Untersuchungen zum Problem der Wachstumsregulation

A growth-regulation-system is defined in mathematical terms in order to interpret the observed behavior of regenerating and growing imaginal disks of the wings inEphestia kühniella. It is assumed that the growth-rate of an imaginal disk depends upon two variables, a variablek which is interpreted as the concentration of the moulting hormone and a second variablez representing the size of the disk measured by the number of cells. A rising hormone concentration tends to increase and a rising number of cells tends to decrease the growth-rate of a disk. If two imaginal disks of different size are present in one larva and the concentration of the moulting hormone is the same for both, then the growth-rate of the smaller imaginal disk can only be greater than or equal to the growth-rate of the larger one. The model contains the possibility that a small imaginal disk grows independently of the hormone level with a maximum and constant rate. On the basis of that model some theorems are derived in order to simplify the interpretation of the empirical data which consist of daily counts of cell divisions on the upper side of the imaginal disks after successive extirpation or one, two of three imaginal disks. The data do not contradict the model and suggest that before reaching a critical size the regenerating imaginal disk grows independently of the hormone level while afterwards the growth-rate depends upon the two variables mentioned above. Some ideas are discussed about the control of the hormone level and the conditions under which the time for the regulation of size differences is minimized.