Czeizler Eugen, Kari Lila
Department of Computer Science, University of Western Ontario London, ON, Canada.
Front Comput Neurosci. 2009 Nov 23;3:20. doi: 10.3389/neuro.10.020.2009. eCollection 2009.
Recent research has showed that tile systems are one of the most suitable theoretical frameworks for the spatial study and modeling of self-assembly processes, such as the formation of DNA and protein oligomeric structures. A Wang tile is a unit square, with glues on its edges, attaching to other tiles and forming larger and larger structures. Although quite intuitive, the idea of glues placed on the edges of a tile is not always natural for simulating the interactions occurring in some real systems. For example, when considering protein self-assembly, the shape of a protein is the main determinant of its functions and its interactions with other proteins. Our goal is to use geometric tiles, i.e., square tiles with geometrical protrusions on their edges, for simulating tiled paths (zippers) with complex neighborhoods, by ribbons of geometric tiles with simple, local neighborhoods. This paper is a step toward solving the general case of an arbitrary neighborhood, by proposing geometric tile designs that solve the case of a "tall" von Neumann neighborhood, the case of the f-shaped neighborhood, and the case of a 3 x 5 "filled" rectangular neighborhood. The techniques can be combined and generalized to solve the problem in the case of any neighborhood, centered at the tile of reference, and included in a 3 x (2k + 1) rectangle.
最近的研究表明，瓦片系统是用于自组装过程的空间研究和建模的最合适的理论框架之一，例如DNA和蛋白质寡聚体结构的形成。王瓦片是一个单位正方形，其边缘带有胶水，可附着到其他瓦片并形成越来越大的结构。尽管相当直观，但在瓦片边缘放置胶水的想法对于模拟某些实际系统中发生的相互作用并不总是很自然。例如，在考虑蛋白质自组装时，蛋白质的形状是其功能及其与其他蛋白质相互作用的主要决定因素。我们的目标是使用几何瓦片，即在其边缘带有几何突起的正方形瓦片，通过具有简单局部邻域的几何瓦片带，来模拟具有复杂邻域的瓦片路径（拉链）。本文朝着解决任意邻域的一般情况迈出了一步，提出了几何瓦片设计，解决了“高”冯·诺依曼邻域的情况、f形邻域的情况以及3×5“填充”矩形邻域的情况。这些技术可以组合并推广，以解决以参考瓦片为中心且包含在3×(2k + 1)矩形内的任何邻域情况下的问题。
