Stochastic simulations reveal how clustering sodium ion channels in thin axons more than doubles the metabolic efficiency of action potentials
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1
Imperial College London, Department of Bioengineering, United Kingdom
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2
Imperial College London, Department of Life Sciences, United Kingdom
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3
Imperial College London, Department of Computing, United Kingdom
The action potential, the fundamental signal of the nervous system, is carried by two types of axons: myelinated and unmyelinated fibres. The former type of axon is generally known to allow faster, more reliable and, as we recently showed [1], considerably more energy efficient propagation of signals than unmyelinated axons. In contrast, only the latter can reach the physical limits to axon diameter at 0.1 µm, thus making the high connection densities of mammalian cortex possible [2].
Myelinated axons feature highly structured distributions of voltage-gated ion channels with characteristic clustering of Na channels at the Nodes of Ranvier, while unmyelinated axons are generally thought to have uniformly distributed ion channels. We recently discovered that in C-fibres, which are the 0.1 µm diameter unmyelinated axons of the peripheral nervous system, Nav1.8 channels [3] are clustered together on lipid rafts. This localised concentration of Na channels resembles ion channel organisation at the Nodes of Ranvier. This prompted us to investigate if this structural similarity translates into functional similarity, making thin unmyelinated axons with lipid raft clustering of ion channels more efficient in terms of velocity, reliability and metabolic cost of action potentials than unmyelinated axons without lipid rafts.
We simulated both uniformly distributed and clustered channels (0.2 µm diameter clusters of channels every 3 µm of axon) along the unmyelinated fibre (0.1 µm diameter), with an average channel density of 125 per µm^2 in both cases. Metabolic cost was defined by the amount of ATP molecules necessary to reverse the Na current by Na-K-ATPase [4].
Biophysically realistic stochastic simulations carried on the Modigliani stochastic simulation framework [5] show that clustering Na channels on lipid raft reduced metabolic cost by over 260% (2.86×10^-6 pmol ATP/mm vs. 1.03×10^-5 pmol ATP/mm), while affecting propagation velocity far less (Velocity reduced by 20% with clustered channels). Crucially, deterministic simulations did not show a significant difference between the two types of axons (Velocity unchanged, metabolic cost 2.29×10^-6 pmol ATP/mm with uniformly distributed NaV1.8 vs. 2.21×10^-6 pmol ATP/mm). This is because channel noise and the discrete nature of ion channel currents can not be accounted for using deterministic models when the number of interacting stochastic elements is small and their effects are non-linearly boosted. Our results show the crucial impact of ion channel stochasticity and clustering on thin axons, and suggest an evolutionary advantageous specialisation in the brain: clustering of Nav1.8 on lipid rafts even in absence of myelination enables thin unmyelinated axons, in analogy to myelinated axon, to support a form of micro-saltatory [5] action potential conduction that makes them more energy efficient than unmyelinated axons with homogeneous distributions of ion channels.
Acknowledgements
This work was supported by the EPSRC and the Wellcome Trust UK (083259/C/07/Z).
References
1. Neishabouri A, Faisal A. The metabolic efficiency of myelinated vs unmyelinated axons. BMC Neuroscience. 2011
2. Faisal A, White J, Laughlin S. Ion-Channel Noise Places Limits on the Miniaturization of the Brain’s Wiring. Current Biology. 2005
3. Baker MD. Protein kinase C mediates up‐regulation of tetrodotoxin‐resistant, persistent Na+ current in rat and mouse sensory neurones. The Journal of Physiology. 2005
4. Alle H, Roth A, Geiger J. Energy-Efficient Action Potentials in Hippocampal Mossy Fibers. Science. 2009
5. Faisal A, Laughlin S. Stochastic Simulations on the Reliability of Action Potential Propagation in Thin Axons. PLoS Comput Biol. 2007
Keywords:
Axon,
Cluster,
Hodgkin-Huxley,
ion channel,
lipid raft,
Nodes of Ranvier,
stochastic,
Unmyelinated
Conference:
Bernstein Conference 2012, Munich, Germany, 12 Sep - 14 Sep, 2012.
Presentation Type:
Poster
Topic:
Other
Citation:
Neishabouri
A,
Finn
A,
Pristera
A,
Okuse
K and
Faisal
AA
(2012). Stochastic simulations reveal how clustering sodium ion channels in thin axons more than doubles the metabolic efficiency of action potentials.
Front. Comput. Neurosci.
Conference Abstract:
Bernstein Conference 2012.
doi: 10.3389/conf.fncom.2012.55.00133
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Received:
11 May 2012;
Published Online:
12 Sep 2012.
*
Correspondence:
Mr. Ali Neishabouri, Imperial College London, Department of Bioengineering, London, SW72AZ, United Kingdom, m.neishabouri10@imperial.ac.uk