Figure 4.37 (page 90):

Deterministic simulation of reaction A + B <-> C compared to stochastic simulation.

Code for Figure 4.37

Text of the GNU GPL.

main.m

%% Copyright (C) 2001, James B. Rawlings and John G. Ekerdt
%%
%% This program is free software; you can redistribute it and/or
%% modify it under the terms of the GNU General Public License as
%% published by the Free Software Foundation; either version 2, or (at
%% your option) any later version.
%%
%% This program is distributed in the hope that it will be useful, but
%% WITHOUT ANY WARRANTY; without even the implied warranty of
%% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
%% General Public License for more details.
%%
%% You should have received a copy of the GNU General Public License
%% along with this program; see the file COPYING.  If not, write to
%% the Free Software Foundation, 59 Temple Place - Suite 330, Boston,
%% MA 02111-1307, USA.

global ca0 cb0 cc0 k1det k2det
%%
%% add a stochastic simulation using Gillespie's algorithm
%%
%% example 1: A + B  --> C
%%            C      --> A + B
%%
nmolec = 400;
k1 = 1;
k2 = 1;
k(1) = k1/(nmolec);
k(2) = k2;
stoi = [-1 -1 1; 1 1 -1];
[nrxs,nspec]=size(stoi);
clear x
x(1,1)= nmolec;
x(2,1)= 0.9*nmolec;
x(3,1)= 0*nmolec;
stoiT = stoi';
nsim = nmolec*4;
clear time;
time = zeros(nsim+1,1);
time(1) = 0;
rand('seed', 0);
for n=1:nsim
  r(1) = k(1)*x(1,n)*x(2,n);
  r(2) = k(2)*x(3,n);
  rtot = sum(r);
  p=rand(2,1);
  tau = -log(p(1))/rtot;
  time(n+1)=time(n)+tau;
  %% determine which reaction (mth) is likely to occur
  m = sum (cumsum (r) <= p(2)*rtot) + 1;
  x(:,n+1) = x(:,n) + stoiT(:,m);
end
%%
%% scale  so ca0=1;
%%
[ts,xs] = stairs(time, x');
ts = ts(:,1);
xscale = xs ./ xs(1,1);
%plot(time,xscale')
%%
%% make a deterministic comparison for nonlinear example 1.
%%
ca0 = x(1,1)/x(1,1);
cb0 = x(2,1)/x(1,1);
cc0 = x(3,1)/x(1,1);
timedet = [0; (logspace (-4,1,100)')];
k1det = k1;
k2det = k2;
%%
%% analytical if k2det = 0
%%
% delc = ca0-cb0;
% ca = delc ./ ( 1 - cb0/ca0 .* exp(-delc*k1det .* timedet));
% cb = ca - delc;
% cc = - ca + ( cc0 + ca0);
opts = odeset ('AbsTol', sqrt (eps), 'RelTol', sqrt (eps));
[tsolver, ca] = ode15s(@f, time, ca0, opts);
cb = ca - ca0 + cb0;
cc = cc0 + ca0 - ca;
%plot(timedet, [ca,cb,cc])
table1 = [ts xscale];
table2 = [time ca cb cc];
save stochnon.dat table1 table2;

plot (table1(:,1),table1(:,2:4), table2(:,1), table2(:,2:4));
axis ([0,5,0,1]);
title ('Figure 4.37')

f.m

function xdot = f(t,x)
  global ca0 cb0 cc0 k1det k2det
  ca = x(1);
  cb = ca - ca0 + cb0;
  cc = cc0 + ca0 - ca;
  xdot(1) = - k1det*ca*cb + k2det*cc;

Data files

stochnon.dat

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# name: table1
# type: matrix
# rows: 3201
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