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biological_systems:examples

Simulation Files

Deterministic model

The hybrid Chi model is:

model MichaelisMenten()=
|[ cont S : real = 0.0000005
      , E : real = 0.0000002
      , C : real = 0.0
      , P : real = 0.0
 , var  k1: real = 1000000.0
     ,  k2: real = 0.000001
     ,  k3: real = 0.1
 , alg  A,D: real
:: eqn     A = k1 * S * E
     , dot S =       k2  * C - A
     ,     D = (k2 + k3) * C - A
     , dot E =  D
     , dot C = -D
     , dot P = k3 * C
]|

The MATLAB model is:

function MM_plot
tspan = [0 50]; 
yzero = [5e-7; 2e-7; 0; 0];
k1 = 1e6; k2 = 1e-4; k3 = 0.1;
 
options = odeset('AbsTol',1e-8);  
[t,y] = ode15s(@mm,tspan,yzero,options);
 
plot(t,y(:,1),'g','LineWidth',2)
hold on
plot(t,y(:,2),'b--','LineWidth',2)
plot(t,y(:,3),'m--','LineWidth',2)
plot(t,y(:,4),'r','LineWidth',2)
 
LEGEND('[S]','[E]','[C]','[P]')
xlabel('Time','FontSize',14)
ylabel('Concentration','FontSize',14)
 
set(gca,'FontWeight','Bold','FontSize',12)
grid on
      %--------------Nested function----------
      function yprime = mm(t,y)
      % MM    Michaelis-Menten reaction Rate Equation 
      yprime = zeros(4,1);
      yprime(1) = -k1*y(1)*y(2) + k2*y(3);
      yprime(2) = -k1*y(1)*y(2) + (k2+k3)*y(3);
      yprime(3) =  k1*y(1)*y(2) - (k2+k3)*y(3);
      yprime(4) =  k3*y(3);
      end
end

The SBToolbox models are:

  • Modeled as reaction rate equations
********** MODEL NAME 
 MM_rr

********** MODEL NOTES

********** MODEL STATES 
 d/dt(S) = U 
 d/dt(E) = V 
 d/dt(C) = W
 d/dt(P) = X

 S(0) = 5e-7 
 E(0) = 2e-7 
 C(0) = 0 
 P(0) = 0

********** MODEL PARAMETERS 
 k1 = 1e6 
 k2 = 1e-4 
 k3 = 0.1

********** MODEL VARIABLES

********** MODEL REACTIONS
 U = k2 * C - k1 * S * E 
 V = (k2 + k3) * C - k1 * S * E
 W = k1 * S * E - (k2 + k3) * C
 X = k3 * C

********** MODEL FUNCTIONS

********** MODEL EVENTS

********** MODEL MATLAB FUNCTIONS
  • Modeled as reaction scheme
********** MODEL NAME
 MM_reaction_scheme

********** MODEL NOTES

********** MODEL STATE INFORMATION
 S(0) = 5e-7 
 E(0) = 2e-7 
 C(0) = 0 
 P(0) = 0

********** MODEL PARAMETERS 
 k1 = 1e6 
 k2 = 1e-4 
 k3 = 0.1

********** MODEL VARIABLES

********** MODEL REACTIONS

 S + E <=> C 	           :R1
	vf = k1 * S * E
	vr = k2 * C
 C => P + E 		   :R2
	vf = k3 * C 
 
********** MODEL FUNCTIONS

********** MODEL EVENTS

********** MODEL MATLAB FUNCTIONS

The files needed for the other simulators are listed below:

Stochastic model

The MATLAB model is:

%SSA_PLOT.M
 
rand('state',100)
 
%stoichiometric matrix
V = [-1 1 0; -1 1 1; 1 -1 -1; 0 0 1];
 
%%%%%%%%%% Parameters and Initial Conditions %%%%%%%%%
nA = 6.023e23;             % Avagadro's number
vol = 1e-15;               % volume of system
X = zeros(4,1);
X(1) = round(5e-7*nA*vol); % molecules of substrate
X(2) = round(2e-7*nA*vol); % molecules of enzyme 
c(1) = 1e6/(nA*vol); c(2) = 1e-4; c(3) = 0.1;
t = 0;
tfinal = 50;
 
count = 1;
tvals(1) = 0;
Xvals(:,1) = X;
 
while t < tfinal
     a(1) = c(1)*X(1)*X(2);
     a(2) = c(2)*X(3);
     a(3) = c(3)*X(3);
     asum = sum(a);
     j = min(find(rand<cumsum(a/asum)));
     tau = log(1/rand)/asum;
     X = X + V(:,j);
 
     count = count + 1;
     t = t + tau;
     tvals(count) = t;
     Xvals(:,count) = X;
end
 
%%%%%%%%%%% Plots
 
L = length(tvals);
tnew = zeros(1,2*(L-1));
tnew(1:2:end-1) = tvals(2:end);
tnew(2:2:end) = tvals(2:end);
tnew = [tvals(1),tnew];
 
Svals = Xvals(1,:);
ynew = zeros(1,2*L-1);
ynew(1:2:end) = Svals;
ynew(2:2:end-1) = Svals(1:end-1);
plot(tnew,ynew,'go-')
hold on
 
Pvals = Xvals(4,:);
ynew = zeros(1,2*L-1);
ynew(1:2:end) = Pvals;
ynew(2:2:end-1) = Pvals(1:end-1);
plot(tnew,ynew,'r*-')
 
xlabel('Time','FontSize',14)
ylabel('Concentration','FontSize',14)
Legend('S', 'P')
 
set(gca,'FontWeight','Bold','FontSize',12)
grid on
biological_systems/examples.txt · Last modified: Thursday, 05 February 2009 : 10:28:12 (external edit)