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Friday, March 16, 2007 - 2:00pm

Mark Alber

University of Notre Dame

Location

University of Pennsylvania

Berger Aud.

The Cellular Potts Model (CPM) has been used at a cellular scale for simulating various biological phenomena such as differential adhesion, fruiting body formation of the slime mold Dictyostelium discoideum, angiogenesis, cancer invasion, chondrogenesis in embryonic vertebrate limbs [1], and many others. It is crucial for developing multiscale biological models to establish a connection between discrete microscopic stochastic models, including CPM, and macroscopic continuous models. There is a vast literature on studying continuous limits of point-wise discrete microscopic models. However, much less work has been done on deriving macroscopic limits of microscopic models which treat cells as extended objects [2]. To demonstrate multiscale approach we will describe in this talk derivation of a continuous limit of a two-dimensional CPM with the chemotactic interactions in the form of a Fokker-Planck equation describing evolution of the cell probability density function. The system of equations is then reduced to the model of Keller-Segel type. We will also demonstrate that CPM Monte Carlo simulations are in excellent agreement with the numerics for the continuous macroscopic model. 1. R. Chaturvedi, C. Huang, J.A. Izaguirre, S.A. Newman, J.A. Glazier, M.S. Alber, On Multiscale Approaches to Three-Dimensional Modeling of Morphogenesis, J. R. Soc. Interface 2 (2005), 237-253. 2. M. Alber, N. Chen, T. Glimm and P. Lushnikov, Multiscale dynamics of biological cells with chemotactic interactions: From a discrete stochastic model to a continuous description, Phys. Rev. E. 73 (2006), 051901.