Comparison of multiple amber force fields and development of improved protein backbone parameters,”

ABSTRACT The ff94 force field that is commonly associated with the Amber simulation package is one of the most widely used parameter sets for biomolecular simulation. After a decade of extensive use and testing, limitations in this force field, such as over-stabilization of a-helices, were reported by us and other researchers. This led to a number of attempts to improve these parameters, resulting in a variety of ''Amber'' force fields and significant difficulty in determining which should be used for a particular application. We show that several of these continue to suffer from inadequate balance between different secondary structure elements. In addition, the approach used in most of these studies neglected to account for the existence in Amber of two sets of backbone u/w dihedral terms. This led to parameter sets that provide unreasonable conformational preferences for glycine. We report here an effort to improve the u/w dihedral terms in the ff99 energy function. Dihedral term parameters are based on fitting the energies of multiple conformations of glycine and alanine tetrapeptides from high level ab initio quantum mechanical calculations. The new parameters for backbone dihedrals replace those in the existing ff99 force field. This parameter set, which we denote ff99SB, achieves a better balance of secondary structure elements as judged by improved distribution of backbone dihedrals for glycine and alanine with respect to PDB survey data. It also accomplishes improved agreement with published experimental data for conformational preferences of short alanine peptides and better accord with experimental NMR relaxation data of test protein systems

Improved conformational sampling methods for molecular dynamics simulations

Understanding conformational dynamics of biomolecules such as proteins is a fundamental challenge in structural biology. Native conformations of proteins can be determined experimentally via X-Ray Crystallography and NMR spectroscopy but usually such methods provide time averaged data. All-atom simulations are commonly used to supplement experimental observations where time dependent trajectories for complex systems can be obtained. However there are major challenges in computer simulations. For successful simulations the potential function has to be accurate enough to correctly rank the local and global energy minima and the barriers in between for the simulated system. We developed an efficient method to test the accuracy of force field parameters where the energies of pre-generated conformations (decoys) were calculated for each parameter set in question and the identified energy minima were compared to experimental measurements. After generating decoy sets the evaluation of force field or other simulation parameters can be done quickly and efficiently. We used this decoy screening procedure to identify α-helical bias in existing force fields in AMBER and to develop improved force field parameters. Another major challenge in simulations is sampling because the time scales reached with standard simulations are 3-6 orders of magnitude shorter than actual comformational transitions observed in proteins. There are several new sampling methods available where transitions between energy minima are enhanced through the use of high temperatures. Such methods are still very computationally demanding and can only be applied to small systems. We have developed two new methods to further enhance the conformational sampling to reduce computational demands and increase the convergence speed of simulations

Optimal investment strategy and liability ratio for insurer with Levy risk process

We investigate an insurer's optimal investment and liability problem by maximizing the expected terminal wealth under different utility functions. The insurer's aggregate claim payments are modeled by a Levy risk process. We assume that the financial market consists of a riskless and a risky assets. It is also assumed that the insurer's liability is negatively correlated with the return of the risky asset. The closed-form solution for the optimal investment and liability ratio is obtained using Pontryagin's Maximum Principle. Moreover, the solutions of the optimal control problems are examined and compared to the findings where the jump sizes are assumed to be constant

MSCALE: A General Utility for Multiscale Modeling

The combination of theoretical models of macromolecules that exist at different spatial and temporal scales has become increasingly important for addressing complex biochemical problems. This work describes the extension of concurrent multiscale approaches, introduces a general framework for carrying out calculations, and describes its implementation into the CHARMM macromolecular modeling package. This functionality, termed MSCALE, generalizes both the additive and subtractive multiscale scheme [e.g., quantum mechanical/molecular mechanical (QM/MM) ONIOM-type] and extends its support to classical force fields, coarse grained modeling [e.g., elastic network model (ENM), Gaussian network model (GNM), etc.], and a mixture of them all. The MSCALE scheme is completely parallelized with each subsystem running as an independent but connected calculation. One of the most attractive features of MSCALE is the relative ease of implementation using the standard message passing interface communication protocol. This allows external access to the framework and facilitates the combination of functionality previously isolated in separate programs. This new facility is fully integrated with free energy perturbation methods, Hessian-based methods, and the use of periodicity and symmetry, which allows the calculation of accurate pressures. We demonstrate the utility of this new technique with four examples: (1) subtractive QM/MM and QM/QM calculations; (2) multiple force field alchemical free energy perturbation; (3) integration with the SANDER module of AMBER and the TINKER package to gain access to potentials not available in CHARMM; and (4) mixed resolution (i.e., coarse grain/all-atom) normal mode analysis. The potential of this new tool is clearly established, and in conclusion, an interesting mathematical problem is highlighted, and future improvements are proposed