Mathematical model of RNA-directed DNA methylation predicts siRNA production in bursts

Abstract

RNA-directed DNA Methylation (RdDM) is a plant-specific de novo methylation pathway that is responsible for maintenance of asymmetric methylation (CHH, where H=A, T, or G) in euchromatin. Loci with CHH methylation are transcriptionally silent and produce 24-nucleotide (nt) short interfering (si) RNAs. These siRNAs direct additional CHH methylation to the locus, thereby maintaining methylation states through DNA replication. To understand the necessary conditions to produce stable CHH methylation, we developed a stochastic mathematical model of RdDM. The model describes DNA target search of DNA or RNA by siRNAs derived from CHH-methylated loci. When the siRNA (bound by an Argonaute protein) finds the matching locus, the model uses the dwell time of the matched complex to determine the degree of CHH reinforcing methylation. Reinforcing methylation occurs either throughout the cell cycle (steady reinforcement), or immediately following replication (bursty reinforcement). Each simulation occurs over 10 cell cycles, and for 7 simulation replicates. We use nonparametric statistics to compare initial and final CHH methylation distributions to determine whether the simulation conditions produce stable maintenance. We apply this method to the low CHH methylation case, wherein the median is only 8%, and many loci have less than 8% methylation. The resulting model predicts that siRNA production must be linearly proportional to CHH methylation levels at each locus, that bursty reinforcement produces more stable systems, and that slightly higher levels of siRNA production are required for DNA target search, compared to RNA target search. Unlike CG methylation, which typically exhibits bi-modality, with loci having either 100% or 0% methylation, CHH methylation putatively exists at a range of methylation fractions. Our model predicts that careful tuning of the negative feedbacks in the system are required to balance the positive feedback loop of increasing CHH methylation and increasing siRNA production, enabling stable maintenance of a range of CHH methylation across replication events.