Predicting DNA kinetics with a truncated continuous-time Markov chain method
Predicting the kinetics of reactions involving nucleic acid strands is a fundamental task in biology and biotechnology. Reaction kinetics can be modeled as an elementary step continuous-time Markov chain, where states correspond to secondary structures and transitions correspond to base pair formation and breakage. Since the number of states in the Markov chain could be large, rates are determined by estimating the mean first passage time from sampled trajectories. As a result, the cost of kinetic predictions becomes prohibitively expensive for rare events with extremely long trajectories. Also problematic are scenarios where multiple predictions are needed for the same reaction, e.g., under different environmental conditions, or when calibrating model parameters, because a new set of trajectories is needed multiple times. We propose a new method, called pathway elaboration, to handle these scenarios. Pathway elaboration builds a truncated continuous-time Markov chain through both biased and unbiased sampling. The resulting Markov chain has moderate state space size, so matrix methods can efficiently compute reaction rates, even for rare events. Also the transition rates of the truncated Markov chain can easily be adapted when model or environmental parameters are perturbed, making model calibration feasible. We illustrate the utility of pathway elaboration on toehold-mediated strand displacement reactions, show that it well-approximates trajectory-based predictions of unbiased elementary step models on a wide range of reaction types for which such predictions are feasible, and demonstrate that it performs better than alternative truncation-based approaches that are applicable for mean first passage time estimation. Finally, in a small study, we use pathway elaboration to optimize the Metropolis kinetic model of Multistrand, an elementary step simulator, showing that the optimized parameters greatly improve reaction rate predictions. Our framework and dataset are available at https://github.com/DNA-and-Natural-Algorithms-Group/PathwayElaboration.
© 2023 Elsevier. The authors would like to thank the annonymous reviewers for their helpful feedback. This research was partially supported by the Natural Sciences and Engineering Research Council of Canada RGPIN-2016-04240, the United States National Science Foundation CHE/CCF 1643606, and the Canada CIFAR AI Chair Program. CRediT authorship contribution statement. Sedigheh Zolaktaf: Formulating the solution, Incorporating the data, Conducting experimental studies, Writing the paper. Frits Dannenberg: Formulating the solution, Incorporating the data, Conducting and guiding experimental studies, Writing the paper. Mark Schmidt: Guiding the experimental studies, Formulating the solution, Incorporating the data, Writing the paper. Anne Condon: Guiding the experimental studies, Formulating the solution, Incorporating the data, Writing the paper. Erik Winfree: Guiding the experimental studies, Formulating the solution, Incorporating the data, Writing the paper. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.