Pre-equilibrating models when performing global sensitivity analyses

Hello,

Is it possible to specify to pre-equilibrate a model, using functionality such as that available in sbiosteadystate, before applying doses when performing global sensitivity analyses?

Thanks,

Abed

Answer 1

[Florian Augustin]

Hi Abed,

You can chain a steady-state analysis and a global sensitivity analysis. For this you first have to run sbiosteadystate to compute the steady-state as you mentioned. The function returns a SimBiology model in steady-state (the third output argument of the function); all non-constant component values are set to the steady-state values and all initial assignment rules are disabled. The latter is important, because if the steady-state variant (that is also returned by sbiosteadystate) is used to simulate the original model in steady-state, then any active initial assignment rules will likely push the model off the steady-state.

Using the steady-state model, you can then perform the global sensitivity analysis. The doses you want to explore can be specified as name-value arguments when calling sbiosobol, sbiompgsa, or sbioelementaryeffects. You can also parameterize the doses to explore the effect of, for example, varying dose amounts.

I hope this helps.

-Florian

[Abed Alnaif]

Hi Florian,

Does this approach take into consideration that the steady-state may be different for the different parameter samples in the GSA?

Thanks,

Abed

[Florian Augustin]

Hi Abed,

My apologies, I was thinking of a different workflow. There is currently (Matlab release R2021b) no flag that allows you to specify that the model should be run to steady-state while running the global sensitivity analysis.

This rules out sbiosobol and sbioelementaryeffects, but you may still be able to use sbiompgsa; assuming the requirement for this type of analysis is met; a way to check this is that the steps in the eCDF plots should become smaller with increasing number of samples.

The workflow to achieve the GSA in steady-state is possible but a bit complicated. Here is the general idea:

1. Use SimBiology.Scenarios to generate parameter samples for the sensitivity analysis. You can specify probability distributions and sampling methods / options in a similar way as you would for sbiompgsa.
2. Compute the steady-state for all scenarios.
3. Generate simulation data by simulating the model based on the steady-state configuration.
4. Run sbiompgsa for parameter samples (from step 1) and the generated simulation data (from step 3).

An example how this could be done is attached. You would have to swap out the model, configure the sensitivity inputs/outputs, adapt the model simulation off of the steady state (lines 43 and 47), and adapt the classifier in line 57. You may also want to change the configuration of how sbiosteadystate is called.

Best,

Florian

Edited (Nov. 22, 21): Correction of the attached script to use independent samples for the sensitivity inputs.

[Abed Alnaif]

Thank you, Florian! I'm able to follow and understand the example workflow. This is very helpful.

[Abed Alnaif]

Florian, one more question related to the workflow: The documentation for sbiosteadystate indicates that the output variant will contain "all non-constant species, compartments, and parameters of the model having the steady-state values". However, I noticed in the workflow that the output variant contains constant parameters, and the workflow as coded depends on this, because only the steady-state variant is passed into the call of the simfunction on Line 48. Can you please confirm the behavior of sbiosteadystate -- does the outputted variant include constant parameters?

[Florian Augustin]

Hi Abed,

Yes, this is the behavior of sbiosteadysteate. The reason is that the variant captures a snapshot of the model components' values at steady-state. This includes values of constant components because values of non-constant components depend on them. Otherwise, changing values of constant components on the model would mean that the variant does not represent a steady-state of the model anymore.

Unrelated to your question, I wanted to point out one subtlety of the script that I hinted at in the first answer I posted on this thread. It assumes that the model does not have inital assignment rules (it uses the original model for running the simulations). If your model has initial assignment rules you would either have to deactivate/reactivate those before/after creating the SimFunction (line 44), or change lines 36 and 44 to use the model returned by sbiosteadystate:

% Get model in steady-state that has initial assigment rules deactivated:

[success, steadyStateVariant, steadyStateModel] = sbiosteadystate(...);

% Use steady-state model with deactivated initial assignment rules to create SimFunction:

simFun = createSimFunction(steadyStateModel, params, sensOutputs, []);

Best,

Florian