Connections have been growing recently between the molecular modeling
community and the computational geometry. Many questions in molecular
modeling can be understood geometrically in terms of arrangements of
spheres in three dimensions. Problems include computing properties of
such arrangements such as their volume and topology, testing
intersections and collisions between molecules, finding offset surfaces
(related to questions of accessability of molecule subregions to
solvents such as water), data structures for computing interatomic
forces and performing molecular dynamics simulations, and
algorithms for rendering molecular models
accurately and efficiently (taking advantage of their special geometric
structure). Classical molecular modeling has dealt with biological
molecules which generally have a tree-like structure, but applications
to nanotechnology require dealing with more complicated diamond-like
structures; it is unclear to what extent this affects the relevant
- Algorithms for finding the axis of a helix, J. Christopher, R. Swanson, and T. Baldwin.
The authors use this problem to detect structural patterns in protein
shapes, defined by H. Edelsbrunner and others at U. Illinois,
provide a useful algorithmic tool for modeling shapes,
especially those formed by unions of spheres.
Art Gallery. Molecular visualization pointers from L. Laaksonen,
Center for Scientific Computation, Finland.
- Computational Topology.
Survey paper by Dey, Edelsbrunner, and Guha, presented at the conference
"Computational Geometry -- Ten Years After". Includes descriptions of
applications in image processing, cartography, graphics, solid modeling,
mesh generation, and molecular modeling.
Worksh. on Geometrical Methods for Conformational Modeling,
Aug. 1995. Program and talk abstracts.
algorithms in biology and chemistry (in German). Molecular modeling
and related projects at the German Nat. Res. Ctr. for Inf. Tech.,
Inst. for Algorithms and Scientific Computing.
hierarchical methods for the n-body problem, CS 267, Berkeley, 1995.
- Geometric aspects of protein structure, Duke U.
computer graphics for molecular studies, UNC.
- Molecular Geometry References, D. Abrahams-Gessel, Dartmouth.
- Nanotechnology, Ralph Merkle, Xerox PARC.
- Nanotechnology and molecular modeling on the WWW,
- Network Science: computational chemistry.
- The NIH Molecular
Modeling home page. (Warning: lots of incredibly annoying cookies.)
n-body simulations using hierarchical octree representations of space.
secondary structure assignment through Voronoi tesselation,
Dupuis, Sadoc, and Mornon.
- Prove protein volume evaluation software. This project at the
Free University of Brussels
uses Voronoi diagrams and weighted Voronoi diagrams to
analyze the portion of a molecule's volume taken up
by each atom in the molecule.
Mark Gerstein at Stanford has a directory with
very similar software and related papers.
molecular modeling toolkit, Shastra project, U. Texas.
- Michel Sanner of Scripps studies algorithms for molecular modeling,
and published a paper on molecular surface accessability
at the 11th ACM Symp. Comp. Geom.
proteins, and rho. In the talk announced here, J. MacGregor Smith
discusses Euclidean Steiner tree theory and describes potential
applications of Steiner trees to protein conformation and molecular
- SMART: A
solvent-accessible triangulated surface generator for molecular graphics
and boundary element applications, R. J. Zauhar,
J. Computer-Aided Molecular Design 9 (1995) 149-159.
Geometry of Protein Structure. I. Vaisman performs statistical analysis
on Delaunay triangulations of protein atoms to find preferred clusters
of amino acids.
Well-Separated Pair Decomposition and its Applications,
Paul Callahan's Johns Hopkins Ph.D. thesis
on hierarchical space decomposition
and its applications to n-body simulation.
Geometry in Action,
a collection of applications of computational geometry.
from a common source file.