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Efficiently estimating kinetics of interacting nucleic acid strands modeled as continuous-time Markov chains Zolaktaf, Sedigheh


Nucleic acid molecules are vital constituents of living beings. These molecules are also utilized for building autonomous nanoscale devices with biological and technological applications, such as toehold switches, algorithmic structures, robots, and logic gates. Predicting the kinetics (non-equilibrium dynamics) of interacting nucleic acid strands, such as hairpin opening and strand displacement reactions, would assist with understanding the functionality of nucleic acids in the cell and with building nucleic-acid based devices. Continuous-time Markov chains (CTMC) are commonly used to predict the kinetics of these reactions. However, predicting kinetics with CTMC models is challenging. Because, first, the CTMCs should be defined with accurate and biophysically realistic kinetic models. Second, the state space of the CTMCs may be large, making predictions time-consuming, particularly for reactions that happen on a long time scale (rare events), such as strand displacement at room temperature. We introduce an Arrhenius kinetic model of interacting nucleic acid strands that relates the activation energy of a state transition with the immediate local environment of the affected base pair. Our model can be used in stochastic simulations to estimate kinetic properties and is consistent with existing thermodynamic models that make equilibrium predictions. We infer the model’s parameters on a wide range of reactions by using mean first passage time (MFPT) estimates. We estimate MFPTs using exact computations on simplified state spaces. We show that our new model surpasses the performance of the previously established Metropolis kinetic model. We further address MFPT estimation and the rapid evaluation of perturbed parameters for parameter inference in the full state space of reactions’ CTMCs. We show how to use a reduced variance stochastic simulation algorithm (RVSSA) to estimate MFPTs. We also introduce a fixed path ensemble inference (FPEI) approach for the rapid evaluation of perturbed parameters. These methods are promising, but they are not suitable for rare events. Thus, we introduce the pathway elaboration method, a time-efficient and probabilistic truncated-based approach for addressing both mentioned tasks. We demonstrate the effectiveness of our methods by conducting computational experiments on nucleic acid kinetics measurements that cover a wide range of rates for different type of reactions.

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