发表机构
King Abdullah University of Science and Technology (KAUST); University of Cambridge（阿卜杜拉国王科技大学; 剑桥大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一个扩展KJMA模型的群体动力学框架，定量揭示复制起始点的密度与空间组织如何约束DNA复制完成，并给出最差位点未复制比例和近完成时间的尖锐上界，为理解复制应激与基因组不稳定性提供理论基础。
AI 中文摘要
DNA复制需要协调复制起始点的激发和复制叉的推进，以确保整个基因组在细胞分裂前及时完成复制。然而，复制起始点的激发是随机的，这引出了经典的随机完成问题：概率性的局部事件如何仍能确保可靠的基因组复制。尽管已有多种生物学机制被提出以解决此问题，但关于异质性起始和复制叉速度如何决定最终未复制区域的持续存在，目前仍缺乏定量解释。为填补这一空白，我们引入了一个群体水平的动力学框架，该框架扩展了KJMA成核-生长模型，通过追踪未复制区间的长度、基因组位置和时间来建模。我们证明了所得平均场系统的适定性和相容数据的全局存在性。值得注意的是，通过引入局部起始质量函数，我们量化了复制起始点的密度和空间组织如何约束复制完成，从而在最差位点未复制比例和位点特异性近完成时间上得到了新颖且尖锐的上界。这些结果为绘制复制完成中的脆弱性图谱以及将持续未复制区域与复制应激和基因组不稳定性联系起来提供了严格且可计算的基础。
英文摘要
DNA replication requires the coordination of origin firing and fork progression to ensure the entire genome is timely duplicated before cell division. Yet origin firing is stochastic, giving rise to the classical random completion problem of how probabilistic local events can nevertheless ensure reliable genome duplication. Although several biological mechanisms have been proposed to resolve this problem, a quantitative account of how heterogeneous initiation and fork speed govern the persistence of the final unreplicated regions is still lacking. To address this gap, we introduce a population-level kinetic framework that extends KJMA nucleation-and-growth models by tracking unreplicated intervals over size, genomic position and time. We establish well-posedness of the resulting mean-field system and global existence for compatible data. Notably, by introducing a local initiation mass function, we quantify how the density and spatial organisation of origin firing constrain replication completion, yielding novel and sharp upper bounds on both the worst-locus unreplicated fraction and locuswise near-completion time. These results provide a rigorous and computable foundation for mapping vulnerabilities in replication completion and relating persistent unreplicated regions to replication stress and genome instability.
