a model of pattern formation in insect embryogenes1s · 2005. 9. 5. · pattern formation in insect...

J. Cell Set. 33, 117-139 (i977) 117Printed 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 shortdiffusion range - the activator - and its more diffusible antagonist - the inhibitor - leads toa local high concentration of activator at the posterior pole of the egg. The inhibitor, whichis then produced mainly in this activated region, diffuses into the rest of the egg, where itacts as a ' morphogen ', forming a concentration gradient which supplies positional information.

This model can account quantitatively for the patterns resulting from a large number ofdifferent experiments performed during early insect development, including ligation, u.v.-irradiation and microsurgical manipulations. The formation of additional posterior structuresis interpreted as the result of the appearance of a new activator peak. Omission of segmentsafter 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 orderto account for certain quantitative features of the ligation experiments it is necessary to assumethat determination in response to the morphogen gradient is a slow, stepwise process, inwhich the nuclei or cells first pass through determination stages characteristic for moreanterior structures until they ultimately form a given structure.

The mutual interactions of activator and inhibitor are expressed as a set of partial differentialequations. The individual experiments are simulated by solving these equations by use ofa computer.

INTRODUCTION

The development of an organism from a comparatively unstructured egg is acomplex 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). Theseattempt to explain aspects of normal development and results of experimentalmanipulation as the consequences of a simple underlying process.

The developing insect embryo is a very convenient organism for studying embryonicorganization for several reasons: the resulting embryo can often be treated to a goodapproximation as a linear array of structures (headlobe, thoracic and abdominalsegments); and a large number of experiments have been published which showthat 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 differentlyto similar manipulations, but it is likely that the underlying basic mechanism issimilar. These experimental data offer an excellent opportunity for testing anymodel. Some results of Sander, Kalthoff and co-workers (Sander, 19756) are sketched

n 8 H. Meinhardt

in Fig. i in order to give an impression of the range of phenomena which a modelmust 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 theegg and further, that the local concentration of this substance determines thedifferentiation pathway of individual cells or cell groups. The intention of thispaper is to show that the published experiments are indeed quantitatively compatiblewith the response of cells to one graded substance and further, to suggest how sucha gradient could be formed and maintained. Some inferences are also drawn as tohow cells measure the local gradient level.

Anterior Posterior100% 0%

60% 6 0 %

(H-1 3-16 JBL

7-16 JCL

50% 50%

'QiBL s*- I -v. CL H ^ - ~-N

( H - 2 10-16^) =f 16-8-16 J)C L

4 0 % 4 0 %c / - "^v BL

T H-7 9-16^) H-2 12-16)CL I

H-16

Fig. i. Results of constriction and irradiation experiments with Smittia eggs (afterSander, 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 firstand last element in each part are designated by numbers, the dash indicates that allelements 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 madeduring the late cellular blastoderm stage (BL) at most one element is missing; thecells appear as already determined - the egg behaves as a mosaic. The segmentaffected by the ligation allows one to estimate the location of that segment in theblastoderm stage. Segments 2, 5, 8 must therefore be located roughly at 60, 50 and40 % EL, respectively, D-F, a ligation made earlier, in the cleavage stage (CL), leadsto 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 Structuresat the anterior pole, a symmetrical arrangement of segments is formed with anabdomen at each end ('double abdomen')- 1, irradiation of the posterior polereduces the probability that irradiation of the anterior pole will induce a doubleabdomen.

THE MODEL

Basic phenomena of insect development

Before describing the model and the experiments which it explains, it is necessaryto introduce a few facts about insect development. After fertilization of the egga set of synchronous divisions of the nuclei takes place (cleavage). The nuclei thenmigrate 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 thecells is fixed. The interesting period in which the cells 'learn' which cell type theymust develop into is therefore the interval between egg deposition and the completionof the blastoderm. In a later stage, a portion of the blastoderm cells form the 'germband', 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 morphogenis produced by a localized source at one pole of an egg and is broken down throughoutthe egg cytoplasm. The concentration gradient is necessarily shallow at the egg

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120 H. Meinhardt

or depend on temperature. The gradient thus provides relatively specific positionalinformation independent of a range of possible disturbing factors only in the internalregion (Fig. 2). Indeed, it appears that only a certain internal portion betweenthe 2 ends of an insect egg is used for the formation of the embryo proper, the restdevelops extraembryonally. Ligation in the middle of the post-blastoderm egg ofEuscelis (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 approximately12 and 65% EL (% EL = percent egg length, 0% = posterior pole) participatesin germ band formation and that the source (Seidel's 'Bildungszentrum', theactivation centre) is located within the posterior tenth of the egg and thereforeoutside of the embryo proper.

The fraction of the blastoderm used for embryo formation varies considerablyamong different insect species (see Krause, 1939). There seems to be a correlationbetween the fraction of the blastoderm used for embryo formation and the precisionwith which the egg length is regulated. Those insects which use a large part of theegg length show low variability in egg length, e.g. in Smittia roughly 70% of theblastoderm is used, the variability is less than 10 %, while in Euscelis less than45% is used and the variability is 25% (Sander, 1959). If only a small part of thegradient 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 singlemorphogen source, that only a portion of the gradient is used to determine allstructures of the embryo, and that through later growth the embryo comes tooccupy the total available egg space. This source has to be located at the posteriorpole. Conversely, additional posterior structures formed in abnormal positions asa result of experimental manipulation can be interpreted as the result of the activationof 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 substanceswithin tissues. The theory is based on the kinetics of molecular reaction and move-ments. According to the theory, a typical, relatively simple model employs twosubstances. Substance A - the activator - stimulates its own production (auto-catalysis) and also the production of the antagonist - the inhibitor, H. The inhibitordiffuses faster than the activator. In an extended area a homogeneous activator-inhibitor distribution is unstable, since any small local increase of the activatorconcentration is amplified. The inhibitor, which is produced in response to theincreased activator concentration, diffuses away and suppresses activator productionoutside the activated area, while, at the activated site, the activator concentrationwill increase via autocatalysis. This local activator concentration increase will con-tinue until, for instance, the loss by diffusion is equal to the net production. Theactivator distribution will show a relatively sharp concentration peak, whereas the


more diffusible inhibitor will form a broader peak. The activitator and inhibitorprofiles are stable, although both substances continue to be made, to diffuse, andto be broken down. When such a steady state is reached, the inhibitor is madepredominantly 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 orenvironmental asymmetries. Only one peak of activity develops at one of the endsif the size of the system is of the order of the activator range (Meinhardt & Gierer,

Iwuzou

Oti

Fig. 3. The generation of a graded distribution of a substance which may act asmorphogen. 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 activatorpeak activates local inhibitor production. The inhibitor has a graded distributionover the total area and is supposed to supply positional information. In a growingfield, 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 thegrowing oocyte before egg deposition. Polarity is determined by the asymmetricenvironment of the oocyte. A final pattern as shown is used in the other simulationsas the initial condition before experimental manipulations are taken into account.Microsurgical experiments (Seidel, 1929) suggest that the source is activated atthe posterior pole of the insect egg.

1974). If the field is then allowed to grow, the activator peak remains at its initialpole. (Growth in an asymmetric environment resembles closely the condition duringoogenesis; for review see Mahowald, 1972.) This is demonstrated in Fig. 3. Whena growing field becomes very large, the inhibitor diffusing from the activated polemay no longer suffice to suppress the formation of a second activator peak at theunactivated pole. The spontaneous formation of a second activator peak can beprevented, 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 ofnumerical solutions of these equations.

A = cA2jH-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 autocatalyticterm (A2); the autocatalysis is slowed with increasing inhibitor concentration (iJH);A decays in a first-order reaction ( — /iA) and diffuses (DaAA). A (small) basicactivator production remains even if no activator is present (pQ). Eq. 2 implies thatthe change of H per time unit (H) is a function of the cross-catalytic influence ofthe activator (A2), of the decay (— vH) and of the diffusion (Dh AH). The regenerationof a high activator concentration after the removal of an existing activator maximumcan be suppressed by a small activator-independent inhibitor production (px). Formore 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 satisfiesthe condition of being activator controlled - provides 'positional information'(Wolpert, 1969) in the developing egg. The differentiation pathway of a cell iscontrolled by the local inhibitor concentration. In other words, a particular structureis formed over a particular range of inhibitor concentration. An example of thecorrespondence between the inhibitor concentration and the structures formed willbe given in Fig. 5 A and B. If the gradient is abnormal as a result of experimentalmanipulations, we can use the same correspondence to predict what pattern ofstructures will be formed.

Formation of additional abdominal structures at the anterior pole - the activation of anew 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 structuresat the anterior pole. Frequently, completely mirror-symmetrical embryos are formedwith a second abdomen at the anterior end ('double abdomen'). The variety ofpossible stimuli which can lead to double abdomen formation suggests that thisformation reflects a general instability at the anterior pole. Such instability existsin the proposed type of gradient formation, since the inhibitor — produced at theposterior pole - has its lowest concentration at the anterior pole and a small artificialreduction of the inhibitor concentration here may allow the initiation of activatorproduction. If the activator concentration surpasses a critical level (determined bythe inhibitor concentration), the further development is independent of the initialinfluence and a new activator peak will be established. If the activator concentrationfails to reach this critical level, the initial disturbance will disappear. Thusthe establishment of a new source is an all-or-nothing event, in agreement with


ACTIVATOR * INHIBITOR

ANT.

POST. POST.

B

POST. FOST.

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 distributionindicates the time of experimental interference.

A, reduction of the inhibitor concentration in the anterior quarter is followed byan increase of the activator to a certain still rather low level which, however, issufficient for subsequent development into a full activator peak at the anteriorpole. A symmetrical inhibitor distribution results in which both ends carry thepositional information which is normally found only at the posterior end (doubleabdomen formation. Fig. 1 G).

B, inhibitor reduction by irradiation of the second quarter is without effect, sinceit is replenished quickly from the source, but the inhibitor reduction in the anteriorhalf (time 2) provokes a very fast formation of the activator peak: the probabilityof 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 activatorand consequently in the inhibitor concentration, but all concentrations of theundisturbed steady state are present in the new distribution. A normal embryocan be determined in a more anterior position in the blastoderm as compared tonormal development. These increased inhibitor concentrations are able to suppressthe formation of a new activator concentration after an irradiation of the anteriorquarter (time 2, compare with A). For the numerical constants of this simulationsee 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.-irradiationdestroys the inhibitor. The individual experiments are explained as follows:

(1) Ultraviolet irradiation of the anterior quarter (75-100% EL) induces doubleabdomen 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 abdomenformation considerably in comparison with a 75-100% irradiation. In terms of themodel, 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% ELirradiation, it delays the restoration of the inhibitor concentration at the anteriorpole; 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 activatorlevel 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 concentrationat the posterior pole leads to an increase in activator production and thus to anovershoot in inhibitor concentration. This has no serious consequences, since allconcentrations necessary for the formation of any structure are present.

(4) The probability of double abdomen formation being induced by anteriorirradiation is reduced by an additional irradiation of the posterior pole (Fig. 1, 1). Interms of the model, the overshoot in inhibitor concentration (above) suppressesactivator production at the anterior pole (Fig. 4c, time 2).

This model allows a prediction. After ligation at 40% EL and irradiation of the40—60% EL area, in both parts structures 10-16 should be formed, both in normalorientation. Ligation at 40% and irradiation around 70% should induce 2 separateabdominal structures 10-16/16-10, opposite to each other in the anterior part. Theinduction of these structures in the anterior portion, however, requires the formationof a new activator peak. The radiation dose required to trigger new activation shoulddecrease with increasing time after the ligation, since the inhibitor in the anteriorportion decays (for inhibitor lifetime see legend to Fig. 10, p. 134).

Irradiation of the posterior pole is, as mentioned, without drastic effects, but asshown in Fig. 4 c, the reduction of posterior inhibitor concentration is followed byan inhibitor overshoot. The location of any particular inhibitor concentration andthus any particular structure will be shifted in the anterior direction. Such a shiftshould be detectable by a ligation at the blastoderm stage. Whereas a late ligationat 50% EL of the unirradiated egg shows a separation of the germ band into anteriorand posterior fragments around segment 5 (Fig. IB), a posteriorly irradiated egg


should show its separation around segment 7-10. Although this effect has not yetbeen demonstrated in Smittia, Kiithe (1966) found such an anterior shift afterposterior irradiation of Dermestes eggs.

The view that a reduced inhibitor concentration after u.v.-irradiation is the reasonfor 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 abdomenformation. It is reasonable to assume that punctures should cause a local loss of therapidly diffusing inhibitor; this would then trigger a new activation, just as withlocal u.v.-irradiation.

The induction of a double abdomen by ultraviolet can be suppressed by subsequentirradiation with near u.v. or visible light (Kalthoff, 19716); a substantial time delaybetween the inducing u.v.-irradiation and the suppressing light irradiation is possible(Kalthoff et al. 1975). In the model, the first small activator increase immediatelyafter the abrupt inhibitor decrease is a fast process, but the following autocatalyticactivator increase (peak formation) is time-consuming, especially if the amount ofactivator produced after u.v.-irradiation is just above the threshold for the activationof a new source (Fig. 4A). We propose therefore that the light irradiation does notreverse the u.v. damage to the inhibitor but blocks the activator production whichnormally 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 inwhich the 'u.v.-damage' is reversible by visible light should be considerablyshortened. We would also predict that the induction of a double abdomen bypuncturing is also photoreversible.

The process of double abdomen formation can be described in a more quantitativeway. Fig. 5 A shows the steady-state concentrations of the activator and the inhibitorin 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, asrevealed by post-blastoderm ligation experiments (Fig. IA-C). The parameters forthis simulation are determined with simulations of ligation experiments in thecleavage stage (see Fig. 10). If each structure is normally evoked by the correspondinginhibitor concentration, as we have suggested, it is possible to determine from thedouble 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 structuresand the segment 8 (or 9) is formed in the middle. This is in substantial agreement withthe experimental results.

The most direct evidence that the posterior pole inhibits the formation of additionalposterior structures has been found in another species (J. van der Meer, privatecommunication). A temporary ligation in the middle of a Callosobruchus maculatusFabr. egg is sometimes sufficient to induce double abdomen formation.

Bull (1966) has isolated a maternal-effect mutant of Drosophila which producesdouble abdomen spontaneously. Our model would suggest that in this mutant theinhibitor may be less effective than normal or that minor amounts of inhibitor mayleak out of the egg, or the basic activator production (p0 in Eq. 1) may be increased.

9 CEL 23

126 H. Meinhardt

1U95 7 B - 6 5 6 B 5 5 5 0 « 4 8 3 5 3 0 2 5 2 O 1 5 10 5 %

B f H 1 2 3 , 4 , 5 6 , 7 , 6 ^ 1 0 ^ 1 1 £ g M B K '

11 12 D M E K

Fig- 5- Quantitative evaluation of double abdomen formation, A, activator andinhibitor distribution in the normal ( , ) and the double abdomen embryo(066-, ##-9-). B, the approximate location of the segments is deduced from lateblastoderm ligation experiments (Fig. IA-C). If one assumes that each of thesesegments is evoked by the corresponding inhibitor concentration, the symmetricinhibitor concentration, as it is formed after irradiation, will lead to an arrangementof segments as shown in c, both ends carry posterior structures; the elements inthe 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 conjunctionwith 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 ofhis results are summarized in Fig. 6. The egg contains a ball of symbiotic bacteriaat the posterior pole. Displacing this ball, and with it probably some adherentcomponents of the egg cell, during early cleavage stage changes the further develop-ment in a dramatic way: Shifting the symbionts anteriorly, following ligation justanterior to the shifted material, has one of two consequences for the developmentin the posterior part. In some cases an abdomen is formed at the original positionand 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 determinedat the new position of the pole material (Fig. 6F). In this case the total number ofsegments formed is less than would be formed if only the ligation had been madeand the abdomen had thus been formed with a normal orientation (Fig. 6 c). Inboth 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 containsthe pole material (Fig. 6G), or if some time passes between shifting of the polematerial and ligation of the egg, the anterior part contains the complete embryo(Fig. 61) or a considerable portion of it (Fig. 6H).


Anterior Posterior100% 0%

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H-16 L) ( H-16 5-16)CL

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Fig. 6. Schematic drawing of some experimental results with eggs of the leafhopperEuscelis (according to Sander, 1959, 1960, 1961a). The segments are called H(headlobe), I , . . . , I 6 , location of the experimental interference is given in percentegg length (% EL), the stage of the operation is indicated (CL = cleavage,BL = blastoderm), the position of posterior pole material, as indicated by the ballof 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 anabdominal structure in reverse polarity (F). In the latter case fewer segments aremade in comparison with ligation experiments, in which the pole material was leftin 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 beformed here.

H, 1, if the ligation is made a few hours after the shift of the pole material, theanterior part may develop the complete embryo (1) or the anterior part of it (H), evenif the symbionts are located in the posterior portion. The segments in the posteriorportion 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 .

ANT.


Our model can explain these results if posterior pole material shifted with thesymbionts is able to trigger the formation of a new source, perhaps because someactivator-containing material sticks to the symbiont ball. Once the activator hasexceeded a critical concentration, further development of an activator peak isindependent of the pole material. A simulation of the experiments shown in Fig. 6E,F, H is illustrated in Fig. 7. If some activator-containing material is shifted, boththe remaining and the shifted activator can develop full activator peaks. The resultinginhibitor distribution has a concentration which specifies terminal structures atboth ends of the ligated posterior section of the egg (Fig. 7 A; for quantitativeevaluation see Fig. 10). If relatively more material is shifted, the new activator peakcan win the competition with the old one (Fig. 7B); only the abnormally situatednew peak survives. The inhibitor remaining from the suppressed original activatorpeak makes the slope of the inhibitor distribution shallower than normal and fewerstructures are thus formed, in agreement with experiment Fig. 6 c, E, F. If theligation is made some time after the shift (Fig. 7 c), the developing secondary activatorpeak spreads out into the anterior part. Minor amounts present in the anterior partafter ligation can develop into a new activator peak, since after the ligation noinhibitor from the posterior part can diffuse into the anterior part. In this case, theinhibitor distribution in the anterior part has a similar shape to that in the undisturbedsystem and a complete embryo can be formed. An interesting detail in this contextis that, in general, the efficiency with which abdominal structures are producedat the site of the shifted material (in the anterior part) increases if the ligation ismade some time after the shift rather than immediately afterwards (Sander, 1968).In terms of the model, activation proceeds faster at the site of the shifted materialif the inhibitor can diffuse away in the, as yet, non-ligated egg.

The autocatalytic property of the model thus provides an explanation for thefact that the morphogen concentration providing positional information for abdominalstructures can be generated in up to 3 places. It explains further, considered togetherwith the lateral inhibition feature, why minor and uncontrollable differences inperforming the experiments can lead to strikingly different but well defined finalpatterns.

Ligation experiments and the interpretation of positional information

A ligation before the cellular blastoderm stage leads in many species to theomission 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 authorsproposed as a possible explanation the accumulation of a controlling substance onone side and a depletion on the other side of the ligation.

The influence of a ligation on the activator and inhibitor distribution is shownin Fig. 8 A. Whereas the activator distribution is nearly unchanged, the inhibitorincreases on the activated side and drops on the other; thus a concentration dis-continuity in the inhibitor distribution appears. Reopening of the ligation (time 2in Fig. 8 A) restores the normal gradient almost immediately, in agreement with the


with the time elapsed between ligation and cellular blastoderm formation, no anteriorstructures are omitted even if the ligation is performed 15 h prior to blastodermformation (Euscelis: Sander, i960; see Fig. 6 A, B). In this experiment, a particular cellgroup appears as determined if located in the anterior part after a ligation, but if locatedin the posterior part, the determination appears still labile. This cannot be explainedon the basis of a morphogen gradient alone.

To account for this result, I propose that the determination of the cells (or nucleiwith their plasma environment) is not a one-step process but consists of a sequenceof steps which corresponds to the antero-posterior sequence of structures formedin the embryo. I propose that all cells begin in a determination state correspondingto the most anterior structure formed, the extraembryonic membrane, and that thedetermination of any other structure involves passing irreversibly through all thelower (more anterior) levels of determination until the final level of determinationcontrolled by the local morphogen concentration is reached. If at a later time themorphogen concentration increases due to an experimental intervention, the levelof determination can also increase ('distalization') but if the morphogen concen-tration decreases, the determination stays unchanged. A lowering of the morphogenconcentration then reveals the level of determination which the system had alreadyattained before intervention.

These considerations are incorporated into the formalism assuming that the levelof determination Y proceeds at a constant rate as long as Y is lower than the inhibitorconcentration (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 biochemicaloscillation of an enzyme capable of advancing the determination. Each oscillationmaximum corresponds to one step in the determination. The drive of the inhibitoris counteracted by a product increasing with the level of determination. The oscillationwill 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 inhours. For example, a Euscelis egg, ligated at 40% EL at the syncytial blastodermstage forms segments 4-16 in the posterior part, while, if the ligation is performed6 h earlier, only segments 5-16 are formed; that is, the only extra omission is segment4. The accumulation of morphogen following a ligation cannot require such a longperiod. 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 determinationto the elevated morphogen concentration is the rate-limiting process, perhaps becausea step upward in the determination requires cell (or nuclear) division. Only if sufficienttime 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 determinedsolely 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 someor all thoracic segments'. According to the model, removal of posterior parts eliminatesthe activated source. Head enlargement will appear if the passing through of thelevels of determination is not completely synchronous but more advanced in themore posterior parts. This can arise due to an earlier generation of a high morphogenconcentration at the posterior pole or because the speed of passing through thedetermination levels depends to some extent on the actual difference between themorphogen concentration and the level of determination. If then, in an experiment,the source is removed and the morphogen concentration decreases before the finaldetermination 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, inother words, the elements will be enlarged. The phenomenon of head enlargementindicates that no separate size-regulation mechanism for the formation of theindividual segments is at work, but that the segments are the direct consequence ofinterpretation of the positional information.

Some of the experimental observations, which would be extremely difficult toaccount for in any static gradient model, can be explained in a rather straightforwardmanner by the catalytic model. A comparison of Fig. 8 A and B shows that theinhibitor concentration quickly finds a new steady state after a ligation in the middleof the egg. However, after a ligation close to the activated source, the inhibitoraccumulates considerably in the posterior portion and this has a pronounced negativefeedback on the activator production (Fig. 8B, Fig. 9) and consequently on theinhibitor itself. Therefore, if a ligation close to the posterior pole is made late, thedetermination may have enough time to adapt to the increased inhibitor concentration(positional information). If, however, the ligation is made earlier, there will beenough time for the negative feedback effect and the inhibitor will already haveattained the lowered concentration at the moment at which the level to which thedetermination will proceed is decided. Therefore, contrary to the situation afterligation in the middle of the egg (see for instance Figs, IB, E; IOC, E), late ligationclose 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 ligationat 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 onits exact position. Seidel (1929) found in Platycnemis that a ligation at 10% EL orless (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 developmenthere. 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 theanterior part which, due to the autocatalytic nature of the activator, then forms a

Pattern formation in insect embryogenesis

W

uou 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 shouldlead to a shift of the structures toward more anterior positions. For ligations closeto the posterior pole, this effect will be partly compensated for by the negativefeedback of accumulating inhibitor on the activator, and consequently on itself.Therefore, the shift of structures in the posterior part towards more anteriorpositions after ligation close to the posterior pole is smaller if an inhibitor-controlledautocatalytic source is involved. In contrast, a larger shift would occur, if a sourceis present which produces the morphogen at a constant rate. The calculation simulatesthe experiments of Jung (1966) with Bruchidius.

A, activator ( ) and inhibitor ( ) distribution (positional information) inthe undisturbed egg and after ligation at 70, 50 and 35 % EL (the curves are markedo, 1, 2).

B, position of the segments in a Bruchidius egg, deduced from late blastodermligation. The experiment of Jung (1966) indicates that the abdominal segmentsrequire 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 and35 % EL, respectively.

F, the assumption of a constant source - the positional information is given in A incurve 3 - would lead to segment 14 as the first posterior element. This simulateslate ligation - where the feedback effect cannot come into play — but early ligationshows the results given in E.

normal activator peak and restores the inhibitor gradient (Fig. 8B). If ligation ismade just a little further away from the activator peak, the residual amount ofactivator included in the anterior portion is too little to overcome the basic inhibitorconcentration.

The (small) basic activator (p0, Eq. 1) and inhibitor (plt Eq. 2) productionsare unimportant for normal development, but decisive for development in the

134 H. Meinhardt

i a B a 6 3 8 8 5 8 B 7 5 7 B 6 5 6 0 5 5 5 B 4 S 4 8 3 5 3 0 2 5 2 e i 5

B ( H | 6 | 7 B | 3 i » | U i E i g i 1 4 | B i > 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 2 3 4 5 6 7

[ H H H H 1 2 3 4 5 6 7 8 3 BUEgKEK

HHH H 1 | g 7 B 3 BU E g 14 S

L(

[ HHH H 1 2 5 458 76 3 MUBBMBK I s , 1 4 . g . >

Fig. io. Quantitative results of the model calculation for the experiments withSmittia (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 disturbedactivator and inhibitor distributions, Eq. i and 2 were used; the simulation of theirreversible stepwise determination is based on Eq. 3. Determination of the positionof 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 theligation.

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 largerregion 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 theblastoderm stage at 45 % EL the posterior part contains the complete embryo, earlyligation has to be placed at 55—60 % EL (H) to obtain this result (since the inhibitoraccumulates).


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 activationis suppressed. The structures formed depend on how far the determination hasalready proceeded (e.g. Smittia) and if the anterior portion of the blastoderm developswithout 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 puncturecan induce, as in Smittia, a second activation (double abdomen). If p0 is low, aspresumably it is in Euscelis, no such unspecific induction is possible.

DISCUSSION

The model contains 2 essential assumptions: (i) A morphogen source is activatedat the posterior pole by autocatalysis and long-range inhibition. The inhibitor itselfor some other substance produced by the autocatalytic substance acts as a morphogen.(ii) Determination proceeds stepwise and irreversibly until it corresponds to thelevel of the morphogen concentration. These 2 assumptions are sufficient to accountfor the experiments with different species. A quantitative description can be givenfor 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 structuresat the anterior end by u.v.-irradiation (Fig. IOF) and after the shift of posterior polematerial (Fig. IOL, M).

A unidirectional, sequential determination similar to the one we propose in theinterpretation 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, butsegments are omitted in the posterior part.

J-K, the result of an early ligation near the posterior pole depends strongly on itsprecise position. If enough activator is included in the anterior portion, regenerationof the gradient occurs and the complete embryo is formed (K), or, if not, only headand thoracic structures (possibly enlarged) are built (j).

L, M, shift of the pole material to anterior positions and ligation just anterior tothe pole material can lead, in the posterior portion, either to reversal of polarityand fewer elements being made (L) compared with the situation shown in I, or tothe 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 cancontain a complete embryo (M).

The simulations are in agreement with the experiments of Sander & Kalthoff (seeFigs. 1, 6). The following constants in Eq. 1, 2 and 3 were used for the simulationof 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 to5 % . The total area was divided into 2r elements, intermediate inhibitor concen-trations are obtained by linear interpolation. If the 500 iterations used correspond to10 h (30 h) of development and the egg length is 0-21 mm (i-omm), the inhibitordiffusion rate would be 5-5 x io~B (2-3 x io~8) cm'/s, the inhibitor life time would be0-92 h (2-7 h).

136 H. Meinhardt

regeneration of insect legs (Bohn, 1970), of imaginal disks (Bryant, 1971) or of chicklimb buds (Summerbell et al. 1973) can occur only unidirectionally (say ' downwards').It is tempting to speculate that similar mechanisms may be involved both in theinterpretation of a gradient and in regeneration. Maintenance of a once-obtaineddetermination level after removal of the organizing zone of polarizing activity hasbeen found also in the development of chick limbs (Tickle, Summerbell & Wolpert

Locke (1959) and Lawrence et al. (1972) explained observations of the ripplepattern 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 portionof 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 thosegoverning the process of segment determination, and it is thus tempting to assumethat organization within the segments is essentially a repetition of the primarypattern formation process, as has been proposed already by Sander (1975 a).

Lawrence (1973) has demonstrated the formation of segment borders in theblastoderm stage of Oncopeltus. Cells visualized by irradiation-induced markers,cannot cross segment borders, although they can move within the segments. Itwould be interesting to determine whether the segment borders are established oneafter another in antero-posterior direction as suggested by the given arguments.

The formation of segment borders - impermeable for certain substances — maybe the prerequisite for the organization of the dorso-ventral dimension. A gradientof the proposed type has the tendency to orient itself so that the largest possibleextension is obtained; this is, at the beginning of the insect's development, certainlythe antero-posterior dimension. But after subdivision of the egg length into at least16 segments, the individual segment has a small antero-posterior length comparedwith 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 arefixed with the formation of segment borders. Krause (1935) and Sander (1971)have shown by longitudinal ligation of Tachycinis or Euscelis eggs, respectively, thatindeed the dorso-ventral organization of the embryo is fixed only after the blastodermstage. Gierer (1976) has proposed a mechanism for the organization of a seconddimension using anisotropic diffusion of a morphogen. The anisotropy is obtainedfrom a polarization of each cell by a primary gradient. The situation in insects seemsto be similar, except that the anisotropy arises from the very different extensions ofthe 2 dimensions in the segment.

Kauffman (1973, 1975) has proposed a model for the transdetermination ofimaginal disks (for review see Gehring & Nothiger, 1973). Each combination of thestates of the postulated 4 bistable control circuits corresponds to a possible stateof determination of an imaginal disk. Transdetermination [is explained as theaccidental switching of one or several control circuits. Segment determination andimaginal disk determination may have a common basis, since both occur during


blastoderm formation or shortly thereafter, but, up to now, no simple correspondencebetween the on-off positions of Kauffman's control circuits within the blastodermand the proposed gradient has been obvious.

In principle, the long-range inhibition can also arise from depletion of a substratewhich is consumed during activator production. However, the unspecific inductionof a secondary morphogen source by u.v.-irradiation or puncture strongly suggeststhe existence of a real inhibitor, since these treatments can only remove a substanceand only the removal of an inhibitor can lead to an activation.

Biochemical isolation of the activator and inhibitor that we envisage is certainlya difficult task, but an understanding of the interactions of the 2 substances, suchas our model provides, could help significantly in the design of appropriate assays.

The same type of reactions - short-range autocatalysis and lateral inhibition — arepresumably involved in different biological pattern formation processes such asregeneration of hydra heads (Gierer & Meinhardt, 1972, 1974) and formation ofvascular structures (Meinhardt, 1976), for example of leaves. The present findingthat with these reactions also a quantitative description of pattern formation ininsect embryogenesis can be given, invites the suspicion that such processes are verygeneral elements in pattern formation.

I am much indebted to A. Gierer, K. Sander, R. Burt and H. MacWilliams for helpfuldiscussions and critical reading of the manuscript.

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{Received 3 June 1976)

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