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

自然界中存在各种各样的自组装系统。在这些系统中，复杂的结构是由相互自主结合的单个分子形成的，只遵守当地的行为规则，没有任何外部指导或放置。这一过程导致了各种各样的无机结构的形成(如雪花状的晶体)，以及众多的生物结构(包括细胞膜和病毒)。为了利用自组装的力量来创造先进的材料、复杂的纳米结构和进行分子计算，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模型。理论计算机科学为自组装理论模型的创建和理解提供了大量见解，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、开发和比较自组装系统理论模型的相对权力的工作主体将通过PI来扩展。特别是，将通过比较各种模型的模拟能力来研究它们的相对功率。此外，还将研究现有和新模型中系统模拟生物过程(如进化和免疫系统行为)的能力。该项目分为两个主要部分。第一部分是对各种理论模型在某些参数固定时相互模拟的能力进行的一系列研究，特别是所谓的温度参数固定为1，这使得合作行为变得困难或不可能。还将探讨某些模型是否本质上是通用的，这些模型也是具有固定参数的。此外，虽然目前比较模型相对功率的大多数理论工作都涉及一种强烈的仿真概念，它既包括仿真系统的产生式，也包括仿真系统的动力学产生式，但只关注仿真系统的结构产生式(即产生式)的宽松概念将被研究。虽然以前的方法已经产生了很好的理论理解，但这种新的方法是面向更实际的理解，可以指导希望建立预定义结构的实验者。该项目的第二个主要组成部分涉及与研究各种自组装系统模拟复杂和重要生物活动的能力有关的工作，如蛋白质折叠、类病毒结构的形成、自我复制、进化和免疫系统行为。对于其中的大部分，将使用利用动态变化的基本组件的现有模型，即信号瓦片组装模型。此外，还将开发和研究一种基于正方形2D组件的新模型，该组件可以沿其边界折叠，允许通过“可折叠的”2D构建块形成3D结构，重点是它们抽象模拟蛋白质类行为的能力。这项工作将包括数学建模和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 y.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.