UNIFORM SPACING MODELS FOR THE MORPHOGENESIS OF HIGH SYMMETRY BIOLOGICAL STRUCTURES: ICOSAHEDRAL CAPSIDS, COAXIAL HELICES, AND HELICAL PHYLLOTAXIS

The following sections are included:

• Introduction

• Mathematical Representation of Uniform Spacing Models

  • The Morphological Unit and the Interaction Function

  • Dynamic and Static Analyses

  • Informing Geometry, Forgetful Dynamics, and Morphogenesis

• Icosahedral Virus Capsids

• Coaxial Helices

  • Fourier Representation of Helical Symmetry: Subhelices

  • Optimally Interacting Coaxial Helices

• Simple Helices

  • The Unperturbed Helix

  • The Perturbed Helix

  • The Least Squares Fit and Gradient Dynamics

  • The Evolution of Σ²

  • The Evolution of Δφ

• Phyllotaxis

  • The Static Problem Via : Disk MUs

  • The Mixed Representation

  • as a Function of Δφ

  • The Numerical Evolution of the Mixed Representation Phyllotaxis Model

• Discussion

• Appendix

  • Fourier Coefficients for a Helically Symmetrical Field

  • Fourier Coefficients A_n for an Azimuthally Symmetrical MU

  • The Unperturbed Interaction

  • The Linear Perturbations

• Acknowledgements

• References