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

Protein Cell. 2012 Mar;3(3):230-8. doi: 10.1007/s13238-012-2035-4. Epub 2012 Mar 31.

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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Cathepsin B / chemistry
  • Cathepsin B / metabolism
  • DNA / metabolism
  • Hydrogen-Ion Concentration
  • Molecular Dynamics Simulation
  • Monte Carlo Method*
  • Muramidase / chemistry
  • Muramidase / metabolism
  • Probability
  • Protein Binding
  • Proteins / chemistry*
  • Proteins / metabolism
  • Protons
  • Thermodynamics

Substances

  • Proteins
  • Protons
  • DNA
  • Muramidase
  • Cathepsin B