A computationally efficient algorithm for fitting ion channel parameters

Zachary R Teed,Jonathan R Silva

doi:10.1016/j.mex.2016.11.001

Abstract

Continuous time Markov models have been widely used to describe ion channel kinetics, providing explicit representation of channel states and transitions. Fitting models to experimental data remains a computationally demanding task largely due to the high cost of model evaluation. Here, we propose a method to efficiently optimize model parameters and structure. Voltage clamp channel protocols can be decomposed into a series of fixed steps of constant voltage resulting in a set of linear systems of differential equations. Given the linear systems, ODE integration can be swapped for the faster matrix exponential routine. With our parallelized implementation, optimized models are able to reproduce a wide range of experimentally collected data within one minute, a 50 times speedup over ODE integration.•The cost of the objective function is reduced by employing the matrix exponential•The likelihood of convergence is improved by applying synchronous start simulated annealing•The approach was tested by optimizing parameters for a model of the cardiac voltage-gated Na+ channel, NaV1.5, and the KCNQ1 K+ channel.

Highlights

Continuous time Markov models have been widely used to describe ion channel kinetics, providing explicit representation of channel states and transitions
We propose to overcome the ordinary differential equation (ODE) barrier by solving these differential equations with the matrix exponential, an approach that has been used to analyze channel kinetics and improve the efficiency of action potential simulations [8,9]
We look at two different ways to simulate the model: traditional ODE solvers and the matrix exponential

Summary

Method

Following the seminal work of Hodgkin and Huxley in 1952 [1], mechanistic ordinary differential equation (ODE) models have been used to simulate dynamics of excitable systems including neurons, myocytes and pancreatic beta cells [2,3]. A simple solution would be to bound rðvÞ; in models where the rates are not linearly independent microscopic reversibility could be violated Another proposed voltage function extends the linear model by adding higher order polynomial terms [17], with f iðvÞ 1⁄4 viÀ1 and rðvÞ 1⁄4 eu1þu2vþ...þunvnÀ1. We attempted a third voltage dependence function in attempt to circumvent some of the limitations of the linear model by bounding transitions rates while not violating microscopic reversibility. Membrane voltage is no longer a series of discrete steps, but rather a continuous variable requiring ODE integration This penalty ensures that fitted models can be efficiently used in larger scale simulations, while constraining transition rates to physically plausible values. If removal results in a disconnected graph, the graph is reconnected by forming a random minimum spanning tree over the disconnected components

Edge Addition

Rate Perturbation

Findings

Conclusions