Issues with Crauste Model

[FFroehlich]

I just had a brief look at the model equations to investigate sources of the notorious integration issues with that model and ... I am not necessarily surprised that this model causes issues: the Memory species is lacking a cell death reaction and is effectively unbounded.

It looks like the issue is already present in the original d2d implementation: https://github.com/Data2Dynamics/d2d/blob/master/arFramework3/Examples/Crauste_ImmuneCells_CellSystems2017/Models/ModelImmuneCells.def

From all I can tell this reaction is supposed to be present in the original model (see attached screenshot of Figure 3, specifically panel C).

There also appear to be other discrepancies with the model in Figure C (baseline and pathogen mediated early effector cell death; baseline late effector cell death are missing), but the authors did model selection so it might be another model that is implemented here. However, other model variants appear to implement other differentiation trajectories, which should not involve cell death reactions.

[FFroehlich]

Looking at Table S3, the kinetic parameters for the omitted reactions appear to be zero, so these implementation decisions might have been intentional (with the exception of EarlyEffector cell death, which is not even listed in the table). Still, having a sink state appears unphysiological and numerical issues are to be expected.

[FFroehlich]

Deeper dive into model dynamics suggest that numerical issues are due to finite time blowup for the EarlyEffector species, not the Memory sink state. Hence, there might not be a link between numerical issues and altered model structure.