Poland-Scheraga model

Fig. 1.8 A schematic view of the two strands of DNA. Some base pairs are in contact, and contribute an energy e, and some are detached, and they give no energy contribution. The base pairs that are not in contact form loops, 3 in the figure, and there is a contact at the end of each loop. In our definition of the Poland—Scheraga model = 1 corresponds just to a contact (and effectively no loop). So the length of a loop is — 1) and a loop of length zero is a contact. In the example N = 35.

The Poland Scheraga model is introduced by assigning the so called loop entropy S ) which is taken with the property... 

With a binary choice of the values of o , that is u>n a, b, a interaction energies of A-T and C-G couples, in view of the discussion in Section 1.4, P, w,/3 inhomogeneous Poland-Scheraga model, which gives a more realistic model for the DNA denaturation transition (we will come back to this issue in Section 1.10 and in Section 5.7). 

Notice in particular that there is no need to ask for k > 0, but of course one has to give up the interpretation of K -) as a sub-probability (it would rather be a combinatorial term, see in particular the way the Poland-Scheraga model has been introduced). Regardless of the value of K, we realize that, if c < —1, then exp( A )Z is the partition function of the homogeneous pinning model with polynomial decay of the return times (and critical point (3c)- Therefore there is a transition, between free energy equal to —k to larger than —k, at (3c- And it is... 

The literature on DNA denaturation and Poland-Scheraga models is extremely vast, including various review articles, see in particular [Richard and Guttmann (2004)]. For a more concise, but still rather clear exposition we suggest [Kafri et al. (2000)]. 

The smoothing effect of disorder in pinning models is a controversial issue in the physical literature, at least for a > 1. These are precisely the return probabilities considered to be of relevance for the DNA denat-uration modeling (see Section 1.4 and relative bibliographic complements). Relevant papers that attack the problem of regularity in disordered Poland-Scheraga models are in particular [Cule and Hwa (1997)], [Tang and Chate (2001)], [Blossey and Carlon (2003)], [Schafer (2005)], [Coluzzi (2005)],... 

Gaxel, T. and Monthus, C. (2005a). Numerical Study of the Disordered Poland-Scheraga Model of DNA Denaturation, J. Stat. Mech., Theory and Experiments, P06004. 

Gaxel, T. and Monthus, C. (2005b). Distribution of Pseudo-critical Temperatures and Lack of Self-averaging in Disordered Poland-Scheraga Models with Different Loop Exponents, Eur. Phys. J. B 48, pp. 393-403. 

Schafer, L. (2005). Can Finite Size Effects in the Poland-Scheraga Model Explain Simulations of a Simple Model for DNA Denaturation arXiv.org e-Print archive cond-mat 0502668... 

The similarities between non-ionic micelles and globular proteins (Nemethy, 1967 Schott, 1968 Jencks, 1969) render micelles potentially useful as models for the investigation of hydrophobic interactions. Indeed, the stability of non-ionic micelles has been treated theoretically in terms of hydrophobic interactions (Poland and Scheraga, 1965). Since the critical micelle concentration is related to the degree and nature of the hydrophobic interactions of the amphiphile, its valne in the presence of additives and at different temperatures can be nsed as a quantitative measure of the effect of these variables on the hydrophobic interactions. In spite of the similarities between proteins and micelles, considerable caution is warranted in extrapolating the results obtained from micellar models to the more complex protein systems. 

A simple model of this DNA denaturation transition was introduced in 1966 by Poland and Scheraga [70,71] (hereinafter referred to as PS) and refined by Fisher [72,73]. The model consists of an alternating sequence (chain) of straight paths and loops, which... 

In order to compare a theoretical model with the melting curves of natural DNAs, it is clear we must treat nonperiodic distributions of A-T and G-C base pairs. There have been a number of calculations which have considered random or Markov distributions of two base pair components. Poland and Scheraga have compared several approximate calculations with the results of Lehman and McTague. Fink and Crothers made a comparison between several theoretical approaches. In this section we review and compare the theories of Montroll and Yu, Vedenov and Dykhne, and Lehman and McTague. 

This one-dimensional intramolecular structural transition, the helix-coil transition, has received extensive theoretical treatment by many investigators.(65-75) Although a variety of models and mathematical techniques have been brought to bear on this problem the basic conclusions have been essentially the same. The methods involved, and the results, have been eloquently summarized in the treatise by Poland and Scheraga.(76) As an example, we will outline the theoretical basis for the transformation in dilute solution of an isolated polypeptide chain from the alpha-helical to the coil form. 

The helix-coil transition has occupied polypeptide chemists as models for such structural transformations in proteins (Poland and Scheraga, 1970). Both theoretical and experimental approaches have been taken in such studies (Scheraga, 1978) in order to obtain quantitative measures of the tendency of each of the 20 naturally occurring amino acids to adopt the helix vs. the coil (i.e. all other, non-helical) conformations. These tendencies are expressed in terms of the Zimm-Bragg (1959) nucleation and growth parameters, O and s, respectively. The values of a and s may be used directly to predict the locations of a-helices in proteins. The values of a and s have been obtained from experimental studies of thermally-induced helix-coil transitions in host-guest random copolymers... 

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