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 (cohesin stabilized by two CTCF molecules) 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 is unbound. We derive expressions for this last passage time that we use to quantify the loop stability for various parameters, such as the chemical rate constant or the number of cross-linkers. The present analysis suggests that the balance between binding and unbinding events regulates the number of cross-linkers in place, based on a positive feed-back mechanism that stabilizes the loop over long-time. To conclude, we found that short- and long-lasting stable loops can vary from minutes to the entire cell cycle lifetime, when the number of cross-linkers increases from 1 to 10. This result suggests that a large spectrum of loop time scales is expected with such a few numbers of cross-linkers per local binding sites.

细胞核内的染色质环可以在很长一段时间内保持稳定，这仍然知之甚少。这样的时间对于染色质组织的维持和稳定性至关重要。我们在这里探索了几种物理场景，其中环的维持是由于扩散的交联剂（由两个 CTCF 分子稳定的粘连蛋白）可以在染色质环的底部结合和解除结合。使用马尔可夫链方法粗粒度结合和解除绑定，我们认为当最后一个交联剂解除绑定时，稳定环消失。我们推导出最后一次通过时间的表达式，用于量化各种参数的环稳定性，例如化学速率常数或交联剂的数量。目前的分析表明，结合和解结合事件之间的平衡调节了交联剂的数量，基于长期稳定循环的正反馈机制。总而言之，我们发现，当交联剂的数量从 1 增加到 10 时，短期和长期稳定循环可以从几分钟到整个细胞周期寿命不等。这一结果表明，循环时间尺度的大范围是预期每个局部结合位点具有如此少量的交联剂。