Chromatin stability generated by stochastic binding and unbinding ofcross-linkers at looping sites revealed by Markov models

Chromatin loops inside the nucleus can be stable for a very long time, which remains poorly understood. Such a time is crucial for chromatin organization maintenance and stability. We explore here several physical scenarios, where loop maintenance is due to diffusing cross-linkers such as cohesin and CTCF that can bind and unbind at the base of chromatin loops. Using a Markov chain approach to coarse-grain the binding and unbinding, we consider that a stable loop disappears when the last cross-linker (CTCF or cohesin molecule) is unbound. We derive expressions for this last passage times that we use to quantify the loop stability for various value parameters, such as the chemical rate constant or the number of cross-linkers. The present analysis suggests that this binding and unbinding mechanism is sufficient to guarantee that there are always cross-linkers in place because they generate a positive feed-back mechanism that stabilizes the loop over long-time. To conclude, we propose that tens to hundreds cross-linkers per loop are sufficient to guarantee the loop stability in the genome over a cell cycle.