Enhanced Sampling Methodologies for Free Energy Calculations in Biomolecular Systems

We developed two enhanced sampling methods, one for configurational sampling of small molecules/peptides, and the other for calculating protein-protein binding free energies to solve interaction/recognition problems. To enhance the configurational sampling which can be very computationally demanding with conventional Molecular Dynamics (MD) simulations, a Hybrid non-equilibrium MD/Monte Carlo propagator is developed in which we apply non-equilibrium work to the system in order to boost the Hamiltonian while a Metropolis-Hastings Monte Carlo (MC) step ensures sampling from the correct Boltzmann distribution. When the sampling of a biomolecular system gets stuck in a kinetic trap (metastable state), the Hybrid neMD/MC propagator helps it to escape. Specific biomolecular peptide systems were used to test validity and performance of the method. We put forth a novel theoretical framework for binding free energy calculations between two proteins, leaning on the optimal curvilinear minimum free-energy path (MFEP) determined from the string method. The curvilinear path connects the fully bound state to the unbound state and is generated from quick simulations using an implicit solvent model, followed by application of the dynamic histogram analysis method (DHAM). In each of the simulations DHAM finds the free energy minimum; minima from all simulations jointly describe the MFEP. The curvilinear path avoids the free energy barrier that the rectilinear path connecting the same bound and unbound states has to cross, leading to a faster convergence of binding-free energy estimates. A host-guest system and a protein complex were used to test validity and performance of the method. With these enhanced sampling methods developed, we tackle two biomolecular problems, namely dissociation of the HIV-1 Nef /SH3 and Colicin/Im9 complexes. The former shows an immense change in binding affinity if a single residue (R96I) is mutated. The binding affinity of both wildtype and R96I mutant complex are investigated using the string method. Additionally, the bound complex is sampled with Hybrid neMD/MC propagator without any restraints to find additional key residue interactions. Knowing these residues allowed us to explain the origin of cognate/non-cognate Colicin binding; Im9 (cognate interaction) shows 6 orders of magnitude stronger binding affinity than Im2 (non-cognate interaction). The binding affinity of both complexes are investigated using the string method