Artem V. Badasyan

Probing Possible Downhill Folding: Native Contact Topology Likely Places a Significant Constraint on the Folding Cooperativity of Proteins with ∼ 40 Residues

Experiments point to appreciable variations in folding cooperativity among natural proteins with approximately 40 residues, indicating that the behaviors of these proteins are valuable for delineating the contributing factors to cooperative folding. To explore the role of native topology in a proteins propensity to fold cooperatively and how native topology might constrain the degree of cooperativity achievable by a given set of physical interactions, we compared folding/unfolding kinetics simulated using three classes of native-centric C(alpha) chain models with different interaction schemes. The approach was applied to two homologous 45-residue fragments from the peripheral subunit-binding domain family and a 39-residue fragment of the N-terminal domain of ribosomal protein L9. Free-energy profiles as functions of native contact number were computed to assess the heights of thermodynamic barriers to folding. In addition, chevron plots of folding/unfolding rates were constructed as functions of native stability to facilitate comparison with available experimental data. Although common Gō-like models with pairwise Lennard-Jones-type interactions generally fold less cooperatively than real proteins, the rank ordering of cooperativity predicted by these models is consistent with experiment for the proteins investigated, showing increasing folding cooperativity with increasing nonlocality of a proteins native contacts. Models that account for water-expulsion (desolvation) barriers and models with many-body (nonadditive) interactions generally entail higher degrees of folding cooperativity indicated by more linear model chevron plots, but the rank ordering of cooperativity remains unchanged. A robust, experimentally valid rank ordering of model folding cooperativity independent of the multiple native-centric interaction schemes tested here argues that native topology places significant constraints on how cooperatively a protein can fold.

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.

Osmotic Pressure Induced Coupling between Cooperativity and Stability of a Helix-Coil Transition

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.

The helix-coil transition in heterogeneous double stranded DNA: Microcanonical method

A microscopic Potts-like one-dimensional model with many-particle interactions is developed to construct a statistical mechanical description of the melting of heterogeneous sequence duplex DNA. For this model, referred as the generalized model of polypeptide chains (GMPC), a closed-form expression for the free energy is derived. The characteristic equation of the model enables estimates on the melting temperature and transition interval, consistent with results obtained from more classical approaches. From the characteristic equation of the model, the temperature-dependent statistical weight parameter for helical states is evaluated. This parameter is shown to change throughout the transition from a harmonic form in early regions of the transition to an arithmetic form in later stages. The GMPC is extended to consider the influence of sequence heterogeneity in the melting of duplex DNA.

Competition for hydrogen-bond formation in the helix-coil transition and protein folding

The problem of the helix-coil transition of biopolymers in explicit solvents, such as water, with the ability for hydrogen bonding with a 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. Results are discussed and compared with those reported in a number of recent publications with which a significant level of agreement is obtained.

Solvent effects in the helix-coil transition model can explain the unusual biophysics of intrinsically disordered proteins.

We analyze a model statistical description of the polypeptide chain helix-coil transition, where we take into account the specificity of its primary sequence, as quantified by the phase space volume ratio of the number of all accessible states to the number corresponding to a helical conformation. The resulting transition phase diagram is then juxtaposed with the unusual behavior of the secondary structures in Intrinsically Disordered Proteins (IDPs) and a number of similarities are observed, even if the protein folding is a more complex transition than the helix-coil transition. In fact, the deficit in bulky and hydrophobic amino acids observed in IDPs, translated into larger values of phase space volume, allows us to locate the region in parameter space of the helix-coil transition that would correspond to the secondary structure transformations that are intrinsic to conformational transitions in IDPs and that is characterized by a modified phase diagram when compared to globular proteins. Here, we argue how the nature of this modified phase diagram, obtained from a model of the helix-coil transition in a solvent, would illuminate the turned-out response of IDPs to the changes in the environment conditions that follow straightforwardly from the re-entrant (cold denaturation) branch in their folding phase diagram.

STACKING DECREASES THE COOPERATIVITY OF MELTING OF HOMOPOLYMERIC DNA

We report on theoretical investigation of interactions of different mechanisms and their influence onto DNA cooperativity of helix–coil transition (melting). Using the modified version of microscopic Potts-like one-dimensional model we showed that increased stacking results in decreased correlation length. The decrease in cooperativity is explained as a result of combined hydrogen bonding and stacking.

Helix–coil transition in closed circular DNA

A simplified model for the closed circular DNA (ccDNA) is proposed to describe some specific features of the helix–coil transition in such molecules. The Hamiltonian of ccDNA is related to the one introduced earlier for the open chain DNA (ocDNA). The basic assumption is that the reduced energy of the hydrogen bond is not constant through the transition process but depends effectively on the fraction of already broken bonds. A transformation formula is obtained which relates the temperature of ccDNA at a given degree of helicity during the transition to the temperature of the corresponding open chain at the same degree of helicity. The formula provides a simple method to calculate the melting curve for the ccDNA from the experimental melting curve of the ocDNA with the same nucleotide sequence.

Intersegment interactions and helix-coil transition within the generalized model of polypeptide chains approach

The generalized model of polypeptide chains is extended to describe the helix-coil transition in a system comprised of two chains interacting side-by-side. The Hamiltonian of the model takes into account four possible types of interactions between repeated units of the two chains, i.e., helix-helix, helix-coil, coil-helix, and coil-coil. Analysis reveals when the energy I(hh)+I(cc) of (h-h, c-c) interactions overwhelms the energy I(hc)+I(ch) of mixed (h-c, c-h) interactions, the correlation length rises substantially, resulting in narrowing of the transition interval. In the opposite case, when I(hh)+I(cc)<I(hc)+I(ch), nontrivial behavior of the system is predicted where an intermediate plateau appears on the denaturation curve. For the latter case, calculations of the number of junctions and the average length of helical segments indicate rearrangement of helical segments at the transition point. Conceptual links are established with experimentally oriented theories of Ghosh and Dill [J. Am. Chem. Soc. 131, 2306 (2009)] and Skolnick and Holtzer [Biochemistry 25, 6192 (1986)], providing a potential explanation for both favorable helix formation and disfavored intersegment interactions from the same theoretical perspective.

Two scale generalized model of polypeptide chains

The generalized model of polypeptide chains (GMPC) is expanded to simultaneously consider two types of interactions occurring over different scales. This new two scale GMPC is applied in several specific cases to examine: The combined influence of stacking or antistacking and hydrogen bonding, or spatial restrictions on the length of helical segments, on the cooperativity and temperature interval of the helix-coil transition of duplex DNA. For the cases of stacking or antistacking in combination with hydrogen bonding the model reduces to the basic uniscale model with a redefined scaling parameter Delta. Antistacking increases the cooperativity, while stacking decreases it. In each case, explanations are given in terms of different lengths of helical segments. Restrictions on the length of helical regions result in the appearance of antiferromagnetic-type correlations where there is no apparent link between cooperativity and transition interval.