Differential Melting Curves in Heterogeneous Biopolymers
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erential Melting Curves in Heterogeneous Biopolymers A. Asatryana, A. Y. Mamasakhlisovb, and V. F. Morozova, * a
Yerevan State University, Yerevan, Armenia Russian–Armenian University, Yerevan, Armenia *e-mail: [email protected]
b
Received February 26, 2020; revised March 23, 2020; accepted April 9, 2020
Abstract—The paper considers the order-disorder transition in a sequence of two varieties of repeating units. It is shown that the reduced free energy converges to the limit at the chain length of more than 3000. The origination of the fine structure of differential melting curves, the order–disorder transition interval, and the behavior of the fraction of junctions between the ordered and disordered phases are considered. In the primary structure, the small-scale correlations are taken into account. Keywords: order-disorder transition, sequence heterogeneity, melting curve DOI: 10.3103/S1068337220030068
1. INTRODUCTION Various processes in biological systems often result in or are accompanied by an order-to-disorder transition in biopolymers. Since the 1960s, the spiral-coil transition in biopolymers has been actively studied: first, Shellman [1] proposed a theoretical description of the spiral–coil transition in polypeptides, then Zimm and Bragg [2–5] worked in the same direction. Theoretical studies were later developed by Lifson, Frank- Kamenetski [6–9] and others [10–12]. The problem of the spiral-coil transition is still one of the most popular problems in structural biology [13–16]. Most of the work is focused on the study of homopolymers. From the experimental point of view, there is no consistent theory describing such an important quantity as the fine structure of the differential melting curves (DMC), at the moment. This work is dedicated to solving this problem. The identification of the mechanism of the appearance of the fine structure on the DMC of heteropolymers will provide additional information on the spiral-coil transition mechanisms in more complex real systems. 2. THE GENERALIZED MODEL OF THE POLYPEPTIDE CHAIN (GPCM) The approach used in this work is based on the model of a generalized polypeptide chain model (GPCM) [13]. Earlier, we proposed a microscopic theory of the spiral-coil transition, acceptable for both polypeptides and DNA [13]. One of the most widely used models in the quantum field theory, the physics of ferromagnets, and the polymer physics is the Potts Q-component model, which is nothing other than a generalization of the Ising model. As was shown [17–19], to study the spiral-coil transition, it is necessary to slightly modify the Potts model. Based on this Potts model, the theory of the spiral-coil transition in polypeptides was developed [17–19]. It was also shown that, neglecting large-scale loops, the characteristic equation for the DNA model coincides with that for the GPCM [19]. Because the further research will be carried out on the basis of the basic GPCM, we will therefore present its main points. One of the important characteristics of the polypeptide chain is the value
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