Microcanonical analysis of association of hydrophobic segments in a heteropolymer

A density of states-based approach to determine temperature-dependent aggregation rates

Here, we establish an approach to determine temperature-dependent aggregation rates in terms of thermostatistical quantities, which can be obtained directly from flat-histogram and statistical temperature algorithms considering the density of states of the system. Our approach is validated through simulations of an Ising-like model with anisotropically interacting particles at temperatures close to its first-order phase transition. Quantitative comparisons between the numerically obtained forward and reverse rates to approximate analytical expressions corroborate its use as a model-independent approach.

Microcanonical Analysis of Helical Homopolymers: Exploring the Density of States and Structural Characteristics

This study investigates the density of states and structural characteristics of helical homopolymers. Comprising repeating identical units, the model enables the exploration of complex behaviors arising from a simple, yet generalized, set of potentials. Utilizing microcanonical analysis, transitions between helical structures are identified and categorized. Through a systematic comparison of results under varying conditions, we develop a nuanced understanding of the system's general behavior. A two-dimensional plot illustrates the relative distribution of different structural types, effectively showcasing their prevalence. The findings of this study substantially advance our understanding of the density of states and structural transformations of helical homopolymers across a range of conditions. Additionally, the prevalence plot offers valuable insights into the occurrence of suppressed intermediate states, particularly in models featuring stiff helix segments. This research significantly enhances our understanding of the complex interactions governing helix bundling phenomena within the context of helical homopolymers.

Microcanonical analysis of a finite-size nonequilibrium system

Microcanonical analysis is a powerful method that can be used to generalize the concept of phase transitions to finite-size systems. However, microcanonical analysis has only been applied to equilibrium systems. I show that it is possible to conduct the microcanonical analysis of a finite-size nonequilibrium system by generalizing the concept of microcanonical entropy. A one-dimensional asymmetric diffusion process is studied as an example for which such a generalized entropy can be explicitly found, and the microcanonical method is used to define a generalized phase transition for the finite-size nonequilibrium system.

Thermodynamic laws in isolated systems

The recent experimental realization of exotic matter states in isolated quantum systems and the ensuing controversy about the existence of negative absolute temperatures demand a careful analysis of the conceptual foundations underlying microcanonical thermostatistics. Here we provide a detailed comparison of the most commonly considered microcanonical entropy definitions, focusing specifically on whether they satisfy or violate the zeroth, first, and second laws of thermodynamics. Our analysis shows that, for a broad class of systems that includes all standard classical Hamiltonian systems, only the Gibbs volume entropy fulfills all three laws simultaneously. To avoid ambiguities, the discussion is restricted to exact results and analytically tractable examples.

Identifying transitions in finite systems by means of partition function zeros and microcanonical inflection-point analysis: a comparison for elastic flexible polymers

For the estimation of transition points of finite elastic, flexible polymers with chain lengths from 13 to 309 monomers, we compare systematically transition temperatures obtained by the Fisher partition function zeros approach with recent results from microcanonical inflection-point analysis. These methods rely on accurate numerical estimates of the density of states, which have been obtained by advanced multicanonical Monte Carlo sampling techniques. Both the Fisher zeros method and microcanonical inflection-point analysis yield very similar results and enable the unique identification of transition points in finite systems, which is typically impossible in the conventional canonical analysis of thermodynamic quantities.

Microcanonical entropy inflection points: key to systematic understanding of transitions in finite systems

We introduce a systematic classification method for the analogs of phase transitions in finite systems. This completely general analysis, which is applicable to any physical system and extends toward the thermodynamic limit, is based on the microcanonical entropy and its energetic derivative, the inverse caloric temperature. Inflection points of this quantity signal cooperative activity and thus serve as distinct indicators of transitions. We demonstrate the power of this method through application to the long-standing problem of liquid-solid transitions in elastic, flexible homopolymers.

Structural basis of folding cooperativity in model proteins: insights from a microcanonical perspective

Two-state cooperativity is an important characteristic in protein folding. It is defined by a depletion of states that lie energetically between folded and unfolded conformations. There are different ways to test for two-state cooperativity; however, most of these approaches probe indirect proxies of this depletion. Generalized-ensemble computer simulations allow us to unambiguously identify this transition by a microcanonical analysis on the basis of the density of states. Here, we present a detailed characterization of several helical peptides obtained by coarse-grained simulations. The level of resolution of the coarse-grained model allowed to study realistic structures ranging from small α-helices to a de novo three-helix bundle without biasing the force field toward the native state of the protein. By linking thermodynamic and structural features, we are able to show that whereas short α-helices exhibit two-state cooperativity, the type of transition changes for longer chain lengths because the chain forms multiple helix nucleation sites, stabilizing a significant population of intermediate states. The helix bundle exhibits signs of two-state cooperativity owing to favorable helix-helix interactions, as predicted from theoretical models. A detailed analysis of secondary and tertiary structure formation fits well into the framework of several folding mechanisms and confirms features that up to now have been observed only in lattice models.

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.