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

Arash Moshkforoush; Lakshmini Balachandar; Carolina Moncion; Karla A. Montejo; Jorge Riera

doi:10.1371/journal.pcbi.1008648

Abstract

Optogenetic targeting of astrocytes provides a robust experimental model to differentially induce Ca²⁺ signals in astrocytes in vivo. However, a systematic study quantifying the response of optogenetically modified astrocytes to light is yet to be performed. Here, we propose a novel stochastic model of Ca²⁺ dynamics in astrocytes that incorporates a light sensitive component—channelrhodopsin 2 (ChR2). Utilizing this model, we investigated the effect of different light stimulation paradigms on cells expressing select variants of ChR2 (wild type, ChETA, and ChRET/TC). Results predict that depending on paradigm specification, astrocytes might undergo drastic changes in their basal Ca²⁺ level and spiking probability. Furthermore, we performed a global sensitivity analysis to assess the effect of variation in parameters pertinent to the shape of the ChR2 photocurrent on astrocytic Ca²⁺ dynamics. Results suggest that directing variants towards the first open state of the ChR2 photocycle (o₁) enhances spiking activity in astrocytes during optical stimulation. Evaluation of the effect of Ca²⁺ buffering and coupling coefficient in a network of ChR2-expressing astrocytes demonstrated basal level elevations in the stimulated region and propagation of calcium activity to unstimulated cells. Buffering reduced the diffusion range of Ca²⁺ within the network, thereby limiting propagation and influencing the activity of astrocytes. Collectively, the framework presented in this study provides valuable information for the selection of light stimulation paradigms that elicit desired astrocytic activity using existing ChR2 constructs, as well as aids in the engineering of future application-oriented optogenetic variants.

Author summary

Optogenetics is a novel technique involving the targeted delivery of light-sensitive ion channels like Channelrhodopsin-2 (ChR2) to cells. Recently, this technique has been expanded to non-neuronal cell types, e.g., astrocytes. Optogenetic control of astrocytes in vivo can aid in further understanding the intricacies of their debated roles in the brain. Here, using a mathematical model, we evaluate the effect of short and long-term light stimulation of ChR2-expressing astrocytes on their Ca²⁺ spiking activity and basal level. We further investigate how ChR2 gating dynamics, buffering, and coupling coefficient of Ca²⁺ influence astrocytic activity in a single cell and a network. Results of our study can serve as a tool for experimental design and engineering of new application-oriented optogenetic constructs targeting astrocytes.

Figures

Citation: Moshkforoush A, Balachandar L, Moncion C, Montejo KA, Riera J (2021) Unraveling ChR2-driven stochastic Ca²⁺ dynamics in astrocytes: A call for new interventional paradigms. PLoS Comput Biol 17(2): e1008648. https://doi.org/10.1371/journal.pcbi.1008648

Editor: Hugues Berry, Inria, FRANCE

Received: September 10, 2020; Accepted: December 20, 2020; Published: February 10, 2021

Copyright: © 2021 Moshkforoush et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Data Availability: This is a theoretical study and the codes associated with this study can be downloaded from http://web.eng.fiu.edu/jrieradi/CaAnalysisCode/.

Funding: This study was supported by the National Institutes of Health 1R56NS094784-01A1 (J.R.D, https://projectreporter.nih.gov/project_info_description.cfm?aid=9291709&icde=51611287) and the Wallace Coulter Foundation BME SEED grant at Florida International University (J.R.D, https://bme.fiu.edu/). Karla Alejandra Montejo was supported by the National Institutes of Health NIGMS R25GM75148 (https://projectreporter.nih.gov/project_info_description.cfm?aid=9851524&icde=51610950&ddparam=&ddvalue=&ddsub=&cr=4&csb=default&cs=ASC&pball=) and NINDS R01 NS107336-02S1 (https://projectreporter.nih.gov/project_info_description.cfm?aid=9693342&icde=51610799) The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

The role of astrocytic calcium signaling in various regulatory mechanisms in the brain is far from being fully understood and is a subject of considerable controversy [see refs [1–6]]. These are fueled in part by the limited in vivo reproducibility of in vitro/in situ experimental observations [7–10], as well as a dearth of cell-specific protocols to induce astrocytic Ca²⁺ signaling in vivo in order to delineate their role from ongoing neuronal activity. Sensory and transcranial direct current stimulation techniques [11–13] have been used to elicit Ca²⁺ changes in astrocytes. However, these methods lack cell specificity due to the concurrent activation of other cell types, including neurons. Studies have also modulated astrocytic Ca²⁺ activity in vivo using cell-specific techniques including Ca²⁺ uncaging [14,15], chemogenetics [16,17] and optogenetics [18,19]. Ca²⁺ uncaging requires invasive site-specific delivery of calcium vehicles, which are rendered inoperative upon depletion via photolysis. Chemogenetics, e.g., designer receptor exclusively activated by designer drugs (DREADDS), offers a platform for controlled, targeted drug delivery; however, they suffer from low temporal resolution. Contrarily, optogenetics is an avant-garde, minimally invasive, and reproducible approach [20,21], providing a platform to genetically target specific cell types with high temporal and spatial precision, which can be employed as a tool to exclusively modulate astrocytic Ca²⁺ signaling in vivo.

Despite the recent inception of the field of optogenetics, a wide variety of optogenetic tools have been constructed, among which channelrhodopsin 2 (ChR2) has been one of the most commonly used. Applications of this technique in astrocytes has helped examine the role of these cells in memory enhancement [22], cortical state switching [23], and hyperemic response [18,19]. The biophysical characterization and the response to light stimulation in several ChR2 variants, predominantly in excitable cells, are available in literature [24,25]. More recently, several ChR2 variants have been engineered for enhanced channel conductance (ChETA) [26], increased calcium permeability (CaTCh) [27], and faster recovery kinetics (ChRET/TC) [28]. ChR2 constructs have also been modified to form chimeric variants to regulate responses and facilitate multiwavelength optogenetics in neurons [29]. Contrary to neurons, a holistic approach to quantify the effect of light stimulation on astrocytes has not yet been formulated. Given that light activation of ChR2-enabled astrocytes alters dynamics of intracellular ionic species, mathematical modeling can be of importance in predicting how laser specifications, as well as the biophysical properties of the ChR2 construct, can affect astrocytic calcium signaling. Available theoretical models of Ca²⁺ dynamics in astrocytes primarily rely on elevating intracellular IP₃ levels to initiate a Ca²⁺ response from the intracellular stores and have not evaluated the effect of direct influx of these ions through transmembrane channels, e.g. ChR2. To achieve predictions with high accuracy, it is also imperative that the model accounts for the stochastic nature of spontaneous calcium oscillations in these cells, which result from the random opening of the inositol trisphosphate receptor (IP₃R) channels in clusters. Such a model can guide experimentalists in optimizing light stimulation paradigms for existing optogenetic variants to achieve desired Ca²⁺ levels in astrocytes, as well as aid in the development of novel application-based constructs targeting these cells.

To this end, we outline a novel stochastic model of astrocytic calcium dynamics with an incorporated optogenetic component—ChR2. Firstly, we quantify and evaluate the effect of different light stimulation paradigms on the Ca²⁺ dynamics of single cells expressing three existing ChR2 variants, i.e., wild type (WT), ChETA, and ChRET/TC. For the WT variant, we use the two channel characterizations provided in ref. [30], namely WT₁ and WT₂. Using the model, we analyze the effect of light stimulation in astrocytes congruent with experimental recording durations (in the order of tens of minutes) [31–33], and also gauge the potential effect of long-term optogenetic stimulation (in the order of several hours or beyond) in these cells. Secondly, we quantify the effect of varying stimulation light intensities on a ChR2-incorporated astrocyte with respect to its spiking rate and basal level. Thirdly, to identify key features necessary for the development of prospective ChR2 constructs, we perform a global sensitivity analysis of different parameters of the single cell model to the model output. Lastly, through the incorporation of gap junctions allowing for the diffusion of IP₃ and Ca²⁺, we analyze the effect of local light stimulation on the global Ca²⁺ response in a network of astrocytes expressing ChR2.

Materials and methods

The biophysical model outlined in Fig 1 consists of our previously developed model of astrocytic calcium dynamics [34,35], based on the Li-Rinzel simplification of the De Young-Keizer model [36,37], and a 4-state model of ChR2 photocurrent kinetics adapted from refs. [30,38]. We incorporated a 4-state model of ChR2 photocycle, as previous studies have demonstrated its superiority in capturing the dynamics of the ChR2 photocurrent compared to 3-state models [30,39]. The ChR2 model assumes two sets of intra-transitional closed/open states, i.e., dark-adapted (c₁ and o₁) and light-adapted (c₂ and o₂), in describing the dynamics of a ChR2 photocycle. Light stimulation window (S₀(t)) is modeled as a pulsed train with unit amplitude and is characterized by a period (T) and a pulse width (δ) (expressed as a percentage of T), indicating the duration within the pulse period for which the light is on.

Download:

Fig 1. Schematic of the biophysical model.

A model for a ChR2-expressing astrocyte is presented, accounting for: 1) Ca²⁺ release from the endoplasmic reticulum (ER) into the cytosol via the IP₃R clusters, 2) Phospholipase-C δ1 (PLC_δ1) mediated production of IP_3, 3) capacitive calcium entry (CCE) via the store operated calcium channel (SOC), 4) passive leak from the ER to the cytosol (J_leak), 5) replenishment of ER stores via sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) pump, 6) extrusion of Ca²⁺ by plasma membrane Ca²⁺ ATPase (PMCA) pump into the extracellular (EC) space, 7) passive leak (J_in) into the cytosol from the EC space, and 8) Ca²⁺ buffering by endogenous buffer proteins. In astrocytic network simulations (bottom panel), each cell is connected to its neighboring cells though Ca²⁺ and IP₃ permeable gap junctions, indicated as and , respectively, and a central region (blue shaded box) is stimulated with light. A 4-state model [closed states (c₁ and c₂) in red and open states (o₁ and o₂) in blue] is used to represent ChR2 gating dynamics. The blue light (λ = 470 nm) stimulation paradigm used to open ChR2, leading to a Ca²⁺ influx (J_ChR2), is characterized by pulse period (T) and pulse width (δ).

https://doi.org/10.1371/journal.pcbi.1008648.g001

The model incorporates Ca²⁺ influx from the extracellular space through a light-evoked ChR2 flux (J_ChR2), a capacitive calcium entry (CCE) flux via store-operated Ca²⁺ channels (SOC) (J_CCE), and a leak flux representing other transmembrane Ca²⁺ channels and exchangers (J_in). It also accounts for the release of Ca²⁺ from the endoplasmic reticulum (ER) into the cytosol through IP₃Rs (), a form of Ca²⁺-induced Ca²⁺ release (CICR) process, and a leak flux (J_Leak). Replenishment of ER Ca²⁺ is done via activation of the sarco(endo)plasmic reticulum Ca²⁺-ATPase (SERCA) pump, while plasma membrane Ca²⁺ ATPase (PMCA) pump extrudes cytosolic Ca²⁺ into the extracellular space. The dynamics of IP₃ concentration in the soma ([IP₃]) is included via Ca²⁺-dependent activation of the Phospholipase C_δ1 (PLC_δ1) pathway. Buffering of Ca²⁺ is explicitly accounted for by a fast buffering approximation process [40]. Intercellular signaling in a network of astrocytes is modeled by incorporation of Ca²⁺ and IP₃ permeable gap junctions between neighboring cells.

Single cell model

The dynamics of a single ChR2-enabled astrocyte can be summarized by the following system of stochastic differential equations (SDEs): (1) where x = ([Ca²⁺]_c, [IP₃], h, [C_o], o₁, o₂, c₁, c₂, s)^T is the vector of state variables, [Ca²⁺]_c is the cytosolic calcium concentration, [C_o] is the total Ca²⁺ concentration in the cell, i.e., cytosol and ER, h is the fraction of open inactivation gates of IP₃R channels, and s captures the temporal kinetics of conformational changes of ChR2 following light stimulation. p denotes the vector of model parameters summarized in Table 1. Components of the f vector, i.e., the drift rate function, contain deterministic equations of the single cell model and are described in detail in later sections. G is a diagonal matrix of diffusion rate components of the stochastic processes (noise) associated with state variables. The Brownian motion vector is denoted as dω.

Download:

Table 1. Model parameters.

https://doi.org/10.1371/journal.pcbi.1008648.t001

The components of the G matrix are generally determined by the rate parameters of the deterministic part of the SDE, which lead to a state-dependent multiplicative noise in the system [32,44]. In calcium dynamics, the source of stochasticity is mainly attributed to the aggregation of a small number of IP₃R channels in clusters, which leads to the formation of intra-cluster Ca²⁺ blips (resulting from random opening of a single IP₃R) or Ca²⁺ puffs and sparks (from the concurrent opening of a large number of IP₃Rs within a cluster). When coupled with other clusters, synchronized Ca²⁺ puffs can originate global Ca²⁺ events in the cell [32]. Several schemes have been developed to model the stochastic dynamics of IP₃Rs in different cell types, ranging from models incorporating detailed Markov Chain processes, to those adapting Fokker-Planck approximations (or their equivalent Langevin equations) of the Markov approaches [refer to ref. [45] for a review of the deterministic and stochastic models of IP₃Rs].

In this study, we adopted the Langevin approach outlined in ref. [43] for the dynamics of open IP₃R inactivation gates in Eq 1, where the associated noise is a Gaussian white noise with zero mean and the variance () depending on the levels of [Ca²⁺]_c, [IP₃], h, and the number of IP₃Rs in a cluster. We have previously estimated the noise level in the equations for [IP₃], [Ca²⁺]_c, and [C_o] in astrocytes as additive, uncorrelated Wiener processes with zero mean and a constant variance () [35] using the local linearization (LL) filter [46] (Table 1). These processes account for potential sources of stochasticity other than the dynamics of the IP₃R channels. We further assume that the dynamics of ChR2 gating is only deterministic, i.e., .

The dynamics of the free cytosolic calcium concentration is given by: (2) where θ = b_tK/([Ca²⁺]_c+K)² is the buffering factor; b_t is the total buffer protein concentration; and K is the buffer rate constant ratio [40].

The efflux of Ca²⁺ from the ER into the cytosol via the IP₃R channel can be described as: (2.1) where (2.2) (2.3) (2.4)

The leak of Ca²⁺ ions from ER into the cytosol is modeled as: (2.5)

A hill-type kinetic model describing the activity of the SERCA pump is given by: (2.6)

The flux through SOC channels is described using the following equation: (2.7)

Ca²⁺ extrusion across the PM via PMCA is given by: (2.8)

PLC_δ1-mediated IP₃ changes in the cell is described as: (3) where denotes the basal rate of IP₃ production in the cell. PLC_δ1 activity is described with a Hill’s kinetic model as: (3.1)

The dynamics of the fraction of open inactivation IP₃R gates is given by: (4) where the opening (α_h) and closing (β_h) rates are defined as: (4.1) (4.2) and (4.3) where N is the number of IP₃Rs within a cluster.

The total free Ca²⁺ in the cell is modeled as: (5) with a zero-mean Gaussian noise component with a constant variance .

The open and closed gating dynamics of ChR2 are given by: (6) (7) (8) (9)

The existence of ChR2 in open and closed states satisfies the following algebraic condition: (10)

The current generated through ChR2 is given by: (11) where G(V_m) is the voltage dependent rectification function determining the shape of ChR2 photocurrent with changing V_m. The resultant flux through ChR2 is then derived as (11.1)

Although ChR2 is a non-selective cation channel, in this study, we assume that J_ChR2 is solely a calcium flux, as calcium dynamics is one of the most prominent modes of signaling in astrocytes.

Quantification of astrocytic activity

Throughout this manuscript, we calculated the light-evoked mean spiking rate and basal level of [Ca²⁺]_c as a measure of astrocytic activity. For spiking rate calculations, we first removed the trend of simulated calcium traces, i.e., ChR2-induced steady rise in the baseline levels as observed in the traces of Figs 2 and 3. Using a threshold of 0.2 μM, calcium spikes were detected from the baseline-corrected traces and used to compute the mean spiking rate over the entire duration of stimulation. This threshold was chosen to exclude small-amplitude Ca²⁺ fluctuations from the calculation of the mean spiking rate. Light-induced elevations in the Ca²⁺ basal levels were calculated at the end of the stimulation window. These two measures were compared to study the effect of different light stimulation paradigms, i.e., varying combinations of T and δ values, as well as model parameters, on the response of optogenetically-stimulated astrocytes.

Download:

Fig 2. Response of ChR2 variants to light stimulation.

Representative traces (90 minutes in duration) of IP₃ concentration ([IP₃]), cytosolic calcium concentration ([Ca²⁺]_c), fraction of open inactivation IP₃R gates (h), and total calcium concentration ([C_o]) for an astrocyte expressing various ChR2 variants (wild type 1 (WT₁), wild type 2 (WT₂), ChETA and ChRET/TC) in response to light stimulation (T = 2 s, δ = 20% (0.4 s), unit amplitude). The blue horizontal solid line indicates the stimulation window.

https://doi.org/10.1371/journal.pcbi.1008648.g002

Download:

Fig 3. Response of a ChETA-expressing astrocyte to various light stimulation paradigms.

Simulations were conducted to evaluate astrocytic Ca²⁺ response to different paradigms ranging from T = 1–5 s and δ = 0–100% of T (trials = 5). A) Heat maps of Ca²⁺ basal level (top panel) and spiking rate (bottom panel) for the T-δ combinations assessed. Each column depicts basal level and spiking rate heat maps up to a certain point, i.e. 45, 90, and 270 minutes, to determine the cell response as light stimulation progresses from short-term to long-term. Scale bars for heat maps of basal level and spiking rate were capped to 3 μM and 0.6 spikes/min, respectively. The △ and ◊ symbols correspond to T-δ combinations that result in the traces of panel B. B) Representative [Ca²⁺]_c traces corresponding to T-δ combinations highlighted in A [Top trace (△): T = 2 s, δ = 1% (0.02 s); Bottom trace (◊): T = 4 s, δ = 45% (1.8 s)]. The inset of each trace highlights a 15-minute section to show the detected Ca²⁺ spikes. For spike detection, a threshold of 0.2 μM above the basal level was utilized. Each vertical solid grey line denotes the time points corresponding to heatmaps of panel A. C) Average (μ_ISI) vs. standard deviation of ISI (σ_ISI) where each point corresponds to a single simulated 270-min [Ca²⁺]_c trace. Solid line shows the linear fit between μ_ISI and σ_ISI values. Throughout the manuscript, △, ○, and ◊ represent paradigms resulting in low, medium, and high Ca²⁺ spiking during short-term (45 min) stimulation of astrocytes, respectively.

https://doi.org/10.1371/journal.pcbi.1008648.g003

Sensitivity analysis

A global sensitivity analysis was performed to assess the sensitivity of the single cell model output, i.e., Ca²⁺ spiking rate and basal level, to variation in parameters determining the magnitude of ChR2 photocurrent and those describing the Ca²⁺ buffering kinetics. Each parameter was allowed to vary around its control value within a lower and upper bound (Table 2), and the Latin hypercube sampling (LHS) method with uniform distribution was used to select 1000 random parameter sets to perform the sensitivity analysis [47,48]. The upper and lower bounds were selected such that the range encompasses reported values of parameters for different variants of ChR2. The single cell model was solved for each parameter set, and the partial rank correlation coefficient (PRCC) for each parameter was then computed to determine the magnitude of the parameter influence (positive or negative) on the desired model output. A 95% confidence interval was chosen to determine if the exerted influence is statistically significant.

Download:

Table 2. Range of parameters for global sensitivity analysis.

https://doi.org/10.1371/journal.pcbi.1008648.t002

Astrocytic network model

To study the network-wide response of astrocytes to light stimulation, we incorporated Ca²⁺ and IP₃ permeable gap junctions between cells in a network of astrocytes. Fluxes: (12) (13) represent the flow of Ca²⁺ and IP₃, respectively, from astrocyte ‘i’ in the network to its neighboring cells (indicated by index k). Local and global calcium events are simulated upon focal light stimulation of astrocytes, i.e., a region in the center of the network. Simulations were performed with varying levels of Ca²⁺ coupling coefficient, , in the presence and absence of Ca²⁺ buffering. Calcium responses in the network, i.e., the basal levels and spiking rates, were fitted with a symmetrical 2D Gaussian profile (H(ζ)) to quantify the peak Ca²⁺-basal/spiking (h_max,ζ), as well as the magnitude of the spread of Ca²⁺-basal/spiking activity (σ_ζ) within the network: (14) where ζ represents calcium basal level or mean spiking rate, h_min,ζ is the minimum value of the ζ in the network, x₀ and y₀ are the indices of the astrocyte at the center, and x and y are the location of cells away from the origin in both directions. The effect of calcium buffering, varying levels of , and the number of cells expressing ChR2 on both the peak and spread of basal/spiking activity was investigated.

All simulations were performed in MATLAB using the Local Linearization method described in refs. [46,49] with an integration step size of 0.1 ms. A listing of all parameters and their descriptions is provided in Tables 1 and 2. The codes associated with this study can be downloaded from http://web.eng.fiu.edu/jrieradi/CaAnalysisCode/.

Results

Effect of ChR2 variants on the light-evoked response of astrocytes

Representative traces for the time evolution of state variables of Eq 1 for astrocytes expressing different variants of ChR2 are illustrated for 90 minutes of light stimulation (Figs 2 and S1). Simulations reveal a progressive increase in the spiking activity of cytosolic calcium in all variants with the duration of stimulus. Apparent in the traces is a lag between the onset of light stimulation and regions with more regular spiking activity, likely reflecting the time required for [Ca²⁺]_c to reach sufficient levels to activate IP₃R channels. Traces show a steady increase in the total calcium content of the cell, and conversely, a decreasing trend in the fraction of open IP₃R inactivation gates (h). The [IP₃] levels, however, show a rather steady profile for WT and ChETA variants, and predict only a slight increase towards the end of the stimulation window for ChRET/TC. This increase can be attributed to the elevated basal [Ca²⁺]_c in ChRET/TC expressing astrocytes, activating the production of IP₃ via the PLC_δ1 pathway ([Ca²⁺] at half- maximal activation of PLC_δ1 is ~0.5 μM, Table 1). Comparison of results across variants suggests that light-induced changes are steepest in astrocytes expressing ChRET/TC. These model predictions are in line with the higher magnitude of the ChR2 flux in ChRET/TC compared to other variants in both transient and plateau regions of the photocurrent during the light stimulus (S2 Fig). Furthermore, results suggest that for the simulation time in this figure, the mechanism of light-evoked increased spiking in cytosolic calcium, predominantly in WT or ChETA enabled astrocytes, is mainly through the activation of IP₃Rs by increases in [Ca²⁺]_c rather than elevations in [IP₃].

Effect of light stimulation paradigm on single cell model response

Heat maps (Fig 3A) show the effect of various light stimulation paradigms on the spiking rate and Ca²⁺ basal level in ChETA-expressing astrocytes for different stimulation times, i.e., 45, 90, and 270 minutes (for other ChR2 variants refer to S3 Fig). Simulations show that as the stimulus duration increases, the Ca²⁺ basal level rises steadily due to a net Ca²⁺ entry into the cytosol (note the upward trend of [C_o] in the traces of Fig 2). This effect is demonstrated in representative traces of Fig 3B, where depending on the T-δ combination, [Ca²⁺]_c may reach supraphysiological, toxic levels which bring the cell outside of the window for regular spiking (i.e., [Ca²⁺]_c window for IP₃R-mediated Hopf bifurcation; notice the bottom trace of Fig 3B). Consequently, T-δ combinations that elicit high spiking activity in astrocytes during short-term stimulation (45 min) will transition into regions with medium and low activity as the stimulus progresses (notice the ◊ symbol in spiking rate heat maps, bottom panel of Fig 3A). Conversely, as seen in the top trace of Fig 3B, combinations with low levels of spiking in short-term stimulations might transition into regions eliciting high calcium activation, with basal levels within the physiological range, as the stimulation progresses. Thus, to remain within optimal spiking and basal [Ca²⁺]_c levels, one might choose stimulus waveforms based on the desired stimulation duration. It should be noted, however, that the predicted behavior is also a consequence of Ca²⁺ buffering capacity of the cell, light intensity, and parameters determining the shape and magnitude of the ChR2 photocurrent (Fig 4).

Download:

Fig 4. Model sensitivity to light intensity, Ca²⁺ buffering, and ChR2 parameters.

A) Effect of different light intensities and stimulation paradigms on the basal level and mean spiking rate of a ChETA-expressing astrocyte. Light intensity was varied as a fraction of the control value (I₀). Stimulation paradigms were selected based on the 45-min spiking rate heat map in Fig 3A for low (△), medium (○), and high (◊) activity regions. Data is shown as mean ± std (trials = 5). B) Global sensitivity analysis of the astrocytic Ca²⁺ response to variations in ChR2 and Ca²⁺ buffering parameters during light stimulation (Δ: T = 2 s, δ = 1% (0.02 s)). Parameters were allowed to vary within a range (Table 2) and 1000 parameter sets were selected using Latin Hypercube Sampling (LHS) with uniform distribution. The partial rank correlation coefficient (PRCC) of each parameter was calculated as a measure of their effect on the basal level (red) and spiking rate (blue) of a ChR2-expressing astrocyte. * denotes statistically significant (p < 0.05) positive or negative influence.

https://doi.org/10.1371/journal.pcbi.1008648.g004

To quantify the regularity of light-evoked calcium spiking in the astrocyte model, we demonstrate the σ_ISI−μ_ISI relationship for the inter-spike interval (ISI) values, i.e., the time between subsequent calcium spikes, of simulations in Fig 3A. The average and standard deviation of ISI of the [Ca²⁺]_c traces are represented by μ_ISI and σ_ISI, respectively. This analysis has been performed for different cell types, including astrocytes, during spontaneous as well as IP₃-induced calcium oscillations [31,32]. In agreement with these experimental observations, results from our simulations also show a positive and linear correlation between μ_ISI and σ_ISI values in the astrocytic calcium spiking during light stimulation (Fig 3C). Regions with Ca²⁺ levels outside of the predicted range for sustained oscillations, i.e., regions with either low or supraphysiological Ca²⁺ basal levels, result in infrequent and irregular spiking with higher μ_ISI and σ_ISI values.

Sensitivity to model parameters

Simulations predict salient features of light-induced responses in our model astrocyte, i.e., regions with elevated calcium spiking and a steady rise in the Ca²⁺ basal level. Results in Fig 4A show the effect of light intensity, or equivalently the amplitude of the waveform, on Ca²⁺ response of ChETA-expressing astrocytes for three distinct T-δ combinations. These paradigms correspond to regions with low (△), medium (○) and high (◊) spiking activity in the 45-minute stimulation heatmap of Fig 3A, respectively. For all combinations, the Ca²⁺ basal level shows an upward trend with increasing light intensity (with varying slopes), indicating a larger Ca²⁺ influx through ChR2. Similar trends are observed for spiking rates in the case of low and medium T-δ combinations. For the stimulus paradigm with highest spiking under control conditions (I₀), the spiking rate plateaus over a range of intensity values and follows a declining trend upon further increase in the light intensity. This indicates that the associated increase in the basal level leads to a decrease in the firing rate of astrocytes as cytosolic calcium levels exit the region where regular oscillations can occur. These model predictions are similar to experimental observations of monotonic increase in the firing of ChR2-positive neurons stimulated with increasing light intensities [50].

We further performed a global sensitivity analysis to evaluate the effect of parameters determining the dynamics of ChR2 photocycle and buffering capacity on the astrocytic Ca²⁺ responses for a low light stimulation paradigm (Fig 4B). Parameters that exerted statistically significant influence on the desired model output are marked with an asterisk. Results indicate differential effects of model parameters on Ca²⁺ response of the astrocyte to light stimulation. For instance, increasing the maximum conductance of ChR2 in o₁ state (g₁) is positively correlated with both spiking rate and basal levels, as the elevated conductance results in higher magnitudes of Ca²⁺ influx through the channel resulting in the elevation of basal levels and further activation of IP₃Rs. Similarly, e₂₁ (the rate of transition from o₂ to o₁) has a positive correlation with both measures, while the rate of the reverse reaction (e₁₂) is shown to be negatively correlated to the model output. These results suggest that by transitioning the state of ChR2 from o₂ to o₁, both spiking rate and basal level of Ca²⁺ will likely increase. This model prediction can be attributed to the higher conductance of the channel in the o₁ state, the transient region of the ChR2 photocurrent in S2 Fig, compared to o₂ state, the plateau region. Sensitivity analysis of the Ca²⁺ buffering parameters demonstrates that with increasing buffering capacity, i.e., increasing total buffer concentration (b_t) or reducing the affinity of buffer proteins to Ca²⁺ (K), both basal Ca²⁺ level and mean spiking rate of astrocytes will expectedly decrease.

Network-wide astrocytic response to light stimulation

A 10-by-10 network of gap-connected astrocytes was modeled in Fig 5 and S1 Movie. Light stimulation (T = 4s, δ = 45%; = 0.1 s^-1) was applied to a central region (the highlighted box in Fig 5A), and simulations were performed for 45 minutes. Fig 5A heatmaps demonstrate the resulting basal Ca²⁺ level in the network after light stimulation, with and without the inclusion of Ca²⁺ buffering. Under both conditions, results show increased basal levels in the stimulated region and the propagation of calcium to unstimulated cells. Basal levels reached in focal and distal astrocytes without buffering were drastically higher compared to those with buffering. In the presence of Ca²⁺ buffering, only the area in close vicinity of the stimulated region exhibits an increase in the basal level; whereas, in the absence of buffering, even the cells farthest from the stimulation region undergo an increase in calcium. This suggests that buffering reduces the diffusion range of Ca²⁺ within the network, thereby limiting propagation. Given the focal and centered stimulation of the network, the distribution of calcium can be suitably quantified using a 2D Gaussian fit (Eq 14). In Fig 5B, the peak basal level, along with the spread from the center (in terms of number of astrocytes), are quantified with varying values. In both cases, an intuitive decrease in peak basal level coupled with an increase in the spread is observed as increases. Both trends plateaued as values reached higher than 0.1 s^-1.

Download:

Fig 5. Network-wide astrocytic Ca²⁺ response to light stimulation.

A 10-by-10 network of astrocytes was employed to analyze the response of cells when the central 4-by-4 astrocytes (white square in heatmaps of panels A and C) were stimulated (◊: T = 4 s, δ = 45% (1.8 s), 45 min). See the network organization schematic in Fig 1. Simulations were conducted in the presence (left panel) and absence (right panel) of Ca²⁺ buffering with varying gap junctional Ca²⁺ coupling coefficient (). A symmetric 2D Gaussian fit was utilized to quantify the response, i.e., peak and magnitude of the spread from the stimulated region. A) Heat maps of network-wide light stimulation-induced Ca²⁺ basal levels. B) Plots of the peak basal level and σ_basal-level obtained from the Gaussian fit with varying values. Vertical dashed grey line denotes the value used to generate the heat maps in panels A and C. C) Heat maps of network-wide spiking rate response corresponding to basal levels in panel A. For spike classification, a threshold of 0.2 μM above the basal level was selected. D) Plots for the peak spiking rate and σ_{spiking rate} with varying values.

https://doi.org/10.1371/journal.pcbi.1008648.g005

Similar responses are observed in the mean spiking rate of the astrocytic network upon light stimulation (Fig 5C). Inclusion of calcium buffering limited the spiking activity of astrocytes only in regions immediately surrounding the stimulated region. On the contrary, without calcium buffering, the spiking activity propagated to unstimulated areas and resulted in higher mean spiking rate values. Analysis of network-wide peak spiking rate and spread with buffering in Fig 5D (left panel) indicates a decreasing trend of peak spiking with . The propagation of the spiking rate, however, remained almost unchanged over the entire range of values examined. Conversely, when buffering was not included (Fig 5D, right panel), the increase in resulted in an increasing trend in the spread of spiking activity while the peak spiking rate remained at high values throughout. Increasing the number of cells expressing ChR2 in the network also resulted in a steady increase in both spiking rate and calcium basal levels in the network (S4 Fig) when buffering was included. Under no buffer condition, the peak basal level showed a steep incline, while the spread of the basal activity remained constant. Both peak spiking rate and spread showed an upward trend with increased expression level, with peak levels reaching a plateau when higher than 50% of the cells expressed ChR2. Collectively, simulations in Fig 5 highlight the role of calcium buffering in limiting the diffusion of free calcium in the network of astrocytes and thereby reducing both basal and spiking levels of calcium in cells. Additionally, comparison of the network results with those of single cells (Fig 3) reveals that the dispersion of calcium into the neighboring cells through gap junctions drastically reduces the supraphysiological values of calcium concentrations predicted in isolated cells.

Discussion

The past few decades have witnessed an upsurge in research on understanding the role of astrocytes in brain function. Aside from providing structural support to neurons [51,52] and regulating the ‘excitatory-inhibitory’ neurotransmitter balance [53], the exact contribution of these cells, particularly in processes involving their Ca²⁺ signaling, is unknown and is highly debated [see refs [1–6]]. For instance, astrocytes are thought to be directly involved in neurovascular coupling by sensing neuronal activity and releasing Ca²⁺-mediated vasoactive agents to relax smooth muscle cells of parenchymal arterioles [14,54,55]. However, recent experimental evidence has thrown the validity of this assumption into disarray by questioning astrocytes’ involvement, and the extent of their influence, in the onset of the hyperemic response [16,56,57]. Another controversy involving astrocytes is their potential role in modulating neuronal activity via Ca²⁺-mediated release of gliotransmitters. While several groups present evidence for the active involvement of gliotransmission in neuromodulation, others argue that this process is not likely to occur under physiological conditions [4,5,58]. Ca²⁺ homeostasis is also dramatically altered in astrocytes under several pathological conditions and during reactive gliosis [59]. These include elevated Ca²⁺ levels, as well as intercellular waves in epilepsy [60], Alzheimer’s disease [34,61], and spreading depression [62,63]. Despite the involvement of astrocytes in these multi-mechanistic phenomena, differentiating their specific contributions from concurrent neuronal activity has remained one of the most enduring challenges in the field. Thus, selectively targeting astrocytes, and their Ca²⁺ signaling, using advanced techniques like optogenetics can provide assistance in resolving the above controversies and help find answers to their exact roles in health and disease. The mathematical modeling framework outlined in our study is a step in this direction in providing a tool for experimentalists to precisely achieve desired astrocytic Ca²⁺ levels to examine their role in the abovementioned phenomena.

Salient features of light-evoked calcium signaling in astrocytes

Simulation results predict that calcium dynamics in astrocytes, as seen in experimental studies [33,64,65], can be heavily regulated by light-induced activation of ChR2. Consistent in all simulations performed in this study, upon light activation, astrocytes underwent increases in their basal calcium level and exhibited changes in the spiking activity (Figs 2 and 3). Our results demonstrate that the extent of the rise in calcium (reflecting the higher magnitude of entry through ChR2 compared to the rate of scavenging by PMCA, SERCA, and buffer proteins) is largely dependent on the specifications of the laser stimulus, i.e., T-δ combination and light intensity, as well as parameters determining the shape of the ChR2 photocurrent (Figs 3 and 4). Additionally, whether astrocytes show high or low spiking activity is also contingent upon the duration of light stimulation. As such, T-δ combinations with high spiking activity of single cells in short-term stimulations may transition to regions with medium or low spiking in longer durations, or vice versa (Fig 3B). These results emphasize the importance of choosing an ‘ideal’ T and δ combination for the desired short-term or long-term astrocytic activity. An inaccurate selection of these combinations could prompt astrocytes to an unphysiological Ca²⁺ signaling regime, which might be detrimental for the health of the cells. Whether these model predictions are physiologically accurate needs to be validated against experimental observations for both short and long-term activation of ChR2. When coupled with other astrocytes in a network, however, the dispersion of calcium to neighboring cells dramatically reduced the basal levels reached in the stimulated region (Fig 5A), with values depending on the magnitude of the calcium and IP₃ coupling coefficients in the network. This indicates that experimental design for optogenetic stimulation of a network of astrocytes, e.g., in vivo recordings, cannot be solely based on predictions drawn from single cells, and that network activity depends on ChR2 expression level (S4 Fig).

Engineering of application-based ChR2 variants

Several research groups have engineered ChR2 variants with distinct characteristics, e.g. enhanced conductance, sensitivity, and faster recovery kinetics [26,28] for specific applications in excitable cells. Results of our study can be useful in the development of future ChR2 constructs for eliciting desired activity targeting astrocytes. More specifically, results of our sensitivity analysis (Fig 4B) indicated that the kinetics of ChR2 photocycle significantly affect the Ca²⁺ spiking rate and basal levels. Intuitively, directing ChR2 to the open states (o₁ and o₂) from the closed states (c₁ and c₂) leads to an increase in astrocytic activity in response to light stimulation. For instance, decreasing and facilitates the existence of ChR2 in the open states as they are negatively correlated to both basal level and spiking rate. Also, an increase in p₂ drives the system to the open state and is positively correlated to both measures. However, less intuitively, for the simulations performed in our study, increased astrocytic activity was achieved when ChR2 resided more in the o₁ state as compared to the o₂ state. This can be observed as an increase in e₂₁ and a decrease in e₁₂ leading to the existence of ChR2 in o₁ (see Fig 1 ChR2 photocycle). The shape of the photocurrents in S2 Fig also confirms that the channel has the highest flux in the o₁ state (the transient phase). Collectively, these results suggest that tailoring new ChR2 constructs such that the photocurrent is directed mainly towards the o₁ state can enhance the astrocytic activity. The same analysis can be performed under different stimulation paradigms and for varying durations of stimulus.

Model limitations and future directions

ChR2 is a non-selective cation channel, with varying permeability for Na⁺, K⁺, Ca²⁺, and H⁺ across different variants [24,25]. Cationic entry has shown to induce membrane depolarization which can activate voltage-gated calcium channels, although their functional role in astrocytes is a subject of ongoing debate [58], and result in further influx of calcium, potentially activating large conductance calcium activated potassium currents [66]. Activation of these channels change the membrane potential of the cell and can thus affect the magnitude of the ChR2 photocurrent, since ChR2 is V_m-sensitive. Our model does not include the dynamics of other major ionic species and does not account for the abovementioned dependencies on the membrane potential. We have also not explicitly accounted for other intracellular compartments, e.g. microdomains and mitochondria, involved in the calcium dynamics of astrocytes. In a recent study [67], it was demonstrated that inclusion of microdomains and mitochondria compartments reduced the calcium and IP₃ levels required for the activation of IP₃Rs in non-excitable cells and can potentially affect the ChR2-induced calcium signaling in our model. Another limitation of the model is that, in this study, we adopted the Langevin approach outlined in ref. [43] for the implementation of stochasticity in the dynamics of IP₃R channels and have not accounted for the detailed diffusion of calcium ions within and between IP₃R clusters. This would require a system of partial differential equations as demonstrated in ref. [32]. In this study, we sought to provide a minimalistic theoretical framework which can readily be employed by researchers for the investigation of light induced Ca²⁺ responses in astrocytes. Combination of the presented model with more detailed models as in [42] and [68] where exhaustive geometry and dynamics of various ionic species are accounted for, can enhance our understanding of the intricacies of the behavior of astrocytes and their response to light.

Supporting information

S1 Fig. ChR2 gating dynamics during light stimulation.

Representative traces of open state (o₁ and o₂) and closed state (c₁ and c₂) gating dynamics during light stimulation, corresponding to the 90-min simulation depicted in Fig 2 (wild type 1 (WT₁), wild type 2 (WT₂), ChETA. and ChRET/TC). A 30-second segment of each trace is shown to highlight details. Prior to light stimulation, all variants reside in the c₁ state. Once stimulation is initiated, the variants reside in different states at varying levels. Within the open states, they mainly reside in o₂. Solid horizontal blue line corresponds to the period during which the light stimulation was on.

https://doi.org/10.1371/journal.pcbi.1008648.s001

(TIF)

S2 Fig. Comparison of the ChR2 flux across variants.

Simulated ChR2 channel flux (J_ChR2) in response to a 1-sec pulse stimulation. Solid horizontal blue line corresponds to the period during which the light pulse was on. The solid grey box highlights a transient phase, during which all variants exhibit a brief large-magnitude flux (ChRET/TC > WT₂ > WT₁ > ChETA), corresponding to the light-induced transition to the o₁ state. The dashed grey box shows the plateau phase of the flux, corresponding to the transition and stabilization in the low-magnitude o₂ state. The plateau phase flux magnitudes are in the order ChRET/TC > ChETA > WT₂ > WT₁.

https://doi.org/10.1371/journal.pcbi.1008648.s002

(TIF)

S3 Fig. Response of astrocytes expressing different ChR2 constructs to various light stimulation paradigms.

Simulations (45 min) were conducted to evaluate astrocytic Ca²⁺ response while expressing various ChR2 constructs. Different stimulation paradigms ranging from T = 1–5 s and δ = 0–100% of T (trials = 5) were applied from 100 seconds, until the end of the simulation. Each column corresponds to an evaluated ChR2 variant, i.e. WT₁ (left), WT₂ (center) and ChRET/TC (right). Heat maps of Ca²⁺ basal level (top panels) and spiking rate (bottom panels) for T-δ combinations are depicted. Scale bar for each heat map was capped to 3 μM and 0.6 spikes/min, respectively. For spike detection, a threshold of 0.2 μM above the basal level was utilized. Results show a similar basal level and spiking rate distribution for WT₁ and WT₂. However, ChRET/TC shows a smaller region of increased spiking activity coupled with a larger region of T-δ combinations eliciting supraphysiological basal level changes.

https://doi.org/10.1371/journal.pcbi.1008648.s003

(TIF)

S4 Fig. Effect of expression heterogeneity on the network-wide response to stimulation.

A 10-by-10 network of astrocytes was used to demonstrate the resulting response when the expression of the central 4-by-4 astrocytes (white square in Fig 5A and 5C) is varied [Light stimulation: (◊) T = 4 s, δ = 45% (1.8 s)]. Simulations were conducted for 45 minutes while the percentage of the central astrocytes randomly selected to express ChETA was varied (25, 50, 75, 100%) in the presence (left panel) and absence (right panel) of Ca²⁺ buffering. A total of 5 trials were conducted for each expression level. A symmetric 2D Gaussian fit was used to quantify the response, i.e. peak and magnitude of the spread from the stimulated region. Top row of plots shows the average and standard deviation of peak basal level and σ_{basal level} as a function of expression. Bottom row of plots shows the average and standard deviation of peak spiking rate and σ_{spiking rate} as a function of expression. For spike classification, a threshold of 0.2 μM above basal level was selected. Increasing the number of cells expressing ChR2 in the stimulation region resulted in a steady increase in both peak basal level and spiking rate in the presence of buffering, coupled with a steady increase in their corresponding σ values. A similar trend can be observed in the absence of buffering; however, after a threshold, the basal level continues to increase, while the spiking rate plateaus.

https://doi.org/10.1371/journal.pcbi.1008648.s004

(TIF)

S1 Movie. Video of network-wide astrocytic Ca²⁺ response to light stimulation.

Video of the 10-by-10 network simulations performed in Fig 5 [Light stimulation: (◊) T = 4 s, δ = 45% (1.8 s); 4-by-4 central stimulated region is highlighted by the white box]. Simulations were conducted for 45 minutes in the presence (left panel) and absence (right panel) of Ca²⁺ buffering.

https://doi.org/10.1371/journal.pcbi.1008648.s005

(MP4)

Acknowledgments

The authors would also like to sincerely thank Mr. Josue Santana for his help in the early stages of the project, and Dr. James Schummers, Dr. Nikolaos Tsoukias, Dr. Rita Alevriadou, Mr. Ramkrishnan Krishnan, and Dr. Ricardo Siu for insightful discussions.

References

1. Araque A, Carmignoto G, Haydon PG, Oliet SH, Robitaille R, Volterra A. Gliotransmitters travel in time and space. Neuron. 2014;81(4):728–39. pmid:24559669
- View Article
- PubMed/NCBI
- Google Scholar
2. Bazargani N, Attwell D. Astrocyte calcium signaling: the third wave. Nature neuroscience. 2016;19(2):182–9. pmid:26814587
- View Article
- PubMed/NCBI
- Google Scholar
3. Volterra A, Liaudet N, Savtchouk I. Astrocyte Ca 2+ signalling: an unexpected complexity. Nature Reviews Neuroscience. 2014;15(5):327–35. pmid:24739787
- View Article
- PubMed/NCBI
- Google Scholar
4. Savtchouk I, Volterra A. Gliotransmission: Beyond Black-and-White. J Neurosci. 2018;38(1):14–25. Epub 2018/01/05. pmid:29298905; PubMed Central PMCID: PMC6705815.
- View Article
- PubMed/NCBI
- Google Scholar
5. Fiacco TA, McCarthy KD. Multiple lines of evidence indicate that gliotransmission does not occur under physiological conditions. Journal of Neuroscience. 2018;38(1):3–13. pmid:29298904
- View Article
- PubMed/NCBI
- Google Scholar
6. Iadecola C. The neurovascular unit coming of age: a journey through neurovascular coupling in health and disease. Neuron. 2017;96(1):17–42. pmid:28957666
- View Article
- PubMed/NCBI
- Google Scholar
7. Filosa JA, Morrison HW, Iddings JA, Du W, Kim KJ. Beyond neurovascular coupling, role of astrocytes in the regulation of vascular tone. Neuroscience. 2016;323:96–109. Epub 2015/04/07. pmid:25843438; PubMed Central PMCID: PMC4592693.
- View Article
- PubMed/NCBI
- Google Scholar
8. Rosenegger DG, Gordon GR. A slow or modulatory role of astrocytes in neurovascular coupling. Microcirculation. 2015;22(3):197–203. Epub 2015/01/06. pmid:25556627.
- View Article
- PubMed/NCBI
- Google Scholar
9. Machler P, Wyss MT, Elsayed M, Stobart J, Gutierrez R, von Faber-Castell A, et al. In Vivo Evidence for a Lactate Gradient from Astrocytes to Neurons. Cell Metab. 2016;23(1):94–102. Epub 2015/12/25. pmid:26698914.
- View Article
- PubMed/NCBI
- Google Scholar
10. Magistretti PJ, Allaman I. Lactate in the brain: from metabolic end-product to signalling molecule. Nat Rev Neurosci. 2018;19(4):235–49. Epub 2018/03/09. pmid:29515192.
- View Article
- PubMed/NCBI
- Google Scholar
11. Monai H, Ohkura M, Tanaka M, Oe Y, Konno A, Hirai H, et al. Calcium imaging reveals glial involvement in transcranial direct current stimulation-induced plasticity in mouse brain. Nat Commun. 2016;7(1):11100. Epub 2016/03/24. pmid:27000523; PubMed Central PMCID: PMC4804173.
- View Article
- PubMed/NCBI
- Google Scholar
12. Monai H, Hirase H. Astrocytic calcium activation in a mouse model of tDCS-Extended discussion. Neurogenesis (Austin). 2016;3(1):e1240055. Epub 2016/11/11. pmid:27830161; PubMed Central PMCID: PMC5079391.
- View Article
- PubMed/NCBI
- Google Scholar
13. Stobart JL, Ferrari KD, Barrett MJP, Stobart MJ, Looser ZJ, Saab AS, et al. Long-term In Vivo Calcium Imaging of Astrocytes Reveals Distinct Cellular Compartment Responses to Sensory Stimulation. Cereb Cortex. 2018;28(1):184–98. Epub 2017/10/03. pmid:28968832.
- View Article
- PubMed/NCBI
- Google Scholar
14. Takano T, Tian GF, Peng W, Lou N, Libionka W, Han X, et al. Astrocyte-mediated control of cerebral blood flow. Nat Neurosci. 2006;9(2):260–7. Epub 2006/01/03. pmid:16388306.
- View Article
- PubMed/NCBI
- Google Scholar
15. Chen Y, Mancuso JJ, Zhao Z, Li X, Cheng J, Roman G, et al. Vasodilation by in vivo activation of astrocyte endfeet via two-photon calcium uncaging as a strategy to prevent brain ischemia. Journal of biomedical optics. 2013;18(12):126012. pmid:24343443
- View Article
- PubMed/NCBI
- Google Scholar
16. Bonder DE, McCarthy KD. Astrocytic Gq-GPCR-linked IP3R-dependent Ca2+ signaling does not mediate neurovascular coupling in mouse visual cortex in vivo. J Neurosci. 2014;34(39):13139–50. Epub 2014/09/26. pmid:25253859; PubMed Central PMCID: PMC4172806.
- View Article
- PubMed/NCBI
- Google Scholar
17. Durkee CA, Covelo A, Lines J, Kofuji P, Aguilar J, Araque A. Gi/o protein-coupled receptors inhibit neurons but activate astrocytes and stimulate gliotransmission. Glia. 2019;67(6):1076–93. Epub 2019/02/26. pmid:30801845; PubMed Central PMCID: PMC6462242.
- View Article
- PubMed/NCBI
- Google Scholar
18. Masamoto K, Unekawa M, Watanabe T, Toriumi H, Takuwa H, Kawaguchi H, et al. Unveiling astrocytic control of cerebral blood flow with optogenetics. Sci Rep. 2015;5:11455. Epub 2015/06/17. pmid:26076820; PubMed Central PMCID: PMC4468581.
- View Article
- PubMed/NCBI
- Google Scholar
19. Takata N, Sugiura Y, Yoshida K, Koizumi M, Hiroshi N, Honda K, et al. Optogenetic astrocyte activation evokes BOLD fMRI response with oxygen consumption without neuronal activity modulation. Glia. 2018;66(9):2013–23. pmid:29845643
- View Article
- PubMed/NCBI
- Google Scholar
20. Fenno L, Yizhar O, Deisseroth K. The development and application of optogenetics. Annu Rev Neurosci. 2011;34:389–412. Epub 2011/06/23. pmid:21692661; PubMed Central PMCID: PMC6699620.
- View Article
- PubMed/NCBI
- Google Scholar
21. Adamantidis AR, Zhang F, de Lecea L, Deisseroth K. Optogenetics: opsins and optical interfaces in neuroscience. Cold Spring Harb Protoc. 2014;2014(8):815–22. Epub 2014/08/03. pmid:25086025.
- View Article
- PubMed/NCBI
- Google Scholar
22. Adamsky A, Kol A, Kreisel T, Doron A, Ozeri-Engelhard N, Melcer T, et al. Astrocytic Activation Generates De Novo Neuronal Potentiation and Memory Enhancement. Cell. 2018;174(1):59–71 e14. Epub 2018/05/29. pmid:29804835.
- View Article
- PubMed/NCBI
- Google Scholar
23. Poskanzer KE, Yuste R. Astrocytes regulate cortical state switching in vivo. Proc Natl Acad Sci U S A. 2016;113(19):E2675–84. Epub 2016/04/29. pmid:27122314; PubMed Central PMCID: PMC4868485.
- View Article
- PubMed/NCBI
- Google Scholar
24. Lin JY. Optogenetic excitation of neurons with channelrhodopsins: light instrumentation, expression systems, and channelrhodopsin variants. Progress in brain research. 196: Elsevier; 2012. p. 29–47. https://doi.org/10.1016/B978-0-444-59426-6.00002-1 pmid:22341319
25. Lin JY, Lin MZ, Steinbach P, Tsien RY. Characterization of engineered channelrhodopsin variants with improved properties and kinetics. Biophys J. 2009;96(5):1803–14. Epub 2009/03/04. pmid:19254539; PubMed Central PMCID: PMC2717302.
- View Article
- PubMed/NCBI
- Google Scholar
26. Gunaydin LA, Yizhar O, Berndt A, Sohal VS, Deisseroth K, Hegemann P. Ultrafast optogenetic control. Nat Neurosci. 2010;13(3):387–92. Epub 2010/01/19. pmid:20081849.
- View Article
- PubMed/NCBI
- Google Scholar
27. Kleinlogel S, Feldbauer K, Dempski RE, Fotis H, Wood PG, Bamann C, et al. Ultra light-sensitive and fast neuronal activation with the Ca(2)+-permeable channelrhodopsin CatCh. Nat Neurosci. 2011;14(4):513–8. Epub 2011/03/15. pmid:21399632.
- View Article
- PubMed/NCBI
- Google Scholar
28. Berndt A, Schoenenberger P, Mattis J, Tye KM, Deisseroth K, Hegemann P, et al. High-efficiency channelrhodopsins for fast neuronal stimulation at low light levels. Proceedings of the National Academy of Sciences. 2011;108(18):7595–600. pmid:21504945
- View Article
- PubMed/NCBI
- Google Scholar
29. Prigge M, Schneider F, Tsunoda SP, Shilyansky C, Wietek J, Deisseroth K, et al. Color-tuned channelrhodopsins for multiwavelength optogenetics. J Biol Chem. 2012;287(38):31804–12. Epub 2012/07/31. pmid:22843694; PubMed Central PMCID: PMC3442514.
- View Article
- PubMed/NCBI
- Google Scholar
30. Stefanescu RA, Shivakeshavan RG, Khargonekar PP, Talathi SS. Computational modeling of channelrhodopsin-2 photocurrent characteristics in relation to neural signaling. Bull Math Biol. 2013;75(11):2208–40. Epub 2013/09/13. pmid:24026336.
- View Article
- PubMed/NCBI
- Google Scholar
31. Skupin A, Kettenmann H, Winkler U, Wartenberg M, Sauer H, Tovey SC, et al. How does intracellular Ca2+ oscillate: by chance or by the clock? Biophysical journal. 2008;94(6):2404–11. pmid:18065468
- View Article
- PubMed/NCBI
- Google Scholar
32. Skupin A, Kettenmann H, Falcke M. Calcium signals driven by single channel noise. PLoS Comput Biol. 2010;6(8):e1000870. Epub 2010/08/12. pmid:20700497; PubMed Central PMCID: PMC2917103.
- View Article
- PubMed/NCBI
- Google Scholar
33. Balachandar L, Montejo KA, Castano E, Perez M, Moncion C, Chambers JW, et al. Simultaneous Ca2+ imaging and optogenetic stimulation of cortical astrocytes in adult murine brain slices. Current Protocols in Neuroscience. 2020;94. pmid:33285041
- View Article
- PubMed/NCBI
- Google Scholar
34. Riera J, Hatanaka R, Uchida T, Ozaki T, Kawashima R. Quantifying the uncertainty of spontaneous Ca2+ oscillations in astrocytes: particulars of Alzheimer's disease. Biophys J. 2011;101(3):554–64. Epub 2011/08/03. pmid:21806923; PubMed Central PMCID: PMC3145292.
- View Article
- PubMed/NCBI
- Google Scholar
35. Riera J, Hatanaka R, Ozaki T, Kawashima R. Modeling the spontaneous Ca2+ oscillations in astrocytes: Inconsistencies and usefulness. J Integr Neurosci. 2011;10(4):439–73. Epub 2012/01/21. pmid:22262535.
- View Article
- PubMed/NCBI
- Google Scholar
36. De Young GW, Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A. 1992;89(20):9895–9. Epub 1992/10/15. pmid:1329108; PubMed Central PMCID: PMC50240.
- View Article
- PubMed/NCBI
- Google Scholar
37. Li YX, Rinzel J. Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol. 1994;166(4):461–73. Epub 1994/02/21. pmid:8176949.
- View Article
- PubMed/NCBI
- Google Scholar
38. Williams JC, Xu J, Lu Z, Klimas A, Chen X, Ambrosi CM, et al. Computational optogenetics: empirically-derived voltage- and light-sensitive channelrhodopsin-2 model. PLoS Comput Biol. 2013;9(9):e1003220. Epub 2013/09/27. pmid:24068903; PubMed Central PMCID: PMC3772068.
- View Article
- PubMed/NCBI
- Google Scholar
39. Nikolic K, Grossman N, Grubb MS, Burrone J, Toumazou C, Degenaar P. Photocycles of channelrhodopsin-2. Photochem Photobiol. 2009;85(1):400–11. Epub 2009/01/24. pmid:19161406.
- View Article
- PubMed/NCBI
- Google Scholar
40. Smith GD, Wagner J, Keizer J. Validity of the rapid buffering approximation near a point source of calcium ions. Biophys J. 1996;70(6):2527–39. Epub 1996/06/01. pmid:8744292; PubMed Central PMCID: PMC1225234.
- View Article
- PubMed/NCBI
- Google Scholar
41. Williams V, Grossman RG, Edmunds SM. Volume and surface area estimates of astrocytes in the sensorimotor cortex of the cat. Neuroscience. 1980;5(7):1151–9. Epub 1980/01/01. pmid:7402464.
- View Article
- PubMed/NCBI
- Google Scholar
42. Savtchenko LP, Bard L, Jensen TP, Reynolds JP, Kraev I, Medvedev N, et al. Disentangling astroglial physiology with a realistic cell model in silico. Nat Commun. 2018;9(1):3554. Epub 2018/09/05. pmid:30177844; PubMed Central PMCID: PMC6120909.
- View Article
- PubMed/NCBI
- Google Scholar
43. Shuai J-W, Jung P. Stochastic properties of Ca2+ release of inositol 1, 4, 5-trisphosphate receptor clusters. Biophysical journal. 2002;83(1):87–97. pmid:12080102
- View Article
- PubMed/NCBI
- Google Scholar
44. Van Kampen N. Stochastic processes in physics and chemistry. 2007.
- View Article
- Google Scholar
45. Sneyd J, Falcke M. Models of the inositol trisphosphate receptor. Prog Biophys Mol Biol. 2005;89(3):207–45. Epub 2005/06/14. pmid:15950055.
- View Article
- PubMed/NCBI
- Google Scholar
46. Ozaki T. A local linearization approach to nonlinear filtering. International Journal of Control. 1993;57(1):75–96.
- View Article
- Google Scholar
47. McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 2000;42(1):55–61.
- View Article
- Google Scholar
48. Marino S, Hogue IB, Ray CJ, Kirschner DE. A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol. 2008;254(1):178–96. Epub 2008/06/24. pmid:18572196; PubMed Central PMCID: PMC2570191.
- View Article
- PubMed/NCBI
- Google Scholar
49. Jimenez J, Ozaki T. Local linearization filters for non-linear continuous-discrete state space models with multiplicative noise. International Journal of Control. 2003;76(12):1159–70.
- View Article
- Google Scholar
50. Wang H, Peca J, Matsuzaki M, Matsuzaki K, Noguchi J, Qiu L, et al. High-speed mapping of synaptic connectivity using photostimulation in Channelrhodopsin-2 transgenic mice. Proceedings of the National Academy of Sciences. 2007;104(19):8143–8. pmid:17483470
- View Article
- PubMed/NCBI
- Google Scholar
51. Theodosis DT, Poulain DA, Oliet SH. Activity-dependent structural and functional plasticity of astrocyte-neuron interactions. Physiol Rev. 2008;88(3):983–1008. Epub 2008/07/16. pmid:18626065.
- View Article
- PubMed/NCBI
- Google Scholar
52. Bernardinelli Y, Muller D, Nikonenko I. Astrocyte-synapse structural plasticity. Neural Plast. 2014;2014:232105. Epub 2014/02/11. pmid:24511394; PubMed Central PMCID: PMC3910461.
- View Article
- PubMed/NCBI
- Google Scholar
53. Riera JJ, Schousboe A, Waagepetersen HS, Howarth C, Hyder F. The micro-architecture of the cerebral cortex: functional neuroimaging models and metabolism. Neuroimage. 2008;40(4):1436–59. Epub 2008/03/18. pmid:18343162; PubMed Central PMCID: PMC4348032.
- View Article
- PubMed/NCBI
- Google Scholar
54. Attwell D, Buchan AM, Charpak S, Lauritzen M, Macvicar BA, Newman EA. Glial and neuronal control of brain blood flow. Nature. 2010;468(7321):232–43. Epub 2010/11/12. pmid:21068832; PubMed Central PMCID: PMC3206737.
- View Article
- PubMed/NCBI
- Google Scholar
55. Lind BL, Brazhe AR, Jessen SB, Tan FC, Lauritzen MJ. Rapid stimulus-evoked astrocyte Ca2+ elevations and hemodynamic responses in mouse somatosensory cortex in vivo. Proc Natl Acad Sci U S A. 2013;110(48):E4678–87. Epub 2013/11/13. pmid:24218625; PubMed Central PMCID: PMC3845114.
- View Article
- PubMed/NCBI
- Google Scholar
56. Nizar K, Uhlirova H, Tian P, Saisan PA, Cheng Q, Reznichenko L, et al. In vivo stimulus-induced vasodilation occurs without IP3 receptor activation and may precede astrocytic calcium increase. Journal of Neuroscience. 2013;33(19):8411–22. pmid:23658179
- View Article
- PubMed/NCBI
- Google Scholar
57. Takata N, Nagai T, Ozawa K, Oe Y, Mikoshiba K, Hirase H. Cerebral blood flow modulation by basal forebrain or whisker stimulation can occur independently of large cytosolic Ca 2+ signaling in astrocytes. PloS one. 2013;8(6):e66525. pmid:23785506
- View Article
- PubMed/NCBI
- Google Scholar
58. Agulhon C, Sun MY, Murphy T, Myers T, Lauderdale K, Fiacco TA. Calcium Signaling and Gliotransmission in Normal vs. Reactive Astrocytes. Front Pharmacol. 2012;3:139. Epub 2012/07/20. pmid:22811669; PubMed Central PMCID: PMC3395812.
- View Article
- PubMed/NCBI
- Google Scholar
59. Burda JE, Bernstein AM, Sofroniew MV. Astrocyte roles in traumatic brain injury. Experimental neurology. 2016;275:305–15. pmid:25828533
- View Article
- PubMed/NCBI
- Google Scholar
60. Heuser K, Nome CG, Pettersen KH, Åbjørsbråten KS, Jensen V, Tang W, et al. Ca2+ Signals in Astrocytes Facilitate Spread of Epileptiform Activity. Cerebral Cortex. 2018;28(11):4036–48. pmid:30169757
- View Article
- PubMed/NCBI
- Google Scholar
61. Kuchibhotla KV, Lattarulo CR, Hyman BT, Bacskai BJ. Synchronous hyperactivity and intercellular calcium waves in astrocytes in Alzheimer mice. Science. 2009;323(5918):1211–5. pmid:19251629
- View Article
- PubMed/NCBI
- Google Scholar
62. Kunkler PE, Kraig RP. Calcium waves precede electrophysiological changes of spreading depression in hippocampal organ cultures. Journal of Neuroscience. 1998;18(9):3416–25. pmid:9547248
- View Article
- PubMed/NCBI
- Google Scholar
63. Peters O, Schipke CG, Hashimoto Y, Kettenmann H. Different mechanisms promote astrocyte Ca2+ waves and spreading depression in the mouse neocortex. Journal of Neuroscience. 2003;23(30):9888–96. pmid:14586018
- View Article
- PubMed/NCBI
- Google Scholar
64. Figueiredo M, Lane S, Tang F, Liu BH, Hewinson J, Marina N, et al. Optogenetic experimentation on astrocytes. Exp Physiol. 2011;96(1):40–50. Epub 2010/11/03. pmid:21041318.
- View Article
- PubMed/NCBI
- Google Scholar
65. Figueiredo M, Lane S, Stout RF, Jr., Liu B, Parpura V, Teschemacher AG, et al. Comparative analysis of optogenetic actuators in cultured astrocytes. Cell Calcium. 2014;56(3):208–14. Epub 2014/08/12. pmid:25109549; PubMed Central PMCID: PMC4169180.
- View Article
- PubMed/NCBI
- Google Scholar
66. Mager T, Wood PG, Bamberg E. Optogenetic control of Ca2+ and voltage-dependent large conductance (BK) potassium channels. Journal of Molecular Biology. 2017;429(6):911–21. pmid:28192090
- View Article
- PubMed/NCBI
- Google Scholar
67. Moshkforoush A, Ashenagar B, Tsoukias NM, Alevriadou BR. Modeling the role of endoplasmic reticulum-mitochondria microdomains in calcium dynamics. Sci Rep. 2019;9(1):17072. Epub 2019/11/21. pmid:31745211; PubMed Central PMCID: PMC6864103.
- View Article
- PubMed/NCBI
- Google Scholar
68. Lallouette J, De Pittà M, Berry H. Astrocyte networks and intercellular calcium propagation. Computational Glioscience: Springer; 2019. p. 177–210. https://doi.org/10.3389/fncom.2019.00092 pmid:32038210

[ref1] 1. Araque A, Carmignoto G, Haydon PG, Oliet SH, Robitaille R, Volterra A. Gliotransmitters travel in time and space. Neuron. 2014;81(4):728–39. pmid:24559669
View Article
PubMed/NCBI
Google Scholar

[2] View Article

[3] PubMed/NCBI

[4] Google Scholar

[ref2] 2. Bazargani N, Attwell D. Astrocyte calcium signaling: the third wave. Nature neuroscience. 2016;19(2):182–9. pmid:26814587
View Article
PubMed/NCBI
Google Scholar

[6] View Article

[7] PubMed/NCBI

[8] Google Scholar

[ref3] 3. Volterra A, Liaudet N, Savtchouk I. Astrocyte Ca 2+ signalling: an unexpected complexity. Nature Reviews Neuroscience. 2014;15(5):327–35. pmid:24739787
View Article
PubMed/NCBI
Google Scholar

[10] View Article

[11] PubMed/NCBI

[12] Google Scholar

[ref4] 4. Savtchouk I, Volterra A. Gliotransmission: Beyond Black-and-White. J Neurosci. 2018;38(1):14–25. Epub 2018/01/05. pmid:29298905; PubMed Central PMCID: PMC6705815.
View Article
PubMed/NCBI
Google Scholar

[14] View Article

[15] PubMed/NCBI

[16] Google Scholar

[ref5] 5. Fiacco TA, McCarthy KD. Multiple lines of evidence indicate that gliotransmission does not occur under physiological conditions. Journal of Neuroscience. 2018;38(1):3–13. pmid:29298904
View Article
PubMed/NCBI
Google Scholar

[18] View Article

[19] PubMed/NCBI

[20] Google Scholar

[ref6] 6. Iadecola C. The neurovascular unit coming of age: a journey through neurovascular coupling in health and disease. Neuron. 2017;96(1):17–42. pmid:28957666
View Article
PubMed/NCBI
Google Scholar

[22] View Article

[23] PubMed/NCBI

[24] Google Scholar

[ref7] 7. Filosa JA, Morrison HW, Iddings JA, Du W, Kim KJ. Beyond neurovascular coupling, role of astrocytes in the regulation of vascular tone. Neuroscience. 2016;323:96–109. Epub 2015/04/07. pmid:25843438; PubMed Central PMCID: PMC4592693.
View Article
PubMed/NCBI
Google Scholar

[26] View Article

[27] PubMed/NCBI

[28] Google Scholar

[ref8] 8. Rosenegger DG, Gordon GR. A slow or modulatory role of astrocytes in neurovascular coupling. Microcirculation. 2015;22(3):197–203. Epub 2015/01/06. pmid:25556627.
View Article
PubMed/NCBI
Google Scholar

[30] View Article

[31] PubMed/NCBI

[32] Google Scholar

[ref9] 9. Machler P, Wyss MT, Elsayed M, Stobart J, Gutierrez R, von Faber-Castell A, et al. In Vivo Evidence for a Lactate Gradient from Astrocytes to Neurons. Cell Metab. 2016;23(1):94–102. Epub 2015/12/25. pmid:26698914.
View Article
PubMed/NCBI
Google Scholar

[34] View Article

[35] PubMed/NCBI

[36] Google Scholar

[ref10] 10. Magistretti PJ, Allaman I. Lactate in the brain: from metabolic end-product to signalling molecule. Nat Rev Neurosci. 2018;19(4):235–49. Epub 2018/03/09. pmid:29515192.
View Article
PubMed/NCBI
Google Scholar

[38] View Article

[39] PubMed/NCBI

[40] Google Scholar

[ref11] 11. Monai H, Ohkura M, Tanaka M, Oe Y, Konno A, Hirai H, et al. Calcium imaging reveals glial involvement in transcranial direct current stimulation-induced plasticity in mouse brain. Nat Commun. 2016;7(1):11100. Epub 2016/03/24. pmid:27000523; PubMed Central PMCID: PMC4804173.
View Article
PubMed/NCBI
Google Scholar

[42] View Article

[43] PubMed/NCBI

[44] Google Scholar

[ref12] 12. Monai H, Hirase H. Astrocytic calcium activation in a mouse model of tDCS-Extended discussion. Neurogenesis (Austin). 2016;3(1):e1240055. Epub 2016/11/11. pmid:27830161; PubMed Central PMCID: PMC5079391.
View Article
PubMed/NCBI
Google Scholar

[46] View Article

[47] PubMed/NCBI

[48] Google Scholar

[ref13] 13. Stobart JL, Ferrari KD, Barrett MJP, Stobart MJ, Looser ZJ, Saab AS, et al. Long-term In Vivo Calcium Imaging of Astrocytes Reveals Distinct Cellular Compartment Responses to Sensory Stimulation. Cereb Cortex. 2018;28(1):184–98. Epub 2017/10/03. pmid:28968832.
View Article
PubMed/NCBI
Google Scholar

[50] View Article

[51] PubMed/NCBI

[52] Google Scholar

[ref14] 14. Takano T, Tian GF, Peng W, Lou N, Libionka W, Han X, et al. Astrocyte-mediated control of cerebral blood flow. Nat Neurosci. 2006;9(2):260–7. Epub 2006/01/03. pmid:16388306.
View Article
PubMed/NCBI
Google Scholar

[54] View Article

[55] PubMed/NCBI

[56] Google Scholar

[ref15] 15. Chen Y, Mancuso JJ, Zhao Z, Li X, Cheng J, Roman G, et al. Vasodilation by in vivo activation of astrocyte endfeet via two-photon calcium uncaging as a strategy to prevent brain ischemia. Journal of biomedical optics. 2013;18(12):126012. pmid:24343443
View Article
PubMed/NCBI
Google Scholar

[58] View Article

[59] PubMed/NCBI

[60] Google Scholar

[ref16] 16. Bonder DE, McCarthy KD. Astrocytic Gq-GPCR-linked IP3R-dependent Ca2+ signaling does not mediate neurovascular coupling in mouse visual cortex in vivo. J Neurosci. 2014;34(39):13139–50. Epub 2014/09/26. pmid:25253859; PubMed Central PMCID: PMC4172806.
View Article
PubMed/NCBI
Google Scholar

[62] View Article

[63] PubMed/NCBI

[64] Google Scholar

[ref17] 17. Durkee CA, Covelo A, Lines J, Kofuji P, Aguilar J, Araque A. Gi/o protein-coupled receptors inhibit neurons but activate astrocytes and stimulate gliotransmission. Glia. 2019;67(6):1076–93. Epub 2019/02/26. pmid:30801845; PubMed Central PMCID: PMC6462242.
View Article
PubMed/NCBI
Google Scholar

[66] View Article

[67] PubMed/NCBI

[68] Google Scholar

[ref18] 18. Masamoto K, Unekawa M, Watanabe T, Toriumi H, Takuwa H, Kawaguchi H, et al. Unveiling astrocytic control of cerebral blood flow with optogenetics. Sci Rep. 2015;5:11455. Epub 2015/06/17. pmid:26076820; PubMed Central PMCID: PMC4468581.
View Article
PubMed/NCBI
Google Scholar

[70] View Article

[71] PubMed/NCBI

[72] Google Scholar

[ref19] 19. Takata N, Sugiura Y, Yoshida K, Koizumi M, Hiroshi N, Honda K, et al. Optogenetic astrocyte activation evokes BOLD fMRI response with oxygen consumption without neuronal activity modulation. Glia. 2018;66(9):2013–23. pmid:29845643
View Article
PubMed/NCBI
Google Scholar

[74] View Article

[75] PubMed/NCBI

[76] Google Scholar

[ref20] 20. Fenno L, Yizhar O, Deisseroth K. The development and application of optogenetics. Annu Rev Neurosci. 2011;34:389–412. Epub 2011/06/23. pmid:21692661; PubMed Central PMCID: PMC6699620.
View Article
PubMed/NCBI
Google Scholar

[78] View Article

[79] PubMed/NCBI

[80] Google Scholar

[ref21] 21. Adamantidis AR, Zhang F, de Lecea L, Deisseroth K. Optogenetics: opsins and optical interfaces in neuroscience. Cold Spring Harb Protoc. 2014;2014(8):815–22. Epub 2014/08/03. pmid:25086025.
View Article
PubMed/NCBI
Google Scholar

[82] View Article

[83] PubMed/NCBI

[84] Google Scholar

[ref22] 22. Adamsky A, Kol A, Kreisel T, Doron A, Ozeri-Engelhard N, Melcer T, et al. Astrocytic Activation Generates De Novo Neuronal Potentiation and Memory Enhancement. Cell. 2018;174(1):59–71 e14. Epub 2018/05/29. pmid:29804835.
View Article
PubMed/NCBI
Google Scholar

[86] View Article

[87] PubMed/NCBI

[88] Google Scholar

[ref23] 23. Poskanzer KE, Yuste R. Astrocytes regulate cortical state switching in vivo. Proc Natl Acad Sci U S A. 2016;113(19):E2675–84. Epub 2016/04/29. pmid:27122314; PubMed Central PMCID: PMC4868485.
View Article
PubMed/NCBI
Google Scholar

[90] View Article

[91] PubMed/NCBI

[92] Google Scholar

[ref24] 24. Lin JY. Optogenetic excitation of neurons with channelrhodopsins: light instrumentation, expression systems, and channelrhodopsin variants. Progress in brain research. 196: Elsevier; 2012. p. 29–47. https://doi.org/10.1016/B978-0-444-59426-6.00002-1 pmid:22341319

[ref25] 25. Lin JY, Lin MZ, Steinbach P, Tsien RY. Characterization of engineered channelrhodopsin variants with improved properties and kinetics. Biophys J. 2009;96(5):1803–14. Epub 2009/03/04. pmid:19254539; PubMed Central PMCID: PMC2717302.
View Article
PubMed/NCBI
Google Scholar

[95] View Article

[96] PubMed/NCBI

[97] Google Scholar

[ref26] 26. Gunaydin LA, Yizhar O, Berndt A, Sohal VS, Deisseroth K, Hegemann P. Ultrafast optogenetic control. Nat Neurosci. 2010;13(3):387–92. Epub 2010/01/19. pmid:20081849.
View Article
PubMed/NCBI
Google Scholar

[99] View Article

[100] PubMed/NCBI

[101] Google Scholar

[ref27] 27. Kleinlogel S, Feldbauer K, Dempski RE, Fotis H, Wood PG, Bamann C, et al. Ultra light-sensitive and fast neuronal activation with the Ca(2)+-permeable channelrhodopsin CatCh. Nat Neurosci. 2011;14(4):513–8. Epub 2011/03/15. pmid:21399632.
View Article
PubMed/NCBI
Google Scholar

[103] View Article

[104] PubMed/NCBI

[105] Google Scholar

[ref28] 28. Berndt A, Schoenenberger P, Mattis J, Tye KM, Deisseroth K, Hegemann P, et al. High-efficiency channelrhodopsins for fast neuronal stimulation at low light levels. Proceedings of the National Academy of Sciences. 2011;108(18):7595–600. pmid:21504945
View Article
PubMed/NCBI
Google Scholar

[107] View Article

[108] PubMed/NCBI

[109] Google Scholar

[ref29] 29. Prigge M, Schneider F, Tsunoda SP, Shilyansky C, Wietek J, Deisseroth K, et al. Color-tuned channelrhodopsins for multiwavelength optogenetics. J Biol Chem. 2012;287(38):31804–12. Epub 2012/07/31. pmid:22843694; PubMed Central PMCID: PMC3442514.
View Article
PubMed/NCBI
Google Scholar

[111] View Article

[112] PubMed/NCBI

[113] Google Scholar

[ref30] 30. Stefanescu RA, Shivakeshavan RG, Khargonekar PP, Talathi SS. Computational modeling of channelrhodopsin-2 photocurrent characteristics in relation to neural signaling. Bull Math Biol. 2013;75(11):2208–40. Epub 2013/09/13. pmid:24026336.
View Article
PubMed/NCBI
Google Scholar

[115] View Article

[116] PubMed/NCBI

[117] Google Scholar

[ref31] 31. Skupin A, Kettenmann H, Winkler U, Wartenberg M, Sauer H, Tovey SC, et al. How does intracellular Ca2+ oscillate: by chance or by the clock? Biophysical journal. 2008;94(6):2404–11. pmid:18065468
View Article
PubMed/NCBI
Google Scholar

[119] View Article

[120] PubMed/NCBI

[121] Google Scholar

[ref32] 32. Skupin A, Kettenmann H, Falcke M. Calcium signals driven by single channel noise. PLoS Comput Biol. 2010;6(8):e1000870. Epub 2010/08/12. pmid:20700497; PubMed Central PMCID: PMC2917103.
View Article
PubMed/NCBI
Google Scholar

[123] View Article

[124] PubMed/NCBI

[125] Google Scholar

[ref33] 33. Balachandar L, Montejo KA, Castano E, Perez M, Moncion C, Chambers JW, et al. Simultaneous Ca2+ imaging and optogenetic stimulation of cortical astrocytes in adult murine brain slices. Current Protocols in Neuroscience. 2020;94. pmid:33285041
View Article
PubMed/NCBI
Google Scholar

[127] View Article

[128] PubMed/NCBI

[129] Google Scholar

[ref34] 34. Riera J, Hatanaka R, Uchida T, Ozaki T, Kawashima R. Quantifying the uncertainty of spontaneous Ca2+ oscillations in astrocytes: particulars of Alzheimer's disease. Biophys J. 2011;101(3):554–64. Epub 2011/08/03. pmid:21806923; PubMed Central PMCID: PMC3145292.
View Article
PubMed/NCBI
Google Scholar

[131] View Article

[132] PubMed/NCBI

[133] Google Scholar

[ref35] 35. Riera J, Hatanaka R, Ozaki T, Kawashima R. Modeling the spontaneous Ca2+ oscillations in astrocytes: Inconsistencies and usefulness. J Integr Neurosci. 2011;10(4):439–73. Epub 2012/01/21. pmid:22262535.
View Article
PubMed/NCBI
Google Scholar

[135] View Article

[136] PubMed/NCBI

[137] Google Scholar

[ref36] 36. De Young GW, Keizer J. A single-pool inositol 1,4,5-trisphosphate-receptor-based model for agonist-stimulated oscillations in Ca2+ concentration. Proc Natl Acad Sci U S A. 1992;89(20):9895–9. Epub 1992/10/15. pmid:1329108; PubMed Central PMCID: PMC50240.
View Article
PubMed/NCBI
Google Scholar

[139] View Article

[140] PubMed/NCBI

[141] Google Scholar

[ref37] 37. Li YX, Rinzel J. Equations for InsP3 receptor-mediated [Ca2+]i oscillations derived from a detailed kinetic model: a Hodgkin-Huxley like formalism. J Theor Biol. 1994;166(4):461–73. Epub 1994/02/21. pmid:8176949.
View Article
PubMed/NCBI
Google Scholar

[143] View Article

[144] PubMed/NCBI

[145] Google Scholar

[ref38] 38. Williams JC, Xu J, Lu Z, Klimas A, Chen X, Ambrosi CM, et al. Computational optogenetics: empirically-derived voltage- and light-sensitive channelrhodopsin-2 model. PLoS Comput Biol. 2013;9(9):e1003220. Epub 2013/09/27. pmid:24068903; PubMed Central PMCID: PMC3772068.
View Article
PubMed/NCBI
Google Scholar

[147] View Article

[148] PubMed/NCBI

[149] Google Scholar

[ref39] 39. Nikolic K, Grossman N, Grubb MS, Burrone J, Toumazou C, Degenaar P. Photocycles of channelrhodopsin-2. Photochem Photobiol. 2009;85(1):400–11. Epub 2009/01/24. pmid:19161406.
View Article
PubMed/NCBI
Google Scholar

[151] View Article

[152] PubMed/NCBI

[153] Google Scholar

[ref40] 40. Smith GD, Wagner J, Keizer J. Validity of the rapid buffering approximation near a point source of calcium ions. Biophys J. 1996;70(6):2527–39. Epub 1996/06/01. pmid:8744292; PubMed Central PMCID: PMC1225234.
View Article
PubMed/NCBI
Google Scholar

[155] View Article

[156] PubMed/NCBI

[157] Google Scholar

[ref41] 41. Williams V, Grossman RG, Edmunds SM. Volume and surface area estimates of astrocytes in the sensorimotor cortex of the cat. Neuroscience. 1980;5(7):1151–9. Epub 1980/01/01. pmid:7402464.
View Article
PubMed/NCBI
Google Scholar

[159] View Article

[160] PubMed/NCBI

[161] Google Scholar

[ref42] 42. Savtchenko LP, Bard L, Jensen TP, Reynolds JP, Kraev I, Medvedev N, et al. Disentangling astroglial physiology with a realistic cell model in silico. Nat Commun. 2018;9(1):3554. Epub 2018/09/05. pmid:30177844; PubMed Central PMCID: PMC6120909.
View Article
PubMed/NCBI
Google Scholar

[163] View Article

[164] PubMed/NCBI

[165] Google Scholar

[ref43] 43. Shuai J-W, Jung P. Stochastic properties of Ca2+ release of inositol 1, 4, 5-trisphosphate receptor clusters. Biophysical journal. 2002;83(1):87–97. pmid:12080102
View Article
PubMed/NCBI
Google Scholar

[167] View Article

[168] PubMed/NCBI

[169] Google Scholar

[ref44] 44. Van Kampen N. Stochastic processes in physics and chemistry. 2007.
View Article
Google Scholar

[171] View Article

[172] Google Scholar

[ref45] 45. Sneyd J, Falcke M. Models of the inositol trisphosphate receptor. Prog Biophys Mol Biol. 2005;89(3):207–45. Epub 2005/06/14. pmid:15950055.
View Article
PubMed/NCBI
Google Scholar

[174] View Article

[175] PubMed/NCBI

[176] Google Scholar

[ref46] 46. Ozaki T. A local linearization approach to nonlinear filtering. International Journal of Control. 1993;57(1):75–96.
View Article
Google Scholar

[178] View Article

[179] Google Scholar

[ref47] 47. McKay MD, Beckman RJ, Conover WJ. A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics. 2000;42(1):55–61.
View Article
Google Scholar

[181] View Article

[182] Google Scholar

[ref48] 48. Marino S, Hogue IB, Ray CJ, Kirschner DE. A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol. 2008;254(1):178–96. Epub 2008/06/24. pmid:18572196; PubMed Central PMCID: PMC2570191.
View Article
PubMed/NCBI
Google Scholar

[184] View Article

[185] PubMed/NCBI

[186] Google Scholar

[ref49] 49. Jimenez J, Ozaki T. Local linearization filters for non-linear continuous-discrete state space models with multiplicative noise. International Journal of Control. 2003;76(12):1159–70.
View Article
Google Scholar

[188] View Article

[189] Google Scholar

[ref50] 50. Wang H, Peca J, Matsuzaki M, Matsuzaki K, Noguchi J, Qiu L, et al. High-speed mapping of synaptic connectivity using photostimulation in Channelrhodopsin-2 transgenic mice. Proceedings of the National Academy of Sciences. 2007;104(19):8143–8. pmid:17483470
View Article
PubMed/NCBI
Google Scholar

[191] View Article

[192] PubMed/NCBI

[193] Google Scholar

[ref51] 51. Theodosis DT, Poulain DA, Oliet SH. Activity-dependent structural and functional plasticity of astrocyte-neuron interactions. Physiol Rev. 2008;88(3):983–1008. Epub 2008/07/16. pmid:18626065.
View Article
PubMed/NCBI
Google Scholar

[195] View Article

[196] PubMed/NCBI

[197] Google Scholar

[ref52] 52. Bernardinelli Y, Muller D, Nikonenko I. Astrocyte-synapse structural plasticity. Neural Plast. 2014;2014:232105. Epub 2014/02/11. pmid:24511394; PubMed Central PMCID: PMC3910461.
View Article
PubMed/NCBI
Google Scholar

[199] View Article

[200] PubMed/NCBI

[201] Google Scholar

[ref53] 53. Riera JJ, Schousboe A, Waagepetersen HS, Howarth C, Hyder F. The micro-architecture of the cerebral cortex: functional neuroimaging models and metabolism. Neuroimage. 2008;40(4):1436–59. Epub 2008/03/18. pmid:18343162; PubMed Central PMCID: PMC4348032.
View Article
PubMed/NCBI
Google Scholar

[203] View Article

[204] PubMed/NCBI

[205] Google Scholar

[ref54] 54. Attwell D, Buchan AM, Charpak S, Lauritzen M, Macvicar BA, Newman EA. Glial and neuronal control of brain blood flow. Nature. 2010;468(7321):232–43. Epub 2010/11/12. pmid:21068832; PubMed Central PMCID: PMC3206737.
View Article
PubMed/NCBI
Google Scholar

[207] View Article

[208] PubMed/NCBI

[209] Google Scholar

[ref55] 55. Lind BL, Brazhe AR, Jessen SB, Tan FC, Lauritzen MJ. Rapid stimulus-evoked astrocyte Ca2+ elevations and hemodynamic responses in mouse somatosensory cortex in vivo. Proc Natl Acad Sci U S A. 2013;110(48):E4678–87. Epub 2013/11/13. pmid:24218625; PubMed Central PMCID: PMC3845114.
View Article
PubMed/NCBI
Google Scholar

[211] View Article

[212] PubMed/NCBI

[213] Google Scholar

[ref56] 56. Nizar K, Uhlirova H, Tian P, Saisan PA, Cheng Q, Reznichenko L, et al. In vivo stimulus-induced vasodilation occurs without IP3 receptor activation and may precede astrocytic calcium increase. Journal of Neuroscience. 2013;33(19):8411–22. pmid:23658179
View Article
PubMed/NCBI
Google Scholar

[215] View Article

[216] PubMed/NCBI

[217] Google Scholar

[ref57] 57. Takata N, Nagai T, Ozawa K, Oe Y, Mikoshiba K, Hirase H. Cerebral blood flow modulation by basal forebrain or whisker stimulation can occur independently of large cytosolic Ca 2+ signaling in astrocytes. PloS one. 2013;8(6):e66525. pmid:23785506
View Article
PubMed/NCBI
Google Scholar

[219] View Article

[220] PubMed/NCBI

[221] Google Scholar

[ref58] 58. Agulhon C, Sun MY, Murphy T, Myers T, Lauderdale K, Fiacco TA. Calcium Signaling and Gliotransmission in Normal vs. Reactive Astrocytes. Front Pharmacol. 2012;3:139. Epub 2012/07/20. pmid:22811669; PubMed Central PMCID: PMC3395812.
View Article
PubMed/NCBI
Google Scholar

[223] View Article

[224] PubMed/NCBI

[225] Google Scholar

[ref59] 59. Burda JE, Bernstein AM, Sofroniew MV. Astrocyte roles in traumatic brain injury. Experimental neurology. 2016;275:305–15. pmid:25828533
View Article
PubMed/NCBI
Google Scholar

[227] View Article

[228] PubMed/NCBI

[229] Google Scholar

[ref60] 60. Heuser K, Nome CG, Pettersen KH, Åbjørsbråten KS, Jensen V, Tang W, et al. Ca2+ Signals in Astrocytes Facilitate Spread of Epileptiform Activity. Cerebral Cortex. 2018;28(11):4036–48. pmid:30169757
View Article
PubMed/NCBI
Google Scholar

[231] View Article

[232] PubMed/NCBI

[233] Google Scholar

[ref61] 61. Kuchibhotla KV, Lattarulo CR, Hyman BT, Bacskai BJ. Synchronous hyperactivity and intercellular calcium waves in astrocytes in Alzheimer mice. Science. 2009;323(5918):1211–5. pmid:19251629
View Article
PubMed/NCBI
Google Scholar

[235] View Article

[236] PubMed/NCBI

[237] Google Scholar

[ref62] 62. Kunkler PE, Kraig RP. Calcium waves precede electrophysiological changes of spreading depression in hippocampal organ cultures. Journal of Neuroscience. 1998;18(9):3416–25. pmid:9547248
View Article
PubMed/NCBI
Google Scholar

[239] View Article

[240] PubMed/NCBI

[241] Google Scholar

[ref63] 63. Peters O, Schipke CG, Hashimoto Y, Kettenmann H. Different mechanisms promote astrocyte Ca2+ waves and spreading depression in the mouse neocortex. Journal of Neuroscience. 2003;23(30):9888–96. pmid:14586018
View Article
PubMed/NCBI
Google Scholar

[243] View Article

[244] PubMed/NCBI

[245] Google Scholar

[ref64] 64. Figueiredo M, Lane S, Tang F, Liu BH, Hewinson J, Marina N, et al. Optogenetic experimentation on astrocytes. Exp Physiol. 2011;96(1):40–50. Epub 2010/11/03. pmid:21041318.
View Article
PubMed/NCBI
Google Scholar

[247] View Article

[248] PubMed/NCBI

[249] Google Scholar

[ref65] 65. Figueiredo M, Lane S, Stout RF, Jr., Liu B, Parpura V, Teschemacher AG, et al. Comparative analysis of optogenetic actuators in cultured astrocytes. Cell Calcium. 2014;56(3):208–14. Epub 2014/08/12. pmid:25109549; PubMed Central PMCID: PMC4169180.
View Article
PubMed/NCBI
Google Scholar

[251] View Article

[252] PubMed/NCBI

[253] Google Scholar

[ref66] 66. Mager T, Wood PG, Bamberg E. Optogenetic control of Ca2+ and voltage-dependent large conductance (BK) potassium channels. Journal of Molecular Biology. 2017;429(6):911–21. pmid:28192090
View Article
PubMed/NCBI
Google Scholar

[255] View Article

[256] PubMed/NCBI

[257] Google Scholar

[ref67] 67. Moshkforoush A, Ashenagar B, Tsoukias NM, Alevriadou BR. Modeling the role of endoplasmic reticulum-mitochondria microdomains in calcium dynamics. Sci Rep. 2019;9(1):17072. Epub 2019/11/21. pmid:31745211; PubMed Central PMCID: PMC6864103.
View Article
PubMed/NCBI
Google Scholar

[259] View Article

[260] PubMed/NCBI

[261] Google Scholar

[ref68] 68. Lallouette J, De Pittà M, Berry H. Astrocyte networks and intercellular calcium propagation. Computational Glioscience: Springer; 2019. p. 177–210. https://doi.org/10.3389/fncom.2019.00092 pmid:32038210

Abstract

Author summary

Figures

Introduction

Materials and methods

Single cell model

Quantification of astrocytic activity

Sensitivity analysis

Astrocytic network model

Results

Effect of ChR2 variants on the light-evoked response of astrocytes

Effect of light stimulation paradigm on single cell model response

Sensitivity to model parameters

Network-wide astrocytic response to light stimulation

Discussion

Salient features of light-evoked calcium signaling in astrocytes

Engineering of application-based ChR2 variants

Model limitations and future directions

Supporting information

S1 Fig. ChR2 gating dynamics during light stimulation.

S2 Fig. Comparison of the ChR2 flux across variants.

S3 Fig. Response of astrocytes expressing different ChR2 constructs to various light stimulation paradigms.

S4 Fig. Effect of expression heterogeneity on the network-wide response to stimulation.

S1 Movie. Video of network-wide astrocytic Ca2+ response to light stimulation.

Acknowledgments

References

Cookie Preference Center

Customize Your Cookie Preference

S1 Movie. Video of network-wide astrocytic Ca²⁺ response to light stimulation.