title: Calculating pH-dependent free energy of proteins by using Monte Carlo protonation probabilities of ionizable residues.
abstract: 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 (lysozyme) 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.
authors.affiliation: State Key Laboratory of Genetic Engineering, School of Life Sciences, Fudan University, Shanghai 200433, China. huangqiang@fudan.edu.cn
authors.forename: Qiang
authors.initials: Q
authors.lastname: Huang
authors.forename: Andreas
authors.initials: A
authors.lastname: Herrmann
mesh_terms: D002401:Cathepsin B / Q000737:chemistry / Q000378:metabolism; D004247:DNA / Q000378:metabolism; D006863:Hydrogen-Ion Concentration; D056004:Molecular Dynamics Simulation; D009010:Monte Carlo Method; D009113:Muramidase / Q000737:chemistry / Q000378:metabolism; D011336:Probability; D011485:Protein Binding; D011506:Proteins / Q000737:chemistry* / Q000378:metabolism; D011522:Protons; D013816:Thermodynamics
chemical_list: D011506:Proteins; D011522:Protons; D004247:DNA; D009113:Muramidase; D002401:Cathepsin B