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. 1. Improved self-guided molecular dynamics (SGLD) simulation methods for ensemble sampling Self-guided molecular dynamics Langevin dynamics was developed for enhanced conformational search. This method makes rare events that otherwise not accessible by regular dynamics simulation observable with current available computing resources. Typical applications include protein folding, signal transaction, water penetration, etc. A major challenge when applying the original SGLD method in simulation studies is how to quantitatively measure the ensemble deviation and how to correct the SGLD results. By analyzing the characteristics 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 in a property, we are able to quantitative describe the enhancement in low frequency motion and correct for the alteration of the conformational distribution. This thermodynamic relation paves the way for many application and extension of the SGMD/SGLD methods. One immediate extension is by introducing the relation into the equation of motion, we developed the SGMDfp/SGLDfp method that can produce directly a correct conformational distribution while enhancing the conformational search. Another application is to combine SGLD with replica exchange with or without temperature increases. The advantage of SGLD-replica exchange without temperature change is that a reduced number of replica needed for large systems, such as a solvated protein. 2. 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. Based 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 as the switching function to account for long range contributions. 3. A novel rigid structure dynamics algorithm, SHAPE Rigid body methods have wide range of applications in molecular dynamics (MD) simulations. The most widely implemented rigid body methods, SHAKE and RATTLE, apply only bond length constraints in MD simulations with limitation on rigid body size. We presented a novel rigid body simulation algorithm, named SHAPE, 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. Numerical tests with four model systems including two proteins demonstrate that the accuracy and reliability of the SHAPE method are comparable to the SHAKE method, but with much more applicability and efficiency. 4. A novel algorithm for free energy method along reaction paths through rigid body simulation Estimation of reaction free energy with multiple reaction coordinates (RCs), especially enzymatic reactions, is a very active topic in computational chemistry and biology. We developed a highly efficient novel algorithm sampling the ffree energy along a reference reaction path with constraints on multiple Rcs. In this method, all the key atoms defining RCs can be selected to form a rigid structure using our SHAPE rigid body method as constraints during simulations. Through a series of MD simulations with rigid structure constraints, the free energy profile can be constructed using line integral along the chosen reference pathway in free energy gradient vector field. We demonstrated that this novel free energy method greatly improve the sampling efficiency through constraints instead of widely applied harmonic restraints. It is proving to be an excellent method to study mechanism of large biological systems, such as enzymes. 5. Combining Conformational Space Annealing (CSA) with Replica Exchange Method (REM) Temperature replica exchange molecular dynamics (T-REM) 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 T-REM is still computationally intensive since the complexity of the free energy landscape and number of replicas required increase 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 standard T-REM. One of these methods is called Reservoir Replica Exchange Method (R-REM) where the conformational search and temperature equilibration are separated. This approach 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 energy minimum of proteins efficiently and has been used in structure prediction successfully. CSA uses a genetic algorithm approach to generate a diverse set of conformations to determine the minimum energy structure. We have used conformations generated through CSA method to build 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. 6. MDMS: Molecular Dynamics Meta-Simulator for evaluating exchange type sampling methods. Replica exchange methods have become popular tools to explore conformational space for small proteins. For larger biological systems, even with enhanced sampling methods, exploring the free energy landscape remains computationally challenging. This problem has led to the development of many improved replica exchange methods. Unfortunately, testing these methods remains expensive. We developed a Molecular Dynamics Meta-Simulator (MDMS) based on transition state theory to simulate a replica exchange simulation, eliminating the need to run explicit dynamics between exchange attempts. MDMS simulations allow for rapid testing of new replica exchange based methods, greatly reducing the amount of time needed for new method development. Other ongoing projects (listed only, due to annual report character count limits) 7. Participation in the SAMPL3 challenge, Binding free energy methods 8. Using SGLD to enhance Bennett's acceptance ratio (BAR) and Enveloping Distribution Sampling (EDS) convergence 9. pKa calculations with the reservoir pH replica exchange method 10. Using normal mode analysis as a technique to evaluate various coarse grained models 11. Replica exchange and expanded ensemble simulations as Gibbs sampling: Extending Gibbs Sampling to peptides and proteins 12. Efficient Calculation of QM/MM Frequencies with the Mobile Block Hessian (MBH) methods 13. Automatic spot identification for high throughput microarray analysis
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