Soliton driven relaxation dynamics and protein collapse in the villin headpiece

Abstract

Protein collapse from a random chain to the native state involves a dynamical phase transition. During the process, new scales and collective variables become excited while old ones recede and fade away. The presence of different phases and many scales causes formidable computational bottle-necks in approaches that are based on full atomic scale scrutiny. Here we propose a way to describe the folding and unfolding processes effectively, using only the biologically relevant time and distance scales. We merge a coarse grained Landau theory that models the static collapsed protein in the low-temperature limit with a Glauber protocol that describes finite-temperature relaxation dynamics in a statistical system which is out of thermal equilibrium. As an example we inspect the collapse of a HP35 chicken villin headpiece subdomain, a paradigm specimen in protein folding studies. We simulate the folding and unfolding process by repeated heating and cooling cycles between a given low-temperature, i.e. bad solvent, environment where the protein is collapsed and various different high-temperature, i.e. good solvent, environments. We find that as long as the high temperature value stays below a value in the range that separates the random walk phase from the self-avoiding walk phase, we consistently recover the native state upon cooling. But, when heated to sufficiently high temperatures, the native state practically never recurs. Our result confirms Anfinsen's thermodynamical hypothesis and estimates a temperature range for its validity, in the case of villin.

Multistage modeling of protein dynamics with monomeric Myc oncoprotein as an example

“…The parameter T is the Monte Carlo temperature factor. In general it does not coincide with the physical temperature factor k B θ, but the two can be related by methods of renormalisation group [40]; here we do not need an explicit relation, ultimately the molecular dynamics step in our algorithm will determine the temperature. A small two-state protein often folds in line with Arrhenius' law [41] and for a simple spin chain the Glauber algorithm reproduces Arrhenius law.…”

Solution x-ray scattering and structure formation in protein dynamics

“…However, the two can be related by a renormalisation procedure. General arguments presented in [43] suggest that the relation between the two should have the form…”

Gauge fields, strings, solitons, anomalies, and the speed of life

“…Thus, the method should provide a statistically meaningful description of near-equilibrium protein folding dynamics, at least during adiabatic temperature variations. In our simulations of near-equilibrium proteins, we renormalize the numerical value of the temperature factor kT so that it coincides with the experimentally observed θ-point temperature [64]. We proceed as follows: We start by training (64), (65) to describe a given, typically very low temperature crystallographic PDB protein configuration as a multi-soliton.…”

“…In figure 8 we show, as an example, how the Cα root-mean-square-distance (RMSD) between the crystallographic X-ray myoglobin structure with PDB entry code 1ABS and its multi-soliton description constructed using (64), (65) evolves, when we increase and decrease the temperature. In this simulation we first heat up the multi-soliton.…”