Eur. Phys. J. E (2013) 36: 46
https://doi.org/10.1140/epje/i2013-13046-7

Regular Article

Helix-coil transition in terms of Potts-like spins

¹⁹⁸⁶¹ Department of Theoretical Physics, J. Stefan Institute, Jamova 39, SI-1000, Ljubljana, Slovenia
²⁹⁸⁶¹ Dipartimento di Scienze Molecolari e Nanosistemi, Università Ca’ Foscari Venezia, Calle Larga S. Marta DD2137, I-30123, Venezia, Italy
³⁹⁸⁶¹ Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, SI-1000, Ljubljana, Slovenia
⁴⁹⁸⁶¹ Department of Molecular Physics, Yerevan State University, A. Manougian Str. 1, 375025, Yerevan, Armenia

^* e-mail: abadasyan@gmail.com

Received: 25 September 2012
Revised: 24 February 2013
Accepted: 22 April 2013
Published online: 14 May 2013

Abstract

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.