Generalized Model Of Polypeptide Chain Research Articles

Construction of Helix–Coil Transition Curves in Heterogeneous Biopolymers Based on Melting Curves of Homopolymers

The theory of helix–coil transition in the model of the heteropolymeric DNA is considered. The theory is based on the Generalized Model of Polypeptide Chain (GMPC) with the use of the method of constrained annealing. The free energy of heteropolymers is obtained by way of the transfer-matrix of homopolymeric GMPC with the redefined parameters. The algorithm of melting curves computation based on the homopolymeric model is obtained.

Possible mechanism of non-monotone behavior of helix-coil transition temperature in two-component solvent

Within the frameworks of generalized model of polypeptide chain (GMPC) the concentrational behavior of helix-coil transition temperature of biopolymer in two-component solvent was observed on the simplest models. It is shown that if the solvent and the ligand interact with the biopolymer at different binding sites, and even if both components influence the helical state in the same way, the model allows one to obtain the non-monotone character of the melting temperature behavior of biopolymer depending on the ligand concentration. It is shown that changes in the regime of helical state stability is not always related with the competition of stabilizing and destabilizing interactions of blend components but can be the result of the cumulative effect of both components.

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.

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.

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.

Helix-coil transition in terms of Potts-like spins

In the spin model of a helix-coil transition in polypeptides a preferred value of spin has to be assigned to the helical conformation, in order to account for different symmetries of the helical vs. the coil states, leading thus to the Generalized Model of Polypeptide Chain (GMPC) Hamiltonian as opposed to the Potts model Hamiltonian, both with many-body interactions. Comparison of explicit transfer matrix secular equations of the Potts model and the GMPC model reveals that the largest eigenvalue of the Potts model with Δ many-body interactions coincides with the largest eigenvalue of the GMPC model with Δ - 1 many-body interactions, indicating the identity of both free energies. In distinction, the second largest eigenvalues in both models do not coincide, indicating a different behavior for the spatial correlation length that in its turn defines the width of the helix-coil transition interval. We explore in detail the thermodynamic consequences, resulting from spin models with and without the built-in spin anisotropy, that should indicate which model to favour as a more appropriate description of the equilibrium physical properties pertaining to the helix-coil transition.

170 GMPC model and the helix–coil transition in biopolymers

The Hamiltonian of the generalized model of polypeptide chain (GMPC) is introduced to describe the system in which the conformations are correlated over some dimensional range Δ. The Hamiltonian does not contain any parameter designed especially for helix–coil transition and uses pure molecular microscopic parameters (the energy of hydrogen bond formation, reduced partition function of repeated unit, the number of repeated units fixed by one hydrogen bond, the flexibility of chain, the energies of interaction between the repeated units and the solvent molecules) (Badasyan et al., 2005, 2004). We evaluate the partition function using transfer-matrix approach. We describe the influence of solvent interaction with biopolymer, both with competing and noncompeting for hydrogen bond formation ways. On handling the problem of solvent influence on helix–coil transition, we obtained dependence on energy of solvent–macromolecule interaction, how solvents change correlation length, transition temperature, and interval. We obtained that two type interaction of solvent results in low temperature coil–helix transition, which we connect with cold denaturation. A 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 (Badasyan et al., 2012). We also took into account two biopolymers’ side-by-side interactions. In the case of effective repulsion; the shape of the melting curve is two-phase with high and wide correlation length in a plateau on denaturation curve (Badasyan et al., 2009). We also took into account structural heterogeneity of biopolymers using constrained annealing approximation (Serva & Paladin, 1993).

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.

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.

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 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.