Randomly charged polymers

Abstract

Polyampholytes (PAs) are polymers with a random sequence of positive and negative charges along their backbone. We have studied systematically the dependence of internal energy and shape of the PA on its excess charge by combining analytic arguments, Monte Carlo simulations, and exact enumeration of all configurations of short chains. The results indicate that the overall excess charge, Q, is the main determinant of the size of the PA. A polymer composed of a mixture of N positive and negative charges ±qo, is compact for Q<Q c ≈qo √N, and expanded otherwise. The transition between the two states at low temperatures is reminiscent of the Rayleigh shape instability of a charged drop. A uniform excess charge causes the breakup of a fluid drop; we show that a uniformly charged polymer stretches out to a necklace shape. The inhomogeneities in charge distort the shape away from an ordered necklace. The freezing transition of a PA, and its relevance to proteins is also discussed.