Zipper transition model

D16.4 The simple zipper model for the conversion of a polypeptide helical (h) chain to a random coil (c) begins with nucleation whereby an h residue makes an independent transition to a c residue with a probability that depends upon as where a < l and s is the stability parameter. After the nucleation conversion, only residues adjacent to a c undergo the h to c transition and they do so non-cooperatively with a probability that depends upon the stability parameter. The Zimm-Brag model allows for multiple nucleation sites. 

Most transitions in the secondary structures of biomacromolecules fall somewhere between the cooperative none-or-all and the noncooperative models. Many of these transitions can be described by the zipper model, which dissects the structural transition of a polymeric chain into a number of discrete steps (Figure 9.1). The model is a special case of the cooperative structural transition of biomacromolecules. In the zipper model, the initiation of the transition is harder than extension (propagation) and therefore low probability. This initiation step is of high energy and provides a nucleation point for the transition. The subsequent extension steps occur by a series of lower energy and consequently higher probability. 

The partition function for the zipper model is derived from the basic relationships of the noncooperative model. The only difference is the statistical weight for the first step Wi that must include a nucleation parameter, a to represent the probability (lower probability therefore a < 1) for initiating the transition. Therefore the statistical weight for the state / = 1 is w, = as. Two possibilities exist for the next step of the transition. In one case,... 

Thus the temperature-dependent transition of polypeptide chains can be modeled by the statistical mechanics treatment of the two-state zipper model. 

Both the coil-to-helix and hehx-to-coil transitions are cooperative and can be described by the two-state zipper model. 

In applying the zipper model, the transitions are characterized by the nucleation parameter o and propagation parameter s. 

The helical transitions from B-DNA to A-DNA and from B-DNA to Z-DNA can be treated as the zipper model. In these transitions, a defines the extra energy AGj° required to form a junction between the two forms. A relatively small AGj° for the nucleation is probably due to the small difference in the bp stacking between A-DNA and B-DNA. The parameter s is associated with the difference in energy between bps in A-DNA versus B-DNA and on environment factors such as temperature, salt and organic solvents, all of which stabilize left-handed Z-DNA. 

The molecule with the charge distribution (73) can be considered as a model for a B-DNA hehx charges on the strands represent the phosphates and the cylinder charge corresponds to adsorbed cations, smeared on the DNA surface (for B-DNA, a 10 A, B 0.4 H [182]). Note that (74) could also be used for the description of electrostatically induced conformational changes of DNA, e.g., for the B- to Z-DNA transition at high salt concentrations [183]. Moreover, the exact theory of electrostatic interaction between two DNA duplexes predicts an attraction between them due to a correlated structure-driven zipper-like charge separation along the molecules [184]. 

For intermediate chain lengths and for double-Helix Coil transitions refined models have to be used with the explicit inclusion of chain-end effects and the possibilities of staggering and sliding zipper, etc. mechanisms. Numerical model calculations have recently been used to approach the right model for the conformational transition of oligonucleotides [21], showing more than one relaxation time. 

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