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. Combining Hamiltonian and temperature based or SGLD based replica exchange methods. Hamiltonian replica exchange methods (H-REX) have been widely used to enhance conformational sampling of biomolecules. Generally, Hamiltonian exchange simulations have been performed with a constant temperature. Recently, we have implemented a new replica exchange code in CHARMM, which combines a Hamiltonian exchange method with a temperature exchange (TH-REX) and a self-guided Langevin dynamics (SGLD) exchange method (SGH-REX). In the new exchange methods, Hamiltonians and temperatures (TH-REX)/SGLD-guiding factors (SGH-REX) are exchanged simultaneously to enhance conformational sampling further. We have tested a new method with an alanine di-peptide and a beta-hairpin peptide in implicit water, and a beta-hairpin in explicit water condition. The benchmark results show that TH-REX and SGH-REX methods can successfully perform the Boltzmann sampling of conformations of biomolecules. In the implicit solvent condition, TH-REX and SGH-REX both enhance the sampling efficiency of H-REX. However, for the explicit water simulation, only SGH-REX can enhance the sampling efficiency because SGLD accelerates a conformational sampling without changing potential energy distributions. Introducing temperature exchange to H-REX of explicit water simulation shifts the potential energy distributions of replica and significantly lowers the exchange ratio of H-REX, which decreases the sampling efficiency of H-REX. These results suggest that a new SGH-REX can be a powerful tool for conformational sampling of biomolecules. Constant pH simulation using enveloping distribution sampling (EDS) method. Cellular pH is an important environmental variable, which can affect the structure and dynamics of proteins. Some proteins, such as viral proteins or human hemoglobin, depend on cellular pH to regulate their functions. Therefore, simulating the dynamics of biomolecules under a constant pH condition is one of the important problems in computational biophysics. However, in explicit water, the protonated and deprotonated states of titratable residues of biomolecules are separated by a large energy barrier, which prevents frequent transitions between states. To facilitate the transition between two states, we are developing a new constant pH simulation method using the enveloping distribution sampling (EDS) method. The EDS enables sampling of energetically separated states by performing molecular dynamics on a hybrid Hamiltonian, which envelops multiple states through non-physical states. The height of energy barrier of hybrid Hamiltonian can be controlled by a smoothing parameter. A low energy barrier can enhance transition but reduces the residence time of physical states. We are developing a new method based on a Hamiltonian exchange framework, where replicas are exchanged between hybrid Hamiltonians with different energy barriers and smoothness. By using this algorithm, we believe that frequent transitions between states and reasonable residence time in physical states can be accomplished simultaneously. 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 and on a challenging system, the V66K variant of Staphylococcal nuclease, 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. Other replica exchange methods development. The lab has been heavily involved in the development of new replica exchange methods. We have combined reservoir replica exchange with the Conformation al Space Annealing method to produce a highly efficient sampling method that can accurately and quickly probe energy barriers between biologically relevant states of a protein system. This method has now been fully integrated into the CHARMM molecular simulation package. However, the use of reservoir methods is challenging because of issues with reservoir bias. A new method, Perturbed Reservoir Replica Exchange (P-RREX), is under development. The primary advantage of this method is that it does not make any assumption about the composition of the reservoir. Although sampling efficiency will be limited by reservoir quality, P-RREX will produce a Boltzmann ensemble using any reservoir. An early implementation of this method has been added to CHARMM and is currently being tested. 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. Novel Rigid Structure Dynamics Algorithm. The rigid body methods have wide range of applications in molecular dynamics (MD) simulations. The most widely implemented rigid body methods, SHAKE and RATTLE, apply bond length constraints in MD simulations with limitation on rigid body size. We developed a novel rigid body simulation algorithm, named SHAPE and implemented in CHARMM, to maintain rigid structures in Verlet based Cartesian MD simulations. This algorithm avoids the calculations of Lagrange multipliers, so that the complexity of computation does not increase with the number of particles in a rigid structure. Through this method, an arbitrary number of particles can be selected to form single rigid structure, and an arbitrary number of such rigid structures can be implemented in simulation. A unique feature of the SHAPE method is that it is interchangeable with SHAKE for any object that can be constrained as a rigid structure using multiple SHAKE constraints. Continuing development of Self Guided Langevin Dynamics (SGLD) continues.

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