Unraveling ChR2-driven stochastic Ca2+ dynamics in astrocytes – A call for new interventional paradigms

Control of astrocytes via modulation of Ca2+ oscillations using techniques like optogenetics can prove to be crucial in therapeutic intervention of a variety of neurological disorders. However, a systematic study quantifying the effect of optogenetic stimulation in astrocytes is yet to be performed. Here, we propose a novel stochastic Ca2+dynamics model that incorporates the light sensitive component – channelrhodopsin 2 (ChR2). Utilizing this model, we studied the effect of various pulsed light stimulation paradigms on astrocytes for select variants of ChR2 (wild type, ChETA, and ChRET/TC) in both an individual and a network of cells. Our results exhibited a consistent pattern of Ca2+ activity among individual cells in response to optogenetic stimulation, i.e., showing steady state regimes with increased Ca2+ basal level and Ca2+ spiking probability. Furthermore, we performed a global sensitivity analysis to assess the effect of stochasticity and variation of model parameters on astrocytic Ca2+ dynamics in the presence and absence of light stimulation, respectively. Results indicated that directing variants towards the first open state of the photo-cycle of ChR2 (o1) enhances spiking activity in astrocytes during optical stimulation. Evaluation of the effect of astrocytic ChR2 expression (heterogeneity) on Ca2+ signaling revealed that the optimal stimulation paradigm of a network does not necessarily coincide with that of an individual cell. Simulation for ChETA-incorporated astrocytes suggest that maximal activity of a single cell reduced the spiking probability of the network of astrocytes at higher degrees of ChR2 expression efficiency due to an elevation of basal Ca2+ beyond physiological levels. Collectively, the framework presented in this study provides valuable information for the selection of light stimulation paradigms that elicit optimal astrocytic activity using existing ChR2 constructs, as well as aids in the engineering of future optogenetic constructs. Author summary Optogenetics – an avant-garde technique involves targeted delivery of light sensitive ion channels to cells. Channelrhodopsin 2 (ChR2), an algal derived light sensitive ion channel has extensively been used in neuroscience to manipulate various cell types in a guided and controlled manner. Despite being predominantly used in neurons, recent advancements have led to the expansion of the application of optogenetics in non-neuronal cell types, like astrocytes. These cells play a key role in various aspects of the central nervous system and alteration of their signaling is associated with various disorders, including epilepsy, stroke and Alzheimer’s disease. Hence, invaluable information for therapeutic intervention can be obtained from using optogenetics to regulate astrocytic activity in a strategic manner. Here, we propose a novel computational model to assess astrocytic response to optogenetic stimulation which implicitly accounts for the stochastic character of Ca2+ signaling in this cell type. We identified light stimulation paradigms suitable for eliciting astrocytic Ca2+ response within physiological levels in widely-used ChR2 variants and identified highly sensitive parameters in ChR2 kinetics conducive for higher probability in Ca2+ spiking. Overall, the results of this model can be used to boost astrocyte light-induced behavior prediction and the development of improved future optogenetic constructs.

, and components of the vector will be described 145 in detail. We have previously estimated the variance of the Weiner processes for IP 3 , Ca c , h and c o , using the 146 local linearization (LL) filter [59, 65] (Weiner processes, Table 1). Potential stochasticity in ChR2 dynamics is 147 included in the model using constant Weiner processes and will be explored in later sections. 148 The dynamics of free cytosolic calcium concentration is given by 149 (2) Where is the gap junctional flux of Ca 2+ flowing from astrocyte 'i' to its neighboring astrocytes (indicated 152 by index k). The efflux of Ca 2+ from the ER to the cytosol via the IP 3 R is described by 153 (2.2)

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The CCE effect is described as a phenomenological model using the following equation 161 (2.6) = Ca 2+ extrusion across the PM via PMCA is given by 163 (2.7) = [ 2 + ] 164 IP 3 changes in astrocytes mediated by PLC δ1 and intercellular diffusion is described as:

Dynamics of the fraction of open inactivation IP 3 R inactivation gates is given by
where describes the laser stimulus paradigm as a pulse train, and: ( ) The existence of ChR2 in various states should satisfy the following algebraic condition: 187 (10) The current generated by cationic influx through ChR2 is given by The diffusion term in equation 1 implies solving of the state-space system as an integrated model. In a 194 deterministic system, due to lack of feedback from Ca 2+ dynamics into that of ChR2, the dynamics of ChR2 can 195 be solved independently. The model was implemented in MATLAB 2018a (Mathworks Inc.) and was numerically solved using the LL method [59] with an integration step size of t = 0.1 ms. A listing of all parameters and their 197 descriptions can be found in Tables 1 and 2. 198 Light stimulation paradigm 199 In all simulations performed in this study, laser stimulus was modeled as a square wave pulse train with period 200 T, pulse width δ (expressed as a percentage of T), and unit pulse amplitude. This paradigm is employed to evaluate 201 the effect of light on astrocytic activity, in both individual and a network of gap junction connected astrocytes.    were calculated for each stimulation paradigm. The T-δ heat (color) maps, useful to determine optimal Ca 2+ 239 signaling behavior in astrocytes exposed to a variety of T and δ combinations, are shown in Figure 3B and C for  Figure 3C). Three representative traces from regions with low, intermediate and high astrocytic Ca 2+ spiking activity with 244 physiological Ca 2+ basal levels are depicted in Figure 3D.  Figure 4B shows the sensitivity of Ca 2+ activity to parameters of ChR2 during light stimulation with the paradigm 257 shown in Figure 3D, trace 1 (T = 4.5s and δ = 30%). Similar to the analysis in Figure 3A, the cutoff prominence 258 of the peaks counted was set to 350 nM to exclude 1/f noise related Ca 2+ spikes. The range of each parameter was 259 chosen such that the four ChR2 variants were encompassed in it (ChR2 parameters, Table 3). 1000 parameter sets  Figure 5D (for the full video, refer to supplementary video S1).

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The spatial arrangement of astrocytes and the subnetwork of astrocytes being stimulated are shown in Figure 5E.

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We developed a novel stochastic model to assess the effect of light stimulation on the Ca 2+ dynamics in astrocytes 309 expressing the widely used opsin -ChR2. We used three ChR2 variants -wild type, ChETA, and ChRET/TC.

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The proposed framework can further be adopted for investigating other opsins. Our model accounts for major 311 intracellular calcium signaling pathways as well as light-activated cationic influx through ChR2. We studied light-  Figure 3C) and low activity (point 1, Figure 3C). Also, with the increase in δ, there is a dynamics is yet to be investigated, we hypothesize that potential protein thermal noise and fluctuations in light 331 intensity due to photon migration dynamics may play a role. Figure 4B indicates that the kinetics of ChR2         Video S1. Movie of complete network-wide behavior of astrocytes to light stimulation. In this video the 531 stimulation window is marked in red. Parameters and stimulation specifics are as in Figure 5.