| Popis: |
To complement the utility of thermodynamic calculations in the design and analysis of nucleic acid secondary structures, we seek to develop efficient and scalable algorithms for the analysis of secondary structure kinetics. Secondary structure kinetics are modeled by a first-order master equation, but the number of secondary structures for a sequence grows exponentially with the length of the sequence, meaning that for systems of interest, we cannot write down the rate matrix, much less solve the master equation. To address these difficulties, we develop a method to construct macrostate maps of nucleic acid free energy landscapes based on simulating the continuous-time Markov chain associated with the microstate master equation. The method relies on the careful combination of several elements: a novel procedure to explicitly identify transitions between macrostates in the simulation, a goodness-of-clustering test specific to secondary structures, an algorithm to find the centroid secondary structure for each macrostate, a method to compute macrostate partition functions from short simulations, and a framework for computing transition rates with confidence intervals. We use this method to study several experimental systems from our laboratory with system sizes in the hundreds of nucleotides, and develop a model problem, the d-cube, for which we can control all of the relevant parameters and analyze our method's error behavior. Our results and analysis suggest that this method will be useful not only in the analysis and design of nucleic acid mechanical devices, but also in wider applications of molecular simulation and simulation-based model reduction. |
