A simple Markov model of sodium channels with a dynamic threshold

Abstract

Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.

Differences in the Electrophysiological Properties of Mouse Somatosensory Layer 2/3 NeuronsIn Vivoand Slice Stem from Intrinsic Sources Rather than a Network-Generated High Conductance State

“…Increasing membrane conductance reduces the depolarization associated with activation of a set amount of Na + conductance; it takes greater depolarization and Na + current to achieve the sustained positive-feedback for spike initiation. As a result of the depolarizing shift in threshold, other voltage-gated factors, such as Na + current inactivation ( Fernandez and White, 2010 ; Chizhov et al, 2014 ) and K + current activation ( Prescott et al, 2006 ), can be recruited that alter overall spike output. Regardless of whether this increase results from ongoing background synaptic activity or neuromodulators, it suggests that neurons can fundamentally change their spike integration properties through any processes that increase membrane conductance at the cell body.…”

A single Markov-type kinetic model accounting for the macroscopic currents of all human voltage-gated sodium channel isoforms

“…The aim to develop the computationally lightest model allows us to make one transition practically irreversible (from O1 to I1), and releases the phenomenological model from the principle of microscopic reversibility, like other kinetic schemes based on macroscopic currents (see [ 54 ], for a recent example). Microscopic reversibility, indeed, only holds when the states are elementary processes (collisions, molecules, elementary reactions, etc).…”

The domain of neuronal firing on a plane of input current and conductance

“…The increase of threshold voltage directly affects the threshold s-u boundary slope. The other aspects of the threshold variability on I/O function were discussed in Brette 2010, 2011;Fontaine et al 2014;Chizhov et al 2014). Second, the extra conductance s decreases the interspike repolarization, which in turn weakens the de-inactivation of sodium channels between spikes (Storm et al 2009).…”

“…Regarding the change in the gain of the rate-current function with the shunting conductance, this less pronounced effect has not been studied here. Readers are referred to the works of Fernandez and White (2010), Fernandez et al (2011), Graham andSchramm (2009) andChizhov et al (2014).…”