July 30-August 2, 2008
Society for Mathematical Biology Conference

Computational Models of Cancer Invasion Driven by Cancer Cells Adaptation to the Microenvironment: Experimental Parameterization and Validation.
Vito Quaranta (Department of Cancer Biology, Vanderbilt University)

Within the NCI Integrative Cancer Biology Program, our Center at Vanderbilt is unique because it focuses on integrating experimentation with mathematical modeling and computer simulations at the cell scale. Three mathematical models were developed:
1) The Evolutionary Hybrid Cellular Automata (EHCA) model;
2) The Immersed Boundary Cell (IBCell) model;
3) The Hybrid Discrete-Continuum (HDC) model.
The EHCA model uses a cellular automata based approach that considers cells as simple grid points. Each cell contains a complex neural network that links genotype to phenotype. The grid itself represents the tumor microenvironment (mE) and the only variable on this grid, apart from the cells, is the concentration of oxygen, controlled by a (continuous) partial differential equation. At every cell doubling, the inner neural network is copied to the daughter cells, but with a probability of error. The model captures one component of cancer progression, the generation of phenotypic variation within a population of growing cancer cells.
The IBCell represents cancer cells as 2D fully deformable objects including an elastic plasma membrane modelled as a network of linear springs that defines cell shape and encloses the viscous incompressible fluid representing the cytoplasm and providing cell mass. These individual cells can interact with other cells and with the mE via a set of discrete membrane receptors located on the cell boundary. These receptors control several cellular processes, such as growth, division, death or polarisation. The mE is represented as physical forces (to include other cells). With experimentally derived receptor behavior values, cells go on to build realistic epithelial structures, such as acini, ducts, tubes. The outcome of these simulations is not predetermined, but is an emergent property of the collective behavior of cells, purely determined by their mechanical interactions with one another and the mE. IBCell is ideal to capture the transition to invasion when epithelial structures (acini, ducts) built or perturbed by cancerous cells become unstable.
The HDC model operates at the cell-to-tissue scale, and represents growth in a one-cell diameter thick 2D slice of a generic 3D solid tumor. The mE consists of a 2D lattice of extracellular matrix (f) upon which oxygen (c) diffuses and is produced/consumed, and matrix degrading proteases (m) are produced/used. The mE variables f ,c and m are controlled by a system of continuous reaction-diffusion equations whereas the tumor cells (Ni,j) are considered as discrete individuals (cell automata) which occupy single lattice points (i, j), hence HDC is a Hybrid between a Discrete and a Continuum model. In HDC the tumor cell population is heterogeneous, from 100 randomly predefined aggregates of traits, including rates of proliferation, death, motility, secretion. HDC examines: tumor morphology outcomes, traits of phenotypes best adapted to a local mE, dynamics of the adaptation process, and influence of a range of different mE on morphology and adaptation outcomes.

To populate these models and simulations with empyrical homogeneous datasets, we adopted a platform cell type, the breast epithelial cell line MCF10A, onto which we established a collection of variants with distinct invasive potentials, generated by transfection of oncogenes or multiple passaging in vivo. We measured many cell parameters, including: oxygen consumption/hypoxia, proliferation, survival, matrix degrading enzyme secretion, morphology patterns in 3D culture.
The EHCA model presents an opportunity for parameterization and validation via an interface with gene expression profiling high-throughput data from these cell lines, which we are currently exploring. The IBCell is being tuned with 2D and 3D growth data from MCF10A cells and derivatives, to test its ability to predict receptor value ranges that lead to acquisition of invasive morpholgy when ErbB2 growth factor receptors are overexpressed or overactive.
For the HDC model, initial simulations with these homogenous datasets are consistent with its prediction that, in order to occur, invasion requires active competition between phenotypes with distinct adaptive traits. To empyrically validate these HDC predictions in vitro, we developed a novel Island Invasion Assay (IIA), which closely mimics the spatial 2-D arrangement of growing tumor cells in the HDC model. Preliminary results suggest that IIA also supports the HDC predictions concerning invasion (fingering) under stressful tmE conditions. In addition, some unexpected results point to novel features that could be included in the HDC model to increase realism. This is an excellent example of synergistic interactions between modeling and experimentation, which will hopefully produce novel insights in the mechanisms underlying cancer invasion.
For in vivo validation, we are comparing orthotopic mE versus subcutaneous mE xenografts of the MCF10A tumorigenic variant lines in mice. Tumor specimens are biopsied at fixed volumes (0.5, 1 and 1.5 cm diameters) for ex vivo analyses, including histology to assess invasion, immunohistochemistry and immunofluorescence to measure cellular proliferation (BrdU incorporation), apoptosis (TUNEL) and hypoxia (hypoxiprobe). Initial results reveal unexpected correlations between in vivo mE and tissue of origin of the cell lines tested (breast gland).
This overall strategy for parameterization of tumor models and validation of their predictions will be discussed in the context of our efforts to build, in line with the ICBP goals, a mathematical oncology group that integrates experimental biologists with physical scientists on equal foot, and produces theory-driven experimentation as well as experiment-driven theory.

This work is reviewed in:
1) Anderson ARA and QuarantaV, Integrative mathematical oncology, Nat Rev
Cancer. 2008, 8:227-34, doi:10.1038/nrc2329
2) QuarantaV et al, Invasion emerges from cancer cell adaptation to
competitive microenvironments: Quantitative predictions from multiscale
mathematical models, Sem Cancer Biol. 2008, in press,
doi:10.1016/j.semcancer.2008.03.018

 

Mathematical and computational modeling holds great promise for personalized medicine to predict outcomes such as tumor metastasis or drug response. However, the first step is to show that data can be incorporated into models and make reasonable predictions. I will discuss our efforts in experimental parameterization of a model of tumor progession and the role of microenvironmental resource limitation in promoting tumor aggressiveness.

Modelling Aspects of Solid Tumour Growth
Philip Maini (Centre for Mathematical Biology, Mathematical Institute, Oxford

We will present some mathematical modelling of the potential effects of acid production on the ability of tumour cells to invade tissue and for the selection of certain mutations. The models will range from very simple partial differential equation type to hybrid cellular automata.

Transformed Epithelial Cells and Fibroblasts/Myofibroblasts Interaction in Breast Tumor: A Mathematical Model and Experiments
Yangjin Kim

Authors : Yangjin Kim, Avner Friedman (Mathematical Biosciences Institute,Ohio State University) Julie Wallace, Fu Li, and Michael Ostrowski (Human Cancer Genetics, Ohio State University)

In order to understand the role of fibroblasts/myofibroblasts in the early evolution of breast cancer in vitro we developed a mathematical model as well as conduct experiments. In the experiments tumor cells are placed on one side of a membrane and fibroblasts are placed on the other side. The membrane is semi-permeable, allowing only growth factors such as EGF,TGF-beta, but not cells, to cross over. The mathematical model describes the dynamics of the various concentrations of cells and growth factors by a system of partial differential equations. The prescence of extracellular matrix have an effect on tumor grwoth. We demonstrate a good agreement between the simulation of the model and the experiments.