Accurate Description of Cation-π Interactions in Proteins with a Nonpolarizable Force Field at No Additional Cost

Cation-π interactions play a significant role in a host of processes eminently relevant to biology. However, polarization effects arising from the interaction of cations with aromatic moieties have long been recognized to be inadequately described by pairwise additive force fields. In the present work, we address this longstanding shortcoming through the nonbonded FIX (NBFIX) feature of the CHARMM36 force field, modifying pair-specific Lennard-Jones (LJ) parameters, while circumventing the limitations of the Lorentz-Berthelot combination rules. The potentials of mean force (PMFs) characterizing prototypical cation-π interactions in aqueous solutions are first determined using a hybrid quantum mechanical/molecular mechanics (QM/MM) strategy in conjunction with an importance-sampling algorithm. The LJ parameters describing the cation-π pairs are then optimized to match the QM/MM PMFs. The standard binding free energies of nine cation-π complexes, i.e., toluene, para-cresol, and 3-methyl-indole interacting with either ammonium, guanidinium, or tetramethylammonium, determined with this new set of parameters agree well with the experimental measurements. Additional simulations were carried out on three different classes of biological objects featuring cation-π interactions, including five individual proteins, three protein-ligand complexes, and two protein-protein complexes. Our results indicate that the description of cation-π interactions is overall improved using NBFIX corrections, compared with the standard pairwise additive force field. Moreover, an accurate binding free energy calculation for a protein-ligand complex containing cation-π interactions (2BOK) shows that using the new parameters, the experimental binding affinity can be reproduced quantitatively. Put together, the present work suggests that the NBFIX parameters optimized here can be broadly utilized in the simulation of proteins in an aqueous solution to enhance the representation of cation-π interactions, at no additional computational cost.