Approximate matrix exponential: a fast and accurate solver for Markov kinetic models of ion channels.
- 1Independent Researcher, Nashua, NH, United States.
Abstract
A new method is presented for simulating Markov kinetic models of ion channels, which are biologically realistic but difficult to simulate. Computing the analytic solution is prohibitively expensive, necessitating the use of numerical methods. The new method creates a piecewise polynomial approximation of the propagator matrix, which is the analytic solution operator. The new method is an order of magnitude faster and more accurate than previous numerical methods, but it is limited to models with one or two input variables and its time complexity scales quadratically with the number of model states. The accompanying program, ame, applies the new method to the NEURON simulator. For comparison, the analytic solution was also added to NEURON. The new method achieves real-time performance on a state-of-the-art GPU for tens to hundreds of thousands of model instances. This method will allow large-scale neuronal simulations to use more detailed models of ion channels.
Related
- Explicit Exponential Sum Estimates and Approximate Functional Equations for the Zeta Function
- Fine asymptotics for approximate simulation of symmetric channels
- Approximate Matrix Multiplication through Joint Leverage Score Sampling
- A novel class of high-order uniformly accurate exponential integrators with local linear extension for the charged-particle dynamics under strong magnetic field
- Weak and Sharp Stretched-Exponential Flocking in the Kinetic Cucker-Smale Model with Noncompactly Supported Initial Data
BibTeX
@article{mcdougall2026approximate,
title = {{Approximate matrix exponential: a fast and accurate solver for Markov kinetic models of ion channels.}},
author = {David Alton McDougall},
journal = {Frontiers in computational neuroscience},
year = {2026},
month = oct,
doi = {10.3389/fncom.2026.1901593},
url = {https://europepmc.org/article/MED/42903225},
note = {CC BY},
}
RIS
TY - JOUR
TI - Approximate matrix exponential: a fast and accurate solver for Markov kinetic models of ion channels.
AU - David Alton McDougall
PY - 2026
DA - 2026/10/06
JO - Frontiers in computational neuroscience
DO - 10.3389/fncom.2026.1901593
UR - https://europepmc.org/article/MED/42903225
AB - A new method is presented for simulating Markov kinetic models of ion channels, which are biologically realistic but difficult to simulate. Computing the analytic solution is prohibitively expensive, necessitating the use of numerical methods. The new method creates a piecewise polynomial approximation of the propagator matrix, which is the analytic solution operator. The new method is an order of magnitude faster and more accurate than previous numerical methods, but it is limited to models with one or two input variables and its time complexity scales quadratically with the number of model states. The accompanying program, ame, applies the new method to the NEURON simulator. For comparison, the analytic solution was also added to NEURON. The new method achieves real-time performance on a state-of-the-art GPU for tens to hundreds of thousands of model instances. This method will allow large-scale neuronal simulations to use more detailed models of ion channels.
SN - 1662-5188
ER -