March 21, 2019

Thematic Program on Mathematical and Quantitative Oncology
July -August 2008

July 2-4, 2008,
Workshop on Growth and Control of Tumors: Theory and Experiment

Davide Ambrosi (Torino)

Adhesion forces in T24 cell migration
The migration of tumor cells is a key aspect of extravasation, when cancer cells exit the capillaries and enter organs. Notwithstanding the relevance to understand the degradation dynamics, the elasticity of the vessel wall and the cell adhesion play a major role. The determination of the mechanical action exerted by a tumor cell on the vessel wall is a specific example of the prediction of the stress field exerted by a cell in a soft environment. In the planar case, this subject has been addressed about ten years ago by Dembo and Wang (1999). They showed how the traction exerted by a cell on a deformable substrate can be indirectly obtained on the basis of the displacement of the underlying layer. The standard approach in this respect is to solve exactly the elasticity problem by Green functions and then minimize the error by discrete optimization, iteratively. One possible alternative strategy to approach this inverse problem is to exploit the adjoint elasticity equations for the substrate, obtained on the basis of the minimization requirement of a suitable functional. In this case the linear elasticity problem is solved in an approximate way, while being intrinsically coupled with the minimization algorithm. In a joint collaboration with the Grenoble University (Claude Verdier, Valentina Peschetola, Alain Duperray) this methodology has been recently applied to determine the force field generated by T24 tumor cells on a polyacrylamide substrate. The shear stress obtained by numerical integration provides quantitative insight of the traction field generated by cells of this line and is a promising tool to investigate the spatial pattern of forces generated in cell motion.

Robyn Araujo (George Mason University)

Combination Therapies: Insights from Mathematical Modeling
Realizing the promise of molecularly targeted inhibitors for cancer therapy will require a new level of knowledge about how a drug target is wired into the control circuitry of a complex cellular network. This presentation will review general homeostatic principles of cellular networks that enable the cell to be resilient in the face of molecular perturbations, while at the same time being sensitive to subtle input signals. Insights into such mechanisms may facilitate the development of combination therapies that take advantage of the cellular control circuitry, with the aim of achieving higher efficacy at a lower drug dosage and with a reduced probability of drug-resistance development.

Khalid Boushaba (Iowa State)

A mathematical model for cell signaling and endothelial migration in a living zebra fish embryos
Angiogenesis in the zebrafish embryo begins after the first day of development. During this time the intersegmental vessels in the trunk develop from the dorsal aorta in the first wave of embryonic angiogenesis. Previous work suggests a link between VEGF and Syndecan-2, which may function as a co-receptor for VEGF. We are currently developing equations that include terms expressing reaction, diffusion, and cell movement biased by "convection" like terms to model this interaction. These terms model the chemotactic influences on cells, and hence the interaction of the cells with the extracellular matrix that results in their directed movement towards the diffusible growth factor. Using this approach as a framework, we expect to develop mathematical models for angiogenesis for zebrafish that are both predictive and descriptive of growth factor signaling and extracellular matrix interactions during cell migration. Based on the high degree of conservation of signaling pathways involved in angiogenesis, we expect that modeling these processes in zebrafish will be directly applicable to tumor angiogenesis.

Lloyd Demetrius (Harvard, Max Planck Institute)

Cancer in Mice and Men: a comparison
Animal models, mostly mice and rats, have contributed to the understanding of growth and control of tumors in humans . I will invoke recent work in evolutionary theory to analyse the extent to which extrapolations from mice models to human systems are justified.

James Glazier (Indiana)

Simple Modeling of Avascular and Vascular Tumors Using the GGH Model and CompuCell3D
While bioinformatics tools for the analysis of DNA sequences, reaction kinetics models of biomolecular networks and molecular dynamics simulations of biomolecules are all widely used, multi-cell modeling of developmental processes (including tumor growth) at the tissue scale is still relatively undeveloped. A key reason for this neglect has been the lack of widely-accepted modeling approaches and the computational difficulty of building such models. Now, a growing community of modelers has settled on the GGH Model (also known as the CPM) as a convenient methodology to create multi-cell simulations of tissues. I will present sample simulations of the front instabilities of a simple "toy" model of growing avascular tumor spheroids and some slightly more sophisticated models of tumor vascularization to illustrate the capabilities and limitations of the GGH model as implemented in the open-source modeling environment CompuCell3D (see

Richard Hill (Ontario Cancer Institute)

Cancer stem cells in tumours
A cancer stem (cancer-initiating) cell is defined as a cell within a tumour that possesses the capacity to self-renew and to generate the heterogeneous lineages of cancer cells that comprise the tumour. This definition directly implies that an anti-cancer therapy can cure a tumour only if all cancer stem cells are killed. A recent milestone in cancer research was the introduction of flow sorting techniques to isolate cell populations based on cell surface markers that are differentially expressed in tumour cell subpopulations that are enriched for cancer stem cells. Application of this technology may allow discrimination of stem cells and non-stem cells on an individual basis, although the interpretation of this data in the context of the exact phenotype of a stem cell is currently evolving. The question of whether cancer stem cells represent a (small) subpopulation of tumour cells which may respond differently to treatment (e.g. radiotherapy or chemotherapy) compared to the bulk of non-stem tumour cells has direct implication for understanding the response of tumours to treatment. Changes in tumour volume after therapy, i.e. tumour response, are governed by the changes in the mass of tumour cells, i.e. primarily by the non-stem cells. In contrast, permanent tumour eradication is expected to be dependent on the complete inactivation of the subpopulation of cancer stem cells. This distinction is extremely important for optimization of cancer research methodology. Today the vast majority of preclinical studies in cancer research use volume dependent parameters such as tumour regression or tumour growth delay as experimental endpoints. An often unrecognised assumption in modelling such data is that cancer stem cells have the same treatment response as non-stem cells in the tumour. The validity of this assumption for different tumour types is currently unknown.

David Hodgson (PMH)

Learning from the Fat Man: Modeling Radiation-related Second Cancer Risk for Clinical Use
Numerous studies have demonstrated increased risks of second malignancy among young cancer survivors, largely attributed to radiation therapy (RT). However, due to the long latency required to observe second solid cancers (SC) and the rapid evolution of RT techniques, many estimates of radiation-related SC risks reflect the outcomes of treatment no longer in use. Moreover, there is large variation in the normal tissue exposure among individuals nominally receiving the same form of RT. Consequently, published risks of SC are not generalizable to contemporary HL patients, and conceal substantial differences in risk among individual patients.

Ideally, patient-specific radiation exposure data could be used to prospectively
estimate RT-related SC risk. This approach would have the potential advantage of providing patient-specific SC risk estimates to newly diagnosed patients undergoing treatment, and could aid the development of more effective RT techniques by helping to quantify the reduction in late toxicity expected from changes in RT practice.

This talk will review studies that have applied methods of modeling cancer risk among atomic-bomb survivors to radiation-related second cancer risk among patients receiving RT. Epidemiologic data are emerging regarding dose-risk relationship following RT that suggest that standard radiobiologic models may not apply to the SC risk seen following RT. Advances in imaging and individual-level dosimetric estimation will facilitate the creation of patient-specific estimates of SC risk, however major challenges exist to create estimates with confidence intervals sufficiently narrow to be clinically interpretable, and to integrate predictive models into a contemporary biologic theory of radiation carcinogenesis.

Yi Jiang (Los Alamos)

Multiscale modeling for tumor angiogenesis
Tumor angiogenesis, the formation of new blood vessels from existing vasculature in response to chemical signals from a tumor, is a crucial step in cancer invasion and metastasis. Though the detailed processes involved in angiogenesis are well established, the biomechanical and biochemical mechanisms behind the vessel formation are largely unresolved. We have developed a cell-based, multiscale modeling framework that has been successfully applied to study tumor induced angiogenesis. Our multiscale model is the first to incorporate intracellular signaling pathways, cellular dynamics, cell-cell, cell-matrix, cell-environment interactions, as well as chemical dynamics, for tumor-induced angiogenesis. It is also the first to simulate emergent vessel branching, anastomosis, and the brush border effect. I will show that the model has not only reproduced realistic sprout morphogenesis, but also generated testable hypotheses regarding mechanistic role of angiogenic factor (VEGF) and the topography of extracellular matrix, on sprout branching and fusion.

Philip Jones (Cambridge Cancer Ctr.)

The self assembling stem cell niche: a new model of epidermal homeostasis
Mammalian epidermis is an ideal system in which to study stem cell behaviour as it is constantly being turned over, has a simple architecture, and is predominantly composed of a single cell lineage, the epidermal keratinocyte. Epidermis consists of layers of keratinocytes. Cells are continually shed from the epidermal surface and replaced by proliferation in the basal cell layer, raising the question of how epidermal homeostasis is achieved.

It has been argued the epidermis is maintained by long-lived, slowly-cycling stem cells, which in turn generate a short-lived population of transit-amplifying (TA) cells that differentiate after a limited number of cell divisions. We have recently reported that this "classical" stem/TA cell model is inconsistent with clonal fate data obtained through inducible genetic labelling in the tail skin of adult mice, which reveals a different mechanism of epidermal homeostasis. Murine epidermis is maintained by a single population of committed progenitor cells which behave stochastically, dividing to generate, on average, equal numbers of cycling or post-mitotic cells. The discovery of a new paradigm of stem-cell independent tissue maintenance in mouse raises the question as to whether similar rules may govern the behaviour of human keratinocytes.

In the basal layer of human interfollicular epidermis, near-quiescent stem cells are localised in a niche consisting of stem cell clusters, separated by proliferating and differentiating keratinocytes. Remarkably, this pattern is reconstituted in vitro. Combining a range of existing observations with new experimental data, we have elucidated the origin of patterning and quiescence in homeostatic tissue, and explained the ability of stem cells to reconstitute their niche in culture. Such behaviour points at a simple set of organisational principles controlling stem and progenitor cell fate, and provides a unified model of epidermal maintenance in mouse and human. In particular, we show that epidermis is maintained by a committed progenitor cell population whose stochastic behaviour enables stem cells to remain largely quiescent unless called upon for repair. These results raise questions as to the role of stem cells in other adult tissues.

Rama Khokha (Ontario Cancer Institute)

Functional and Biological Variables in Metastasis
Metastasis is the multistep process by which cancer cells target and colonize secondary organs. Cancer cells locally invade by breaching extracellular matrix barriers, gaining access to vasculature, and extravasating into the distant organs. This is followed by their growth in the new environment, culminating in metastatic colonization. Lung, liver, brain and bone are common sites of metastasis for many human cancers. There is a considerable debate concerning the identity of rate limiting steps in metastasis, thus modeling individual steps, and gaining molecular understanding of this process presents significant challenges. We will discuss the recent technologies and genetic mouse models which are emerging to meet these challenges.

Mike Milosevic (PMH)

Angiogenesis, Interstitial Fluid Dynamics and Hypoxia in Tumors
It is now well established that the clinical behaviour of many human cancers is determined by molecular interactions between the malignant cells and the environment in which they exist. Abnormal blood vessels that arise from aberrant angiogenesis are an important cause of tumour hypoxia, which stimulates further angiogenesis and leads to radioresistance, altered repair of DNA damage and changes in the expression of genes important in tumour progression and metastasis formation. In addition, the abnormal tumor vessels contribute to high interstitial fluid pressure (IFP), an important predictor of reduced survival in women receiving radiotherapy for cervix cancer and a barrier to drug penetration. These and other aspects of the abnormal microenvironment in tumors, while conferring poor prognosis and impeding the effectiveness of currently available treatments, also present unique opportunities for improving cure rates. Combinations of radiotherapy or chemotherapy with novel molecular treatments that target angiogenesis or hypoxia are the focus of ongoing laboratory and clinical studies. Mathematical models of how these treatments interact can generate new hypotheses for laboratory and clinical testing, inform the design of future studies with respect to important issues such as optimal dosing and sequencing of the various treatments, and help to explain unexpected preclinical or clinical findings.

Lance Munn (Harvard)

Multi-scale analyses of tumor physiology and blood vessel dynamics
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. We are developing analytical approaches--both experimental and computational-- that span the size scale from single cells to bulk tumor in order to 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 provide a framework for studying the effects of anti-tumor therapies and improving their efficacy.

Leonard M. Sander (Michigan)

Micromechanics of collagen-gels and invasion by glioma cells
Glioma is a highly invasive form of brain tumor. We have studied the invasion process in a in vitro experiment where tumor spheroids are seeded in collagen gels. We find that invasion involves strong and complex interactions with the gel; the cells deform and align the matrix. In order to better understand this process we study a micromechanical model of collagen-I. We can reproduce the non-linear elasticity of the gel, and we show that deformations are non-affine. We discuss the relationship of the mechanics to the invasive process.

Shiladitya Sengupta (MIT)

Spatiotemporal targeting of tumor parenchyma and stroma by hybrid nanoparticles
The talk shall focus on the design of a novel nanoscale platform that enables the spatiotemporal targeting of tumor stroma and parenchyma with an antiangiogenic agemt followed by a cytotoxic. This enables the intratumoral exposure of the hypoxic tumor to a chemotherapeutic agent resulting in disruption of the HIF1a-autocrine loop and increased antitumor efficacy.

Jack Tuszynski (Cross Cancer Inst.)

MD and QMMM modeling successfully predict binding and effectiveness of novel colchicine derivatives against multiple cancer cell lines
Colchicine is a highly toxic plant-derived alkaloid which inhibits microtubule polymerization by binding to tubulin dimers. Currently, the chemotherapeutic value of colchicine is limited by its toxicity against normal cells. Theoretically, this could be remedied by derivatizing colchicine to preferentially bind tubulin isotypes which are more common in cancer cells than in normal body tissues, and particularly in those cancer types which are resistant to conventional therapies. In recent studies, it has been demonstrated that class III ß-Tubulin over-expression is associated with taxane-resistant subsets of non small cell lung cancer, advanced ovarian cancer, breast cancer and cancer of unknown primary origin. Our study investigates the uses of Quantum Mechanics Molecular Mechanics (QMMM) and Molecular Dynamics (MD) modeling to construct derivatives of colchicine which will bind class III ß-Tubulin with increased affinity. Using QMMM and MD modeling techniques, 21 colchicine derivatives were designed to increase affinity for class III ß-Tubulin by offering a better steric fit into the binding pocket . Derivatives were designed and tested in silico before being synthesized by organic chemists at Oncovista Inc. of San Antonio, TX. The colchicine derivatives were then tested in MTS cytotoxicity assays against up to seven different cancer cell lines with differing characteristics and morphologies. Results were obtained by graphing the MTS absorbance readings, and calculating an EC50 Value (drug concentration at which 50% of the drug's effects are seen) using sigmoidal dose-response analysis. Colchicine has an EC50 Value in the range of 10-7 M, and several of our novel derivatives (ie. CH-32, CH-34 and CH-35) were found to have EC50 Values in the range of 10-9 M, while other derivatives (ie. CH-6, CH-7 and CH-21) were found to have EC50 values in the range of 10-5 M to 10-6 M. These results indicate that our derivatives have up to 100X greater and lesser effectiveness than colchicine. Interestingly, comparative derivative cytotoxicity was found to correlate with theoretical QMMM and MD modeling predictions. Successful derivatives warrant continued investigation, screening and development. We propose that our modeling system may be used to design any variety of drugs for specific targets such as vinca alkaloids, taxanes and peloruside.

Zhihui Wang (Harvard-MIT, HST)

Multiscale Lung Cancer Modeling
Lung cancer accounts for one third of all cancer related deaths worldwide. Computational models simulating cancer cell behavior can provide valuable insights into the quantitative understanding of the inherent complexity of neoplastic systems through an interdisciplinary approach. We have been working on the development and analysis of multiscale agent-based models to investigate the growth dynamics of non-small cell lung cancer (NSCLC). Our proposed innovative methods can be used to help identify biomarkers across different biological levels, thereby generate novel hypotheses and help guide further experiments.

Glenn F. Webb (Vanderbilt)

Models of Tumor Growth in vitro
Two models of in vitro tumor growth will be presented. (1) Transforming growth factor TGF is known to have properties of both tumor suppressor and tumor promoter. While it inhibits cell proliferation, it also increases cell motility. A mathematical model quantifies the growth of MCF10A/HER2 cell cultures in vitro under exposure to TGF. The model supports the hypothesis that TGF increases the tendency of cells and cell clusters to move randomly, while simultaneously diminishing cell proliferation. (2) P-glycoprotein (P-gp) is a protein over-expressed in cancer cells that causes multi-drug resistance to cancer therapy. Recent experimental evidence demonstrates that P-gp is transferred directly cell-to-cell in in vitro tumor cell lines. A mathematical model quantifies the transfer process of P-gp in in vitro cultures of MCF-7 human breast adenocarcinoma cells. The model supports the hypothesis that P-gp is transferred directly cell-to-cell and provides a framework for optimizing chemotherapy regimens.

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