A. V. Tsarukyan

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.

Stacking heterogeneity: A model for the sequence dependent melting cooperativity of duplex DNA

A microscopic Potts-like one-dimensional model with many particle interactions [referred as the generalized model of polypeptide chains (GMPCs)] is developed to investigate cooperativity of DNA sequence dependent melting. For modeling sequence, regular homogeneous sequences were arranged in heterogeneous blocks of various lengths. Within the framework of the GMPC the authors show that the inclusion of stacking interaction heterogeneity relative to homogeneous hydrogen bond interactions leads to an unexpected and quite remarkable increase in melting cooperativity for small blocks. In some cases this tendency persists for long blocks having sharp sequence heterogeneity.

Helix-coil transition of biopolymers in solvents interacting in competitive and non-competitive ways

Within the framework of generalized model of polypeptide chain, on the basis of the Hamiltonian of model of solvent, which interacts with a biopolymer in both competitive and noncompetitive ways, introduced earlier, analytical expressions are obtained and thermodynamic and other averaged parameters are calculated for both the repeating units of the biopolymer and the solvent molecules. Different cases of relations between parameters of competitive and non-competitive bonding are considered and processes of melting and alignment are studied. It is shown that these processes are accompanied by changes in solvation and redistribution of solvent molecules between the helical and coiled portions of the chain.

Competitive and non-competitive interaction of solvent with biopolymers at the helix-coil transition

On the basis of generalized model of polypeptide chain (GMPC) as a microscopic theory of the helix-coil transition applicable to both polypeptides and DNA, the Hamiltonian of the model of solvent, which interacts with a biopolymer in both competitive and non-competitive ways, is introduced. It is shown that the partition function of this model is reduced to multipliers to the model without solvent. In this case thermal and entropic parameters of the theory are redefined. Based on calculation of the helicity degree and correlation length different cases of relation between parameters of competitive and non-competitive interaction are discussed.

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.

Hamiltonian and partition function of the generalized model of polypeptide chain in competing and non-competing solvents in the presence of interchain interactions

For the generalized model of polypeptide chain in competing and non-competing solvents, the Hamiltonian is constructed with allowance for interchain interactions. It is shown that the partition function for the model in a solvent coincides to inessential factor with the partition function without solvent, if redefinition is made of the reduced interaction energy J for a competing solvent and of the number of conformations Q for a non-competing solvent.

Helix-coil transition in the case of interaction between two chains

Based on the generalized model of polypeptide chain the helix-coil transition in two chains, which are interacting abreast, is studied. There are four types of interaction (hh, hc, ch, cc). The Hamiltonian of system includes the basic Hamiltonian for two chains and the term which is responsible for interactions. It is shown that, when the energy of one type interaction (hh, cc) is more than the energy of mixed-type interaction (hc, ch), the correlation length grows sharply and melting interval becomes narrower. The system has a nontrivial behavior when the energy of mixed-type interactions (hc, ch) is higher than that of the one-type interaction (hh, cc). In this case one can observe the growth of the correlation length, and the melting curve has a two-stage character. The portion of junctions and the average length of helical fractions show that the merging and breakup of helical fractions take place.

Generalized model of polypeptide chain with limitations on the length of helical fractions

A model is proposed described by a Hamiltonian consisting of two terms corresponding to Hamiltonians of the generalized model of polypeptide chain (GMPC) with different scales of interaction. We consider a case where the long-scale interaction corresponds to attraction, while the short-scale interaction corresponds to repulsion; this case models the melting of the system in compact packing conditions (globularized polypeptide or DNA in capsid). In the framework of the transfer-matrix approach we calculate the correlation length and the helicity degree. It is shown that the temperature dependence of the correlation length is determined by the complex second eigenvalue of the transfer-matrix. In this regime the system displays a new type of correlations when the melting interval cannot be a measure of the system cooperativity.

STRUCTURAL INVESTIGATION OF ORDERING IN BIOPOLYMERS

The Generalized Model of the Polypeptide Chain is developed for the conformational transitions in double-strand polynucleotides. The melting temperature and interval and the correlation length have been calculated. The inter-chain interaction, effects of heterogeneity and the stacking-interaction influence have been incorporated into the model and the corresponding parameters have been estimated.