In our simulation, as in experiments, a grafted Kohler's sickle will form a 2nd primitive streak but the two will veer away from each other.
Computational Biology
A fundamental question in biology is how the enormous genome, through the relatively slow process of transcription, can so precisely control biological pattern formation (morphogenesis) under unpredictable circumstances. One possible answer is that it doesn't. It may be that the genome is efficient by triggering physical processes that are ready to self-organize. A result of this hypothesis would be that many aspects of morphogenesis should be reproducible by just a few physical mechanisms.
My postdoctoral advisor, James Glazier, has been a pioneer in testing this hypothesis through unique computer simulations. His method, called the cellular Potts model (CPM) is a leading approach for cell-level modeling which treats cells as spatially extended objects with individual behaviors. This method differs from ones that treat tissues as continua or as composed of point like cells. Many extensions and flavors of this method are being developed.
Computational models of living tissue generally come in two flavors: continuum and pointillistic. Continuum models ignore cells and treat tissues as homogeneous materials with pre-specified mechanical properties. Pointillistic models treat biological tissues as collections of point-like cells, ignoring the cell characteristics that are most important to their biological behaviors, such as cell polarization, or the interactions between cells at their membranes. While both approaches are convenient (continuum models lend themselves to mathematical analysis, and engineering has provided us with a wealth of computational tools for solving them; pointillistic models are easy to design and implement and computationally inexpensive) neither has been widely successful. Any successful model must focus on the most fundamental unit in biology-the individual cell. Unfortunately, full agent-based modeling using individual cells can be computationally expensive.
The Cellular Potts Model ({it CPM}) is a lattice-based, stochastic model, which describes biological mechanisms in terms of interaction energies and constraints ~ te{Graner1,Glazier2}. This model is a clever and efficient algorithm for treating cells as individual, spatially extended, physically interacting agents with a compact set of relevant biological behaviors. It uses the cell as a natural level of abstraction for mathematical and computational modeling of biological development. Treating cells phenomenologically immediately reduces the interactions of about ^5-10^6 products to approximately 10 behaviors: motility, adhesivity, cell growth, division and death, secretion and absorption of chemicals and electrical charges, cell differentiation, chemotactic and haptotactic responses, elasticity and viscosity.