1st International Conference on Applied Engineering and Natural Sciences, Konya, Turkey, 1 - 03 November 2021, pp.732
We discuss the feedback algorithm for the optogenetic control over the membrane conductance in the frame of Grossman-Nikolic-Toumazou-Degenaar (GNTD) ordinary differential system modeling the response of channelrhodopsin-2 (ChR2) expressing neurons to the light stimulation with the various types of ChR2 mutants. The GNTD population dynamics contains four functional states (two open and two closed) with the transitions among them due to photo-excitations with the stimulating light or decays back from the open to the closed states. The control signal in the model is defined via the photon flux per one ChR2 in the dimensionless form. The control goal is the total conductance of a neural section due to ChR2. We formulate the control algorithm in the form of Fradkov’s speed gradient method driving the dynamical system in the phase space such that the target function for the discrepancy between the actual total conductance and its desired level is minimized. We derive the explicit equation for the photon flux field stabilizing the conductance characteristics and perform the numerical simulation for the controlled GNTD differential system to prove the achievability of the control goal. Our approach can be useful for modeling different experimental problems of optogenetics, particularly, for driving the collective dynamics of neural cells in epilepsy, depression, and tumors of the central nervous system.