端粒长度维持交替机制的数学模型
Mathematical model of alternative mechanism of telomere length maintenance
摘要：
生物聚合物长度调节是一个复杂的过程，涉及大量的子过程同时作用于多个空间和时间尺度。对基因组稳定性很重要的一个例证是端粒的长度调节-线性染色体末端的核蛋白结构。端粒的维持通常由端粒酶促进，但是，特别是在无端粒酶的系统中，染色体末端的维持依赖于由重组介导的端粒的替代性延长（ALT）机制。各种线性和环状DNA结构被确定参与ALT，然而，整个过程的动力学仍然知之甚少。我们提出了一个化学动力学模型ALT动力学速率系统地来自生物物理学的DNA扩散和循环。通过准稳态近似，将反应体系简化为凝聚-破碎体系。动力学速率的详细治疗产生明确的公式预期的端粒的大小分布，展示了J-因子，聚合物的弯曲的定量测量所发挥的关键作用。结果与实验数据一致，并指出有趣的现象：出现很长的端粒圈，如果总端粒密度超过一个临界值（过量质量）和非线性响应的端粒大小分布的端粒DNA的量在系统中。这些结果对于理解端粒在非依赖于端粒酶的系统中的动力学具有普遍的重要性，因为这种端粒维持模式与缺乏端粒酶活性的肿瘤细胞中的情况相似。此外，由于其普遍性，该模型也可以作为一个原型的线性和环状DNA结构之间的相互作用，在各种设置。
英文摘要：
Biopolymer length regulation is a complex process that involves a large number of subprocesses acting simultaneously across multiple spatial and temporal scales. An illustrative example important for genomic stability is the length regulation of telomeres---nucleo-protein structures at the ends of linear chromosomes. Maintenance of telomeres is often facilitated by the enzyme telomerase but, particularly in telomerase-free systems, the maintenance of chromosomal termini depends on alternative lengthening of telomeres (ALT) mechanisms mediated by recombination. Various linear and circular DNA structures were identified to participate in ALT, however, dynamics of the whole process is still poorly understood. We propose a chemical kinetics model of ALT with kinetic rates systematically derived from the biophysics of DNA diffusion and looping. The reaction system is reduced to a coagulation-fragmentation system by quasi-steady state approximation. The detailed treatment of kinetic rates yields explicit formulae for expected size distributions of telomeres that demonstrate the key role played by the J-factor, a quantitative measure of bending of polymers. The results are in agreement with experimental data and point out interesting phenomena: an appearance of very long telomeric circles if the total telomere density exceeds a critical value (excess mass) and a nonlinear response of the telomere size distributions to the amount of telomeric DNA in the system. The results can be of general importance for understanding dynamics of telomeres in telomerase-independent systems as this mode of telomere maintenance is similar to the situation in tumor cells lacking telomerase activity. Furthermore, due to its universality, the model may also serve as a prototype of an interaction between linear and circular DNA structures in various settings.
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