Steady-state

Simulation

Temporal simulation is performed using the Systems Biology Toolbox 2 http://www.sbtoolbox.org/ environment with numerical integration using ode45. The catalytical model is specified by

********** MODEL NAME
Dimensionless form. Catalytical.

********** MODEL NOTES
Kinetic model of trap-RNA system.
Parameters are estimated from literature.

********** MODEL STATES
d/dt(m) = 1 - m - k_s*alpha_m*m*s/(beta_m*beta_s)
d/dt(s) = (beta_s/beta_m)*(alpha_s/alpha_m - s - k_r*alpha_m * s * r /(beta_s*beta_r))
d/dt(r) = (beta_r/beta_m)*(alpha_r/alpha_m - r)

m(0) = 1
s(0) = 0
r(0) = 0                                    

********** MODEL PARAMETERS
alpha_m = 10
alpha_s = 0
alpha_r = 0
beta_m = 0.0257
beta_s = 0.0257
beta_r = 0.0257
k_s = 0.00082
k_r = 0.0082

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

********** MODEL REACTIONS
	
********** MODEL FUNCTIONS

********** MODEL EVENTS
event = gt(time,1), alpha_s, 40
event = gt(time,3), alpha_r, 200
event = gt(time,6), alpha_r, 0
********** MODEL MATLAB FUNCTIONS

File:DTU Model7.txt

The partly stoichiometric model is specified by

********** MODEL NAME
Dimensionless form. Stoichiometric.

********** MODEL NOTES
Kinetic model of trap-RNA system.
Parameters are estimated from literature.

********** MODEL STATES
d/dt(m) = 1 - m - k_s*alpha_m*m*s/(beta_m*beta_s)
d/dt(s) = (beta_s/beta_m)*(alpha_s/alpha_m - s - k_r*alpha_m * s * r /(beta_s*beta_r))
d/dt(r) = (beta_r/beta_m)*(alpha_r/alpha_m - r - k_r*alpha_m * s * r /(beta_s*beta_r))

m(0) = 1
s(0) = 0
r(0) = 0                                    

********** MODEL PARAMETERS
alpha_m = 1
alpha_s = 0
alpha_r = 0
beta_m = 0.0257
beta_s = 0.0257
beta_r = 0.0257
k_s = 0.00082
k_r = 0.0082

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

********** MODEL REACTIONS
	
********** MODEL FUNCTIONS

********** MODEL EVENTS
event = gt(time,1), alpha_s, 40
event = gt(time,3), alpha_r, 200
event = gt(time,6), alpha_r, 0
********** MODEL MATLAB FUNCTIONS

File:DTU Model8.txt

The script running simulation and generating figures.

%ksim runs a dynamic simulation using Systems Biology Toolbox 2 and plots 
clear;
model = SBmodel('model7.txt');  %initialize model

%parameters
alpha_m = 1;
alpha_s = 40;    %at induced
alpha_r = 200;    %at induced

%%Simulation
time = 6;  %running time. Glucose event at t = 6
[out] = SBsimulate(model,time);

%%PLot
t = out.time;
m = out.statevalues(:,1);   %m
s = out.statevalues(:,2);
r = out.statevalues(:,3);

%scale to max steady_state at induced levels

s = s .* (alpha_m/alpha_s);
r = r .* (alpha_m/alpha_r);

%ss_r = alpha_r/beta_r;
%r = r ./ss_r;
%Binary on off of s and r
%s = gt(t, 1);   %Check model for event time   
%r = gt(t, 3);

width = 4;  %Line width


subplot(3,1,1)
h1 = plot(t,m); %handle
set(h1, 'color', [51/255, 102/255, 204/255], 'LineWidth',width)
set(gca, 'XTickLabel',[])

subplot(3,1,2)
h2 = plot(t,s);
set(h2, 'color', [237/255, 28/255, 36/255],'LineWidth',width)
set(gca, 'XTickLabel',[])

subplot(3,1,3)
h3 = plot(t,r,'g-');
set(h3, 'color', [102/255, 204/255, 0],  'LineWidth',width)

File:DTU Ksim.m