Predicting non-equilibrium folding behavior of polymer chains using the steepest-entropy-ascent quantum thermodynamic framework

Abstract

The Replica Exchange Wang-Landau Method is used to estimate the energy landscape of a polymer composed of a simple hydrophobic and polar sequence using the HP protein model. Calculations of state transitions between the energy levels of the derived energy landscape are made using an equation of motion from the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework. The SEAQT framework makes it possible to determine the unique kinetic paths from an arbitrary quasi-equilibrium or non-equilibrium initial state to stable equilibrium. Calculations performed with SEAQT require significantly reduced computational time versus comparable Monte Carlo simulations while providing otherwise unavailable thermodynamic and structural properties. Expected values for state averaged structural parameters are used to produce representative reconstructions of the calculated state-based evolution. Results show continuous transitions between states with no distinct folding phases. Changes in chain conformations during heating and cooling are more drastic along non-equilibrium paths than along quasi-equilibrium paths. In addition, SEAQT-derived kinetics are compared to experimentally derived intensity profiles describing the kinetics of the cytochrome c protein using Rouse dynamic relations.

Predicting Polymer Brush Behavior in Solvents Using the Steepest-Entropy-Ascent Quantum Thermodynamic Framework

“…The accuracy of the density of states calculation is represented by the error bars shown in Figure . These correspond to the relative error determined from six runs of the replica-exchange Wang–Landau algorithm on a 58-monomer chain in previous work . The error bars for the monomer chain represented ±1 standard deviation of the degeneracy determined from the six independent simulations completed with the same Wang–Landau parameters as those used here for the brush system.…”

“…A similar extension of the Onsager formalism to the far-from-equilibrium region using the steepest-entropy-ascent hypo-equilibrium formalism has been derived by Li and von Spakovsky . While the steepest-entropy-ascent principle is treated here as a postulate, it has a long history, has a firm mathematical basis, − ,, and has been tested in a wide range of quantum and classical applications. − ,− ,,, Additional discussion of the generality of the steepest-entropy-ascent principle, can be found in refs , , , and .…”

“…Recent research has established a link between SEAQT paths in state space and physical conformations. , To accomplish this, representative microstructures or conformations are connected to SEAQT-predicted state evolution through the expectation values of a set of structural parameters or descriptors that characterize the microstructure at each time step. These expectation values are computed using the predicted probability distribution, and the arithmetic average values of these parameters are determined for each eigenlevel during the execution of the Wang–Landau algorithm.…”

“…As this evolution occurs through the state space and not the phase space utilized in molecular dynamics and Monte Carlo simulations, the relaxation parameter must be tied to either experiment or a theoretical yet semiempirical model that correlates changes in state to specific constituent movements between precise locations within a representative conformation. One such method involves using proportionalities from Rouse dynamics that relate changes in the component of the radius of gyration perpendicular to the grafting plane to the relaxation parameter (an analogous method was used to determine τ for a free polymer chain). Specifically, the relationship for the relaxation parameter can be expressed as where …”

“…To treat nonequilibrium processes explicitly, this work applies the steepest-entropy-ascent quantum thermodynamic (SEAQT) framework − to determine a brush system’s kinetic path from an arbitrary initial state to stable equilibrium. The framework uses a postulated equation of motion to calculate how energy is redistributed among a brush’s discrete energy levels as it evolves through transition states to equilibrium.…”