Y. Sh. Mamasakhlisov

Generalized Model of Polypeptide Chain with two-scale interactions

On the basis of the Generalized Model of Polypeptide Chain (GMPC) introduced earlier, which describes the helix-coil transition in both polypeptides and polynucleotides, a Hamiltonian is proposed consisting of two different-scale GMPC Hamiltonians. Within the framework of the transfer-matrix approach the degree of helicity and the correlation length are calculated. It is shown that the two-scale-interaction model may be reduced to a single-scale model with redefined parameter of the hydrogen bond closure.

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.

Helix-coil transition in biopolymers with multicomponent heterogeneity of energy and number of conformations

We consider the theory of helix-coil transition in heteropolymeric biopolymers with an arbitrary number of components in cases of heterogeneity with respect to both energy and number of conformations. The theory is based on the Generalized Model of Polypeptide Chain (GMPC) with employing the constrained annealing method. Expression for the free energy of heteropolymer is derived using averaged transfer-matrix of homopolymer GMPC with redefined energy and conformation parameters. We obtain an algorithm of calculation of the melting curve of a heteropolymeric system and compare that with the homopolymeric curve. We show that bimodal heterogeneity determines qualitatively the basic properties of melting of a random heteropolymer. We also show that heterogeneity with respect to energy and heterogeneity with respect to number of conformations provide essentially the same characteristics of melting curves.

Two-dimensional random walk and critical behavior of double-strand DNA

The phase behavior in a double-strand homopolynucleotide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of base pairs between the complementary units. We obtain a completely denatured state below the finite temperature Tc. It was shown that Tc is the point of the infinite-order phase transition. The specific behavior of the order parameter, free energy and correlation functions has been addressed.

On the theory of helix-coil transition in heterogeneous biopolymers. Constrained annealing method

A theory of helix-coil transition in DNA, heteropolymeric with respect to energies of H-bond formation, is considered. The theory is based on the Generalized Model of Polypeptide Chain (GMPC) with employing the constrained annealing method. Expression for the free energy of heteropolymer is derived using transfer-matrix of homopolymer with redefined energy parameter. The technique of calculation of broadening of melting interval depending on the GC-composition and hydrogen bonding energy of AT and GC pairs is developed. Two maxima are revealed on the differential melting curve of heteropolymer. The temperature dependence of the correlation length is considered as well.

Two-dimensional random walk and loop factor in helix-coil transition theory of DNA

Theory of helix-coil transition in double-stranded homopolypeptides is considered. The theory develops an approach, which takes into account fundamental properties of the system (loop formation under complementary binding). Calculations are done in the framework of random walk theory. Partition function of the system is obtained in terms of arbitrary and first returns. It is shown that the loop factor of the theory has a power law behavior depending on the length of the chain.

Generalized model of polypeptide chain for helix-coil transition in two-component solvent

Within the frameworks of Generalized Model ofPolypeptide Chain (GMPC) the influence of the ligands interacting by different ways in the helix-coil transition is studied. It is shown that the model is reduced to the base model by converting the energy and the entropic parameters. In contrast to the case of the pure solvent, both the competitive and the noncompetitive interactions affect to these parameters. As a result, the temperature curve of melting shows more transitions. The influence of polyethylene glycol on the helix-coil transition in the polyalanine is discussed.

Theory of DNA condensation in the presence of stretching force: Zimm-Bragg model

A theory of DNA condensation by multivalent cations in the presence of an external stretching force is presented. It is shown that in the mean-field approximation the system is described by the Zimm-Bragg model with effective parameters of growth of ordered phase and cooperativity. Within the frames of the proposed model the experimental results on stretching of a double-stranded DNA of λ-phage are interpreted. Possible scenarios of homo- and heteropolymeric behavior of DNA during condensation are analyzed. A possible mechanism restricting the growth of linear size of DNA is proposed.

Sensitivity of DNA Sensors in the Presence of Charged Ligands

Factors that influence both the thermodynamics of hybridization and the stability of the DNA–DNA duplexes are analyzed. The noncompetitive DNA hybridization cases in the presence of mono- and bivalent positively charged ligands have been investigated and the comparison is made with the case of uncharged ligands. It has been shown that the charged ligands enhance the sensitivity of the DNA chips as compared with the uncharged ones.