How to introduce a delay in a simbiology model?

I have a model here for transcription and translation which I am trying to fit to data containing a column for mRNA and for protein.

TsR and TlR are transcription and translation resources.

The data has a delay and is pretty sigmoidal. The michaelis-menten based ODEs I used don't fit. How do a introduce that delay time factor so that it fits by recognizing the t-t0 time delay? (mS or GDmS is the protein)

Data attached.

Answer 1

[Arthur Goldsipe]

SimBiology does not directly support delays. One approach would be a more mechanistic model of the delay. For exampe, you might try switching to Hill kinetics to see if that can reproduce the sigmoidal response. Alternatively, you could implement the model with basic MATLAB code and use dde23 to solve the equations.

[Archishman Ghosh]

I was afraid of this. I really wanted to use the simbiology module. I tried Hill, didn't work. I suppose I will have to use the delay differential equations solver.

[Jeremy Huard]

@Archishman Ghosh

One way to do this in SimBiology would be to approximate the delay with a chain of reactions of type with a reaction rate where

sbioloadproject('timeDelay_reactionchain.sbproj')
cs = getconfigset(m1);
cs.SolverOptions.OutputTimes = 0:0.05:25;
simdata = sbiosimulate(m1);

[time,data] = selectbyname(simdata,{'y','ydelay'});
plot(time, data(:,1), time, data(:,2));
xlabel('Time [hrs]');
legend('y','y_{delay}');
title('Delay = 2.5 hrs');
grid on;
set(gca, XLimitMethod="padded", YLimitMethod="padded");

Alternatively, one could write a function that keep tracks of the previous values of y and interpolate between them to find .

I hope this helps.

Jérémy