Improvements to the APBS biomolecular solvation software suite

The Adaptive Poisson-Boltzmann Solver (APBS) software was developed to solve the equations of continuum electrostatics for large biomolecular assemblages that has provided impact in the study of a broad range of chemical, biological, and biomedical applications. APBS addresses three key technology challenges for understanding solvation and electrostatics in biomedical applications: accurate and efficient models for biomolecular solvation and electrostatics, robust and scalable software for applying those theories to biomolecular systems, and mechanisms for sharing and analyzing biomolecular electrostatics data in the scientific community. To address new research applications and advancing computational capabilities, we have continually updated APBS and its suite of accompanying software since its release in 2001. In this manuscript, we discuss the models and capabilities that have recently been implemented within the APBS software package including: a Poisson-Boltzmann analytical and a semi-analytical solver, an optimized boundary element solver, a geometry-based geometric flow solvation model, a graph theory based algorithm for determining p$K_a$ values, and an improved web-based visualization tool for viewing electrostatics

Speed and accuracy tradeoffs in molecular electrostatic computation

textIn this study, we consider electrostatics contributed from the molecules in the ionic solution. It plays a significant role in determining the binding affinity of molecules and drugs. We develop the overall framework of computing electrostatic properties for three-dimensional molecular structures, including potential, energy, and forces. These properties are derived from Poisson-Boltzmann equation, a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. In order to compute these properties, we derived new boundary integral equations and designed a boundary element algorithm based on the linear time fast multipole method for solving the linearized Poisson-Boltzmann equation. Meanwhile, a higher-order parametric formulation called algebraic spline model is used for accurate approximation of the unknown solution of the linearized Poisson-Boltzmann equation. Based on algebraic spline model, we represent the normal derivative of electrostatic potential by surrounding electrostatic potential. This representation guarantees the consistent relation between electrostatic potential and its normal derivative. In addition, accurate numerical solution and fast computation for electrostatic energy and forces are also discussed. In addition, we described our hierarchical modeling and parameter optimization of molecular structures. Based on this technique, we can control the scalability of molecular models for electrostatic computation. The numerical test and experimental results show that the proposed techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules.Computer Science

Large-scale parallelised boundary element method electrostatics for biomolecular simulation

Large-scale biomolecular simulations require a model of particle interactions capable of incorporating the behaviour of large numbers of particles over relatively long timescales. If water is modelled as a continuous medium then the most important intermolecular forces between biomolecules can be modelled as long-range electrostatics governed by the Poisson- Boltzmann Equation (PBE). We present a linearised PBE solver called the "Boundary Element Electrostatics Program"(BEEP). BEEP is based on the Boundary Element Method (BEM), in combination with a recently developed O(N) Fast Multipole Method (FMM) algorithm which approximates the far-�field integrals within the BEM, yielding a method which scales linearly with the number of particles. BEEP improves on existing methods by parallelising the underlying algorithms for use on modern cluster architectures, as well as taking advantage of recent progress in the �field of GPGPU (General Purpose GPU) Programming, to exploit the highly parallel nature of graphics cards. We found the stability and numerical accuracy of the BEM/FMM method to be highly dependent on the choice of surface representation and integration method. For real proteins we demonstrate the critical level of surface detail required to produce converged electrostatic solvation energies, and introduce a curved surface representation based on Point-Normal G1-continuous triangles which we �find generally improves numerical stability compared to a simpler surface constructed from planar triangles. Despite our improvements upon existing BEM methods, we �find that it is not possible to directly integrate BEM surface solutions to obtain intermolecular electrostatic forces. It is, however, practicable to use the total electrostatic solvation energy calculated by BEEP to drive a Monte-Carlo simulation

Developing and validating Fuzzy-Border continuum solvation model with POlarizable Simulations Second order Interaction Model (POSSIM) force field for proteins

The accurate, fast and low cost computational tools are indispensable for studying the structure and dynamics of biological macromolecules in aqueous solution. The goal of this thesis is development and validation of continuum Fuzzy-Border (FB) solvation model to work with the Polarizable Simulations Second-order Interaction Model (POSSIM) force field for proteins developed by Professor G A Kaminski. The implicit FB model has advantages over the popularly used Poisson Boltzmann (PB) solvation model. The FB continuum model attenuates the noise and convergence issues commonly present in numerical treatments of the PB model by employing fixed position cubic grid to compute interactions. It also uses either second or first-order approximation for the solvent polarization which is similar to the second-order explicit polarization applied in POSSIM force field. The FB model was first developed and parameterized with nonpolarizable OPLS-AA force field for small molecules which are not only important in themselves but also building blocks of proteins and peptide side chains. The hydration parameters are fitted to reproduce the experimental or quantum mechanical hydration energies of the molecules with the overall average unsigned error of ca. 0.076kcal/mol. It was further validated by computing the absolute pKa values of 11 substituted phenols with the average unsigned error of 0.41pH units in comparison with the quantum mechanical error of 0.38pH units for this set of molecules. There was a good transferability of hydration parameters and the results were produced only with fitting of the specific atoms to the hydration energy and pKa targets. This clearly demonstrates the numerical and physical basis of the model is good enough and with proper fitting can reproduce the acidity constants for other systems as well. After the successful development of FB model with the fixed charges OPLS-AA force field, it was expanded to permit simulations with Polarizable Simulations Second-order Interaction Model (POSSIM) force field. The hydration parameters of the small molecules representing analogues of protein side chains were fitted to their solvation energies at 298.15K with an average error of ca.0.136kcal/mol. Second, the resulting parameters were used to reproduce the pKa values of the reference systems and the carboxylic (Asp7, Glu10, Glu19, Asp27 and Glu43) and basic residues (Lys13, Lys29, Lys34, His52 and Lys55) of the turkey ovomucoid third domain (OMTKY3) protein. The overall average unsigned error in the pKa values of the acid residues was found to be 0.37pH units and the basic residues was 0.38 pH units compared to 0.58pH units and 0.72 pH units calculated previously using polarizable force field (PFF) and Poisson Boltzmann formalism (PBF) continuum solvation model. These results are produced with fitting of specific atoms of the reference systems and carboxylic and basic residues of the OMTKY3 protein. Since FB model has produced improved pKa shifts of carboxylic residues and basic protein residues in OMTKY3 protein compared to PBF/PFF, it suggests the methodology of first-order FB continuum solvation model works well in such calculations. In this study the importance of explicit treatment of the electrostatic polarization in calculating pKa of both acid and basic protein residues is also emphasized. Moreover, the presented results demonstrate not only the consistently good degree of accuracy of protein pKa calculations with the second-degree POSSIM approximation of the polarizable calculations and the first-order approximation used in the Fuzzy-Border model for the continuum solvation energy, but also a high degree of transferability of both the POSSIM and continuum solvent Fuzzy Border parameters. Therefore, the FB model of solvation combined with the POSSIM force field can be successfully applied to study the protein and protein-ligand systems in water

Progress in the Prediction of pKa Values in Proteins

The pKa-cooperative aims to provide a forum for experimental and theoretical researchers interested in protein pKa values and protein electrostatics in general. The first round of the pKa-cooperative, which challenged computational labs to carry out blind predictions against pKas experimentally determined in the laboratory of Bertrand Garcia-Moreno, was completed and results discussed at the Telluride meeting (July 6–10, 2009). This article serves as an introduction to the reports submitted by the blind prediction participants that will be published in a special issue of PROTEINS: Structure, Function and Bioinformatics. Here, we briefly outline existing approaches for pKa calculations, emphasizing methods that were used by the participants in calculating the blind pKa values in the first round of the cooperative. We then point out some of the difficulties encountered by the participating groups in making their blind predictions, and finally try to provide some insights for future developments aimed at improving the accuracy of pKa calculations