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The basic models of helix-coil transitions in biomolecules are introduced. These include phenomenological, zipper (Bragg-Zimm) models of polypeptides, loop-entropy (Poland-Scheraga) and Hamiltonian (Peyrard-Bishop) models of homogeneous DNA…
We study helix-coil transitions in an all-atom model of polyalanine. Molecules of up to length 30 residues are investigated by multicanonical simulations. Results from two implicit solvent models are compared with each other and with that…
The thermodynamic behavior of collapse transition in a fully flexible coarse-grained model of energy polydisperse polymer (EPP), a statistical model of random heteropolymer, is investigated in an implicit solvent by means of molecular…
A self-consistent field theory was developed in the grand-canonical ensemble formulation to study transitions in a helix-coil multiblock globule. Helical and coil parts are treated as stiff rods and self-avoiding walks of variable lengths…
For arbitrary Ising-like models of any dimension and Hamiltonians with a finite support with all possible multispin interactions and boundary conditions with a shift, the exact value of the free energy in the thermodynamic limit is obtained…
We explore the coupling between the helix-coil and coil-globule transitions of a helical polymer using Monte Carlo simulations. A very rich state diagram is found. Each state is characterized by a specific configuration of the chain which…
We have performed exhaustive multicanonical Monte Carlo simulations of three 12-residue synthetic peptides in order to investigate the thermodynamic and structural properties as well as the characteristic helix-coil transitions. In these…
We perform Monte Carlo simulations of a three-dimensional spin system with a Hamiltonian which contains only four-spin interaction term. This system describes random surfaces with extrinsic curvature - gonihedric action. We study the…
The force laws governing the extension behavior of homopolypeptides are obtained from a phenomenological free energy capable of describing the helix-coil transition. Just above the melting temperature of the free chains, T*, the plot of…
We discuss the effects of the solvent composition on the helix-coil transition of a polypeptide chain. We use a simple model to demonstrate that improving the hydrogen-bonding ability of the solvent can make the transition less cooperative,…
A small model polypeptide represented in atomic detail is folded using Monte Carlo dynamics. The polypeptide is designed to have a native conformation similar to the central part of the helix-turn-helix protein ROP. Starting from a…
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm for phase transitions in finite dimensions, describing ferromagnets and even some fluids…
Mixed order phase transitions (MOT), which display discontinuous order parameter and diverging correlation length, appear in several seemingly unrelated settings ranging from equilibrium models with long-range interactions to models far…
For a model deca-alanine peptide the cavity (ideal hydrophobic) contribution to hydration favors the helix state in the coil-to-helix transition and the paired helix bundle in the assembly of two helices. The energetic contributions of…
A diathermal wall between two heat baths at different temperatures can be mimicked by a layer of independent spin pairs with some internal energy and where each spin $\sigma_a$ is flipped by thermostat $a$ ($a=1,2$). The transition rates…
PT-symmetric Hamiltonians and transfer matrices arise naturally in statistical mechanics. These classical and quantum models often require the use of complex or negative weights and thus fall outside of the conventional equilibrium…
Thermodynamics of helix-coil transitions in amino-acid homo-oligomers are studied by the recently proposed multicanonical algorithms. Homo-oligomers of length 10 are considered for three characteristic amino acids, alanine (helix former),…
We report on multicanonical simulations of the helix-coil transition of a polypeptide. The nature of this transition was studied by calculating partition function zeros and the finite-size scaling of various quantities. Estimates for…
We develop a general method for constructing the many-body Hamiltonian of pairwise interactions describing homonuclear mixtures of atoms occupying states with different total angular momenta or other quantum numbers. The advantage of the…
We consider the interaction-round-a-face version of the six-vertex model for arbitrary anisotropy parameter, which allow us to derive an integrable one-dimensional quantum Hamiltonian with three-spin interactions. We apply the quantum…