Microcanonical analyses of peptide aggregation processes

Replica exchange statistical temperature Monte Carlo

The replica exchange statistical temperature Monte Carlo algorithm (RESTMC) is presented, extending the single-replica STMC algorithm [J. Kim, J. E. Straub, and T. Keyes, Phys. Rev. Lett. 97, 050601 (2006)] to alleviate the slow convergence of the conventional temperature replica exchange method (t-REM) with increasing system size. In contrast to the Gibbs-Boltzmann sampling at a specific temperature characteristic of the standard t-REM, RESTMC samples a range of temperatures in each replica and achieves a flat energy sampling employing the generalized sampling weight, which is automatically determined via the dynamic modification of the replica-dependent statistical temperature. Faster weight determination, through the dynamic update of the statistical temperature, and the flat energy sampling, maximizing energy overlaps between neighboring replicas, lead to a considerable acceleration in the convergence of simulations even while employing significantly fewer replicas. The performance of RESTMC is demonstrated and quantitatively compared with that of the conventional t-REM under varying simulation conditions for Lennard-Jones 19, 31, and 55 atomic clusters, exhibiting single- and double-funneled energy landscapes.

All-or-none proteinlike folding transition of a flexible homopolymer chain

Here we report a first-order all-or-none transition from an expanded coil to a compact crystallite for a flexible polymer chain. Wang-Landau sampling is used to construct the complete density of states for square-well chains up to length 256. Analysis within both the microcanonical and canonical ensembles shows a direct freezing transition for finite length chains with sufficiently short-range interactions. This type of transition is a distinctive feature of "one-step" protein folding and our findings demonstrate that a simple homopolymer model can exhibit protein-folding thermodynamics.

Relationship between protein folding thermodynamics and the energy landscape

The origin of protein folding thermodynamics is examined in terms of the energy landscape, employing an off-lattice protein model with scaled non-native attractions, which is continuously tunable between a Go-like model and a highly frustrated system. Extensive statistical temperature molecular dynamics simulations, combined with inherent structure analysis, reveal the intimate connection between the global geometric properties of the energy landscape and the statistical temperature. The basin depth of the energy landscape is shown to play a key role in the first-order-like characteristics of the statistical temperature, which are easily identified by the squared modulus of the potential energy gradient in the microcanonical ensemble.

Comparative molecular dynamics and Monte Carlo study of statistical properties for coarse-grained heteropolymers

Employing a simple hydrophobic-polar heteropolymer model, we compare thermodynamic quantities obtained from Andersen and Nosé-Hoover molecular dynamics as well as replica-exchange Monte Carlo methods. We find qualitative correspondence in the results, but serious quantitative differences using the Nosé-Hoover chain thermostat. For analyzing the deviations, we study different parameterizations of the Nosé-Hoover chain thermostat. Autocorrelations from molecular dynamics and Metropolis Monte Carlo runs are also investigated.

Microcanonical analyses of homopolymer aggregation processes

Using replica-exchange multicanonical Monte Carlo simulation, the aggregates of two homopolymers were numerically investigated through the microcanonical analysis method. The microcanonical entropy showed one convex function in the transition region, leading to a negative microcanonical specific heat. The origin of temperature backbending was the rearrangement of the segments during the process of aggregation; this aggregation process proceeded via a nucleation and growth mechanism. It was observed that the segments with a sequence number from 10 to 13 in the polymer chain have leading effects on the aggregation.

Microcanonical versus canonical analysis of protein folding

The microcanonical analysis is shown to be a powerful tool to characterize the protein folding transition and to neatly distinguish between good and bad folders. An off-lattice model with parameter chosen to represent polymers of these two types is used to illustrate this approach. Both canonical and microcanonical ensembles are employed. The required calculations were performed using parallel tempering Monte Carlo simulations. The most revealing features of the folding transition are related to its first-order-like character, namely, the S-bend pattern in the caloric curve, which gives rise to negative microcanonical specific heats, and the bimodality of the energy distribution function at the transition temperatures. Models for a good folder are shown to be quite robust against perturbations in the interaction potential parameters.

Thermodynamics of peptide aggregation processes: an analysis from perspectives of three statistical ensembles

We employ a mesoscopic model for studying aggregation processes of proteinlike hydrophobic-polar heteropolymers. By means of multicanonical Monte Carlo computer simulations, we find strong indications that peptide aggregation is a phase separation process, in which the microcanonical entropy exhibits a convex intruder due to non-negligible surface effects of the small systems. We analyze thermodynamic properties of the conformational transitions accompanying the aggregation process from the multicanonical, canonical, and microcanonical perspective. It turns out that the microcanonical description is particularly advantageous as it allows for unraveling details of the phase-separation transition in the thermodynamic region, where the temperature is not a suitable external control parameter anymore.

Microcanonical quantum fluctuation theorems

Previously derived expressions for the characteristic function of work performed on a quantum system by a classical external force are generalized to arbitrary initial states of the considered system and to Hamiltonians with degenerate spectra. In the particular case of microcanonical initial states, explicit expressions for the characteristic function and the corresponding probability density of work are formulated. Their classical limit as well as their relations to the corresponding canonical expressions are discussed. A fluctuation theorem is derived that expresses the ratio of probabilities of work for a process and its time reversal to the ratio of densities of states of the microcanonical equilibrium systems with corresponding initial and final Hamiltonians. From this Crooks-type fluctuation theorem a relation between entropies of different systems can be derived which does not involve the time-reversed process. This entropy-from-work theorem provides an experimentally accessible way to measure entropies.

Freezing and collapse of flexible polymers on regular lattices in three dimensions

We analyze the crystallization and collapse transition of a simple model for flexible polymer chains on simple-cubic and face-centered-cubic lattices by means of sophisticated chain-growth methods. In contrast to the bond-fluctuation polymer model in certain parameter ranges, where these two conformational transitions were found to merge in the thermodynamic limit, we conclude from our results that the two transitions remain well separated in the limit of infinite chain lengths. The reason for this qualitatively distinct behavior is presumably due to the ultrashort attractive interaction range in the lattice models considered here.

Microcanonical analysis of association of hydrophobic segments in a heteropolymer

Using the replica-exchange multicanonical Monte Carlo simulation, the intra-association of hydrophobic segments in a heteropolymer was numerically investigated by the microcanonical analysis method. We demonstrated that the microcanonical entropy shows the features of one or multiple convexes in the association transition region depending on the number and distribution of hydrophobic segments in the chain. We found that one or multiple negative specific heats imply a first-order-like transition with the coexistence of multiple phases.

Quantum master equation for the microcanonical ensemble

By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the authors in Phys. Rev. E 68, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly interacting with an environment of finite heat capacity and initially described by a microcanonical distribution. After applying the rotating wave approximation to the equation, we show that the subsystem dynamics preserves the energy of the total system (subsystem plus environment) and tends towards an equilibrium state which corresponds to equipartition inside the energy shell of the total system. For infinite heat capacity environments, this equation reduces to the Redfield master equation for a subsystem interacting with a thermostat. These results should be of particular interest to describe relaxation and decoherence in nanosystems where the environment can have a finite number of degrees of freedom and the equivalence between the microcanonical and the canonical ensembles is thus not always guaranteed.

Microcanonical approach to the simulation of first-order phase transitions

A simple microcanonical strategy for the simulation of first-order phase transitions is proposed. At variance with flat-histogram methods, there is no iterative parameters optimization nor long waits for tunneling between the ordered and the disordered phases. We test the method in the standard benchmark: the Q-states Potts model (Q=10 in two dimensions and Q=4 in D=3). We develop a cluster algorithm for this model, obtaining accurate results for systems with more than 10(6) spins.