Comparison of the MSMS and NanoShaper molecular surface triangulation codes in the TABI Poisson-Boltzmann solver

Bridging Eulerian and Lagrangian Poisson-Boltzmann solvers by ESES

The Poisson-Boltzmann (PB) model is a widely used electrostatic model for biomolecular solvation analysis. Formulated as an elliptic interface problem, the PB model can be numerically solved on either Eulerian meshes using finite difference/finite element methods or Lagrangian meshes using boundary element methods. Molecular surface generators, which produce the discretized dielectric interfaces between solutes and solvents, are critical factors in determining the accuracy and efficiency of the PB solvers. In this work, we investigate the utility of the Eulerian Solvent Excluded Surface (ESES) software for rendering conjugated Eulerian and Lagrangian surface representations, which enables us to numerically validate and compare the quality of Eulerian PB solvers, such as the MIBPB solver, and the Lagrangian PB solvers, such as the TABI-PB solver. Furthermore, with the ESES software and its associated PB solvers, we are able to numerically validate an interesting and useful but often neglected source-target symmetric property associated with the linearized PB model.

Arbitrary-Shape Dielectric Particles Interacting in the Linearized Poisson-Boltzmann Framework: An Analytical Treatment

This work considers the interaction of two dielectric particles of arbitrary shape immersed into a solvent containing a dissociated salt and assuming that the linearized Poisson-Boltzmann equation holds. We establish a new general spherical re-expansion result which relies neither on the conventional condition that particle radii are small with respect to the characteristic separating distance between particles nor on any symmetry assumption. This is instrumental in calculating suitable expansion coefficients for the electrostatic potential inside and outside the objects and in constructing small-parameter asymptotic expansions for the potential, the total electrostatic energy, and forces in ascending order of Debye screening. This generalizes a recent result for the case of dielectric spheres to particles of arbitrary shape and builds for the first time a rigorous (exact at the Debye-Hückel level) analytical theory of electrostatic interactions of such particles at arbitrary distances. Numerical tests confirm that the proposed theory may also become especially useful in developing a new class of grid-free, fast, highly scalable solvers.

TABI-PB 2.0: An Improved Version of the Treecode-Accelerated Boundary Integral Poisson-Boltzmann Solver

This work describes TABI-PB 2.0, an improved version of the treecode-accelerated boundary integral Poisson-Boltzmann solver. The code computes the electrostatic potential on the molecular surface of a solvated biomolecule, and further processing yields the electrostatic solvation energy. The new implementation utilizes the NanoShaper surface triangulation code, node-patch boundary integral discretization, a block preconditioner, and a fast multipole method based on barycentric Lagrange interpolation and dual tree traversal. Performance-critical portions of the code were implemented on a GPU. Numerical results for protein 1A63 and two viral capsids (Zika, H1N1) demonstrate the code's accuracy and efficiency.

Probabilistic Pocket Druggability Prediction via One-Class Learning

The choice of target pocket is a key step in a drug discovery campaign. This step can be supported by in silico druggability prediction. In the literature, druggability prediction is often approached as a two-class classification task that distinguishes between druggable and non-druggable (or less druggable) pockets (or voxels). Apart from obvious cases, however, the non-druggable class is conceptually ambiguous. This is because any pocket (or target) is only non-druggable until a drug is found for it. It is therefore more appropriate to adopt a one-class approach, which uses only unambiguous information, namely, druggable pockets. Here, we propose using the import vector domain description (IVDD) algorithm to support this task. IVDD is a one-class probabilistic kernel machine that we previously introduced. To feed the algorithm, we use customized DrugPred descriptors computed via NanoShaper. Our results demonstrate the feasibility and effectiveness of the approach. In particular, we can remove or mitigate biases chiefly due to the labeling.