Department of Energy Engineering and Physics, Amirkabir University of Technology, Tehran, Iran.
Department of Physics, Kyungpook National University, 80 Daehakro, Bukgu, Daegu 41566, Republic of Korea.
J Chem Phys. 2024 Mar 21;160(11). doi: 10.1063/5.0190768.
Self-assembly of functional branched filaments, such as actin filaments and microtubules, or dysfunctional ones, such as amyloid fibrils, plays important roles in many biological processes. Here, based on the master equation approach, we study the kinetics of the formation of the branched fibrils. In our model, a branched fibril has one mother branch and several daughter branches. A daughter branch grows from the side of a pre-existing mother branch or daughter branch. In our model, we consider five basic processes for the self-assembly of the branched filaments, namely, the nucleation, the dissociation of the primary nucleus of fibrils, the elongation, the fragmentation, and the branching. The elongation of a mother branch from two ends and the elongation of a daughter branch from two ends can, in principle, occur with four different rate constants associated with the corresponding tips. This leads to a pronounced impact of the directionality of growth on the kinetics of the self-assembly. Here, we have unified and generalized our four previously presented models of branched fibrillogenesis in a single model. We have obtained a system of non-linear ordinary differential equations that give the time evolution of the polymer numbers and the mass concentrations along with the higher moments as observable quantities.
功能性分支纤维（如肌动蛋白纤维和微管）或非功能性分支纤维（如淀粉样纤维）的自组装在许多生物过程中起着重要作用。在这里，我们基于主方程方法研究了分支纤维形成的动力学。在我们的模型中，一个分支纤维有一个母支和几个子支。一个子支从一个预先存在的母支或子支的侧面生长。在我们的模型中，我们考虑了分支纤维自组装的五个基本过程，即成核、原纤维初级核的解离、延伸、断裂和分支。母支从两端延伸，子支从两端延伸，原则上可以与对应的尖端相关联的四个不同的速率常数发生。这导致生长的方向性对自组装动力学有显著影响。在这里，我们将之前提出的四个分支纤维形成模型统一并推广到一个单一的模型中。我们得到了一个非线性常微分方程组，给出了聚合物数量和质量浓度的时间演化以及作为可观测量的更高阶矩。
