Chronic myeloid leukemia (CML) is a blood cancer in which there is dysregulation of maturing myeloid cells (granulocytes) driven by a chromosomal mutation which creates the fusion gene, BCR-ABL1. Although there has been much progress in the treatment of CML using tyrosine kinase inhibitors (TKI), there are still unmet clinical needs. For example, there is still a small cohort of patients who, for reasons that are still unknown, do not respond to TKI treatment. Further, a significant proportion of patients who appear to have a complete molecular remission while on TKIs experience a relapse of CML when TKI treatment is discontinued. Mathematical modeling of CML hematopoiesis can provide insight on these processes. Current mathematical models of CML are highly simplified (e.g., linear) and have been used to estimate treatment-related model parameters, but fail to describe the mechanisms that underlie primary resistance and treatment-free remission. Here, we explore how more physiologically accurate, data-driven mathematical models of CML hematopoiesis that incorporate feedback control and lineage branching can provide such insight. Although it is recognized that feedback plays a role in CML hematopoiesis, the interactions are poorly understood. In many cases, we don’t know which cell types are providing and receiving the feedback, what signals are used, and what aspects of proliferative cell behavior they influence (i.e. cell cycle speed, renewal probability, or progeny fate choice). Here, we propose to use mathematical modeling combined with data from single cell transcriptomics to help sort this out. We develop an automated method for model selection that integrates data gleaned from experiments and single cell RNA sequencing to select plausible classes of feedback models. We first apply this approach to normal hematopoiesis and identify models that have desired system properties, e.g., stable equilibria, and make predictions about system behavior upon perturbation. New experiments are presented that validate model predictions. We use a Bayesian utility theory approach to determine the optimal experimental design that allows for identification of model parameters with maximum precision. When extended to incorporate CML hematopoiesis, our initial assessment shows that feedback/branching models are more robust, have a better fit to alternative patterns of patient response than simple linear models, and suggest new treatment strategies.

The objective of this work is to use mathematical modeling to understand the mechanisms that regulate tumor growth and metabolism. A hallmark of cancer is cell-intrinsic metabolic reprogramming that enhances anabolic support of cell proliferation and leads to metabolic heterogeneity in tumors at larger scales. Here we report a self-organizing pattern of metabolism in xenograft colon tumors, where Pyruvate Dehydrogenase Kinase (PDK1), a negative regulator of oxidative phosphorylation, is highly active in clusters of cells arranged in a spotted array. To explore the basis for this pattern, we developed reaction-diffusion models describing the interactions between two different metabolic cell types, nutrients, and growth factors. Our first model is based on Gierer-Meinhardt's activator-depleted substrate model and characterizes the relationship between cells, glucose, and lactate. In the other mathematical models reported here, we incorporated Wnt, a signal known to upregulate PDK1 and Warburg metabolism, so that Wnt promotes a metabolic switch to glycolysis. Diffusive instability analysis, or classic Turing analysis, is used to determine parameter sets in which patterns are expected to form and is found to be in good agreement with numerical simulations. Partial inhibition of Wnt alters the pattern in tumors and in the model, which also predicts that inhibition of Wnt alters the expression of proteins that increase the range of Wnt ligand diffusion. This prediction is validated in xenograft tumors and is consistent with expression data in primary human colon cancer. The model also predicts that inhibitors that target glycolysis or Wnt signaling are not so effective as single therapies for cancer as they are in combination for synergistic reduction of tumor growth. We present another mathematical model similar to the Wnt signaling model, but which includes other factors known to be involved in cancer metabolism. This larger mathematical model and numerical results demonstrate good agreement with the Wnt signaling model, and we therefore conclude that the smaller model contains all essential elements necessary to capture the effects we observe, to make predictions for the mechanisms that cause the altered metabolic pattern in Wnt-inhibited tumors, and to investigate treatment programs in silico. It is hoped that these mathematical models will be useful in informing researchers and collaborators about cancer and metabolism.

In this thesis we explore tumor-microenvironment dynamics using three models of decreasing complexity. The first is a multispecies, spatiotemporal model of tumor development in tumor-derived growth factor responsive stroma that is activated to secrete the tumor growth and dispersal activator HGF. We show that HGF-induced invasive tumor morphology is promoted by increased heterogeneity at the tumor-host boundary. The second model is a system of ODEs that explores hypotheses based on experimental observations that tumor growth inhibition can occur at high levels of HGF. The model allows for the prediction of the molecular mechanism of HGF action via dose-response curve analysis. The final model is a system of two ODEs for stem cell and chemical activator of stem cell self-renewal concentrations, and allows for the approximation of the separatrix of the phase space that divides the space into basins of attraction for tumor eradication and tumor maintenance. The multiple models allow us to consider tumor-host interactions at various levels of abstraction and thus to infer both qualitative and quantitative results regarding tumor response to host and tumor-derived growth activators.

The objective of this work is to develop data-driven mechanistic mathematical modeling to understand and make predictions on how metabolic and tumor heterogeneity impact tumor growth and resistance to treatment. Cell-intrinsic metabolic reprogramming is a hallmark of cancer that provides anabolic support to cell proliferation. How reprogramming influences tumor heterogeneity or drug sensitivities is not well understood. Here we report a self-organizing spatial pattern of glycolysis in xenograft colon tumors where pyruvate dehydrogenase kinase (PDK1), a negative regulator of oxidative phosphorylation, is highly active in clusters of cells arranged in a spotted array. To understand this pattern, we developed a reaction-diffusion model that incorporates Wnt signaling, a pathway known to upregulate PDK1 and Warburg metabolism. Partial interference with Wnt alters the size and intensity of the spotted pattern in tumors and in the model. The model predicts that Wnt inhibition should trigger an increase in proteins that enhance the range of Wnt ligand diffusion. Not only was this prediction validated in xenograft tumors, but similar patterns also emerge in radiochemotherapy-treated colorectal cancer. Finally, to investigate how self-organized, patterned communities of colon cancer cells emerge, and how heterogeneity influences growth we performed single cell RNA sequencing (scRNAseq) on xenograft tumors. Single cell RNA sequencing also indicates the interactions between cell types. We then developed a multispecies mathematical model that incorporates cellular interactions informed by scRNAseq analysis. This multispecies model recapitulates the spotted patterns, stromal content, morphologies and their spatial variations in the tumor. The model predicts that blocking positive feedback signaling will alter population heterogeneity and the spatial patterning of Wnt signaling, resulting in significant reduction of a cell type. However, the tumor retains the capacity to grow indicating that there is a possible link between heterogeneity and drug resistance.

The proliferation of and continual improvement in sequencing technologies over the last three decades have vastly increased the rate of biological data generation, while concurrently reducing cost per base sequenced. However, in many ways, statistical and computational strategies for extracting meaningful biological insights from this unprecedented wealth of data have not kept pace with these molecular advances. For instance, biological features such as genomic structural variants (SVs) can remain challenging to capture and evaluate with the most common types of sequencing, despite their implication in complex traits including adaptive phenotypes and disease predisposition. To address these unmet needs in this rapidly changing scientific landscape, we developed novel algorithms and applied cutting-edge computational and quantitative techniques to a diverse set of scientific questions.

First, we developed a method called FREQ-Seq², along with associated algorithms and software, to enable the rapid and targetable study of allele frequencies, while addressing the challenges inherent to traditional techniques, such as throughput and scalability. We applied our approach to studying evolutionary genetics in E. coli, demonstrating its accuracy and precision in characterizing population dynamics and genotype distributions. We also contributed a valuable resource to the scientific community by presenting a new reference-quality genome assembly for the model organism Drosophila melanogaster based on long-read sequencing, along with a thorough investigation of hidden genetic variation and evolutionary insights that we uncovered. For example, we discovered previously unidentified SVs potentially linked to complex traits, such as a duplication associated with nicotine resistance, as well as novel understanding about the cosmopolitan distribution of SVs in Drosophila. Additionally, we leveraged advancements in machine learning to further explore SVs, training a deep convolutional neural network-based model to identify SVs with high precision using widely available short-read Drosophila datasets. Finally, we demonstrated the utility of applying computer vision and machine learning techniques to ongoing initiatives to digitize herbaria catalogs, by developing algorithms and a pipeline to extract phenological and ecological data from digitized specimen images, facilitating rapid and accurate labeling and annotation as well as expanding ease of end-user access to these resources. Taken as a whole, this thesis provides a comprehensive study of computational and quantitative approaches and their application to wide-ranging challenges in genetics, ecology, and evolutionary biology.

Hematopoiesis is the complex mechanism by which hematopoietic stem cells produce a variety of functional blood cells through multiple stages of differentiation. Since the numbers of various blood cell types need to be maintained in homeostasis, with occasional short-lived departures from it, hematopoiesis must have multiple regulatory mechanisms. However, these are still not fully understood. Although many mathematical models of hematopoiesis regulation have been proposed, more work on developing methods for fitting and interpreting experimental data that integrate statistical and mechanistic models is needed. Here, using a new chemical reaction ordinary differential equation model of negative feedback regulation in hematopoiesis, we develop a scalable, hierarchical Bayesian framework using a latent variables approach that takes cross heterogeneity into account and infers division, differentiation, and feedback regulation parameters of hematopoietic cells. We designed and performed an experiment where mice were injected with the chemotherapy drug 5-FU that reduces the number of stem and progenitor cells by blocking DNA synthesis and repair, to perturb the hematopoietic equilibrium. In order to count the number of cells in the BM, the mouse must be sacrificed. Therefore, each mouse can contribute their cell count data at a one time point only. To work with partially observed datasets, we use an ODE model to interpolate the noisy means of the experimental cell count data (the missing data is inferred). We evaluate the performance of the new model and inferential framework using synthetic data and find that we are able to distinguish between models that account for biological variation and models that include only technical variation/measurement error. We find that the experimental data are best described by a hierarchical model in which the hematopoiesis model parameters are allowed to vary among mice, suggesting the presence of significant biological variability. Our experimental data and the model show that, after perturbation, hematopoiesis returns to equilibrium via damped oscillations, with a notable overshoot of depleted cell counts that happens shortly after the system is perturbed from equilibrium. We then explore an alternative way of accounting for data heterogeneity by employing stochastic differential equations instead of letting division and feedback regulation parameters vary across mice. Computational tractability of the likelihood in a Bayesian inference framework is achieved by using the linear noise approximation (LNA) derived from the chemical Langevin equation. This enables us to approximate the joint posterior density for the hematopoietic rate value parameters and missing data. We evaluate the performance of the new Bayesian LNA model framework and compare it to the Bayesian ODE model frameworks we developed previously. We find that the new framework can further improve the out-of-sample prediction, as indicated by leave-one-out cross-validation. We identify limitations of inference for our LNA model when multiple sources of biological and technical variation of the dataset are significant and then develop a procedure for overcoming them. Finally, we investigate experimental designs that optimize the amount of information gained about the model parameter and missing data. We employ a new adversarial approach that uses a game theory framework for experimental design without the need for the calculation of the posterior probability distributions. This enables us to overcome the cost of traditional Bayesian optimal design methodology that requires repeated approximations of the posterior distributions, which are expensive to generate and prohibitively costly for high dimensional models.

Cancer is one of the deadliest diseases; vast resources have been used to understand its root causes and to elucidate the intricacies of cancer progression in order to develop effective prevention and treatment strategies. Unfortunately, there are a lot of factors in the tumor microenvironment that contribute to cancer development and progression. Consequently, a better understanding of the tumor niche has become an important goal of cancer research. Here we have approached the problem using a combination of in vitro assays and computational modeling. Firstly we studied extracellular matrix (ECM).

Recently, it has been found that the ECM surrounding tumors has significant effects on tumor cell growth and migration. However, there is a shortage of information on how cells respond to normal vs tumor ECM. In order to overcome this problem, we have isolated human tumor ECM (tECM) and compared its chemical and mechanical properties to ECM derived from matched normal tissue (nECM). We next examined the ability of each of these matrices to support the development of new vasculature – a key event in tumor progression. We found that the capillaries that form in the tECM have

characteristics similar to those seen in in vivo tumors. We also found that tumor growth and tumor metabolism is different in these two ECMs, with tumor growth being faster, and tumor cell metabolism more glycolytic, in the tECM. Taken together, these data identify the importance of the ECM in tumor progression and suggest that normalization of ECM morphology and composition could provide a novel strategy to limit tumor growth.

Our second approach used mathematical models to study the interaction of different tumor cell lineages with the vascular niche. We find evidence to support the idea of endothelial cell transdifferentiation into tumor cells. And, the computational simulations of the model indicated that the transdifferentiated glioblastoma cells to have a major contribution in tumor therapy resistance.