Abstract
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 their spatial 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 morphogen-dependent 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.