The similarity in the thermodynamic properties of two completely different theoretical models for the helix-coil transition is examined critically. The first model is an all-atomic representation for a poly-alanine chain, while the second model is a minimal helix-forming model that contains no system specifics. Key characteristics of the helix-coil transition, in particular, the effective critical exponents of these two models agree with each other, within a finite-size scaling analysis.Pacs: 87.15. He, 64.70Cn, 02.50.Ng The importance of understanding the statistical physics of the protein-folding problem has been stressed recently [1, 2]. For instance, it is now often assumed that the energy landscape of a protein resembles a partially rough funnel. Folding occurs by a multi-pathway kinetics and the particulars of the folding funnel determine the transitions between the different thermodynamic states [1, 3]. This "new view" [1] of folding was derived from studies of minimal protein models which capture only a few, but probably dominant parameters (chain connectivity, excluded volume, etc.) in real proteins.An implicit yet fundamentally crucial assumption is that the basic mechanism of structural transitions in biological molecules depends solely on gross features of the energy function, not on their details, and that a law of corresponding states can be used to explain dynamics and structural properties of real proteins from studies of related minimal models. This assumption needs to be proven. An even stronger notion in statistical physics is the universality hypothesis for critical phenomena. The 1 critical exponents are identical for different theoretical models and realistic systems belonging to the same universality class. Many theoretical concepts in protein folding, such as coil-helix or coil-globular transitions involve phase transition or phase transition-like behavior. Thus, one wonders if physical measurements between two model systems for the same transition would have any "universal" properties.The purpose of this article is to examine these questions for the helix-coil transition in homopolymers of amino acids [4,5]. Traditionaly, the coil-helix transition is described by theories such as the Zimm-Bragg model [6] in which the homopolymers are regarded as one dimensional systems with only local interactions; as such a true thermodynamic phase transition is impossible. However, recently there have been [4,5] indications that the coil-helix transition near the transition temperature displays phase-transition like behavior. We use here finite-size scaling analysis, a common tool in statistical physics, to examine the question of universality of the helix-coil transition in two completely different, illuminating models. On one hand, we have a detailed, all-atomic representation of a homo poly-alanine chain [7]. On the other hand, we have a simple coarse-grained model describing the general features of helix-forming polymers [4]. In this article, our interest lies in finding out how fa...
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