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对其周围环境有重大影响的生化过程。这种影响范围很广，从引发疾病到提供新型抗生素，再到通过在土壤中固定氮素来帮助作物生长。元基因组学是通过提取的DNA来研究这些微生物群落。在研究这样的群落时，首先要问的问题之一是：“存在哪些有机体，数量有多大？”对于这个所谓的群落概况问题，目前的大多数方法都采取了一种节俭的方法：推断出与观测数据仍然一致的尽可能少的生物体的存在。然而，将每一种生物完全区别对待，可能会导致对存在的不同种类和数量的生物的错误估计，这被称为生物多样性。从历史上看，对于分析衡量生物多样性的适当方式一直存在很大分歧，这一事实使情况变得更加复杂。在这个项目中，研究人员利用最近定义的、统一的生物多样性概念来解决正确描绘具有不同相似性的生物体的微生物群落的问题。为此，提出了一种新的数学框架，该框架利用了压缩传感的大数据方法。在提出数学理论后，研究人员将创建一个软件实现，允许生物医学研究人员研究元基因组群落，同时适当地考虑到不同的生物体相似性。在推进发现的同时，这个项目也促进了研究生和本科生的教与学。特别是，指导学生在数学和生物领域的跨学科工作中表现出色。此外，除了会议和论文的传统传播途径外，还通过与广受欢迎的YouTube频道SciShow的合作，吸引了广泛的受众，该频道将与PI合作，制作适合普通公众的以元基因组学为特色的剧集。微生物群落概况，通过测序DNA确定特定环境样本中存在的所有微生物的身份和相对丰度，是研究此类群落的重要第一步。已经提出了许多工具和方法来描述微生物群落，虽然这些工具利用微生物遗传学的特殊性质来执行分类任务，但普遍缺乏严格的数学方法来允许对这种分类作出明确的陈述。此外，根据所使用的计算方法，一个群落的估计生物多样性可能会有很大的差异。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的衡量标准，而且这种数量的异常与许多疾病有关。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衡量标准。在这个项目中，PI利用生物多样性的这一定义来开发一种严格的数学方法，以同时描述微生物群落并表征其生物多样性。从数学上讲，这归结为开发(和证明有关结果)优化程序，其中目标函数包括生物多样性。有趣的是，这种方法与压缩感知和其他促进优化的“大数据”稀疏性方法类似。主要的方法将是将这种生物多样性的度量减少到一个准正规型，并适当地修改关于这种优化例程的收敛和有保证的重构的现有证明。这将产生一个优化框架，允许同时描绘微生物群落，并在考虑生物体相似性的同时直接表征其生物多样性。这将在用户友好的软件中实施，并用于分析健康和患病的早产儿的肠道样本。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.