QuBBD: Fast, Efficient Mathematical Approach to the Analysis of the Human Microbiome through Biodiversity Optimization

微生物群落参与并驱动各种生化过程，对周围环境产生重大影响。这种影响范围很广，从引起疾病到提供新型抗生素，再到通过固定土壤中的氮来帮助作物生长。宏基因组学是通过提取的DNA研究这些微生物群落。在研究这样一个群落时，首先要问的问题之一是：“哪些生物存在，丰度如何？“目前大多数解决这个所谓的群落特征分析问题的方法都采取了一种简约的方法：推断出仍然与观察数据一致的最少生物体的存在。然而，将每一种生物体视为完全不同于任何其他生物体，可能会导致对存在的不同种类和数量的生物体（称为生物多样性）的错误估计。由于历史上对分析性衡量生物多样性的适当方法存在很大分歧，这一点进一步复杂化。在这个项目中，研究人员利用最近定义的生物多样性的统一概念来解决正确分析微生物群落的问题，其中包含不同相似性的生物体。为了实现这一目标，提出了一种新的数学框架，利用压缩感知的大数据方法。在推进数学理论之后，研究人员将创建一个软件实现，使生物医学研究人员能够研究宏基因组群落，同时适当考虑不同的生物体相似性。 在推进发现的同时，该项目促进了研究生和本科生的教学和学习。特别是，引导学生在数学和生物学领域的跨学科工作中脱颖而出。此外，除了传统的会议和论文传播途径外，还通过与SciShow的合作吸引了广泛的受众，SciShow是一个受欢迎的YouTube频道，将与PI合作制作适合公众的宏基因组学剧集。微生物群落分析，通过DNA测序确定给定环境样本中存在的所有微生物的身份和相对丰度，是研究这类群落的重要的第一步。已经提出了许多工具和方法来分析微生物群落，并且虽然这些工具利用微生物遗传学的特定特性来执行分类任务，但是普遍缺乏严格的数学方法来允许对这种分类进行明确的陈述。此外，一个群落的生物多样性估计值可能因所用计算方法的不同而有很大差异。这是有问题的，因为在研究细菌群落对其周围环境的影响时，生物多样性是一个关键指标，并且这种数量的畸变与许多疾病有关。科学界对如何衡量生物多样性存在很大分歧，这进一步加剧了这一困难。然而，最近的研究表明，一个单一的公式包含和统一了许多最流行的生物多样性措施。在这个项目中，PI利用生物多样性的定义来开发一种严格的数学方法，同时分析微生物群落并表征其生物多样性。从数学上讲，这简化为开发（和证明有关）目标函数包括生物多样性的优化程序。有趣的是，这种方法与压缩感知和其他此类“大数据”稀疏性促进优化例程的方法相似。主要的方法将是减少这种生物多样性的措施，一个quasinquiry和适当地修改现有的证据的收敛性和保证重建这样的优化例程。这将产生一个优化框架，允许同时分析微生物群落并直接表征其生物多样性，同时考虑生物相似性。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Communities of microorganisms participate in and drive a variety of biochemical processes that have significant impact on the environment around them. This impact ranges widely from causing diseases to offering new kinds of antibiotics, to helping crops grow by fixing nitrogen in the soil. Metagenomics is the study of such microbial communities through their extracted DNA. One of the first questions to ask when studying such a community is: "which organisms are present and at what abundance?" Most current approaches to this so-called community profiling problem take a parsimonious approach: infer the presence of the fewest organisms possible that still agrees with the observed data. However, treating each organism as completely different from any other can lead to mis-estimates of the different kinds and amounts of organisms present, referred to as biological diversity. This is further complicated by the fact that historically there has been much disagreement about the proper way to analytically measure biological diversity. In this project, the investigators leverage a recently defined, unifying notion of biological diversity to address the problem of correctly profiling a microbial community which has in it organisms of varying similarity. To accomplish this, a new mathematical framework is put forward that utilizes the big data approach of compressive sensing. After advancing the mathematical theory, the investigators will create a software implementation that will allow biomedical researchers to study metagenomic communities while properly accounting for varying organism similarity. While advancing discovery, this project promotes graduate and undergraduate student teaching and learning. In particular, students are guided to excel at interdisciplinary work in the fields of mathematics and biology. Furthermore, beyond the traditional dissemination routes of conferences and papers, a wide audience is also engaged through a collaboration with SciShow, a popular YouTube channel that will work with the PIs in creating episodes featuring metagenomics suitable for the general public.Microorganismal community profiling, determining the identity and relative abundance of all microbial organisms present in a given environmental sample through their sequenced DNA, is an important first step in the study of such communities. Many tools and approaches have been proposed to profile microbial communities, and while these tools take advantage of particular properties of microbial genetics to perform the classification task, there is a general lack of rigorous mathematical approaches that allow for definitive statements to be made about such classifications. Furthermore, the estimated biological diversity of a community can vary widely depending on the computational approach used. This is problematic given that biological diversity is a key metric when studying the impact of a bacterial community on its surrounding environment and aberrations of this quantity have been implicated in a number of diseases. This difficulty is further compounded by the fact that there is much disagreement in the scientific community on how to measure biodiversity. Recently, however, it was shown that a single formula subsumes and unifies many of the most popular biodiversity measures. In this project, the PIs utilize this definition of biodiversity to develop a rigorous mathematical approach to simultaneously profile a microbial community and characterize its biological diversity. Mathematically, this reduces to developing (and proving results about) an optimization procedure where the objective function includes biological diversity. Intriguingly, such an approach parallels that of compressive sensing and other such "big data" sparsity promoting optimization routines. The main approach will be to reduce this measure of biodiversity to a quasinorm and appropriately modify existing proofs about the convergence and guaranteed reconstruction of such optimization routines. This will result in an optimization framework that allows for simultaneously profiling a microbial community and characterizing its biodiversity directly while considering organism similarity. This will be implemented in user-friendly software and used to analyze gut samples from healthy and sick pre-term infants.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.