Efficient Parameter Estimation for DNA Kinetics Modeled as Continuous-Time Markov Chains

Abstract

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.