The dynamic and heterogeneous nature of tumor systems constitutes a challenge to cancer treatment and is a major cause of therapy failure. Transformed cells within a tumor can be diverse with respect to the genetic and epigenetic alterations they bear. In addition, the tumor microenvironment is heterogeneous by nature of its cellular composition and activation states. Our research spans several areas of activity with the goal of understanding the role of cellular heterogeneity and cell-to-cell signaling in tumor progression:

High-throughput characterization of the tumor ecosystem in various cancer types. Single-cell technologies afford the opportunity to study the cellular composition of a tumor and its micro-environment, uncovering relationships among different forms of heterogeneity. We utilize innovative computational approaches to analyze and integrate single-cell transcriptomic data from individual tumors leading to comprehensive characterizations of their intra-tumor heterogeneity. The goals are elucidating the molecular mechanisms of tumor progression and identifying consequent targets for potential immunotherapeutic intervention. Juxtaposition of these results with those of large-scale cross-sectional cancer studies provides additional, novel, population-based perspectives on intra-tumor heterogeneity. Within this area of research, we are currently working on the cellular characterization of pediatric brain tumors and on the functional characterization of chimeric antigen receptor (CAR) T-cell immunotherapy in B-cell leukemia and lymphoma.

Development of computational approaches to the study of cellular heterogeneity and its role in disease. Characterizing the cellular composition and activation states of a tissue sample requires the development of computational tools capable of extracting relevant biological information from data generated using high-throughput single-cell technologies and large-scale population studies. Building upon ideas from geometry, topology, computer science, physics and statistics, we are devising novel approaches to the analysis of genomic data that allow us to gain insights into the pathogenesis of cancer. Within this area, we are currently developing unsupervised and scalable methods for the integration of different forms of high-throughput single-cell data.

Identification and characterization of elusive mutated cancer genes. Developing targeted cancer therapies requires the stratification of cancer patients according to the molecular alterations that are relevant for tumor progression. Commonly used methods for identifying cancer-associated mutations seek signatures of positive selection based on recurrence across large cohorts of patients. However, because of the large complexity involved in modeling the neutral background mutation rate, these strategies have limited power to identify functional variants that occur at low frequencies or in hyper-mutated tumors. Nonetheless, most cancer mutations occur at low frequencies, and some of these low-prevalence mutations are potentially actionable therapeutic targets. Building upon topological methods, we are developing an unsupervised statistical framework for the identification of cancer-associated mutated genes that combines expression and exome data from large-scale cross-sectional cancer studies. Our goal is to identify new potential therapeutic targets that, because of their low prevalence, have remained elusive to current methods of detection.

Applied mathematics. The development of computational tools for the analysis of genomic data often prompts general interesting questions in applied mathematics that require theory beyond the realm of computational biology. We are particularly interested in the interface among algebraic geometry, topology, and statistics/machine learning. Within this area of research, we are currently working on geometric methods for feature selection and statistical association motivated by the needs of our research in biology.

 Topological reconstruction of the expression space of low-grade glioma

Topological reconstruction of the expression space of low-grade glioma