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Mini-workshop: Quantitative mathematical modeling of gene regulatory networks (December 2-4, 2004)

(Cosponsored by the MRI (Mathematical Research Institute))

Organizers: Erik M. Boczko, Tomas Gedeon, and Konstantin Mischaikow

The goal of this workshop is to bring together mathematicians interested in the interplay between the structure of gene regulatory networks and their dynamics, biologists working with regulatory networks, and biophysicists who measure the essential quantities necessary for modeling, to jointly develop new approaches toward modeling and understanding the dynamics of gene regulatory networks. The central biological example considered at this workshop is yeast nitrogen metabolism. Nitrogen metabolism is an essential, diverse and ancient extant network, that provides intricate yet tractable examples of feedback circuits.

There are three central themes of our workshop:

• Network structure and its relation to dynamics. This includes structure theorems, symmetry, and phenotypic attractors.
• Mathematical issues surrounding models. This includes fixed and state-dependent delays, cell division and dilution, transport, transcription, translation and stochasticity.
• The dynamics, biology and evolution of nitrogen regulation in yeast.

Each theme involves both experimental and analytical issues that are to be explored in formal presentations and informal discussions.

Structure and dynamics: Gene regulatory networks naturally involve and exploit feedback control. To what extent biological circuits exploit deeper structure theorems is an intriguing question both from a mathematical and a biological perspective. From the biological perspective, structure theorems would provide a solid foundation on which to base systems level simulations of cellular response and adaptation. For the mathematician, they are the crucial stepping stone which allows movement beyond the well explored monotone cyclic feedback systems. The existence of structure theorems and the search for them is a unifying theme of the workshop.

We also wish to consider the relationship between dynamical attractors and biological design and outcome. We have dubbed this concept "phenotypic attractors." It arises quite naturally in the segment polarity network studied by von Dassow and Odell, but needs further refinement in the setting of sensory networks. We anticipate that presentations and discussion will be especially productive in this area and will require the joint effort of biologists and mathematicians. Mathematical Issues: Much of the interdisciplinary work in the area of gene regulatory networks has involved the construction, measurement and modeling of synthetic circuitry in bacteria. Even in this simplified setting, time delays are unavoidable, and the existence of state-dependent delays are at least within the realm of possibility. Furthermore, state-dependent degradation rates are well documented if not commonplace. There are compelling reasons to try to understand genetic regulation in preparation closer to humans. One of the favorite eucaryotes for these experiments is yeast. The advance to eucaryotes introduces further time delays associated with transport to and from nucleus and other mathematical obstacles. The workshop will explore mathematical issues relating to modeling and analysis of these networks.