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.

中文翻译：

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马尔可夫模型揭示了在环状位点上的交联剂的随机结合和非结合所产生的染色质稳定性。

核内的染色质环可以在很长一段时间内保持稳定，对此知之甚少。这样的时间对于染色质组织的维持和稳定性至关重要。我们在这里探讨了几种物理方案，其中环路维护是由于扩散的交联剂（由两个CTCF分子稳定的黏着蛋白）导致的，它们可以在染色质环路的底部进行结合和解结合。使用马尔可夫链方法对绑定和取消绑定进行粗粒度处理，我们认为当最后一个交联剂未绑定时，稳定的循环就会消失。我们导出了最后通过时间的表达式，可用于量化各种参数（例如化学速率常数或交联剂的数量）的环稳定性。目前的分析表明，结合和解离事件之间的平衡决定了适当的交联剂数量，基于积极的反馈机制，可长期稳定环路。总而言之，我们发现，当交联剂的数量从1增加到10时，短期和持久的稳定循环可能会在几分钟到整个细胞周期生命周期内变化。该结果表明，较大的循环时间尺度是预期每个局部结合位点具有如此数量的交联剂。