Comparison of low-power, high-frequency and temporally precise optogenetic inhibition of spiking in NpHR, eNpHR3.0 and Jaws-expressing neurons

Photoisomerization of all-trans-retinal to the 13-cis isomer in halorhopsins initiates a series of several intermediates [33–36]. The transitions between these intermediates are accompanied by the transport of chloride-ions across the membrane, that allows light to inhibit neuronal activity.

The photocycle of NpHR and kinetics of ion transfer have been extensively studied [33, 37, 38]. It is reported that the photocycle of NpHR consists of six kinetic states as P₁ → P₆, which are characterized by archetypical spectral states K, L₁, L₂, O, N and the precursor of the ground state NpHR', besides the ground state (P₀). P₄ and P₅ states are responsible for release and uptake of chloride ions, respectively [33]. The transition P₆ → P₀ is called the rate-determining transition of the NpHR photocycle [33]. Since, eNpHR3.0 and Jaws are also chloride pumps with altered kinetics and photocurrent amplitude, we model their photoresponse similar to NpHR. For simplicity, we consider a three-state model of the photocycle that involves the ground state P₀, the active state P₄ responsible for chloride release, and a rate-limiting state P₆. We consider the photocurrent in all three opsins to be expressed as,

$$\begin{eqnarray}&&{I}_{j}={g}_{j}\left(V-E\right)\,\end{eqnarray} \tag{ 1 }$$

where, j ≡ NpHR/eNpHR3.0/Jaws, ${g}_{j}$ accounts for both single molecule conductance and expression density, $V$ is the membrane voltage and $E$ is the reversal potential of the pump, which is −400 mV for all three variants [38, 39]. In general, the conductance ${g}_{j}$ depends on various factors given as,${g}_{j}={g}_{j}\left(t,\lambda ,\phi ,pH,T,{\rm{\Psi }}\right),$ where $t$ is the time, $\lambda$ is wavelength, $\phi$ is the photon flux per unit area, $T$ is temperature and, Ψ is local ion concentration across the membrane [33, 39]. Consider ${g}_{j}$ to depend on three factors, with the conductance defined as ${g}_{j}={g}_{0j}\left(\lambda \right)f\left(\phi ,t\right){\rm{\Psi }}\left(\left[C{l}_{out}^{-}\right]\right),$ where, (i) ${g}_{0j}$(λ) is maximum conductance, (ii) $f\left(\phi ,t\right)$ is a normalized light-dependent function and, (iii) ${\rm{\Psi }}\left(\left[C{l}_{out}^{-}\right]\right)$ is a normalized function to account for the dependence on outer membrane chloride concentration.

Considering P₀, P₄, and P₆ to denote the fraction of opsin molecules in each of the three states at any instant of time. The kinetics can be described by the following rate equations,

$$\begin{eqnarray}&&\mathop{{P}_{0}}\limits^{\cdot }={G}_{r}{P}_{6}-{G}_{a}\left(\phi \right){P}_{0}\,\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&\mathop{{P}_{4}}\limits^{\cdot }={G}_{a}\left(\phi \right){P}_{0}-{G}_{d}{P}_{4}\end{eqnarray} \tag{ 3 }$$

$$\begin{eqnarray}&&\mathop{{P}_{6}}\limits^{\cdot }={G}_{d}{P}_{4}-{G}_{r}{P}_{6}\end{eqnarray} \tag{ 4 }$$

where, ${P}_{0}+{P}_{4}+{P}_{6}=1.$ ${G}_{a},$ ${G}_{d}$ and ${G}_{r}$ are the rate constants for ${P}_{0}\to {P}_{4},$ ${P}_{4}\to {P}_{6}$ and ${P}_{6}\to {P}_{0}$ transitions respectively, determined from the experimental data and defined as ${G}_{a}\left(\phi \right)={k}_{a}{\phi }^{p}/({\phi }^{p}+{\phi }_{m}^{p}),$ ${G}_{d}=1/({\tau }_{off})$ and ${G}_{r}=1/({\tau }_{r})$ [39]. Since the three-state model assumes only one active-state ${P}_{4},$ $f\left(\phi ,t\right)={P}_{4}.$ The photon flux per unit area $\phi =\lambda I/hc,$ where $I$ is irradiance, $h$ is Planck's constant and $c$ is the speed of light in vacuum. Other model parameters $\left({\phi }_{m},p,q,{k}_{a},{G}_{r},{G}_{d}\right)$ have been determined empirically (table 1) [18–22, 33]. The dependence of photocurrent on $\left[C{l}_{out}^{-}\right]$ has been determined by fitting the experimental data using Michaelis-Menten type saturation such that $\left(\left[C{l}_{out}^{-}\right]\right)=\left({\vartheta }_{\max }\,\left[C{l}_{out}^{-}\right]\right)/\left.\left({k}_{d}+\left[C{l}_{out}^{-}\right]\right)\right)/{{\rm{\Psi }}}_{0},$ with ${\vartheta }_{max}$ = 5 mM sec⁻¹ and ${k}_{d}$ = 16 mM [18, 22]. Here, ${{\rm{\Psi }}}_{0}$ = 4.4286, is the value of function ${\rm{\Psi }}$ calculated at $\left[C{l}_{out}^{-}\right]$ = 124 mM.

Table 1.  Opsin model parameters [18–22, 33].

Parameter	NpHR	eNpHR3.0	Jaws
${G}_{d}\left(m{s}^{-1}\right)$	0.1099	0.25	0.167
${G}_{r0}\left(m{s}^{-1}\right)$	0.05	0.05	0.05
${k}_{a}\left(m{s}^{-1}\right)$	0.005	1	1
$p$	0.5	0.7	0.8
$q$	0.2	0.1	1
${\phi }_{m}\left(ph.{{\rm{mm}}}^{-2}{s}^{-1}\right)\,$	1.5e+18	1.2e+18	0.95e+18
$E\left(mV\right)$	−400	−400	−400
$\lambda \left(nm\right)$	593	593	593
${g}_{0}\left(nS\right)$	17.7	7.6	12.6
$a$	0.02e-2	0.02e-2	0.02e-2
$b$	5	12	6.5

The rebound of chloride concentration to its resting value, through naturally occurring ionotropic GABA receptors, has been considered as a leak chloride current $\left({I}_{Cl-leak}\right)$, due to change in resting potential of these channels,

$$\begin{eqnarray}&&{I}_{Cl-leak}={g}_{Cl}\left({E}_{C{l}_{0}}-{E}_{Cl}\right)\,\end{eqnarray} \tag{ 5 }$$

where,${g}_{Cl}$ is the channel conductance fitted to match with experimental results (2.3 mS cm⁻²) [18–21]. ${E}_{C{l}_{0}}$ denotes the resting potential of chloride leak channel and is −70 mV. ${E}_{Cl}$ is the reversal potential of the channel, which depends on concurrent values of inner and outer chloride concentrations, and calculated using Goldman-Hodgkin-Katz equation [22],

$$\begin{eqnarray}&&{E}_{Cl}=-\left(\displaystyle \frac{RT}{F}\right)\mathrm{ln}\left(\left[C{l}_{out}^{-}\right]/\left[C{l}_{in}^{-}\right]\right)\,\end{eqnarray} \tag{ 6 }$$

where, $R$ is the universal gas constant, $T$ is temperature, $F$ is Faraday constant, such that $RT/F$ = 26.67 mV. $\left[C{l}_{out}^{-}\right]$ and $\left[C{l}_{in}^{-}\right]$ denote the outer and inner chloride concentrations across the membrane at any instant of time. The total change in chloride concentration inside the membrane due to halorhodopsin mediated inward pumping and chloride channel mediated outward leakage is calculated by using the differential equation,

$$\begin{eqnarray}&&\dot{\left[C{l}_{in}^{-}\right]}=a\left({I}_{j}+b\,{I}_{Cl-leak}\right)\,\end{eqnarray} \tag{ 7 }$$

where, $a$ and $b$ are the rate constants, fitted to match with experimental results, shown in table 1 [18–21]. The total chloride current across the membrane is a combination of both currents and expressed as,

$$\begin{eqnarray}&&{I}_{j}^{{\prime} }=\left({I}_{j}+{I}_{Cl-leak}\right)\,\end{eqnarray} \tag{ 8 }$$

To analyze the response of halorhodopsin-expressing hippocampal neurons to light stimuli, we incorporate the kinetic model of the photocycle of NpHR/eNpHR3.0/Jaws, with the well-established single compartment CA3 hippocampal spiking neuron model, i.e. Hemond neuron model [40, 41]. The neuron model incorporating the light-driven ion pump current (${I}_{NpHR/eNpHR3.0/Jaws}^{{\prime} }$) can be expressed as a system of equations expressed as,

$$\begin{eqnarray}&&{C}_{m}\dot{V}=-{I}_{ionic}+{I}_{DC}+{I}_{NpHR/eNpHR3.0/Jaws}^{{\prime} }\end{eqnarray} \tag{ 9 }$$

where, ${C}_{m}$ is the membrane capacitance, and ${I}_{DC}$ is the external constant DC bias current that controls the excitability of the neuron, and ${I}_{ionic}$ is the sum of the membrane ion-channel currents (${I}_{Na},$ ${I}_{Kdr},$ ${I}_{H},$ ${I}_{CaL},$ ${I}_{KD}$ and ${I}_{L}$) [40–42].

Each ion-channel current in ${I}_{ionic}$ has been modelled as ${I}_{i}={g}_{i}{m}^{p}{h}^{q}\left(V-{E}_{i}\right),$ where ${g}_{i}$ is maximal conductance, $m$ is activation variable (with exponent $p$), $h$ is inactivation variable (with exponent $q$), and ${E}_{i}$ is the reversal potential. The kinetic equation for each of the gating functions $x$ ($m$ or $h$) obeys the first-order kinetics as $\dot{x}=\,\left({x}_{\infty }-x\right)/{\tau }_{x}.$ The voltage-dependent functions and values of parameters are given in tables 2 and 3, respectively [40, 41]. A time-step of 0.01 ms has been used for all simulations in MATLAB R2015a.

Table 2.  Gating function parameters of ion channels in neuron model [40, 41].

${I}_{ionic}$	Gating variable	$\alpha$	$\beta$	${x}_{\infty }$	${\tau }_{x}$ (ms)
${I}_{Na}$	$p=3$	$\displaystyle \frac{-0.4\left(V+6\right)}{\exp \left[-\tfrac{V+6}{7.2}\right]-1}$	$\displaystyle \frac{0.124\left(V+6\right)}{\exp \left[\tfrac{V+6}{7.2}\right]-1}$	$\displaystyle \frac{\alpha }{\alpha +\beta }$	$\displaystyle \frac{0.4665}{\alpha +\beta }$
	$q=1$	$\displaystyle \frac{-0.03\left(V+21\right)}{\exp \left[-\displaystyle \frac{\left(V+21\right)}{1.5}\right]-1}$	$\displaystyle \frac{0.01\left(V+21\right)}{\exp \left[\tfrac{V+21}{1.5}\right]-1}$	$\displaystyle \frac{1}{\exp \left[\tfrac{V+26}{4}\right]+1}$	$\displaystyle \frac{0.4662}{\alpha +\beta }$
${I}_{Kdr}$	$p=1$	$\exp \left[-0.113\left(V-37\right)\right]$	$\exp \left[-0.0791\left(V-37\right)\right]$	$\displaystyle \frac{1}{1+\alpha }$	$\displaystyle \frac{50+\beta }{1+\alpha }$
${I}_{H}$	$q=1$	$\exp \left[0.0833\left(V+75\right)\right]$	$\exp \left[0.0333\left(V+75\right)\right]$	$\displaystyle \frac{1}{\exp \left[\tfrac{V+73}{8}\right]+1}$	$\displaystyle \frac{\beta }{0.0149\left(1+\alpha \right)}$
${I}_{CaL}$	$p=2$	$\displaystyle \frac{15.69* \left(-V+81.5\right)}{\exp \left[\tfrac{-V+81.5}{10}\right]-1}$	$0.29* \exp \left[-\displaystyle \frac{V}{10.86}\right]$	$\displaystyle \frac{\alpha }{\alpha +\beta }$	$\displaystyle \frac{2* \exp \left[0.00756\left(V-4\right)\right]}{1+\exp \left[0.0756\left(V-4\right)\right]}$
${I}_{KD}$	$p=1$	$\exp \left[0.113\left(V+33\right)\right]$	$\exp \left[0.0791\left(V+33\right)\right]$	$\displaystyle \frac{1}{1+\alpha }$	$\displaystyle \frac{100* \beta }{1+\alpha }$

Table 3.  Neuron model parameters [40, 41].

Parameter	Value
${g}_{Na}(mS/{{\rm{cm}}}^{{\rm{2}}})$	22
${g}_{Kdr}(mS/{{\rm{cm}}}^{{\rm{2}}})$	10
${g}_{H}(mS/{{\rm{cm}}}^{{\rm{2}}})$	0.01
${g}_{CaL}(mS/{{\rm{cm}}}^{{\rm{2}}})$	0.01
${g}_{KD}(mS/{{\rm{cm}}}^{{\rm{2}}})$	0.015
${g}_{L}(mS/{{\rm{cm}}}^{{\rm{2}}})$	0.0394
${E}_{H}\left(mV\right)$	−30
${E}_{Na}\left(mV\right)$	55
${E}_{K}\left(mV\right)$	−62
${E}_{L}\left(mV\right)$	−61
${E}_{Ca}\left(mV\right)$	140
${I}_{DC}(\mu A/{{\rm{cm}}}^{{\rm{2}}})$	0
${C}_{m}(\mu F/{{\rm{cm}}}^{{\rm{2}}})$	1.41

The photoresponse of NpHR, eNpHR3.0 and Jaws, expressed in neurons, has been studied through numerical simulations using equations (1)–(8), taking into account the effect of change in $\left[C{l}_{out}^{-}\right]$, considering the reported experimental parameters shown in table 1. On illumination with 593 nm wavelength light, the photocurrent of NpHR, eNpHR3.0 and Jaws has been shown in figure 1. To study the effect of change in chloride concentration on the photocurrent, the variation of photocurrent with time in NpHR, has been shown in figure 1(a). The simulated photocurrent exactly matches with the reported experimental results, while considering the effect of change in chloride concentration [18]. Light-induced transportation of chloride ions from outside to inside of the membrane results in a decrease in $\left[C{l}_{out}^{-}\right]$, which results in lower plateau photocurrent. Also, due to long-light stimulation, larger changes in $\left[C{l}_{out}^{-}\right]$ gradient results in rebound of chloride ions from inside to outside of the membrane. This rebound chloride current becomes prominent after light turn-off, as the pumping from outside to inside gets turned-off as shown in figure 1(a).

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To compare theoretical simulations with reported experimental results, the variation of photocurrent with time at corresponding irradiances and pulse widths, considering the effect of change in $\left[C{l}_{out}^{-}\right],$ has been shown in figure 1(b). Again, the simulated results are in good agreement with the reported experimental results [6, 18, 21]. The simulated peak and plateau photocurrents of 43 pA, 210 pA and 37 pA, 183 pA match with the reported experimental values for NpHR and Jaws, respectively [18, 21]. The simulated peak photocurrent of 195 pA for eNpHR3.0 also matches with the reported experimental value [6]. For comparison, the variation of photocurrent with time in NpHR, eNpHR3.0 and Jaws, at 5 mW mm⁻² and 500 ms pulse width has been shown in figure 1(c). Jaws shows largest photocurrent among all three variants. Larger photocurrent causes higher change in chloride concentration gradient across the membrane, which results in a larger reverse current after light turn-off. Consequently, this reverse current is also highest for Jaws (figure 1(c)). To compare the turn-off kinetics of photocurrent of these opsins, variation of normalized photocurrent with time, at 5 ms pulse width and 5 mW mm⁻² irradiance, is shown in figure 1(d). Among all three halorhodopsin variants, eNpHR3.0 shows fastest turn-off kinetics.

As NpHR, eNpHR3.0 and Jaws, are light-driven chloride pumps, their capacity to generate photocurrent depends on the outer membrane chloride concentration [18]. Hence, it is necessary to study the effect of change in outer chloride concentration on the photocurrent. The variation of photocurrent with time, at different $\left[C{l}_{out}^{-}\right],$ is shown in figures 2(a)–(c). Higher chloride concentration gradient across the membrane helps these ionic-pumps in pumping chloride inside the membrane, even in the presence of opposing membrane potential. As is evident, the photocurrent in all three variants is more sensitive to lower values of $\left[C{l}_{out}^{-}\right]$ rather than higher values. The variation of peak and plateau photocurrent, and corresponding adaptation ratio with $\left[C{l}_{out}^{-}\right]$ is shown in figures 2(d)–(f). The variation of peak photocurrent of NpHR with $\left[C{l}_{out}^{-}\right]$ exactly matches with the reported experimental result (figure 2(d)) [18]. Adaptation ratio of all three variants decreases on increase in $\left[C{l}_{out}^{-}\right],$ but in the case of Jaws, the adaptation ratio has a minimum value of 0.75 at $\left[C{l}_{out}^{-}\right]$ = 40 mM, beyond which it slightly increases with $\left[C{l}_{out}^{-}\right]$ (figure 2(f)).

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The effect of irradiance on photocurrent characteristic measures and time constants, at different pulse widths, is shown in figure 3. The variation of peak photocurrent and adaptation ratio with irradiance, at 500 ms pulse stimulation, is shown in figures 3(a) and (b), respectively. The peak photocurrent (I_peak) increases with an increase in irradiance for all three variants, as more molecules populate the active state-P₄. In all three variants, under long light stimulation, the photocurrent in the opsin reaches the peak, which decays to a steady-state plateau. It is evident that the higher peak photocurrent results in lower plateau photocurrent, which is not only due to molecular transition to P₆ state, but also due to larger changes in outer chloride concentration gradient. Jaws shows minimum adaptation ratio among all three variants (figure 3(b)).

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The variation of t_peak, time to peak, and t_off, time taken by the photocurrent from the point where light is turned off, to the time it reaches 0.01 % of its magnitude, with irradiance, at 20 and 500 ms pulse widths, is shown in figures 3(c)–(f). For NpHR, t_peak does not vary with irradiance and is higher for longer pulse excitation. For Jaws and eNpHR3.0, it decreases monotonically on increase in irradiance and saturates to lower values at higher irradiances (figures 3(c) and (d)). The difference between the initial t_peak values of NpHR, Jaws and eNpHR3.0 is also large at 500 ms pulse excitation. t_off does not vary with irradiance, for all three variants, but has lower values for longer pulse widths (figures 3(e) and (f)).

The effect of pulse width on photocurrent of NpHR, eNpHR3.0 and Jaws has been shown in figure 4. Variation of I_peak, I_plateau and I_Cl-leak with pulse width is shown in figures 4(a)–(c). I_peak of all three variants increases on increase in pulse width and saturates at higher values, which is 43, 10 and 15 ms for NpHR, eNpHR3.0 and Jaws respectively, at 5 mW mm⁻² (figure 4(a)). For all three variants, I_plateau slightly decreases on increase in pulse width and saturates for longer pulse widths, which is 800 ms for NpHR, 400 ms for eNpHR3.0 and 1200 ms for Jaws, at 5 mW mm⁻² (figure 4(b)). The peak value of the leak chloride current (I_Cl-leak) increases with increase in pulse width and saturates at 3, 23 and 95 pA at a pulse width of 500 ms for NpHR and eNpHR3.0, and 1500 ms for Jaws, respectively (figure 4(c)). The saturation of I_plateau and I_Cl-leak indicates that after a long pulse excitation, the chloride transportation in opsin-expressing system gets stabilized.

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The variation of t_peak and t_off with pulse width, at 5 mW mm⁻² is shown in figures 4(d) and (e). t_peak increases with increase in pulse width and saturates after a certain pulse width, which is 43 ms for NpHR, 15 ms for Jaws and 10 ms for eNpHR3.0, at 5 mW mm⁻² (figure 4(d)). t_off decreases on increase in pulse width and is shortest for eNpHR3.0 among all three variants (figure 4(e)). Variation of minimum pulse width required to achieve peak photocurrent at particular irradiance, termed photocurrent saturation pulse width (PSPW), with irradiance is shown in figure 4(f). PSPW remains nearly constant for NpHR (∼41 ms), whereas it decreases exponentially with increase in irradiance for Jaws and eNpHR3.0, respectively (figure 4(f)). PSPW has lower values for Jaws and eNpHR3.0, which is desirable to empirically obtain good values of light power with maximum output and useful for avoiding unwanted heating effects for high frequency photostimulations.

Comparison of photocurrent under multiple pulse illumination, at varying irradiances and pulse widths, is shown in figure 5. The peak photocurrents remain same for subsequent photostimulations and increase with increase in irradiance or pulse width for all three variants (figure 5). At 10 Hz, the modulation ratio, I_peak10/I_peak1, remains ∼1, and does not vary with irradiance and pulse width, which indicates the utility of these opsins in targeting long sequence of spike trains.

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Comparison of the effect of light pulse stimulation frequency on the photocurrent has been shown in figure 6. Due to its fastest kinetics, among all three variants, eNpHR3.0 shows no photocurrent plateau up to a photostimulation frequency of 50 Hz, and lowest photocurrent plateau at higher frequencies (figure 6). The modulation in the peaks of photocurrent is higher at higher frequencies for NpHR, whereas it is nearly same for eNpHR3.0 and Jaws (figure 6). At higher frequencies, the first peak of photocurrent in NpHR is lower in comparison to subsequent photocurrent peaks, while it is higher for other variants. For Jaws, at lower irradiance of 1 mW mm⁻², the first peak of photocurrent is smaller than subsequent peaks, due to longer t_peak at lower irradiances.

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Light-induced hyperpolarization and silencing of neuronal spiking in NpHR/eNpHR3.0/Jaws-expressing hippocampal neurons has been simulated using equations (1)–(9) considering parameters shown in tables 1–3. Light-induced hyperpolarization and the effect of irradiance on membrane potential are shown in figure 7. At 500 ms pulse stimulation, λ = 593 nm, and I = 5 mW mm⁻², the variation of membrane potential in NpHR, eNpHR3.0 and Jaws-expressing neurons with time is shown in figure 7(a). As is evident, the rebound of $\left[C{l}_{out}^{-}\right]$ to its resting value results in post-illumination depolarization, which is highest for Jaws, due to highest hyperpolarization among all three variants. To compare with the reported experimental results, the variation of membrane potential with time, at corresponding irradiances and pulse widths, is shown in figure 7(b). Simulated results are in good agreement with reported experimental results with peak voltage of −83 mV for NpHR and −86 mV for Jaws, respectively (figure 7(b)) [18, 21]. For NpHR-expressing neurons, the match is at C_m = 5 μF cm⁻². Variation of hyperpolarization peak voltage with irradiance, at 500 ms pulse width, has been shown in figure 7(c).

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The effect of varying irradiances and expression densities on spike inhibition capacity in NpHR, eNpHR3.0 and Jaws-expressing neurons, has been shown in figure 8. For the analysis, high frequency spike train has been evoked using a 2 s continuous step current. The effect of concurrent delivery of 1 s continuous 593 nm light at different percentage irradiances on spike inhibition has been shown in figures 8(a)–(c). Complete spike inhibition takes place at 21.7 mW mm⁻², 1.2 mW mm⁻², and 0.4 mW mm⁻² for NpHR, eNpHR3.0 and Jaws, respectively. The simulated result of variation of percentage spike inhibition in NpHR-expressing neurons exactly matches with the reported experimental results (figure 8(a)) [18]. Corresponding inhibition in eNpHR3.0 and Jaws has been achieved at much lower irradiances, which highlights their utility over NpHR, as low-power silencing tools.

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It is important to study how the expression density of these opsins alters the irradiance threshold for complete inhibition. Corresponding variation of percentage inhibition with irradiance at different expression densities has been shown in figures 8(d)–(f). In general, higher expression density results in lower irradiance thresholds. It is found that a minimum irradiance of 5 mW mm⁻² with expression density of 1.7 mS cm⁻² for NpHR, 0.4 mW mm⁻² with expression density of 0.1 mS cm⁻² for eNpHR3.0, and 0.2 mW mm⁻² with expression density of 0.2 mS cm⁻² for Jaws, is sufficient to achieve 100% spiking suppression.

The effect of outer chloride concentration on the capacity of light-mediated spike inhibition in NpHR, eNpHR3.0 and Jaws-expressing neurons has been shown in figure 9. Lower values of $\left[C{l}_{out}^{-}\right]$ results in lower photocurrents and, hence leads to failure in spike inhibition. It is evident that there is no effect of photostimulation of these opsins, in the absence of outer chloride molecules (figure 9). Minimum irradiance has been used such that 100% spike inhibition takes place at $\left[C{l}_{out}^{-}\right]$ = 124 mM, for all three variants. However, it is possible to get 100% spike inhibition at lower $\left[C{l}_{out}^{-}\right]$ values, but it would require higher irradiances.

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To test whether NpHR, eNpHR3.0 and Jaws activation can suppress target spike and also to avoid unwanted heating effects due to continuous illumination of light, it is important to analyze their capacity under pulsed illumination. The effect of pulse width and irradiance on spiking inhibition has been shown in figure 10. Spikes have been evoked by applying pulsed step currents at 10 Hz. Inhibition has been achieved using light pulses of indicated pulse widths and irradiances at same frequency (figure 10), where Δt is the time delay between dc current and the light stimulus. As is evident from figure 10, a minimum irradiance of 0.6 mW mm⁻² and pulse width of 5 ms can achieve 100% spike inhibition in Jaws-expressing neurons. The analysis also reveals that increase in irradiance and pulse width, higher than that sufficient to suppress the target spike, results in generation of inhibitory signal (figure 10).

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To assess the temporal resolution of light-mediated spike inhibition at higher frequencies, pairs of spikes, both closely timed and temporally separated, at different frequencies have been inhibited. For this, a sequence of spikes has been evoked electrically, in NpHR-expressing neurons. Further, selected pairs of spikes, both closely timed and temporally separated, at 5, 10, 20 and 30 Hz have been precisely inhibited with brief pulses of 593 nm light (figure 11). The simulated result in figure 11 exactly matches with reported experimental results [18].

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To compare the temporal resolution of light-mediated spike inhibition in NpHR, eNpHR3.0 and Jaws-expressing neurons, trains of action potentials at 50 and 100 Hz have been evoked (figure 12). Again, both closely timed and temporally separated pair of spikes have been targeted using short pulses of light (figure 12). As is evident from figure 12, NpHR and Jaws fail to sustain temporal precision at 50 Hz and 100 Hz, respectively, whereas, eNpHR3.0 is able to sustain upto 100 Hz.

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It is experimentally shown that by stimulating trains of small light pulses, barrages of inhibitory post synaptic potential (IPSP)-like events with precise, reliable timing and amplitudes at different frequencies can be generated in NpHR-expressing neurons [18]. NpHR-mediated precisely timed IPSP barrages at 5, 10 and 100 Hz have been simulated as shown in figure 13(a). The results exactly match with the reported experimental results [18]. The match at 100 Hz is at C_m = 3.24 μF cm⁻². IPSP sequences in NpHR-expressing neurons shows IPSP plateau voltage above 10 Hz, which increases on increase in stimulation frequency. Further, we analyzed this characteristic for all the three variants at different frequencies (figure 13(b)). As is evident, at higher frequencies, eNpHR3.0 shows the lowest IPSP plateau in comparison to NpHR and Jaws (figure 13(b)). Irradiance and expression density are chosen such that at 5 Hz, IPSP of 12 mV amplitude can be generated in each opsin-expressing neuron.

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Theoretical simulations show that the difference between the temporal position of inhibitory light pulse and exciting step current pulse, is a crucial factor for irradiance and expression level thresholds g_NpHR for NpHR, g_eNpHR3.0 for eNpHR3.0, and g_Jaws for Jaws. Hence, the analysis has been carried out by inhibiting single action potential by varying Δt (figure 14). As is evident from figure 14, the variants having shorter t_peak leads to shorter value of Δt for better results. Empirically obtained good values of Δt are 8 ms, 3 ms and 5 ms for NpHR, eNpHR3.0 and Jaws, respectively (figure 14).

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After a detailed analysis of photostimulation protocol that includes irradiance, pulse width, frequency, Δt, and expression density, good values of these factors have been obtained empirically to get temporally precise optogenetic inhibition at very high-frequencies. Under the obtained set of photostimulation protocols and expression density, Jaws and eNpHR3.0 are able to precisely inhibit single spike, or pair of spikes, both closely timed and temporally separated, up to 160 and 200 Hz, respectively (figure 15). As is evident from figure 15, the inhibition at higher frequencies, beyond the limit, can also be achieved, although it is not possible to maintain single spike temporal resolution.

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