Modeling the dynamics of history dependent neuronal systems at all scales
Fidel Santamaria, PI
My lab has developed a mathematical and computational framework to model and analyze history dependent processes, from the diffusion of molecules inside, on the surface, and around neurons, to electrical network activity. What I can offer to experimentalists are unique tools to study scale free processes. This is not your traditional scale free statistical studies that look at long tail probability distributions, instead we can write and model differential equations that give you access to the dynamics of the problem. Our advantage is that we use fractional order integro-differential equations. This mathematical objects are the natural tool to study history dependent phenomena. The type of data I like are long term recordings, either in resting or active states. These recordings can be fluorescent traces from synaptic or neuronal activity, EEG, single- or multi-unit recordings. As an example, my collaborator in this grant, Maurice Chacron at McGill, records from weakly electric fish as they receive natural stimuli. We have been able to replicate the non-linear response of the neurons he records from using models but also, recently, implementing neuromorphic circuits.