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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: lbkier@vcu.edu)
b
) Life Sciences, Department of Biology, Virginia Commonwealth University, Richmond, VA, USA
(e-mail: rtombes@vcu.edu)
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.
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Received December 11, 2012