Dynamics of Boolean Networks and Gene Expression

细胞的物理结构在很大程度上由其每个基因的表达水平决定。这些水平由复杂的转录和翻译过程控制，这些过程形成蛋白质，这些蛋白质的存在可以改变这些过程，从而影响产生它们的基因的表达水平。在其最深的层面上，这种复杂的物理结构可以被表示为基因之间相互作用的网络--一个通过基因表达模式的抽象空间来控制细胞进程的网络。索科勒和考夫曼要求为研究此类复杂网络的动力学属性提供资金。选择要研究的数学网络是因为它们与基因表达的生物学相关。这项拟议的研究旨在开发复杂的调控网络的有用模型，这些网络决定了真核细胞中所有基因的活动。实验技术的最新进展促进了功能基因组学的爆炸性活动，目前主要是通过分析基因表达模式中的相关性来推断网络的特定亚结构。这项研究提出了一系列补充问题，集中在复杂布尔网络的一般性质上，目的是阐明不同类型网络体系结构的功能含义。工作假设是，某些类型的布尔网络阐明了构成生物有机体结构的组织原理。具体地说，该研究将提供实际决定在各种约束下构建的大型随机布尔网络中的长时间动态的节点数的解析计算，并确定相互连接这些相关节点的子网络的统计信息。在完成目前关于每个节点具有固定输入数目的随机网络的工作之后，将研究具有随机结构和对应于模块体系结构的相关性的无标度网络。相关节点子网络支持的动态行为将被描述为确定性和随机性的动态规则。数学/物理问题的选择将强烈地受到其生物相关性的潜在影响。中间结果将与基因芯片实验收集的统计信息进行比较，以确定这些实验是否包含任何特定全球网络结构的特征。了解遗传调控网络的全球特征有望为进化和个体发生过程带来新的见解，并为涉及基因组特定部分的功能基因组学实验的设计提供有用的信息。拟议的研究是高度交叉的，需要动力系统理论和细胞与发育生物学专家之间的合作。它为功能基因组学和生物信息学等新兴领域的所有水平的学生提供跨学科培训的机会，在这些领域，传统上在物理学背景下教授的分析技能以及细胞和分子生物学的原理同样重要。

The physical structure of a cell is largely determined by the expression level of each of itsgenes. These levels are governed by complicated transcriptional and translational processesthat form proteins, whose presence can then alter those processes and hence influence theexpression levels of the very genes that produced them. At its deepest level, this complexphysical structure can be represented as a network of interactions among genes - a network that governs the progression of the cell through an abstract space of gene expression patterns. Socolar and Kauffman request funding for research addressing the dynamical properties of such complex networks. The mathematical networks to be studied are selected specifically for their relevance to the biology of gene expression. The proposed research aims to develop useful models of the complex regulatory networksthat determine the activities of all of the genes in a eukaryotic cell. Recent advances in experimental technique have prompted an explosion of activity in functional genomics, dominated at present by efforts to deduce particular substructures of a network by analyzing correlations in gene expression patterns. The proposed research addresses a complementary set of questions, focusing on the generic properties of complex Boolean networks with the goal of elucidating the functional implications of different types of network architecture.The working hypothesis is that certain classes of Boolean networks illustrate principles oforganization that underlie the structure of biological organisms. Specifically, the proposed research will provide analytic calculations of the numbers of nodes that actually determine the long-time dynamics in large random Boolean networks constructed under various constraints, and determine the statistics of the sub-networks linking these relevant nodes with each other. After the completion of current work on random networks with a fixed number of inputs per node, scale-free networks will be studied, bothwith random structures and with correlations corresponding to modular architectures. The dynamical behavior supported by the sub-networks of relevant nodes will be characterized, both for deterministic and stochastic dynamical rules.Choices of mathematical/physical problems will be strongly influenced by their potentialfor biological relevance. Intermediate results will be compared to statistical informationgathered from gene chip experiments to determine whether those experiments contain signaturesof any particular global network architecture. Understanding the global features of genetic regulatory networks is expected to lead to new insights into evolutionary and ontogenic processes, as well as provide useful information for the design of functional genomics experiments involving selected portions of the genome.The proposed research is highly cross-disciplinary, requiring a collaboration between experts in dynamical systems theory and cell and developmental biology. It provides opportunities for interdisciplinary training for students at all levels in the burgeoning fields of functional genomics and bio-informatics, where analytical skills traditionally taught in physics contexts and principles of cell and molecular biology are equally important.