String Method for Protein–Protein Binding Free-Energy Calculations

A powerful computational strategy to determine the equilibrium association constant of two macromolecules with explicit-solvent molecular dynamics (MD) simulations is the "geometric route", which considers the reversible physical separation of the bound complex in solution. Nonetheless, multiple challenges remain to render this type of methodology reliable and computationally efficient in practice. In particular, in one, formulation of the geometric route relies on the potential of mean force (PMF) for physically separating the two binding partners restrained along a straight axis, which must be selected prior to the calculation. However, practical applications indicate that the calculation of the separation PMF along the predefined rectilinear pathway may be suboptimal and slowly convergent. Recognizing that a rectilinear straight separation pathway is generally not representative of how the protein complex physically separates in solution, we put forth a novel theoretical framework for binding free-energy calculations, leaning on the optimal curvilinear minimum free-energy path (MFEP) determined from the string method. The proposed formalism is validated by comparing the results obtained using both rectilinear and curvilinear pathways for a prototypical host-guest complex formed by cucurbit[7]uril (CB[7]) binding benzene, and for the barnase-barstar protein complex. On the basis of multi-microsecond MD calculations, we find that the calculations following the traditional rectilinear pathway and the string-based curvilinear pathway agree quantitatively, but convergence is faster with the latter.