Mathematical Approaches to Biomolecular Structure and Dynamics

1. Front Matter

   Pages i-x

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2. Biomolecular Topology

   1. Tangle Complexity and the Topology of the Chinese Rings

      • Louis H. Kauffman

      Pages 1-10

   2. Lattice Invariants for Knots

      • E. J. Janse Van Rensburg

      Pages 11-20

   3. Topology and Geometry of Biopolymers

      • E. J. Janse van Rensburg, Enzo Orlandini, De Witt Sumners, M. Carla Tesi, Stuart G. Whittington

      Pages 21-37

   4. Energy Functions for Knots: Beginning to Predict Physical Behavior

      • Jonathan Simon

      Pages 39-58

3. Biomolecular Structure and Dynamics: Theory

   1. The Elastic Rod Provides a Model for DNA and Its Functions

      • John E. Hearst, Yaoming Shi

      Pages 59-70

   2. Hamiltonian Formulations and Symmetries in Rod Mechanics

      • Donald J. Dichmann, Yiwei Li, John H. Maddocks

      Pages 71-113

   3. Statistical Mechanics of Supercoiled DNA

      • John F. Marko, Eric D. Siggia

      Pages 115-116

   4. Determination of the DNA Helical Repeat and of the Structure of Supercoiled DNA by Cryo-Electron Microscopy

      • Andrzej Stasiak, Jan Bednar, Patrick Furrer, Vsevolod Katritch, Jacques Dubochet

      Pages 117-138

   5. Dynamics of Twist and Writhe and the Modeling of Bacterial Fibers

      • Michael Tabor, Isaac Klapper

      Pages 139-159

4. Biomolecular Structure and Dynamics: Computation

   1. Integration Methods for Molecular Dynamics

      • Benedict J. Leimkuhler, Sebastian Reich, Robert D. Skeel

      Pages 161-185

   2. On the Parallelization of CHARMM on the CM-5/5E

      • Jill P. Mesirov, Pablo Tamayo, Robert J. Nagle

      Pages 187-194

   3. Computational Studies of Spatially Constrained DNA

      • Wilma K. Olson, Timothy P. Westcott, Jennifer A. Martino, Guo-Hua Liu

      Pages 195-217

   4. Pursuing Laplace’s Vision on Modern Computers

      • Tamar Schlick

      Pages 219-247

5. Back Matter

   Pages 248-253

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This IMA Volume in Mathematics and its Applications MATHEMATICAL APPROACHES TO BIOMOLECULAR STRUCTURE AND DYNAMICS is one of the two volumes based on the proceedings of the 1994 IMA Sum­ mer Program on "Molecular Biology" and comprises Weeks 3 and 4 of the four-week program. Weeks 1 and 2 appeared as Volume 81: Genetic Mapping and DNA Sequencing. We thank Jill P. Mesirov, Klaus Schulten, and De Witt Sumners for organizing Weeks 3 and 4 of the workshop and for editing the proceedings. We also take this opportunity to thank the National Institutes of Health (NIH) (National Center for Human Genome Research), the National Science Foundation (NSF) (Biological Instrumen­ tation and Resources), and the Department of Energy (DOE), whose fi­ nancial support made the summer program possible. A vner Friedman Robert Gulliver v PREFACE The revolutionary progress in molecular biology within the last 30 years opens the way to full understanding of the molecular structures and mech­ anisms of living organisms. Interdisciplinary research in mathematics and molecular biology is driven by ever growing experimental, theoretical and computational power. The mathematical sciences accompany and support much of the progress achieved by experiment and computation as well as provide insight into geometric and topological properties of biomolecular structure and processes. This volume consists of a representative sample of the papers presented during the last two weeks of the month-long Institute for Mathematics and Its Applications Summer 1994 Program in Molecular Biology.

• DNA
• DNA sequencing
• Termination
• biology
• electron microscopy
• genome
• molecular biology

• Computer Science Department, Boston University, Boston, USA

  Jill P. Mesirov

• Beckman Institute, Theoretical Biophysics Group, University of Illinois, Urbana, USA

  Klaus Schulten

• Department of Mathematics, Florida State University, Tallahassee, USA

  De Witt Sumners

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