Centrale Marseille, I2M, UMR 7373, CNRS, Aix-Marseille université, Marseille, France.
Universidad del País Vasco, Departamento de Matemat́icas, Bilbao, Spain.
PLoS Comput Biol. 2021 Sep 3;17(9):e1008964. doi: 10.1371/journal.pcbi.1008964. eCollection 2021 Sep.
The dynamics by which polymeric protein filaments divide in the presence of negligible growth, for example due to the depletion of free monomeric precursors, can be described by the universal mathematical equations of 'pure fragmentation'. The rates of fragmentation reactions reflect the stability of the protein filaments towards breakage, which is of importance in biology and biomedicine for instance in governing the creation of amyloid seeds and the propagation of prions. Here, we devised from mathematical theory inversion formulae to recover the division rates and division kernel information from time-dependent experimental measurements of filament size distribution. The numerical approach to systematically analyze the behaviour of pure fragmentation trajectories was also developed. We illustrate how these formulae can be used, provide some insights on their robustness, and show how they inform the design of experiments to measure fibril fragmentation dynamics. These advances are made possible by our central theoretical result on how the length distribution profile of the solution to the pure fragmentation equation aligns with a steady distribution profile for large times.
在生长可以忽略不计的情况下，例如由于游离单体前体耗尽，聚合蛋白丝的分裂动力学可以用“纯断裂”的通用数学方程来描述。断裂反应的速率反映了蛋白质丝的稳定性，在生物学和生物医学中，这一点很重要，例如，它可以控制淀粉样蛋白种子的形成和朊病毒的传播。在这里，我们从数学理论中推导出反演公式，以便从纤维大小分布的时变实验测量中恢复分裂速率和分裂核信息。还开发了系统分析纯断裂轨迹行为的数值方法。我们说明了如何使用这些公式，提供了一些关于它们的稳健性的见解，并展示了它们如何为测量原纤维断裂动力学的实验设计提供信息。这些进展是通过我们关于纯断裂方程的解的长度分布轮廓如何与大时间的稳定分布轮廓对齐的中心理论结果实现的。
