Partition function helical model

A partition function is derived for a simple model of interacting helices in a short (20 residues) chain of poly-L-alanine. It Is found that interhelical hydrophobic bonds effect a marked stabilization of helical forms, and give rise to a sharp transition of the type found in many polymers. 

As before, the total free energy is minimized with respect to 0. Minimization leads to the following results [41]. (a) The minimum value of 0 is identical with Eq. (7) from the line model. This implies that the number of condensed ions is unaffected by the helix and is governed only by the linear charge-density parameter E,. (b) The partition function <2heiix is influenced by the helical structure of the phosphate charges... 

The above-mentioned results may be alternatively described in terms of the one dimensioned Ising model in order to extract the feature of the interactions. There are several theories that treat DNA-ligand interactions, but one of the simplest was conveniently chosen to express cooperative nature of the phenomena. The phosphate groups on DNA u e viewed as an array of binding sites along the poly(nucleotide) helices, each site being occupied or vacant. The partition function, z, for such system is written as. 

You can check Equation (26.22) by noting that it gives the same sum as adding all the statistical weights in Table 26.3. From the partition function, Equation (26.21), you can compute the properties of the model, such as the fractional helicity. 

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