Abstract
Ionotropic receptors are transmembrane ion channels that play central roles in regulating synaptic transmission in the nervous system and cellular activity underlying immune responses. However, a unified mathematical model capturing their dynamics remains elusive. In this paper a generalised Hodgkin-Huxley (gHH) model is introduced, which seamlessly represents different activation, inactivation and recovery dynamics of the entire human P2X receptor family and the human AMPA-type glutamate receptor. The model incorporates two activation gates (m(1), m(2)) and two inactivation gates (h(1), h(2)) to connect electrophysiological recordings to the underlying kinetics of ligand-gated receptor currents beyond voltage-gated channels. We propose five distinct forms of whole-cell currents to describe the gating kinetics of ion channels. The model takes receptor-specific cooperativity, binding kinetics and desensitisation pathways into account. Validation using a wide range of datasets demonstrates the model's robustness in quantitatively predicting receptor responses. It is shown that the framework exhibits multi-scale temporal dynamics by which rapid activation and prolonged recovery are seamlessly captured, ranging from milliseconds and seconds to minutes. Notably, the model replicates the prolonged ATP-dependent recovery time of hP2X(3) receptor over several minutes and the millisecond recovery time of hGluA1 receptor reported experimentally. This work provides a single mathematical structure by parametrising the kinetics of all major human ionotropic receptors, thereby providing a universal, biophysically interpretable and predictive framework with applications in neuroscience, drug discovery and neurophysiological modelling. It also represents a closer step towards a unified theory of electrophysiological modelling for understanding ion channel function in health and disease. KEY POINTS: The Hodgkin-Huxley model was generalised to ligand-gated receptors beyond voltage-gated dynamics. The framework offers a unified, biophysically interpretable mathematical structure to capture the gating properties of human ionotropic receptors (validated against experimental data from hP2X(1-7) and hGluA1 receptors). The model provides quantitative insights into how P2XRs and AMPA receptors control ion channel function. The proposed tool establishes an in-silico modelling infrastructure with applications in synaptic physiology, neuroinflammation and drug discovery.