Control of neural synchrony using channelrhodopsin-2: a computational study

Abstract

In this paper, we present an optical stimulation based approach to induce 1:1 in-phase synchrony in a network of coupled interneurons wherein each interneuron expresses the light sensitive protein channelrhodopsin-2 (ChR2). We begin with a transition rate model for the channel kinetics of ChR2 in response to light stimulation. We then define "functional optical time response curve (fOTRC)" as a measure of the response of a periodically firing interneuron (transfected with ChR2 ion channel) to a periodic light pulse stimulation. We specifically consider the case of unidirectionally coupled (UCI) network and propose an open loop control architecture that uses light as an actuation signal to induce 1:1 in-phase synchrony in the UCI network. Using general properties of the spike time response curves (STRCs) for Type-1 neuron model (Ermentrout, Neural Comput 8:979-1001, 1996) and fOTRC, we estimate the (open loop) optimal actuation signal parameters required to induce 1:1 in-phase synchrony. We then propose a closed loop controller architecture and a controller algorithm to robustly sustain stable 1:1 in-phase synchrony in the presence of unknown deviations in the network parameters. Finally, we test the performance of this closed-loop controller in a network of mutually coupled (MCI) interneurons.

Computational Optogenetics: Empirically-Derived Voltage- and Light-Sensitive Channelrhodopsin-2 Model

“…This non-linear voltage dependence has been omitted in most prior models [9], [11], and in general, ChR2's voltage dependence has not been accurately represented in previous quantitative descriptions. Therefore, we collected a comprehensive experimental data set using multiple combinations of voltage and irradiances.…”

“…Versions of a four-state model are currently favored based on experimental evidence for four kinetic intermediates with differing time constants [12], [26], [27]. Current efforts also include modeling of different mutants [8], [11], as well as the integration of ChR2 into comprehensive cell models – neurons [8], [11], [28] and cardiomyocytes [10], [29]. While ChR2's light sensitivity has been studied extensively [13], data on its voltage dependence are limited [30].…”

“…While ChR2's light sensitivity has been studied extensively [13], data on its voltage dependence are limited [30]. Early models [9], [11] assumed a linear current-voltage relationship and no voltage-dependent gating. Since experimental results demonstrate prominent inward rectification [6], [18], [20], [21], [30], [31], more recent ChR2 models have incorporated some nonlinearity [8], [10].…”

Cardiac optogenetics

“…Conceptual and quantitative understanding of the function of ChR2 is aided by recent mathematical models, proposed by Hegemann and colleagues (53) and modified by others (49,101,121). A four-state model is currently favored, with two open states (a high-conductance and a low-conductance, lightadapted one) and two closed states.…”

“…It is harder to speculate about the performance of optogenetic pulses for cardioversion and defibrillation; computer modeling and in vitro experiments can provide more insight how the prestimulus state may affect the outcome. Figure 3 illustrates the response of a ventricular myocyte to comparable electrical and optical stimulation using computer simulations (unpublished data) with the ten Tusscher ventricular cell model (122), including a version of ChR2 modified from earlier papers (101,121).…”