Phenomenological models of NaV1.5. A side by side, procedural, hands-on comparison between Hodgkin-Huxley and kinetic formalisms

Abstract

Computational models of ion channels represent the building blocks of conductance-based, biologically inspired models of neurons and neural networks. Ion channels are still widely modelled by means of the formalism developed by the seminal work of Hodgkin and Huxley (HH), although the electrophysiological features of the channels are currently known to be better fitted by means of kinetic Markov-type models. The present study is aimed at showing why simplified Markov-type kinetic models are more suitable for ion channels modelling as compared to HH ones, and how a manual optimization process can be rationally carried out for both. Previously published experimental data of an illustrative ion channel (NaV1.5) are exploited to develop a step by step optimization of the two models in close comparison. A conflicting practical limitation is recognized for the HH model, which only supplies one parameter to model two distinct electrophysiological behaviours. In addition, a step by step procedure is provided to correctly optimize the kinetic Markov-type model. Simplified Markov-type kinetic models are currently the best option to closely approximate the known complexity of the macroscopic currents of ion channels. Their optimization can be achieved through a rationally guided procedure, and allows to obtain models with a computational burden that is comparable with HH models one.

Modelling the spatial and temporal constrains of the GABAergic influence on neuronal excitability

“…Because it was not possible to generate a reasonable sharp AP onset with a standard Hodgkin-Huxley (HH) model and since we are particularly interested in the AP threshold properties, we heuristically developed a modified Markov model, massively simplified from published Markov models [82,83] to simulate the AP with a considerably precision. For this modified Markov model we consider only 3 different states for the Na+ channels [84]: …”

Macroscopic currents of ionic channels using Mass Action Law: A mathematical model

“…The total number of channels in the cell membrane is constant 2. The ion channels have three closed states one open and one inactive, the passage between these states AS a Markov´s-type (Andreozzi, Carannante, D'Addio, Cesarelli, & Balbi, 2019)chemical reaction (reaction 1). 3.…”

Ion Channel Modeling beyond State of the Art: A Comparison with a System Theory-Based Model of the Shaker-Related Voltage-Gated Potassium Channel Kv1.1

“…Mathematical models of individual ion channels form the building blocks of electrophysiological in silico approaches, allowing the investigation of biophysical mechanisms and the bioelectric activity of excitable and non-excitable cells [ 1 , 2 ]. A variety of whole-cell models of different levels of complexity and abstraction have been introduced for the simulation of ion current kinetics and action potential alterations in neural and cardiac cells, facilitating the prediction of disease processes and the development of therapeutic interventions, which have become an integral part in neuroscience and cardiac electrophysiology [ 1 , 3 , 4 , 5 , 6 , 7 ]. Furthermore, single-channel models predicting emergent ion channel drug effects on both cellular and tissue levels are increasingly under consideration in pharmacological research, in conjunction with experimental investigations, opening up an innovative and efficient way of early preclinical drug screenings [ 4 ].…”

“…The mathematical modeling of channel kinetics is commonly based on either a Hodgkin–Huxley (HH) or a hidden Markov model (HMM) description [ 1 , 8 , 9 , 10 , 11 ]. The HH model offers a basic paradigm in which the channel can be either open or closed depending on a set of gates, controlled by a number of gating particles, representing the activation, deactivation, and inactivation characteristics of the ion channel type.…”

“…The kinetic behavior of each gating particle between a permissive and non-permissive state is described as a first-order process, independent of all states of the other gates, and, thus, does not consider the possible dependences between the activation and inactivation of the channel [ 9 , 10 , 12 ]. However, although these models lack the underlying electrophysiological processes of channel gating, HH models closely reproduce the macroscopic currents with a small number of variables and a low computational burden and are, hence, still widely used in computational electrophysiology [ 1 , 11 ].…”