Mathematical modeling of cell metabolism
Michael Reed, Fred Nijhout, Cornelia Ulrich

This research area involves the applications of mathematics to the study of various aspects of cell metabolism, in particular, folate and methionine metabolism. The folic acid cycle plays a central role in cell metabolism. Among the important functions of the folate cycle are the synthesis of pyrimidines and purines and the delivery of one carbon units to the methionine cycle for use in methylation reactions. Dietary folate deficiencies as well as mutations in enzymes of the folate cycle are associated with megaloblastic anemia, cancers of the colon, breast and cervix, affective disorders, cleft palate, neural tube defects, Alzheimers disease, Down's syndrome, preeclampsia and early pregnancy loss and several enzymes in the cycle are the targets of anti-cancer drugs.

The methionine cycle is important for the regulation of homocysteine, an important risk factor for heart disease, and for the control of DNA methylation. Both hyper- and hypomethylation have been proposed as crucial steps in chains of events that turn normal cells into cancerous cells. The purpose of the project is to use mathematics to understand normal folate and methionine metabolism, DNA methylation, and purine and pyrimidine synthesis and then to understand how they are affected by alterations in diet and gene abnormalities.

Chemotropism
Anita Layton and Danny Lew

Many cells are able to detect spatial gradients of chemicals and either move (chemotaxis) or grow (chemotropism) towards or away from them. Experimental analyses indicate that cells are remarkably good at this, efficiently detecting minuscule spatial differences in concentration between the front and rear of the cell. We work on yeast cells, which detect mating pheromones and grow towards mating partners by chemotropism.

Many of the molecular players in this pathway are known, but the remarkable sensitivity of the process in the face of large amounts of noise is not understood. We are combining a mathematical model of the Turing process that establishes polarity in yeast with a stochastic model of vesicle delivery and retrieval to generate and test hypotheses about the process in silico. In parallel, we use genetic manipulation and sophisticated imaging of living cells undergoing chemotropism to test our ideas in vivo. Recent technical advances have allowed us to probe relevant protein dynamics with unprecedented resolution, revealing unexpected oscillatory aspects of polarization, which we would also like to model.

Dorsal closure
Stephanos Venakides, John Harer, Anita Layton, Glenn Edwards, and Dan Kiehart

The interdisciplinary modeling team, led by Venakides, studies the movements of cell layers in developing fruit flies (Drosophilia) — movements that may serve as a model for the development of cells and the healing of wounds in human tissues. Experimental data generated by the Laser Laboratory show that when the fruit-fly embryo is cut in different places the cells perform different closure behaviors. The mathematical model explains these data and will help us to understand the forces produced by the cellular interactions.

John Harer leads the effort in the development of topology-based segmentation methods for data sets and their application to the study of dorsal closure. Information from the segmentation analysis provides a framework for structuring and testing of mathematical models. Harer is extending previous segmentation methods by including global structure using persistent homology, a method that improves data quality based on global, rather than local, considerations. The goals of the dorsal closure segmentation project are to: (a) Accurately identify cell boundaries that have been tagged with fluorescent proteins. (b) Assemble z-slices and 3D segmentation of the epithelial cells in the embryo, (c) Develop appropriate descriptors of cell-shape, and use them to understand the evolution of cellular shape and interactions through time.