Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
Insights into the dynamic trajectories of protein filament division revealed by numerical investigation into the mathematical model of pure fragmentation.
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通过对纯断裂数学模型的数值研究揭示了蛋白质丝分裂的动态轨迹。
DOI：
10.1371/journal.pcbi.1008964
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发表时间：
2021-09
影响因子：
4.3
通讯作者：
Doumic M
中科院分区：
文献类型：
--
作者：
Tournus M;Escobedo M;Xue WF;Doumic M
聚合蛋白细丝在生长可以忽略不计的情况下分裂的动力学，例如由于自由单体前体的耗尽，可以用普遍的数学方程‘纯碎裂’来描述。碎裂反应的速率反映了蛋白质细丝断裂的稳定性，这在生物学和生物医学中具有重要意义，例如在控制淀粉样蛋白种子的产生和Pron的繁殖方面。在这里，我们从数学理论上推导出了从细丝尺寸分布的随时间变化的实验测量中恢复分割率和分割核信息的公式。发展了系统分析纯碎裂轨迹行为的数值方法。我们说明了如何使用这些公式，对它们的稳健性提供了一些见解，并展示了它们如何为测量纤维碎裂动力学的实验设计提供信息。这些进展是由我们的中心理论结果实现的，即纯碎裂方程的解的长度分布曲线如何与大时间内稳定的分布曲线一致。淀粉样纤维是一种纤维蛋白结构，与许多神经退行性疾病有关，如帕金森氏病或阿尔茨海默病。为了在疾病中繁殖，这些错误折叠的蛋白质聚集体必须生长和分裂以增殖。因此，它们的分裂的内在特征，包括分裂比率和分裂模式，无论是纤维在中间还是在边缘断裂，都影响着疾病的病因学。在这里，我们发现了数学公式，可以用来直接从最近的实验数据中提取纤维分裂特征，这些数据是由随时间变化的纤维长度分布测量获得的。我们解释了如何使用这些公式，并证明了分割率公式的稳健性，其中测量中的小误差导致分割率的小误差。我们还证明了数学公式不足以准确地破译数据中的分裂模式，并建议了新的未来实验设计，从所有纤维具有相似尺寸的纤维悬浮液开始，在实验中进行短时间测量，这将适合提供更好的估计。
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. Amyloid fibrils are fibrillar protein structures involved in many neurodegenerative illnesses, such as Parkinson’s disease or Alzheimer’s disease. To propagate in disease, these misfolded protein aggregates must grow and divide to proliferate. Therefore, the intrinsic characteristics of their division, including the division rate and the pattern of division in terms of whether the fibrils are likely to break in the middle or at the edges, impact the disease aetiology. Here, we discovered mathematical formulae that can be used to directly extract the fibril division characteristics from recent experiments data obtained from time-dependent fibril length distribution measurements. We explain how these formulae can be used, and prove the robustness of the division rate formula where small errors in the measurement leads to small errors in the division rate. We also demonstrate that the mathematical formula is not robust enough to precisely decipher the pattern of division in the data, and suggest instead new future experimental design with short time measurements in experiments starting with fibril suspensions where all fibrils have similar size, which would be suitable to provide improved estimates.
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