MATLAB: Perturbing Values and determing an SFO

mitotic oscillatorperturb constantssfo ranking of constant

I am using the following code
K1 = 0.005;
K2 = 0.005;
K3 = 0.005;
K4 = 0.005;
Kc = 0.5;
Kd = 0.02;
kdd = 0.01;
V2 = 1.5;
V4 = 0.5;
vd = 0.25;
VM1 = 3;
VM3 = 1.;
Synth = 0.025;
% Original Equations:
% PhsKnsKnt = [Synth-vd*X*(C/(Kd+C)) – kdd*C; M*VM3*((1-X)/(K3+(1-X))) – V4*
(X/(K4+X)); VM1*(C/(Kc+C))*((1-M)/(K1+(1-M))) – V2*(M/(K2+M))]; % Anonymous Function with substitutions:
PhsKnsKnt = @(T, P) [Synth – vd*P(2)*(P(1)/(Kd+P(1))) – kdd*P(1); P(3)*VM3*((1- P(2))/(K3+(1-P(2)))) – V4*(P(2)/(K4+P(2))); VM1*(P(1)/(Kc+P(1)))*((1-P(3))/(K1+(1- P(3)))) – V2*(P(3)/(K2+P(3)))];
[T P] = ode45(PhsKnsKnt, [0 100], [0.01; 0.01; 0.01]);
C = P(:,1);
X = P(:,2);
M = P(:,3);
figure(1)
plot(T, P)
legend('[C] (µ\itM\rm)', '[X] (µ\itM\rm)', '[M] (µ\itM\rm)', 'Location','NorthWest')
xlabel('Time (s)')
ylabel('Concentration')
grid
I am trying to perturb each of the values from K1- VM3 by 5%. For example for kd i tried to following : Kd = 0.02 -(0.02*0.05); I have changed the other constants accordingly by 5%. My issue is that my "C" value when running this code has yet to change even when i perturb different values. I am trying to figure out SFO to rank variables using the following:
%change in C / % change of the constant (being 5%).

Best Answer

Actually, it does change. It just doesn’t change very much.
Run this:
Tvct = linspace(0,33);
Kdv = [0.95  1  1.05]*Kd;
for k1 = 1:3
    Kd = Kdv(k1);
    PhsKnsKnt = @(T, P)  [Synth - vd*P(2)*(P(1)/(Kd+P(1))) - kdd*P(1);    P(3)*VM3*((1-P(2))/(K3+(1-P(2)))) - V4*(P(2)/(K4+P(2)));    VM1*(P(1)/(Kc+P(1)))*((1-P(3))/(K1+(1-P(3)))) - V2*(P(3)/(K2+P(3)))];
    [T P] = ode45(PhsKnsKnt, [Tvct],  [0.01;  0.01;  0.01]);
    CXM(:,:,k1) = P;
end
Csq = squeeze(CXM(:,1,:));
Csqr = [Csq(:,1)./Csq(:,2)    Csq(:,3)./Csq(:,2)];
Csqd = [Csq(:,1)-Csq(:,2)    Csq(:,3)-Csq(:,2)];
I put in Tvct to be sure the function was evaluated at the same time points (since the ode solvers are adaptive). I created Csq, a matrix of the three runs for C(t) with values for Kd varying from 0.95 to 1.05, and then calculated the ratios of them in Csqr. Csqd are the differences, since that may be what you want.
(I put up a transient earlier post about sensitivity functions. That works, but only on actual objective functions. I forgot for a minute that this is a DE. Doesn’t apply to DEs.)
Related Question