J. A. Sherratt1,2, P. K. Maini2, W. Jäger3 and W. A. Müller4
1Nonlinear Systems Laboratory, Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K.
2Centre for Mathematical Biology, Mathematical Institute, 24-29 St. Giles', Oxford OX1 3LB, U.K.
3Institut für Angewandte Mathematik, INF 294, D-69120 Heidelberg, Germany
4Zoologisches Institut der Universität Heidelberg, INF 230, D-69120 Heidelberg, Germany
(Received April 16, 1995; Accepted June 19, 1995)
Keywords: Hydra, Pattern Formation, Positional Value, Mathematical Models
Abstract. We propose a new theoretical model for pattern regulation in Hydra. Our model treats positional value and "head activation potential" as manifestations of the same cellular property, the amount of a regulatory biochemical bound to the cells via surface receptors. The model centres on the recently discovered interaction between the head- and foot-forming mechanisms, and we propose that both head and foot formation could be controlled by receptor-biochemical binding. Positional value is determined by the density of bound receptors, and polarity is established by a gradient in the number of receptors per cell. The local competition between cells for this biochemical regulator means that transplantation of tissue from a higher to a lower region of the body column causes an increase in the positional value of the transplanted tissue, at the expense of its new neighbours. We show that a local competition effect of this kind occurs if, in addition to the gradient in receptor density, there is also a gradient in the secretion rate of an enzyme that actively degrades the biochemical regulator. We show that with the combination of these two parallel gradients, the model is able to capture a wide range of results from cutting and grafting experiments. In particular, the model predicts that supernumerary heads induce the formation of supernumerary feet, whereas supernumerary feet do not induce new heads to form.