Need help with Matlab Function of Differential Equations

[Dionisio Mendoza]

Homework Statement

I am trying to imitate a model of differential equations in Matlab about G proteins but I can not achieve it.

Relevant Equations

-d/dt=x2
d/dt=x1

WHAT HAPPENS IS That I need to model the example of A Protein G example, using a function f in Matlab, but when I execute the script, the graphics I get do not correspond to those of the example.
The problem is that I can not understand what the model seeks to represent, besides that I do not know if my script is correct.
The function is the following:

function dydx = examenisb (x,y)

ki = 1;
ku = 1;
global Km1;
global Km2;

V1 = y(2)*ki*x(1)/(Km1+y(2));
V2 = y(1)*ku*x(1)/(Km2+y(1));dadx = V1-V2;
dbdx = -V1-V2;
dydx = [dadx -dbdx]';

The scrypt is this:

global Km1;
global Km2;
Km1=.001;
Km2=.001;
[x,y]=ode45(@examenisb,[0,2],[0.1 0.1]);
plot(x,y);

xlabel('tiempo (h)')
ylabel('biomasa')
title('Biomasa')

The section of the PDF is that of 3.2.4.1 G proteins

[Mentor Note -- Added code tags. Please always post code using code tags]

 

[BvU]

Hello,

Not an expert, but I tried your function and it does something (at least in Octave).

If this is the same picture you get (which you did not post -- why not ?), it isn't corresponding to the example (which you did not post -- why not ?)

Do we have to guess which variable in the example corresponds to which variable in your script ?

Do you know how to work with break points to check what is going on ?

I notice you do v2=-... and then dydx = - ... minus sign twice ?

Note: your post looks a lot better when enclosed in $[$code=matlab$]$ ... $[$/code$]$

function dydx = examenisb (x,y)

ki = 1;
ku = 1;
global Km1;
global Km2;

V1 = y(2)*ki*x(1)/(Km1+y(2));
V2 = y(1)*ku*x(1)/(Km2+y(1));dadx = V1-V2;
dbdx = -V1-V2;
dydx = [dadx -dbdx]';

The scrypt is this:

global Km1;
global Km2;
Km1=.001;
Km2=.001;
[x,y]=ode45(@examenisb,[0,2],[0.1 0.1]);
plot(x,y);

xlabel('tiempo (h)')
ylabel('biomasa')
title('Biomasa') [/

 

[BvU]

Ah, I see: you want something like fig 3.13 (b) ?

Your values now are such that V1 = V2 so one derivative is 0 and stays 0.
The other is so small I suspect a scale error (units?)

With y0 =[0 1] instead of [0.1 0.1] :

[x,y]=ode45(@dydx,[0,2],[0 1]);

% and 

function dydx = examenisb (x,y)

ki = 1000;
ku = 1000;
global Km1;
global Km2;

V1 = y(2)*ki*x(1)/(Km1+y(2));
V2 = y(1)*ku*x(1)/(Km2+y(1));dadx = V1-V2;
dbdx = -V1+V2;
dydx = [dadx dbdx]';

I get

Looks better eh ?

 

[Dionisio Mendoza]

Hello,

Not an expert, but I tried your function and it does something (at least in Octave).

If this is the same picture you get (which you did not post -- why not ?), it isn't corresponding to the example (which you did not post -- why not ?)
View attachment 243504

Do we have to guess which variable in the example corresponds to which variable in your script ?

Do you know how to work with break points to check what is going on ?

I notice you do v2=-... and then dydx = - ... minus sign twice ?

Note: your post looks a lot better when enclosed in $[$code=matlab$]$ ... $[$/code$]$

function dydx = examenisb (x,y)

ki = 1;
ku = 1;
global Km1;
global Km2;

V1 = y(2)*ki*x(1)/(Km1+y(2));
V2 = y(1)*ku*x(1)/(Km2+y(1));dadx = V1-V2;
dbdx = -V1-V2;
dydx = [dadx -dbdx]';

The scrypt is this:

global Km1;
global Km2;
Km1=.001;
Km2=.001;
[x,y]=ode45(@examenisb,[0,2],[0.1 0.1]);
plot(x,y);

xlabel('tiempo (h)')
ylabel('biomasa')
title('Biomasa') [/

THIS GRAPH