can I directly change the ODE?

I want to ensure that I truly understand how to use Simbiology by reconstructing an old model. I have the diagram, parameters (rates), initial values, ODEs, and result plots. After using this information to rebuild the model, I found that my results differ from the original ones. I would like to know if any other factors can affect the simulation results besides the data mentioned above. Can I directly modify the ODEs?

Thank you!

[Walter Roberson]

Is there a choice of ode solver?

[Lo]

hello Walter Roberson

I use ode15s

[Sam Chak]

Hi @Lo,

Can you show (i) the ODEs as well as (ii) the expected results/plots from original model based on the same initial values?

[Lo]

Hi Sam Chak

they ode

my ode

they result

my result (StopTime : 60 mins, unitconversion : false)

my result (StopTime : 60 mins, unitconversion : ture, DefaultSpeciesDimension : concentration)

[Sam Chak]

Hi @Lo, Can you paste the copyable code here?

Also provide the initial values of the 12 states and constants of the parameters from k_padlock to k8.

[Lo]

Hi Sam Chak

sorry I don't know how view my model in code form, but I can first provide the parameter and value

parameter

initial value

[Sam Chak]

Thanks @Lo. Only the ODEs are left.

Can you type out or paste the 12 ODEs like this? It is for testing the ODEs in MATLAB.

dM/dt = - k_payload*M*P - Mdeg*M
dP/dt = - k_payload*M*P
...

[Lo]

hi Sam Chak

like this ways ?

d(M)/dt = -(k_padlock*M*P) - (Mdeg*M)
d(P)/dt = -(k_padlock*M*P)
d(MP)/dt = (k_padlock*M*P) - (Vmcircular*MP/(Kmcircular+MP))
d(SplR)/dt = -(Vmcircular*MP/(Kmcircular+MP))
d([MP-circular])/dt = (Vmcircular*MP/(Kmcircular+MP)) - (Vmphi29*[MP-circular]/(Kmphi29+[MP-circular]))
d(phi29)/dt = -(Vmphi29*[MP-circular]/(Kmphi29+[MP-circular]))
d([R-free])/dt = (Vmphi29*[MP-circular]/(Kmphi29+[MP-circular])) - (RCPdeg*[R-free]) - (k1*[R-free]*[F-free]-k2*RF) - (k3*[R-free]*[Q-free]-k4*RQ)
d([F-free])/dt = -(k1*[R-free]*[F-free]-k2*RF) - (k7*[F-free]*RQ-k8*RFQ)
d(RF)/dt = (k1*[R-free]*[F-free]-k2*RF) - (k5*RF*[Q-free]-k6*RFQ)
d([Q-free])/dt = -(k3*[R-free]*[Q-free]-k4*RQ) - (k5*RF*[Q-free]-k6*RFQ)
d(RQ)/dt = (k3*[R-free]*[Q-free]-k4*RQ) - (k7*[F-free]*RQ-k8*RFQ)
d(RFQ)/dt = (k5*RF*[Q-free]-k6*RFQ) + (k7*[F-free]*RQ-k8*RFQ)

Answer 1

[Fulden Buyukozturk]

You cannot edit ODEs directly but you can inspect them using getequations from the command-line or Show model equations option from Model Builder. You can also inspect quantity initial conditions by selecting Initial Conditions option on the Home tab.

Also, please see this page that describes how SimBiology derives ODEs: https://www.mathworks.com/help/simbio/ug/deriving-simbiology-odes-equations-from-reactions.html

Answer 2

[Sam Chak]

Hi @Lo

The initial values for MP0 and MPcircular0 are not provided. So I made up some values and it displays the trend similar to the following:

tspan       = [0 600];
M0          = 0.5;
P0          = 0.05;
MP0         = 0.5;      % not provided
SplR0       = 25;
MPcircular0 = 0;        % not provided
phi290      = 12.5;
Rfree0      = 0;
Ffree0      = 180664245;
RF0         = 0;
Qfree0      = 361328490;
RQ0         = 0;
RFQ0        = 0;
x0          = [M0 P0 MP0 SplR0 MPcircular0 phi290 Rfree0 Ffree0 RF0 Qfree0 RQ0 RFQ0];
% options     = odeset('RelTol', 1e-4, 'AbsTol', 1e-6);

[t, x]      = ode15s(@odefcn, tspan, x0);

% Solution Plot
plot(t/60, x(:,12), 'linewidth', 1.5), 
grid on, xlabel('Time / minutes'), ylabel('RFQ')

function xdot  = odefcn(t, x)
    xdot       = zeros(12, 1);
    % definitions
    M          = x(1);
    P          = x(2);
    MP         = x(3);
    SplR       = x(4);
    MPcircular = x(5);
    phi29      = x(6);
    Rfree      = x(7);
    Ffree      = x(8);
    RF         = x(9);
    Qfree      = x(10);
    RQ         = x(11);
    RFQ        = x(12);
    
    % parameters
    k_padlock  = 32000;
    Mdeg       = 0.000019254;
    Vmcircular = 0.008;
    Kmcircular = 1;
    Vmphi29    = 112;
    Kmphi29    = 31;
    RCPdeg     = 0;
    k1         = 1e12;
    k2         = 0;
    k3         = 1e12;
    k4         = 0;
    k5         = 1e12;
    k6         = 0;
    k7         = 1e12;
    k8         = 0;
    
    % dynamics
    xdot(1)    = - k_padlock*M*P - Mdeg*M;
    xdot(2)    = - k_padlock*M*P;
    xdot(3)    =   k_padlock*M*P - (Vmcircular*MP)/(Kmcircular + MP);
    xdot(4)    = - (Vmcircular*MP)/(Kmcircular + MP);
    xdot(5)    =   (Vmcircular*MP)/(Kmcircular + MP) - (Vmphi29*MPcircular)/(Kmphi29 + MPcircular);
    xdot(6)    = - (Vmphi29*MPcircular)/(Kmphi29 + MPcircular);
    xdot(7)    =   (Vmphi29*MPcircular)/(Kmphi29 + MPcircular) - RCPdeg*Rfree - (k1*Rfree*Ffree - k2*RF) - (k3*Rfree*Qfree - k4*RQ);
    xdot(8)    = - (k1*Rfree*Ffree - k2*RF)  - (k7*Ffree*RQ - k8*RFQ);
    xdot(9)    =   (k1*Rfree*Ffree - k2*RF)  - (k5*RF*Qfree - k6*RFQ);
    xdot(10)   = - (k3*Rfree*Qfree - k4*RQ)  - (k5*RF*Qfree - k6*RFQ);
    xdot(11)   =   (k3*Rfree*Qfree - k4*RQ)  - (k7*Ffree*RQ - k8*RFQ);
    xdot(12)   =   (k5*RF*Qfree    - k6*RFQ) + (k7*Ffree*RQ - k8*RFQ);
end

[Lo]

hi Sam Chak

I notice that the number of RFQ seems not right or I just misunderstand the figure ?

[Sam Chak]

Hi @Lo

I do not understand about the physical meaning of this 12th-order Simbiology system. The result is directly obtained from mathematically solving the ODEs based on the initial values and the parameters that you supplied, so that you can compare it with the result from the Simbiology Toolbox.

By the way, what is the right number of RFQ?

[Lo]

Hi Sam Chak

the right number of RFQ should be near 10^-4, maybe 9.xxx*10^-4.

[Sam Chak]

Hi @Lo

The final value of RFQ in the simulation depends on the initial values of all 12 states. But you only gave 10 initial values (scoll up). The other two initial values of MP0 and MPcircular were not provided. What are they?

Please insert the values in the MATLAB code and run it. Then show your result of the RFQ here.

[Lo]

hi Sam Chak

I apologize for the late response due to being busy. The result I obtained is exactly the same as yours, but I still don't know what caused the difference in results before.