Molecular Interaction Probability Calculation Framework

Build a sophisticated PostgreSQL database and query system for calculating molecular interaction probabilities in complex biochemical systems. Develop stored procedures that can: 1) Model probabilistic interactions between protein structures, 2) Apply Bayesian inference techniques for predicting potential molecular bindings, 3) Generate multi-dimensional interaction likelihood matrices. Implement a solution that can process datasets from large-scale protein interaction studies, with optimization for handling complex computational biology scenarios.