Extending a Hodgkin-Huxley Model for Larval Drosophila Muscle Excitability via Particle Swarm Fitting

Abstract

We present a model of excitability in larval Drosophila muscles. Our model was initially based on modified Hodgkin-Huxley equations, adapted to represent variable, regenerative depolarisations (action potentials) we have occasionally observed in intracellular recordings and that can be triggered by excitatory junction potentials at neuromuscular synapses. We modified several kinetic equations describing voltage sensitive Ca2 + and K+ ionic currents, previously used to predict excitability in muscle cells of the mammalian cardiac atrioventricular node. The resulting nonlinear differential equations had multiple unknown parameters. Thus, to fit the model to experimental observations of variable excitability, we developed a new implementation of particle swarm optimisation. This GPU-based implementation allows us to adopt an ensemble model approach in which each experimental observation is used to find a plausible parameterisation, resulting in a set of models accounting for cell-to-cell variability of muscle excitability in Drosophila larvae, and with potential applications to population-based modeling of other excitable cell types.