Proton Hopping - Wiley Online Library

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b) Life Sciences, Department of Biology, Virginia Commonwealth University, Richmond, VA, USA. (e-mail: [email protected]vcu.edu). Myelinated axon nerve impulses ...

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Proton Hopping: A Proposed Mechanism for Myelinated Axon Nerve Impulses by Lemont B. Kier* a ) and Robert M. Tombes b ) a

) Life Sciences, Center for the Study of Biological Complexity, Virginia Commonwealth University, Richmond, VA, USA (e-mail: [email protected]) b ) Life Sciences, Department of Biology, Virginia Commonwealth University, Richmond, VA, USA (e-mail: [email protected])

Myelinated axon nerve impulses travel 100 times more rapidly than impulses in non-myelinated axons. Increased speed is currently believed to be due to hopping or saltatory propagation along the axon, but the mechanism by which impulses flow has never been adequately explained. We have used modeling approaches to simulate a role for proton hopping in the space between the plasma membrane and myelin sheath as the mechanism of nerve action-potential flow.

Introduction. – Myelination of axons occurs primarily in the nervous system of vertebrates and is associated with an increase in the speed of nerve impulses (action potentials) by ca. 100-fold compared to unmyelinated axons. Myelin is a protrusive, insulating membrane sheath derived from surrounding cells that wrap around the axon. Demyelinating diseases are endemic in the human population and, therefore, understanding the mechanism by which myelination accelerates action potentials is important to human conditions. Myelinated axons are accompanied by stereotypically sized and spaced unmyelinated regions known as nodes of Ranvier. These nodes are enriched by voltage-gated ion channels necessary for action-potential generation and propagation, but they are missing from the myelinated, insulated internodal spaces [1]. It has been proposed that the action potential developed in these nodes passes along the axon by a jump, hop, or saltatory movement between nodes, but the mechanism of this flow has never been adequately explained. Myelin is a protein-lipid membrane that surrounds the axon between each node of Ranvier [2] [3]. The spaces between the laminar layers of myelin, and the myelin and axon, called the periaxonal space, is filled with water [2]. Action potentials travel at speeds up to 150 m/s in myelinated axons and are more rapid in axons of increased diameter. Action potentials travel at 0.5 to 10 m/s along unmyelinated axons. Passive diffusion of water (0.0001 m/s) is too slow to explain this flow. Proton hopping is a proposed mechanism by which action potentials could flow. Proton hopping was first described by Grotthuss in the early 19th century and refers to a virtual exchange of the proton (H þ ) through bulk water [4]. The H þ does not move or diffuse, but the hydronium ion (H3O þ ) state shuttles along the path in bulk water [5 – 7]. This has also been referred to as a water wire. Proton hopping can be initiated by ionic imbalance and is random unless the spatial characteristic of bulk water is limited.  2013 Verlag Helvetica Chimica Acta AG, Zrich

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In a recent study, we have modeled an impulse down a membrane channel where focus was on the mechanism [8]. That model explored the proton-hopping mechanism as a simulation of the process. In this study, we use cellular automata to model proton hopping along such a water wire in the space between the plasma membrane and the myelination sheath. This periaxonal space provides a water channel through which proton hopping can be spatially restricted. This water wire is initiated by an action potential at the post-synaptic terminus of the axon, resulting in impulse propagation along a series of nodes and internode axons. Modeling of Proton Hopping. – In our cellular automata model of proton hopping through membrane protein channels [8], we have obtained some results that apply to our proposal here about the axon action potential. That study employed cellular automata models of proton hopping, yielding results consistent with experimental observations. The process we modeled occurs within a cluster of bulk H2O molecules which is an evanescent structure providing a neighborhood where a protonated H2O molecule may pass a proton to a neighbor H2O molecule. The modeled system was enclosed in a grid 100-cells-long with stationary boundaries at all sides. The width of the grid was varied depending on the particular study conducted. The rules are probabilities. The movement rule, Pm , of a H2O molecule is 1.0. At predetermined iterations, a proton-laden H2O cell, H3O þ, labeled G, is released from the top row of the grid into the column of water. The relationship of H3O þ, G, to itself is PB(GG) ¼ 1.0, J(GG) ¼ 0. The effect of this rule is to prohibit any encounter of two protonated cells. The relationship of a H3O þ , G, with a H2O molecule, W, is determined by the rules PB(WG) and J(WG). The rule for each H2O molecule carrying out its movements, in turn, is invoked. When each cell in the grid has exercised its response to its associated probability rules, then an iteration has been completed. This is a unit of time in the model. The effect of G on an encountered W neighbor is to exchange identities, thus: G þ W ! GW ! WG ! W þ G The G cell moves continuously, thus an encounter with a W cell will produce an immediate exchange of identities. The new G cell may encounter another W cell, and the process repeats. If the newly formed G cell has no neighbors, it moves in its turn and continues this movement, until it encounters a H2O molecule, W. Then, the transfer process resumes. Model Results. – The width of the channel was observed to have a modest influence on the rate of hopping movement down the channel. The rate of movement of the hopping front down the channel was slightly faster when the channel width was increased up to ca. 16-cells-wide. Channels wider than that had about the same movement of the front down the channel. This pattern corresponds to reported experimental observations [9] [10]. A significant observation was made when the locations of the encounters of the G cells with the bottom of the grid. Depending on the width of the grid, the locations of the encounters with the grid bottom was uniformly distributed over the entire width. Thus, if an encounter of G with a small, designated

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section of the bottom of the grid was considered to be of importance in producing a physical event, a wider grid width would produce fewer G encounters with that designated section (see the Table). This places a premium on the grid width to determine the effective concentration of G encounters over a period of time.

Figure. The model of the column with proton hopping under way. The left figure is the top segment of the channel, and the right figure is the bottom segment. The green cells are the H3O þ molecules, while the blue cells are H2O molecules. Table. Concentration of Protons Encountering the End of the Channel at the First Four Cells out from a Wall. This is based on 100 protons entering the system. Channel cell width

Number of protons

8 16 30 50

50 28 14 8

Discussion. – On the basis of earlier modeling results and this study, we propose that axon action potentials arise from proton hopping through the periaxonal space separating the axon surface from the myelin sheath. This extracellular gap contains H2O in a narrow space that is ideal for rapid passage of proton-hopping information between nodes of Ranvier. The Table shows the progressively fewer average number of encounters possible at a designated space at the end of a modeled axon internode section when the sheath of myelin is further out from the axon surface. We can extrapolate this reduction to a state created when there is no myelin sheath. In that situation, the action potential would have very modest encounter information near the axon. This is the nature of the comparisons between a myelin and a non-myelinated

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neurons. It is also a situation, when a myelin sheath is disturbed as in the case of several diseases. REFERENCES [1] M. N. Rasband, Encyclopedia of Life Sciences, 2001, 1. [2] C. Laule, I. M. Vavasour, S. H. Kolind, D. K. B. Li, T. L. Traboulsee, G. R. W. Moore, A. L. MacKay, Neurotherapeutics 2007, 4, 460. [3] K. M. Van De Graff,  Human Anatomy, 6th edn., Raven Press, New York, 2002. [4] C. T. D. Grotthuss, Ann. Chim. 1806, 58, 54. [5] N. Agmon, J. Phys. Chem. A 2005, 109, 13. [6] A. A. Kornyshev, A. M. Kuznetsov, E. Spohr, J. Ulstrup, J. Phys. Chem. B 2003, 107, 3351. [7] E. Gileadi, E. Kirowa-Eisner, Electrochim. Acta 2006, 51, 6003. [8] L. B. Kier, R. Tombes, L. H. Hall, C.-K. Cheng, Chem. Biodiversity 2013, 10, 338. [9] L. R. Forest, A. Kukol, I. T. Arkin, D. P. Tieleman, M. S. P. Sansom, Biophys. J. 2000, 78, 55. [10] M. L. Breweer, U. W. Schmitt, G. A. Voth, Biophys. J. 2001, 80, 1691. Received December 11, 2012

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