The shape of knots
Wednesday, October 3, 2007 - 11:15am - 12:15pm
What do the knots that occur in natural macromolecules look like? What about those arising in random equilateral spatial polygons such as those used to model DNA or polymers? The asphericity is a number between 1.0 and 0.0 that measures the degree to which the ellipsoid of inertia is more like a sausage (near 1.0), a rugby ball (near 0.5) or, a soccer ball (near 0.0). An analogous measure, the spatial asphericity, is defined by considering the smallest ellipsoid containing the knot. Computer simulations and examples of proteins will be used to illustrate these measures. Via the simulations, we will consider the influence of constrained topology on these measures in comparison to the unconstrained averages. In a continuation of earlier research, we will look at the equilibrium lengths defined by the asphericity, the lengths at with the constrained and unconstrained have equal values, and compare these with those determined earlier. We present computer simulations to examine the differences between the average asphericity of polygons with constrained and unconstrained topology.