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RNA secondary structure folding kinetics is known to be important for thebiological function of certain processes, such as the hok/sok system in E.coli. Although linear algebra provides an exact computational solution ofsecondary structure folding kinetics with respect to the Turner energy modelfor tiny (~ 20 nt) RNA sequences, the folding kinetics for larger sequences canonly be approximated by binning structures into macrostates in a coarse-grainedmodel, or by repeatedly simulating secondary structure folding with either theMonte Carlo algorithm or the Gillespie algorithm. Here we investigate therelation between the Monte Carlo algorithm and the Gillespie algorithm. Weprove that asymptotically, the expected time for a K-step trajectory of theMonte Carlo algorithm is equal to <N> times that of the Gillespie algorithm,where <N> denotes the Boltzmann expected network degree. If the network isregular (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 theGillespie algorithm multiplied by <N>; however, this is not true fornon-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 timesare roughly correlated. Simulation software for RNA secondary structure foldingaccording 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 secondarystructures of a given RNA sequence { see http://bioinformatics.bc.edu/clote/RNAexpNumNbors.

RNA folding kinetics using Monte Carlo and Gillespie algorithms?