Collaborative Research: RESEARCH-PGR: Predicting Phenotype from Molecular Profiles with Deep Learning: Topological Data Analysis to Address a Grand Challenge in the Plant Sciences

生物体是嵌入其基因组中的信息通过分子过程表达的结果。测序技术使生物学家能够从基因组中提取几乎所有的信息内容。然而，测量生物体是什么还没有进展到基因组测序的程度：与基因组不同，还不可能测量生物体形式中嵌入的全部信息。如果可以提取生物体中包含的所有信息，就可以开发出一种模型，解决生物学中的一个重大挑战，即从基因组信息预测生物体是什么的能力。在该项目中，生物学中尚未充分探索的数学方法将用于通过测量其结构来提取数据中的信息。这个数学领域有一个座右铭：所有的形状都是数据，所有的数据都有形状。通过测量叶子的形状和基因表达模式，该项目将把它们作为数据，从中提取嵌入的信息。然后，深度学习方法将用于从基因表达谱中预测叶子的形状。作为该项目及其对社会影响之间联系的一部分，来自美国和梅西科的学生将通过Plants Python帮助分析数据，Plants Python是一门双语免费课程，旨在将从未编码过的植物生物学家和植物科学新数据科学家与美国农业团体聚集在一起。&使用X射线计算机断层扫描（CT）测量植物形态和转录组分析（RNA-seq）测量基因表达，该项目将使用欧拉特征变换（ECT）和映射算法，两种拓扑数据分析（TDA）技术，以提取嵌入拟南芥叶形态的总信息，并对比发育再现性。ECT在数学上被证明可以区分任何对象，Mapper算法用于将底层数据结构可视化为图形。具体目标包括：1）使用ECT来测量嵌入在叶子形状中的总信息，并与传统方法进行基准测试，以查看在全面测量时揭示了多少"隐藏"的表型信息; 2）从相同的叶子生成RNA-Seq基因表达谱，将底层数据结构可视化为Mapper图;对于由ECT测量的表型数据也将这样做;以及，3）使用深度学习预测与基因表达特征相关的精确叶片形状特征。通过将潜在的分子和表型数据结构转换为节点嵌入，编码器-解码器神经网络将对齐分子和表型Mapper图。其结果将是基因表达谱与叶片形状特征的映射，如使用底层数据结构的深度学习方法所预测的那样。所有项目成果将通过长期数据库公开提供。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。

Organisms are a consequence of information embedded in their genome expressed through molecular processes. Sequencing technologies allow biologists to extract nearly all information content from the genome. However, measuring what an organism is has not advanced as far as genomic sequencing: unlike the genome, it is not yet possible to measure the totality of information embedded in the organismal form. If all the information that is contained within organisms could be extracted, a model could be developed that would address one of the Grand Challenges in biology, the ability to predict what an organism is from its genomic information. In this project, mathematical approaches that have not been fully explored in biology will be used to extract information in data by measuring its structure. This field of mathematics has a motto: that all shape is data, and all data have shape. By measuring the shapes and gene expression patterns of leaves, the project will treat them as data from which embedded information can be extracted. Deep learning methods will then be used to predict the shapes of leaves from their gene expression profiles. As part of the connection between the project and its impact to society, students from both the U.S. and México will help analyze the data through Plants&Python, a bilingual, freely available curriculum initiated as a means to bring together plant biologists who have never coded and data scientists new to plant science, with groups that comprise U.S. agriculture. Using X-ray Computed Tomography (CT) to measure plant morphology and transcriptome profiling (RNA-seq) to measure gene expression, the project will use the Euler Characteristic Transform (ECT) and the Mapper algorithm, two Topological Data Analysis (TDA) techniques, to extract the total information embedded in the leaf morphology of Arabidopsis accessions with contrasting developmental reproducibility. The ECT is mathematically proven to distinguish any object from any other, and the Mapper algorithm is used to visualize underlying data structures as a graph. Specific aims include: 1) using the ECT to measure the total information embedded in leaf shape and benchmarking against traditional methods to see how much “hidden” phenotypic information is revealed when measured comprehensively; 2) generating RNA-Seq gene expression profiles from identical leaves, visualizing the underlying data structure as a Mapper graph; the same will be done for phenotypic data as measured by the ECT; and, 3) predicting the precise leaf shape features associated with gene expression signatures using deep learning. By converting underlying molecular and phenotypic data structures into node embeddings, an encoder-decoder neural network will align molecular and phenotypic Mapper graphs. The result will be a mapping of gene expression profiles to features of leaf shape as predicted using deep learning methods on underlying data structures. All project outcomes will be made publicly available through long term data repositories.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.