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; 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/U_k). 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.