New theoretical techniques are being developed and characterized. These efforts are usually coupled with software development, and involve the systematic testing and evaluation of new ideas. Estimating accurate binding free energy calculations by constant-pH simulation Solution pH often has a large impact on the structure and energetics of biomolecules by changing protonation/tautomeric states. The results from the recent binding free energy calculation competitions show that determining a correct protonation state is critical in obtaining accurate binding free energy estimates. However, conventional binding free energy methods depend on a fixed charge model in which protonation states and partial charges are determined before a free energy calculation based on experimental data and remain constant during the calculation. However, this approach cannot reflect the effect of solution pH properly. Especially, if the pKa value of a target molecule is similar to the solution pH, the pH effect becomes more significant. Therefore, developing a new binding free energy estimation procedure by using a constant-pH simulation is essential for pushing the boundaries of binding free energy calculation. Recently, we developed a new constant pH simulation method that can work with explicit solvents. Our method results in more accurate canonical ensemble under a given pH condition than other existing methods. Therefore, we expect that combining our method with binding free energy calculation will allow a highly accurate calculation of binding free energies. Developing a new replica-exchange methodology Efficient conformational sampling is one of the most important problems in computational biology. In most problems, a sampling algorithm should result in the Boltzmann distribution for a given condition, and overcome energy barriers efficiently to observe rare events. To achieve these goals, a replica-exchange sampling methods have been widely used. Conventional replica-exchange methods use a simple 1 dimensional chain of states with different conditions, such as temperature and Hamiltonians. We developed a new 2 dimensional replica exchange method, and implemented in CHARMM. With the 2 dimensional replica exchange method, replicas are exchange along two different criteria, such as temperature-Hamiltonian or Hamiltonian-Hamiltonian. We benchmarked this 2 dimensional replica exchange method by using a newly developed EDS-HREM constant pH simulation method: exchanges are performed between different EDS potentials as well as different pH conditions. The benchmark results show that 2 dimensional replica exchange can increase sampling efficiency significantly with the same amount of computational resources. Double reservoir pH replica exchange method MD simulations at constant pH allow for the change in protonation states of ionizable groups during the course of a trajectory and are potentially an excellent tool for both a more realistic description of protein dynamics, and a calculation of pKa values of ionizable groups. In some cases constant pH simulations suffer from sampling issues. We have previously improved sampling in constant pH simulations by developing the pH replica exchange (pH-Rex) method. However, for some challenging cases, sampling still remained an issue. We have now developed the double reservoir pH replica exchange method (DR-pH-Rex) which relies on generation of two reservoirs of conformations at very low and very high pH values that correspond to the fully protonated and fully deprotonated states. When tested on a small peptide the DR-pH-rex method exhibits improved conformational sampling as compared to the pH-Rex method, faster convergence and less noise in the calculated pKa values. For the V66K variant the pH-Rex method fails to properly sample conformational transitions of Lys-66 and results in two different pKa values when different conformations are used as starting structure, while the DR-pH-Rex method, results in convergence of pKa values. Developing a hybrid quantum-chemical/molecular mechanical approach for free energy calculations. The reliability of free energy simulations is limited by two factors: a) the need for correct sampling and b) the accuracy of the parameters in classical molecular modeling. Parametrization is especially problematic in drug design, where ligands often contain non-standard chemical groups. On the other hand, parameter-free ab initio methods tend to be too computationally expensive for adequate sampling in biomolecular systems. A simple way to address this problem is by post-processing molecular dynamics simulations with quantum-chemical calculations. First, a molecular dynamics trajectory is generated to perform proper sampling of all relevant degrees of freedom. In a second step, the potential energies of each frame of the trajectory are evaluated with a quantum mechanics (QM) or quantum mechanics/molecular mechanics (QM/MM) approach. Free energy differences are then calculated based on the QM or QM/MM energies using the Non-Boltzmann Bennett (NBB) method. Since all energy evaluations of the post-processing stage are independent of each other, this approach is trivial to parallelize. Thus, highly parallel computer architectures can be employed with high efficiency, which allows us to perform the post-processing very rapidly. The approach has been successfully employed in the SAMPL4 blind hydration free energy prediction competition. High-order multipole moments and polarizable dipoles provide a mechanism for greatly increasing the accuracy of classical force field methods, and they are employed in next-generation force fields such as AMOEBA. Despite their demonstrated accuracy, these force fields have not gained widespread use because of their high computational cost, relative to their simpler fixed-charge counterparts. To overcome this steep computational penalty, we developed an extremely efficient method for evaluating interactions between multipole moments, using a novel combination of spherical harmonic basis functions and particle mesh Ewald (PME) theory. We are currently extending this treatment to include an efficient treatment of polarizable dipoles, which remain the bottleneck in AMOEBA calculations. Although spherical harmonics offer no rank reduction, with respect to Cartesian representations, for evaluating dipole-dipole interactions, we have developed an efficient guess and preconditioner using the properties of the spherical harmonic interaction tensor, and are currently using these to improve our CHARMM implementation of the AMOEBA force field. The crux of our multipole method is that we can use PME theory to shorten real-space cutoffs, and evaluate many of the terms in reciprocal space;the multipole terms may be treated in reciprocal space with little extra computational cost than is required for a point-charge only treatment. The concomitant reduced real-space cutoffs result in fewer explicit pairwise interactions that must be evaluated, leading to a reduction in the computational cost. The current handling of dispersion interactions, which are long-ranged, is not consistent with the explicit consideration of only short-ranged pairwise interactions. To be able to treat electrostatics and dispersion on the same footing, i.e., with short cutoffs, we have developed a PME method for evaluating dispersion interactions. By considering only the short-ranged interactions in real space, the new method introduces significant computational savings and is far more amenable to parallel implementation using a domain decomposition approach. Moreover, the new method offers great improvements in accuracy for highly anisotropic systems, such as lipid bilayers, as it is able to capture the long-ranged dispersion effects that are missing in the current approach.
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