Mathematical model of RNA-directed DNA methylation predicts tuning of negative feedback required for stable maintenance

RNA-directed DNA methylation (RdDM) is a plant-specific de novo methylation pathway that is responsible for maintenance of asymmetric methylation (CHH, H = A, T or G) in euchromatin. Loci with CHH methylation produce 24 nucleotide (nt) short interfering (si) RNAs. These siRNAs direct additional CHH methylation to the locus, maintaining methylation states through DNA replication. To understand the necessary conditions to produce stable methylation, we developed a stochastic mathematical model of RdDM. The model describes DNA target search by siRNAs derived from CHH methylated loci bound by an Argonaute. Methylation reinforcement occurs either throughout the cell cycle (steady) or immediately following replication (bursty). We compare initial and final methylation distributions to determine simulation conditions that produce stable methylation. We apply this method to the low CHH methylation case. The resulting model predicts that siRNA production must be linearly proportional to methylation levels, that bursty reinforcement is more stable and that slightly higher levels of siRNA production are required for searching DNA, compared to RNA. Unlike CG methylation, which typically exhibits bi-modality with loci having either 100% or 0% methylation, CHH methylation exists across a range. Our model predicts that careful tuning of the negative feedback in the system is required to enable stable maintenance.