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## Zimm-Bragg modelIn statistical mechanics, the ## Additional recommended knowledge
## Helix-coil transition modelsHelix-coil transition models assume that polypeptides are linear chains composed of interconnected segments. Further, models group these sections into two broad categories: Thus, it is possible to loosely represent a macromolecule as a string such as CCCCHCCHCHHHHHCHCCC and so forth. The number of coils and helices factors into the calculation of fractional helicity, , defined as where - is the average helicity and
- is the number of helix or coil units.
## Zimm-Bragg
The Zimm-Bragg model takes the cooperativity of each segment into consideration when calculating fractional helicity. The probability of any given monomer being a helix or coil is affected by which the previous monomer is; that is, whether the new site is a nucleation or propagation. By convention, a coil unit ('C') is always of statistical weight 1. Addition of a helix state ('H') to a previously coiled state (nucleation) is assigned a statistical weight , where is the nucleation parameter and - .
Adding a helix state to a site that is already a helix (propagation) has a statistical weight of . For most proteins, which makes the propagation of a helix more favorable than nucleation of a helix from coil state. From these parameters, it is possible to compute the fractional helicity . The average helicity is given by where is the statistical weight and is the partition function given by the sum of the probabilities of each site on the polypeptide. The fractional helicity is thus given by the equation - .
## Statistical mechanicsThe Zimm-Bragg model is equivalent to a one-dimensional Ising model and has no long-range interactions, i.e., interactions between residues well separated along the backbone; therefore, by the famous argument of Rudolf Peierls, it cannot undergo a phase transition. The statistical mechanics of the Zimm-Bragg model where the 2x2 transfer matrix The ## See also- Alpha helix
- Lifson-Roig model
- Random coil
- Statistical mechanics
## References**^**Samuel Kutter; Eugene M. Terentjev (16 October 2002). "Networks of helix-forming polymers".*The European Physical Journal E - Soft Matter***8**(5): 539-47. EDP Sciences. PMID 15015126.**^**Ken A. Dill; Sarina Bromberg (2002).*Molecular Driving Forces - Statistical Thermodynamics in Chemistry and Biology*. Garland Publishing, Inc., 505.**^**Zimm, BH; Bragg JK (1959). "Theory of the Phase Transition between Helix and Random Coil in Polypeptide Chains".*Journal of Chemical Physics***31**: 526-531.
Categories: Polymer physics | Protein structure | Statistical mechanics | Thermodynamics |
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Zimm-Bragg_model". A list of authors is available in Wikipedia. |