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

hosted by the Centre for Mathematical Medicine, Fields Institute
held at University of Toronto, Medical Sciences Bldg


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6) Multiscale modeling of biological systems
Principal organiser: Dr. Yi Jiang

Yi Jiang & Mark Alber
Theoretical Division, Los Alamos National Laboratory

Biological problems typically involve processes at multiple scales, from gene to molecules to cell to tissue or organ and system. It has been realized that studies of any single scale is not sufficient to describe the complete picture. Multiscale modeling is becoming an increasingly important approach to studying biological systems. We propose a minisymposium to highlight recent efforts at this front and encourage discussions on how best integrate multiscale, multiphysics models, for complex biological problems.

Confirmed speakers :

1. Mark Alber (University of Notre Dame)

Multiscale Model of Thrombus Development
To prevent the loss of blood following a break in blood vessels, components in blood and the vessel wall interact rapidly to form a
thrombus (clot) to limit hemorrhage. In this talk we will describe a multiscale model of thrombus formation consisting of components for modeling viscous, incompressible blood plasma; coagulation pathway; quiescent and activated platelets; blood cells; activating chemicals; fibrinogen; the vessel walls and their interactions. At macro scale blood flow field is described by the incompressible Navier-Stokes equations and is numerically solved using the projection method. At micro scale, cell movement, cell-cell adhesion, cell-flow and cell-vessel wall interactions are described through an extended stochastic discrete Cellular Potts Model (CPM). Model is tested for robustness with respect to fluctuations of basic parameters. Simulation results demonstrate the development of an inhomogeneous internal structure of the thrombus which is conformed by the preliminary experimental data. We also make predictions about different stages in thrombus development which can be tested experimentally and suggest specific experiments. Lastly, we demonstrate that dependence of the thrombus size on the blood flow rate in simulations is close to the one observed experimentally.

2. Amy Bauer (Los Alamos National Lab)

From Molecule to Morphology:A Multi-Scale Cell-Based Model of Angiogenesis
Tumor-induced angiogenesis, which is 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. Although the sequential steps involved in tumor-induced angiogenesis are well known, the interplay between the biochemical and biomechanical mechanisms (e.g., cell-cell and cell-matrix interactions, and intracellular signaling pathways) that affect angiogenesis is largely unresolved. In this talk, I will introduce a novel multi-scale cell-based model of tumor-induced angiogenesis and present results from numerical simulations that elucidate some mechanisms controlling vascular formation in the context of pro- and anti-angiogenesis treatment strategies. In particular, I will discuss how extracellular matrix topology influences cell migration and vascular structure, and the relationship between external stimuli, cell phenotype, and vascular morphology. This model is the first to simulate emergent vessel branching, anastomosis, and the brush border effect. These macroscale structures arise as a result of microscale behavior without any rules prescribing the formation of such complex structures. Key features of this biophysical model include: (1) linking processes occurring on multiple time scales, (2) controlling processes at the level of the individual cell, (3) using physical and energy reduction constraints to capture emergent behaviors without prescribing phenomenological rules, and (4) quantifying morphological details that are not currently possible to capture with continuous models alone. These results translate and synthesize a large body of compartmentalized research on angiogenesis and are meant to inform and advance efforts to develop new approaches for treating cancer and other angiogenesis-dependent diseases.

3. Bridget S. Wilson and Tomáš Mazel (University of New Mexico)

Influence of 3D cellular geometry on IP3-mediated calcium responses: a multi-scale mathematical modeling problem
Release of inflammatory mediators by mast cells in type 1 immediate hypersensitivity allergic reactions relies on the antigen-dependent increase in cytosolic calcium. Here we used a series of electron microscopy images to build a 3D reconstruction of a rat tumor mast cell, which then served as a basis for modeling IP3-mediated calcium responses. We consider the influence of IP3 receptor clustering on IP3-mediated release, as well as the local proximity of the endoplasmic reticulum (ER) to both the plasma membrane and to mitochondria. We find that both flux and local cytoplasmic/ER luminal calcium concentrations are markedly affected by nearby organelles. In addition to compartmental and PDE-based approaches, we describe the first application of stochastic reaction-diffusion modeling within a complete 3D cell geometry. These combined approaches help to bridge the gap between measured single molecule kinetic constants and overall cellular calcium dynamics.

4. Qing Nie (UC Irvine)

Specificity and Robustness of Cell Signalling
Intra-cellular and cell-to-cell signalling are the fundamental biological processes. In this talk, through examples I shall study specificity of signalling pathways in yeast and robustness of morphogen systems in Drosophila embryo. In particular, I shall discuss mathematical and computational challenges associated with such study, and present a new class of numerical algorithms for reaction-diffusion equations.


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