Year: 2026
Type: preprint
Abstract: A novel mathematical framework to define the threshold of action potentials in excitable cells is presented. Unlike previously applied methods that rely on approximations or bifurcations, the approach focuses on the geometry action potentials. First the changes in concavity directly obtained from a time series of voltages are used to identify action potentials thresholds. This concavity-based framework is subsequently extended to autonomous dynamical systems, enabling the analytical determination of curvature transitions directly from the manifold of inflection points in phase space. The inflection point manifold delineates the boundary of the excitability region, establishing a necessary and sufficient geometric condition where a phase-space trajectory contains an action potential if and only if it intersects this manifold. This geometric framework not only formalises cellular excitability within a single dynamical system but also introduces a measure to compare different electrophysiological phenotypes and stimulus conditions. The measure provides a way to compare the excitabilities of systems that model neurons with different electrophysiological phenotypes and consider different stimulus conditions. The traditionally vague physiological concept of electrical excitability is transformed into a rigorous analytical description by considering the time-dependent curvature of the membrane potential. The criterion is robust across smooth, single compartment models of electrical excitability and can be can be extended to single compartment models in higher dimensions, and multicompartment models as well.
Author: Marco Arieli Herrera-Valdez
Institution: Universidad Nacional Autónoma de México
Language: English
Subfield: Cognitive Neuroscience
Field: Neuroscience
Domain: Life Sciences
Open Access status: green
Awards: G339156159, G8880213284
OpenAlex ID: W7204223953