Physical modeling of the spreading of epigenetic modifications through transient DNA looping

Abstract

We utilize theoretical modeling to explore the physical mechanisms that govern the spreading of epigenetic modifications along chromosomal DNA. We focus on a particular modification, methylation of lysine 9 of histone H3 (H3K9), which is a representative and critical epigenetic mark that affects chromatin structure and gene expression. Our model captures transient loop formation in chromosomal DNA that enables distal segments to be in close spatial proximity and permits methyltransferase to confer methyl marks over a broad range of genomic distances. Using our exact results for the statistical behavior of a semiflexible polymer, we find the looping rate for a chromosomal segment based on a mean first-passage time process on a free-energy landscape. From this treatment, looping kinetics are predicted to be the rate-limiting process for methyl spreading at large genomic distances, which explains the considerable variability in the methyl profile at such scales. We then develop a ‘phase diagram’ for methylation spreading versus the methylation rate and the concentration of HP1, which we identify as a global regulator of the state of the chromosomal DNA.