发表机构
University of Sheffield; University of Edinburgh; Umm Al-Qura University; University of Massachusetts Amherst（谢菲尔德大学; 爱丁堡大学; 乌姆古拉大学; 马萨诸塞大学阿默斯特分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构建质量守恒反应-扩散模型，揭示平面极性斑点的成核、数量设定及取向分离机制，发现斑点数量与取向排序由可分离的数学成分调控。
AI 中文摘要
平面细胞极性的形成先于极性蛋白聚集为离散、低周转的膜亚结构域（斑点），但触发斑点成核、设定其数量及分离相反取向的最小相互作用仍不明确。我们采用质量守恒反应-扩散模型解决这些问题，其中两种可扩散单体跨细胞-细胞连接可逆结合为两种取向的反式复合物，反馈仅通过浓度依赖速率引入。在临界密度以上，均匀态会发生长波质量再分布失稳，而非有限波长的图灵分岔。反馈形式进而在两种形态间选择：饱和反馈下由麦克斯韦构造固定的宽台地，以及无界反馈下受质量限制的窄尖峰。对于尖峰，我们获得了闭式表达式，清晰区分了振幅（质量与反馈）、宽度（复合物扩散长度）和间距（单体筛选长度）。在快单体简化下，我们证明，对于任意数量和排列的斑点，同向阵列会粗化，因此多重性是亚稳态且由动力学决定。第二个单体储库引入了第二个筛选长度，通过单体扩散率的调和均值限制竞争速率，且斑点的频谱始终无振荡（“闪烁”）失稳。最后，周转的符号确定交叉调节将聚类转化为取向排序——沿单个接触的取向相互排斥：质量再分布设定斑点数量，交叉耦合的符号决定取向是否分离。因此，斑点数量和取向排序由数学上可分离的成分调控。
英文摘要
Planar cell polarity is preceded by the clustering of polarity proteins into discrete, low-turnover membrane subdomains (puncta), yet the minimal interactions that nucleate puncta, set their number, and segregate opposite orientations remain unclear. We address these questions with a mass-conserving reaction-diffusion model in which two diffusible monomers bind reversibly across a cell-cell junction into trans-complexes of two orientations, with feedback entering only through concentration-dependent rates. Above a critical density, the uniform state undergoes a long-wavelength mass-redistribution instability rather than a finite-wavelength Turing bifurcation. The form of the feedback then selects between two morphologies: broad mesas fixed by a Maxwell construction under saturating feedback, and narrow mass-limited spikes under unbounded feedback. For spikes we obtain closed-form expressions exhibiting a clean separation of amplitude (mass and feedback), width (the complex diffusion length), and spacing (the monomer screening length). Within a fast-monomer reduction we prove, for any number and arrangement of puncta, that like-oriented arrays coarsen, so multiplicity is metastable and kinetically determined. The second monomer reservoir introduces a second screening length that rate-limits competition by the harmonic mean of the monomer diffusivities, and the spectrum of a punctum remains free of oscillatory ("blinking") instabilities throughout. Finally, sign-definite cross-modulation of turnover converts clustering into orientation sorting - the mutual exclusion of orientations along a single contact: mass redistribution sets puncta number, and the sign of the cross-coupling determines whether orientations segregate. Puncta number and orientation sorting are thus governed by mathematically separable ingredients.
Comments44 pages, 12 figures
