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. This development is driven by current needs and interests. Self-guided molecular simulation for ensemble sampling Self-guided molecular dynamics (SGMD)/Langevin dynamics (SGLD) was developed for enhanced conformational search. This method makes rare events that otherwise not accessible by molecular dynamics simulation observable with modest computing resources. Typical applications include protein folding, signal transaction, water penetration, etc. A major challenge when applying SGMD/SGLD method in simulation studies is to quantitatively measure the deviation of the ensemble of states from a canonical ensemble and how to correct SGMD/SGLD results. This challenge has been a hurdle for the application of the method. By analyzing the characters of the guiding force and SGMD/SGLD simulation behavior, we derived a thermodynamic relation between a regular simulation and a self-guided simulation. By separating low frequency part from high frequency part, we are able to quantitative describe the enhancement in low frequency motion and correct by reweighing the deviation in the conformational distribution. This thermodynamic relation paves the way for many application and extension of the SGMD/SGLD method. One immediate extension is by introducing the relation into the equation of motion, we developed the so called SGMDfp/SGLDfp method that can produce directly a correct conformational distribution while enhances the conformational search using both force and momentum. Another application is to combine SGMD/SGLD with replica exchange with or without temperature differences. The advantage of SGMD/SGLD-replica exchange without temperature change is the reduction of the number of replicas needed for large systems such as solvated proteins. Multi-scale modeling Multi-scale modeling methods and application have become increasingly important for modeling important cellular events that are too complex to be studied at the rigorous QM level or even the all-atom classical force-field level. Usually, multi-scale techniques use high-level techniques to parameterize the coarser ones, however, it is also possible to couple these methods within a single framework to allow energies, forces, and NMA calculations to be done. MSCALE, a generalized approach for multi-scale modeling has therefore been developed and implemented within CHARMM. The MSCALE communication paradigm has also been made to work with other codes including Gaussian03, MOLPRO, NWCHEM, and the SANDER module of AMBER. The MSCALE communications protocol is easy to adopt for use with other programs. The following functionality exists within the CHARMM MSCALE implementation: 1. Triple-parallel scheme: (a) replicas, (b) Hamiltonian term or layer distribution, (c) parallelization of individual energy terms. 2. Multi-scale normal mode analysis with analytic Hessians. 3. Generalized approach to combining multiple physical and theoretical scales within a single calculation. For example, additive QM/MM, subtractive QM/MM, and all-atom/coarse-grained calculations are supported. 4. A general method for combining different multiscale approaches in a single calculation is supported. For example, both additive and subtractive QM/MM methods can be used in a single calculation. 5. Generalized free-energy perturbation calculations using multi-scale models. Hessian based methods for multi-scale modeling As part of the effort to develop generalized approaches to multi-scale simulations, new analysis techniques must be developed to interpret the results of multi-scale normal mode analysis calculations. Validating the results of these calculationss is a difficult problem because both the number of modes and frequencies and the lengths of the individual mode vectors differ from those produced by all-atom or more traditional coarse-grained NMA calculation (e.g. via the Elastic Network Model). Various approaches to this problems such as measuring spatial extents of modes or mapping lower level modes on a higher level representation are being studied and benchmarked. Excited states methods and applications The time-dependent density functional theory (TDDFT) is the method of choice for studying excited states in biological systems. In our recent benchmark calculations on the valence excited states in 20 small molecule, we found that TDDFT is more twice more accurate than configuration interaction singles (CIS), but only at a comparable computational cost. We also found that that TDDFT even produces more accurate excited state bond lengths than much more expensive correlation methods (such as CC2), while the adiabatic excitation energies are about the same quality. Recently, we achieved an efficient serial and parallel implementation of the analytical gradient for TDDFT (specificly its Tamm-Dancoff approximation). With that, we will study excited state dynamics of tryptophan in water and protein environments. Combining Conformational Space Annealing with Replica Exchange Method Replica exchange molecular dynamics (REMD) has been successfully used to improve the conformational search for model peptides and small proteins. However for larger and more complicated systems the use of REMD is still computationally intensive since the number of replicas required increases with system size. Achieving convergence with systems with slow transition kinetics is also very difficult. Several methods have been proposed to overcome the size and convergence speed issues of REMD. One of these methods is called Reservoir Replica Exchange Method (R-REMD) where the conformational search and temperature equilibration are separated. This allows integrating computationally efficient search algorithms with replica exchange. The Conformational Space Annealing (CSA) method has been shown to be able to determine the global free energy of proteins efficiently and has been used in structure prediction successfully. CSA uses a genetic algorithm approach to perform the conformational search and determine the minimum energy structure. We have used conformations generated through CSA method and collected them in a reservoir. Replica exchange was then performed where the top replica was seeded with the reservoir structures and fast convergence at every temperature is observed. Preliminary tests with model peptides show significant improvement on sampling efficiency and more thorough testing with small proteins is being done. Isotropic Periodic Sum Method for multipole interactions Multipole interactions play an important role in biological systems and increasing amount of effort have been contributed to include multipole interactions in force field development. The computation expense of multipole interactions are overwhelming for simulation. IPS method provides a convenient approach to tackle this problem. Base on IPS concept, we developed IPS potentials for multipole interactions. As a result, multipole interaction calculation can be carried out exactly as the cutoff method, with the IPS potentials to account for long range contributions. This development makes including multipole interactions a convenient way to extend force field developments and to speed up simulations with multipole interactions. Other ongoing method development projects: Improved conformational sampling by combining SGLD with replica exchange molecular dynamics QM/MM full Hessian and MBH Hessian Constant pH simulations with pH replica exchange Development and benchmarking of coarse-grained models in CHARMM Determination of test and evaluation criteria for sampling methods, CASA (Comparative Assessment of Sampling Algorithms)

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National Heart, Lung, and Blood Institute
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