title: Properties of low-dimensional collective variables in the molecular dynamics of biopolymers.
abstract: The description of the dynamics of a complex, high-dimensional system in terms of a low-dimensional set of collective variables Y can be fruitful if the low-dimensional representation satisfies a Langevin equation with drift and diffusion coefficients that depend only on Y. We present a computational scheme to evaluate whether a given collective variable provides a faithful low-dimensional representation of the dynamics of a high-dimensional system. The scheme is based on the framework of a finite-difference Langevin equation, similar to that used for molecular-dynamics simulations. This allows one to calculate the drift and diffusion coefficients in any point of the full-dimensional system. The width of the distribution of drift and diffusion coefficients in an ensemble of microscopic points at the same value of Y indicates to what extent the dynamics of Y is described by a simple Langevin equation. Using a simple protein model, we show that collective variables often used to describe biopolymers display a non-negligible width both in the drift and in the diffusion coefficients. We also show that the associated effective force is compatible with the equilibrium free energy calculated from a microscopic sampling, but it results in markedly different dynamical properties.
authors.affiliation: Department of Physics, Università degli Studi di Milano, and INFN, via Celoria 16, 20133 Milano, Italy.
authors.forename: Roberto
authors.initials: R
authors.lastname: Meloni
authors.affiliation: Department of Chemistry and Institute for Advanced Study, Technische Universität München, Lichtenbergstrasse 4, 85747 Garching, Germany.
authors.forename: Carlo
authors.initials: C
authors.lastname: Camilloni
authors.affiliation: Center for Complexity and Biosystems and Department of Physics, Università degli Studi di Milano, and INFN, via Celoria 16, 20133 Milano, Italy.
authors.forename: Guido
authors.initials: G
authors.lastname: Tiana
mesh_terms: D001704:Biopolymers / Q000737:chemistry*; D008968:Molecular Conformation; D056004:Molecular Dynamics Simulation; D011506:Proteins / Q000737:chemistry
chemical_list: D001704:Biopolymers; D011506:Proteins