Models of nucleic acid thermal stability are calibrated to a wide range of experimental observations, and typically predict equilibrium probabilities of nucleic acid secondary structures with reasonable accuracy. By comparison, a similar calibration and evaluation of nucleic acid kinetic models to a broad range of measurements has not been attempted so far. We introduce an Arrhenius model of interacting nucleic acid kinetics 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. We infer parameters for our model using an ensemble Markov chain Monte Carlo (MCMC) approach on a training dataset with 320 kinetic measurements of hairpin closing and opening, helix association and dissociation, bubble closing and toehold-mediated strand exchange. Our new model surpasses the performance of the previously established Metropolis model both on the training set and on a testing set of size 56 composed of toehold-mediated 3-way strand displacement with mismatches and hairpin opening and closing rates: reaction rates are predicted to within a factor of three for 93.4% and 78.5% of reactions for the training and testing sets, respectively.
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Efficient Parameter Estimation for DNA Kinetics Modeled as Continuous-Time Markov Chains
Nucleic acid kinetic simulators aim to predict the kinetics of interacting nucleic acid strands. Many simulators model the kinetics of interacting nucleic acid strands as continuous-time Markov chains (CTMCs). States of the CTMCs represent a collection of secondary structures, and transitions between the states correspond to the forming or breaking of base pairs and are determined by a nucleic acid kinetic model. The number of states these CTMCs can form may be exponentially large in the length of the strands, making two important tasks challenging, namely, mean first passage time (MFPT) estimation and parameter estimation for kinetic models based on MFPTs. Gillespie’s stochastic simulation algorithm (SSA) is widely used to analyze nucleic acid folding kinetics, but could be computationally expensive for reactions whose CTMC has a large state space or for slow reactions. It could also be expensive for arbitrary parameter sets that occur in parameter estimation. Our work addresses these two challenging tasks, in the full state space of all non-pseudoknotted secondary structures of each reaction. In the first task, we show how to use a reduced variance stochastic simulation algorithm (RVSSA), which is adapted from SSA, to estimate the MFPT of a reaction’s CTMC. In the second task, we estimate model parameters based on MFPTs. To this end, first, we show how to use a generalized method of moments (GMM) approach, where we minimize a squared norm of moment functions that we formulate based on experimental and estimated MFPTs. Second, to speed up parameter estimation, we introduce a fixed path ensemble inference (FPEI) approach, that we adapt from RVSSA. We implement and evaluate RVSSA and FPEI using the Multistrand kinetic simulator. In our experiments on a dataset of DNA reactions, FPEI speeds up parameter estimation compared to inference using SSA, by more than a factor of three for slow reactions. Also, for reactions with large state spaces, it speeds up parameter estimation by more than a factor of two.
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- Award ID(s):
- 1643606
- NSF-PAR ID:
- 10112046
- Date Published:
- Journal Name:
- DNA Computing and Molecular Programming
- Volume:
- 11648
- Page Range / eLocation ID:
- 80-99
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-030-26807-7_5
