Regulative feedback in pattern formation: towards a general relativistic theory of positional information

Abstract

Positional specification by morphogen gradients is traditionally viewed as a two-step process. A gradient is formed and then interpreted, providing a spatial metric independent of the target tissue, similar to the concept of space in classical mechanics. However, the formation and interpretation of gradients are coupled, dynamic processes. We introduce a conceptual framework for positional specification in which cellular activity feeds back on positional information encoded by gradients, analogous to the feedback between mass-energy distribution and the geometry of space-time in Einstein's general theory of relativity. We discuss how such general relativistic positional information (GRPI) can guide systems-level approaches to pattern formation. IntroductionEver since Hans Driesch's famous experiments on sea urchin embryos, it has been evident that developmental processes are capable of global regulation (Driesch, 1892). A small part of an embryo, such as a single totipotent cell, can regenerate a whole intact embryo. Driesch was so baffled by his results that he rejected a materialist explanation for this phenomenon and turned to vitalism instead (Driesch, 1914). The problem of embryonic regulation essentially reduces to the problem of regulative positional specification: how do cells adopt a state that is appropriate to their relative position within a developing embryo?Classical embryology introduced the notion of a morphogenetic field to explain global regulatory capacities (reviewed by Gilbert et al., 1996). The morphogenetic field aims to capture the ability of the cells in a developing tissue to establish a pervasive influence that imparts information about the state of the whole tissue. Local interactions within the field then allow cells to access global information, and, in principle, to adopt states that lead to appropriate patterning of the tissue or embryo as a whole. However, owing to the lack of molecular evidence, the mechanistic basis of such fields has remained obscure.Lewis Wolpert sought to address the issue of the missing mechanistic basis of embryonic regulation and developmental fields in 1968, when he proposed his French flag model to illustrate the concept of positional information ( Fig. 1) (Wolpert, 1968). At the time, gene expression in development was largely considered to be a problem of temporal regulation based on the paradigm established by Jacob and Monod from their work on the lac operon of Escherichia coli (Jacob and Monod, 1961;Monod and Jacob, 1962). To shift focus back to the spatial aspects of pattern formation, Wolpert argued that cells must have some means of determining their relative position in a developing field (Wolpert, 1969). In contrast to the concept of the morphogenetic field, Wolpert suggested that this happens by a mechanism imposed on, instead of arising from within, the field. According to this view, embryonic fields are defined by their boundaries (Irvine and Rauskolb, 2001), and positional information provides a mechanism by which cells can measure their d...

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