Contemporary synaptic plasticity models often lack a unified integration of biophysical enzyme kinetics, metabolic energy constraints, and intrinsic stochastic variability, limiting their fidelity in replicating empirical neural dynamics. This study addresses these limitations through a comprehensive biophysical framework extending the Hodgkin-Huxley model to incorporate calcium-dependent stochastic plasticity mediated by competitive enzyme kinetics (CaMKII for long-term potentiation, LTP; calcineurin for long-term depression, LTD), modulated by spike-timing-dependent plasticity (STDP) traces. Key advancements include ATP-regulated calcium extrusion for metabolic realism, Ornstein-Uhlenbeck noise for stochasticity, BCM-like sliding thresholds for homeostasis, and AMPAR trafficking for synaptic efficacy. The model is rigorously evaluated using Bayesian inference for parameter estimation, global sensitivity analysis via Sobol indices over an expanded parameter space (encompassing STDP time constants), uncertainty quantification through bootstrapping and Monte Carlo methods, and direct validation against the Allen Institute Synaptic Physiology Dataset (comprising over 1800 synapses, achieving a mean RMSE of 0.03 mV and KL divergence ∼ 0.05 for PSP distributions). Simulations reproduce observed synaptic strengths (medians ∼ 0.1–0.5 mV), kinetics, and short-term facilitation/depression. Parameter sweeps (n=100 per variable) confirm robustness, with 85% of iterations maintaining weight variance 20% from empirical medians (KL >1.0) or discordant sensitivity rankings (e.g., S_i(g_K) < S_i(K_p)). This approach advances biophysical neuroscience and informs neuromorphic hardware design, with implications for adaptive neuromodulation in disorders such as epilepsy and depression.