Unified description of solvent effects in the helix-coil transition.

We analyze the problem of the helix-coil transition in explicit solvents analytically by using spin-based models incorporating two different mechanisms of solvent action: explicit solvent action through the formation of solvent-polymer hydrogen bonds that can compete with the intrinsic intra-polymer hydrogen bonded configurations (competing interactions) and implicit solvent action, where the solvent-polymer interactions tune biopolymer configurations by changing the activity of the solvent (non-competing interactions). The overall spin Hamiltonian is comprised of three terms: the background in vacuo Hamiltonian of the "Generalized Model of Polypeptide Chain" type and two additive terms that account for the two above mechanisms of solvent action. We show that on this level the solvent degrees of freedom can be explicitly and exactly traced over, the ensuing effective partition function combining all the solvent effects in a unified framework. In this way we are able to address helix-coil transitions for polypeptides, proteins, and DNA, with different buffers and different external constraints. Our spin-based effective Hamiltonian is applicable for treatment of such diverse phenomena as cold denaturation, effects of osmotic pressure on the cold and warm denaturation, complicated temperature dependence of the hydrophobic effect as well as providing a conceptual base for understanding the behavior of intrinsically disordered proteins and their analogues.

DNA stretching and multivalent-cation-induced condensation.

Motivated by measurements on stretched double-stranded DNA in the presence of multivalent cations, we develop a statistical mechanical model for the compaction of an insoluble semiflexible polymer under tension. Using a mean-field approach, we determine the order of the extended-to-compact transition and provide an interpretation for the magnitude and interval of tensions over which compaction takes place. In the simplest thermodynamic limit of an infinitely long homogeneous polymer, compaction is a first-order transition that occurs at a single value of tension. For finite length chains or for heterogeneous polymers, the transition progresses over an interval of tension. Our theory provides an interpretation for the result of single-molecule experiments in terms of microscopic parameters such as persistence length and free energy of condensation.

Stacking and hydrogen bonding: DNA cooperativity at melting.

By taking into account base-base stacking interactions we improve the Generalized Model of Polypeptide Chain (GMPC). Based on a one-dimensional Potts-like model with many-particle interactions, the GMPC describes the helix-coil transition in both polypeptides and polynucleotides. In the framework of the GMPC we show that correctly introduced nearest-neighbor stacking interactions against the background of hydrogen bonding lead to increased stability (melting temperature) and, unexpectedly, to decreased cooperativity (maximal correlation length). The increase in stability is explained as due to an additional stabilizing interaction (stacking) and the surprising decrease in cooperativity is seen as a result of mixing of contributions of hydrogen bonding and stacking.