brown Supervisors: Dr Andrew Angel, Prof. Jane Mellor Project 1

Transcription

1 Supporting Information Tom Brown Supervisors: Dr Andrew Angel, Prof. Jane Mellor Project 1 Steady State Test To determine after how many time steps the simulated system reached a steady state, the system was run for a varying number of time steps and compared to a long-run simulation. Under a steady state assumption, the distribution of nuclear and cytoplasmic transcripts would not change if any more time steps were simulated. After 5 time steps the system produced distributions that were identical to a the system after having undergone 1, time steps. Therefore it was assumed that the system had reached a steady state after 5 time steps and this number was used for further simulations (Fig. S1)..4 5 iterations - nuclear data.15 5 iterations - cytoplasmic data iterations - nuclear data iterations - cytoplasmic data iterations - nuclear data iterations - cytoplasmic data iterations - nuclear data iterations - cytoplasmic data Fig. S 1: A test to determine when the simulated system reached a steady state. Shown are the simulated distributions of nuclear and cytoplasmic transcripts. After 5 and 1 iterations the system has not yet reached a steady state, whereas after 5 iterations the system can be assumed to be in a steady state. This was further tested by comparison to a long-run simulation with 1, simulations. Unweighted Metric To determine whether the changes in parameter values described were consistent when using a different fitting metric, MCMC parameter search simulations were repeated with an unweighted χ 2 statistic. For O i observed counts and E i 1

2 expected counts from the simulated distributions, the χ 2 statistic used was given by: N (O i E i ) 2 i= wheren isthetotalnumberofnuclearandcytoplasmicdatapointswith5ormorecounts(cf. Searching the parameter space - main document). This statistic was used to see which distributions fit the data points in the nucleus and cytoplasm where each data point was equally weighted, rather than the nuclear and cytoplasmic data as a whole having equal weight. The fits obtained using this metric show better fits to the cytoplasmic data as there are consistently many more data points with 5 or more counts in the cytoplasm Fig. S2. Given the poor fits that are then obtained in the nucleus, it is unsurprising that the relationships between the initiation rate and the on frequency is not as clear with this metric (Fig. S4) and the similarly for the nuclear rates (Fig. S3B). However, one can still see a separation between the gradient of the ADH4 and SH9 transcription initiation frequencies (Fig. S3A) with the ADH4 strain having a higher transcription initiation frequency than the antisense-less SH9 strain. The change in nuclear rates is also repeated with this new metric (Fig. S3C) with nuclear transcripts spending less tie in the nucleus in the presence of antisense transcription (ADH4) compared to the strain without antisense transcription (SH9). E i Real Data - Nucleus Simulated Data - Nucleus Real Data - Nucleus Simulated Data - Nucleus Real Data - Cytoplasm Simulated Data - Cytoplasm Real Data - Cytoplasm Simulated Data - Cytoplasm A B Fig. S 2: Fits to the nuclear and cytoplasmic data obtained via MCMC parameter space searches using an unweighted χ 2 statistic. Fits here are to the GAL1 ADH4 (A) and SH9, antisense-less, (B) data. 2

3 Initiation (min -1 ) Transcription initiation frequencies ADH4 SH /On A Elong x Exp (min -2 ) ADH4 SH9 Nuclear rates Elong + Exp (min -1 ) B Transcript initiation frequency (min -1 ) Transcription initiation and nuclear rates ADH4 SH Elong x Exp / (Elong + Exp) (min -1 ) C Fig. S 3: Detected changes in the transcription initiation frequencies ( ) (A) and time transcripts spent in the nucleus (B & C) between the two strains. A shows the increase in the ratio:, the transcription initiation frequency in the presence of init on on+off antisense transcription (ADH4), demonstrated by the increase in gradient of the determined parameter values. B & C show the increase in nuclear rate, the rate at which nuclear transcripts go from starting transcription to being exported, in the presence of antisense transcription (ADH4). 3 ADH4 transcription initiation, mode: SH9 transcription initiation, mode: Transcription Initiation Rate (min -1 ) Transcription Initiation Rate (min -1 ) A ( Fig. S 4: Histograms of the determined values of the transcription initiation rate, given by: B init on on+off ). The transcription initiation frequency of the antisense-less strain, SH9, was found to be lower (B) than the strain with antisense transcription, ADH4 (A). 3

4 Selected Code MCMC parameter search #include <stdio.h> #include <stdlib.h> #include <math.h> #include <mpi.h> #include <time.h> #define PI #define int_numtimesteps 5 #define int_numiterations 3 // This will be multiplied by the number of worker processors #define flt_standdev.2 #define flt_degrate.45 // Rate at which cytoplasmic transcripts are degraded #define int_numparametersteps 1 // READ ME!!!! // To run this code, compile as follows: // > mpicc -lm -O3 complete_systemsearch.c -o complete_systemsearch // > mpirun -np # complete_systemsearch.exe <Nucleus data file> <Cytoplasm Data file> <Output data filename> // // The script is set up with one root node distributing simulations to other worker // nodes after randomly sampling new parameters to be tested. The script as it // currently stands will not work if run on one processor. // Main function int main(int argc,char* argv[]){ if (argc < 3){ printf("incorrect number of input arguments (Pass file names (nucleus_data, cytoplasm_data, output_file) to function on command line)\n"); abort(); // Initialise the MPI environment int rank, worker_rank, n_procs; MPI_Init (&argc,&argv); MPI_Comm_rank(MPI_COMM_WORLD, &rank); MPI_Comm_size(MPI_COMM_WORLD, &n_procs); MPI_Status status; // Open file to write parameters to FILE *fp; fp = fopen(argv[3],"w"); fprintf(fp,"iteration_no\tchi_square\ton_rate\toff_rate\tinitiation_rate\telongation_rate\texport_rate\tdegradation_rate\n"); int int_rootfinished,int_workerfinished; int i,j,k; int int_currentiteration; double flt_newmeasure; // These values will assess the fit of the parameters double flt_currentmeasure = 1; // Array for storing histogram of results double fltarr_localnucresults[5], fltarr_rootnucresults[5]; double fltarr_localcytresults[5], fltarr_rootcytresults[5]; double fltarr_globalnucresults[5]; double fltarr_globalcytresults[5]; int int_nucleusresult; int int_cytoplasmresult; int int_currenttimestep; // Concentrations are as follows: // : Gene promoter state, = off, 1 = on // 1: Partial transcript undergoing transcription 4

5 // 2: Complete transcript in nucleus // 3: Complete transcript in cytoplasm int intarr_currentconcentrations[4]; int intarr_newconcentrations[4]; double flt_currenttime; double flt_newtime; int intarr_conc[4]; double flt_time; double fltarr_propensities[6]; double flt_totalpropensity; double fltarr_cumulpropensities[6]; double flt_timerand; double flt_tau; double flt_proposedtime; double flt_rand2; double flt_onrate, flt_offrate; // Rate at which gene moves between off and on transcription state double flt_initiationrate; // Rate at which transcription is initiated double flt_elongationrate; // Rate at which transcription elongation takes place, determining time for complete RNA molecule to be transcribed double flt_exportrate; // Rate at which transcripts are exported from the nucleus double flt_mcmcurand1,flt_mcmcurand2,flt_mcmcurand3,flt_mcmcurand4,flt_mcmcurand5,flt_mcmcurand6; double flt_mcmcnrand1,flt_mcmcnrand2,flt_mcmcnrand3,flt_mcmcnrand4,flt_mcmcnrand5,flt_mcmcnrand6; double flt_comparerand; double flt_proposedon; double flt_proposedoff; double flt_proposedinit; double flt_proposedelong; double flt_proposedexp; double fltarr_proposedparameters[6]; double fltarr_currentparameters[6]; double flt_totalnuc; double fltarr_normnucresults[5]; double fltarr_cytresults[5]; double flt_totalcyt; double fltarr_normcytresults[5]; int int_currentparameterstep; double flt_chisq; double fltarr_cumulnucdata[5]; double fltarr_cumulcytodata[5]; double fltarr_cumulnucresults[5]; double fltarr_cumulcytoresults[5]; // Seed random numbers to be different for each processor srand(time(null)+rank); // Read nucleus and cytoplasm transcript data from file double fltarr_nucleusdata[5],fltarr_cytodata[5]; double flt_totalnucdata = ; double flt_totalcytdata = ; double flt_nucbins =, flt_cytbins = ; int int_fileline; char chararr_nuc[128],chararr_cyt[128]; int int_linelength = 128; FILE *nucleus_file, *cyto_file; nucleus_file = fopen(argv[1],"r"); cyto_file = fopen(argv[2],"r"); for (int_fileline=;int_fileline<5;int_fileline++){ fgets(chararr_nuc, int_linelength, nucleus_file); fltarr_nucleusdata[int_fileline] = atof(chararr_nuc); fgets(chararr_cyt, int_linelength, cyto_file); fltarr_cytodata[int_fileline] = atof(chararr_cyt); flt_totalnucdata += fltarr_nucleusdata[int_fileline]; flt_totalcytdata += fltarr_cytodata[int_fileline]; // Count number of bins included in Chi-Square statistic to perform the weighting if (fltarr_nucleusdata[int_fileline] >= 5){ flt_nucbins ++; if (fltarr_cytodata[int_fileline] >= 5){ flt_cytbins ++; 5

6 // Set the initial values of the constant parameters all in units of /min flt_onrate =.5; flt_offrate =.5; flt_initiationrate =.5; flt_elongationrate =.5; flt_exportrate =.5; for (int_currentparameterstep=;int_currentparameterstep<int_numparametersteps;int_currentparameterstep++){ if (rank == ){ //Do root tasks for (j=;j<5;j++){ fltarr_globalnucresults[j] = ; fltarr_globalcytresults[j] = ; // Simulate 6 standard normal random numbers via Box-Muller transform flt_mcmcurand1 = (double)rand()/(rand_max); flt_mcmcurand2 = (double)rand()/(rand_max); flt_mcmcurand3 = (double)rand()/(rand_max); flt_mcmcurand4 = (double)rand()/(rand_max); flt_mcmcurand5 = (double)rand()/(rand_max); flt_mcmcurand6 = (double)rand()/(rand_max); flt_mcmcnrand1 = sqrt(-2*log(flt_mcmcurand1))*cos(2*pi*flt_mcmcurand2); flt_mcmcnrand2 = sqrt(-2*log(flt_mcmcurand2))*sin(2*pi*flt_mcmcurand1); flt_mcmcnrand3 = sqrt(-2*log(flt_mcmcurand3))*cos(2*pi*flt_mcmcurand4); flt_mcmcnrand4 = sqrt(-2*log(flt_mcmcurand4))*sin(2*pi*flt_mcmcurand3); flt_mcmcnrand5 = sqrt(-2*log(flt_mcmcurand5))*cos(2*pi*flt_mcmcurand6); // Use normal random numbers to sample new parameters flt_proposedon = fabs(flt_onrate + flt_mcmcnrand1 * flt_standdev); flt_proposedoff = fabs(flt_offrate + flt_mcmcnrand2 * flt_standdev); flt_proposedinit = fabs(flt_initiationrate + flt_mcmcnrand3 * flt_standdev); flt_proposedelong = fabs(flt_elongationrate + flt_mcmcnrand4 * flt_standdev); flt_proposedexp = fabs(flt_exportrate + flt_mcmcnrand5 * flt_standdev); // Prepare array to be passed to worker processors fltarr_proposedparameters[] = flt_proposedon; fltarr_proposedparameters[1] = flt_proposedoff; fltarr_proposedparameters[2] = flt_proposedinit; fltarr_proposedparameters[3] = flt_proposedelong; fltarr_proposedparameters[4] = flt_proposedexp; fltarr_proposedparameters[5] = flt_degrate; for (worker_rank = 1;worker_rank<n_procs;worker_rank++){ // Send proposed parameters to the worker processors MPI_Send(fltarr_proposedParameters,6,MPI_DOUBLE,worker_rank,,MPI_COMM_WORLD); for (worker_rank = 1;worker_rank<n_procs;worker_rank++){ for (j=;j<5;j++){ fltarr_rootnucresults[j] = ; fltarr_rootcytresults[j] = ; // Receive the simulated nuclear and cytoplasmic data from the worker processors MPI_Recv(fltarr_localNucResults,5,MPI_DOUBLE,worker_rank,1,MPI_COMM_WORLD,&status); MPI_Recv(fltarr_localCytResults,5,MPI_DOUBLE,worker_rank,2,MPI_COMM_WORLD,&status); for (j=;j<5;j++){ fltarr_globalnucresults[j] += fltarr_localnucresults[j]; fltarr_globalcytresults[j] += fltarr_localcytresults[j]; flt_totalnuc = ; flt_totalcyt = ; // Normalise the values in the results to give frequency for (j=;j<5;j++){ flt_totalnuc += fltarr_globalnucresults[j]; flt_totalcyt += fltarr_globalcytresults[j]; // Ensure simulated data is on the same scale as the experimental data for (j=;j<5;j++){ fltarr_normnucresults[j] = flt_totalnucdata * (fltarr_globalnucresults[j]/flt_totalnuc); fltarr_normcytresults[j] = flt_totalcytdata * (fltarr_globalcytresults[j]/flt_totalcyt); // If simulated data give transcript values that are too high, there will be no // results less than 5, so will divide by zero causing NaN. Make the Chi-Square 6

7 // value incredibly large so that these parameters will not be accepted for (j=;j<5;j++){ if (isnan(fltarr_normnucresults[j])){ fltarr_normnucresults[j] = ; else if (isnan(fltarr_normcytresults[j])){ fltarr_normcytresults[j] = ; // Calculate un-weighted Chi-Squared statistic, ignoring data with fewer than 5 experimental results flt_chisq = ; for (j = ;j<5;j++){ if ((fltarr_nucleusdata[j] >= 5)){ if (fltarr_normnucresults[j] == ){ flt_chisq += 1; else { flt_chisq += ((fltarr_normnucresults[j]-fltarr_nucleusdata[j]) * (fltarr_normnucresults[j]-fltarr_nucleusdata[j]))/(fltarr_normnucresults[j if ((fltarr_cytodata[j] >= 5)){ if (fltarr_normcytresults[j] == ){ flt_chisq += 1; else { flt_chisq +=((fltarr_normcytresults[j]-fltarr_cytodata[j]) * (fltarr_normcytresults[j]-fltarr_cytodata[j]))/(fltarr_normcytresults[j]); if (flt_chisq == ){ flt_chisq = 1; flt_newmeasure = flt_chisq; // Compare the measures from the previous parameters with the proposed parameters and accept/reject flt_comparerand = (double)rand()/(rand_max); if ((.5 + (.5 * flt_comparerand)) < (flt_currentmeasure/flt_newmeasure)){ // Accept new parameters flt_onrate = flt_proposedon; flt_offrate = flt_proposedoff; flt_initiationrate = flt_proposedinit; flt_elongationrate = flt_proposedelong; flt_exportrate = flt_proposedexp; flt_currentmeasure = flt_newmeasure; // Print chi-square every 1 parameter jumps to monitor progress if (int_currentparameterstep%1 == ){ printf("current iteration: %d, Current rank: %f\n",int_currentparameterstep,flt_currentmeasure); // Write the parameters from this timestep to file fprintf(fp,"%d\t%.1lf\t%.1f\t%.1f\t%.1f\t%.1f\t%.1f\t%.1f\n",int_currentparameterstep,flt_currentmeasure,flt_onrate,flt_offrate,flt_initia else if (rank > ) { // Do worker tasks for (j=;j<5;j++){ fltarr_localnucresults[j] = ; fltarr_localcytresults[j] = ; fltarr_globalnucresults[j] = ; fltarr_globalcytresults[j] = ; //Receive proposed parameter values from the root processor MPI_Recv(fltarr_currentParameters,6,MPI_DOUBLE,,,MPI_COMM_WORLD,&status); // Run the Gillespie simulation multiple times for (int_currentiteration=;int_currentiteration<int_numiterations;int_currentiteration++){ for (k=;k<4;k++){ intarr_newconcentrations[k] = ; flt_newtime = ; flt_currenttime = ; // Run the single timestep multiple times to perform the Gillespie simulation for (int_currenttimestep=;int_currenttimestep<int_numtimesteps;int_currenttimestep++){ for (k=;k<4;k++){ intarr_currentconcentrations[k] = intarr_newconcentrations[k]; 7

8 //flt_currenttime = flt_newtime; // Calculate the propensities for the current reaction // Promoter site switches from off to on configuration fltarr_propensities[] = fltarr_currentparameters[]*(1-intarr_currentconcentrations[]); // Promoter site switches from on to off configuration fltarr_propensities[1] = fltarr_currentparameters[1]*intarr_currentconcentrations[]; // Gene begins to be transcribed fltarr_propensities[2] = fltarr_currentparameters[2]*intarr_currentconcentrations[]; // Partial transcript is given a finishing time for transcription fltarr_propensities[3] = fltarr_currentparameters[3]*intarr_currentconcentrations[1]; // Transcript is exported from the nucleus to the cytoplasm fltarr_propensities[4] = fltarr_currentparameters[4]*intarr_currentconcentrations[2]; // Transcript is degraded in the cytoplasm fltarr_propensities[5] = fltarr_currentparameters[5]*intarr_currentconcentrations[3]; // Calculate cumulatve propensity array flt_totalpropensity = ; for (i=;i<6;i++){ flt_totalpropensity += fltarr_propensities[i]; fltarr_cumulpropensities[] = fltarr_propensities[]/flt_totalpropensity; for (i=1;i<6;i++){ fltarr_cumulpropensities[i] = fltarr_cumulpropensities[i-1] + fltarr_propensities[i]/flt_totalpropensity; flt_rand2 = (double)rand()/(rand_max); // Establish which reaction occurred and update the current concentrations if (flt_rand2 <= fltarr_cumulpropensities[]){ // Promoter changes from off to on configuration intarr_newconcentrations[] = intarr_currentconcentrations[]+1; intarr_newconcentrations[1] = intarr_currentconcentrations[1]; intarr_newconcentrations[2] = intarr_currentconcentrations[2]; intarr_newconcentrations[3] = intarr_currentconcentrations[3]; else if (flt_rand2 <= fltarr_cumulpropensities[1]){ // Promoter changes from on to off configuration intarr_newconcentrations[] = intarr_currentconcentrations[]-1; intarr_newconcentrations[1] = intarr_currentconcentrations[1]; intarr_newconcentrations[2] = intarr_currentconcentrations[2]; intarr_newconcentrations[3] = intarr_currentconcentrations[3]; else if (flt_rand2 <= fltarr_cumulpropensities[2]){ intarr_newconcentrations[] = intarr_currentconcentrations[]; // New partial transcript begins the transcription process intarr_newconcentrations[1] = intarr_currentconcentrations[1]+1; intarr_newconcentrations[2] = intarr_currentconcentrations[2]; intarr_newconcentrations[3] = intarr_currentconcentrations[3]; else if (flt_rand2 <= fltarr_cumulpropensities[3]){ intarr_newconcentrations[] = intarr_currentconcentrations[]; // Partial transcript finishes transcribing intarr_newconcentrations[1] = intarr_currentconcentrations[1]-1; // Completed transcript enters the nucleus intarr_newconcentrations[2] = intarr_currentconcentrations[2]+1; intarr_newconcentrations[3] = intarr_currentconcentrations[3]; else if (flt_rand2 <= fltarr_cumulpropensities[4]){ intarr_newconcentrations[] = intarr_currentconcentrations[]; intarr_newconcentrations[1] = intarr_currentconcentrations[1]; // Transcript is exported from the nucleus intarr_newconcentrations[2] = intarr_currentconcentrations[2]-1; // Transcript enters the cytoplasm intarr_newconcentrations[3] = intarr_currentconcentrations[3]+1; else if (flt_rand2 <= fltarr_cumulpropensities[5]){ intarr_newconcentrations[] = intarr_currentconcentrations[]; intarr_newconcentrations[1] = intarr_currentconcentrations[1]; intarr_newconcentrations[2] = intarr_currentconcentrations[2]; // Transcript is degraded in the cytoplasm intarr_newconcentrations[3] = intarr_currentconcentrations[3]-1; else { 8

9 // Occasional rounding error produces cumulative propensities that do not add up to 1 // In these cases, no reaction occurs. Go back to original time printf("error, no reaction final propensity: %.2lf random number: %.2lf\n",fltarr_cumulPropensities[5],flt_rand2); intarr_newconcentrations[] = intarr_currentconcentrations[]; intarr_newconcentrations[1] = intarr_currentconcentrations[1]; intarr_newconcentrations[2] = intarr_currentconcentrations[2]; intarr_newconcentrations[3] = intarr_currentconcentrations[3]; //flt_newtime = flt_currenttime; // Count any partially formed or complete transcript in the final result int_nucleusresult = intarr_newconcentrations[1] + intarr_newconcentrations[2]; int_cytoplasmresult = intarr_newconcentrations[3]; // Update the result histogram if (int_nucleusresult < 5){ fltarr_localnucresults[int_nucleusresult]++; if (int_nucleusresult < 5){ fltarr_localcytresults[int_cytoplasmresult]++; // Send simulated results back to root processor MPI_Send(fltarr_localNucResults,5,MPI_DOUBLE,,1,MPI_COMM_WORLD); MPI_Send(fltarr_localCytResults,5,MPI_DOUBLE,,2,MPI_COMM_WORLD); if (rank == ){ fclose(fp); printf("file closed\n"); int_rootfinished = 1; for (j=1;j<n_procs;j++){ MPI_Send(&int_rootFinished,1,MPI_INT,j,3,MPI_COMM_WORLD); int MPI_Finalize (); else{ int_workerfinished = ; // Ensure process finalizes after the file has been completely written to avoid file corruption MPI_Recv(&int_workerFinished,1,MPI_INT,,3,MPI_COMM_WORLD,&status); int MPI_Finalize (); Degradation rate simulations #include <stdio.h> #include <stdlib.h> #include <math.h> #include <time.h> #include "omp.h" // READ ME!! // This file is to be compiled and run as follows: // gcc -fopenmp -lm -O3 calculate_degrate.c -o calculate_degrate // //./calculate_degrate // // // The names of the data and results files are included in the code. Ensure this // script is run in the same directory as the relevant data files void main(int argc, char* argv[]){ // Extract Cytoplasmic data from file FILE *ADH4_7minCytFile; 9

10 FILE *ADH4_15minCytFile; FILE *SH9_7minCytFile; FILE *SH9_15minCytFile; ADH4_7minCytFile = fopen("14514_adh4_7mindch2cyto.txt","r"); ADH4_15minCytFile = fopen("14514_adh4_15mindch2cyto.txt","r"); SH9_7minCytFile = fopen("14514_sh9_7mindch2cyto.txt","r"); SH9_15minCytFile = fopen("14514_sh9_15mindch2cyto.txt","r"); double ADH4_7minCytData[5], ADH4_15minCytData[5]; double SH9_7minCytData[5], SH9_15minCytData[5]; //Read raw transcript data from file char chararr_buffer[128]; int int_linelength = 128; int int_currentline; for (int_currentline=;int_currentline<5;int_currentline++){ fgets(chararr_buffer,int_linelength,adh4_7mincytfile); ADH4_7minCytData[int_currentLine] = atof(chararr_buffer); for (int_currentline=;int_currentline<5;int_currentline++){ fgets(chararr_buffer,int_linelength,adh4_15mincytfile); ADH4_15minCytData[int_currentLine] = atof(chararr_buffer); for (int_currentline=;int_currentline<5;int_currentline++){ fgets(chararr_buffer,int_linelength,sh9_7mincytfile); SH9_7minCytData[int_currentLine] = atof(chararr_buffer); for (int_currentline=;int_currentline<5;int_currentline++){ fgets(chararr_buffer,int_linelength,sh9_15mincytfile); SH9_15minCytData[int_currentLine] = atof(chararr_buffer); fclose(adh4_7mincytfile); fclose(adh4_15mincytfile); fclose(sh9_7mincytfile); fclose(sh9_15mincytfile); //Normalise the 15 minute data to the 7 minute data double total_adh47min, total_adh415min, total_sh97min, total_sh915min; int i; total_adh47min = ; total_adh415min = ; total_sh97min = ; total_sh915min = ; for (i=;i<5;i++){ total_adh47min += ADH4_7minCytData[i]; total_adh415min += ADH4_15minCytData[i]; total_sh97min += SH9_7minCytData[i]; total_sh915min += SH9_15minCytData[i]; for (i=;i<5;i++){ ADH4_15minCytData[i] = floor(((adh4_15mincytdata[i] * total_adh47min)/total_adh415min) +.5); SH9_15minCytData[i] = floor(((sh9_15mincytdata[i] * total_sh97min)/total_adh415min) +.5); FILE *ADH4degOutput_file; FILE *SH9degOutput_file; ADH4degOutput_file = fopen("adh4gal1deg_rates.txt","w"); SH9degOutput_file = fopen("sh9gal1deg_rates.txt","w"); int iteration_no; double deg_rate, exp_rate; int bin, cell; double ADH4_cytTranscripts7min, ADH4_cytTranscripts15min; double SH9_cytTranscripts7min, SH9_cytTranscripts15min; // Calculate total number of transcripts in the nuclei and cytoplasms of all cells for (bin=1;bin<49;bin++){ ADH4_cytTranscripts7min += bin*adh4_7mincytdata[bin]; ADH4_cytTranscripts15min += bin*adh4_15mincytdata[bin]; SH9_cytTranscripts7min += bin*sh9_7mincytdata[bin]; 1

11 SH9_cytTranscripts15min += bin*sh9_15mincytdata[bin]; double deg_propensity; double current_time, tau, time_rand; double current_cyttranscripts; int hist_bin; double ADH4_degHistogram[1]; //Simulate the cytoplasmic degradation for all cells whilst varying the degradation rates #pragma omp parallel default(none) private (i, hist_bin, time_rand, iteration_no, deg_rate, current_cyttranscripts, tau, current_time, deg_propensity { srand((int)time(null) + omp_get_thread_num()); #pragma omp for for (iteration_no=;iteration_no<2;iteration_no++){ for (deg_rate=.1;deg_rate<.2;deg_rate+=.1){ current_time = ; current_cyttranscripts = ADH4_cytTranscripts7min; //Simulate 8 minutes of reactions while (current_time < 8){ // Calculate the propensities of a reaction occurring deg_propensity = deg_rate*current_cyttranscripts; time_rand = (double)rand()/(rand_max); tau = (1/(deg_propensity))*log(1/time_rand); current_time += tau; current_cyttranscripts = current_cyttranscripts - 1; if (current_cyttranscripts == ){ break; //If end results match the 15 minute data, record the degradation and export rates if (current_cyttranscripts == ADH4_cytTranscripts15min){ #pragma omp critical { fprintf(adh4degoutput_file,"%f\n",deg_rate); //Group rates into 1 bins hist_bin = (int)((deg_rate - fmod(deg_rate,.2))/.2); ADH4_degHistogram[hist_bin] ++; if (iteration_no%25 == ){ printf("%d ADH4 iterations completed\n",iteration_no); #pragma omp barrier printf("adh4 simulations completed\n"); fclose(adh4degoutput_file); //Repeat the process for the SH9 data double SH9_degHistogram[1]; for (i=;i<1;i++){ SH9_degHistogram[i] = ; #pragma omp parallel default(none) private (i, hist_bin, time_rand, iteration_no, deg_rate, current_cyttranscripts, tau, current_time, deg_propensity { srand((int)time(null) + omp_get_thread_num()); #pragma omp for for (iteration_no=;iteration_no<2;iteration_no++){ for (deg_rate=.1;deg_rate<.2;deg_rate+=.1){ current_time = ; current_cyttranscripts = SH9_cytTranscripts7min; //Simulate 8 minutes of reactions while (current_time < 8){ // Calculate the propensities of a reaction occurring 11

12 deg_propensity = deg_rate*current_cyttranscripts; time_rand = (double)rand()/(rand_max); tau = (1/(deg_propensity))*log(1/time_rand); current_time += tau; current_cyttranscripts = current_cyttranscripts - 1; if (current_cyttranscripts == ){ break; //If end results match the 15 minute data, record the degradation and export rates if (current_cyttranscripts == SH9_cytTranscripts15min){ #pragma omp critical { fprintf(sh9degoutput_file,"%f\n",deg_rate); //Group rates into 1 bins hist_bin = (int)((deg_rate - fmod(deg_rate,.2))/.2); SH9_degHistogram[hist_bin] ++; if (iteration_no%25 == ){ printf("%d SH9 iterations completed\n",iteration_no); #pragma omp barrier printf("sh9 simulations completed\n"); fclose(sh9degoutput_file); //Calculate total number of values in the rates histograms to normalise the beta distributions double total_adh4degtranscripts; double total_sh9degtranscripts; for (i=;i<1;i++){ if (!isnan(adh4_deghistogram[i])){ total_adh4degtranscripts += ADH4_degHistogram[i]; if (!isnan(sh9_deghistogram[i])){ total_sh9degtranscripts += SH9_degHistogram[i]; printf("fitting beta distributions...\n"); //Fit beta distributions for varying values of alpha and beta using a chi-square statistic double global_adh4degchisq, global_sh9degchisq; double local_adh4degchisq, local_sh9degchisq; double global_adh4degalpha, global_adh4degbeta; double global_sh9degalpha, global_sh9degbeta; double beta_values[1], norm_betavalues[1]; double total_betavalues; double alpha, beta, x; FILE *ADH4_ratesFile; FILE *SH9_ratesFile; ADH4_ratesFile = fopen("adh4gal1beta_rates.txt","w"); SH9_ratesFile = fopen("sh9gal1beta_rates.txt","w"); fprintf(adh4_ratesfile,"deg_alpha\tdeg_beta\n"); fprintf(sh9_ratesfile,"deg_alpha\tdeg_beta\n"); global_adh4degchisq = 1; global_sh9degchisq = 1; for (alpha=1;alpha<2;alpha+=.1){ for (beta=1;beta<2;beta+=.1){ for (x=;x<1;x+=.1){ beta_values[(int)(x*1)] = ((pow(x,(alpha-1)))*(pow((1-x),(beta-1)))); total_betavalues = ; for (i = ;i<1;i++){ total_betavalues += beta_values[i]; for (i=;i<1;i++){ norm_betavalues[i] = beta_values[i]/total_betavalues; local_adh4degchisq = ; 12

13 local_sh9degchisq = ; //Calculate the chi-square statistic for each histogram for (i=;i<1;i++){ if (norm_betavalues[i] > ){ if (ADH4_degHistogram[i] > 4){ local_adh4degchisq += ((ADH4_degHistogram[i] - total_adh4degtranscripts*norm_betavalues[i])*(adh4_deghistogram[i] - total_adh4degtranscript if (SH9_degHistogram[i] > 4){ local_sh9degchisq += ((SH9_degHistogram[i] - total_sh9degtranscripts*norm_betavalues[i])*(sh9_deghistogram[i] - total_sh9degtranscripts*nor //Accept the values of alpha and beta if the chi-square statistic is better than //the previous best value if ((!isinf(local_adh4degchisq) && (!isnan(local_adh4degchisq)))){ if (local_adh4degchisq < global_adh4degchisq){ global_adh4degchisq = local_adh4degchisq; global_adh4degalpha = alpha; global_adh4degbeta = beta; if ((!isinf(local_sh9degchisq) && (!isnan(local_sh9degchisq)))){ if (local_sh9degchisq < global_sh9degchisq){ global_sh9degchisq = local_sh9degchisq; global_sh9degalpha = alpha; global_sh9degbeta = beta; fprintf(adh4_ratesfile,"%f\t%f\n",global_adh4degalpha,global_adh4degbeta); fprintf(sh9_ratesfile,"%f\t%f\n",global_sh9degalpha,global_sh9degbeta); fclose(adh4_ratesfile); fclose(sh9_ratesfile); printf("adh4 deg alpha: %f, deg beta: %f, deg rate: %f\n",global_adh4degalpha,global_adh4degbeta,(global_adh4degalpha-1)/((global_adh4degalpha+global printf("sh9 deg alpha: %f, deg beta: %f, deg rate: %f\n",global_sh9degalpha,global_sh9degbeta,(global_sh9degalpha-1)/((global_sh9degalpha+global_sh9d 13