Dynamics of Boolean Networks and Gene Expression

细胞的物理结构在很大程度上是由细胞中每个基因的表达水平决定的。这些水平是由形成蛋白质的复杂转录和翻译过程控制的，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。在其最深层次上，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。Socolar和Kauffman为解决这种复杂网络的动态特性的研究申请资金。所要研究的数学网络是根据它们与基因表达生物学的相关性而选择的。提出的研究旨在开发复杂调控网络的有用模型，确定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活动的爆发，目前主要是通过分析基因表达模式的相关性来推断网络的特定亚结构。提出的研究解决了一组互补的问题，重点关注复杂布尔网络的一般属性，目的是阐明不同类型的网络架构的功能含义。工作假设是，某些类别的布尔网络说明了构成生物有机体结构的组织原则。具体而言，本研究将提供在各种约束下构建的大型随机布尔网络中实际决定长期动态的节点数的分析计算，并确定将这些相关节点相互连接的子网络的统计量。在完成当前对每个节点有固定输入数的随机网络的研究后，将研究无标度网络，既有随机结构，也有与模块化体系结构相对应的相关性。相关节点的子网络支持的动态行为将被表征，包括确定性和随机动态规则。数学/物理问题的选择将受到其潜在的生物学相关性的强烈影响。中间结果将与从基因芯片实验中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架构的特征。了解遗传调控网络的全局特征有望导致对进化和个体发生过程的新见解，并为设计涉及基因组选定部分的功能基因组学实验提供有用的信息。拟议的研究是高度跨学科的，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新兴领域的各级学生提供了跨学科培训的机会，在这些领域，传统上在物理背景下教授的分析技能以及细胞和分子生物学原理同样重要。

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.