Modelling ion channels with a view towards identifiability

by Ivo Siekmann.

Can we gain insight into the molecular structure of an ion channel from observing its opening and closing over time? Intuitively, we might expect that by mimicking the architecture of the channel in a model, the time scales of transitions between different biophysical states can be inferred from these observations. But on the one hand, many models are nonidentifiable which makes them unsuitable for mechanistic modelling of ion channels. On the other hand, models that represent completely different biophysical mechanisms can nevertheless be equivalent. Motivated by these challenges we suggest alternative approaches how opening and closing as well as biophysical dynamics of ion channels can be represented in mathematical models.

The fully-connected model is always non-identifiable model and therefore unsuitable for mechanistic modelling. But for some parameter sets it can be reduced to the models CCO or COC. CCO and COC are always equivalent although both represent different biophysical processes.