Folding and collapse in string-like structures
Seminar Room 1, Newton Institute
We argue that the the physics of folding and collapse of string-like structures can be described in terms of topological solitons. For this we use extrinsic geometry of filamental curves in combination of general geometrical arguments, to derive a universal form of energy function, which we propose is essentially unique. We then show that the ensuing equations of motion support topological solitons that are closely related to the solitons in the discrete nonlinear Schrodinger equation. We then argue that with proper parameters, a soliton supporting filament can describe proteins, which are mathematically one dimensional piecewise linear polygonal chains. As an example we show a movie of a simulation, how to model the folding of a medium length protein. The precision we reach is around 40 pico-meters root-mean-square distance form the experimentally constructed structure. Our result proposes that there are at least some 10^20 topological solitons in each human body.