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Patrice Koehl's research web site

Room 4319, Genome Center, GBSF
University of California Davis
451 East Health Sciences Drive
Davis, CA 95616

(530) 754 5121 phone
(530) 754 9658 fax

> Xinwei Shi, Ph. D.

# Shi Xinwei (时新伟)

### Postdocotal Researcher

Genome Center

Room 4337, Genome Center, GBSF

451 East Health Sciences Drive

University of California

Davis, CA 95616

Phone: (530) 754 9738

xshi@ucdavis.edu

## Biographical Information

2006 - present, Postdoctoral Researcher, Genome Center, University of California, Davis

2002 - 2005 PH.D, Computer Science Department, National University of Singapore

2000 - 2002, Software Engineer, Huawei Technology

1994 - 2000, B.S and M.S, Department of Computer Science and Engineering, Harbin Institute of Technology

## Research

My primary research interests are mesh generation, computational geometry and computational structure biology. I developed algorithms and software for generating high quality surface and volumetric meshes for the biomolecules using the skin surface shape representations. Recently, I am working on the computation of electrostatic potentials for proteins and RNA by solving the Poisson Boltzmann Equation with Finite Element methods based on unstructured meshes. I am also working on the modeling of non-polar solvation energy of biomolecules using the surface area and volume of molecular skin surfaces. I am also part of the project that study of protein-protein interaction using an integrated approach combing Mathematics, Computational Geometry and structure biology.

## Software

##### Skin Meshing Software
Skin meshing software can construct high quality surface meshes and volumetric meshes with different resolutions. The input is the coordinates of the center and radii of a set of spheres. The software also can import the pdb files. The outputs are the triangular and tetrahedral meshes with guaranteed quality for the skin surface specified by the set of spheres or the molecular skin model of the input pdb file.

The software is based on a Delaunay based meshing algorithm using restricted union of balls  which is described in the papers in the publication part. A Windows version is available at software page for download. The latest Linux version with PBE solver will be released in the near future

## Publications

###### Submitted to Journal of Mathematical Biology

Years of research in biology have established that all cellular functions are deeply connected to the shape and dynamics of their molecular actors. In particular, the function of most biomolecules is fully defined by their shapes, as it is the geometry of their surfaces that defines their connections with the environment as well as the specificity of their interactions. In this paper, we focus on the representation of biomolecules and on the definitions of their surface. We cover the four major models used to define the surface of a molecule represented as a union of hard-sphere balls, namely the vdW model, the accessible surface model, the molecular surface model and the skin surface. We review the geometric and topological properties associated with these four models,as well as the methods that have been derived for computing measures of the surfaces they define. Specifically, we describe a few numerical and analytical methods that compute the area of a biomolecular surface and the volume it encloses, including our own algorithms. We apply these methods on a database of 51 high resolution protein domains. We fined that the areas and volumes of the four types of biomolecular surfaces considered correlate well with molecular weight. The vdW surface model is found to be uninformative, as it is directly proportional to the molecular weight. The power laws observed for the three other models reveal their ability to detect overlaps and voids in the structure. While the skin surface has better geometric properties (it is smooth and devoid of the singularities that can be observed in the other models), it is not clear at this stage that it is better for biomolecular modeling.

###### submitted to Computer Aided Geometric Design

In this paper, we present efficient algorithms for generating hierarchical molecular skin meshes with decreasing size and guaranteed quality. Our algorithms generate a sequence of coarse meshes for both the surface and the bounded volumes. Each coarser surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface with guaranteed mesh quality. The corresponding tetrahedral mesh is conforming to the interface surface mesh and contains high quality tetrahedra that decompose both the interior of the molecule and the surrounding region (enclosed in a sphere). Our hierarchical tetrahedral meshes have a number of advantages that will facilitate fast and accurate multigrid PDE solvers. Firstly, the quality of both the surface triangulations and tetrahedral meshes is guaranteed. Secondly, the interface in the tetrahedral mesh is an accurate approximation of the molecular boundary. In particular, all the boundary points lie on the skin surface. Thirdly, our meshes are Delaunay meshes. Finally, the meshes are adaptive to the geometry.

###### COMMUNICATIONS IN COMPUTATIONAL PHYSICS Vol. 3, No. 5, pp. 1032-1050

Electrostatics interactions play a major role in the stabilization of biomolecules: as such, they remain a major focus of theoretical and computational studies in biophysics. Electrostatics in solution is strongly dependent on the nature of the solvent and on the ions it contains. While methods that treat the solvent and ions explicitly provide an accurate estimate of these interactions, they are usually computationally too demanding to study large macromolecular systems. Implicit solvent methods provide a viable alternative, especially those based on Poisson theory. The Poisson-Boltzmann equation (PBE) treats the system in a mean field approximation, providing reasonable estimates of electrostatics interactions in a solvent treated as continuum. In the first part of this paper, we review the theory behind the PBE, including recent improvement in which ions size and dipolar features of solvent molecules are taken into account explicitly. The PBE is a non linear second order differential equation with discontinuous coefficients, for which no analytical solution is available for large molecular systems. Many numerical solvers have been developed that solve a discretized version of the PBE on a mesh, either using finite difference, finite element, or boundary element methods. The accuracy of the solutions provided by these solvers highly depend on the geometry of their underlying meshes, as well as on the method used to embed the physical system on the mesh. In the second part of the paper, we describe a new geometric approach for generating unstructured tetrahedral meshes as well as simplifications of these meshes that are well fitted for solving the PBE equation using multigrid approaches.

###### Fall Workshop on Computational Geometry 2009

In this paper, we propose a new method for computing the geometric measures of biomolecules using skin surfaces to represent their shapes. Specifically, we give the formulas for measuring the total area A and volume V of the skin surface defined by n weighted points, as well as the contributions of the individual points to A and V.

###### Computer Graphics International 2009

In this paper, we present a novel surface meshes coarsening algorithm for generating hierarchical skin surface meshes with decreasing size and guaranteed quality. Each coarse surface mesh is adaptive to the surface curvature and maintains the topology of the skin surface as well.

###### IEEE Visualization 2005

Quality surface meshes for molecular models are desirable in the studies of protein shapes and functionalities. However, there is still no robust software that is capable to generate such meshes with good quality. In this paper, we present a Delaunay-based surface triangulation algorithm generating quality surface meshes for the molecular skin model. We expand the restricted union of balls along the surface and generate an $\varepsilon$-sampling of the skin surface incrementally. At the same time, a quality surface mesh is extracted from the Delaunay triangulation of the sample points. The algorithm supports robust and efficient implementation and guarantees the mesh quality and topology as well. Our results facilitate molecular visualization and have made a contribution towards generating quality volumetric tetrahedral meshes for the macromolecules.

###### IEEE Visualization 2004,

We present an efficient algorithm to mesh the macromolecules surface model represented by the skin surface defined by Edelsbrunner. Our algorithm overcomes several challenges residing in current surface meshing methods. First, we guarantee the mesh quality with a provable lower bound of 21◦ on its minimum angle. Second, we ensure the triangulation is homeomorphic to the original surface. Third, we improve the efficiency of constructing the Restricted Delaunay Triangulation(RDT) of smooth surfaces. We achieve this by constructing the RDT using the advancing front method without computing the Delaunay tetrahedrization of the sample points on the surfaces. The difficulty of handling the front collision problem is tackled by employing the Morse theory. In particular, we construct the Morse-Smale complex to simplify the topological changes of the front. Our implementation results suggest that the algorithm decrease the time of generating high quality homeomorphic skin mesh from hours to a few minutes.

###### Japan Conference on Discrete and Computational Geometry (JCDCG) 2004

We present an approach to define and extract the cavities on the surfaces of macromolecules. Each cavity is represented by a triangular mesh enclosing a depression on a molecule such as a protein and a DNA. These surface patches would facilitate the study of ligand docking problem and similarity matching of proteins.

###### International Conference on Image and Graphics 2000

In virtual environment, the integration of video images and computer graphics can produce a more convincing 3D-scene. This paper mainly discusses some key techniques about the application of camera-dependent-video as the background of real-time 3D-scene. We focus on the multi-layers windows display technology, camera-dependent-video playing, and control parameters passing. A framework of the realization and some experimental results are illustrated in the paper.