Continuum treatment of long-range interactions in free energy calculations. Application to protein-ligand binding.

A method is proposed to include long-range electrostatic interactions in free energy calculations that involve the creation or deletion of net charges in a macromolecule. The vicinity of the mutation site is treated microscopically, while distant bulk solvent is treated macroscopically. A three-step mutation pathway is used. First, the mutation is introduced with a molecular dynamics simulation for the macromolecule, solvated by a limited number of explicit water molecules and surrounded by vacuum. Selected charges may be reduced during this step to mimic the effect of bulk solvent on the dynamics and to obtain a simulation in which the structures sampled are correct. The full effect of bulk solvent is accounted for in the next two steps. In the second step, the reduced charges are increased to their original values and the corresponding free energy change is obtained from continuum electrostatics. In the third step, the system is transferred into bulk solvent, modeled as a dielectric continuum, and the transfer free energy is obtained from continuum electrostatics. A potential-based charge scaling can be used in step I for the selected charges, which reduces each one in proportion to the screening by bulk solvent of its potential at the mutation site. With this method, the a priori scaling of a charged group in step I is formally equivalent to its solvation by bulk solvent in step m. Thus, for a given charged group, a priori scaling or a posteriori bulk solvation should give similar results. The method is illustrated by a calculation of the free energy change associated with the mutation of an aspartate ligand into asparagine in the active site of aspartyl-tRNA synthetase, a process that removes a negative charge. The results of five free energy runs with three different charge scaling schemes are in good agreement. This indicates that the method is robust with respect to implementation details and that the continuum approximation in steps II and III is valid for this case.