[论文解读] Chirality-driven edge flow and non-Hermitian topology in active nematic cells

Lisa Yamauchi, Tomoya Hayata+3 more|arXiv (Cornell University)|Aug 25, 2020

Photoreceptor and optogenetics research被引用 15

一句话总结

本研究证明，手性活性向列细胞——特别是神经 progenitor 细胞——表现出由内在手性驱动的稳健单向边缘流动，该流动具有拓扑保护特性，类似于非厄米拓扑边缘模式。通过实验、基于代理的模拟以及映射到非厄米薛定谔方程的流体动力学理论，作者在局域于边缘的密度涨落中识别出一种类似凯尔文波的拓扑模式，建立了手性活性与生物系统中拓扑物理之间的直接联系。

ABSTRACT

Many of the biological phenomena involve collective dynamics driven by self-propelled motion and nonequilibrium force (i.e., activity) that result in features unexpected from equilibrium physics. On the other hand, biological experiments utilizing molecular motors, bacteria, and mammalian cells have served as ideal setups to probe the effect of activity in materials and compare with theory. As has been established, however, biomolecules are chiral in nature, which can lead to the chiral patterning of cells and even to the left-right symmetry breaking in our body. The general mechanism of how the dynamics of bio-matters can couple with its own inherent chirality to produce macroscopic patterns is yet to be elucidated. Here we report that cultured neural progenitor cells (NPCs), which undergo self-propelled motion with nematic cell-to-cell interactions, exhibit large scale chiral patterns when flowing out from containers made by gel. Moreover, a robust chiral cell flow is produced along the boundary when the NPCs are cultured on substrates with edges. Perturbation by actomyosin inhibitors allowed control over the chirality, resulting in the switching of the direction of the chiral patterning and boundary flow. As predicted by a hydrodynamic theory analogous to the non-Hermitian Schrodinger equation, we find an edge-localized unidirectional mode in the Fourier spectrum of the cell density, which corresponds to the topological Kelvin wave. These results establish a novel mechanism of flow that emerges from a pool of bipolar cells, and demonstrate how topological concepts from condensed matter physics can naturally arise in chiral active systems and multi-cellular phenomena.

研究动机与目标

• 研究内在手性在活性生物材料中如何驱动稳健的单向边缘流动。
• 确定在手性活性向列系统中是否会出现凝聚 matter 物理中已知的拓扑边缘模式。
• 建立非厄米拓扑与多细胞系统集体动力学之间的联系。
• 通过肌动蛋白-肌球蛋白抑制剂实验控制并切换手性边缘流动。
• 通过基于代理的模拟和密度涨落的傅里叶分析验证流体动力学理论。

提出的方法

• 在具有圆形和线性边界的基底上培养的神经 progenitor 细胞中，实验观察手性边缘流动。
• 使用肌动蛋白-肌球蛋白抑制剂（blebbistatin、mitomycin C、jasplakinolide）扰动并反转手性动力学。
• 开发基于代理的模型，模拟具有随机重定向和定义手性速率 θ 的手性向列相互作用。
• 对活性向列的流体动力学方程进行线性化，推导出非厄米有效哈密顿量。
• 在周期性边界条件和开放（条带）边界条件下，分析非厄米哈密顿量的能带结构。
• 对细胞密度涨落进行傅里叶分析，以识别类似拓扑凯尔文波的局域于边缘的单向模式。

实验结果

研究问题

• RQ1 活性向列细胞中的内在手性是否能导致稳健的单向边缘流动？
• RQ2 所观察到的边缘流动是否具有拓扑保护特性，类似于非厄米拓扑边缘态？
• RQ3 是否能通过药理学试剂实验控制并反转手性边缘流动？
• RQ4 手性活性向列的流体动力学理论是否能预测与实验观测相匹配的拓扑边缘模式？
• RQ5 非厄米拓扑在稳定活性系统中局域于边缘的密度涨落中起什么作用？

主要发现

• 神经 progenitor 细胞在从凝胶限制容器中流动时表现出大尺度手性图案和单向边缘流动，流动方向由肌动蛋白-肌球蛋白抑制剂控制。
• 药物扰动反转了手性流动方向，证实肌动蛋白-肌球蛋白活性决定了边缘电流的手性。
• 对边缘密度涨落的傅里叶分析揭示了一个单向模式，其功率谱峰值出现在 k_y ≈ 0.02 μm⁻¹，与预测的拓扑凯尔文波一致。
• 具有非厄米哈密顿量的流体动力学模型预测了与实验和模拟结果匹配的局域于边缘的模式，且在绝热地变形为厄米系统时，实能量间隙得以保持。
• 能带结构分析在开放边界条件下确认了复能级平面中存在边缘模式，其强度在 E_+(k_y) 处达到峰值。
• 非厄米哈密顿量的陈数在不同 k_max 下保持量化（C = 1），证实了其拓扑鲁棒性。