Protein folding,stability,and function are usually influenced by pH.And free energy plays a fundamental role in analysis of such pH-dependent properties,Electrostatics-based theoretical framework using dielectric solvent continuum model and solving Poisson-Boltzmann equation numerically has been shown to be very successful in understanding the pH-dependent properties.However,in this approach the exact computation of pH-dependent free energy becomes impractical for proteins possessing more than several tens of ionizable sites (e.g.＞ 30),because exact evaluation of the partition function requires a summation over a vast number of possible protonation microstates.Here we present a method which computes the free energy using the average energy and the protonation probabilities of ionizable sites obtained by the well-established Monte Carlo sampling procedure.The key feature is to calculate the entropy by using the protonation probabilities.We used this method to examine a well-studied protein (lysozyms) and produced results which agree very well with the exact calculations.Applications to the optimum pH of maximal stability of proteins and protein-DNA interactions have also resulted in good agreement with experimental data.These examples recommend our method for application to the elucidation of the pH-dependent properties of proteins.