F-model-type phase transition in the 2D Flory model of polymer melting

Statistical mechanics of the two-dimensional hydrogen-bonding self-avoiding walk including solvent effects

A two-dimensional square-lattice model for the formation of secondary structures in proteins, the hydrogen-bonding model, is extended to include the effects of solvent quality. This is achieved by allowing configuration-dependent nearest-neighbor interactions. The phase diagram is presented and found to have a much richer variety of phases than either the pure hydrogen-bonding self-avoiding walk model or the standard Theta-point model.

Conformal field theory of the Flory model of polymer melting

We study the scaling limit of a fully packed loop model in two dimensions, where the loops are endowed with a bending rigidity. The scaling limit is described by a three-parameter family of conformal field theories, which we characterize via its Coulomb-gas representation. One choice for two of the three parameters reproduces the critical line of the exactly solvable six-vertex model, while another corresponds to the Flory model of polymer melting. Exact central charge and critical exponents are calculated for polymer melting in two dimensions. Contrary to predictions from mean-field theory we show that polymer melting, as described by the Flory model, is continuous. We test our field theoretical results against numerical transfer matrix calculations.

Continuous melting of compact polymers

The competition between chain entropy and bending rigidity in compact polymers can be addressed within a lattice model introduced by Flory in 1956 [Proc. R. Soc. London A 234, 60 (1956)]]. It exhibits a transition between an entropy dominated disordered phase and an energetically favored crystalline phase. The nature of this order-disorder transition has been debated ever since the introduction of the model. Here we present exact results for the Flory model in two dimensions relevant for polymers on surfaces, such as DNA adsorbed on a lipid bilayer. We predict a continuous melting transition and compute exact values of critical exponents at the transition point.

Folding of bundles of alpha-helices in solution, membranes, and adsorbed overlayers

We propose a coarse-grained lattice model for Monte Carlo simulations of folding of proteins consisting of several alpha-helices. A chain representing a protein is considered to contain A and B monomers forming relatively stiff A subchains, mimicking helices, and flexible B links between these subchains, respectively. Using this model, we simulate (1) folding of four-helix proteins in solution; (2) folding of membrane proteins containing one, two, or four helices; and (3) refolding of four-helix proteins adsorbed at the liquid-solid interface. For these cases, we show typical scenarios of protein folding and refolding and study the dependence of the folding time on the chain length. Combining the latter results with those already available in the literature, we discuss the relative rates of folding of proteins belonging to different classes.