Effect of disorder on 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 to or above the θ 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 cutoff, dependent on temperature and on the interaction range. In many cases this cutoff 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 nontrivial effect at high temperature.