No abstract

A microscopic spin model is proposed for the phenomenological Zimm-Bragg model for the helix-coil transition in biopolymers. This model is shown to provide the same thermophysical properties of the original Zimm-Bragg model and it allows a very convenient framework to compute statistical quantities. Physical origins of this spin model are made transparent by an exact mapping into a one-dimensional Ising model with an external field. However, the dependence on temperature of the reduced external field turns out to differ from the standard one-dimensional Ising model and hence it gives rise to different thermophysical properties, despite the exact mapping connecting them. We discuss how this point has been frequently overlooked in the recent literature.

The problem of the helix-coil transition of biopolymers in explicit solvents, like water, with the ability for hydrogen bonding with solvent is addressed analytically using a suitably modified version of the Generalized Model of Polypeptide Chains. Besides the regular helix-coil transition, an additional coil-helix or reentrant transition is also found at lower temperatures. The reentrant transition arises due to competition between polymer-polymer and polymer-water hydrogen bonds.The balance between the two types of hydrogen bonding can be shifted to either direction through changes not only in temperature, but also by pressure, mechanical force, osmotic stress or other external influences. Both polypeptides and polynucleotides are considered within a unified formalism. Our approach provides an explanation of the experimental difficulty of observing the reentrant transition with pressure; and underscores the advantage of pulling experiments for studies of DNA.

Most helix-coil transition theories can be characterized by three parameters: energetic, describing the (free) energy cost of forming a helical state in one repeating unit; entropic, accounting for the decrease of entropy due to formation of the helical state; and geometric, indicating how many repeating units are affected by the formation of one helical state. Depending on their effect on the helix-coil transition, solvents or cosolutes can be classified with respect to their action on these parameters. Solvent interactions that alter the entropic cost of helix formation by their osmotic action can affect both the stability (transition temperature) and the cooperativity (transition interval) of the helix-coil transition. Consistent inclusion of osmotic pressure effects in a description of helix-coil transition, for poly(L-glutamic acid) in solution with polyethylene glycol, can offer an explanation of the experimentally observed linear dependence of transition temperature on osmotic pressure as well as the concurrent changes in the cooperativity of the 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.

We use a micro-canonical Wang-Landau technique to study the equilibrium properties of a single flexible homopolymer where consecutive monomers are represented by impenetrable hard spherical beads tangential to each other, and non-consecutive monomers interact via a square-well potential. To mimic the characteristics of a protein-like system, the model is then refined in two different directions. Firstly, by allowing partial overlap between consecutive beads, we break the spherical symmetry and thus provide a severe constraint on the possible conformations of the chain. Alternatively, we introduce additional spherical beads at specific positions in the direction normal to the backbone, to represent the steric hindrance of the side chains in real proteins. Finally, we consider also a combination of these two ingredients. In all three systems, we obtain the full phase diagram in the temperature-interaction range plane and find the presence of helicoidal structures at low temperatures in the intermediate range of interactions. The effect of the range of the square-well attraction is highlighted, and shown to play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.

ABSTRACT:Coarse-grained chain simulations were used to study fragments of two homologous proteins of the peripheral subunit-binding domain (PSBD) family, Bacillus stearothermophilus PSBD (E3BD) and Escherichia coli 2-oxo-glutarate dehydrogenase PSBD (BBL). To ascertain a robust rank order of folding cooperativity, native-centric intraprotein interactions were modeled by (i) a common Gō-like potential, and (ii) native-centric potentials with desolvation barriers or (iii) many-body terms. Homologous proteins can possess substantially different folding cooperativity. Consistent with experiment, our calculations indicated that E3BD fragments fold more cooperatively than BBL fragments of approximately the same chain length. For a given fragment, native contacts deduced from Protein Data Bank structures can vary significantly depending on the number of residues that the structure encompasses in addition to those of the fragment itself, resulting in variation in model folding cooperativity predicted using different native contact sets for the NONCOOPERATIVE FOLDING OF SMALL PROTEINS same fragment. This observation underscores that folding cooperativity of these fragments can be extremely sensitive to change in chain length. Thus, a ∼40-residue protein fragment's folding cooperativity, or lack thereof, does not necessarily imply essentially identical behaviors for super-or sub-fragments with only several residues more, or less, than the given fragment. Ramifications for experimental investigations of downhill folding are discussed.

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.