All cells in a single organism contain the same DNA, and there is an almost one-to-one correspondence between genes and proteins. But the level of production of various types of proteins depends on spatial and temporal variables such as tissue location and extra-cellular stimuli.
With the recent development of gene expression arrays, it has become possible to simultaneously measure the level of expression of thousands of genes by measuring the amount of each type of mRNA present in a collection of cells. Biologists study differences in gene expression among cell types to elucidate the steps of normal development and tissue differentiation. By examining the level of gene expression in cell populations of disease and pre-disease states, investigators will attempt to understand the steps of disease development and to identify the genes involved in disease susceptibility and gene-environment interactions.
The greatest hurdles to the effective development and use of DNA microarrays are problems of mathematics and statistics, such as image analysis of the fluorescent signals; problems of combinatorial mathematics for the design of oligonucleotides; problems of how to elucidate genetic networks based on time-sequenced gene expression data; how to classify cells based on expression pattern; and how to develop diagnostic disease classifications systems. Because of the high dimensionality of the data obtained from microarray experiments, there are many challenging problems of multiplicity and multivariate analysis that must be addressed.
DNA microarrays will finally provide the data to attempt to understand simple organisms as entire systems and this will require new levels of collaboration among mathematical scientists and biologists. The program will help to identify and crystallize the formulation of the mathematical, statistical and computational issues, and form a working group of interdisciplinary researchers.
Michael Waterman (University of Southern California, Mathematics)