A discrete-to-continuum model of protein complexes

Abstract

On the basis of a tensor representation of protein shape, obtained by an affine decomposition of residue velocity, we show how to identify actions at continuum scale for both single proteins and their complexes in terms of power equivalence. The approach constructs and justifies a continuum modeling of protein complexes, which avoids a direct, atomistic-based, simulation of the whole complex, rather it focuses (in a statistical sense) on a single protein and its interactions with the neighbors. In the resulting setting we also prove the existence of equilibrium configurations (native states) under large strains.

Homogenization of Complex Lattices for Metamaterials: Open Problems and Conjectures

“…The associated affine deformation gradient G, itself a function of x and t, is a solution to the equation Ġ = BG , with initial datum that can be selected equal to the second-rank identity tensor; the superposed dot indicates total time derivative. The resulting equations are such that the scheme is, in general, multi-field (compare [48] with [49,50] for different settings where these ideas apply). In the presence of internal constraints, the picture simplifies because the resulting balances collapse, reducing the equations (also depending on whether we consider fluctuations c := w * − v − By).…”

“…The affine component is chosen to be optimal with respect to the kinetic energy [47,48]; in other words, it minimizes a difference between the mass-point kinetic energy and the sum of the mass center and affine motion kinetic energies. In this case, although the prototypical discrete structure is taken as a simple, statistically periodical (i.e., the distribution of masses is independent of the specific space window) discrete one, the resulting representation becomes always multi-field: the gross deformation describes the motion of the window center of mass, and a tensor field represents the around-mass-center motion of mass points into the window.…”