FOLDING RATE DEPENDENCE ON THE CHAIN-LENGTH FOR RNA-LIKE HETEROPOLYMERS

Background: Computer experiments and analytical estimates have shown t hat protein and RNA chains can reach their most stable folds without a n exhaustive search over all their possible conformations. Protein-lik e chain folding proceeds via a specific nucleus and under conditions o ptimal for the fastest folding of these chains the dependence of the f olding time (t) on the chain length (L) is in accord with the power la w t similar to L-b (b is a constant). Results: Using Monte-Carlo foldi ng simulations for a simple model of RNA secondary structure formation , we estimate the RNA chain length dependence of the time necessary to reach the lowest energy fold. Our results are compatible with a relat ively weak power dependence of the folding time on the chain length, t similar to L-b. Such dependencies have been observed for different fo lding conditions, both for random sequences (here, b > 5) and for sequ ences edited to stabilize their lowest energy folds (for extremely edi ted 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-speci fic. Conclusions: We have obtained a general scaling for the dependenc e of the RNA secondary structure on the chain length, The obtained pow er dependence is very weak compared with an exponential dependence for an exhaustive sorting.