LIFSON-ALLEGRA THEORIES OF HELIX-COIL TRANSITION FOR RANDOM COPOLYMERS - COMPARISON WITH EXACT RESULTS AND EXTENSION

The theories of the helix–coil transition of Lifson, Lifson and Allegra, and Allegra for random copolymers are compared with the exact results of Lehman and McTague, as was done by Fink and Crothers in an earlier test of the approximate theories of Fixman and Zeroka, Reiss et al, and Montroll and Goel. The Fixman‐Zeroka theory is the best approximation to the exact result (under the conditions used), and the Allegra theory is next best, the calculated slope of the transition curve in the Allegra theory being too small by a factor of two. An alternative derivation of the Allegra approximation, using the method of sequence generating functions, is given, and the resulting equations are of very simple form. A hybrid method, based on the work of Lifson and Allegra, is also developed here; it involves a technique of successive approximations, and reduces to the Allegra theory in first order. The fourth‐order approximation gives a slope that is too small by 10%; however, the value of the slope, extrapolated to infinite order of approximation, converges to the exact result‐ of Lehman and Mc‐Tague. By using illustrative calculations of helix–coil transition curves, some physical insight into the behavior of a copolymer in the transition region is provided: it is found that an important feature determining the shape of the transition curve is the variation in composition over the correlation length. The question of the application of copolymer theory to DNA is discussed. Copyright © 1969 John Wiley & Sons, Inc.