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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.