Biophysical Modeling of Enzyme-Kinetic Calcium-Dependent Stochastic Synaptic Plasticity: Integrating STDP, Metabolic Constraints, Local and Global Sensitivity Analysis, Grid-Based Bayesian Parameter Recovery, and Comparison to Allen Institute Benchmarks

Contemporary synaptic-plasticity models often integrate biophysical enzyme kinetics, metabolic energy constraints, and intrinsic stochastic variability only partially, which limits their transparency and reproducibility. This study presents a biophysical framework that extends the Hodgkin–Huxley (HH) formalism with calcium-dependent stochastic plasticity governed by competing enzyme kinetics (CaMKII-like kinetics for long-term potentiation, LTP; calcineurin-like kinetics for long-term depression, LTD), modulated by spike-timing-dependent plasticity (STDP) eligibility traces. The model couples ATP-gated calcium extrusion, Ornstein–Uhlenbeck (OU) synaptic noise, a BCM-like homeostatic threshold, and activity-dependent AMPA-receptor (AMPAR) trafficking. Every quantitative result reported here – the representative simulation trace, the local (one-factor-at-a-time, OAT) sensitivity analysis, the small-sample global variance-based (Sobol) screen, and the grid-based Bayesian parameter-recovery test – was generated by the single, self-contained script accompanying this paper (fixed seeds, reported in full) and is directly reproducible from it. Spike generation is governed almost entirely by the sodium and potassium conductances (gNa, gK), consistent with standard HH behavior, while the calcium-mediated plasticity variables (Kp, Kd, τtr, η) have a negligible measured effect on spike count under the tested input regime. A key structural finding is that, as formulated in Eq. (4), the OU noise term enters the synaptic-weight equation unconditionally (i.e., independent of pre/post spike coincidence), so that at baseline parameters the weight trajectory is dominated by this additive noise rather than by the Hebbian enzyme-kinetic term; this is reported and discussed as a methodological limitation with a proposed mitigation. A grid-based Bayesian recovery test further shows that spike count alone is a weakly identifying summary statistic for potassium conductance over the biophysically plausible range, indicating that richer observables (e.g., inter-spike-interval distributions, PSP amplitude) would be required for tight posterior inference. Direct quantitative benchmarking against the raw Allen Institute Synaptic Physiology Dataset was not performed because the dataset itself was not accessible in the computational environment used to prepare this study; comparison is instead limited to the published summary statistics of that dataset. Falsifiability criteria, parameter tables, a dedicated risk assessment, and a roadmap toward experimental validation are provided