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

A 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 , U k ; U 1 and – U 2 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 U 1 / U 2 . For integer values of U 2 / U 1 and U 1 / U 2 a solution is obtained with an accuracy exp(– V / U k ). The ground‐state energy as a function of U 1 and U 2 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 U 1 / U 2 and U 2 / U 1 . The accuracy of the approximation f ≈ E is estimated and the correctional term of order T / V is determined.