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.
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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
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£) f H>li2i3|4|5 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. How to generate a gradient We have proposed earlier (Gierer & Meinhardt, 1972, 1974; Meinhardt & Gierer, 1974) a theory for the formation of spatial distributions of morphogenetic substances within tissues. The theory is based on the kinetics of molecular reaction and move- ments. According to the theory, a typical, relatively simple model employs two substances. Substance A - the activator - stimulates its own production (auto- catalysis) and also the production of the antagonist - the inhibitor, H. The inhibitor diffuses faster than the activator. In an extended area a homogeneous activator- inhibitor distribution is unstable, since any small local increase of the activator concentration is amplified. The inhibitor, which is produced in response to the increased activator concentration, diffuses away and suppresses activator production outside the activated area, while, at the activated site, the activator concentration will increase via autocatalysis. This local activator concentration increase will con- tinue until, for instance, the loss by diffusion is equal to the net production. The activator distribution will show a relatively sharp concentration peak, whereas the Pattern formation in insect embryogenesis 121 more diffusible inhibitor will form a broader peak. The activitator and inhibitor profiles are stable, although both substances continue to be made, to diffuse, and to be broken down. When such a steady state is reached, the inhibitor is made predominantly in the region of the activator peak. As we have previously shown, the initial polarity of an activator pattern can be determined by (weak) internal or environmental asymmetries. Only one peak of activity develops at one of the ends if the size of the system is of the order of the activator range (Meinhardt & Gierer, I w u z o u Oti Fig. 3. The generation of a graded distribution of a substance which may act as morphogen. Through the interaction of a short-ranging autocatalytic substance - the activator- and its long-ranging antagonist - the inhibitor -a local high con- centration of activator is formed (Gierer & Meinhardt, 1972). The narrow activator peak activates local inhibitor production. The inhibitor has a graded distribution over the total area and is supposed to supply positional information. In a growing field, the process of gradient formation starts if a critical extension has been surpassed. Only one terminal peak is formed. It can be assumed that this happens in the growing oocyte before egg deposition. Polarity is determined by the asymmetric environment of the oocyte. A final pattern as shown is used in the other simulations as the initial condition before experimental manipulations are taken into account. Microsurgical experiments (Seidel, 1929) suggest that the source is activated at the posterior pole of the insect egg. 1974). If the field is then allowed to grow, the activator peak remains at its initial pole. (Growth in an asymmetric environment resembles closely the condition during oogenesis; for review see Mahowald, 1972.) This is demonstrated in Fig. 3. When a growing field becomes very large, the inhibitor diffusing from the activated pole may no longer suffice to suppress the formation of a second activator peak at the unactivated pole. The spontaneous formation of a second activator peak can be prevented, however, if one assumes a small 'constitutive' (activator-independent) inhibitor production. Equations (1) and (2) give a mathematical formulation of the mutual interaction 122 H. Meinhardt of the activator A and inhibitor H. All figures shown are computer displays of numerical solutions of these equations. 2 A = cA jH-fiA + DaAA+p0, (i) H=cA*-vH+DhAH+p1. (2) Eq. 1 means that the change of A per time unit (A) is proportional to an autocatalytic term (A2); the autocatalysis is slowed with increasing inhibitor concentration (iJH); A decays in a first-order reaction ( — /iA) and diffuses (DaAA). A (small) basic activator production remains even if no activator is present (pQ). Eq. 2 implies that the change of H per time unit (H) is a function of the cross-catalytic influence of 2 the activator (A ), of the decay (— vH) and of the diffusion (Dh AH). The regeneration of a high activator concentration after the removal of an existing activator maximum can be suppressed by a small activator-independent inhibitor production (px). For more details see Gierer & Meinhardt (1972). The morphogen production has to be controlled by the localized activator con- centration. For the sake of simplicity, we assume that the inhibitor — which satisfies the condition of being activator controlled - provides 'positional information' (Wolpert, 1969) in the developing egg. The differentiation pathway of a cell is controlled by the local inhibitor concentration. In other words, a particular structure is formed over a particular range of inhibitor concentration. An example of the correspondence between the inhibitor concentration and the structures formed will be given in Fig. 5 A and B. If the gradient is abnormal as a result of experimental manipulations, we can use the same correspondence to predict what pattern of structures will be formed. Formation of additional abdominal structures at the anterior pole - the activation of a new source Various experimental treatments of the egg, such as centrifugation (Yajima, i960), puncture (Schmidt, Zissler, Sander & Kalthoff, 1975), u.v.-irradiation (Yajima, 1964; Kalthoff & Sander, 1968), temporary ligation (van der Meer, personal communication) and also a certain genotype (Bull, 1966) can evoke the formation of posterior structures at the anterior pole. Frequently, completely mirror-symmetrical embryos are formed with a second abdomen at the anterior end ('double abdomen'). The variety of possible stimuli which can lead to double abdomen formation suggests that this formation reflects a general instability at the anterior pole. Such instability exists in the proposed type of gradient formation, since the inhibitor — produced at the posterior pole - has its lowest concentration at the anterior pole and a small artificial reduction of the inhibitor concentration here may allow the initiation of activator production. If the activator concentration surpasses a critical level (determined by the inhibitor concentration), the further development is independent of the initial influence and a new activator peak will be established. If the activator concentration fails to reach this critical level, the initial disturbance will disappear. Thus the establishment of a new source is an all-or-nothing event, in agreement with Pattern formation in insect embryogenesis 123 ACTIVATOR * INHIBITOR ANT. POST. POST. B FOST. POST. FOST. FOST. Fig. 4. Simulation of the u.v.-irradiation experiments of Kalthoff & Sander (1968), Kalthoff (1971a): formation of posterior structures at the anterior end (see Fig. 1G-1). Ultraviolet treatment is supposed to destroy inhibitor. A cleft in the distribution indicates the time of experimental interference. A, reduction of the inhibitor concentration in the anterior quarter is followed by an increase of the activator to a certain still rather low level which, however, is sufficient for subsequent development into a full activator peak at the anterior pole. A symmetrical inhibitor distribution results in which both ends carry the positional information which is normally found only at the posterior end (double abdomen formation. Fig. 1 G). B, inhibitor reduction by irradiation of the second quarter is without effect, since it is replenished quickly from the source, but the inhibitor reduction in the anterior half (time 2) provokes a very fast formation of the activator peak: the probability of double abdomen formation is increased compared with the treatment shown in A. c, removal of inhibitor at the posterior side produces an overshoot in the activator and consequently in the inhibitor concentration, but all concentrations of the undisturbed steady state are present in the new distribution. A normal embryo can be determined in a more anterior position in the blastoderm as compared to normal development. These increased inhibitor concentrations are able to suppress the formation of a new activator concentration after an irradiation of the anterior quarter (time 2, compare with A). For the numerical constants of this simulation see legend Fig. 10. 124 H. Meinhardt experimental results. As an example we cite the u.v.-irradiation experiments of Kalthoff & Sander (1968), and Kalthoff (1971 a; Kalthoff et al. 1975) with Smittia eggs. Sander (19756) labelled the elements in the embryo asH, 1,2,..., 15, 16, where, for example, H is the head lobe, 5 is the mesothoracic segment, and 16 the most posterior element. The location of the experimental intervention is given in percent egg length (% EL), 100% EL corresponding to the anterior pole, 0% to the posterior pole. The experi- mental results are explained by the model through the assumption that u.v.-irradiation destroys the inhibitor. The individual experiments are explained as follows: (1) Ultraviolet irradiation of the anterior quarter (75-100% EL) induces double abdomen formation (Fig. 1 G). In terms of the model, the reduced inhibitor con- centration at the anterior pole allows the formation of a new activator peak (Fig. 4A). (2) Irradiation of the 50-75 % EL quarter is without effect, but applied in con- junction with a 75-100% irradiation it increases the probability of double abdomen formation considerably in comparison with a 75-100% irradiation. In terms of the model, the reduced inhibitor concentration at 50-75 % is rapidly replenished (Fig. 4B, time 1) from the source at the posterior pole, but when combined with 75-100% EL irradiation, it delays the restoration of the inhibitor concentration at the anterior pole; new activation then occurs more rapidly here than if only the anterior quarter, had been irradiated. The chances are thus improved of reaching the critical activator level before the inhibitor concentration is restored. (3) Irradiation of the posterior pole is - except for 1-2 h delay in development - without dramatic effects. In terms of the model, reducing the inhibitor concentration at the posterior pole leads to an increase in activator production and thus to an overshoot in inhibitor concentration. This has no serious consequences, since all concentrations necessary for the formation of any structure are present. (4) The probability of double abdomen formation being induced by anterior irradiation is reduced by an additional irradiation of the posterior pole (Fig. 1, 1). In terms of the model, the overshoot in inhibitor concentration (above) suppresses activator production at the anterior pole (Fig. 4c, time 2). This model allows a prediction. After ligation at 40% EL and irradiation of the 40—60% EL area, in both parts structures 10-16 should be formed, both in normal orientation. Ligation at 40% and irradiation around 70% should induce 2 separate abdominal structures 10-16/16-10, opposite to each other in the anterior part. The induction of these structures in the anterior portion, however, requires the formation of a new activator peak. The radiation dose required to trigger new activation should decrease with increasing time after the ligation, since the inhibitor in the anterior portion decays (for inhibitor lifetime see legend to Fig. 10, p. 134). Irradiation of the posterior pole is, as mentioned, without drastic effects, but as shown in Fig. 4 c, the reduction of posterior inhibitor concentration is followed by an inhibitor overshoot. The location of any particular inhibitor concentration and thus any particular structure will be shifted in the anterior direction. Such a shift should be detectable by a ligation at the blastoderm stage. Whereas a late ligation at 50% EL of the unirradiated egg shows a separation of the germ band into anterior and posterior fragments around segment 5 (Fig. IB), a posteriorly irradiated egg Pattern formation in insect embryogenesis 125 should show its separation around segment 7-10. Although this effect has not yet been demonstrated in Smittia, Kiithe (1966) found such an anterior shift after posterior irradiation of Dermestes eggs. The view that a reduced inhibitor concentration after u.v.-irradiation is the reason for a new activation is supported by a recent finding of Schmidt et al. (1975). Puncturing of the anterior pole of Smittia eggs can also lead to double abdomen formation. It is reasonable to assume that punctures should cause a local loss of the rapidly diffusing inhibitor; this would then trigger a new activation, just as with local u.v.-irradiation. The induction of a double abdomen by ultraviolet can be suppressed by subsequent irradiation with near u.v. or visible light (Kalthoff, 19716); a substantial time delay between the inducing u.v.-irradiation and the suppressing light irradiation is possible (Kalthoff et al. 1975). In the model, the first small activator increase immediately after the abrupt inhibitor decrease is a fast process, but the following autocatalytic activator increase (peak formation) is time-consuming, especially if the amount of activator produced after u.v.-irradiation is just above the threshold for the activation of a new source (Fig. 4A). We propose therefore that the light irradiation does not reverse the u.v. damage to the inhibitor but blocks the activator production which normally follows and that the activator concentration will then decrease to a sub- threshold value. This view leads to a prediction. Following 50-100% EL irradiation, after which the autocatalytic activator increase is especially rapid, the period in which the 'u.v.-damage' is reversible by visible light should be considerably shortened. We would also predict that the induction of a double abdomen by puncturing is also photoreversible. The process of double abdomen formation can be described in a more quantitative way. Fig. 5 A shows the steady-state concentrations of the activator and the inhibitor in a normal embryo and in a double abdomen embryo with 2 activator peaks. Fig. 5B shows the approximate positions of the segments in the blastoderm, as revealed by post-blastoderm ligation experiments (Fig. IA-C). The parameters for this simulation are determined with simulations of ligation experiments in the cleavage stage (see Fig. 10). If each structure is normally evoked by the corresponding inhibitor concentration, as we have suggested, it is possible to determine from the double abdomen inhibitor profile which structure will be formed at each position. The prediction of the model is given in Fig. 5 c. Both ends form abdominal structures and the segment 8 (or 9) is formed in the middle. This is in substantial agreement with the experimental results. The most direct evidence that the posterior pole inhibits the formation of additional posterior structures has been found in another species (J. van der Meer, private communication). A temporary ligation in the middle of a Callosobruchus maculatus Fabr. egg is sometimes sufficient to induce double abdomen formation. Bull (1966) has isolated a maternal-effect mutant of Drosophila which produces double abdomen spontaneously. Our model would suggest that in this mutant the inhibitor may be less effective than normal or that minor amounts of inhibitor may leak out of the egg, or the basic activator production (p0 in Eq. 1) may be increased. 9 CEL 23 126 H. Meinhardt 1U95 7B-656B5550«483530252O15 10 5% B f H 1 2 3,4,5 6,7,6^10^11 £ g M B K ' 11 12 D M E K Fig- 5- Quantitative evaluation of double abdomen formation, A, activator and inhibitor distribution in the normal ( , ) and the double abdomen embryo (066-, ##-9-). B, the approximate location of the segments is deduced from late blastoderm ligation experiments (Fig. IA-C). If one assumes that each of these segments is evoked by the corresponding inhibitor concentration, the symmetric inhibitor concentration, as it is formed after irradiation, will lead to an arrangement of segments as shown in c, both ends carry posterior structures; the elements in the middle may be enlarged, in agreement with the experiments of Kalthoff & Sander, 1968. Shift of posterior pole material Additional support for the hypothesis of autocatalytic activation in conjunction with long-ranging inhibition can be derived from the experiments of Sander (1959, i960, 1961a, b, 1962, 1968, 1975&) with the egg of the leafhopper Euscelis. Some of his results are summarized in Fig. 6. The egg contains a ball of symbiotic bacteria at the posterior pole. Displacing this ball, and with it probably some adherent components of the egg cell, during early cleavage stage changes the further develop- ment in a dramatic way: Shifting the symbionts anteriorly, following ligation just anterior to the shifted material, has one of two consequences for the development in the posterior part. In some cases an abdomen is formed at the original position and a second one with reversed polarity at the new location of the pole material (Fig. 6E). In the other case a single abdomen with reversed polarity is determined at the new position of the pole material (Fig. 6F). In this case the total number of segments formed is less than would be formed if only the ligation had been made and the abdomen had thus been formed with a normal orientation (Fig. 6 c). In both these cases that portion of the egg anterior to the ligation forms only extra- embryonic material. However, if the ligation is made so that the anterior part contains the pole material (Fig. 6G), or if some time passes between shifting of the pole material and ligation of the egg, the anterior part contains the complete embryo (Fig. 61) or a considerable portion of it (Fig. 6H). Pattern formation in insect embryogenesis 127 Anterior Posterior 100% 0% 35% 10% 30% CL (^H-2 44f) H-16 L) ( H-16 5-16) 35% 50% 40% CL/BL H-2 7-16) f 16-6-16) ( H-8 16-6) 50% 50% 40% c F s' --NCL /^ CL/BL 7T7 H-16 16-6-16) ( 4-16 -) ( Fig. 6. Schematic drawing of some experimental results with eggs of the leafhopper Euscelis (according to Sander, 1959, 1960, 1961a). The segments are called H (headlobe), I,...,I6, location of the experimental interference is given in percent egg length (% EL), the stage of the operation is indicated (CL = cleavage, BL = blastoderm), the position of posterior pole material, as indicated by the ball of symbiotic bacteria, is given by the black dot. A, a ligation in the blastoderm leads to only a few missing structures. B, more segments are omitted in the posterior part, if the ligation is made at cleavage. C, the same number of elements as in A can be formed in the posterior part if the ligation at cleavage stage is made in a more anterior position. D, normal development can occur if the ligation is made very near to the posterior pole. E, F, a shift of the pole material with the symbionts anteriorly and ligation just anterior to the symbiont ball lead to either 2 abdominal structures (E) or to an abdominal structure in reverse polarity (F). In the latter case fewer segments are made in comparison with ligation experiments, in which the pole material was left in its normal location and the orientation of the abdomen is therefore normal (as in c). G, if the anterior portion contains the pole material, the complete embryo can be formed here. H, 1, if the ligation is made a few hours after the shift of the pole material, the anterior part may develop the complete embryo (1) or the anterior part of it (H), even if the symbionts are located in the posterior portion. The segments in the posterior portion are similarly arranged as found in the experiments represented in E, F. j, schematic drawing of an isolated germ band (according to Sander, 19756); t (telson) is the last element formed which follows in this case segment number 15. 9-2 128 H. Meinhardt INHIBITOR POST. FOST. B F05T. POST . # V ANT. Ligation experiments and the interpretation of positional information A ligation before the cellular blastoderm stage leads in many species to the omission of segments formed in the embryo, e.g. in Smittia and Euscelis (Sander, 1975 ft, 1959) as shown in Figs, ID-F, 6B, in Bruchidius (Jung, 1966), Calliphora (Nitschmann, 1959) and Protophormia (Herth & Sander, 1973). The last authors proposed as a possible explanation the accumulation of a controlling substance on one side and a depletion on the other side of the ligation. The influence of a ligation on the activator and inhibitor distribution is shown in Fig. 8 A. Whereas the activator distribution is nearly unchanged, the inhibitor increases on the activated side and drops on the other; thus a concentration dis- continuity in the inhibitor distribution appears. Reopening of the ligation (time 2 in Fig. 8 A) restores the normal gradient almost immediately, in agreement with the Pattern formation in insect embryogenesis 131 with the time elapsed between ligation and cellular blastoderm formation, no anterior structures are omitted even if the ligation is performed 15 h prior to blastoderm formation (Euscelis: Sander, i960; see Fig. 6 A, B). In this experiment, a particular cell group appears as determined if located in the anterior part after a ligation, but if located in the posterior part, the determination appears still labile. This cannot be explained on the basis of a morphogen gradient alone. To account for this result, I propose that the determination of the cells (or nuclei with their plasma environment) is not a one-step process but consists of a sequence of steps which corresponds to the antero-posterior sequence of structures formed in the embryo. I propose that all cells begin in a determination state corresponding to the most anterior structure formed, the extraembryonic membrane, and that the determination of any other structure involves passing irreversibly through all the lower (more anterior) levels of determination until the final level of determination controlled by the local morphogen concentration is reached. If at a later time the morphogen concentration increases due to an experimental intervention, the level of determination can also increase ('distalization') but if the morphogen concen- tration decreases, the determination stays unchanged. A lowering of the morphogen concentration then reveals the level of determination which the system had already attained before intervention. These considerations are incorporated into the formalism assuming that the level of determination Y proceeds at a constant rate as long as Y is lower than the inhibitor concentration (positional information) but remains unchanged if Y is higher (homeo- stasis): t = d (iftf > Y), (3 a) Y = o (if H < Y). (36) A molecular mechanism to effect this could be constructed on the basis of the idea (which will not be discussed here in detail) that the inhibitor drives a biochemical oscillation of an enzyme capable of advancing the determination. Each oscillation maximum corresponds to one step in the determination. The drive of the inhibitor is counteracted by a product increasing with the level of determination. The oscillation will thus come to rest at a level of determination correlated with the inhibitor (morphogen) concentration. The time required for a determination step may be quite long, measurable in hours. For example, a Euscelis egg, ligated at 40% EL at the syncytial blastoderm stage forms segments 4-16 in the posterior part, while, if the ligation is performed 6 h earlier, only segments 5-16 are formed; that is, the only extra omission is segment 4. The accumulation of morphogen following a ligation cannot require such a long period. If it did, it would be impossible to establish a gradient in reasonable time. Instead, it appears necessary to assume that adaptation of the level of determination to the elevated morphogen concentration is the rate-limiting process, perhaps because a step upward in the determination requires cell (or nuclear) division. Only if sufficient time is available between the ligation and the late blastoderm stage - when the 132 H. Meinhardt determination of the cell is fixed - is the number of segments omitted determined solely by the new inhibitor concentration profile. Counce (1973, p. 128) has summarized a set of experiments as follows: 'Sur- prisingly, head enlargement is typical of embryos lacking all abdominal and some or all thoracic segments'. According to the model, removal of posterior parts eliminates the activated source. Head enlargement will appear if the passing through of the levels of determination is not completely synchronous but more advanced in the more posterior parts. This can arise due to an earlier generation of a high morphogen concentration at the posterior pole or because the speed of passing through the determination levels depends to some extent on the actual difference between the morphogen concentration and the level of determination. If then, in an experiment, the source is removed and the morphogen concentration decreases before the final determination levels are reached, the attained levels of determination remain un- changed. The result would be that the points of transition from one state of deter- mination to the next would have a larger physical distance from one another, or, in other words, the elements will be enlarged. The phenomenon of head enlargement indicates that no separate size-regulation mechanism for the formation of the individual segments is at work, but that the segments are the direct consequence of interpretation of the positional information. Some of the experimental observations, which would be extremely difficult to account for in any static gradient model, can be explained in a rather straightforward manner by the catalytic model. A comparison of Fig. 8 A and B shows that the inhibitor concentration quickly finds a new steady state after a ligation in the middle of the egg. However, after a ligation close to the activated source, the inhibitor accumulates considerably in the posterior portion and this has a pronounced negative feedback on the activator production (Fig. 8B, Fig. 9) and consequently on the inhibitor itself. Therefore, if a ligation close to the posterior pole is made late, the determination may have enough time to adapt to the increased inhibitor concentration (positional information). If, however, the ligation is made earlier, there will be enough time for the negative feedback effect and the inhibitor will already have attained the lowered concentration at the moment at which the level to which the determination will proceed is decided. Therefore, contrary to the situation after ligation in the middle of the egg (see for instance Figs, IB, E; IOC, E), late ligation close to the posterior end will lead to a partial embryo in the posterior portion, beginning with a more posterior structure (Fig. 9F) as compared with early ligation at the same location (Fig. 9E). These considerations are supported by the experi- mental observations of Jung (1966). The results of ligations very near the posterior pole can depend very strongly on its exact position. Seidel (1929) found in Platycnemis that a ligation at 10% EL or less (3-5 units in Seidel's paper) leads to normal development in the anterior part, but a constriction at 15% EL, only slightly more anteriorly, gives no development here. Sander (1959) obtained similar results in Euscelis. In terms of the model, ligation so very near the activated area can bring some activated plasma in the anterior part which, due to the autocatalytic nature of the activator, then forms a Pattern formation in insect embryogenesis W u o u t- •»- > + t BC H 1 2 3 4 5 £ 8 12 14 K cC 8 » 12 14 K Df 12 14 K Ef FT 1 14 Fig. 9. The accumulation of inhibitor in the posterior part after a ligation should lead to a shift of the structures toward more anterior positions. For ligations close to the posterior pole, this effect will be partly compensated for by the negative feedback of accumulating inhibitor on the activator, and consequently on itself. Therefore, the shift of structures in the posterior part towards more anterior positions after ligation close to the posterior pole is smaller if an inhibitor-controlled autocatalytic source is involved. In contrast, a larger shift would occur, if a source is present which produces the morphogen at a constant rate. The calculation simulates the experiments of Jung (1966) with Bruchidius. A, activator ( ) and inhibitor ( ) distribution (positional information) in the undisturbed egg and after ligation at 70, 50 and 35 % EL (the curves are marked o, 1, 2). B, position of the segments in a Bruchidius egg, deduced from late blastoderm ligation. The experiment of Jung (1966) indicates that the abdominal segments require half as much space in the blastoderm as compared with the other segments. C-E, positions of the elements in the posterior portion after a ligation at 70, 50 and 35 % EL, respectively. F, the assumption of a constant source - the positional information is given in A in curve 3 - would lead to segment 14 as the first posterior element. This simulates late ligation - where the feedback effect cannot come into play — but early ligation shows the results given in E. normal activator peak and restores the inhibitor gradient (Fig. 8B). If ligation is made just a little further away from the activator peak, the residual amount of activator included in the anterior portion is too little to overcome the basic inhibitor concentration. The (small) basic activator (p0, Eq. 1) and inhibitor (plt Eq. 2) productions are unimportant for normal development, but decisive for development in the 134 H. Meinhardt iaBa638858B757B6560555B4S483530252ei5 B( H|6|7B|3i»|UiEigi14|Bi>6|) C( D( H[l| 2 3 1 2 3 4 S| 8 9 g U E g M E >6 ) IBB 36 38 85 SB 75 7B 65 60 55 50 45 40 35 SB 25 20 15 10 5% EL HHHH 1 234 56 7 [H H H H 1 234567 8 3 BUEgKEK HHH H 1 | g 7 B 3 BU Eg 14 S L( [ HHH H 125 458 76 3 MUBBMBK Is,14. g . > Fig. io. Quantitative results of the model calculation for the experiments with Smittia (A-F) and Euscelis eggs (G-M) (for the summary of the experimental results, see Fig. i and Fig. 6). For calculation of the normal and experimentally disturbed activator and inhibitor distributions, Eq. i and 2 were used; the simulation of the irreversible stepwise determination is based on Eq. 3. Determination of the position of the segments is shown in more detail in Fig. 5. A, approximate location of segments in the blastoderm stage of a Smittia egg. B-D, ligation at the cleavage stage leads to omission of segments; the head region may be enlarged. Which segment is actually omitted depends on the location of the ligation. E, few, if any, segments are missing after a ligation at the blastoderm stage. F, double abdomen formation, as shown in Fig. 5. G, approximate location of the segments in the blastoderm stage of an Euscelis egg, segments are assumed to be of equal size; the head lobe seems to occupy a larger region in the blastoderm, therefore a larger portion is assigned to form the head (HHHH). H-K, results of early ligation at different locations. Whereas after ligation at the blastoderm stage at 45 % EL the posterior part contains the complete embryo, early ligation has to be placed at 55—60 % EL (H) to obtain this result (since the inhibitor accumulates). Pattern formation in insect embryogenesis 135 anterior portion after ligation when no inhibitor can diffuse into the anterior part. If px is small and p0 is larger, a new activation can be formed spontaneously. An example is the double abdomen formation in Callosobruchus maculatus Fabr. (Van der Meer, personal communication). If px is sufficiently high, such activation is suppressed. The structures formed depend on how far the determination has already proceeded (e.g. Smittia) and if the anterior portion of the blastoderm develops without experimental interference extra-embryonal, it will also do so after ligation (e.g. Euscelis). But artificial lowering of the inhibitor by u.v.-irradiation or puncture can induce, as in Smittia, a second activation (double abdomen). If p0 is low, as presumably it is in Euscelis, no such unspecific induction is possible. DISCUSSION The model contains 2 essential assumptions: (i) A morphogen source is activated at the posterior pole by autocatalysis and long-range inhibition. The inhibitor itself or some other substance produced by the autocatalytic substance acts as a morphogen. (ii) Determination proceeds stepwise and irreversibly until it corresponds to the level of the morphogen concentration. These 2 assumptions are sufficient to account for the experiments with different species. A quantitative description can be given for the omissions of segments as a function of the location and time of the ligation (Fig. 10B-E, H-K), for the segments formed after induction of posterior structures at the anterior end by u.v.-irradiation (Fig. IOF) and after the shift of posterior pole material (Fig. IOL, M). A unidirectional, sequential determination similar to the one we propose in the interpretation of a gradient is found also in another context. It was proposed that 1, in early ligation at 35 % the head appears as determined in the anterior part, but segments are omitted in the posterior part. J-K, the result of an early ligation near the posterior pole depends strongly on its precise position. If enough activator is included in the anterior portion, regeneration of the gradient occurs and the complete embryo is formed (K), or, if not, only head and thoracic structures (possibly enlarged) are built (j). L, M, shift of the pole material to anterior positions and ligation just anterior to the pole material can lead, in the posterior portion, either to reversal of polarity and fewer elements being made (L) compared with the situation shown in I, or to the production of abdominal structures at both ends of the posterior fragment (M). If some time has elapsed between the shift and the ligation, the anterior part can contain a complete embryo (M). The simulations are in agreement with the experiments of Sander & Kalthoff (see Figs. 1, 6). The following constants in Eq. 1, 2 and 3 were used for the simulation of the Smittia (Euscelis) experiments: c = o-oi; ju, = o-oi; Da = 001 (0-005); p0 = o-ooi (o-o); v = 0-015; DK = 0-4 (02); Pi = 0-004 (0001); d = 0-012. Irra- diation is supposed to reduce the inhibitor concentration in the irradiated area to 5%. The total area was divided into 2r elements, intermediate inhibitor concen- trations are obtained by linear interpolation. If the 500 iterations used correspond to 10 h (30 h) of development and the egg length is 0-21 mm (i-omm), the inhibitor diffusion rate would be 5-5 x io~B (2-3 x io~8) cm'/s, the inhibitor life time would be 0-92 h (2-7 h). 136 H. Meinhardt regeneration of insect legs (Bohn, 1970), of imaginal disks (Bryant, 1971) or of chick limb buds (Summerbell et al. 1973) can occur only unidirectionally (say ' downwards'). It is tempting to speculate that similar mechanisms may be involved both in the interpretation of a gradient and in regeneration. Maintenance of a once-obtained determination level after removal of the organizing zone of polarizing activity has been found also in the development of chick limbs (Tickle, Summerbell & Wolpert Locke (1959) and Lawrence et al. (1972) explained observations of the ripple pattern in the cuticle of Rhodnius by a repetitive gradient within each segment. Consequently, the segment borders seem to be impermeable for the morphogen. Locke (1959) has shown by grafting small pieces of cuticle that an anterior portion of the cuticle can adapt more easily to a more posterior environment than vice versa. This indicates that determination within a segment obeys rules similar to those governing the process of segment determination, and it is thus tempting to assume that organization within the segments is essentially a repetition of the primary pattern formation process, as has been proposed already by Sander (1975 a). Lawrence (1973) has demonstrated the formation of segment borders in the blastoderm stage of Oncopeltus. Cells visualized by irradiation-induced markers, cannot cross segment borders, although they can move within the segments. It would be interesting to determine whether the segment borders are established one after another in antero-posterior direction as suggested by the given arguments. The formation of segment borders - impermeable for certain substances — may be the prerequisite for the organization of the dorso-ventral dimension. A gradient of the proposed type has the tendency to orient itself so that the largest possible extension is obtained; this is, at the beginning of the insect's development, certainly the antero-posterior dimension. But after subdivision of the egg length into at least 16 segments, the individual segment has a small antero-posterior length compared with the dorso-ventral extension and an additional gradient can be formed dorso- ventrally. The antero-posterior gradient within a segment can nevertheless be con- served if the primary gradient has a strong polarizing effect or sources and sinks are fixed with the formation of segment borders. Krause (1935) and Sander (1971) have shown by longitudinal ligation of Tachycinis or Euscelis eggs, respectively, that indeed the dorso-ventral organization of the embryo is fixed only after the blastoderm stage. Gierer (1976) has proposed a mechanism for the organization of a second dimension using anisotropic diffusion of a morphogen. The anisotropy is obtained from a polarization of each cell by a primary gradient. The situation in insects seems to be similar, except that the anisotropy arises from the very different extensions of the 2 dimensions in the segment. Kauffman (1973, 1975) has proposed a model for the transdetermination of imaginal disks (for review see Gehring & Nothiger, 1973). Each combination of the states of the postulated 4 bistable control circuits corresponds to a possible state of determination of an imaginal disk. Transdetermination [is explained as the accidental switching of one or several control circuits. Segment determination and imaginal disk determination may have a common basis, since both occur during Pattern formation in insect embryogenesis 137 blastoderm formation or shortly thereafter, but, up to now, no simple correspondence between the on-off positions of Kauffman's control circuits within the blastoderm and the proposed gradient has been obvious. In principle, the long-range inhibition can also arise from depletion of a substrate which is consumed during activator production. However, the unspecific induction of a secondary morphogen source by u.v.-irradiation or puncture strongly suggests the existence of a real inhibitor, since these treatments can only remove a substance and only the removal of an inhibitor can lead to an activation. Biochemical isolation of the activator and inhibitor that we envisage is certainly a difficult task, but an understanding of the interactions of the 2 substances, such as our model provides, could help significantly in the design of appropriate assays. The same type of reactions - short-range autocatalysis and lateral inhibition — are presumably involved in different biological pattern formation processes such as regeneration of hydra heads (Gierer & Meinhardt, 1972, 1974) and formation of vascular structures (Meinhardt, 1976), for example of leaves. 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