Comparison of Conformational Phase Behavior for Flexible and Semiflexible Polymers

Secondary-structure phase formation for semiflexible polymers by bifurcation in hyperphase space

Canonical analysis has long been the primary analysis method for studies of phase transitions. However, this approach is not sensitive enough if transition signals are too close in temperature space. The recently introduced generalized microcanonical inflection-point analysis method not only enables the systematic identification and classification of transitions in systems of any size, but it can also distinguish transitions that standard canonical analysis cannot resolve. By applying this method to a generic coarse-grained model for semiflexible polymers, we identify a mixed structural phase dominated by secondary structures such as hairpins and loops that originates from a bifurcation in the hyperspace spanned by inverse temperature and bending stiffness. This intermediate phase, which is embraced by the well-known random-coil and toroidal phases, is testimony to the necessity of balancing entropic variability and energetic stability in functional macromolecules under physiological conditions.

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.

Aggregation and crystallization of small alkanes

We present a computer simulation study of the aggregation and ordering of short alkane chains using a united atom model description. Our simulation approach allows us to determine the density of states of our systems and, from those, their thermodynamics for all temperatures. All systems show a first order aggregation transition followed by a low-temperature ordering transition. For a few chain aggregates of intermediate lengths (up to N = 40), we show that these ordering transitions resemble the quaternary structure formation in peptides. In an earlier publication, we have already shown that single alkane chains fold into low-temperature structures, best described as secondary and tertiary structure formation, thus completing this analogy here. The aggregation transition in the thermodynamic limit can be extrapolated in pressure to the ambient pressure for which it agrees well with experimentally known boiling points of short alkanes. Similarly, the chain length dependence of the crystallization transition agrees with known experimental results for alkanes. For small aggregates, for which volume and surface effects are not yet well separated, our method allows us to identify the crystallization in the core of the aggregate and at its surface, individually.

Stable intermediate phase of secondary structures for semiflexible polymers

Systematic microcanonical inflection-point analysis of precise numerical results obtained in extensive generalized-ensemble Monte Carlo simulations reveals a bifurcation of the coil-globule transition line for polymers with a bending stiffness exceeding a threshold value. The region, enclosed by the toroidal and random-coil phases, is dominated by structures crossing over from hairpins to loops upon lowering the energy. Conventional canonical statistical analysis is not sufficiently sensitive to allow for the identification of these separate phases.

Evidence for additional third-order transitions in the two-dimensional Ising model

We employ the microcanonical inflection-point analysis method, developed for the systematic identification and classification of phase transitions in systems of any size, to study the two-dimensional Ising model at various lattice sizes and in the thermodynamic limit. Exact results for the density of states, which were obtained by exact algorithmic computation, provide evidence for higher-order transitions in addition to the well-studied second-order ferromagnetic-paramagnetic phase transition. An independent third-order phase transition is identified in the ferromagnetic phase, whereas another third-order transition resides in the paramagnetic phase. The latter is a dependent transition, i.e., it is inevitably associated with the critical transition, but it remains separate from the critical point in the thermodynamic limit. For a deeper insight into the nature of these additional transitions, a detailed analysis of spin clusters is performed.