“Unmixing” Tissue Gene Expression Signatures from Tumor Biopsies

Emergent molecular measurement methods, such as DNA microarray, qRTPCR, and many others, offer tremendous promise for the personalized treatment of cancer. These technologies measure the amount of specific proteins, RNA, DNA or other molecular targets from tumor specimens with the goal of “fingerprinting” individual cancers. Tumor specimens are heterogeneous; an individual specimen typically contains unknown amounts of multiple tissues types. Thus, the measured molecular concentrations result from an unknown mixture of tissue types, and must be normalized to account for the composition of the mixture. For example, a breast tumor biopsy may contain normal, dysplastic and cancerous epithelial cells, as well as stromal components (fatty and connective tissue) and blood and lymphatic vessels. Our diagnostic interest focuses solely on the dysplastic and cancerous epithelial cells. The remaining tissue components serve to “contaminate” the signal of interest. The proportion of each of the tissue components changes as a function of patient characteristics (e.g., age), and varies spatially across the tumor region. Because each of the tissue components produces a different molecular signature, and the amount of each tissue type is specimen dependent, we must estimate the tissue composition of the specimen, and adjust the molecular signal for this composition. Using the idea of a chemical mass balance, we consider the total measured concentrations to be a weighted sum of the individual tissue signatures, where weights are determined by the relative amounts of the different tissue types. We develop a compositional source apportionment model to estimate the relative amounts of tissue components in a tumor specimen. We then use these estimates to infer the tissuespecific concentrations of key molecular targets for sub-typing individual tumors. We anticipate these specific measurements will greatly improve our ability to discriminate between different classes of tumors, and allow more precise matching of each patient to the appropriate treatment

Front spreading in population dynamic models. Theory and application to the Neolithic transition

This thesis presents population dynamics models that can be applied to predict the rate of spread of the Neolithic transition (change from hunter-gathering to farming economics) across the European continent, which took place about 9000 to 5000 years ago. The first models in this thesis provide predictions at a continental scale. We develop population dynamics models with explicit kernels and apply realistic data. We also derive a new time-delayed reaction-diffusion equation which yields speeds about a 10% slower than previous models. We also deal with a regional variability: the slowdown of the Neolithic front when reaching the North of Europe. We develop simple reaction-diffusion models that can predict the measured speeds in terms of the non-homogeneous distribution of pre-Neolithic (Mesolithic) population in Europe, which were present in higher densities at the North of the continent. Such models can explain the observed speeds.