Arsen V. Grigoryan

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.

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.

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.

The invariance of order parameter and temperature redefinition in helix-coil transition theory of circular closed DNA

The order-disorder (helix-coil) transition in circular closed DNA (ccDNA) is described on the basis of the open chain DNA (ocDNA) model, proposed earlier, which considers the transition as loop formation. The Hamiltonian of the ccDNA model is constructed on the basis of the open chain model taking into account topological restrictions. These restrictions are taken into account through hydrogen bond reduced energy dependence on the fraction of broken hydrogen bonds in the macromolecule. The invariance of the order parameter (helicity degree) has been shown for ocDNA and ccDNA. This invariance results in the interdependence between temperatures of ocDNA and ccDNA with the same value of helicity degree. The dependence can be obtained with the help of the derivative of reduced energy of hydrogen bonding dependence on instantaneous denaturation degree. Thus, it has been shown that the melting curve of ccDNA can be obtained from the consequent curve of ocDNA through the redefinition of temperature scale. The calculated and experimentally measured melting curves have been compared under inversion conditions and qualitative agreement between them is found.

Order-disorder transition in one-dimensional system with disorder in composition

The influence of structural inhomogeneity onto order-disorder transitions in 1D systems is considered in the scope of the Potts-like model with many-particle interactions. The helix-coil transition in DNAs, heterogeneous by hydrogen bonding energy, is considered as an example. The microcanonical method is employed to evaluate the free energy. The secular equation for the heteropolymer is constructed. Both the melting temperature and interval of DNA melting are obtained. In the limit of small difference between inverse melting temperatures of poly(A-T) and poly(G-C), the coincidence with classical results is obtained.