Atomic radius and charge parameter uncertainty in biomolecular solvation energy calculations

Atomic radii and charges are two major parameters used in implicit solvent electrostatics and energy calculations. The optimization problem for charges and radii is under-determined, leading to uncertainty in the values of these parameters and in the results of solvation energy calculations using these parameters. This paper presents a new method for quantifying this uncertainty in implicit solvation calculations of small molecules using surrogate models based on generalized polynomial chaos (gPC) expansions. There are relatively few atom types used to specify radii parameters in implicit solvation calculations; therefore, surrogate models for these low-dimensional spaces could be constructed using least-squares fitting. However, there are many more types of atomic charges; therefore, construction of surrogate models for the charge parameter space requires compressed sensing combined with an iterative rotation method to enhance problem sparsity. We demonstrate the application of the method by presenting results for the uncertainties in small molecule solvation energies based on these approaches. The method presented in this paper is a promising approach for efficiently quantifying uncertainty in a wide range of force field parameterization problems, including those beyond continuum solvation calculations.The intent of this study is to provide a way for developers of implicit solvent model parameter sets to understand the sensitivity of their target properties (solvation energy) on underlying choices for solute radius and charge parameters

Variational Methods for Biomolecular Modeling

Structure, function and dynamics of many biomolecular systems can be characterized by the energetic variational principle and the corresponding systems of partial differential equations (PDEs). This principle allows us to focus on the identification of essential energetic components, the optimal parametrization of energies, and the efficient computational implementation of energy variation or minimization. Given the fact that complex biomolecular systems are structurally non-uniform and their interactions occur through contact interfaces, their free energies are associated with various interfaces as well, such as solute-solvent interface, molecular binding interface, lipid domain interface, and membrane surfaces. This fact motivates the inclusion of interface geometry, particular its curvatures, to the parametrization of free energies. Applications of such interface geometry based energetic variational principles are illustrated through three concrete topics: the multiscale modeling of biomolecular electrostatics and solvation that includes the curvature energy of the molecular surface, the formation of microdomains on lipid membrane due to the geometric and molecular mechanics at the lipid interface, and the mean curvature driven protein localization on membrane surfaces. By further implicitly representing the interface using a phase field function over the entire domain, one can simulate the dynamics of the interface and the corresponding energy variation by evolving the phase field function, achieving significant reduction of the number of degrees of freedom and computational complexity. Strategies for improving the efficiency of computational implementations and for extending applications to coarse-graining or multiscale molecular simulations are outlined.Comment: 36 page

A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equation for neutral and ionic solutions, respectively. In the present work solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented to the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of a ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency, and allow for the treatment of different boundary conditions, as for example surface systems. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes

A Continuum Poisson-Boltzmann Model for Membrane Channel Proteins

Membrane proteins constitute a large portion of the human proteome and perform a variety of important functions as membrane receptors, transport proteins, enzymes, signaling proteins, and more. The computational studies of membrane proteins are usually much more complicated than those of globular proteins. Here we propose a new continuum model for Poisson-Boltzmann calculations of membrane channel proteins. Major improvements over the existing continuum slab model are as follows: 1) The location and thickness of the slab model are fine-tuned based on explicit-solvent MD simulations. 2) The highly different accessibility in the membrane and water regions are addressed with a two-step, two-probe grid labeling procedure, and 3) The water pores/channels are automatically identified. The new continuum membrane model is optimized (by adjusting the membrane probe, as well as the slab thickness and center) to best reproduce the distributions of buried water molecules in the membrane region as sampled in explicit water simulations. Our optimization also shows that the widely adopted water probe of 1.4 {\AA} for globular proteins is a very reasonable default value for membrane protein simulations. It gives an overall minimum number of inconsistencies between the continuum and explicit representations of water distributions in membrane channel proteins, at least in the water accessible pore/channel regions that we focus on. Finally, we validate the new membrane model by carrying out binding affinity calculations for a potassium channel, and we observe a good agreement with experiment results.Comment: 40 pages, 6 figures, 5 table

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