Speed Gradient Control Algorithm for Optogenetic Modeling

We discuss the feedback algorithm for optogenetic control over membrane conductance in frame of Grossman-Nikolic-Toumazou-Degenaar (GNTD) ordinary differential system modeling response channelrhodopsin-2 (ChR2) expressing neurons to light stimulation with various types ChR2 mutants. The GNTD population dynamics contains four functional states (two open and two closed) transitions among them due photo-excitations stimulating or decays back from closed states. signal model is defined via photon flux per one dimensionless form. goal total a neural section ChR2. formulate form Fradkov’s speed gradient method driving dynamical phase space such that target function discrepancy between actual its desired level minimized. derive explicit equation field stabilizing characteristics perform numerical simulation controlled prove achievability goal. Our approach can be useful different experimental problems optogenetics, particularly, collective cells epilepsy, depression, tumors central nervous system.