[Paper Review] Pressure wave model for action potential propagation in excitable cells

M. Rvachev|arXiv (Cornell University)|Jan 24, 2003

Neuroscience and Neural Engineering14 references3 citations

TL;DR

The paper proposes a pressure wave model in which action potential propagation is driven by mechanoactivation of voltage-gated ion channels via traveling pressure pulses in the axoplasm, rather than by ionic currents as in the local circuit theory. It explains conduction velocity scaling with axon diameter, temperature dependence, and AP duration changes, with predictions matching experimental data for myelinated axons and requiring higher axial resistance for unmyelinated ones.

ABSTRACT

Speed of propagation of small-amplitude pressure waves through the cytoplasmic interior of myelinated and unmyelinated axons of different diameters is theoretically estimated and is found to generally agree with the action potential (AP) conduction velocities. This remarkable coincidence allows to surmise a model in which AP spread along axon is propelled not by straggling ionic currents as in the widely accepted local circuit theory, but by mechanoactivation of the membrane ion channels by a traveling pressure pulse. Hydraulic pulses propagating in the viscous axoplasm are calculated to decay over ~1 mm distances, and it is further hypothesized that it is the role of influxing during the AP calcium ions to activate membrane skeletal protein network attached to the membrane cytoplasmic side for a brief radial contraction amplifying the pressure pulse and preventing its decay. The model correctly predicts that the AP conduction velocity should vary as the one-half power of axon diameter for large unmyelinated axons, and as the first power of the diameter for myelinated axons, provided that specific mechanical properties of axons are independent from diameter; that myelinization increases the conduction velocity; that the conduction velocity increases with the temperature. Unlike the local circuit theory, the model is able to qualitatively explain observed increase in the AP duration in axons of smaller diameters. Predictions of absolute AP conduction velocities are limited by the knowledge of relevant to propagation of pressure waves mechanical properties of axons, still, the velocities are predicted well for myelinated axons, while an agreement for unmyelinated axons requires 3 orders of magnitude higher resistance of...

Motivation & Objective

• To explain the mechanism underlying action potential conduction velocity in axons, particularly its dependence on axon diameter and myelination.
• To challenge the conventional local circuit theory by proposing a mechanical alternative involving pressure waves in the axoplasm.
• To account for the observed increase in action potential duration in smaller-diameter axons, which the local circuit theory struggles to explain.
• To investigate whether hydraulic pressure pulses in the viscous axoplasm can propagate with velocities matching known action potential conduction speeds.
• To explore the role of calcium influx and cytoskeletal contraction in amplifying and sustaining pressure pulses to prevent decay.

Proposed method

• Theoretical estimation of pressure wave speed in the cytoplasm of unmyelinated and myelinated axons of varying diameters using hydrodynamic principles.
• Modeling of hydraulic pulse decay in viscous axoplasm, predicting decay over approximately 1 mm distances.
• Incorporation of calcium-induced radial contraction of the membrane-associated cytoskeletal network to amplify and sustain pressure pulses.
• Use of mechanical properties of axons (e.g., viscosity, elasticity) to predict conduction velocity scaling with diameter.
• Derivation of conduction velocity dependence on axon diameter: ∝ √diameter for unmyelinated axons and ∝ diameter for myelinated axons.
• Comparison of model predictions with experimental conduction velocities, assessing agreement under varying assumptions about mechanical properties.

Experimental results

Research questions

• RQ1 Can pressure wave propagation in the axoplasm explain the observed conduction velocities of action potentials in axons of different diameters?
• RQ2 How does myelination affect pressure wave propagation and conduction velocity according to the mechanical model?
• RQ3 What role do calcium influx and cytoskeletal contraction play in preventing decay of pressure pulses in the axoplasm?
• RQ4 Why does action potential duration increase in smaller-diameter axons, and can this be explained by the pressure wave model?
• RQ5 To what extent do the predicted conduction velocities match experimental data, and what mechanical assumptions are required for agreement?

Key findings

• The theoretical speed of small-amplitude pressure waves in axoplasm closely matches experimentally measured action potential conduction velocities.
• The model predicts that conduction velocity scales with the square root of axon diameter for large unmyelinated axons, consistent with experimental observations.
• For myelinated axons, the model predicts a linear dependence of conduction velocity on diameter, matching empirical data when mechanical properties are diameter-independent.
• The model qualitatively explains the increase in action potential duration in smaller-diameter axons, a feature not well accounted for by the local circuit theory.
• Conduction velocity increases with temperature in the model, consistent with experimental findings.
• Agreement with experimental conduction velocities for myelinated axons is good, but for unmyelinated axons, the model requires an axial resistance 1000 times higher than typical values to achieve quantitative agreement.