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.

中文翻译：

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在环状位点通过黏附蛋白样相互作用产生的染色质记忆

核内的染色质环可以很长时间保持稳定，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（例如粘着蛋白和CTCF）所致，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粗化结合和未结合，我们认为当最后一个交联剂（CTCF或粘着素分子）未结合时，稳定的环消失。我们导出了最后通过时间的表达式，用于量化各种值参数（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，这种结合和解除结合机制足以确保始终存在交联剂，因为它们会产生积极的反馈机制，从而长期稳定环。总而言之，我们提出每个环数十至数百个交联剂足以保证整个细胞周期中基因组中环的稳定性。