Last update, May 20, 2000

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General references on Shape languages :

• Connolly, Michael L. :
  • Molecular Surfaces: A Review, 1996.
• S. Hyde et al.:
  • The Language of Shape : The Role of Curvature in Condensed Matter: Physics, Chemistry, and Biology, 1997.

BibTeX references .

Web link.

This article reviews computations and visualizations of molecular surfaces. Emphasis is placed on the solvent-accessibility ideas of Lee and Richards (1971) and the work that grew out of them. There is also some material on physical molecular models, X-ray crystallography, molecular graphics, and rational drug design. Other molecular surface review articles include (Richards, 1977; Max 1983; Max, 1984; Richards, 1985a; Mezey, 1990). The last web page of this article contains an extensive bibliography going back to the early molecular modeling work of the 1960's.

Editorial Review

Book News, Inc.

Develops the thesis that structure and function in a variety of condensed systems can be unified when curvature and surface geometry are taken together with molecular shape and forces. Contains chapters on the mathematics of curvature, organic and inorganic chemistry, molecular forces and self-assembly, lipid self-assembly and function in biological systems, folding and function in proteins and DNA, cytomembranes and cubic membrane systems, and miscellaneous speculations. Of interest to those in the physical and biological sciences. -- Copyright © 1999 Book News, Inc., Portland, OR All rights reserved

• Chapter 1 The Mathematics of Curvature
  • 1.1 Introductory remarks
  • 1.2 Curvature
  • 1.3 Differential geometry of surfaces
  • 1.4 The Gauss map
  • 1.5 Geodesic curvature and geodesics
  • 1.6 Torsion
  • 1.7 The Gauss-Bonnet theorem
  • 1.8 Topology
  • 1.9 A provisional catalogue of surface forms
  • 1.10 A historical perspective
  • 1.11 Periodic minimal surfaces
  • 1.12 The Bonnet transformation: the P-surface, the D-surface and the gyroid
  • 1.13 Parallel surfaces
  • 1.14 Future directions
  • Appendix: A catalogue of some minimal surfaces
  • Mathematical Bibliography
  • References
• Chapter 2 The Lessons of Chemistry
  Inorganic Chemistry: From the discrete lattice of crystal symmetry to the continuous manifolds of differential geometry
  • 2.1 The background
  • 2.2 The unravelling of complex structures
  • 2.3 Defects
  • 2.4 The intrinsic curvature of solids
  • 2.5 Hydrophobic zeolites and adsorption
  • 2.6 Phase transitions, order and disorder
  • 2.7 Quantitative analysis of hyperbolic frameworks: silicate densities
  • 2.8 Tetrahedral frameworks: Three-or two-dimensional structures?
  • 2.9 Quasicrystals Organic Chemistry: The Shape of Molecules
  • 2.10 The hyperbolic nature of sp(3) orbitals
  • 2.11 Organic sculptures: carcerands, crowns, etc.
  • 2.12 Beyond graphite: fullerenes and schwarzites
  • Appendix: The problem of quasicrystals
  • References
• Chapter 3 Molecular Forces and Self-Assembly
  • 3.1 The background
    • 3.2.1 The nature of force, shape and size
    • 3.2.2 Self-energy, molecular size and shape
    • 3.2.3 Self-energy and adsorption
    • 3.2.4 The shape of bonds
  • 3.3 The background to surface forces
  • 3.4 Molecular forces in detail
    • 3.4.1 van der Waals forces
    • 3.4.2 Lifshitz forces
    • 3.4.3 Double-layer forces
  • 3.5 A gallimaufry of forces
    • 3.5.1 Forces due to liquid structure
    • 3.5.2 Surface-induced liquid structure
    • 3.5.3 Hydration forces in phospholipids
    • 3.5.4 Surface dipole correlations
    • 3.5.5 Secondary hydration forces and ion-binding
    • 3.5.6 Range of the double-layer force and implications
    • 3.5.7 Hydrophobic interactions
    • 3.5.8 Non-ionic surfactant forces
    • 3.5.9 Forces of thermodynamic origin
    • 3.5.10 The Helfrich force
    • 3.5.11 Forces of very long range
    • 3.5.12 Summary
  • 3.6 Self-organisation in surfactant solutions
    • 3.6.1 Aggregate structure in the Euclidean desert
    • 3.6.2 Curvature as the determinant of microstructure
    • 3.6.3 Genesis of the surfactant parameter
    • 3.6.4 The tyranny of theory
  • Appendix A: Evolution of concepts on long range molecular forces responsible for organisation and interactions in colloidal systems
  • Appendix B: Modern concepts of self-assembly
  • Appendix C: Remarks on the nature of the hydrophobic interaction and water structure
  • References
• Chapter 4 Beyond Flatland The Geometric Forms due to Self-Assembly
  • 4.1 Introduction: molecular dimensions and curvature
  • 4.2 The local geometry of aggregates
  • 4.3 The composition of surfactant mixtures: the global constraint
  • 4.4 Bilayers in surfactant-water mixtures
  • 4.5 Monolayers in surfactant-water mixtures
  • 4.6 Geometrical physics: bending energy
  • 4.7 The mesophase behaviour of surfactant-and lipid-water mixtures
  • 4.8 The hyperbolic realm: cubic and intermediate phases
  • 4.9 Mesostructure in ternary surfactant-water-oil systems: microemulsions
  • 4.10 Block copolymer melts: an introduction
  • 4.11 Copolymer self-assembly
  • 4.12 Relation between material properties and structure
  • 4.13 Protein assemblies in bacteria: a mesh phase
  • 4.14 Self-assembly of chiral molecules
  • References
• Chapter 5 Lipid Self-Assembly and Function In Biological Systems
  • 5.1 Self-association of lipids in an aqueous environment
    • 5.1.1 Introduction
    • 5.1.2 General behaviour of lipids in water
    • 5.1.3 Cubic phases
    • 5.1.4 Cubic lipid-protein-water phases
    • 5.1.5 Dispersions of bicontinuous cubic phases: cubosomes
    • 5.1.6 Liposomal dispersions
    • 5.1.7 Vesicles and membranes
    • 5.1.8 Cholesteric liquid-crystals and low-density lipoprotein structures
  • 5.2 Cell membranes
    • 5.2.1 Introduction
    • 5.2.2 On intrinsic periodic bilayer curvature in membrane function: A model membrane bilayer phase transition involving periodic curvature
    • 5.2.3 Lipid composition control in membranes
    • 5.2.4 The nerve membrane, signal transmission and anaesthesia Bilayer conformation during the action potential Anaesthetic effects
    • 5.2.5 Anaesthetic agents and cancer, immunosuppression
    • 5.2.6 On the metastatic mechanism of malignant cells
    • 5.2.7 Membranes in micro-organisms and anti-microbial agents
    • 5.2.8 Plant cell membranes
    • 5.2.9 The C(2D) conformation and membrane fusion
    • 5.2.10 Membranes encapsulating oil/fats and biliquid foams
    • 5.2.11 Sugar groups, receptor-ligand binding and cooperativity
    • 5.2.12 A C(2D) membrane structure in a Streptomyces strain
  • References
• Chapter 6 Folding and Function In Proteins and DNA
  • 6.1 Overall features of protein structure
  • 6.2 XXX-helix domains
  • 6.3 XXX-helix / XXX-sheet domains
  • 6.4 XXX-sheet domains
  • 6.5 Membrane proteins
  • 6.6 Enzymatic action
  • 6.7 Protein function and dioxin poisoning
  • 6.8 Geometry in hormone-receptor interactions
  • 6.9 Self / non-self recognition
  • 6.10 DNA folding
  • 6.11 Self-assembly and crystallisation of proteins
  • References
• Chapter 7 Cytomembranes and Cubic Membrane Systems Revisited
  • 7.1 Membrane organisation
  • 7.2 Recognition of hyperbolic periodic cytomembrane morphologies in electron microscopic sections
  • 7.3 The structure and occurrence of cubic membranes
  • 7.4 Cubic membranes in unicellular organisms: prokaryotes and protozoa
  • 7.5 Cubic membranes in plants
  • 7.6 Cubic membranes in fungi
  • 7.7 Cubic membranes in metazoa
  • 7.8 Relationships betweentubuloreticular structures, annulate lamellae, and cubic membranes
  • 7.9 Biogenesis of cubic membranes
  • 7.10 Relationships between cubic membranes and cubic phases
  • 7.11 Functionalities of cubic membranes
  • 7.12 Cell space organisation and topology
  • 7.13 Specific structure-function relations
  • Abbreviations
  • References
• Chapter 8 Some Miscellaneous Speculations
  • 8.1 Templating
    • 8.1.1 Templating and curvature: DNA templating
    • 8.1.2 Templating by electric fields: equipotential and tangential field surfaces
    • 8.1.3 Diffusion within fast-ion conductors
    • 8.1.4 The templating of zeolites
    • 8.1.5 Templating organic molecules: the caesium effect
    • 8.1.6 Templating of the morphology of a calcite crystal
  • 8.2 Supra self-assembly
    • 8.2.1 Biological superstructures based on self-assembly
    • 8.2.2 Collagen and plant cell walls
    • 8.2.3 The molecular packing in native starch
    • 8.2.4 Saddles in the kitchen: bread from wheat flour
    • 8.2.5 Muscle contraction
  • 8.3 The origin of life: a role for cubosomes?
  • 8.4 A final word
  • References
  • Index

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