Theoretical principles underlying optical stimulation of myelinated axons expressing channelrhodopsin-2

doi:10.1016/j.neuroscience.2013.06.031

Neuroscience

Volume 248, 17 September 2013, Pages 541-551

https://doi.org/10.1016/j.neuroscience.2013.06.031 Get rights and content

Highlights

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Light-axon model for peripheral optogenetic neural stimulation.
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Reproduced the small-to-large diameter axon recruitment order seen experimentally.
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Hypothesize that the internodal spacing relationship plays an important role in recruitment.

Abstract

Numerous clinical conditions can be treated by neuromodulation of the peripheral nervous system (PNS). Typical electrical PNS therapies activate large diameter axons at lower electrical stimulus thresholds than small diameter axons. However, recent animal experiments with peripheral optogenetic neural stimulation (PONS) of myelinated axons expressing channelrhodopsin-2 (ChR2) have shown that this technique activates small diameter axons at lower irradiances than large diameter axons. We hypothesized that the small-to-large diameter recruitment order primarily arises from the internodal spacing relationship of myelinated axons. Small diameter axons have shorter distances between their nodes of Ranvier, which increases the number of nodes of Ranvier directly illuminated relative to larger diameter axons. We constructed “light-axon” PONS models that included multi-compartment, double cable, myelinated axon models embedded with ChR2 membrane dynamics, coupled with a model of blue light dynamics in the tissue medium from a range of different light sources. The light-axon models enabled direct calculation of threshold irradiance for different diameter axons. Our simulations demonstrate that illumination of multiple nodal sections reduces the threshold irradiance and enhances the small-to-large diameter recruitment order. In addition to addressing biophysical questions, our light-axon model system could also be useful in guiding the engineering design of optical stimulation technology that could maximize the efficiency and selectivity of PONS.

Introduction

Optogenetic neural stimulation is a powerful technique for providing insight into the function of the nervous system (Deisseroth, 2011). Recently, the optogenetic toolbox has been applied in the peripheral nervous system (Llewellyn et al., 2010, Sharp and Fromherz, 2011). Peripheral optogenetic neural stimulation (PONS) of the motor system preferentially activates small diameter axons which are typically connected to fatigue-resistant motor units (Llewellyn et al., 2010). In contrast, traditional electrical stimulation strategies preferentially activate large diameter axons that typically innervate fatigue-prone motor units (Singh et al., 2000). The biophysical basis for the large-to-small diameter recruitment order of myelinated axons via electrical stimulation is primarily due to the internodal spacing relationship (Nilsson and Berthold, 1988). When an extracellular electrical stimulus is applied to the axon, the larger internodal spacing of larger diameter axons generates a larger second difference of the extracellular voltage distribution at nodes of Ranvier (McNeal, 1976). This results in a larger transmembrane driving force in larger diameter axons for a given level of current injection from the stimulating electrode (Rattay, 1989).

The biophysical mechanism(s) of the small-to-large diameter recruitment order for optogenetic stimulation of motor axons are less clear. The goal of this study was to generate computational models of PONS to characterize the basic features of action potential initiation in myelinated axons expressing channelrhodopsin-2 (ChR2). We hypothesized that the small-to-large diameter recruitment order in PONS also primarily arises from the internodal spacing relationship, but for the opposite reason as in electrical stimulation. Specifically, when a light stimulus is applied to the axon, the smaller internodal spacing of smaller diameter axons increases the probability of illuminating higher numbers of nodes of Ranvier. We explored this hypothesis with a computational model, which followed the general optogenetic stimulation modeling methodology of Foutz et al. (2012). We then compared optical and electrical stimulation of a range of different diameter myelinated axons to identify basic principles that dictate action potential initiation. Finally, we directly compared our simulation predictions to the experimental work of Llewellyn et al. (2010) which first characterized the small-to-large diameter recruitment order of PONS.

Section snippets

Experimental procedures

Our PONS model system was created in NEURON (v 7.1) using Python (2.7.1) (Hines et al., 2009).

Results

A light-axon model system was used to evaluate irradiance thresholds for action potential generation in myelinated axons of varying diameters. We created several stimulation representations including: 16 LED cuff, 4 LED ring, singular LED, singular fiber optic, and a point source cathodic electrode. We then compared our model predictions to experimental measurements of muscle recruitment during optical stimulation with 0.5-ms pulses applied to the Thy1-ChR2 transgenic mouse sciatic nerve with a

Discussion

The goal of this study was to develop a model system to characterize optogenetic stimulation of the peripheral nervous system. We investigated the hypothesis that the internodal spacing relationship plays an important role in the small-to-large diameter recruitment order of PONS. We found that detailed light-axon models were able to simulate the diameter-dependence of optical stimulation (Fig. 4, Fig. 5, Fig. 6) and were capable of reproducing many features of the available experimental data (

Conflict of Interest

The authors declare no competing financial interests related to this work.

Acknowledgements

This project was supported by the National Institutes of Health R01 NS047388. The authors would like to thank Dominique Durand for insight into the underlying theory of the diameter dependence of axonal activation.

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This result opens a new avenue of investigation into the biophysical properties of neurons being electrically excitable in functional neural circuits when inducing light sensitive channels. It is possible that cell bodies or even axons with different diameters may have varying thresholds of being activated when channel rhodopsins are activated due to varied input resistance of the cells., Also a larger surface area of the cell membrane which may provide for a higher density of channel rhodopsin proteins (Arlow et al., 2013). Fictive locomotion patterns measured in isolated larval Drosophila CNS, with genetically encoded Ca2+ indicators, demonstrated left-right asymmetry across segments (Pulver et al., 2015).
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The same physiological recruitment of ChR2 expressing motor units and prevention of muscle fatigue was also verified in our recent study [3••], discussed below. Theoretical modelling of the orderly recruitment of motor units in peripheral optogenetic neural stimulation (PONS) suggests that the reduced internodal distance in small diameter myelinated motor axons is an essential parameter underlying this phenomenon [27]. In addition to the major advantage of physiological, graded recruitment of motor units, optical stimulation also has the significant advantage that it only induces activity in neurons that express the light-responsive opsin.
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As such, the theoretical efficiency, or otherwise optimality, of a particular optogenetic stimulation modality must be evaluated per cell type and over a wide range of stimulation protocols. Recent progress has been made to develop in silico tools for such analysis of optical stimulation in the contexts of neuroscience (31–35) and cardiac research (13,16,19,36). In this report, using computational modeling and analysis, we focus on comparing and contrasting optogenetic and electrical stimulation of excitable cells to address the following subjects.
Optogenetics provides an alternative to electrical stimulation to manipulate membrane voltage, and trigger or modify action potentials (APs) in excitable cells. We compare biophysically and energetically the cellular responses to direct electrical current injection versus optical stimulation mediated by genetically expressed light-sensitive ion channels, e.g., Channelrhodopsin-2 (ChR2). Using a computational model of ChR2(H134R mutant), we show that both stimulation modalities produce similar-in-morphology APs in human cardiomyocytes, and that electrical and optical excitability vary with cell type in a similar fashion. However, whereas the strength-duration curves for electrical excitation in ventricular and atrial cardiomyocytes closely follow the theoretical exponential relationship for an equivalent RC circuit, the respective optical strength-duration curves significantly deviate, exhibiting higher nonlinearity. We trace the origin of this deviation to the waveform of the excitatory current—a nonrectangular self-terminating inward current produced in optical stimulation due to ChR2 kinetics and voltage-dependent rectification. Using a unifying charge measure to compare energy needed for electrical and optical stimulation, we reveal that direct electrical current injection (rectangular pulse) is more efficient at short pulses, whereas voltage-mediated negative feedback leads to self-termination of ChR2 current and renders optical stimulation more efficient for long low-intensity pulses. This applies to cardiomyocytes but not to neuronal cells (with much shorter APs). Furthermore, we demonstrate the cell-specific use of ChR2 current as a unique modulator of intrinsic activity, allowing for optical control of AP duration in atrial and, to a lesser degree, in ventricular myocytes. For self-oscillatory cells, such as Purkinje, constant light at extremely low irradiance can be used for fine control of oscillatory frequency, whereas constant electrical stimulation is not feasible due to electrochemical limitations. Our analysis offers insights for designing future new energy-efficient stimulation strategies in heart or brain.
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Moreover, the combination of genes that express ChR-2 with genes that express the light-generating protein luciferase revealed that it is possible to activate neurons by exogenous application of the luciferase substrate, leading to cell luminescence and light-driven autoactivation in vitro.59 Finally, computational modeling evidence has illustrated that optogenetic activation of axons follows a physiologic, small- to large-diameter axon recruitment order,60 which could prove invaluable for restoring motor function following SCI. Applications of optogenetic technology for restoring function after SCI are already under way in small animal models.
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View full text

Theoretical principles underlying optical stimulation of myelinated axons expressing channelrhodopsin-2

Highlights

Abstract

Introduction

Section snippets

Experimental procedures

Results

Discussion

Conflict of Interest

Acknowledgements

Biophys J

FEBS Lett

An optical neural interface: in vivo control of rodent motor cortex with integrated fiberoptic and optogenetic technology

J Neural Eng

Optogenetics

Nat Meth

Theoretical principles underlying optical stimulation of a channelrhodopsin-2 positive pyramidal neuron

J Neurophysiol

Optical deconstruction of parkinsonian neural circuitry

Science

Modeling study of the light stimulation of a neuron cell with channelrhodopsin-2 mutants

IEEE Trans Biomed Eng

Neuron and python

Front Neuroinform

Ein beitrag zur optik der farbanstriche

Z Tech Physik

Orderly recruitment of motor units under optical control in vivo

Nat Med