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matlab_exercise_4_9.m
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matlab_exercise_4_9.m
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% 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.
clear
% number of cells
num_cell = 20;
% simulation time values
time_current = 0; % initial time
time_final = 300; % final time [min]
time_record = time_current; % data record time
dt_record = 0.1; % minimum time interval for data recording
max_num_data = 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 = [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;
% robustness
delta_worst = [-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);
num_reaction = length(ki_para);
% nominal initial number of molecules
ACA_n = 66535; % [# of molecules]
PKA_n = 24282; % [# of molecules]
ERK2_n = 996; % [# of molecules]
REGA_n = 25443; % [# of molecules]
icAMP_n = 14638; % [# of molecules]
ecAMP_n = 6365; % [# of molecules]
CAR1_n = 21697; % [# of molecules]
% initial conditions for each cell
ACA = ACA_n*ones(1,num_cell) + randi(ACA_n,1,num_cell);
PKA = PKA_n*ones(1,num_cell) + randi(PKA_n,1,num_cell);
ERK2 = ERK2_n*ones(1,num_cell) + randi(ERK2_n,1,num_cell);
REGA = REGA_n*ones(1,num_cell) + randi(REGA_n,1,num_cell);
icAMP = icAMP_n*ones(1,num_cell) + randi(icAMP_n,1,num_cell);
CAR1 = CAR1_n*ones(1,num_cell) + randi(CAR1_n,1,num_cell);
% total external cAMP
ecAMP_total = num_cell*ecAMP_n + randi(ecAMP_n,1);
% the total external cAMP distributed equally to each cell
ecAMP = (ecAMP_total/num_cell)*ones(1,num_cell);
% storing data: only store the total external cAMP
species_all = zeros(max_num_data, 2);
species_all(1,:) = [time_current ecAMP_total];
data_idx = 1;
propensity_a = zeros(num_reaction,num_cell);
while data_idx < max_num_data
% each cell
for idx_cell=1:num_cell
propensity_a(1,idx_cell) = ki_para(1)*CAR1(idx_cell);
propensity_a(2,idx_cell) = ki_para(2)*ACA(idx_cell)*PKA(idx_cell)/(NA*Cell_Vol*1e-6);
propensity_a(3,idx_cell) = ki_para(3)*icAMP(idx_cell);
propensity_a(4,idx_cell) = ki_para(4)*PKA(idx_cell);
propensity_a(5,idx_cell) = ki_para(5)*CAR1(idx_cell);
propensity_a(6,idx_cell) = ki_para(6)*PKA(idx_cell)*ERK2(idx_cell)/(NA*Cell_Vol*1e-6);
propensity_a(7,idx_cell) = ki_para(7)*(NA*Cell_Vol*1e-6);
propensity_a(8,idx_cell) = ki_para(8)*ERK2(idx_cell)*REGA(idx_cell)/(NA*Cell_Vol*1e-6);
propensity_a(9,idx_cell) = ki_para(9)*ACA(idx_cell);
propensity_a(10,idx_cell) = ki_para(10)*REGA(idx_cell)*icAMP(idx_cell)/(NA*Cell_Vol*1e-6);
propensity_a(11,idx_cell) = ki_para(11)*ACA(idx_cell);
propensity_a(12,idx_cell) = ki_para(12)*ecAMP(idx_cell);
propensity_a(13,idx_cell) = ki_para(13)*ecAMP(idx_cell);
propensity_a(14,idx_cell) = ki_para(14)*CAR1(idx_cell);
end
% determine the reaction time tau
sum_propensity_a = sum(propensity_a(:));
tau = exprnd(1/sum_propensity_a);
% determine the reaction
normalized_propensity_a = propensity_a(:)/sum_propensity_a;
cumsum_propensity_a = cumsum(normalized_propensity_a);
which_reaction = rand(1);
reaction_idx = cumsum((cumsum_propensity_a-which_reaction)<0);
active_reaction = reaction_idx(end)+1;
reaction = rem(active_reaction,num_reaction);
if reaction==0
reaction = num_reaction;
end
reaction_cell_num = ceil(active_reaction/num_reaction);
% update number of molecules
switch reaction
case 1
ACA(reaction_cell_num) = ACA(reaction_cell_num) + 1;
case 2
ACA(reaction_cell_num) = ACA(reaction_cell_num) - 1;
case 3
PKA(reaction_cell_num) = PKA(reaction_cell_num) + 1;
case 4
PKA(reaction_cell_num) = PKA(reaction_cell_num) - 1;
case 5
ERK2(reaction_cell_num) = ERK2(reaction_cell_num) + 1;
case 6
ERK2(reaction_cell_num) = ERK2(reaction_cell_num) - 1;
case 7
REGA(reaction_cell_num) = REGA(reaction_cell_num) + 1;
case 8
REGA(reaction_cell_num) = REGA(reaction_cell_num) - 1;
case 9
icAMP(reaction_cell_num) = icAMP(reaction_cell_num) + 1;
case 10
icAMP(reaction_cell_num) = icAMP(reaction_cell_num) - 1;
case 11
%ecAMP(reaction_cell_num) = ecAMP(reaction_cell_num) + 1;
ecAMP_total = ecAMP_total + 1;
case 12
%ecAMP(reaction_cell_num) = ecAMP(reaction_cell_num) - 1;
ecAMP_total = ecAMP_total - 1;
case 13
CAR1(reaction_cell_num) = CAR1(reaction_cell_num) + 1;
case 14
CAR1(reaction_cell_num) = CAR1(reaction_cell_num) - 1;
otherwise
error('Wrong reaction number!');
end
% distribute the total ecAMP equally to all cells, where allows
% non-integer numbers
ecAMP = floor(ecAMP_total/num_cell+0.5)*ones(1,num_cell);
time_current = time_current + tau;
if time_record < time_current
data_idx = data_idx + 1;
species_all(data_idx,:) = [time_current ecAMP_total];
time_record = time_record + dt_record;
disp(time_record);
end
end
figure;
plot(species_all(:,1),species_all(:,2),'-');
set(gca,'FontSize',14);
xlabel('time [min]');
ylabel('[# of molecules]');
title('total external cAMP');