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As an adoptive cellular therapy, Chimeric Antigen Receptor T cell (CAR T cell) therapy has shown remarkable success in hematological malignancies but only limited efficacy against solid tumors. Compared with blood cancers, solid tumors present a series of challenges that ultimately combine to neutralize the function of CAR T cells. These challenges include, but are not limited to, antigen heterogeneity - variability in the expression of the antigen on tumor cells, as well as trafficking and infiltration into the solid tumor tissue. A critical question for solving the heterogeneity problem is whether CAR T therapy induces bystander effects, such as antigen spreading. Antigen spreading occurs when CAR T cells activate other endogenous antitumor CD8 T cells against antigens that were not originally targeted. In this work, we develop a mathematical model of CAR T cell therapy for solid tumors that considers both antigen heterogeneity and bystander effects. Our model is based on in vivo treatment data that includes a mixture of target antigen-positive and target antigen-negative tumor cells. We use our model to simulate large cohorts of virtual patients to better understand the relationship involving bystander killing. We also investigate several strategies for enhancing bystander effects, thus increasing CAR T cell therapy's overall efficacy for solid tumors. [ABSTRACT FROM AUTHOR]

Simple Summary: Clinical data sets incorporate continuous data like blood pressure or sodium levels, categorical data like cancer grade or stage, and binary data like sex or marital status. Measurements on an individual patient define a point in a high-dimensional space; data from many patients defines a "point cloud". The "shape" of the point cloud influences experimental design by describing patient variability. Topological data analysis (TDA) is a mathematical technique for understanding the shape of point clouds by finding "holes" that correspond to combinations of patient characteristics that are never observed. TDA results are stratified by dimension. Zero-dimensional features define patient subtypes. One-dimensional features ("loops") are analogs of the inside of a circle or a donut hole. Two-dimensional features ("voids") are analogs of the inside of a balloon. Here, we apply TDA to a clinical data set of previously untreated patients with Chronic Lymphocytic Leukemia to find loops and voids. Patients are complex and heterogeneous; clinical data sets are complicated by noise, missing data, and the presence of mixed-type data. Using such data sets requires understanding the high-dimensional "space of patients", composed of all measurements that define all relevant phenotypes. The current state-of-the-art merely defines spatial groupings of patients using cluster analyses. Our goal is to apply topological data analysis (TDA), a new unsupervised technique, to obtain a more complete understanding of patient space. We applied TDA to a space of 266 previously untreated patients with Chronic Lymphocytic Leukemia (CLL), using the "daisy" metric to compute distances between clinical records. We found clear evidence for both loops and voids in the CLL data. To interpret these structures, we developed novel computational and graphical methods. The most persistent loop and the most persistent void can be explained using three dichotomized, prognostically important factors in CLL: IGHV somatic mutation status, beta-2 microglobulin, and Rai stage. In conclusion, patient space turns out to be richer and more complex than current models suggest. TDA could become a powerful tool in a researcher's arsenal for interpreting high-dimensional data by providing novel insights into biological processes and improving our understanding of clinical and biological data sets. [ABSTRACT FROM AUTHOR]

A time series is an extremely abundant data type arising in many areas of scientific research, including the biological sciences. Any method that compares time series data relies on a pairwise distance between trajectories, and the choice of distance measure determines the accuracy and speed of the time series comparison. This paper introduces an optimal transport type distance for comparing time series trajectories that are allowed to lie in spaces of different dimensions and/or with differing numbers of points possibly unequally spaced along each trajectory. The construction is based on a modified Gromov–Wasserstein distance optimization program, reducing the problem to a Wasserstein distance on the real line. The resulting program has a closed-form solution and can be computed quickly due to the scalability of the one-dimensional Wasserstein distance. We discuss theoretical properties of this distance measure, and empirically demonstrate the performance of the proposed distance on several datasets with a range of characteristics commonly found in biologically relevant data. We also use our proposed distance to demonstrate that averaging oscillatory time series trajectories using the recently proposed Fused Gromov–Wasserstein barycenter retains more characteristics in the averaged trajectory when compared to traditional averaging, which demonstrates the applicability of Fused Gromov–Wasserstein barycenters for biological time series. Fast and user friendly software for computing the proposed distance and related applications is provided. The proposed distance allows fast and meaningful comparison of biological time series and can be efficiently used in a wide range of applications. [ABSTRACT FROM AUTHOR]