A Calcium-Dependent Anion Channel Framework for the Numerical Simulation of Action Potentials in Mimosa pudica

Electrical signaling in plants serves as a primary mechanism for systemic communication and rapid physiological adaptation to environmental stressors (Volkov & Brown, 2006). A quintessential example is the thigmonastic response of Mimosa pudica, where mechanical stimuli trigger action potentials (APs) that propagate along the petiole to induce rapid leaf closure (Hagihara & Toyota, 2020). While animal action potentials are driven by voltage-gated sodium \left(Na^+\right)influx, plant electrophysiology relies on an entirely distinct ionic cascade: an initial influx of calcium (Ca^{2+}) that subsequently activates a massive efflux of chloride ions (Cl^-) to drive depolarization, followed by a slow, rectifying potassium (K^+) efflux for repolarization (De Luccia & Friedman, 2011). Historically, computational models of plant APs have heavily borrowed from the classic Hodgkin-Huxley (HH) framework developed for animal axons. However, these models frequently introduce a fundamental biological inaccuracy: they treat the chloride gating kinetics as a purely voltage-dependent variable. In planta, patch-clamp and biochemical data reveal that the primary anion channels involved in AP propagation are explicitly calcium-activated anion channels (CaCCs), shifting open probabilities based on local ion availability (Jane Beilby & Al Khazaaly, 2016). Here, we present a modified HH-style framework that eliminates arbitrary voltage-gating for anions and establishes a direct, dynamic coupling between intracellular calcium concentration (\left[Ca^{2+}\right]_i) and chloride channel activation.