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 (PLCδ1) mediated production of IP3, 3) capacitive calcium entry (CCE) via the store operated calcium channel (SOC), 4) passive leak from the ER to the cytosol (Jleak), 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 (Jin) 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 (JChR2), is characterized by pulse period (T) and pulse width (δ).
Table 1.
Model parameters.
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 ([Co]) 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.
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 (μISI) vs. standard deviation of ISI (σISI) where each point corresponds to a single simulated 270-min [Ca2+]c trace. Solid line shows the linear fit between μISI and σISI values. Throughout the manuscript, △, ○, and ◊ represent paradigms resulting in low, medium, and high Ca2+ spiking during short-term (45 min) stimulation of astrocytes, respectively.
Table 2.
Range of parameters for global sensitivity analysis.
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.
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 σbasal-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 σspiking rate with varying
values.