Our Research


The Columbia University Center for Topology of Cancer Evolution and Heterogeneity is a member of the National Cancer Institute’s Physical Sciences in Oncology Network. Founded in 2009, the Network was created to support research that integrates perspectives from the fields of physics, mathematics, chemistry, and engineering in ways that address key questions and obstacles in cancer research.

The Center for Topology of Cancer Evolution and Heterogeneity opened in May 2015 as an interdisciplinary center formed to develop an integrated experimental and computational pipeline for characterizing the evolution of subclonal populations within solid tumors. Our experimental techniques include novel organoid systems for tracing cellular lineages, as well as innovative single-cell sequencing technologies. We are combining these methods with emerging mathematical approaches from the field of topological data analysis that are well suited to analyzing the high-dimensional data that single-cell approaches generate.

Our team includes experts in cancer genomics, the genetics of brain tumors, developmental biology, single-cell genomics, machine learning, and topological data analysis. Working together in close collaboration, our goal is to provide the scientific community with experimentally validated geometric and topological structures of causal inference of clonal evolution, single-cell genomic protocols for fast and reliable uncovering of clonal heterogeneity, experimentally validated machine learning approaches for predicting drug sensitivities, and a strong multi-institutional, interdisciplinary program that creates bridges between researchers in pure mathematics, the technology sector, and cancer research.


Recent large-scale genomic projects have begun to reveal the complex landscape of genetic alterations that cause cancer, pointing toward a powerful new paradigm for precision medicine. Despite some early successes against blood cancers, however, currently available experimental and computational methods have made limited progress in the identification of targeted therapies for solid tumors. One reason is that cells in a solid tumor are not all the same, but form many genetically distinct subpopulations of cellular clones. Recent studies have shown, for example, that gene expression signatures vary across different regions in the same tumor and that the most abundant mutations in a tumor are not always the ones that drive its growth. In addition, very small subclonal populations are often immune to the therapies that target more abundant clones, evading the effects of treatment and initiating relapse and metastasis. Such findings suggest that genomic methods that do not account for clonal heterogeneity and the dynamics of tumor development will continue to be insufficient for identifying effective targeted therapies.

The mission of the Columbia University Physical Sciences-Oncology Center for Topology of Cancer Evolution and Heterogeneity is to develop, validate, and deliver a set of complementary approaches that will provide the cancer research community with a framework for unraveling such tumor complexity. Driving our efforts is the hypothesis that as a tumor grows from a single mutated cell, it undergoes an evolutionary process that leads to subclonal diversification. This process results from selection pressures, including how the tumor responds to therapy. Gaining a clearer understanding of precisely how tumors evolve will require the development of new, more precise experimental methods for studying the genetics of tumors at the single-cell level. Moreover, new quantitative methods are critically needed for analyzing the enormous data sets that this kind of study can generate.

Project 1: Modeling tumor evolution in mouse and organoid models


In previous work at Columbia University Medical Center, we developed a reductionist model system for investigating clonal histories and demonstrated its feasibility for tracing clonal evolution. Preliminary studies showed that multi-color lineage-tracing can be used to follow clonal fates in genetically-engineered mouse models of prostate cancer, and that a novel organoid culture approach, in which three-dimensional buds of organs are grown in the laboratory, can be used to assess clonal growth and response to therapy across multiple time points. In ongoing work at the Center, we will combine such approaches with single-cell transcriptome analyses of tumor heterogeneity. This project has three specific aims:

Investigation of clonal evolution during tissue homeostasis and regeneration. We are using multi-color lineage-tracing and organoid culture to follow clonal histories.

Analysis of clonal evolution during cancer progression. We are using multi-color lineage tracing in mouse models of prostate cancer together with organoid culture for longitudinal analyses, with data analyzed by single-cell transcriptomics and mathematical modeling.

Investigation of the clonal response to therapy. This involves longitudinal analyses of clonal evolution in organoid culture after drug treatments.

These studies will be greatly facilitated by the analyses of evolutionary moduli spaces and topological data analyses performed in collaboration with the Mathematical Core, as well as by interactions with Projects 2 and 3.

Project 2: Dissecting clonal architecture and evolution in solid tumors

Ayasdi1Focusing on human glioblastoma, one of the most incurable and genetically heterogeneous tumors, we will predict and validate the landscape of driver alterations that mark initiation, founder evolution, and therapy adaptation within individual patients. To do so, we will develop and apply novel technologies for high-throughput transcriptomic and genomic analysis of individual cells within malignant glioma tissues.

Our current system is capable of single-cell mRNA capture, cDNA barcoding, and on-chip amplification, generating amplicons for direct conversion into a standard, pooled sequencing library. We will adapt the same device for massively parallel, on-chip capture of genomic DNA from individual cells for whole genome amplification and exome capture. Next, we will functionally validate the single-cell glioma models in orthotopic mouse and human systems in vitro and in vivo.

If successful, this project will deliver an integrated computational-experimental pipeline that will be able to predict forthcoming evolutionary changes of any solid tumor in the presence of a defined set of selective pressures. This information will be invaluable for deciphering evolving tumor dependencies and should enable highly accurate therapeutic predictions.

Project 3: Predicting therapeutic sensitivity in cancer

Somatic genetic alterations in cancer have been linked with how tumors respond to targeted therapeutics and develop resistance to therapy. Therefore, the development of methods that model and predict therapeutic sensitivity of cancer should be extremely useful in the development of more effective treatments.

tumor-fusionIn this project, our goal is to model, predict, and target therapeutic sensitivity and resistance of cancer. To do so, we will utilize three-dimensional models of glioblastoma (gliomaspheres) that recapitulate the nature of genetic lesions in primary tumors to experimentally validate computational machine learning predictions based on genomic information.

We will first build a computational framework that incorporates genomic data, drug properties and responses, and known drug targets and network models of pathways and protein complexes to predict the therapeutic response of 80 genomically annotated gliomaspheres. Then, we will experimentally validate our computational predictions of therapeutic sensitivity across the library of gliomaspheres, test combinatorial predictions, and examine the molecular mechanisms by which candidate genes alter drug responses. We will evaluate single- or multi-lesion sensitivity using RNA interference or cDNA overexpression. Finally, we will investigate the role of cell heterogeneity in the mechanism of drug resistance at the single-cell level using topological methods, developed in Project 2 and in the Mathematical Core.

The ultimate goal of this project will be to uncover mechanistic insights into genotype-dependent sensitivity to drugs or synthetic lethal relationships. Ultimately, our studies will deliver key information for the development of multiple gene- and pathway-based biomarkers for personalized cancer therapies.

Mathematical Core

fluspaceThe Center for Topology of Cancer Evolution and Heterogeneity is pioneering the development and large-scale genomic application of topological data analysis (TDA), a new mathematical framework for capturing global structural properties of large data sets that is particularly well suited for high-dimensional, high-throughput biological data. (Topology is the branch of mathematics that characterizes robust global properties of spaces.)

Previous work in the Center labs has shown that TDA offers unique capabilities for analyzing high-dimensional data sets. In particular, single-cell analyses put into question the standard bulk expression-based classification approaches and uncover a much more complex structure that is missed by consensus-based sequencing and standard clustering techniques. The Center for Topology of Cancer Evolution and Heterogeneity aims to extend this work and to develop and implement mathematical approaches to tackle the inherent complexity and biological interpretability of single-cell approaches to cancer evolution and heterogeneity. In order to develop an appropriately expressive language, we rely on ideas from geometry and topology (phylogenetic moduli spaces and TDA), modal logic, model-checking algorithms, and a probabilistic theory of causality. These tools complement each other and will be further developed in the context of single-cell data and applied in the specific research projects undertaken at the Center.