Folding rate dependence on the chain length of RNA-like heteropolymers

Computer experiments and analytical estimates have shown that protein and RNA chains can reach their most stable folds without an exhaustive search over all their possible conformations. Protein-like chain folding proceeds via a specific nucleus and under conditions optimal for the fastest folding of these chains the dependence of the folding time (t) on the chain length (L) is in accord with the power law t integral of Lb (b is a constant).

Using Monte-Carlo folding simulations for a simple model of RNA secondary structure formation, we estimated the RNA chain length dependence of the time necessary to reach the lowest energy fold. Our results are compatible with a relatively weak power dependence of the folding time on the chain length, t integral of Lb. Such dependencies have been observed for different folding conditions, both for random sequences (here, b > 5) and for sequences edited to stabilize their lowest energy folds (for extremely edited sequences b < 2). Although folding transitions in RNA chains are not an all-or-none type in terms of thermodynamics, they proceed via a folding nucleus in terms of kinetics. The peculiarity (compared with protein folding) is that the RNA critical nucleus is big and non-specific.

We have obtained a general scaling for the dependence of the RNA secondary structure on the chain length. The obtained power dependence is very weak compared with an exponential dependence for an exhaustive sorting.