The looping probability of random heteropolymers helps to understand the scaling properties of biopolymers

Random heteropolymers are a minimal description of biopolymers and can provide a theoretical framework to the investigate the formation of loops in biophysical experiments. A two–state model provides a consistent and robust way to study the scaling properties of loop formation in polymers of the size of typical biological systems. Combining it with self–adjusting simulated–tempering simulations, we can calculate numerically the looping properties of several realizations of the random interactions within the chain. Differently from homopolymers, random heteropolymers display at different temperatures a continuous set of scaling exponents. The necessity of using self–averaging quantities makes finite–size effects dominant at low temperatures even for long polymers, shadowing the length–independent character of looping probability expected in analogy with homopolymeric globules. This could provide a simple explanation for the small scaling exponents found in experiments, for example in chromosome folding.