IThe Morphogenetic Construction Kit (MoCK) provides students with a virtual lab where they can examine mathematical models of developmental pattern formation. The main object in the laboratory is a one-dimensional tissue of cells that represents (at a fairly high level of abstraction!) a developing embryo. The cells contain a compound called an activator, and the concentration of activator is represented by cell color: dark for low, gray for medium, and white for high concentrations. A cellís concentration is controlled by one of several mathematical models, which describe how concentration changes with time. Currently, MoCK supports three models of pattern formation. The first two are variants of a simple diffusion system: fixed cells as sources of activators, or fixed positions as sources of activators. The third is a reaction diffusion model.
Students interact with MoCK in either an experimental mode or an analytic mode. In experimental mode, MoCK provides students with a representation of a developing organism, and with tools that can be used to determine which of the models cause the observed patterns. The student can watch the pattern form, but has no informationabout which mathematical model is at work. Indeed, many different models can produce the same sorts of patterns, so the resulting pattern by itself is not much of a clue. The student can, however, perform a number of operations on the tissue, using software tools that MoCK provides: copies can be made, and it can be cut into pieces which can be rearranged and sewn together in a new order, and so forth. In this version, MoCKís tools are reminiscent of tools used in classical embryology.
Once a student has learned about the types of tools available, he or she can begin to design experimental protocols that allow the underlying mathematical models to be distinguished. The idea here is to represent some of the work that might take place in an actual developmental biology laboratory. There are many mathematical models of pattern formation, but definitive support for any particular model is in short supply. One goal, therefore, is to learn to design experiments that help identify which mathematical model may be at work in a particular organism.
In analytic mode, students (and instructors) are able to set up their own problems. They select a model, specify relevant parameters, and run the simulation to examine the pattern (if any) that forms. One goal here is to help students understand the relationships among parameters in the model. Most combinations of parameters produce no pattern: activator concentration uniformly drops to zero or skyrockets to infinity. Since pattern-producing combinations are rare, searching for them can be a frustrating exercise, but it does provide an appreciation of just how fine-tuned developmental systems must be for patterns to arise in real organisms.
By varying parameter values in systematic ways, students eventually can discover for themselves how the parameters interact and the constraints necessary for patterns to form. This is essentially the same information, although in a more qualitative form, that one gets from an analytical stability analysis of the model. Thus, MoCK provides tools that help students understand mathematical models, even if the students donít have the background necessary to perform a full-fledged mathematical analysis.