A Model of Pattern Formation in Insect Embryogenes1s
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J. Cell Set. 33, 117-139 (i977) 117 Printed in Great Britain A MODEL OF PATTERN FORMATION IN INSECT EMBRYOGENES1S H. MEINHARDT Max-Planck-Jnstitut fUr Virusforschung, 74 Tubingen, Germany SUMMARY A model is proposed in which the interaction of an autocatalytic substance with a short diffusion range - the activator - and its more diffusible antagonist - the inhibitor - leads to a local high concentration of activator at the posterior pole of the egg. The inhibitor, which is then produced mainly in this activated region, diffuses into the rest of the egg, where it acts as a ' morphogen ', forming a concentration gradient which supplies positional information. This model can account quantitatively for the patterns resulting from a large number of different experiments performed during early insect development, including ligation, u.v.- irradiation and microsurgical manipulations. The formation of additional posterior structures is interpreted as the result of the appearance of a new activator peak. Omission of segments after ligation of the egg is explained as the result of accumulation of morphogen (the inhibitor) at the posterior side of the ligation and a decrease of morphogen on the anterior side. In order to account for certain quantitative features of the ligation experiments it is necessary to assume that determination in response to the morphogen gradient is a slow, stepwise process, in which the nuclei or cells first pass through determination stages characteristic for more anterior structures until they ultimately form a given structure. The mutual interactions of activator and inhibitor are expressed as a set of partial differential equations. The individual experiments are simulated by solving these equations by use of a computer. INTRODUCTION The development of an organism from a comparatively unstructured egg is a complex phenomenon. A number of mechanisms capable of directing spatial organi- zation have been proposed (Goodwin & Cohen, 1969; Gierer & Meinhardt, 1972; Summerbell, Lewis & Wolpert, 1973; Lawrence, Crick & Munro, 1972). These attempt to explain aspects of normal development and results of experimental manipulation as the consequences of a simple underlying process. The developing insect embryo is a very convenient organism for studying embryonic organization for several reasons: the resulting embryo can often be treated to a good approximation as a linear array of structures (headlobe, thoracic and abdominal segments); and a large number of experiments have been published which show that embryonic organization can be affected by simple experimental manipulations, such as ligation, u.v.-irradiation, or centrifugation (for recent review see Sander, 1976; Counce, 1973). Different species, in some instances, react quite differently to similar manipulations, but it is likely that the underlying basic mechanism is similar. These experimental data offer an excellent opportunity for testing any model. Some results of Sander, Kalthoff and co-workers (Sander, 19756) are sketched n8 H. Meinhardt in Fig. i in order to give an impression of the range of phenomena which a model must successfully describe. One possible model of the development of spatial order supposes that a con- centration gradient of a particular substance - a 'morphogen' - is generated in the egg and further, that the local concentration of this substance determines the differentiation pathway of individual cells or cell groups. The intention of this paper is to show that the published experiments are indeed quantitatively compatible with the response of cells to one graded substance and further, to suggest how such a gradient could be formed and maintained. Some inferences are also drawn as to how cells measure the local gradient level. Anterior Posterior 100% 0% 60% 60% BL CL (H-1 3-16 J 7-16 J 50% 50% BL s*- I -v. CL H^- ~-N CL 'Qi (H-2 10-16^) =f 16-8-16 J) 40% 40% c /- "^v BL CL I T H-7 9-16^) H-2 12-16) H-16 Fig. i. Results of constriction and irradiation experiments with Smittia eggs (after Sander, 19756; Kalthoff & Sander, 1968; Kalthoff, 1971a; Schmidt et al. 1975). The elements in the normal germ band are called H (headlobe), 1,2,...,16. The first and last element in each part are designated by numbers, the dash indicates that all elements in between are formed. The location of a constriction is given in % EL (EL = egg length, 100% = anterior pole at the left). A-c, if a constriction is made during the late cellular blastoderm stage (BL) at most one element is missing; the cells appear as already determined - the egg behaves as a mosaic. The segment affected by the ligation allows one to estimate the location of that segment in the blastoderm stage. Segments 2, 5, 8 must therefore be located roughly at 60, 50 and 40 % EL, respectively, D-F, a ligation made earlier, in the cleavage stage (CL), leads to an omission in the segments formed. The terminal structures are always present. G, u.v.-irradiation or H, puncture (>) of the anterior pole evokes posterior Structures at the anterior pole, a symmetrical arrangement of segments is formed with an abdomen at each end ('double abdomen')- 1, irradiation of the posterior pole reduces the probability that irradiation of the anterior pole will induce a double abdomen. THE MODEL Basic phenomena of insect development Before describing the model and the experiments which it explains, it is necessary to introduce a few facts about insect development. After fertilization of the egg a set of synchronous divisions of the nuclei takes place (cleavage). The nuclei then migrate through the cytoplasm towards the egg periphery. It is only now that cell Pattern formation in insect embryogenesis 119 walls are formed between the nuclei, leading to a cell sheet called the blastoderm. With the completion of the cellular blastoderm the further general pathway of the cells is fixed. The interesting period in which the cells 'learn' which cell type they must develop into is therefore the interval between egg deposition and the completion of the blastoderm. In a later stage, a portion of the blastoderm cells form the 'germ band', the proper embryo, in which individual segments are already distinguishable (for review see Sander, 1976; Counce, 1973). Generation of a concentration gradient by a local source A graded distribution of a diffusible morphogen can be obtained if the morphogen is produced by a localized source at one pole of an egg and is broken down throughout the egg cytoplasm. The concentration gradient is necessarily shallow at the egg A t 2 • pa K y O EH O 2 y cu u OH 2 £o oU ? +" "*" ** POSITION — 1CCS5SO8580757065605550 45 4035302520 1? B f HI 2345678910 11 1213 14 15: c C H .' . 2 3 4 5678910 111213141516 £) f H>li2i3|4|5 <i?&$)b\\X£.p\A 15 16 J Fig. 2. Regulation of the segment pattern of the insect egg. All segments of an embryo will be formed within eggs of different sizes if only a certain concentration range is used for positional information. The embryo proper is then laid down only in a portion of the egg (B-D). A, distribution of a substance produced by a locally activated source (here at right side); and B 'normal' distribution; ^HHJ^and C, a shorter field changes the concentration at the end opposite the source; ttil and D, distribution from a 36% less-powerful source, B-D, only the precise location of the determination of the segments varies under these different conditions. This simple mechanism makes a separate size regulation mechanism unnecessary. pole opposite the source and the absolute concentration at this pole will depend on the size of the egg. The concentration in the immediate surroundings of the source depends on the source strength, which may vary from individual to individual 120 H. Meinhardt or depend on temperature. The gradient thus provides relatively specific positional information independent of a range of possible disturbing factors only in the internal region (Fig. 2). Indeed, it appears that only a certain internal portion between the 2 ends of an insect egg is used for the formation of the embryo proper, the rest develops extraembryonally. Ligation in the middle of the post-blastoderm egg of Euscelis (Sander, 1959) leads to complete embryo formation in the posterior part, indicating that the source is located at the posterior pole. Experiments with Platycnemis (Seidel, 1929,1935) reveal that only that part of the blastoderm between approximately 12 and 65% EL (% EL = percent egg length, 0% = posterior pole) participates in germ band formation and that the source (Seidel's 'Bildungszentrum', the activation centre) is located within the posterior tenth of the egg and therefore outside of the embryo proper. The fraction of the blastoderm used for embryo formation varies considerably among different insect species (see Krause, 1939). There seems to be a correlation between the fraction of the blastoderm used for embryo formation and the precision with which the egg length is regulated. Those insects which use a large part of the egg length show low variability in egg length, e.g. in Smittia roughly 70% of the blastoderm is used, the variability is less than 10 %, while in Euscelis less than 45% is used and the variability is 25% (Sander, 1959). If only a small part of the gradient is used, constancy of egg length would provide no selective advantage. It is thus attractive to suppose that the insect embryo is organized by a single morphogen source, that only a portion of the gradient is used to determine all structures of the embryo, and that through later growth the embryo comes to occupy the total available egg space. This source has to be located at the posterior pole. Conversely, additional posterior structures formed in abnormal positions as a result of experimental manipulation can be interpreted as the result of the activation of a secondary morphogen source.