Theoretical optimization of high-frequency optogenetic spiking of red-shifted very fast-Chrimson-expressing neurons

Abstract

A detailed theoretical analysis and optimization of high-fidelity, high-frequency firing of the red-shifted very-fast-Chrimson (vf-Chrimson) expressing neurons is presented. A four-state model for vf-Chrimson photocycle has been formulated and incorporated in Hodgkin-Huxley and Wang-Buzsaki spiking neuron circuit models. The effect of various parameters that include irradiance, pulse width, frequency, expression level, and membrane capacitance has been studied in detail. Theoretical simulations are in excellent agreement with recently reported experimental results. The analysis and optimization bring out additional interesting features. A minimal pulse width of 1.7 ms at $23\mathrm{mW}/{\mathrm{mm}}^2$ induces a peak photocurrent of 1250 pA. Optimal irradiance ( $0.1\mathrm{mW}/{\mathrm{mm}}^2$ ) and pulse width ( $50\mu s$ ) to trigger action potential have been determined. At frequencies beyond 200 Hz, higher values of expression level and irradiance result in spike failure. Singlet and doublet spiking fidelity can be maintained up to 400 and 150 Hz, respectively. The combination of expression level and membrane capacitance is a crucial factor to achieve high-frequency firing above 500 Hz. Its optimization enables 100% spike probability of up to 1 kHz. The study is useful in designing new high-frequency optogenetic neural spiking experiments with desired spatiotemporal resolution, by providing insights into the temporal spike coding, plasticity, and curing neurodegenerative diseases.

Keywords: channelrhodopsins; computational optogenetics; neural spiking; red-shifted opsins; very-fast-Chrimson.

Fig. 1

Equivalent circuit diagram of the vf-Chrimson-expressing neuron.

Fig. 2

Optostimulation of photocurrent in vf-Chrimson at different pulse widths and $I=23\mathrm{mW}/{\mathrm{mm}}^2$. (a) Comparison with Chrimson and f-Chrimson at $\lambda =594\mathrm{nm}$ and 3-ms pulse width; (b) at 500-ms pulse width. Inset: corresponding variation of normalized population density with time.

Fig. 3

Effect of irradiance on the photocurrent of vf-Chrimson. (a) At irradiances 0.05, 0.2, 0.4, 0.7, 1.2, 2, 4, 10, and $30\mathrm{mW}/{\mathrm{mm}}^2$, at $\lambda =594\mathrm{nm}$, and 3-ms pulse width; (b) corresponding variation at 500-ms pulse width. (c) Variation in $I_{\text{peak}}$ and $t_{\text{off}}$ with irradiance under 3-ms pulse stimuli. Inset: corresponding $t_{\text{peak}}$ variation with irradiance (on the same scale). (d) Variation of $I_{\text{peak}}$, $t_{\text{off}}$, and $t_{\text{inact}}$ with irradiance at 500-ms pulse stimuli. Inset: corresponding variation of $t_{\text{peak}}$ with irradiance (on the same scale).

Fig. 4

Effect of irradiance on $I_{\text{peak}}$ and $I_{\text{plateau}}$ of the vf-Chrimson; (a) 500-ms pulse width and (b) corresponding variation of adaptation ratio at $\lambda =594\mathrm{nm}$.

Fig. 5

Effect of pulse width on the photocurrent of vf-Chrimson. Variation of photocurrent with time at $I=23\mathrm{mW}/{\mathrm{mm}}^2$, $\lambda =594\mathrm{nm}$, and at (a) shorter pulse widths (0.5, 0.9, 2, 3, 4, and 5 ms). (b) Variation of photocurrent at longer pulse widths (50 to 1000 ms). (c) Corresponding variation of $t_{\text{peak}}$ and $I_{\text{peak}}$ with pulse width. (d) Variation of SPW with irradiance.

Fig. 6

Effect of multiple pulse optostimulation on the vf-Chrimson photocurrent. At indicated irradiances and pulse widths at a photostimulation protocol of 10 stimuli, at 10 Hz, and at $\lambda =594\mathrm{nm}$.

Fig. 7

Light-induced spiking in the vf-Chrimson-expressing neurons. At indicated frequencies and optostimulation protocol of 40 stimuli each of 3-ms pulse width, at $I=23\mathrm{mW}/{\mathrm{mm}}^2$, at $\lambda =594\mathrm{nm}$, and $g_0=10\mathrm{mS}/{\mathrm{cm}}^2$.

Fig. 8

Comparison of light-induced spiking fidelity in the vf-Chrimson-expressing neurons. At different irradiances and two pulse widths, under optostimulation protocol of 10 stimuli, at 10 Hz, at $\lambda =594\mathrm{nm}$, and $g_0=0.5\mathrm{mS}/{\mathrm{cm}}^2$.

Fig. 9

Spiking fidelity in the vf-Chrimson-expressing neurons. At different irradiances and frequencies at 10 stimuli each of 3-ms pulse width and $g_0=0.5\mathrm{mS}/{\mathrm{cm}}^2$.

Fig. 10

Light-induced spiking in the vf-Chrimson-expressing interneurons at optostimulation protocol of 20 stimuli, each of 0.5 ms pulse widths, at $\lambda =565\mathrm{nm}$, (a) at $I=2.6$, 2.6. 4.9, 4.9, 4.9, 4.9, 4.9, and $8\mathrm{mW}/{\mathrm{mm}}^2$ and $g_0=0.5$, 0.4, 0.34, 0.35, 0.41, 0.42, 0.55, and $0.54\mathrm{mS}/{\mathrm{cm}}^2$, respectively; (b) at $I=2.2\mathrm{mW}/{\mathrm{mm}}^2$ and $g_0=0.5\mathrm{mS}/{\mathrm{cm}}^2$, at indicated frequencies. Upper and lower frequency labels indicate output spiking frequency and input stimulation frequency, respectively.

Fig. 11

Spiking fidelity in the vf-Chrimson-expressing interneurons. At indicated irradiances and frequencies, at 20 stimuli each of pulse width 0.5 ms and $g_0=0.6\mathrm{mS}/{\mathrm{cm}}^2$.

Fig. 12

Variation of spike probability in the vf-Chrimson-expressing interneurons under stimulation protocol of $10\mathrm{Hz}$ and 20 stimuli. (a) Irradiance (0 to $5\mathrm{mW}/{\mathrm{mm}}^2$) at different expression levels (0.1 to $5\mathrm{mS}/{\mathrm{cm}}^2$) and pulse width of 0.5 ms. (b) Pulse width (0 to 0.5 ms) at different irradiances (0.5 to $20\mathrm{mW}/{\mathrm{mm}}^2$) and $g_0=0.5\mathrm{mS}/{\mathrm{cm}}^2$.

Fig. 13

Effect of irradiance, pulse width, and expression level on the spiking fidelity in vf-Chrimson-expressing interneurons. At $\lambda =565\mathrm{nm}$ and (a) irradiances when $g_0=0.25\mathrm{mS}/{\mathrm{cm}}^2$ and (b) expression level at $I=10\mathrm{mW}/{\mathrm{mm}}^2$.

Fig. 14

Effect of the stimulation frequency on spiking fidelity in vf-Chrimson-expressing interneurons. (a) Variation of spiking frequency (singlets) of neurons at $I=10\mathrm{mW}/{\mathrm{mm}}^2$, 0.5 ms pulse width, and $G_{d1}=0.625{\mathrm{ms}}^{-1}$. (b) Variation of multispiking frequency (doublets) of neurons at different combinations of expression level and irradiance at 0.5-ms pulse width.

Fig. 15

Maximum vf-Chrimson-expressing interneuron firing frequency with 100% spiking probability, at $I=10\mathrm{mW}/{\mathrm{mm}}^2$, $G_{d1}=0.625{\mathrm{ms}}^{-1}$ and 0.5-ms pulse width, for optimal combinations of $C_m$ and $g_0$ as indicated.