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Luis B. Walter
Last activity on 17 Jun 2024

Different dilution effect on the kinetics of a time course

Hi to everyone!

To simplify the explanation and the problem, I simulated the kinetics of an irreversible first-order reaction, A -> B. I implemented it in two independent compartments, R and P. I simulated the effect of a dilution in R by doubling at t= 0,1 the R volume. I programmed in P that, at t = 0.1, the instantaneous concentration of A and B would be reduced by half. I am sending an attach with the implementation of these simulations in the Simbiology interface.

When the simulations of the two compartments are plotted, it can be seen that the responses are not equal. That is, from t = 0.1 s, the reaction follow an exponential function in R with half of the initial amplitude and half of the initial value of k1. That is, the relaxation time is doubled. Meanwhile, in P, from t = 0.1, the reaction follows exponential kinetics with half the amplitude value but maintaining the initial value of k = 10. Without a doubt, the correct simulation is the latter (compartment P) where only the effect is observed in the amplitude and not in the relaxation time. Could you tell me what the error is that makes these kinetics that should be equal not be?

Thank you in advance!

Luis B.

SimBiology

Daniel Bending
Last activity on 10 Jun 2024

Integration Tolerance Bizarre Reaction:

Hi All,

I've been producing a QSP model of glucose homeostasis for a while now for my PhD project, recently I've been able to expand it to larger time series, i.e. 2 days of data rather than a singular injection or a singular meal. My problem is as follows: If I put 75g of glucose into my stomach glucose species any later than (exactly) 8.5 hours I get an integration tolerance error. Curiosly, I can put 25g of glucose in at any time up to 15.9 hours, then any later an error. I have disabled all connections to my glucose absorption chain, i.e. stomach -> duodenum -> jenenum -> ileum -> removal, to isolate the cause of this. I had initially thought it may be because I mechanistically model liver glycogen and that does deplete over time, but I've tested enough to show that that does nothing. My next test is to isolate the glucose absorption chain into a seperate model and see if the issue persists but I'm completely baffled!

These are the equations, to my eye there's no reason why there would be such a sharp glucose quantity/time dependence, they all begin at a value of 0:

d(Gs)/dt = -(kw*(1-Gd^14/(Igd^14+Gd^14))*Gs) #Stomach glucose

d(Gd)/dt = (kw*(1-Gd^14/(Igd^14+Gd^14))*Gs) - (kdj*Gd) #Duodenal Glucose

d(Gj)/dt = (kdj*Gd) - (kji*Gj) #Jejunal Glucose

d(Gi)/dt = (kji*Gj) - (kic*Gi) #Ileal Glucose

(The sigmoidicity of gastric emptying slowing term (^14) was parameterised off of paracetamol absorption data and appears to be correct!)

Thank you for your help, best regards,

Dan

Pre-Edit: I changed the run time to 30 hours and now I can't use the 75g input any later than 7.9 hours not 8.5 hours anymore!

Edit: This is how it appears at all times prior to it failing for 75g:

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