Talks Part 1: Modeling Cells

I always enjoy attending good talks, and we’ve had quite a few lately: they’ve either been relevant to my current research, interesting applications of concepts I’ve encountered before, or just plain cool. (And of course, going to talks - or blogging, for that matter - is always a good way of taking a break from working all the time i.e. staying sane.) The material presented is always a good springboard for learning more. Here are a few summaries and references for the talks that stuck out the most, mainly because they dealt with things that I hadn’t directly encountered before.

Modelling Cell Motion and Morphogenesis: Mark Alber (Notre Dame)
Although this was billed as an applied math talk, it felt more like a physics talk: the speaker focused on trying to convey what was actually going on and less on the mathematical details involved in modeling it, which was refreshing. I’ve been to too many math talks where the speaker gets hung up on mathematical details, and the big picture somehow gets left out. Anyway, Prof. Alber is an applied mathematician at Notre Dame who spends a good deal of time modeling cells and biological processes at various scales (hence the term multiscale modeling) using ideas from statistical mechanics. The point is this: different modeling methods have their advantages and disadvantages. For example, macroscopic continuum methods abstract away many (often crucial) things and can miss different kinds of phenomena, while microscopic cell-level models - in which stochasticity is very important - can be computationally very intensive. This is particularly important in biological systems, where important processes take place at pretty much all scales; ideally, one would be able to construct a 3-dimensional model of a system and be able to zoom in and out with ease. This is what Alber et al. have been working on, in two different ways.

The first method is a 3D stochastic model of myxobacteria dynamics based on a lattice-gas cellular automata model, and using this, they’re able to study experimentally-observed phenomena like rippling, the formation of things like ’streams’ and ‘traffic jams’, and cell swarming/aggregation. The second method treats the cells as extended objects and goes off the philosophy that “while individual organisms and organs have very different structures and behaviors, many of the underlying interactions and components are the same.” In particular, it is an implementation of the Cellular Potts Model (CPM) of statistical mechanics, a non-equilibrium variant of the Ising model, coupling this to a continuum reaction-diffusion model for morphogen production/diffusion and a set of conditions dictating how genes are regulated. In particular, each cell is represented as a cluster of pixels in the CPM (with a multidimensional index indicating the type of cell) and interacts with other cells via a pairwise adhesion, and the cool thing is that they can use this to model - to a certain extent - limb formation in things like growing chicken embryos.

Further reading…
- Modeling myxobacteria dynamics: O. Sozinova et al., “A Three-Dimensional Model of Myxobacterial Aggregation by Contact-mediated Interactions“, PNAS 102 11308 (2005) and D. Kaiser, “Coupling Cell Movement to Multicellular Development in Myxobacteria“, Nature Reviews Microbiol. 1 45 (2003).
- Modeling limb formation: R. Chaturvedi et al., “On Multiscale Approaches to 3-Dimensional Modeling of Morphogenesis“, J. R. Soc. Interface 2 237 (2005).
- Somewhat related: D. A. Beysens et al., “Cell Sorting is Analogous to Phase Ordering in Fluids“, PNAS 97 9467 (2000) and W. Zeng et al., “Non-Turing Stripes and Spots: a Novel Mechanism for Biological Cell Clustering“, Physica A 341 482 (2004). In particular, I find the similarities between figure 2 of the latter reference and this picture of stripe formation in ferrofluids in one of my previous posts on electronic liquid crystals are striking.