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