Spherical Crystallography: Virus Buckling and the Folding of Pollen Grains

NBI Lecture by David R. Nelson

Abstract: The difficulty of constructing ordered states on spheres was recognized by J. J. Thomson, who discovered the electron and then attempted regular tilings of the sphere in an ill-fated attempt to explain the periodic table.
We discuss how protein packings in virus shells solve a related "Thomson problem", and the remarkable modifications in the theory necessary to account for grain boundary scars in colloidal particles packed on spheres.
We then apply related ideas to the folding strategies and shapes of pollen grains during dehydration when they are released from the anther after maturity. The grain can be modeled as a pressurized high-Young-modulus sphere with a weak sector and a nonzero spontaneous curvature. In the absence of such a weak sector, these shells crumple irreversibly under pressure via a strong first order phase transition. The weak sectors (both one and three-sector pollen grains are found in nature) eliminate the hysteresis and allow easy re-hydration at the pollination site, somewhat like the collapse and subsequent reassembly of a folding chair.

About the speaker:  David Nelson has through 25 years been one of the leading physicists in the world in the fields of statistical mechanics and complex systems. Already during his Ph.D. he proposed a new phase for the melting of two-dimensional systems, the socalled "hexatic phase". On the basis of this work he was hired as a professor at Harvard University, where he became tenured at the age of 26 - one of the youngest professors ever at Harvard! During the last decades Prof. Nelson has contributed to theoretical physics with one fundamental work after the other in a broad variety of fields, like polymers, flux-lines in super conductors, molecular motors, unzipping of DNA and population genetics - just to mention a few. Prof. Nelson has published more than 250 scientific papers and is very highly cited.