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. 2012 Mar 31;3(3):230–238. doi: 10.1007/s13238-012-2035-4

Calculating pH-dependent free energy of proteins by using Monte Carlo protonation probabilities of ionizable residues

Qiang Huang 1,✉, Andreas Herrmann 2
PMCID: PMC4875427  PMID: 22467263

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.

Keywords: protein protonation, protein electrostatics, pH-dependent free energy, Poisson-Boltzmann equation, Monte Carlo simulation

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