Bloch spin waves and emergent structure in protein folding with HIV envelope glycoprotein as an example

Abstract: We inquire how structure emerges during the process of protein folding. For this we scrutinise col- lective many-atom motions during all-atom molecular dynamics simulations. We introduce, develop and employ various topological techniques, in combination with analytic tools that we deduce from the concept of integrable models and structure of discrete nonlinear Schroedinger equation. The example we consider is an alpha-helical subunit of the HIV envelope glycoprotein gp41. The helical structure is stable when the subunit is part of the biological oligomer. But in isolation the helix becomes unstable, and the monomer starts deforming. We follow the process computationally. We interpret the evolving structure both in terms of a backbone based Heisenberg spin chain and in terms of a side chain based XY spin chain. We find that in both cases the formation of protein super-secondary structure is akin the formation of a topological Bloch domain wall along a spin chain. During the process we identify three individual Bloch walls and we show that each of them can be modelled with a very high precision in terms of a soliton solution to a discrete nonlinear Schroedinger equation.