The effect of disorder in the contact probability of elongated conformations of biopolymers

Biopolymers are characterized by heterogeneous interactions, and usually perform their biological tasks forming contacts within domains of limited size. Combining polymer theory with a replica approach, we study the scaling properties of the probability of contact formation in random heteropolymers as a function of their linear distance. It is found that close or above the theta--point, it is possible to define a contact probability which is typical (i.e. "self-averaging") for different realizations of the heterogeneous interactions, and which displays an exponential cut--off, dependent on temperature and on the interaction range. In many cases this cut--off is comparable with the typical sizes of domains in biopolymers. While it is well known that disorder causes interesting effects at low temperature, the behavior elucidated in the present study is an example of a non--trivial effect at high temperature.