Principles of Protein Structural Organization - H. Schultz 1982

Statistical Mechanics of the Helix-Coil Transition
Comparison with Experimental Data: Helix-Coil Transition Curves and the Zimm-Bragg Model

Experimental helix—coil transition curves are described using the Zimm—Bragg model. To test the Zimm—Bragg model, the theoretical helix—coil transition curves (Equation (A.15)) shown in Fig. A.1, a should be compared with the experimental ones. When the helix content (n) is measured as a function of Temperature T, sigmoidal curves similar to those shown in Fig. A.1, a are obtained. For comparison, the temperature T must be converted into the relative statistical weight s. In the transition region, T is approximately proportional to s (Section A.4 and Fig. A.2). If the enthalpy difference ∆H of the transition is known, T can be replaced by s using Equation (A.18). The resulting experimental transition curve (n) as a function of s can then be compared with the theoretical curve corresponding to the appropriate nucleation parameter a. In most cases, a quite satisfactory agreement is achieved, which validates the Zimm—Bragg model.

Approximate values of σ for synthetic polymers

In the case of a temperature-induced helix—coil transition, the nucleation parameter can be estimated from the slope of the curve at the inflection point. As shown above, the experimental temperature-induced helix—coil transition curve can be compared with the theoretical curve if the value of ∆H is known. This comparison makes it possible to obtain the nucleation parameter. However, in many cases the value of ∆H is unknown. Nevertheless, the value of a can still be estimated. According to Equation (A.15) and taking into account Equation (A.10), the slope of the transition curve at the inflection point (s = 1) must be equal to

Class="center">

The value of ∆H is typically on the order of 1 kcal/mol. Using this value, we convert the experimental derivative ∂(n)/∂T into ∂(n)/∂s (Fig. A.2) and obtain The values of a using Equation (A.20). The observed values of a for synthetic polymers are on the order of 10-⁴. This means that each junction between the helical and coil segments lowers the statistical weight of the corresponding chain conformation by a factor of 100 (Equation (A.6)). At the transition temperature, the average length of the helical segments is 100 residues (Equation (A.17)). It should be noted that these values were obtained under the assumption of very large values of N.