Pohley Heinz-Joachim
Arbeitsgruppe Kybernetik, Institut für Entwicklungsphysiologie an der Universität zu Köln, Deutschland.
Wilhelm Roux Arch Entwickl Mech Org. 1965 Mar;156(1):1-19. doi: 10.1007/BF00576716.
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.
为了解释粉斑螟（Ephestia kühniella）翅膀再生和生长的成虫盘的观察行为，用数学术语定义了一种生长调节系统。假设成虫盘的生长速率取决于两个变量，一个变量k被解释为蜕皮激素的浓度，另一个变量z表示通过细胞数量测量的成虫盘大小。激素浓度升高往往会增加成虫盘的生长速率，而细胞数量增加则往往会降低其生长速率。如果在一个幼虫体内存在两个大小不同的成虫盘，且两者的蜕皮激素浓度相同，那么较小成虫盘的生长速率只能大于或等于较大成虫盘的生长速率。该模型包含这样一种可能性，即小的成虫盘以最大且恒定的速率独立于激素水平生长。基于该模型推导了一些定理，以便简化对经验数据的解释，这些数据包括在连续摘除一个、两个或三个成虫盘后，对成虫盘上侧细胞分裂的每日计数。数据与该模型不矛盾，并表明在达到临界大小之前，再生的成虫盘独立于激素水平生长，而在此之后，生长速率取决于上述两个变量。讨论了一些关于激素水平控制以及使大小差异调节时间最小化的条件的观点。
