Boundary-Sensing Mechanism in Branched Microtubule Networks

Meisam Zaferani, Ryungeun Song, Ned S Wingreen, Howard A Stone, Sabine Petry
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Abstract

The self-organization of cytoskeletal networks in confined geometries requires sensing and responding to mechanical cues at nanometer to micron scales that allow for dynamic adaptation. Here, we show that the branching of microtubules (MTs) via branching MT nucleation combined with dynamic instability constitutes a boundary-sensing mechanism within confined spaces. Using a nanotechnology platform, we observe the self-organization of a branched MT network in a channel featuring a narrow junction and a closed end. Our observations reveal that branching MT nucleation occurs in the post-narrowing region only if that region exceeds a certain length before it terminates at the channel's closed end. The length-dependent occurrence of branching MT nucleation arises from the dynamic instability of existing MTs when they interact with the channel's closed end, combined with the specific timescale required for new MTs to nucleate at a point distant from the closed end, creating a mechanical feedback. Increasing the concentration of the base branching factor TPX2 accelerates nucleation kinetics and thus tunes the minimum length scale needed for occurrence of branching MT nucleation. As such, this feedback not only allows for adaptation to the local geometry, but also allows for tunable formation of MT networks in narrow (micron and submicron scale) channels. However, while a high concentration of TPX2 increases the kinetic rate of branching MT nucleation, it also stabilizes MTs at the channel's closed end leading to MT growth and nucleation in the reversed direction, and thus hinders boundary sensing. After experimental characterization of boundary-sensing feedback, we propose a minimal model and execute numerical simulations. We investigate how this feedback, wherein growing MTs dynamically sense their physical environment and provide nucleation sites for new MTs, sets a length/time scale that steers the architecture of MT networks in confined spaces. This "search-and-branch" mechanism has implications for the formation of MT networks during neuronal morphogenesis, including axonal growth and the formation of highly branched dendritic networks, as well as for plant development and MT-driven guidance in fungi, and engineering nanotechnologies.
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分支微管网络中的边界感应机制
细胞骨架网络在封闭几何结构中的自组织需要感知并响应纳米到微米尺度的机械线索,从而实现动态适应。在这里,我们展示了微管(MT)通过分支MT成核与动态不稳定性相结合而形成的分支,这构成了密闭空间内的边界感应机制。利用纳米技术平台,我们观察了一个具有狭窄交界处和封闭末端的通道中分支 MT 网络的自组织过程。我们的观察结果表明,只有当后狭窄区域超过一定长度后,才会在通道的封闭端发生分支 MT 成核。分支 MT 成核的发生与长度有关,这是由于现有 MT 与通道封闭端相互作用时的动态不稳定性,再加上新 MT 在远离封闭端处成核所需的特定时间尺度,从而产生了机械反馈。增加碱基分支因子 TPX2 的浓度会加速成核动力学,从而调整发生分支 MT 成核所需的最小长度范围。因此,这种反馈不仅能适应局部几何形状,还能在狭窄(微米和亚微米级)通道中形成可调的 MT 网络。然而,高浓度的 TPX2 在提高分支 MT 成核的动力学速率的同时,也会使 MT 稳定在通道的封闭端,导致 MT 反向生长和成核,从而阻碍了边界感应。在对边界感应反馈进行实验表征后,我们提出了一个最小模型并进行了数值模拟。我们研究了这种反馈--生长中的MT动态地感知其物理环境并为新的MT提供成核点--如何设定长度/时间尺度,从而引导密闭空间中MT网络的结构。这种 "搜索-分支 "机制对神经元形态发生过程中MT网络的形成(包括轴突生长和高分支树突网络的形成)、植物发育、真菌中MT驱动的引导以及工程纳米技术都有影响。
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