Efficient determination of protein-protein standard binding free energies from first principles

Characterizing protein-protein association quantitatively has been a longstanding challenge for computer simulations. Here, a theoretical framework is put forth that addresses this challenge on the basis of detailed all-atom molecular dynamics simulations with explicit solvent. The proposed methodology relies upon independent potential of mean force (PMF) free-energy calculations carried out sequentially, wherein the biological objects are restrained in the conformation, position and orientation of the bound state, using adequately chosen biasing potentials. These restraints systematically narrow down the configurational entropy available to the system and effectively guarantee that the relevant network of interactions is properly sampled as the two proteins reversibly associate. Decomposition of the binding process into consecutive, well-delineated stages, for both the protein complex and the individual, unbound partners, offers a rigorous definition of the standard state, from which the absolute binding free energy can be determined. The method is applied to the difficult case of the extracellular ribonuclease barnase binding to its intracellular inhibitor barstar. The calculated binding free energy is -21.0 ± 1.4 kcal/mol, which compares well with the experimental value of -19.0 ± 0.2 kcal/mol. The relatively small statistical error reflects the precision and convergence afforded by the PMF-based simulation methodology. In addition to providing an accurate reproduction of the standard binding free energy, the proposed strategy offers a detailed picture of the protein-protein interface, illuminating the thermodynamic forces that underlie reversible association. The application of the present formal framework to barnase:barstar binding provides a foundation for tackling nearly any protein-protein complex.