Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA, 92093-0411, USA.
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA, 92093-0213, USA.
Bull Math Biol. 2020 Feb 6;82(2):30. doi: 10.1007/s11538-020-00703-4.
Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood. Therefore, understanding the spatial patterns that can emerge on the PM solely through protein-protein interaction, lateral diffusion, and feedback is an important step toward a complete description of the mechanisms behind protein clustering on the cell surface. In this work, we investigate the pattern formation of a reaction-diffusion model that describes the dynamics of a system of ligand-receptor complexes. The purely diffusive ligand in the cytosol can bind receptors in the PM and the resultant ligand-receptor complexes not only diffuse laterally but can also form clusters resulting in different oligomers. Finally, the largest oligomers recruit ligands from the cytosol using positive feedback. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. Our main result is a threshold phenomenon, in which a sufficiently high recruitment of ligands promotes the input of new monomeric components and consequently drives the formation of a single-patch spatially heterogeneous steady state.
蛋白质在质膜（PM）上的聚集对于许多细胞过程至关重要，如细胞黏附、内吞作用、纤维状构象和囊泡运输。蛋白质聚集体或簇在 PM 表面上的横向扩散在控制其异质表面分布方面起着重要作用。然而，蛋白质聚集体表面分布的稳定性行为仍知之甚少。因此，仅通过蛋白质-蛋白质相互作用、侧向扩散和反馈来理解 PM 上可能出现的空间模式，是对细胞表面蛋白质聚类背后机制进行完整描述的重要步骤。在这项工作中，我们研究了描述配体-受体复合物系统动力学的反应-扩散模型的模式形成。细胞质中的纯扩散配体可以与 PM 中的受体结合，由此产生的配体-受体复合物不仅可以横向扩散，还可以形成簇，从而产生不同的低聚物。最后，最大的低聚物利用正反馈从细胞质中招募配体。从方法学的角度来看，我们基于图灵机制为蛋白质聚集体的扩散驱动不稳定性提供了理论估计。我们的主要结果是一个阈值现象，其中足够高的配体募集促进了新单体成分的输入，从而驱动了单个斑块空间异质稳定状态的形成。
