Computational topology and geometry for systems biology

系统生物学的计算拓扑和几何

• 批准号: EP/Z531224/1
• 负责人: Heather Harrington
• 金额: $ 159.89万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2024
• 资助国家: 英国
• 起止时间: 2024 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FZ531224%2F1
• 关键词: Computational; topology; geometry; systems; biology

The proposed project focuses on creating novel mathematical tools to analyse complex datasets in biology using topology, geometry, and machine learning. Building upon the success of the Centre for Topological Data Analysis (TDA), this new initiative aims to establish and strengthen collaborations with researchers in Saxony, Germany, specifically at the Max Planck Institute for Mathematics in the Sciences (MPI-MiS) and the Max Planck Institute of Molecular Cell Biology and Genetics (MPI-CBG). These institutes are closely associated with the Center for Scalable Data Analytics and Artificial Intelligence in Dresden/Leipzig (ScaDS.AI) and the Centre for Systems Biology Dresden (CSBD). These institutions are at the forefront of cutting-edge research in computational geometry, machine learning, and systems biology. The project's main objective is to advance topological data analysis (TDA) through the integration of data science techniques, algebraic and geometric methods, and topology. By working closely with experimentalists and modellers at MPI-CBG, the project aims to push the boundaries of TDA and apply it to biological systems, creating an iterative cycle between real-world applications and methodological advancements. This collaborative programme seeks to uncover shapes and structures within biological data, ultimately leading to groundbreaking insights in molecular biology.Biological datasets are often complex, noisy, and high-dimensional. Traditional methods, such as clustering or regression, have limitations when it comes to capturing the intricate shape of the data and cannot identify higher-order structures. TDA offers a unique approach to understanding multiscale systems by characterising and quantifying their inherent shape or structure. While TDA has already demonstrated its effectiveness in medicine, including applications in tumour-immune interactions and vascular networks--even led to the discovery of new subtypes of breast cancer-- the focus of this proposal is to expand the field of topological data analysis (TDA) to handle biological datasets encountered in (spatial) systems biology. Extending the mathematics in TDA will provide a versatile toolkit that can handle a wide range of data with multiple parameters. Through close collaboration with experimentalists and modellers at the Max Planck Institute of Molecular Cell Biology and Genetics, the project will have access to diverse biological datasets, enabling the team to push the theoretical, computational, and practical boundaries of TDA.The core focus of this programme is the expansion of TDA with other areas of mathematics and data science techniques. This multidisciplinary approach will create an iterative cycle between practical applications and methodological advancements. Through collaborations with leading researchers in applied algebraic geometry, differential geometry, and the AI/TDA interface, the project aims to develop new theoretical frameworks, case studies, and software. These resources will demonstrate the immediate applicability of topological and geometric tools for data analysis.In summary, the programme will contribute to the expansion of the UK topological data analysis (TDA) community and pave the way for future involvement in larger-scale projects. The proposed research project aims to develop innovative mathematical approaches for analysing spatial and temporal multi-parameter biological datasets. By harnessing the power of topology, geometry, and machine learning, the project seeks to unlock mechanistic insights and reveal structures within biological systems and revolutionise our understanding of biology. The collaboration with international research centres will maximise impact.

拟议的项目着重于创建新颖的数学工具，以使用拓扑，几何学和机器学习来分析生物学中的复杂数据集。在拓扑数据分析中心（TDA）成功的基础上，这项新计划旨在与德国萨克森州的研究人员建立和加强合作，特别是在Max Planck Sciences（MPI-MIS）的Max Planck数学研究所（MPI-MIS）和Max Planck Max Planck Institute of Max Planck Institute of Max Planck Institute of Molecular Cell Biology and Genetics（MPI-CBG）。这些机构与Dresden/Leipzig（SCADS.AI）的可扩展数据分析和人工智能中心和系统生物学中心Dresden（CSBD）紧密相关。这些机构位于计算几何，机器学习和系统生物学方面的尖端研究的最前沿。该项目的主要目标是通过集成数据科学技术，代数和几何方法以及拓扑来推进拓扑数据分析（TDA）。通过与MPI-CBG的实验者和建模者紧密合作，该项目旨在推动TDA的界限并将其应用于生物系统，从而在现实世界应用和方法论进步之间创造了迭代周期。该协作计划旨在发现生物学数据中的形状和结构，最终导致了分子生物学的开创性见解。生物学数据集通常很复杂，嘈杂且高维。传统方法（例如聚类或回归）在捕获复杂的数据形状并且无法识别高阶结构时具有局限性。 TDA通过表征和量化其固有的形状或结构来提供一种独特的方法来理解多尺度系统。尽管TDA已经证明了其在医学方面的有效性，但包括在肿瘤免疫相互作用和血管网络中的应用，甚至导致发现了新的乳腺癌亚型 - 该提案的重点是扩大拓扑数据分析（TDA）的领域，以处理（空间）系统生物学中遇到的生物学数据集。扩展TDA中的数学将提供一个多功能工具包，该工具包可以处理具有多个参数的广泛数据。通过与Max Planck分子细胞生物学和遗传学研究所的实验者和模板的密切合作，该项目将可以访问多种生物学数据集，使团队能够将TDA的理论，计算和实践界限推向该计划的核心重点。这种多学科的方法将在实际应用和方法学进步之间创造一个迭代周期。通过与应用代数几何形状，差异几何形状和AI/TDA接口的领先研究人员的合作，该项目旨在开发新的理论框架，案例研究和软件。这些资源将证明拓扑和几何工具在数据分析中的直接适用性。总而言之，该计划将有助于扩大英国拓扑数据分析（TDA）社区，并为未来参与大型项目的参与铺平道路。拟议的研究项目旨在开发创新的数学方法，用于分析空间和时间多参数生物数据集。通过利用拓扑，几何学和机器学习的力量，该项目试图释放机械洞察力并揭示生物系统中的结构，并彻底改变了我们对生物学的理解。与国际研究中心的合作将使影响最大化。