In this seminar, I will talk about two topics on mathematical approaches to developmental biology.
Robust positioning of cells in a tissue against unavoidable noises is important for achieving normal and reproducible morphogenesis. The position in a tissue is represented by morphogen concentrations, and cells read them to recognize theirspatial coordinates. From the engineering viewpoint, these positioning processes can be regarded as an information coding. Organisms are conjectured to adopt good coding designs with high reliability for a given number of available morphogen species and their chemical properties. To answer, quantitatively, the questions of how good coding is adopted, and subsequently when, where, and to what extent each morphogen contributes to positioning, we need a way to evaluate the goodness of coding. In this article, by introducing basic concepts of computer science, we mathematically formulate coding processes in morphogendependent positioning, and define some key concepts such as encoding, decoding, and positional information and its precision. We demonstrate the best designs for pairs of encoding and decoding rules, and show how those designs can be biologically implemented by using some examples. We also propose a possible procedure of data analysis to validate the coding optimality formulated here.
Accurate patterning in developing tissues is one of the important steps to achieve normal development. Differently from static situations without tissue growth, relative positions of cells in growing tissues dynamically changes. Cell trajectories in growing tissues include different kinds of noises originating from the rearrangement of cell positions through cell division and embryo-to-embryo variability of tissue deformation dynamics itself. Such a kinematic randomness is magnified by the growth of tissues, which can be a barrier for achieving accurate spatial patterning in growing tissues. In this study, from the theoretical side, we propose a design criterion about when cell fates should be determined or when spatial patterning should be done in growing tissues in the presence of kinematic randomness, and apply the theory to chick limb developmental process.