RNA folding kinetics using Monte Carlo and Gillespie algorithms?

TL;DR

This paper compares Monte Carlo and Gillespie algorithms for modeling RNA folding kinetics, proving their asymptotic relation and analyzing differences in mean first passage times, with software tools provided.

Contribution

It establishes the theoretical relationship between Monte Carlo and Gillespie algorithms in RNA folding kinetics and explores their differences in practical scenarios.

Findings

Expected time for Monte Carlo trajectory equals <N> times that of Gillespie.

Mean first passage time by Monte Carlo correlates with Gillespie but differs for non-regular networks.

Software tools for RNA folding kinetics simulation are publicly available.

Abstract

RNA secondary structure folding kinetics is known to be important for the biological function of certain processes, such as the hok/sok system in E. coli. Although linear algebra provides an exact computational solution of secondary structure folding kinetics with respect to the Turner energy model for tiny (~ 20 nt) RNA sequences, the folding kinetics for larger sequences can only be approximated by binning structures into macrostates in a coarse-grained model, or by repeatedly simulating secondary structure folding with either the Monte Carlo algorithm or the Gillespie algorithm. Here we investigate the relation between the Monte Carlo algorithm and the Gillespie algorithm. We prove that asymptotically, the expected time for a K-step trajectory of the Monte Carlo algorithm is equal to <N> times that of the Gillespie algorithm, where <N> denotes the Boltzmann expected network degree. If the network is regular (i.e. every node has the same degree), then the mean first passage time (MFPT) computed by the Monte Carlo algorithm is equal to MFPT computed by the Gillespie algorithm multiplied by <N>; however, this is not true for non-regular networks. In particular, RNA secondary structure folding kinetics, as computed by the Monte Carlo algorithm, is not equal to the folding kinetics, as computed by the Gillespie algorithm, although the mean first passage times are roughly correlated. Simulation software for RNA secondary structure folding according to the Monte Carlo and Gille- spie algorithms is publicly available, as is our software to compute the expected degree of the net- work of secondary structures of a given RNA sequence { see http://bioinformatics.bc.edu/clote/ RNAexpNumNbors.