The Random Surface Model Describing the Helix-Coll Transition in Polypeptides

One dimensional Potts model with many-body interactions and the Generalized Model of Polypeptide Chain for the helix-coil transition

“…To summarize, statistical description of the helix-coil transition requires three basic parameters: an energetic parameter, W = exp(U/T ), where U is the energy of a hydrogen bond; an entropic parameter, Q, that stands for the number of spin values; and a geometric parameter, ∆, that describes the many-body geometry of the hydrogen bond formation. The corresponding Hamiltonian can thus be built in terms of the γ i spins [15,16,17,18,20,23] and corresponds to the GMPC model if the proper helix formation demands that ∆ successive γ's are all in the same preferred conformation number, e.g. 1 (see Fig.…”

“…It is obvious, that there are ∆ non-trivial eigenvalues, so that to construct the thermodynamics of the model, it is enough to consider a transfer matrix of a much smaller, (∆ × ∆) size. Such a matrix has been derived in [15] by doing elementary transformation over G ∆ and looks like…”

“…The effects of the former can be analyzed within the many-valued (Potts) spin model with an arbitrary but finite range of many-body interactions, while the latter forms the basis of The Generalized Model of Polypeptide Chain (GMPC), accounting for the preferred spin orientation. GMPC has been formulated several decades ago [15,16,17] and has been extensively studied specifically in the context of the helix-coil transition [18,20,23]. It was shown that the Zimm-Bragg model [13] and the Lifson-Roig model [14] both correspond to particular cases of the GMPC variety with ∆ = 2 and ∆ = 3, respectively [17,18].…”