Generalised Hodgkin-Huxley model captures human P2X and AMPA receptor currents

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 (m₁, m₂) and two inactivation gates (h₁, h₂) 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 hP2X₃ 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.