Growth, movement and differentiation of cells are three key processes involved in pattern formation and morphogenesis in developing systems. Pattern formation involves the expression of genes at the correct point in space at the correct time, and this in turn typically involves spatially- and temporally-varying signals, and mechanisms for signal transduction and activation or repression of gene expression. Gene expression during embryonic development is not a cell-autonomous process, because cell fate in a multicellular embryo usually depends on the cell's location. This fact led to the theory of positional information, which posits that a cell must `know' its position relative to other cells in order to adopt the correct developmental pathway. Positional information is viewed as a necessary part of pattern formation. Frequently pattern formation results from the response of individual cells to a spatial pattern of chemicals called morphogens: molecules that move through a tissue by diffusion or other means, and regulate gene expression in a concentration-dependent manner. Morphogenesis refers to the processes that shape tissues, organs and organisms and necessarily involves both signaling and force generation for movement and cell rearrangement. While there are many variations on how the different processes are involved in different organisms, it is striking how conserved the basic processes are across the phyla. Also not surprisingly, these same processes are involved in various diseases such as cancer, and this unity and conservation of basic processes provides the rationale for studying various experimental model systems. This same unity and conservation also implies that mathematical models of the fundamental processes can have a wide-ranging impact across the spectrum of normal and pathological development.
In the last two decades much has been learned about the molecular components involved in signal transduction and gene expression in a number of systems, and the focus is now shifting to understanding how these components are integrated into networks, and how these networks transduce the inputs they receive and produce the desired pattern of gene expression. Several model systems, including Drosophila and limb development, will play a major role during the year. Development is a sequential process in which later stages build on earlier stages, but within stages there are often multiple feedback loops in signaling and gene control networks that may serve to buffer against perturbations caused by fluctuations in morphogen concentration and other components. This suggests two areas in which theoreticians can contribute: (i) the understanding of the relationship between network topology and functionality, and (ii) the development of computational tools for simulating growth, cell movement and differentiation in developing systems. The purpose of the year in Mathematical Challenges in Developmental Biology is to bring together theoreticians who have made significant contributions to various basic processes involved in development with experimentalists working on specific systems for which a quantitative approach has been or may be productive.