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Seminars in Mechanics and Materials

Sponsored by
UCSD Department of Mechanical and Aerospace Engineering

11:00 - 12:00, Monday, December 3, 2007

CMRR Auditorium

# Lessons on Structure from the Structure of Viruses

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RICHARD D. JAMES

Russell J. Penrose Professor and
Distinguished McKnight University Professor

Department of Aerospace Engineering and Mechanics

University of Minnesota

# Abstract

**
As the most primitive organisms, occupying the gray area between the
living and nonliving, viruses are the least complex biological
system. One can begin to think about them in a quantitative way,
while still being at some level faithful to biochemical processes.
We make some observations about their structure, formalizing in
mathematical terms some rules-of-construction discovered by Watson
and Crick and Caspar and Klug. We call the resulting structures
objective structures. It is then seen that objective structures
include many of the most important structures studied in science
today: carbon nanotubes, the capsids, necks, tails and other parts
of many viruses, the cilia of some bacteria, DNA octahedra,
buckyballs, actin and collagen and many other common proteins, and
numerous atomic-scale rods, springs and wires now being synthesized.
Objective structures also have an intriguing relation to the
crystalline and noncrystalline structures adopted by elements in the
Periodic Table. The rules defining them relate to the basic
invariance group of quantum mechanics. We develop a methodology for
computing such structures. Some of the nonperiodic structures
revealed by the formulas exhibit beautifully subtle relations of
symmetry. This common mathematical structure paves the way toward
many interesting calculations for such structures: the likelihood of
unusual electromagnetic and other collective properties, simplified
schemes for exact molecular dynamics of such structures, phase
transformations between them, defects and failure, new x-ray methods
of determination of structure not relying on crystallization, and
their growth by self-assembly.
**