Baillou Renaud, Ranft Jonas
<a href="https://ror.org/03mxktp47">Institut de Biologie de l'ENS</a>, Ecole Normale Supérieure, <a href="https://ror.org/02feahw73">CNRS</a>, <a href="https://ror.org/02vjkv261">Inserm</a>, <a href="https://ror.org/013cjyk83">Université PSL</a>, 46 rue d'Ulm, 75005 Paris, France.
Phys Rev E. 2024 Sep;110(3-1):034410. doi: 10.1103/PhysRevE.110.034410.
Nonequilibrium cluster-cluster aggregation of particles diffusing in or at the cell membrane has been hypothesized to lead to domains of finite size in different biological contexts, such as lipid rafts, cell adhesion complexes, or postsynaptic domains in neurons. In this scenario, the desorption of particles balances a continuous flux to the membrane, imposing a cutoff on possible aggregate sizes and giving rise to a stationary size distribution. Here, we investigate the case of nonequilibrium cluster-cluster aggregation in two dimensions where diffusing particles and/or clusters remain fixed in space at specific anchoring sites, which should be particularly relevant for synapses but may also be present in other biological or physical systems. Using an effective mean-field description of the concentration field around anchored clusters, we derive an expression for their average size as a function of parameters such as the anchoring site density. We furthermore propose and solve appropriate rate equations that allow us to predict the size distributions of both diffusing and fixed clusters. We confirm our results with particle-based simulations and discuss potential implications for biological and physical systems.
据推测，在细胞膜内或细胞膜上扩散的粒子的非平衡簇团-簇团聚集会在不同的生物学环境中导致有限大小的区域，如脂筏、细胞粘附复合物或神经元中的突触后区域。在这种情况下，粒子的解吸平衡了向膜的连续通量，对可能的聚集体大小施加了一个截止值，并产生了一个稳定的大小分布。在这里，我们研究二维非平衡簇团-簇团聚集的情况，其中扩散的粒子和/或簇团在特定的锚定位点固定在空间中，这对于突触应该特别相关，但也可能存在于其他生物或物理系统中。使用围绕锚定簇团的浓度场的有效平均场描述，我们推导出它们的平均大小作为诸如锚定位点密度等参数的函数的表达式。我们还提出并求解了适当的速率方程，这使我们能够预测扩散簇团和固定簇团的大小分布。我们用基于粒子的模拟证实了我们的结果，并讨论了对生物和物理系统的潜在影响。
