Biophysical Modeling of Enzyme-Kinetic Calcium-Dependent Stochastic Synaptic Plasticity: Integrating STDP, Metabolic Constraints, Bayesian Inference, Sensitivity Analysis, and Validation with Allen Institute Data

This paper introduces a novel framework for modeling enzyme-kinetic calcium-dependent stochastic synaptic plasticity in neural networks, grounded in biophysical principles. We extend the Hodgkin-Huxley model to incorporate intracellular calcium dynamics linked to NMDA receptor activation, driving synaptic weight changes through a stochastic plasticity rule based on competitive enzyme kinetics between CaMKII and calcineurin, enhanced by trace-based spike-timing-dependent plasticity (STDP) as a modulator of calcium influx. The framework integrates nonlinear dynamics, stochastic differential equations with colored noise, dynamic metabolic energy constraints via evolving ATP levels affecting calcium extrusion, Bayesian inference, global sensitivity analysis (including STDP time constants), uncertainty quantification, weight bounding for stability, homeostatic plasticity with a sliding threshold, and empirical validation using the Allen Institute Synaptic Physiology Dataset. Mathematical derivations, reproducible Python simulations with network scaling and stationary state analysis, quantitative statistics (sample sizes, confidence intervals, Kullback-Leibler divergence), Bayesian evidence, falsifiability criteria, and visualizations (time-course curves for calcium, enzyme activation, weight stability, parameter heatmaps) demonstrate model fidelity to observed synaptic strengths, kinetics, and short-term plasticity. Parameter sweeps over 100 values, comparative plots overlaying predictions with empirical data, and a roadmap for neuromorphic hardware implementation highlight applications in neuromodulation for neurological disorders.