论文标题
3D曲面的DNA瓷砖自组装：朝向属识别
DNA tile self-assembly for 3D-surfaces: Towards genus identification
论文作者
论文摘要
我们引入了一个新的DNA瓷砖自组装模型：表面柔性瓷砖组装模型（SFTAM），其中2D瓷砖被放置在由轴平行的单位立方体制成的主机3D表面上，将其与其脸部粘合在一起，称为Polycubes。键是柔性的，因此组件可以结合到polycube的边缘。为了比较其不同的行为并计算宿主表面的拓扑特性，我们对3D表面上的SFTAM自组件的研究感兴趣。 我们专注于一个称为Cuboids的多层型家族。 0订单-0立方体是具有六个矩形面的聚皮，并且订单1的立方体是通过从另一个订单的两个立方体制成的。因此，订单1的立方体可以是属0或属1的（然后是隧道）。我们对这些结构的属感兴趣，并提出了一个SFTAM瓷砖组装系统，该系统决定给定的订单1 cuboid的属。我们设计的SFTAM瓷砖组装系统包含具有以下属性的特定集合$ y $ y $。如果在主机1 cuboid $ c $ 0属0上进行组件，则在任何生产的组件中都不会出现$ y $的瓷砖，但是如果$ c $具有1属1，则每个终端组件至少包含一个瓷砖$ y $。 因此，我们能够根据组件中使用的瓷砖根据宿主表面来区分宿主表面。该系统是特定于订单1的立方体的，但是我们使用的技术应该推广到其他形状家族。
We introduce a new DNA tile self-assembly model: the Surface Flexible Tile Assembly Model (SFTAM), where 2D tiles are placed on host 3D surfaces made of axis-parallel unit cubes glued together by their faces, called polycubes. The bonds are flexible, so that the assembly can bind on the edges of the polycube. We are interested in the study of SFTAM self-assemblies on 3D surfaces which are not always embeddable in the Euclidean plane, in order to compare their different behaviors and to compute the topological properties of the host surfaces. We focus on a family of polycubes called cuboids. Order-0 cuboids are polycubes that have six rectangular faces, and order-1 cuboids are made from two order-0 cuboids by substracting one from the other. Thus, order-1 cuboids can be of genus 0 or of genus 1 (then they contain a tunnel). We are interested in the genus of these structures, and we present a SFTAM tile assembly system that determines the genus of a given order-1 cuboid. The SFTAM tile assembly system which we design, contains a specific set $Y$ of tile types with the following properties. If the assembly is made on a host order-1 cuboid $C$ of genus 0, no tile of $Y$ appears in any producible assembly, but if $C$ has genus 1, every terminal assembly contains at least one tile of $Y$. Thus, we are able to distinguish the host surfaces according to their genus, by the tiles used in the assembly. This system is specific to order-1 cuboids but the techniques we use should be generalizable to other families of shapes.
