A Fast Synaptic Parameter Estimation Method Based on First- and Second-Order Moments for Short-Term Facilitating Synapses

Background: Short-term facilitation (STF) is a key form of synaptic plasticity driven by activity-dependent increases in presynaptic release probability. However, estimating core synaptic parameters—quantal size (q), vesicle pool size (N), and release probability (pi)—remains challenging due to nonlinear dynamics and unobservable presynaptic states, limiting the applicability of conventional methods. Methods: We developed a fast analytical framework based on first- and second-order statistical moments of evoked EPSCs, including mean, variance, and cross-stimulus covariance. By constructing composite moment relationships, latent variables were algebraically eliminated, yielding closed-form estimators of synaptic parameters. To improve robustness under strong facilitation, a Tsodyks–Markram (T–M) model-based calibration step was introduced to refine N and pi using the estimated q as a constraint. Results: Applied to hippocampal CA3–CA1 synapses, the method produced accurate and stable estimates of q across varying noise and sampling conditions. Incorporation of cross-stimulus covariance enabled effective characterization of structured variability that is neglected in classical approaches. While direct estimates of N and pi showed dispersion, T–M calibration significantly improved stability and physiological consistency. Compared with mean–variance analysis, the proposed method achieved superior performance under facilitating conditions. Conclusions: This hybrid framework enables rapid and reliable estimation of synaptic parameters in STF synapses by exploiting second-order statistical structure. It provides a practical tool for investigating presynaptic mechanisms and may facilitate quantitative studies of synaptic dysfunction in neurological and psychiatric disorders.