Tumor growth and progression is a complex phenomenon dependent on the interaction of multiple intrinsic and extrinsic factors. Necessary for tumor development is a small sub-population of potent cells, so-called cancer stem cells, that live forever, can undergo an unlimited number of cell divisions, and with a small probability divide symmetrically to produce more such cancer stem cells. The majority of a tumor is made up of progeny cancer cells, that have a limited life span and a limited replicative potential. The development of the tumor is dependent on the proliferation capacity, migratory ability, and frequency of cell death of its component cancer cells. With increasing number of cells in the tumor, competition for space limits tumor progression and the majority of cancer cells become quiescent, with proliferation primarily occurring on the outer rim where space is available. We present an agent-based model early tumor development that captures the spatial heterogeneity of proliferating and quiescent cells and the spatio-temporal morphology evolution. We show that in a heterogeneous tumor the cancer stem cell compartment is a minor sub-population.
Work done in collaboration with Lynn Hlatky and Philip Hahnfeldt.
Cancer is a complex disease that has been very difficult to manage using conventional approaches and continues to be a major national and international health issue. Over the past 10 years, cancer has been viewed more and more as a systems disease of various environmental, genetic and molecular changes interacting at a cellular level with the host micro-environment. Beyond the micro-environment, there are other host systems, such as the immune system, that play critical roles and once again contribute to the overall complexity of the disease. Another way to look at the issue of complexity is through the view of scale. The complexity here is dealing with and integrating various components whether they are genetic mutations, signaling networks, or cellular processes. The complex nature of the disease has led to the view among many that cancer is an end result of a systems failure, and therefore a systems biology approach to studying cancer is needed. In an attempt to address this need, the National Cancer Institute (NCI) began the Integrative Cancer Biology Program (ICBP). This program is unique in its approach and use of predictive mathematical models of cancer. In addition, these mathematical and statistical approaches will be necessary to understand and integrate the vast amount of data being generated. An overview of the ICBP will be presented along with other programs and potential funding opportunities of the NIH and the NCI.
It is generally accepted that carcinogenesis is formally analogous to Darwinian evolution as environmental selection forces act on new phenotypes that are continuously generated through accumulating genetic mutations and epigenetic changes. Those intracellular phenotypes that yield a proliferative advantage are rewarded by clonal expansion and persistence in the population. This process yields progressive fitter populations until a fitness maximum is reached and an invasive cancer emerges.
Since the pioneering studies of Warburg, it has been consistently demonstrated that invasive cancers maintain a high rate of anaerobic glucose metabolism even in the presence of oxygen. Widespread application clinical of FDG-PET imaging has demonstrated the vast majority (perhaps all) clinical primary and metastatic cancers exhibit significantly increased glucose flux as a result of glycolytic metabolism.
Within the context of somatic evolution, selective use of glycolytic pathways even in the presence of oxygen seems paradoxic. Anaerobic metabolism of glucose is inefficient (yielding 2 ATP /glucose vs. 36-38 ATP/glucose for aerobic metabolism) and produces acid as a byproduct. It would seem that, in general, Darwinian principles would favor more efficient and less potentially toxic metabolism.
We investigate development of aerobic glycolysis using quantitative methods from evolutionary game theory. The models demonstrate a previously unknown era during carcinogenesis in which cellular evolution is driven by limited substrate availability. Specifically we find that adaptation to cyclical hypoxia within premalignant lesions will result in constitutive upregulation of glycolysis. The reduction in extracellular pH caused by upregulation of glycolysis then requires additional cellular evolution to overcome acid-induced toxicity. We find this evolutionary sequence is critical to formation of an invasive cancer because it produces a phenotype that alters its environment (through increased acid production) in a way that is toxic to its competitors but less harmful to itself.
This suggests that cancer cells use an evolutionary strategy previously described as "spite." That is, they reduce their own fitness through aerobic glycolysis but, by doing so, reduce the fitness of their competitors even more.
Experimental support for the acid-mediated tumor invasion hypothesis will be presented along with new treatment strategies that emerge from the model.
A critical challenge of experimental therapeutics for cancer is to decide which drugs are the best candidates for clinical trials. Mathematical modeling strategies can be of help in this regard. By accurately quantifying how cells interpret coupled signals from a variety of stimuli and connecting these molecular processes to the temporal changes in tumor cell and microvessel density, mathematical oncology can help to determine which anti-cancer agents have the most potential for therapeutic benefit for a given tumor profile. Recent experiments show that vascular endothelial growth factor (VEGF) is the crucial mediator of downstream events that ultimately lead to enhanced endothelial cell survival and increased vascular density within many tumors. A key pathway involves up-regulation of the anti-apoptotic protein Bcl-2, which in turn leads to increased production of interleukin-8 (CXCL8). The VEGF - Bcl-2 - CXCL8 pathway suggests new targets for the development of anti-angiogenic strategies. I will discuss a mathematical model that is able to connect the molecular events associated with VEGFR2 dimerization and intracellular signaling with the temporal changes in endothelial cell proliferation, migration and survival. The model is validated by comparing its predictions to in vitro experimental data that reports microvessel density prior to, and following the administration of BL193, a promising small molecule inhibitor of Bcl-2. Numerical simulations of the treatment of tumors in vivo predict the existence of a threshold for the amount of therapy required for successful treatment and quantify how this threshold varies with the stage of tumor growth. Further, the model demonstrates how rapidly the least effective dosage of BL193 decreases if an even moderately better inhibitor of Bcl-2 is used.
It was proposed by Hanahan & Weinberg (Cell 2000, 100: 57-70) that most if not all cancers acquire the same set of universal phenotypic traits, or "Hallmarks," through a variety of mechanistic strategies. Namely, the ability to evade programmed cell death, self-sufficiency in growth signals, insensitivity to anti-growth signals, limitless replicative potential, sustained angiogenesis and tissue invasion and metastasis. More recently, Gatenby and Gillies (Nature Reviews Cancer 2008, 8: 56-61) have proposed a microenvironmental model of carcinogenesis that includes the glycolytic phenotype (Warburg effect) and adaptation to growth in the presence of chronic acidosis as an additional "Hallmark." A number of ex vivo and in vivo imaging strategies have been developed which interrogate the morphological, physiological and metabolic phenotype of the evolving tumor microenvironment. Diffusion-weighted magnetic resonance imaging (DW-MRI) and magnetic resonance spectroscopic imaging (MRSI) of choline metabolites can both be used to observe cell proliferation and death. Positron emission tomography (PET) is used to image hypoxia and glucose uptake by uptake of 18F-fluoromisonidazole (FMISO) or 18F-2-fluoro-2-deoxy-D-glucose (FDG) respectively. FMISO accumulates in hypoxic cells but there is no accumulation at pO2 > 10mmHg. FDG is an analog of glucose. Tumor pH is measured by MRSI or fluorescence imaging of pH sensitive agents, e.g. 3-aminopropylphosphonate and SNARF-1 fluorescent dye. Metastasis can be observed and quantified by optical imaging of metastases originating from cells expressing fluorescent protein or luciferase. Hence, these imaging modalities can be used to study tumor phenotypic parameters that are related to the hallmarks of cancer.
Recent cancer therapies have targeted tumor blood vessels with inconsistent results. Some treatments show promise while others fail, underscoring a frustrating lack of understanding of the mechanisms that control blood vessel formation, destruction and function. A major difficulty lies in the fact that the mechanisms of vessel formation and remodeling operate at multiple scales, each with its own set of controls, and each critical to the overall function of the blood vessel network. Most importantly, "rare" events occurring at the single cell level can dominate overall vessel network function, and therefore, tumor growth. Analytical approaches--both experimental and computational-- that span the size scale from single cells to the bulk tumor should incorporate the relevant parameters critical for understanding tumor growth. Experimentally, intravital microscopy allows determination of single-vessel hematocrit, blood velocity, permeability as well as vessel and network morphology over time. Mathematical models of blood flow, vessel growth & remodeling, and tumor growth and invasion span the size scale from cells to tissue to elucidate the cellular events that influence tissue-scale physiology. These tools will provide a framework for studying the effects of anti-tumor therapies and improving their efficacy.
Pharmacokinetics (PK) is the study of the disposition of drugs (absorption, distribution, metabolism, and elimination) in the body and pharmacodynamics (PD) is the study of the effects of the drugs on the body. Over the last several decades PK/PD modeling has evolved into a complete mathematical/statistical subfield in pharmaceutical research and is now involved in all aspects of drug development from in vitro to clinical studies. There are several reasons why PK/PD models are developed. First, they are used to describe data such as plasma concentrations of a drug and/or its metabolite (PK) or the effect of the drug on a target such as a cell or receptor (PD). This descriptive information can be used to determine if effective concentrations are being obtained to cause the desired effect without causing excessive toxicity. In addition, PK/PD models are used to predict drug concentrations and/or effects. For example the drug disposition for a multiple dosing regimen can be predicted given the data from just one dose. The PK/PD modeling process first involves model building which is as much of an art as a science. This is followed by model parameter estimation using methods such as weighted least squares, maximum likelihood estimation, or maximum a posteriori probability estimation (Bayesian estimation). This session will provide an introduction to the process of PK/PD modeling using examples from pediatric oncology.
Within the NCI Integrative Cancer Biology Program, our Center focuses on cell scale models of cancer invasion. In the Evolutionary Hybrid Cellular Automata (EHCA) model, each cell is a grid point containing a neural network linking genotype to phenotype. The grid represents tumor microenvironment (mE) with oxygen level controlled by a partial differential equation. At cell doublings, the neural network is copied to daughter cells with an error probability, to capture phenotypic adaptation in cancer progression. The Immersed Boundary Cell (IBCell) model represents cells as 2D deformable objects bounded by linear spring nets (plasma membranes) studded with discrete receptors controlling growth, division, death or polarisation. The mE is represented as physical forces. In IBCell, cells build realistic epithelial structures (acini, ducts) that capture invasion dynamics if perturbed by cancerous cells. The Hybrid Discrete-Continuum (HDC) model represents tumor growth in a one-cell thick 2D slice. The mE contains extracellular matrix, oxygen and matrix degrading proteases controlled by continuous reaction-diffusion equations, while tumor cells are discrete individuals on single lattice points, containing predefined random aggregates of traits (e.g., proliferation, death, motility rates). HDC examines effects on tumor morphology of cell adaptation to mE. We parameterize these models with homogeneous datasets from a platform breast epithelial cell, MCF10A, and its invasive variants. Data include oxygen consumption, proliferation, survival, matrix-degrading enzyme secretion, growth patterns in 3D. High-throughput data collection is being developed for EHCA model parameterization. IBCell, tuned with 2D and 3D growth data, is being tested for ability to predict receptor value ranges that lead to invasive morphology of epithelial structures. Parameterized simulations of HDC confirm its prediction that invasion requires competition between cell phenotypes with distinct adaptive value. For empyrical validation, we developed an Island Invasion Assay that closely mimics the spatial 2D arrangement of HDC tumor slices. Preliminary results support HDC predictions: invasion (fingering) occurs when competing phenotypes adapt to stressful mE conditions. For in vivo validation, we are performing orthotopic versus subcutaneous mouse xenografts of MCF10A tumorigenic variants. In line with ICBP goals, this mathematical oncology strategy closely integrates experimental biologists with physical scientists. It should produce novel insights in cancer by theory-driven experimentation and experiment-driven theory.
To effectively monitor protein phosphorylation events governing signaling cascades, we have developed a mass spectrometry-based methodology enabling the simultaneous quantification of tyrosine phosphorylation of specific residues on dozens of key proteins at multiple time points under a variety of perturbations. We have recently applied this technique to identify key signaling nodes regulating tamoxifen resistance in breast cancer as well as proliferation in glioblastoma. Inhibition of these nodes with small molecule kinase inhibitors results in reversion of resistance or decrease in proliferation in each system. Overall, we have now demonstrated that the combination of mass spectrometry-based analysis of protein phosphorylation with phenotypic measurements and computational modeling yields novel insights into the regulation of cellular signaling on a network scale.