二维圆柱伊辛模型的成核动力学与趋化性
Nucleation dynamics in 2d cylindrical Ising models and chemotaxis
摘要：
我们工作的目的是研究几何形状变化对成核时间的影响，并在真核细胞趋化性（即允许细胞识别和遵循化学引诱剂梯度的过程）的背景下解决其作用。作为在这个方向上的第一步，我们研究的成核动力学的2D伊辛模型定义的圆柱形晶格的半径作为时间的函数的变化。通过改变紧化（垂直）方向上自旋之间的耦合相对于水平方向的相对值来获得几何变化。这使我们能够保持晶格尺寸不变，并在一个单一的模拟研究的值随时间变化的紧化半径。我们表明，无论是与理论参数和数值模拟，挤压的几何形状允许系统加速成核时间，即使在存在一个非常小的能隙之间的稳定和亚稳态。然后，我们解决我们的分析方向趋化性的影响。趋化性的初始步骤可以被建模为细胞膜上发生的成核过程，作为外部化学梯度的结果（其在稳定相和亚稳相之间起能隙的作用）。在自然界中，大多数细胞通过延伸准一维突起（丝状伪足）来改变其几何形状，从而增强其对化学引诱物的敏感性。我们的研究结果表明，这种几何形状的变化确实大大降低了成核过程的时间尺度的影响，即使在存在非常少量的化学引诱剂。
英文摘要：
The aim of our work is to study the effect of geometry variation on nucleation times and to address its role in the context of eukaryotic chemotaxis (i.e. the process which allows cells to identify and follow a gradient of chemical attractant). As a first step in this direction we study the nucleation dynamics of the 2d Ising model defined on a cylindrical lattice whose radius changes as a function of time. Geometry variation is obtained by changing the relative value of the couplings between spins in the compactified (vertical) direction with respect to the horizontal one. This allows us to keep the lattice size unchanged and study in a single simulation the values of the compactification radius which change in time. We show, both with theoretical arguments and numerical simulations that squeezing the geometry allows the system to speed up nucleation times even in presence of a very small energy gap between the stable and the metastable states. We then address the implications of our analysis for directional chemotaxis. The initial steps of chemotaxis can be modelled as a nucleation process occurring on the cell membrane as a consequence of the external chemical gradient (which plays the role of energy gap between the stable and metastable phases). In nature most of the cells modify their geometry by extending quasi-onedimensional protrusions (filopodia) so as to enhance their sensitivity to chemoattractant. Our results show that this geometry variation has indeed the effect of greatly decreasing the timescale of the nucleation process even in presence of very small amounts of chemoattractants.
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