Analysis of Spatial and Spatiotemporal Anomalies Using Persistent Homology: Case Studies with COVID-19 Data

We develop a method for analyzing spatial and spatiotemporal anomalies in geospatial data using topological data analysis (TDA). To do this, we use persistent homology (PH), which allows one to algorithmically detect geometric voids in a data set and quantify the persistence of such voids. We construct an efficient filtered simplicial complex (FSC) such that the voids in our FSC are in one-to-one correspondence with the anomalies. Our approach goes beyond simply identifying anomalies;it also encodes information about the relationships between anomalies. We use vineyards, which one can interpret as time-varying persistence diagrams (which are an approach for visualizing PH), to track how the locations of the anomalies change with time. We conduct two case studies using spatially heterogeneous COVID-19 data. First, we examine vaccination rates in New York City by zip code at a single point in time. Second, we study a year-long data set of COVID-19 case rates in neighborhoods of the city of Los Angeles.

Topological data analysis in medical imaging: current state of the art.

Machine learning, and especially deep learning, is rapidly gaining acceptance and clinical usage in a wide range of image analysis applications and is regarded as providing high performance in detecting anatomical structures and identification and classification of patterns of disease in medical images. However, there are many roadblocks to the widespread implementation of machine learning in clinical image analysis, including differences in data capture leading to different measurements, high dimensionality of imaging and other medical data, and the black-box nature of machine learning, with a lack of insight into relevant features. Techniques such as radiomics have been used in traditional machine learning approaches to model the mathematical relationships between adjacent pixels in an image and provide an explainable framework for clinicians and researchers. Newer paradigms, such as topological data analysis (TDA), have recently been adopted to design and develop innovative image analysis schemes that go beyond the abilities of pixel-to-pixel comparisons. TDA can automatically construct filtrations of topological shapes of image texture through a technique known as persistent homology (PH); these features can then be fed into machine learning models that provide explainable outputs and can distinguish different image classes in a computationally more efficient way, when compared to other currently used methods. The aim of this review is to introduce PH and its variants and to review TDA's recent successes in medical imaging studies.

Topology and redescriptions detect multiple alternative biological pathways from clinical phenotypes.

Biological pathways play a crucial role in the properties of diseases and are important in drug discovery. Identifying the logical relationships among distinctive phenotypic clusters could reveal possible connections to the underlying pathways. However, this process is challenging since clinical phenotypes are often available through unstructured electronic health records. Moreover, in the absence of a standardized questionnaire, there could be bias among physicians toward selecting certain medical terms. In this article, we develop an efficient pipeline to address these challenges and help practitioners to reveal the pathways associated with the disease. We use topological data analysis and redescriptions and propose a pipeline of four phases: (1) pre-processing the clinical notes to extract the salient concepts, (2) constructing a feature space of the patients to characterize the extracted concepts, (3) leveraging the topological properties to distill the available knowledge and visualize the extracted features, and finally, (4) investigating the bias in the clinical notes of the selected features and identify possible pathways. Our experiments on a publicly available dataset of COVID-19 clinical notes testify that our pipeline can indeed extract meaningful pathways.

Mathematical artificial intelligence design of mutation-proof COVID-19 monoclonal antibodies

Emerging severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) variants have compromised existing vaccines and posed a grand challenge to coronavirus disease 2019 (COVID-19) prevention, control, and global economic recovery. For COVID-19 patients, one of the most effective COVID-19 medications is monoclonal antibody (mAb) therapies. The United States Food and Drug Administration (U.S. FDA) has given the emergency use authorization (EUA) to a few mAbs, including those from Regeneron, Eli Elly, etc. However, they are also undermined by SARS-CoV-2 mutations. It is imperative to develop effective mutation-proof mAbs for treating COVID-19 patients infected by all emerging variants and/or the original SARS-CoV-2. We carry out a deep mutational scanning to present the blueprint of such mAbs using algebraic topology and artificial intelligence (AI). To reduce the risk of clinical trial-related failure, we select five mAbs either with FDA EUA or in clinical trials as our starting point. We demonstrate that topological AI-designed mAbs are effective for variants of concerns and variants of interest designated by the World Health Organization (WHO), as well as the original SARS-CoV-2. Our topological AI methodologies have been validated by tens of thousands of deep mutational data and their predictions have been confirmed by results from tens of experimental laboratories and population-level statistics of genome isolates from hundreds of thousands of patients.

Tlife-GDN: Detecting and Forecasting Spatio-Temporal Anomalies via Persistent Homology and Geometric Deep Learning

Most recently, the tools of geometric deep learning (GDL) and, in particular, graph neural networks emerge as a promising new alternative in unsupervised anomaly detection problems where the data exhibit a sophisticated nonlinear dependence structure such as various geospatial surveillance systems. However, prevailing GDL-based methods for anomaly detection tend to exhibit limited capabilities to capture multiscale spatio-temporal variability which is ubiquitous in many applications, particularly, related to biosurveillance and biothreats. Motivated by the problem of assessing COVID-19 severity, we develop a novel approach to unsupervised anomaly detection in spatio-temporal data by fusing the notion of GDL with the emerging direction of persistent homologies and topological data analysis. In particular, our key idea is to bolster the GDL performance by leveraging the complementary insight on the intrinsic multiscale data organization which topological descriptors can provide. We also go one step further and show how our ideas at the interface of topological and geometric deep learning can be used not only for detection but for prediction of future anomalies. We show the utility of the new approach to detecting, forecasting and interpreting risks in COVID-19 clinical severity, measured in terms of hospitalization rates, in three U.S. states: California, Texas, and Pennsylvania. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Inferring COVID-19 Biological Pathways from Clinical Phenotypes Via Topological Analysis

COVID-19 has caused thousands of deaths around the world and also resulted in a large international economic disruption. Identifying the pathways associated with this illness can help medical researchers to better understand the properties of the condition. This process can be carried out by analyzing the medical records. It is crucial to develop tools and models that can aid researchers with this process in a timely manner. However, medical records are often unstructured clinical notes, and this poses significant challenges to developing the automated systems. In this article, we propose a pipeline to aid practitioners in analyzing clinical notes and revealing the pathways associated with this disease. Our pipeline relies on topological properties and consists of three phases: (1) pre-processing the clinical notes to extract the salient concepts, (2) constructing a feature space of the patients to characterize the extracted concepts, and finally, (3) leveraging the topological properties to distill the available knowledge and visualize the result. Our experiments on a publicly available dataset of COVID-19 clinical notes testify that our pipeline can indeed extract meaningful pathways. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Vaccine-escape and fast-growing mutations in the United Kingdom, the United States, Singapore, Spain, India, and other COVID-19-devastated countries.

Recently, the SARS-CoV-2 variants from the United Kingdom (UK), South Africa, and Brazil have received much attention for their increased infectivity, potentially high virulence, and possible threats to existing vaccines and antibody therapies. The question remains if there are other more infectious variants transmitted around the world. We carry out a large-scale study of 506,768 SARS-CoV-2 genome isolates from patients to identify many other rapidly growing mutations on the spike (S) protein receptor-binding domain (RBD). We reveal that essentially all 100 most observed mutations strengthen the binding between the RBD and the host angiotensin-converting enzyme 2 (ACE2), indicating the virus evolves toward more infectious variants. In particular, we discover new fast-growing RBD mutations N439K, S477N, S477R, and N501T that also enhance the RBD and ACE2 binding. We further unveil that mutation N501Y involved in United Kingdom (UK), South Africa, and Brazil variants may moderately weaken the binding between the RBD and many known antibodies, while mutations E484K and K417N found in South Africa and Brazilian variants, L452R and E484Q found in India variants, can potentially disrupt the binding between the RBD and many known antibodies. Among these RBD mutations, L452R is also now known as part of the California variant B.1.427. Finally, we hypothesize that RBD mutations that can simultaneously make SARS-CoV-2 more infectious and disrupt the existing antibodies, called vaccine escape mutations, will pose an imminent threat to the current crop of vaccines. A list of most likely vaccine escape mutations is given, including S494P, Q493L, K417N, F490S, F486L, R403K, E484K, L452R, K417T, F490L, E484Q, and A475S. Mutation T478K appears to make the Mexico variant B.1.1.222 the most infectious one. Our comprehensive genetic analysis and protein-protein binding study show that the genetic evolution of SARS-CoV-2 on the RBD, which may be regulated by host gene editing, viral proofreading, random genetic drift, and natural selection, gives rise to more infectious variants that will potentially compromise existing vaccines and antibody therapies.

HiDeF: identifying persistent structures in multiscale 'omics data.

In any 'omics study, the scale of analysis can dramatically affect the outcome. For instance, when clustering single-cell transcriptomes, is the analysis tuned to discover broad or specific cell types? Likewise, protein communities revealed from protein networks can vary widely in sizes depending on the method. Here, we use the concept of persistent homology, drawn from mathematical topology, to identify robust structures in data at all scales simultaneously. Application to mouse single-cell transcriptomes significantly expands the catalog of identified cell types, while analysis of SARS-COV-2 protein interactions suggests hijacking of WNT. The method, HiDeF, is available via Python and Cytoscape.

Review of COVID-19 Antibody Therapies.

In the global health emergency caused by coronavirus disease 2019 (COVID-19), efficient and specific therapies are urgently needed. Compared with traditional small-molecular drugs, antibody therapies are relatively easy to develop; they are as specific as vaccines in targeting severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2); and they have thus attracted much attention in the past few months. This article reviews seven existing antibodies for neutralizing SARS-CoV-2 with 3D structures deposited in the Protein Data Bank (PDB). Five 3D antibody structures associated with the SARS-CoV spike (S) protein are also evaluated for their potential in neutralizing SARS-CoV-2. The interactions of these antibodies with the S protein receptor-binding domain (RBD) are compared with those between angiotensin-converting enzyme 2 and RBD complexes. Due to the orders of magnitude in the discrepancies of experimental binding affinities, we introduce topological data analysis, a variety of network models, and deep learning to analyze the binding strength and therapeutic potential of the 14 antibody-antigen complexes. The current COVID-19 antibody clinical trials, which are not limited to the S protein target, are also reviewed.