Markovian Dynamics in Chromatin Loop Extrusion Factors

Markov properties can be used to model different dynamic processes at various stages of the loop extrusion process. The current methods are proposed to gain insight on how Markov models may illustrate chromatin behaviour once the appropriate observed data becomes available. We find that single molecule FRET experiments are able to identify the conformational states chromatin using Gaussian mixture models. The unbinding and binding rates of loop extrusion factors (LEFs) were applied in an immigration-death model, and found to play a role in influencing the frequency of loop extrusion. By including the additional parameter of the presence of nucleosomes with LEF binding on a strand of DNA, we find that the theoretical timescale of DNA exposure decreased upon LEF binding. The binding behaviour of LEFs is also dependent on the location of nucleosomes on a strand of DNA. This is modeled with the Gillespie algorithm to simulate LEF binding activity with single cell dynamics.