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qs_stochastic.py
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qs_stochastic.py
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#!/bin/python3
import numpy as np
import matplotlib.pyplot as plt; plt.rc('font', size=16)
import pandas as pd
from numba import njit
# Default parameters
#-----------------------------------------------------------------------------------------------------------------------
ensemble_size = 100 #int(0.5e3)
N = 10
AI1_ext = 0
t_max = 470 #600
dt_reg = 0.01
x0=np.array([0, 0, 0, 0, 0, 0, 0, 0], dtype=np.int32)
reactions = np.array([[1, 0, 0, 0, 0, 0, 0, 0], # + lasR
[-1, 0, 0, 0, 0, 0, 0, 0], # - lasR
[0, 1, 0, 0, 0, 0, 0, 0], # + LasR
[0, 1, 0, 0, 0, 0, 1, -1], # + LasR ; + AI1 ; - LasRAI1
[0, -1, 0, 0, 0, 0, -1, 1], # - LasR ; - AI1 ; + LasRAI1
[0, -1, 0, 0, 0, 0, 0, 0], # - LasR
[0, 0, 1, 0, 0, 0, 0, 0], # + rsaL
[0, 0, -1, 0, 0, 0, 0, 0], # - rsaL
[0, 0, 0, 1, 0, 0, 0, 0], # + RsaL
[0, 0, 0, -1, 0, 0, 0, 0], # - RsaL
[0, 0, 0, 0, 1, 0, 0, 0], # + lasI
[0, 0, 0, 0, -1, 0, 0, 0], # - lasI
[0, 0, 0, 0, 0, 1, 0, 0], # + LasI
[0, 0, 0, 0, 0, -1, 0, 0], # - LasI
[0, 0, 0, 0, 0, 0, 1, 0], # + AI1
[0, 0, 0, 0, 0, 0, -1, 0], # - AI1
[0, 0, 0, 0, 0, 0, -1, 0], # - AI1 ; + AI1_ext
[0, 0, 0, 0, 0, 0, 0, -1], # - LasRAI1
[0, 0, 0, 0, 0, 0, 1, 0]], # + AI1 ; - AI1_ext
dtype=np.int32)
k_lasR = 1 # 0
g_lasR = 0.247 # 1
k_LasR = 50 # 2
g_LasR = 0.027 # 3
a_rsaL = 0.01 # 4
b_rsaL = 1.5 # 5
K1 = 4000 # 6
h1 = 1.2 # 7
g_rsaL = 0.247 # 8
k_RsaL = 50 # 9
g_RsaL = 0.027 # 10
a_lasI = 0.01 # 11
b_lasI = 1.5 # 12
K2 = 6500 # 13
h2 = 1.4 # 14
g_lasI = 0.247 # 15
k_LasI = 50 # 16
g_LasI = 0.015 # 17
k_AI1 = 0.04 # 18
g_AI1 = 0.008 # 19
s_LasRAI1 = 10 # 20
u_LasRAI1 = s_LasRAI1/100 # 21
g_LasRAI1 = 0.017 # 22
D = 8 # 23
params = np.array([k_lasR, g_lasR, k_LasR, g_LasR, a_rsaL, b_rsaL, K1, h1, g_rsaL, k_RsaL, g_RsaL, a_lasI, \
b_lasI, K2, h2, g_lasI, k_LasI, g_LasI, k_AI1, g_AI1, s_LasRAI1, u_LasRAI1, g_LasRAI1, D], dtype=np.float32)
@njit()
def pa_qs1(x, params, N, AI1_ext, reactions):
lasR, LasR, rsaL, RsaL, lasI, LasI, AI1, LasRAI1 = x
propensities = np.empty(len(reactions), dtype=np.float64)
V_cell = 1.8e-9
V_ext = 1e-6
k_lasR = params[0]
g_lasR = params[1]
k_LasR = params[2]
g_LasR = params[3]
a_rsaL = params[4]
b_rsaL = params[5]
K1 = params[6]
h1 = params[7]
g_rsaL = params[8]
k_RsaL = params[9]
g_RsaL = params[10]
a_lasI = params[11]
b_lasI = params[12]
K2 = params[13]
h2 = params[14]
g_lasI = params[15]
k_LasI = params[16]
g_LasI = params[17]
k_AI1 = params[18]
g_AI1 = params[19]
s_LasRAI1 = params[20]
u_LasRAI1 = params[21]
g_LasRAI1 = params[22]
D = params[23]
V_c = (N*V_cell)/V_ext
LasRAI1_ = (LasRAI1/K1)**h1
RsaL_ = (RsaL/K2)**h2
propensities[0] = k_lasR # + lasR
propensities[1] = lasR*g_lasR # - lasR
propensities[2] = lasR*k_LasR # + LasR
propensities[3] = LasRAI1*s_LasRAI1 # + LasR ; + AI1 ; - LasRAI1
propensities[4] = AI1*LasR*u_LasRAI1 # - LasR ; - AI1 ; + LasRAI1
propensities[5] = LasR*g_LasR # - LasR
propensities[6] = a_rsaL + b_rsaL*(LasRAI1_/(1+LasRAI1_)) # + rsaL
propensities[7] = rsaL*g_rsaL # - rsaL
propensities[8] = rsaL*k_RsaL # + RsaL
propensities[9] = RsaL*g_RsaL # - RsaL
propensities[10] = a_lasI + (b_lasI*(LasRAI1_/((1+LasRAI1_)*(1+RsaL_)))) # + lasI
propensities[11] = lasI*g_lasI # - lasI
propensities[12] = lasI*k_LasI # + LasI
propensities[13] = LasI*g_LasI # - LasI
propensities[14] = LasI*k_AI1 # + AI1
propensities[15] = AI1*g_AI1 # - AI1
propensities[16] = AI1*D # - AI1 ; "+ AI1_ext"
propensities[17] = LasRAI1*g_LasRAI1 # - LasRAI1
propensities[18] = AI1_ext*D*V_c # + AI1 ; "- AI1_ext"
Stot = propensities.sum()
U = np.random.rand()
Tau = np.random.exponential(scale=1/Stot)
s = 0
while s < len(propensities):
if U < propensities[:s+1].sum()/Stot:
return Tau, s
s += 1
@njit()
def ensemble_simulation(N=N, AI1_ext=AI1_ext, x0=x0, params=params, reactions=reactions, t_max=t_max, dt_reg=dt_reg, ensemble_size=ensemble_size):
t_size = round(t_max/dt_reg)
time = np.zeros(t_size, dtype=np.float32)
ensemble = np.zeros((ensemble_size, x0.size, t_size), dtype=np.int32)
ensemble[:, :, 0] = x0.copy()
cell = 0
while cell < ensemble_size:
t = 0
x = x0.copy()
i = 1
while i < t_size:
t_i = i*dt_reg
while t < t_i:
Tau, j = pa_qs1(x, params, N, AI1_ext, reactions)
x += reactions[j]
t += Tau
ensemble[cell, :, i] = x
time[i] = t_i
i += 1
cell += 1
print(f'Simulation completed! \n Population size: {N} \n AI1_ext: {AI1_ext} \n Simulation time: {t_max} minutes \n Ensemble size: {ensemble_size}')
return ensemble, time
@njit
def regularized_ensemble_stats(ensemble, time, ss=-1):
x = ['lasR', 'LasR', 'rsaL', 'RsaL', 'lasI', 'LasI', 'AI1', 'LasRAI1']
x_size = len(x)
ensemble_size = ensemble.shape[0]
t_size = time.size
x_means = np.zeros((x_size, t_size), dtype=np.float64)
x_stds = np.zeros((x_size, t_size), dtype=np.float64)
for t in range(t_size):
for i in range(x_size):
x_ensemble = np.zeros(ensemble_size, dtype=np.int32)
for n in range(ensemble_size):
x_ensemble[n] = ensemble[n, i, t]
x_means[i,t] = x_ensemble.mean()
x_stds[i,t] = x_ensemble.std()
time_ss = time[ss]
x_ss = np.zeros((x_size, ensemble_size), dtype=np.int32)
for i in range(x_size):
for n in range(ensemble_size):
x_ss[i,n] = ensemble[n,i,ss]
x_ss_mean = np.zeros(x_size, dtype=np.float64)
x_ss_std = np.zeros(x_size, dtype=np.float64)
x_ss_noise = np.zeros(x_size, dtype=np.float64)
for i in range(x_size):
x_ss_mean[i] = x_ss[i].mean()
x_ss_std[i] = x_ss[i].std()
x_ss_noise[i] = 0 if x_ss[i].mean()==0 else x_ss_std[i]/x_ss[i].mean()
return x_means, x_stds, time_ss, x_ss, x_ss_mean, x_ss_std, x_ss_noise
def save_ensemble_ss_stats(x_ss, x_ss_mean, x_ss_std, x_ss_noise, N=N, AI1_ext=AI1_ext):
ensemble_size = x_ss.shape[1]
ss_stats = pd.DataFrame(np.array((x_ss_mean, x_ss_std, x_ss_noise)).T, \
columns=['x_ss_mean', 'x_ss_std', 'x_ss_noise'])
ss_stats.insert(0, 'x', ['lasR', 'LasR', 'rsaL', 'RsaL', 'lasI', 'LasI', 'AI1', 'LasRAI1'])
ss_stats.insert(0, 'AI1_ext', AI1_ext)
ss_stats.set_index('AI1_ext', inplace=True)
ss_stats.to_csv(f'PaQS1ss_{ensemble_size}_{N}_{AI1_ext}.tsv', sep='\t')
del ss_stats
def plot_ensemble(ensemble, time, x_means, x_stds, N=N, AI1_ext=AI1_ext, action='display'):
ensemble_size = ensemble.shape[0]
x = ['lasR', 'LasR', 'rsaL', 'RsaL', 'lasI', 'LasI', 'AI$_1$', 'LasR$\cdot$AI$_1$']
fig = plt.figure(figsize=(20,25))
fig.subplots_adjust(hspace=0.3)
subplot = 1
for i in range(len(x)):
plt.subplot(4,2,subplot)
for j in ensemble:
plt.plot(time, j[i], alpha=0.4)
plt.plot(time, x_means[i], 'k', label='$\mu$', lw=2.5)
plt.legend(loc=0)
plt.xlabel('Time (s)')
plt.ylabel(f'# {x[i]}')
plt.title(f'{x[i]} evolution in ensemble')
plt.grid()
subplot += 1
if action == 'save':
fig.savefig(f'PaQS1_{ensemble_size}_{N}_{AI1_ext}.pdf', format='pdf', bbox_inches='tight')
else:
return fig
def plot_ensamble_ss(time_ss, x_ss, x_ss_mean, x_ss_std, x_ss_noise, N=N, AI1_ext=AI1_ext, action='display'):
ensemble_size = x_ss.shape[1]
x = ['lasR', 'LasR', 'rsaL', 'RsaL', 'lasI', 'LasI', 'AI$_1$', 'LasR$\cdot$AI$_1$']
fig = plt.figure(figsize=(20,25))
fig.subplots_adjust(hspace=0.3)
subplot = 1
for i in range(len(x)):
plt.subplot(4,2,subplot)
plt.hist(x_ss[i], color='grey', label=f'$\mu=${np.around(x_ss_mean[i],2)} \n $\sigma=${np.around(x_ss_std[i],2)} \n $\eta=${np.around(x_ss_noise[i],2)}')
plt.legend(loc=0)
plt.xlabel(f'# {x[i]}')
plt.ylabel('# Cells')
plt.title(f'# {x[i]} at {np.around(time_ss)} minutes')
plt.grid()
subplot += 1
if action == 'save':
fig.savefig(f'PaQS1ss_{ensemble_size}_{N}_{AI1_ext}.pdf', format='pdf', bbox_inches='tight')
else:
return fig