The formation of elongated supra-molecular structures from protein building blocks generates functional intracellular filaments, but this process is also at the heart of many neurodegenerative conditions including Alzheimer’s and Parkinson’s diseases, where it occurs in an uncontrolled manner. When observed at appropriate concentration and time scales, the chemical kinetics of filamentous protein self-assembly exhibits the remarkable property of self-similarity: the dynamics appears similar as the observation scale changes. We discuss here how this property leads to crucial simplifications of the fundamental laws governing protein filament formation and the emergence of scaling laws that provide the basis for connecting microscopic events with macroscopic realisations of such processes. In particular, we review recent developments in the modelling of linear protein self-assembly phenomena in the light of the concepts of dimensional analysis and physical self-similarity. We show how these tools and concepts can be used to elucidate the nature of the scaling laws for filamentous protein self-assembly, which illuminate the ultimately simple mathematical and physical principles underlying this seemingly highly complex phenomenon, and are expected to guide further developments in the field of linear self-assembly.

中文翻译：

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蛋白质丝形成化学动力学的缩放和维数

从蛋白质构建块形成细长的超分子结构会产生功能性细胞内细丝，但这个过程也是许多神经退行性疾病的核心，包括阿尔茨海默病和帕金森病，它以不受控制的方式发生。在适当的浓度和时间尺度下观察时，丝状蛋白质自组装的化学动力学表现出显着的自相似性：随着观察尺度的变化，动力学看起来相似。我们在这里讨论了这种特性如何导致控制蛋白质丝形成的基本定律的关键简化以及缩放定律的出现，这些定律为将微观事件与此类过程的宏观实现联系起来提供了基础。特别是，我们根据维度分析和物理自相似性的概念回顾了线性蛋白质自组装现象建模的最新进展。我们展示了如何使用这些工具和概念来阐明丝状蛋白质自组装缩放定律的性质，这些定律阐明了这种看似高度复杂的现象背后的最终简单的数学和物理原理，并有望指导线性自组装领域。