AF: Small: Using Notions of Simulation to Explore the Power of Self-Assembling Systems

自然界中存在着各种各样的自组装系统。在这些系统中，复杂的结构是由单个分子自主地结合在一起形成的，它们只服从局部的行为规则，没有任何外部的指导或放置。这一过程负责形成种类繁多的无机结构（如雪花一样的晶体），以及许多生物结构（包括细胞膜和病毒）。希望利用自组装的力量来创造先进的材料，复杂的纳米级结构，并执行分子计算，研究人员已经开始开发人工自组装系统。这项工作包括实验室实现以及数学和计算建模。理论计算机科学为创建和理解自组装的理论模型提供了许多见解，这些模型提供了有价值的理解，有效地指导了实验室实验。在这个项目中，定义、发展和比较自组装系统理论模型的相对能力的工作主体将由PI扩展。特别是，将通过比较各种模型的相互模拟能力来研究它们的相对功率。此外，系统的能力在现有的和新的模型模拟生物过程，如进化和免疫系统的行为将被调查。本项目分为两个主要部分。第一部分包括一系列研究，当某些参数固定时，特别是所谓的“温度”参数固定为1，使合作行为变得困难或不可能时，各种理论模型相互模拟的能力。同样具有固定参数的某些模型是否具有本质上的普遍性也将被探讨。此外，虽然目前大多数比较模型相对能力的理论工作都涉及强大的仿真概念，其中包括仿真系统的产生和动力学，但将研究仅关注仿真系统产生的结构（即产生）的宽松概念。虽然以前的方法已经产生了很大的理论理解，但这种新方法是面向更实际的理解，可以指导希望构建预定义结构的实验家。该项目的第二个主要组成部分涉及研究各种自组装系统模拟复杂而重要的生物活动的能力，如蛋白质折叠、朊病毒样结构的形成、自我复制、进化和免疫系统行为。对于其中的大部分，将采用利用动态变化的基本组件的现有模型，即信号瓷砖组装模型。此外，将开发和研究一种基于方形2D组件的新模型，该模型可以沿其边界折叠，允许通过“可折叠”的2D构建块形成3D结构，特别关注它们抽象模拟蛋白质样行为的能力。这项工作将包括数学建模以及模拟软件形式的计算建模。结果和软件将与已有的软件和内容一起在www.self-assembly.net上免费提供。

A wide variety of self-assembling systems exist in nature. These are systems in which complex structures are formed from individual molecules that combine with each other autonomously, obeying only local rules of behavior and without any external guidance or placement. This process is responsible for the formation of a huge diversity of inorganic structures (such as crystals like snowflakes), as well as numerous biological structures (including cellular membranes and viruses). Hoping to harness the power of self-assembly to create advanced materials, complex nanoscale structures, and perform molecular computing, researchers have begun developing artificial self-assembling systems. This work has consisted of laboratory implementations as well as mathematical and computational modeling.Theoretical computer science has provided numerous insights into the creation and understanding of theoretical models of self-assembly, and these models have provided valuable understanding which has productively guided laboratory experiments. In this project, the body of work in defining, developing, and comparing the relative powers of theoretical models of self-assembling systems will be extended by the PI. In particular, the relative powers of various models will be studied by comparing their abilities to simulate each other. Additionally, the abilities of systems within existing and new models to mimic biological processes such as evolution and immune system behavior will be investigated.This project is divided into two main components. The first consists of a series of studies of the abilities of various theoretical models to simulate each other when certain parameters are fixed, especially the so-called "temperature" parameter fixed at 1, making cooperative behaviors difficult or impossible. Whether or not certain models, again with fixed parameters, are intrinsically universal will also be explored. Additionally, while most current theoretical work comparing the relative powers of models is concerned with a strong notion of simulation which includes both the productions and dynamics of the simulating systems, relaxed notions which focus solely on the structures produced (i.e. the productions) of simulating systems will be investigated. While the previous method has produced great theoretical understanding, this new approach is geared toward a more practical understanding which can guide experimentalists desiring to build predefined structures.The second main component of this project involves work related to studying the abilities of various self-assembling systems to simulate complex and important biological activities such as protein folding, the formation of prion-like structures, self-replication, evolution, and immune system behaviors. For much of this, an existing model utilizing dynamically changing basic components, the Signal Tile Assembly Model, will be employed. Further, a new model based on square 2D components which can fold along their boundaries, allowing for the formation of 3D structures by "foldable" 2D building blocks, will be developed and studied, with special focus on their abilities to abstractly mimic protein-like behaviors.The work will consist of mathematical modeling as well as computational modeling in the form of simulation software. Results and software, will be made freely available with already existing software and content on www.self-assembly.net.