Interpreting Steady State Sensitivity data

[Terrell]

Hello COPASI community,

I am in dire need of help in interpreting the steady state sensitivity analysis outputted by COPASI.

[sven....@gmail.com]

Without knowing the model it is difficult to interpret what happened here. What the tables explicitly say it the following:

The first table: Changing k0 k5 and k6 does not change the steady state concentrations. Changing k1 k9 and k19 changes them a tiny bit in absolute numbers.

second table: Now the sensitivities are scaled by the actual values of the parameters and steady state concentrations. I.e. the values is the first table are multiplied by the parameter values and divided by the steady state concentrations. This seems to indicate that the concentrations are tiny or the parameter values are huge. Concentration of G is probably 0, so that division is not possible. Since the scaled sensitivities are negative where the sensitivities are positive, either some parameter values or the concentrations are negative, possibly just a tiny bit below zero. In any case (without knowing the model) these are extreme values that could indicate some numerical instability.

last table: Just the euclidian norm  of the colums of table 2, so  basically a summary of the effect of the parameters. If table 2 is already questionable, it does not make any more sense to interprete these.

So in summary, I suspect the results are not really meaningful for numerical reasons, and without knowing the model I cannot exactly see what happened.

Hope that helps,,

Sven

[Terrell]

Hi Sven, thank you for taking the time to respond. With regards to table 2, none of the plots I have has zero concentration; although, I'm not sure what you meant by a parameter being negative. Did you mean they have a negative sign in the ODE involved. My model only used ODEs and I've highlighted them below. Also the parameters I have are positive rate constants, and none of the concentration plots converges to zero.

[Terrell]

Although number of particles for E is very very small at the end of the simulation.

[Terrell]

For the sake of completeness, I've included the model used in the simulation.

[sven....@gmail.com]

OK. From the simulation results you give I do not immeditately see why the steady state sensitivities should give such strange results. Possibly the model has several steady states and the steady state task of COPASI finds a different one. In order to understand what happens here I would have to try the model myself. If you wish you could send the model to me privately and it will be treated confidentially.

Sven

[Terrell]

This is very nice of you. I'm sharing the model here. The ODE model I have constructed is my attempt at simplifying the known interactions of the insulin signaling pathway components (e.g. G for the arbitrary growth factor, K stands for the AKT-kinase PIP3, and A for AKT) with the MAPK, ERK denoted by E. Although, I have already changed the parameters using the parameter estimation task (The measured data does not fit though :( ). Also, the particle number plots does not show the plot for E which I am utterly confused. I have also attached the data from literature used for parameter estimation, just in case. Thank you!

[Terrell]

Please use this model instead.

[sven....@gmail.com]

It seems the model is numerically very demanding, but while I find out why this is (and I suspect it is because the differential equations mix particle numbers and concentrations, which are on a dramatically different numerical scale) there is a workaround for the steady state sensitivities:

Since the steady state calculation for this model does not seem to work reliably, you can use time course instead, if you have previously manually confirmed that the system runs into a steady state. This seems to be the case here, so if you choose "time course" in the sensitivities task, and in the time course task set the duration that is long enough to reach the steady state, e.g. 100h, you will basically get the steady state sensitivities. This works for me.

[sven....@gmail.com]

Ok, I have looked at the model in more detail, and the RHS of the ODEs contains references to the particle numbers of the chemical species, and since the volume in the model is 1 litre, and the units are set to molar, this is a huge number. This would not be a problem in itself (COPASI always uses particle numbers internally for calculation) but in the denominator of the ODEs somtimes the absolute value "1" is added to a particle number to get a saturation dynamics. I suspect that this is not the intended scaling. I can see to solutions: The clean way would be to rewrite the ODEs to use concentrations instead of particle numbers. The quick way would be to set the "amount" unit to "1" instead of "mole", this means the particle numbers and concentrations are identical as long as the volume is also 1.

[Terrell]

Thank you Sven, this is informative!

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