#!/usr/bin/env python3 # -*- coding: utf-8 -*- """ MIT License Copyright (c) 2022 Jongrae.K Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions: The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software. THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. """ import numpy as np # number of cells num_cell = 2 # simulation time values time_current = 0 # initial time time_final = 300.0 # final time [min] time_record = time_current # data record time dt_record = 0.1 # minimum time interval for data recording max_num_data = np.floor((time_final-time_current)/dt_record+0.5); # kinetic parameters for the Laub-Loomis Dicty cAMP oscillation # network model from k1 to k14 ki_para_org = np.array([2.0, 0.9, 2.5, 1.5, 0.6, 0.8, 1.0, 1.3, 0.3, 0.8, 0.7, 4.9, 23.0, 4.5]) Cell_Vol = 3.672e-14; # [litre] NA = 6.022e23; # Avogadro's number num_molecule_species = 7 num_reactions = 14 # robustness delta_worst = np.array([-1, -1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, 1]) p_delta = 2; ki_para=ki_para_org*(1+(p_delta/100)*delta_worst) # nominal initial number of molecules ACA_n = 35403 # [# of molecules] PKA_n = 32888 # [# of molecules] ERK2_n = 11838 # [# of molecules] REGA_n = 27348 # [# of molecules] icAMP_n = 15489 # [# of molecules] ecAMP_n = 4980 # [# of molecules] CAR1_n = 25423 # [# of molecules] # initial conditions for each cell ACA = ACA_n*np.ones(num_cell) + np.random.randint(1,ACA_n+1,num_cell) PKA = PKA_n*np.ones(num_cell) + np.random.randint(1,PKA_n+1,num_cell) ERK2 = ERK2_n*np.ones(num_cell) + np.random.randint(1,ERK2_n+1,num_cell) REGA = REGA_n*np.ones(num_cell) + np.random.randint(1,REGA_n+1,num_cell) icAMP = icAMP_n*np.ones(num_cell) + np.random.randint(1,icAMP_n+1,num_cell) CAR1 = CAR1_n*np.ones(num_cell) + np.random.randint(1,CAR1_n+1,num_cell) # total external cAMP ecAMP_total = num_cell*ecAMP_n + np.random.randint(1,ecAMP_n+1) # the total external cAMP distributed equally to each cell ecAMP = (ecAMP_total/num_cell)*np.ones(num_cell) # storing data species_all = np.zeros((int(max_num_data), 2)) species_all[0,:] = np.array([time_current, ecAMP_total]) data_idx = 0 propensity_a = np.zeros((num_reactions,num_cell)) while data_idx < max_num_data-1: # each cell for idx_cell in range(num_cell): propensity_a[0,idx_cell] = ki_para[0]*CAR1[idx_cell] propensity_a[1,idx_cell] = ki_para[1]*ACA[idx_cell]*PKA[idx_cell]/(NA*Cell_Vol*1e-6) propensity_a[2,idx_cell] = ki_para[2]*icAMP[idx_cell] propensity_a[3,idx_cell] = ki_para[3]*PKA[idx_cell] propensity_a[4,idx_cell] = ki_para[4]*CAR1[idx_cell] propensity_a[5,idx_cell] = ki_para[5]*PKA[idx_cell]*ERK2[idx_cell]/(NA*Cell_Vol*1e-6) propensity_a[6,idx_cell] = ki_para[6]*(NA*Cell_Vol*1e-6) propensity_a[7,idx_cell] = ki_para[7]*ERK2[idx_cell]*REGA[idx_cell]/(NA*Cell_Vol*1e-6) propensity_a[8,idx_cell] = ki_para[8]*ACA[idx_cell] propensity_a[9,idx_cell] = ki_para[9]*REGA[idx_cell]*icAMP[idx_cell]/(NA*Cell_Vol*1e-6) propensity_a[10,idx_cell] = ki_para[10]*ACA[idx_cell] propensity_a[11,idx_cell] = ki_para[11]*ecAMP[idx_cell] propensity_a[12,idx_cell] = ki_para[12]*ecAMP[idx_cell] propensity_a[13,idx_cell] = ki_para[13]*CAR1[idx_cell] # determine the reaction time tau propensity_vec = propensity_a.T.flatten() sum_propensity_a = np.sum(propensity_vec) tau = np.random.exponential(1/sum_propensity_a) # determine the reaction normalized_propensity_a = propensity_vec/sum_propensity_a cumsum_propensity_a = np.cumsum(normalized_propensity_a) which_reaction = np.random.rand(1) reaction_idx = np.cumsum((cumsum_propensity_a-which_reaction)<0) active_reaction = reaction_idx[-1] reaction = np.remainder(active_reaction,num_reactions) reaction_cell_num = np.int(np.floor(active_reaction/num_reactions)) # update number of molecules if reaction==0: ACA[reaction_cell_num] = ACA[reaction_cell_num] + 1 elif reaction==1: ACA[reaction_cell_num] = ACA[reaction_cell_num] - 1 elif reaction==2: PKA[reaction_cell_num] = PKA[reaction_cell_num] + 1 elif reaction==3: PKA[reaction_cell_num] = PKA[reaction_cell_num] - 1 elif reaction==4: ERK2[reaction_cell_num] = ERK2[reaction_cell_num] + 1 elif reaction==5: ERK2[reaction_cell_num] = ERK2[reaction_cell_num] - 1 elif reaction==6: REGA[reaction_cell_num] = REGA[reaction_cell_num] + 1 elif reaction==7: REGA[reaction_cell_num] = REGA[reaction_cell_num] - 1 elif reaction==8: icAMP[reaction_cell_num] = icAMP[reaction_cell_num] + 1 elif reaction==9: icAMP[reaction_cell_num] = icAMP[reaction_cell_num] - 1 elif reaction==10: #ecAMP[reaction_cell_num] = ecAMP[reaction_cell_num] + 1 ecAMP_total = ecAMP_total + 1 elif reaction==11: #ecAMP[reaction_cell_num] = ecAMP[reaction_cell_num] - 1 ecAMP_total = ecAMP_total - 1 elif reaction==12: CAR1[reaction_cell_num] = CAR1[reaction_cell_num] + 1 elif reaction==13: CAR1[reaction_cell_num] = CAR1[reaction_cell_num] - 1 else: print(reaction,'Wrong reaction number!') # distribute the total ecAMP equally to all cells, # where allows non-integer numbers ecAMP = (ecAMP_total/num_cell)*np.ones(num_cell) time_current = time_current + tau if time_record < time_current: data_idx = data_idx + 1 species_all[data_idx,:] = np.array([time_current, ecAMP_total]) time_record = time_record + dt_record print(time_record) import matplotlib.pyplot as plt figure, axis = plt.subplots(1,1) tout = species_all[:,0] ecAMP_total = species_all[:,1] axis.plot(tout,ecAMP_total,'b-') axis.set_ylabel('[# of molecules]', fontsize=14) axis.set_xlabel('time [min]', fontsize=14) axis.set_title('Total external cAMP')