Information Transfer in Biological Systems

以理解信息在生物系统中的作用为高级目标，该项目将重点关注数学、生物学和信息科学界面的一些重要问题——生物系统中信息流的数学建模和分析技术，生物序列中信号（信息子结构）的提取，以及生物网络中信号的量化和提取。这些问题是由生物抽象的结构和功能特征引起的，对理解疾病和干预具有重要意义。这些问题的核心是基本的数学挑战。为了解决这些问题，该项目引入了突变和达尔文通道的概念来模拟遗传信息的流动。它利用幂零李群上的随机游动来寻找有意义的子序列并求解删除通道的容量。它的目标是一系列分析和概率技术，用于发现生物序列和网络中的基序和信息结构。信息几乎是我们生活的每一个方面的核心，并以基本的方式塑造着我们的宇宙——理解和利用信息是生命科学取得基础进步的关键。基因中包含的信息及其相互关系是“通知”生物体并以其形式表现出来的东西。生物体的基本功能包括信息的产生、消耗、处理、保存和复制。生物系统中的量化、表示和信息流构成了这个项目的基本组成部分，构成了具有巨大影响的重要问题。除了用于理解信息在生物系统中的作用的分析方法、算法和软件之外，该项目还以教学材料的形式为本科和研究生水平的教育做出了重大贡献，并通过重点招聘和保留努力向代表性不足的群体伸出了援助之手。

With the high-level goal of understanding the role of information in biological systems, the proposed project focuses on a number of important problems at the interface of mathematics, biology, and information science -- mathematical modeling and analytical techniques for information flow in biological systems, extraction of signals (informative substructures) in biological sequences, and quantification and extraction of signals in biological networks. These problems are motivated by structural and functional characterization of biological abstractions, with significant implications for understanding disease and intervention. There are foundational mathematical challenges at the heart of these problems. To address these, the project introduces the concept of mutation and Darwin channels to model flow of genetic information. It uses random walks on nilpotent Lie groups to find significant subsequences and to solve the capacity of the deletion channel. It targets a range of analytic and probabilistic techniques for discovering motifs and informative structures in biological sequences and networks.Information is at the core of virtually every aspect of our lives and shapes our universe in fundamental ways -- understanding and harnessing it holds the key to foundational advances in life sciences. Information contained in the genes and their interrelationships is what `informs' the organism and manifests in its form. Essential functions of living organisms involve generation, consumption, processing, preservation, and duplication of information. Quantification, representation, and flow of information in biosystems, which form the essential components of this project, pose important problems with tremendous impact. In addition to analytical methods, algorithms, and software for understanding the role of information in biological systems, this project also makes significant contributions to education at undergraduate and graduate levels in the form of instructional material, and outreach to underrepresented groups through focused recruitment and retention efforts.