Helix‐coiled transition in heteropolymers. I. Ground‐state energy

Abstract

AbstractA new technique is presented for treating the ground state of an heteropolymer with a random sequence of components. An exact system of equations is found for determining the ground state energy E which is equal to the polymer free energy f in the lowest‐order approximation in T/V (V/2 is the large “surface” energy arising at the boundaries between coiled and “helical” sections: V ≫ T, Uk; U1 and –U2 are the free energies of the components counted from the corresponding coiled state energies). These equations are essentially simplified at certain fixed values of the ratio U1/U2. For integer values of U2/U1 and U1/U2 a solution is obtained with an accuracy exp(–V/Uk). The ground‐state energy as a function of U1 and U2 is shown to be highly irregular: its derivatives have jumps at an infinite number of points. These jumps provide a fine structure of the melting curves. A smoothed over the jumps function E′ is found by way of analytic continuation from the integer values of U1/U2 and U2/U1. The accuracy of the approximation f ≈ E is estimated and the correctional term of order T/V is determined.