Non-deterministic self-assembly of two tile types on a lattice
Non-deterministic self-assembly of two tile types on a lattice
复制标题
晶格上两种瓦片类型的非确定性自组装
作者：
S. Tesoro;S. Ahnert
自组装在自然界中普遍存在，特别是在生物学中，它是蛋白质四级结构和蛋白质聚集形成的基础。四级结构确定性地组装，并在细胞中执行广泛的重要功能，而蛋白质聚集是许多疾病的标志，代表了非确定性的自组装过程。在这里，我们建立在以前的工作上的确定性自组装的晶格模型来研究非确定性的自组装的单晶格瓦片和混合物的两个瓦片在不同的相对浓度。尽管将模型的简单性限制为两种界面类型，这导致13个拓扑上不同的单个瓦片和106个拓扑上不同的两个瓦片的集合，但我们观察到各种各样的浓度依赖性行为。几个两瓷砖集显示关键的行为，从绑定到未绑定结构的急剧过渡的形式，作为一个瓷砖的相对浓度增加到另一个。其他集合表现出结构密度的逐渐单调变化，或非单调变化，而其他集合则完全没有浓度依赖性。我们编目这一广泛的行为范围，并提出了一个模型，提供了一个合理的好估计的临界浓度的一个子集的关键转变。此外，我们表明，从这些瓦片集的结构是分形的，有两个不同的分形维数之一。
Self-assembly is ubiquitous in nature, particularly in biology, where it underlies the formation of protein quaternary structure and protein aggregation. Quaternary structure assembles deterministically and performs a wide range of important functions in the cell, whereas protein aggregation is the hallmark of a number of diseases and represents a nondeterministic self-assembly process. Here we build on previous work on a lattice model of deterministic self-assembly to investigate nondeterministic self-assembly of single lattice tiles and mixtures of two tiles at varying relative concentrations. Despite limiting the simplicity of the model to two interface types, which results in 13 topologically distinct single tiles and 106 topologically distinct sets of two tiles, we observe a wide variety of concentration-dependent behaviors. Several two-tile sets display critical behaviors in the form of a sharp transition from bound to unbound structures as the relative concentration of one tile to another increases. Other sets exhibit gradual monotonic changes in structural density, or nonmonotonic changes, while again others show no concentration dependence at all. We catalog this extensive range of behaviors and present a model that provides a reasonably good estimate of the critical concentrations for a subset of the critical transitions. In addition, we show that the structures resulting from these tile sets are fractal, with one of two different fractal dimensions.
影响因子：
3.4
作者：
SEEMAN, NC;KALLENBACH, NR
通讯作者：
KALLENBACH, NR
影响因子：
5.6
作者：
ZLOTNICK, A
通讯作者：
ZLOTNICK, A