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gill_oneCell_2022.py
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# One cell Gillespie simulation to quantify intrinsic noise
# Written by Madeline Galbraith
# Last modified July 2022
import numpy as np
import matplotlib.pyplot as plt
import pandas as pd
import json
####################
## Allow the calculation to be parallelized
####################
from mpi4py import MPI
myrank = MPI.COMM_WORLD.Get_rank()
nprocs = MPI.COMM_WORLD.Get_size()
stat = MPI.Status()
####################
### The values in the checkerboard
####################
## Sender: N = 567, D = 1561, I = 1.2
## Receiver: N = 5138.8, D = 21.7, I = 802
####################
#### parameters ####
####################
N0 = 5.0e+2
D0 = 1.0e+3
I0 = 2.0e+2 ## hill factor
kc = 5.0e-4 #1/hour/molecule
kt = 5.0e-5 #1/hour/molecule
nI = 2.0e+0
lambdaN = 2.0e+0 # no dimension
lambdaD = 0.0e+0 # no dimension
gamma = 1.0e-1 #1/hour
gamma_i = 5.0e-1 #1/hour
####################
####################
#################
def shiftedHill(X,X0,nX,lambdY):
return lambdY+(1.0 - lambdY)/(1.0+(X/X0)**nX)
####################
def simulate_gill(iterations,ss,Next,Dext,equil=30000):
## set up the simulation
np.random.seed(ss)
time=0.
results={}
N,D,I = np.random.randint(0,6000,1)[0],np.random.randint(0,2000,1)[0],np.random.randint(0,1000,1)[0]
results['time']=[time]
results['N']=[N]
results['D']=[D]
results['I']=[I]
## run gillespie algorithm
for ind in range(iterations):
tmp=[]
r1,r2 = np.random.uniform(0,1,2)
itt = 1./__a0(N,D,I,Next,Dext)*np.log(1./r1)
[N,D,I] = __updateRes(N,D,I,r2,Next,Dext)
time+=itt
results['time']+=[time]
results['N']+=[N]
results['D']+=[D]
results['I']+=[I]
results['time'] = results['time'][equil:]
results['N'] = results['N'][equil:]
results['D'] = results['D'][equil:]
results['I'] = results['I'][equil:]
return results
#### Functions and definitions directly related to Gillespie algorithm
def __updateRes(N,D,I,r2,Next,Dext):
if (__X1(N,D,I,Next,Dext)<=r2) and (r2< __X2(N,D,I,Next,Dext)):
return [N-1,D,I+1]
elif (__X2(N,D,I,Next,Dext)<=r2) and (r2< __X3(N,D,I,Next,Dext)):
return [N,D-1,I]
elif (__X3(N,D,I,Next,Dext)<=r2) and (r2< __X4(N,D,I,Next,Dext)):
return [N-1,D-1,I]
elif (__X4(N,D,I,Next,Dext)<=r2) and (r2< __X5(N,D,I,Next,Dext)):
return [N-1,D,I]
elif (__X5(N,D,I,Next,Dext)<=r2) and (r2< __X6(N,D,I,Next,Dext)):
return [N,D-1,I]
elif (__X6(N,D,I,Next,Dext)<=r2) and (r2< __X7(N,D,I,Next,Dext)):
return [N,D,I-1]
elif (__X7(N,D,I,Next,Dext)<=r2) and (r2< __X8(N,D,I,Next,Dext)):
return [N+1,D,I]
#return [N,D+1,I]
else:#if (__X8(N,D,I,Next,Dext)<=r2) and (r2< __X9(N,D,I,Next,Dext)):
return [N,D+1,I]
#return [N+1,D,I]
##############
### propensities
##############
def __a1(N,D,I,Next,Dext):
return kt*N*Dext # 0.00005*N*Dext*(I-1) gives N=[0]
def __a2(N,D,I,Next,Dext):
return kt*D*Next # 0.00005*D*Next gives N=[0]
def __a3(N,D,I,Next,Dext):
return kc*N*D # 0.0005*N*D gives N=[0,6000]
def __a4(N,D,I,Next,Dext):
return gamma*N # 0.1*N gives N=[0,600]
def __a5(N,D,I,Next,Dext):
return gamma*D # 0.1*D gives N=[0,200]
def __a6(N,D,I,Next,Dext):
return gamma_i*I # 0.5*I gives N=[0,500]
def __a7(N,D,I,Next,Dext):
return N0*shiftedHill(I,I0,nI,lambdaN) # 500 gives N=[500]
def __a8(N,D,I,Next,Dext):
return D0*shiftedHill(I,I0,nI,lambdaD) # 1000 gives N=[1000]
def __a0(N,D,I,Next,Dext):
return __a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext)+__a3(N,D,I,Next,Dext)+__a4(N,D,I,Next,Dext)+__a5(N,D,I,Next,Dext)+__a6(N,D,I,Next,Dext)+__a7(N,D,I,Next,Dext)+__a8(N,D,I,Next,Dext)
##############
## probabilities
##############
def __X1(N,D,I,Next,Dext):
return 0
def __X2(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X3(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X4(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext)+__a3(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X5(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext)+__a3(N,D,I,Next,Dext)+__a4(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X6(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext)+__a3(N,D,I,Next,Dext)+__a4(N,D,I,Next,Dext)+__a5(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X7(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext)+__a3(N,D,I,Next,Dext)+__a4(N,D,I,Next,Dext)+__a5(N,D,I,Next,Dext)+__a6(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X8(N,D,I,Next,Dext):
return (__a1(N,D,I,Next,Dext)+__a2(N,D,I,Next,Dext)+__a3(N,D,I,Next,Dext)+__a4(N,D,I,Next,Dext)+__a5(N,D,I,Next,Dext)+__a6(N,D,I,Next,Dext)+__a7(N,D,I,Next,Dext))/__a0(N,D,I,Next,Dext)
def __X9(N,D,I,Next,Dext):
return 1
###############
##############################
############ Start simulation ###########
##############################
def main():
seedList=pd.read_csv(filepath_or_buffer='seedsForSims.txt',header=None).values[:,0]
simNum=10
iterations=200000
Next = 567
Dext = 1561
simList=[myrank,myrank+nprocs]
etime=0
pairs = [[567,1561],[5139,22]]
for [Next,Dext] in pairs:
for seedInd in simList:
ss = seedList[seedInd]
res = simulate_gill(iterations,ss,Next,Dext,equil=etime)
fullRes={'res':res,'Next':Next,'Dext':Dext,'equil':etime,'seed':ss,'iterations':iterations}
title='data_gil/oneCell/data_'+str(Next)+"_"+str(Dext)+"_s"+str(seedInd)
json_data=json.dumps(fullRes,indent=4)
with open(title+'.json','w') as outfile:
outfile.write(json_data)
main()