Thresholds in development

Abstract

The interpretation of gradients in positional information is considered in terms of thresholds in cell responses, giving rise to cell states which are discrete and persistent. Equilibrium models based on co-operative binding of control molecules do not show true thresholds of discontinuity, though with a very high degree of co-operativity they could mimic them; in any case they do not provide the cells with any memory of a transient signal. A simple kinetic model based upon positive feedback can account both for memory and for discontinuities in the pattern of cell states. The model is an example of a bistable control circuit, and transitions from one state to another may be brought about not only by morphogenetic signals, but also by disturbances in the parameters determining the kinetics of the system. This might explain some aspects of transdetermination in insects. An attempt is made to analyse the precision with which a spatial gradient of a diffusible morphogen could be interpreted by a kinetic threshold mechanism, in terms of the length of the field, the steepness of the concentration gradient, and the intrinsic random variability of cells. It is concluded that it would be possible to specify as many as 30 distinct cell states in a positional field 1 mm long with a concentration span of 10 3. Mechanisms for reducing the positional error are considered.