We describe a chain of algorithms for molecular surface and volumetric mesh generation. We take as inputs the centers and radii of all atoms of a molecule and the toolchain outputs both triangular and tetrahedral meshes that can be used for molecular shape modeling and simulation. Experiments on a number of molecules are demonstrated, showing that our methods possess several desirable properties: feature-preservation, local adaptivity, high quality, and smoothness (for surface meshes). We also demonstrate an example of molecular simulation using the finite element method and the meshes generated by our method. The approaches presented and their implementations are also applicable to other types of inputs such as 3D scalar volumes and triangular surface meshes with low quality, and hence can be used for generation/improvment of meshes in a broad range of applications.

with depth cues (Depth Darkening [24] and fogging). Right: Surface colored according to the temperature factor of the protein with silhouettes. Abstract—Molecular dynamics simulations of proteins play a growing role in various fields such as pharmaceutical, biochemical and medical research. Accordingly, the need for high quality visualization of these protein systems raises. Highly interactive visualization techniques are especially needed for the analysis of time-dependent molecular simulations. Beside various other molecular representations the surface representations are of high importance for these applications. So far, users had to accept a trade-off between rendering quality and performance—particularly when visualizing trajectories of time-dependent protein data. We present a new approach for visualizing the Solvent Excluded Surface of proteins using a GPU ray casting technique and thus achieving interactive frame rates even for long protein trajectories where conventional methods based on precomputation are not applicable. Furthermore, we propose a semantic simplification of the raw protein data to reduce the visual complexity of the surface and thereby accelerate the rendering without impeding perception of the protein’s basic shape. We also demonstrate the application of our Solvent Excluded Surface method to visualize the spatial probability density for the protein atoms over the whole period of the trajectory in one frame, providing a qualitative analysis of the protein flexibility.

Abstract. The Poisson-Boltzmann equation is a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. Significant efforts have been devoted to accurate and efficient computation for solving this equation. In this paper, we developed a boundary element framework based on the linear time fast multipole method for solving the linearized Poisson-Boltzmann equation. A higher-order parametric formulation called algebraic spline model is used for accurately approximation of the unknown solution of the linearized Poisson-Boltzmann equation. The numerical test and experimental results show that these techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules. 1. Introduction. Accurate

We present a variational approach to smooth molecular (proteins, nucleic acids) surface constructions, starting from atomic coordinates, as available from the protein and nucleicacid data banks. Molecular dynamics (MD) simulations traditionally used in understanding protein and nucleic-acid folding processes, are based on molecular force fields, and require smooth models of these molecular surfaces. To accelerate MD simulations, a popular methodology is to employ coarse grained molecular models, which represent clusters of atoms with similar physical properties by psuedo- atoms, resulting in coarser resolution molecular surfaces. We consider generation of these mixed-resolution or adaptive molecular surfaces. Our approach starts from deriving a general form second order geometric partial differential equation in the level-set formulation, by minimizing a first order energy functional which additionally includes a regularization term to minimize the occurrence of chemically infeasible molecular surface pockets or tunnel-like artifacts. To achieve even higher computational efficiency, a fast cubic B-spline C 2 interpolation algorithm is also utilized. A narrow band, tri-cubic B-spline level-set method is then used to provide C 2 smooth and resolution adaptive molecular surfaces.

Abstract. The total free energy of a molecule includes the classical molecular mechanical energy (which is understood as the free energy in vacuum) and the solvation energy which is caused by the change of the environment of the molecule (solute) from vacuum to solvent. The solvation energy is important to the study of the inter-molecular interactions. In this paper we develop a fast surface-based generalized Born method to compute the electrostatic solvation energy along with the energy derivatives for the solvation forces. The most time-consuming computation is the evaluation of the surface integrals over an algebraic spline molecular surface (ASMS) and the fast computation is achieved by the use of the nonequispaced fast Fourier transform (NFFT) algorithm. The main results of this paper involve (a) an efficient sampling of quadrature points over the molecular surface by using nonlinear patches, (b) fast linear time estimation of energy and inter-molecular forces, (c) error analysis, and (d) efficient implementation combining fast pairwise summation and the continuum integration using nonlinear patches.