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This is a reformatted version of an article appeared in Seminars Cell Dev. Biol. 2015 doi:10.1016/j.semcdb.2015.06.005 Models for patterning primary embryonic body axes: the role of space and time Hans Meinhardt Max Planck Institute for Developmental Biology Spemannstr. 35, D- 72076 T¨ ubingen http://www.eb.tuebingen.mpg.de/meinhardt; [email protected] Models for the generation and interpretation of spa- tial patterns are discussed. Crucial for these pro- cesses is an intimate link between self-enhancing and antagonistic reactions. For spatial patterning, long-ranging antagonistic reactions are required that restrict the self-enhancing reactions to gener- ate organizing regions. Self-enhancement is also required for a permanent switch-like activation of genes. This self-enhancement is antagonized by the mutual repression of genes, making sure that in a particular cell only one gene of a set of possible genes become activated - a long range inhibition in the ‘gene space’. The understanding how the main body axes are initiated becomes more straightfor- ward if the evolutionary ancestral head/brain pat- tern and the trunk pattern is considered separately. To activate a specific gene at particular concentra- tion of morphogenetic gradient, observations are compatible with a systematic and time-requiring ‘promotion’ from one gene to the next until the lo- cal concentration is insufficient to accomplish a further promotion. The achieved determination is stable against a fading of the morphogen, as re- quired to allow substantial growth. Minor modifi- cations lead to a purely time-dependent activation of genes; both mechanisms are involved to pattern the anteroposterior axis. A mutual activation of cell states that locally exclude each other accounts for many features of the segmental patterning of the trunk. A possible scenario for the evolutionary in- vention of segmentation is discussed that is based on a reemployment of interactions involved in asex- ual reproduction. Key words: Pattern formation / gene activation / seg- mentation / main body axes / interpretation of gradients Development of a higher organism starts, as a rule with a single cell and proceeds, of course, under the control of genes. Since the genetic material is es- sentially the same in every cell, a central question is how the correct arrangement of differentiated cells is achieved. A most important step on the way from the fertilized egg to an adult organism is the setting up of the primary body axes, anteroposterior (AP) and medi- olateral/ dorsoventral (DV). In this process, organizing regions - small nests of cells that act as sources or sinks of signalling molecules - play an important role. The Spemann organizer is a prominent example. This organizer is usually regarded as the only organizer that exists in vertebrates, raising the question how a sin- gle organizer can specify the cells along the two ma- jor body axes that are oriented perpendicular to each other. Moreover, DV patterning has to occur along the long extended AP axis. This task cannot be accom- plished by a patch-like organizer directly. A local sig- nalling source would lead to a conical positional infor- mation profile with a constant slope into all directions, which is clearly insufficient to specify the DV axis. Mod- els will be discussed that account for the generation and alignment of the main body axes. The formation of organizing regions requires in- teractions in which local self-enhancement and long- range inhibition is involved, discussed in detail else- where [1, 2, 3]. The interaction of the self-enhancing Nodal with the antagonistically acting Lefty is an exam- ple [4, 5]. Such interactions can generate patterns in an initially homogeneous assembly of cells. For em- bryos that start with a large size such as the amphibian embryo, the employment of maternal determinants is an appropriate strategy. By making only a small part of the embryo competent for organizer formation, local- ized determinants only allow a single organizer to be formed. Maternal determinants are not required if de- velopment starts as a small nest of cells such as it is the case in mouse or chick development. In this case, 1

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  • This is a reformatted version of an article appeared in Seminars Cell Dev. Biol. 2015 doi:10.1016/j.semcdb.2015.06.005

    Models for patterning primary embryonic body axes: the role ofspace and time

    Hans MeinhardtMax Planck Institute for Developmental Biology

    Spemannstr. 35, D- 72076 Tübingenhttp://www.eb.tuebingen.mpg.de/meinhardt; [email protected]

    Models for the generation and interpretation of spa-tial patterns are discussed. Crucial for these pro-cesses is an intimate link between self-enhancingand antagonistic reactions. For spatial patterning,long-ranging antagonistic reactions are requiredthat restrict the self-enhancing reactions to gener-ate organizing regions. Self-enhancement is alsorequired for a permanent switch-like activation ofgenes. This self-enhancement is antagonized bythe mutual repression of genes, making sure that ina particular cell only one gene of a set of possiblegenes become activated - a long range inhibition inthe ‘gene space’. The understanding how the mainbody axes are initiated becomes more straightfor-ward if the evolutionary ancestral head/brain pat-tern and the trunk pattern is considered separately.To activate a specific gene at particular concentra-tion of morphogenetic gradient, observations arecompatible with a systematic and time-requiring‘promotion’ from one gene to the next until the lo-cal concentration is insufficient to accomplish afurther promotion. The achieved determination isstable against a fading of the morphogen, as re-quired to allow substantial growth. Minor modifi-cations lead to a purely time-dependent activationof genes; both mechanisms are involved to patternthe anteroposterior axis. A mutual activation of cellstates that locally exclude each other accounts formany features of the segmental patterning of thetrunk. A possible scenario for the evolutionary in-vention of segmentation is discussed that is basedon a reemployment of interactions involved in asex-ual reproduction.

    Key words: Pattern formation / gene activation / seg-mentation / main body axes / interpretation of gradients

    Development of a higher organism starts, as a rulewith a single cell and proceeds, of course, under thecontrol of genes. Since the genetic material is es-sentially the same in every cell, a central question ishow the correct arrangement of differentiated cells isachieved. A most important step on the way from thefertilized egg to an adult organism is the setting up ofthe primary body axes, anteroposterior (AP) and medi-olateral/ dorsoventral (DV). In this process, organizingregions - small nests of cells that act as sources orsinks of signalling molecules - play an important role.The Spemann organizer is a prominent example. Thisorganizer is usually regarded as the only organizer thatexists in vertebrates, raising the question how a sin-gle organizer can specify the cells along the two ma-jor body axes that are oriented perpendicular to eachother. Moreover, DV patterning has to occur along thelong extended AP axis. This task cannot be accom-plished by a patch-like organizer directly. A local sig-nalling source would lead to a conical positional infor-mation profile with a constant slope into all directions,which is clearly insufficient to specify the DV axis. Mod-els will be discussed that account for the generationand alignment of the main body axes.

    The formation of organizing regions requires in-teractions in which local self-enhancement and long-range inhibition is involved, discussed in detail else-where [1, 2, 3]. The interaction of the self-enhancingNodal with the antagonistically acting Lefty is an exam-ple [4, 5]. Such interactions can generate patterns inan initially homogeneous assembly of cells. For em-bryos that start with a large size such as the amphibianembryo, the employment of maternal determinants isan appropriate strategy. By making only a small partof the embryo competent for organizer formation, local-ized determinants only allow a single organizer to beformed. Maternal determinants are not required if de-velopment starts as a small nest of cells such as it isthe case in mouse or chick development. In this case,

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  • the self-regulatory features of pattern-forming reactionsallow complete development in fragments even if theorganizer is removed [6]. The formation of several em-bryos after early fragmentation of a chicken embryo isan example [7].

    The generation of organizing regions requires com-munication between cells. If based on diffusion, therange of this signalling is restricted to short distances.Thus, these patterns can only be generated at smallscales during early stages of development and haveto be converted into a pattern of stable cell determi-nations by activating particular genes. The activities ofthese genes have to be maintained even if the evok-ing signals are no longer available. Complementary tomodels for setting up positional information for the bodyaxes, models for the stable activation of genes underthe influence of the resulting signal distributions will bediscussed. It will be shown that activation of the correctgene at a particular position is a time-requiring process.

    1. Axes formation in two steps: the head andthe trunk

    Understanding of the patterning along the main bodyaxes of vertebrates is much facilitated if it is realizedthat different mechanisms are involved in patterning thehead and in the trunk. This is true for both the pattern-ing along the AP and the DV axes. Several observa-tions suggest that the AP pattern in the brain is undercontrol of a Wnt gradient that is generated at the blasto-pore/marginal zone [8, 9, 10]; (reviewed in [11]). Theregion of forebrain formation has the largest distance tothe blastopore and emerges at a low WNT concentra-tion, suggesting that the forebrain is the default state.Thus, the first steps in the AP patterning of the braincan be regarded as an example where a morphogengradient accomplishes posteriorization by gene activa-tion in a concentration- and thus position-dependingmanner. In contrast, the AP patterning of the trunk isachieved by a sequential posterior elongation. In cellsclose to the blastopore but with the exemption of the or-ganizer region, new Hox genes become activated in asequential way, causing specification of more and moreposterior structures - a time-dependent process [12];(Durston and Zhu, this issue). Although both mecha-nisms overtly look very different, as shown below, mod-elling revealed that gene activation under the influenceof a static gradient has also a strong time-dependentcomponent, suggesting that interpretation of a gradient,e.g., in the brain and the time-dependent posterioriza-tion in the trunk shares common elements.

    Pronounced differences between brain and trunkpatterning also exist for the patterning of the DV axis.For the patterning of amphibian brain it is crucial thatcells derived from the Spemann organizer move under-neath the ectoderm, forming the prechordal plate and

    induce neuronal tissue in the overlying ectoderm [13].The prechordal plate is the precondition to form themidline, the dorsal-most structure from which the dis-tance of the cells is measured, so to say, a referenceline. In contrast, for midline formation of the trunk, cellsnear the blastopore (marginal zone) move towards theorganizer (node), causing a conversion a ring perpen-dicular to the AP axis into a rod-like structure parallel tothe AP axis. This process will be discussed further be-low in more details. The two very different functions ofthe organizer become established very early by a sub-division into a head- and a tail-organizer [14].

    Frequently the Spemann-organizer is assumed toprovide the positional information for organizing the APaxis [14]. In the view of the model proposed, this con-clusion is partially misleading and results from the factthat most AP-markers are absent if the organizer ismissing. However, most of these markers are neu-ronal markers that disappear if no midline is formed.Thus, the loss of anterior AP markers in the absenceof the organizer is caused by a non-functional DV pat-terning. In this relation a very instructive set of ex-periments has been done by Ober and Schulte-Merkerin the zebra fish [15]. By removing required mater-nal components, they obtained embryos reliably devoidof any organizer. To visualize the AP patterning theyremoved all BMP signalling, allowing in this way theexpression of neuronal markers. Genes like Otx andKrox20 were expressed at nearly normal positions butin a completely radially-symmetric way, illustrating thatthe activation of the anterior AP genes do not requirethe organizer. However, as discussed further below,the organizer plays a crucial role in the AP patterningof the trunk by terminating the time-dependent posteri-orization.

    2. The separation of axes formation into abrain- and a trunk-part has an evolutionary

    justificationCoelenterates are assumed to represent a basalbranch of the metazoan evolutionary tree. A com-parison of the gene expression patterns in theradial-symmetric freshwater polyp Hydra - a much-investigated Coelenterate - and homologous genes inhigher organisms suggested that the body column ofan ancestral sac-like creature with a single openingevolved into the brain of higher organisms; the ances-tral oral-aboral pattern evolved in the head/brain AP-pattern [16]. Wnt and Brachyury are expressed at thetip of the hypostome and at the most posterior regionin higher organisms, suggesting that, in contrast toa naı̈ve expectation, the so-called Hydra head is themost-posterior structure, corresponding to the blasto-pore in higher organisms (Fig. 1). This view is sup-

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  • Fig. 1: Generation of the primary body axes and a near-Cartesian coordinate system. (A-C) The body pattern of an ancestral radial-symmetricorganism (A), generated under control of a Wnt-driven organizer (green) at the oral opening (blastopore), is assumed to represent the ancestralAP axis, corresponding to the brain-part of the AP axis in contemporary higher organisms. The pattern of the freshwater polyp Hydra (B)is assumed to be a living fossil of this ancestral pattern. This ancestral body pattern evolved into the pattern as seen in the early vertebrategastrula, giving rise to fore- and midbrain (Otx, blue) and the heart (Nkx2.5, pink). (D-J) The secondary DV axis requires a stripe-like line ofreference along the entire AP axis. Nature found different solution for this intricate patterning problem that is intimately linked to the inductionof mesoderm (pink). In vertebrates (E-G), mesoderm is induced at the most posterior position, i.e., at the oral opening that was enlargedto a huge ring. The induction of the Spemann-Organizer on this ring is necessarily connected with a symmetry break and the generation ofbilaterality. The midline for the brain is generated dorsally with the movement of organizer-derived cells underneath the ectoderm (yellow)[13]. The midline of the trunk results from a ring-to-rod transformation (see Fig. 2). The simulation (G) shows a stripe-like midline thatis induced by a moving patch-like signaling center. A second organizer (blue), induced but repelled by the midline, can lead to a left-rightsymmetry break [108]. (H-J) In contrast, in insects and in the spider, signaling from the dorsal side (yellow) represses mesoderm and midlineformation. Ventrally a narrow signal with a stripe-like AP-extension induces first mesoderm and then the ventral midline that specifies theDV-patterning. The simulation (J) shows a stripe-like ventral midline (pink) that results from the repression emanating from a dorsal signalingcenter (green). These different mechanisms are assumed to be at the core of the DV-VD reversal in vertebrates and insects [35].

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  • ported by the expression patterns of several genes.Otx, a gene characteristic for the fore- and midbrainin vertebrates, is expressed in the whole body columnof hydra except of the hypostome and the foot [17].The posterior border of Otx expression, located in hy-dra between the tentacles and the hypostome, becamean important secondary organizer in vertebrates, themidbrain-hindbrain border. In other words, the poste-rior end of ancestral organism was at a position thatcorresponds in today’s animal to the midbrain/hindbrainborder. This is in agreement with the expression of anAristaless-related gene in Hydra at the tentacle zone[18] and in Xenopus in the telen- and diencephalon[19]. In this view, the aboral side of Cnidarians, e.g.,the foot in hydra evolved into the most anterior partof the brain. This fits the expression of six3/6 in Ne-matostella [20] on the one hand and in vertebrates [21]and insects [22] on the other. Usually, heart formationin higher organisms is initiated at a very anterior posi-tion. The (anterior) hydra foot is under the control ofthe same master gene as the vertebrate heart, Nkx2.5,suggesting a common ancestry for these two so differ-ently looking organs [23]. Indeed, the hydra foot actsalready as a pump for circulating the gastric fluid.

    This scenario provides a rationale why brain for-mation of insects and vertebrates is under control ofclosely related genes [24, 25,26], although their com-mon ancestor certainly did not had an evolved brain;these expression patterns are the relicts from an an-cestral body pattern.

    The trunk is an evolutionary later invention and, asthe rule, is also formed later during individual develop-ment of an organism. This view is supported by theobservation that Hydra does not posses the 3’-5’ Hoxgene sequence typical for trunk patterning [27]. Withthe insertion of the trunk, the posterior organizer real-ized by Wnt/Brachyury obtained an increasing distancefrom the original position at the posterior Otx border.The midbrain/hindbrain organizer can be regarded as areplacement that remains at the position of the originalorganizer. In his gastrea concept, Ernst Haeckel [28]proposed already that development of higher organ-isms generally proceed through a gastrula-like stage.The scenario I propose modifies this view by postulat-ing that this gastrea stage is equivalent not to the wholebody but only to the brain.

    3. The generation of the two main body axesand their correct alignment as a self-organizing

    processAlthough frequently regarded as the only existing or-ganizer, the Spemann-type organizer in vertebrates,based on the Chordin-BMP interaction, is neither theonly nor, evolutionary, the earliest organizer. The set-

    ting up of the oral-aboral axis in the radially-symmetricHydra by the Wnt-Brachyury system [29, 30] and itsconservation in higher systems [31, 32] for the orga-nization of the AP axis suggest that the WNT pathwaywas involved in organizing an ancestral axial system.Its self-organizing properties are well investigated in theCnidarian system and are theoretically well understood[33]. This originally small organizer evolved in verte-brates into a large ring, the blastopore. A possible rea-son for this enlargement could be that this signallingsystem became also engaged in mesoderm formation(Fig. 1). Thus, the geometry of the early AP organizerin vertebrates is a large ring, not a localized patch asusual. This could be the reason why this ancestral or-ganizer was often not regarded as such, in contrast tothe patch-like Spemann organizer.

    To specify positional information in a two-dimensional field, two reference lines are requiredto set up a near Cartesian coordinate system, so tosay, an X and a Y axis. Especially for the patterningof the DV- (or mediolateral-) axis, a stripe-like arrayof signalling cells have to generated that extendsalong the entire AP axis. The generation of suchan organizing line is an intricate pattern-formingproblem. Stripe-like patterns can be generated ifthe self-enhancing component of a pattern-formingreaction saturates at high concentrations [34]. Dueto this upper bound, the activation has a lower peakheight but obtains a larger extension. Stripes are thepreferred pattern since the activated regions are largebut, nevertheless, non-activated regions are nearbyinto which, for instance, the inhibitor can be dumped.

    On its own, however, this mechanism would lead toa periodic stripe pattern as seen in the proverbial ze-bra stripes. The formation of a single solitary stripe re-quires cooperation with a second pattern-forming sys-tem that makes sure that only a single stripe canemerge. It was proposed that different mechanism formidline formation evolved (Fig. 1) [35]. In vertebrates,the secondary Spemann-type organizer, localized onthe much-enlarged blastopore, initiates and elongatesmidline formation in two directions, towards anterior bygiving rise of the prechordal plate and towards posteriordue to the ring-to-rod conversion (Fig. 2). Thus, unusu-ally, for the positional specification of a cell not the dis-tance to the organizer but the distance to the stripe-likemidline induced by the organizer, i.e., to the notochordand floor plate is decisive [36]. Since the organizer isdorsally located, the midline emerges also dorsally, hasfrom the beginning a narrow DV extension but becomeselongated in the course of time. Since posterior elon-gation of the midline requires time, the reference linefor DV patterning also emerges in the course of timewith the same pace. This view provides a straightfor-ward explanation why AP and DV patterning in the trunk

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  • Fig. 2: Different modes for the ring-to-rod conversion in amphibian and chick development [36]. (A-C) The early amphibian gastrula corre-sponds to an ancestral body pattern (see Fig. 1). During trunk formation a sequential posteriorization takes place in cells near the blastoporeby activating HOX genes (1, 2, 3..) [12]; (Durston and Zhu, this volume). Cells move towards the organizer (red arrow), leaving the mostposterior zone in which the sequential posteriorization takes place and obtain therewith their final determination. Note that the DV or medio-lateral determination can only take place after the corresponding part of the midline is formed; accounting for the observation that AP and DVdetermination is under the control of the same developmental clock [37]; (Mullins et al., this volume). Cells antipodal to the organizer (bluearrow), classically assigned as being ventral, form posterior structures since they remain longest in the zone of posterior transformation. (D-F)In the chick the ancestral sac-like arrangement became distorted to a near flat disk. The entire outer border (red) resembles the blastopore, aview supported by the early β-catenin expression there [109]. As in amphibians, the organizer forms on this blastopore. As shown by Gräper[110], cells at the left and at the right of the organizer move in a ‘polonaise movement’ over the yolk, a movement that can be regarded asa ‘partial epiboly’ [36]. This leads to a hair-pin like deformation of the blastopore, the primitive streak. In contrast to the notion in manytextbooks, there is no anterior movement of the organizer [110]. Later the organizer (node) moves over the deformed blastopore like the handleof a zipper. Thus, in amphibians, the ring-to-rod transformation occurs in parallel with posteriorization, relative movement of the organizer andshrinkage of the blastopore. In the chick, the ring-to-rod transformation occurs first; the movement of the node starts only afterwards.

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  • is under control of the same developmental clock [37],(Mullins et al., this issue). At a particular AP level, theDV pattern can only be generated after the correspond-ing part of the midline is generated (Fig. 2). This alsosolves some confusion concerning ‘ventral’ in the earlyamphibian embryo. Frequently the region antipodal tothe dorsal organizer is declared as ventral. Fate map-ping has shown, however, that these cells form the mostposterior structure [38, 39]. In terms of the model, cellantipodal to the organizer remain longest in the zonewhere sequential posteriorization takes place (Fig. 2 B,C).

    In insects and spiders the situation is completelydifferent. An inhibition spreading from a dorsal signal-ing center restricts midline formation to the ventral side.The midline has from the beginning the full AP exten-sion of the embryo but sharpens in the course of timeto a narrow ventral line. The sharpening of the Dor-sal transcription in Tribolium [40] is an impressive ex-ample for this theoretically predicted mode [41]. In aspider, a clump of BMP-expressing cells, the cumulus,move from the center of the germ disk, the blastopore,towards the periphery - a posterior-to-anterior move-ment - defining in this way the dorsal side. The mid-line proper, however, is not formed dorsally behind themoving cumulus but ventrally due to a cumulus-BMP-mediated inhibition of Chordin. Chordin expression andthus midline formation is focused to a narrow ventralstripe at maximum distance from the cumulus [42]. Themuch discussed DV-VD reversal between vertebratesand insects [43] was proposed to have its origin in thesedifferent modes of midline formation, invented duringearly evolution of bilateral-symmetric body patterning[35]. In protostomes, a dorsal organizer repels the mid-line that appears, therefore, ventrally. In contrast, indeuterostomes, the dorsal organizer elongates the mid-line that appears, therefore, at the dorsal side.

    Most remarkably, these different modes of mid-line formation are intimately connected with the inven-tion and positioning of mesoderm. In vertebrates, themesoderm is formed around the large blastopore at amost posterior position. A reason for this enlargementcould be that a sufficient number of cells can be speci-fied as mesodermal. In contrast, in insects, mesodermis initiated by a newly generated stripe-like signal thatstretches from anterior to posterior; it precedes the for-mation of the ventral midline and occurs under controlof a different set of genes. These basically differentmechanisms for mesoderm and midline formation sug-gest that different mechanisms evolved for generatinga bilaterally-symmetric body plan in originally more orless radial-symmetric organisms. These early differ-ences are in contrast to the concept of an urbilaterianas a unique bilaterally-symmetric ancestor.

    It should also be noted that this view is very different

    from the amphistomy concept according to which theblastopore is closed in a slit-like manner [44]. Accord-ing to this view, in protostomes the mouth, in deuteros-tomes the anus remained open. However, in insectsand spiders the blastopore is not involved in the local-ization of the ‘slit’ at which mesoderm invaginates. Invertebrates, the blastopore does not close in a slit-likemanner but resembles more a ring that shrinks due tothe preferential removal of material at the site of theorganizer, a closing noose. For a system that was re-garded as a prototypical example for a closing slit, theonychophoran blastopore, it was recently shown thatthe posterior end of the slit is not coincident with theblastopore [45].

    4. The role of Wnt antagonists in the view ofthe proposed mode of axes formation

    There is a surprising diversity of Wnt antagonist, inspir-ing Brown and Moon to entitle a review “Wnt signaling:why is everything so negative?” [46]. In terms of themodel, Wnt antagonists are required in several steps forproper cell specification [36]; (see also Sokol, this vol-ume).The Wnt pathway is crucially involved in amphib-ians to trigger the Spemann organizer in the marginalzone. However, due to the posteriorizing nature of theWNT signal, it is necessary to rapidly switch off Wnt sig-naling in the organizer shortly after organizer formation.If not, organizer-derived prechordal plate cells wouldcarry a posteriorizing activity into the region that shouldform the most anterior structure, the forebrain, whichrequires low Wnt signalling. Indeed, forebrain forma-tion is lost if the Wnt inhibition in the organizer by Dkk-1is non-functional [47]. Further, it is necessary to main-tain Wnt-signaling restricted to the marginal zone al-though these cells also ingress; otherwise there wouldbe no localized source to set up the Wnt gradient. Inthe fish, for instance Dkk-1 is expressed first in the or-ganizer and extends later throughout the germ ring [48].Thus, Dkk-1 could be involved in restricting Wnt to partsof the marginal zone in spite of the ingression. Analo-gously, in the ancestral hydra system Dkk seems alsoto be involved keeping Wnt signalling localized at theoral opening [33]. A third expected function of Wnt an-tagonists is to accomplish a necessary delay in the inthe sequential posteriorization; this will be discussedfurther below.

    5. From totipotent to differentiated cells: notas in Waddington’s morphogenetic landscape

    Waddington [49] used a well-known analogy to illus-trate his view how cell fates become more and morerestricted on the way from the totipotent fertilized egg toa terminally-differentiated cells: a sphere rolls down ina valley; new hills within existing valleys lead to branch

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  • points at which the sphere has to make a decision; itcan only take the one or the other path. At the end ofits journey the sphere will end up in one of the manyvalleys, one of the possible alternative stable states.

    This analogy, however, is misleading. It suggeststhat the decisions are made at unstable points; thedecision for the one or the other possibility would oc-cur essentially by chance and is essentially irreversible.Such a mechanism would not be robust. If the positionof a new valley-separating hill would be slightly shifted,all cells would end up in one valley only. Cell differ-entiation is achieved by activation of genes under theinfluence of transcription factors. At such a delicate sit-uation, a minute change in the ability of transcriptionfactors to activate the one or the other gene would havedramatic effects. In Waddington’s analogy, the majorityof cells would end up at the same side; there would beno chance to obtain differently determined cells in thecorrect ratio. Also the situation that precedes the de-cision would have a decisive impact; a slight deviationform the correct initial situation would lead to a catas-trophic imbalance.

    It is not only important that eventually differently de-termined cells are formed in a correct proportion; theyhave to emerge at the correct positions. The frequentlyobserved ability to regenerate lost structures empha-sizes that in many situations later corrections are possi-ble, in contrast to Waddington’s analogy. Nature solvedthis sensitivity problem by making decisions not at in-stable points where minute shifts would have dramaticand irreversible consequences. To use Waddington’sanalogy, one strategy is that for a particular determi-nation process, all cells start in a particular valley. Bymorphogenetic signals, a certain fraction of cells at par-ticular positions are shifted ‘over the hill’ into an adja-cent valley. In other words, a determination processcan start with the activation of a default gene. A mor-phogenetic signal, if high enough and available for asufficient time, can lead to the activation of a ‘higher’gene, which is usually connected with a repressionof the previously-active gene. Mechanisms that allowsuch gene activation under the control of a graded mor-phogen distribution will be discussed in the next sec-tion.

    A second mechanism involves feedback mecha-nisms. To use Waddington’s analogy once again, if toomany spheres went to the right valley, the probability in-creases that other spheres go preferentially to the left.A corresponding mechanism requires that determin-ing gene activities not only exclude each other locally(e.g., within the same cell) but mutually support eachother on a longer range. This interaction allows bal-anced and patterned distributions of differentiated cellswith strong self-regulatory capabilities. The engrailed-wingless-hedgehog interaction involved in segmenta-

    tion is a typical example of such an interaction; it willbe discussed further below.

    This list is not exhaustive. In many cases, fate de-termination is closely connected to cell division; in eachdaughter cell a different set of transcription factors be-comes activated - clearly a non-random decision mech-anism.

    6. Switch-like gene activations by positiveautoregulatory feedback loops

    A stable switch-like activation of a single gene can re-sult from a non-linear saturating autocatalytic feedbackof a gene product on the activation of its own gene(Fig. 3) [50, 51, 2]. The condition of non-linearity issatisfied if gene activation is not accomplished by thetranscription factor itself but by a dimer. This require-ment is easy to understand. At low concentration thechance of finding a partner for building a dimer is low.Therefore, the normal first-order decay is dominatingand gene activation will decrease further. If the mor-phogen signal has an additional activating influence onthis gene activation, with increasing signalling strength,the rate of dimerization will increases too. From acertain threshold level onwards, the rate of the non-linear auto-activation becomes larger than the first or-der decay rate; gene activation will become strongeruntil a saturation level is reached. In other words, un-der morphogen control gene activation can switch froman OFF- into an ON-state. This switch requires timesince a certain concentration of the gene product has tobe reached before the activation becomes irreversible.Due to the positive feedback, the activation can (butneed not) remain in the ON state even if the signal is nolonger available (Fig. 3). The required autoregulationcan be direct but also can be realized by an inhibitionof an inhibition of two transcription factors [2].

    7. Gene activation by a graded distribution: atime-requiring process

    According to a classical view and most clearly formu-lated by Wolpert in his positional information concept[52], a graded distribution of a morphogen causes anordered activation of several genes in a concentration-dependent response. This raises the question howcells can measure the local concentrations with such aprecision. At particular positions different genes shouldreliably be activated in adjacent cells although the dif-ferences in the morphogen concentrations are minute.An analysis of ligation experiments made by KlausSander in the early seventies with non-Drosophila in-sects [53] suggested that cells do not obtain their finaldetermination in a single step; instead, they are step-wise ‘promoted’ from one state to the next until the sig-nal concentration is insufficient to accomplish a further

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  • Fig. 3: Model for stable activation of a gene under the influence of a morphogen signal. (A) A gene with a non-linear saturating feedback onits own activation. (B) Such feedback can lead two stable steady states (dg/dt = 0), one at a low and one at a high activation of the gene (redand blue circles). Whenever the gene activation is higher than the instable steady state (yellow circle), the change is positive; the activationincreases further until the upper steady state is reached. In the presence of an inducing morphogen that causes an additional production of thegene activator (green curve), only the high steady state may exist (pink circle) leading to the switch from low to high activation that will bemaintained even after the signal is gone [50, 2]. (C) Simulation of gene activation (red) under the control of a gradient (green). All cells thatare above a certain threshold switch into the activated state and remain there even if the gradient is later removed (blue arrow). Note that cellsjust above the threshold level need much longer to accomplish the switch. (D) If the saturation of the self-enhancement occurs at a lower levelof activation (higher κ in equation 1, BOX1), the high steady state in the absence of the signal may no longer exist; the switching remains butthe activation ceases after signal removal. The activation of Monopterus under Auxin control [111] is an example.

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  • Figure 4: Model for the space-dependent activation of several genes under the control of a morphogenetic gradient. Genes are assumed whosegene products have a positive non-linear feedback on the activation of their own gene. They compete with each other for activity (Box 1;equation 2). In a given cell, only one of the alternative genes can be fully active [51, 55, 2]. (A) Starting with activation of a default gene 1(blue), the genes 2, 3 and 4 become activated in the course of time. Regions with sharp borders are formed. A later reduction of the morphogen(green to red distribution) remains without effect. The sequential activation of genes proceeds faster in regions of high signal concentration,which leads to the apparent wave-like movement of gene activities as observed in neural tube determination [56]. Activation of new genesoccurs only in one direction (distal or posterior transformation). (B) Upon a later increase, gene activation adapts to the new level. (C) After apremature drop of morphogen level, the activation of the gene that is usually activated close to the source (yellow) may fail since the availabletime was insufficient; an example can be found in ref [59]. The pixel density indicates activation of particular genes. (D) The unidirectionalpromotion allows arbitrary growth without that cells lose their achieved determination (local gene activation indicated by the height of thebars). (E, F) At an early stage, cells could be too close to the source and the signal so high that activation of the default gene (blue) is lost (E).A fading maternal antagonist such as Cerberus [112, 113, 114] (yellow,) could delay the promotion until a sufficient extension is achieved; theactivation of the default gene is maintained (F).

    9

  • BOX 1: Models for gene activation undermorphogen control

    A switch-like activation of a gene is possible if thegene product g has a non-linear self-activating feed-back on the activation of its own gene [50] (Fig. 3):

    ∂g

    ∂t=

    cg2

    1 + κg2− rg +m 1

    Equation 2 describes an interaction that allows theactivation of several genes under the influence of agraded signal m (Fig. 4). A set of genes whose geneproducts feed back on the activation of their own genecompete with each other for activity; the sum termin the denominator is responsible for the local exclu-sion; each active gene has an inhibitory influence onthe other genes, including a self-inhibition that leadsto an upper bound in the self-activation. A particulargene i, i = 1....n becomes activated by the precedinggene i− 1 in collaboration with the signal m:

    ∂gi∂t

    =cig

    2i + bigi−1m∑n

    i=1 cigi− rigi 2

    There are several possibilities to make sure that theactivation of each subsequent gene requires a highermorphogen concentration. One possibility is thatgenes which are less sensitive for the morphogen arebetter in the autoregulation. In the equation above,this requires ci+1 > ci; (i = gene number; i = 1 cor-responds to the default gene; the gene with a highernumber requires a higher morphogen concentrationfor its activation). Due to this condition, with eachactivation of a subsequent gene, the denominator in-creases. This has the consequence that the activationof each further gene requires an even higher signalconcentration. Such an increasing negative feedbackhas been observed during neural tube patterning [56].Under this condition the influence of the signal m inthe activation of the subsequent gene, bi, can remainessentially the same.Alternatively, the self-enhancement can remain theabout the same for all genes, but the activating influ-ence of the signal becomes lower with the activationof a subsequent gene, i.e., bi+1 < bi, causing alsothat the signal m has to be higher to achieve a furtherstep. In both cases, although the signal is smoothlygraded, there is an all-or-nothing response in the ac-tivation of the particular genes. This stepping troughrequires time. However, a too-low signal concentra-tion cannot be compensated by a longer exposure ofthe responding cell.

    step [54]. The situation may be compared with a barrelat the base of a staircase that is lifted up by a flood.The level at which the barrel comes to rest dependson the highest level of the flood. A later fading of theflood remains without effect; a later even higher floodcan deposit the barrel at an even higher level. A corre-sponding model for gene activation [51, 55, 2] predictedthe following components (Fig. 4):

    1. A set of genes exists that could be active at a par-ticular stage. The genes have a positive non-linearfeedback on their own activation. The auto-activationmay be realized by a mutual repression of two genes.

    2. The activations of such genes are locally exclusive.For instance, in a particular cell only one gene of theset can be active.

    3. Gene activation starts with a particular default gene.4. The morphogenetic signal leads to a sequential ac-

    tivation of ‘higher’ genes. Each further step requiresa higher signal concentration and requires a certaintime to activate the subsequent feedback loop. Thistime-consuming promotion comes to rest if the localsignal concentration is insufficient to accomplish afurther step.

    Such a mechanism has regulatory properties as ex-perimentally observed. A once achieved gene activa-tion can be stable against a lowering of the signal con-centration (Fig. 4). This is a most important featuresince embryos grow (or are subdivided in more andmore cells). Thus, due to the increasing distance be-tween a particular cell and the signaling source, thelocal concentration at a particular cell will decrease.Which of the ever-changing concentration a cell shouldmeasure? The answer given by this model: a cellmeasures the highest concentration to which it was ex-posed at least for a certain time. Due to time averag-ing and the restriction to unidirectional changes, thismechanism reduces inherently possible perturbationsby noise in the gradient or in the interpretation machin-ery.

    The predicted stepwise activation has a remarkableconsequence [51, 55] that is now well-known for geneactivation under hedgehog control in the neural tube[56, 57]. Those genes that are eventually activated ata distance from the signaling source, i.e., the gene thatrequires the lowest signal concentration, become firstactivated close to the source at the ventral center, i.e.,close to the hedgehog-signaling notochord. Later, newgenes become activated at this position that quenchesthe activity of the previously activated genes. Gene ac-tivation appears to become shifted in a wave-like man-ner. This shifting reflects only the increasing time re-quired to reach the finally stable activation; it does notdepend on signaling between adjacent cells: the cellslisten only to the local morphogen concentration (Fig.

    10

  • 4). The correct neighborhood depends solely on theinterpretation of the graded signal. This has the conse-quence that mismatches caused by transplantation atlater stages might be neither detected nor repaired.

    A systematic change in the threshold level was pre-dicted in order that the stepwise activation of genescomes to rest if the morphogen concentration is insuf-ficient to accomplish a further step [51, 55]. Possiblemechanisms are outlined in BOX 1, including that theactivation of a subsequent gene has a negative effecton the sensitivity. Recently such an increasing neg-ative feedback has been described; the sensitivity forthe hedgehog signal become reduced by upregulationof patched [56]. For Nodal signaling observations areavailable that support both a threshold model and time-requiring dose model (reviewed in [58]). According tothe model proposed, these are just two sides of thesame coin. A certain threshold concentration is re-quired to activate a particular gene, but this activationis not achieved at once but requires substantial time.A too-low signal level cannot be compensated by elon-gating the time of exposure. Also evidence for the pre-dicted behavior that a premature removal of the mor-phogen source causes that the ‘higher’ genes may notbe activated (Fig. 4C) has been observed, in this caseexperimentally achieved by an inhibition of Nodal sig-naling [59].

    A characteristic feature of such systems is that aonce obtained determination can be changed only ina unidirectional way (distal or posterior transformation).Therefore, upon transplantation from a region of highto a region of low concentration, the cells maintain theiralready achieved determination. In contrast, after alow-to-high transplantation, the cells change their de-termination according to the new level. Strong evidencefor such a unidirectional promotion exists for the hind-brain [60, 61], in the commitment of CNS progenitorsalong the dorsoventral axis of Drosophila neuroecto-derm [62], and for the response to activin signalling inthe early amphibian gastrula - called there a ‘ratchet’ -like behavior [63]. A stepwise posterior transformationwas proposed for the AP-specification in the anteriorneural tube [64]. The involvement of one gene in theactivation of the subsequent gene - a crucial feature fortime-dependent gene activation - has been also shownin the specification of neural crest cells [65].

    The described stepwise promotion is not the onlymechanism that allows the interpretation of a gradient.An alternative possibility works as follows: If the mor-phogen has an activating influence on a particular geneat low and an inhibitory influence at high concentra-tions, there is an optimal concentration for the activationof that gene. Other genes of the set have other optimallevels for activation. Although these activating profilesare smooth, sharp borders are formed due to the mu-

    tual repression of the genes. A characteristic feature ofsuch a mechanism is that if one gene is missing due toa mutation, the expression regions of both adjacentlyexpressed genes expands, indicating that there is nolower threshold. This is the situation in the activation ofgap genes in Drosophila [66, 67].

    This model for the activation of a particular genehas an interesting formal similarity to pattern formationin space. In the latter, e.g., for organizer formation, aparticular region has to become activated; the remain-ing region has to be suppressed. In gene activation,one gene should become activated while alternativegenes should be repressed. Thus, the activation of aparticular gene can be regarded as a patterning pro-cess in the ‘gene space’. Reproducible development isachieved by a specific coupling between pattern forma-tion in space and pattern formation between alternativegenes.

    8. Models for segmentation and the sequentialactivation of HOX genes in insects

    With a head alone, rapid swimming is impossible. Thus,the addition of a long extended trunk was a major evo-lutionary achievement. Characteristic for many phyla isa segmented trunk. Segments are clearly a periodicstructure, manifested, for instance, by the alternation ofanterior and posterior compartments. Superimposedis a sequential activation pattern of HOX genes, en-abling that individual segments undergo specific devel-opments. Both patterns are precisely in register.

    In contrast to Drosophila, in many species the pe-riodic pattern emerges in the course of time duringposterior outgrowth, suggesting that segmentation isbased on genuine pattern-forming reactions. Alreadyan inspection of morphological structures suggests thatthe periodic pattern consists of adjacent narrow stripeswith a short extension along the AP but a long DV ex-tension. To account for a periodic pattern of narrowstripes we proposed the mechanism of Mutual activa-tion of locally exclusive cell states [68, 2]. A particularcell type needs cells of another cell type in close prox-imity. Both cell types provide mutual support for eachother. Narrow adjacent stripes are the preferred patternsince the long common border allows an efficient mu-tual stabilization (Fig. 5). The shortly later discoveredengrailed-wingless-hedgehog interaction in segmenta-tion provided direct support. The gene engrailed (en),the key gene for posterior compartmental specification,is autocatalytically activated. Via the diffusible moleculehedgehog (hh), en activates the gene wingless (wg)that is crucial for the anterior compartment (reviewedin [69]). The gene cuD, on which wingless-expressiondepends, is involved in the local exclusion of en and wgexpression [70]. The gene sloppy paired contributes tothe wg-autoregulation. The wg protein can reach adja-

    11

  • Fig. 5: Mutual activation of locally exclusive cell states: a basic mechanism in segmentation. (A) Prototypical reaction scheme: two feedbackloops locally exclude each other but activate each other on a longer range [68]. The engrailed-wingless-hedgehog system has turned out to beof this type [76]. (B) Such a system has pattern-forming capabilities, forming preferentially narrow stripes. (C) Small asymmetries such as agradient from a posterior organizer can orient the emergent stripes. (D) With growth at the posterior pole (right), the periodic pattern can beelongated. Whenever the extension of a particular specification becomes too large, it will switch to the other specification (blue arrow). Thus,the most posterior cells oscillate - a feature that important for a model of somite formation (Fig. 7).

    cent cells via vesicle transport and is required there tostabilize en [71, 72]. As expected from the theory, theen gene activity requires an active wg gene in its neigh-bourhood and vice versa, although both genes are tran-scribed in non-overlapping regions.

    Such a mechanism has interesting features appro-priate to describe segmentation (Fig. 5). Narrow stripescan emerge spontaneously. To obtain stripes with anorientation perpendicular to the AP axis, almost anyasymmetry resulting from the posterior organizing re-gion is sufficient. During posterior outgrowth, morestripes will be added. This can be connected with anoscillation at the posterior pole. For example, when-ever the size of cells with anterior compartmental spec-ification exceeds a critical limit, a switch to a posteriorspecification will occur in the posterior region, and viceversa. In other words, posterior outgrowth leads to aperiodic change between two (or more) specificationsat the most posterior position (Fig. 5D). The on-off-on activation of the hairy gene in the Spider is an ex-ample [73]. If stripes obtain a certain width due to anoverall growth, the central part of a thicker stripe canchange its activation, leading to a split. For instance,in Tribolium the initial even-skipped stripes split at alater stage [74]. A small diffusion of the self-enhancingcomponents makes stripes more robust against disin-tegration into patches or into a salt-and pepper pattern.

    In this respect it is interesting that engrailed and someother homeobox genes can be actively exchanged be-tween cells [75].

    In contrast to a simple alternation between twostates ....APAPAP.... segments have an internal polar-ity. For this reason I proposed that, in addition to theanterior and posterior compartment, at least one addi-tional element, termed S, must be present, such that asequence ....SAP/SAP/SAP/.... results. The region Sseparates one A-P pair from the next [2]. Now it is gen-erally assumed that the AP pattern of each paraseg-ment is founded by four differently determined cells(see [76]). Four cells also establish the parasegmentsin crustaceans [77]). A subdivision into three or morecompartments has the consequence that only one A/Pborder exists per segment. This is important since theA/P border was proposed to generate a precondition toform imaginal disks and thus legs or wings [78].

    9. Formation of a precise number of differentsegments during terminal outgrowth

    Segments are not only a periodic pattern, but they ob-tain different specifications, known to be under controlof the HOX gene (reviewed in [79]). Classical observa-tions have shown that the number of segments is pre-cisely controlled. The polychaet Clymenelly torquata,

    12

  • Fig. 6: Model for HOX gene activation in insects in register with the compartmental specification during posterior outgrowth. Assumedare three compartmental specifications, A (red), P (green) and S (blue) that activate each other in a cyclic way. During outgrowth, a regularsequence ...A,P,S,A,P,S... emerges (see also Fig. 5). With an at least threefold subdivision, each periodic unit has an intrinsic polarity and onlyone AP border per (para-)segment, the precondition that only one wing or leg per segment is formed [78]. To achieve Hox gene activationin register, a component is assumed to be produced in the anterior compartment that activates of next HOX gene, but its actual activationis blocked. After a switch to the posterior specification, this activation is no longer blocked but the corresponding component is no longerproduced; the available component concentration allows only a single switch. Thus, a transition from one HOX gene to the next can only occurwith an A-to-P transition in the compartmental specification [2]. (A-D) snapshots at subsequent time points. In (B), the system is ready toswitch from A to P at the posterior position. Shortly later (C), this transition is achieved and the next HOX gene is active (blue arrows) [2].

    13

  • for instance, has 22 segments. If posterior segmentsare removed, regeneration occurs such that eventually22 segments will be present independent of the numberof segments removed [80]. In the leech, initially morethan the final 32 segments might be formed. The sur-plus segments are later removed by programmed celldeath [81, 82]. These observations indicate that somesort of counting mechanism exists. In an early modelI proposed that the oscillation between compartmentalspecifications at the outgrowing posterior pole is usedto drive the activation of new specifying HOX-genes [2],similar as the periodic movement of a pendulum drivesthe sequential advancement of the pointer of a grand-father’s clock. Each full cycle leads to the advance-ment by one and only one unit - a stop and go mech-anism. Fig. 6 shows a simulation. According to ourpresent knowledge, this early model has to be mod-ified and extended because particular HOX genes areknown to be active in several segments. However, thereare segment-specific cis-regulatory units on the chro-mosome, which are separated by chromosomal insula-tors [83,84, 85] In terms of the model, each oscillatorycycle may cause the advancement from one such in-sulator to the next, suggesting that a certain number ofinsulators have to be passed until the activation of thesubsequent HOX gene takes place.

    10. Somite formation: the conversion of aperiodic pattern in time into a periodic pattern

    in spaceIn contrast to insects, segmentation in vertebratestakes place in the mesoderm. In the hemichordate Am-phioxus somites form similar as in short germ insectsin a growth zone at the posterior pole [86]. In con-trast, in higher vertebrates, somite formation occurs ata considerable distance from the posterior pole by a se-quential separation from a non-segmented presomiticmesoderm (PSM) in an anterior-to-posterior sequence.Somite formation has been reviewed extensively [87,88] (see also the article of Oates in this volume). There-fore, the following remarks are restricted to some histor-ical notes in somite modeling and to inherent parallelsto insect segmentation.

    The first model for somite formation has been pro-posed by Cooke and Zeeman [89]. Their ‘clock andwave front model’ was name-giving for many later mod-els. It has an interesting background. In careful exper-iments Jonathan Cooke found that removal of materialfrom the ventral side of an amphibian embryo leads toshorter embryos. Thus, most remarkable, the AP, notthe DV extension of the somites became smaller, al-though the material was removed from the ventral side.In an attempt to find an explanation, Cooke and Zee-man considered a model according to which a wave

    moves from anterior to posterior that initiates somiteformation. In addition, an oscillation was assumed;each full activation causes for a short period the sup-pression of somite formation and thus the separation ofone somite from the next. The frequency of the os-cillation was assumed to depend on the overall sizeof the embryo, the smaller the embryo the higher thefrequency. Assuming a constant velocity of the wave,this would lead to a regulation of A-P extension ofthe somites in relation to the total size of the embryo.Cooke found shortly later that the frequency of the os-cillation is not size-dependent, but the clock and wavefront model was born. Cooke and Zeeman did not for-mulate their model in a mathematical way. However,such a model can be easily provided by the toolkits ofpattern-forming reactions (Fig. 7A).

    Already in the early eighties it became clear that theclock and wave front model was not tenable in this form.Important information in this pre-molecular time camefrom heat shock experiments [90]. After a short heatshock - much shorter then the time required to from asomite - about fife additional somites formed in an un-perturbed manner, indicating that these somites werealready determined. In later-formed somites, charac-teristic perturbations occurred such as partial Y-shapedsplits of somites into two or to an incomplete border be-tween two somites (Fig. 7B). Such an irregularity is fre-quently followed by a second irregularity that compen-sates partially the first, allowing that subsequent somiteformation can return to normal. In my view, this is astrong indication that a component of spatial pattern-ing is involved that attempts to maintain a certain spa-tial wavelength. This feature has been disregarded inmany contemporary models but has found recently di-rect experimental support. Somite formation has beenobserved in cell culture in the absence of any waves[91].

    To maintain the posterior oscillation in a model forsomite formation I proposed that an oscillation betweentwo states takes place in the posterior portion of the ver-tebrate embryo [2, 92]. In contrast to the insect case(Fig. 5) the oscillation was proposed to be no longerrestricted to the posterior pole but to extend anteriorlyup to region in which somite formation occurs. Themechanism explained above for segmental patterningin space (Fig. 5) also can act as an oscillator (Fig. 7).For instance, if only A cells are present, the P-cell statewill get strong support, while the support of the A stateby cells in the P state is missing. Thus, cells will switchfrom A to P and, for the same reason, later back to A.In other words, the cells will oscillate between the twostates (Fig. 7C). How can the transition from a poste-rior oscillating into an anterior stable spatial pattern beenforced? Imagine that initially only one A region existsat the anterior end, the remaining cells are all in the P

    14

  • Fig. 7: Different concepts in oscillation-driven models of somite formation. (A) A mathematically-formulated version of the ‘clock and wavefront model’ of Cooke and Zeeman [89]. Similar as in an infection wave, a wave is generated by a self-enhancing activator (dark green) anda non-diffusible inhibitor (red) that has a longer half life. The diffusion of the activator leads to the wave-like spread [115], showing up in thetime record as an oblique line. The wave triggers the irreversible activation of a gene causing somite formation (brown) in a switch-like manner(see Fig. 3). A similar assumption was made for the oscillation; a more rapid spread of both components (blue and light green) leads to aglobal synchronization. A burst in the oscillation blocks gene activation for somite formation, leading to a separation between two somites. (B)Experiments of Elsdale and Pearson [90] have shown that characteristic perturbations can occur after a short heat shock. If a somite becomestoo large, a partial border will be inserted or an existing border can split, suggesting that a pattern-forming mechanism is involved that has aninherent spatial wave length. (C) The mutual activation mechanism (Fig. 5) can work as an oscillator. An A region (red) next to a P region(green) is stabilized, the remaining P cells switch to the A state, forming a new stable A-region, and so on. With each full cycle, one new stableA-P pair is added. During later terminal growth, further A-P pairs can be added without oscillations, allowing a smooth transition betweenboth modes. (D) Model of somite formation based on posterior oscillations between two cell states [2, 92]. Oscillation becomes arrested andstable patters are formed whenever the level of a gradient (pink) drops below a certain level, determining the AP level at which stable patternsemerge. The gradient is now known to be FGF [96]. The mechanism, proposed in 1982, predicted correctly many unexpected features thatwere later experimentally observed [93].

    15

  • BOX 2: Time-dependent gene activation

    For the purely time-dependent gene activation it is as-sumed that each active gene i produce a component pithat has an activating influence on the activation of thesubsequent gene: The region in which posterior trans-formation can take place is restricted, for instance,due to the requirement of a high BMP/Brachyury con-centration [100]. This signal s in cooperation with thesignal pi produced by presently active gene drives theactivation of the subsequent gene:

    ∂pi∂t

    = αgi − βi pi 3

    The region in which posterior transformation can takeplace is restricted, for instance, due to the requirementof a high BMP/Brachyury concentration [100]. Thissignal s in cooperation with the signal pi producedby presently active gene drives the activation of thesubsequent gene:

    ∂gi+1∂t

    =ci+1g

    2i+1 + bpis∑ni=1 cigi

    − ri+1gi+1 4

    Although models for gene activation under the influ-ence of a morphogen gradient and the time-dependentgene activation share many formal similarities, the ac-tual mechanisms are presumably more different. Thefirst process depends on a direct activation of tran-scriptional feedback loops. In the second, the acti-vation of HOX genes, on the opening of chromatinregions play a decisive role [116]. In this model, anewly activated gene suppresses completely the previ-ously activated gene (Fig. 8). In reality, the switchingoff is not as abrupt.

    state. The direct P-neighbors of the A-cells are stabi-lized, while the other will switch to the alternative state.With each complete cycle one new pair of A/P spec-ifications is added. In the course of time the regionof stable periodic patterning would enlarge on the ex-pense of regions in which cells still oscillate. To obtaina first border and to get a regular and size-regulatedpattern, I assumed that a gradient with a high posteriorpoint exist; in a region of high concentration the oscilla-tion is maintained. Thus, formation of a stable patternneeds a low gradient level as given at a certain dis-tance from the posterior pole. The posterior-spreadingfront where somite formation occurs is an indirect con-sequence of the sequential stabilization, not of an inde-pendent wave-forming mechanism as in the ‘Clock andwave front’ mechanism.

    Although the posterior oscillation and spread of this

    activities towards anterior appeared counter-intuitive,it was the only mechanism I found to be compatiblewith classical observations and to have some relationsto the model derived for insect segmentation. It tookfifteen years until essential points of this model wereshown to be correct [93, 94]. It turned out that themodel predicted correctly that there is

    1. An out of phase oscillation between two activities(one turned out to involve components of the Wntpathway [94]).

    2. Each of these alternating activities gives rise to onehalf-somite. The existence of half-somites was alsoa prediction since this feature has been shown onlytwo years later [95].

    3. A gradient assumed to control the posterior main-tenance versus the anterior block of oscillation; itturned out that this gradient is realized by FGF [96].

    Although the model predicted the essential and un-expected elements correctly, it was frustrating for methat in the seminal experimental paper the model wasquoted as follows [93]: “Our results also argue againstmodels in which a reaction-diffusion mechanism pat-terns the rostral PSM into two states that lead to thesegregation of alternating anterior and posterior somiticcompartments (Meinhardt, 1986)” [92]. There was nodiscussion that the main features were correctly pre-dicted.

    In the model I proposed there is only a moder-ate slowing down of the waves on their way towardsanterior; there is a rather abrupt separation betweenstill oscillating cells and cells that obtained their ante-rior/posterior half-somitic specification (Fig. 7D). Thisis in contrast to what was later observed [97]. However,as expected from the model, it was found that cells stoposcillation in discrete groups, not in a continuous wave-like process that moves towards posterior [98]. This isnot surprising since in nonlinear oscillations it is to beexpected that cells either go through another cycle orstop. Any model according to which an oscillation canbe arrested at an arbitrary phase of the cycle is molec-ularly not realistic. An interesting feature not yet under-stood is that the slowing down of the wave is connectedwith an increase in the amplitude [98].

    It should be emphasized that the 1982-model [2]was very different from the original clock and wave frontmodel [89]. In the latter there are no waves movingfrom posterior towards anterior that come to rest in thesomite-forming zone; the oscillation was assumed toseparate two somites, not being involved in the forma-tion of half-somites. Thus, the original clock and wavefront model predicted a completely different mechanismwith little resemblance to what was later found.

    16

  • Fig. 8: Simulation of space- and time-dependent gene activationfor the regionalizing the AP axis. (A-C) Genes in the anterior partare activated by a promotion of under the influence of a gradient(red) generated by an organizer (green), as described in Fig. 4. As-sumed is an activator-inhibitor system; the inhibitor (red) has a dou-ble function, keeping the organizer localized and act by its longerrange as signal for gene activation. Gene activations are indicatedby pixel densities. To achieve a time-dependent gene activation ofthe more posterior genes 4 to 8, whenever the terminal signal ishigh enough, each gene produces a component that activates thesubsequent gene (BOX 2). The accumulation of this component isdecisive when the next switch will occur. Thus, the time-based pos-teriorization is restricted to a region near the organizer; in the moreanterior region the determination is fixed. (D) If growth would bearrested in a stage as shown in (B), the posterior transformationwould proceed autonomously until the most posterior gene is acti-vated. (E) If the time-dependent posteriorization would not work,only the anterior (head-) genes can be activated.

    11. Time-dependent activation of HOX-genesIronically, one of the reasons to predict the oscillation -the possibility to achieve a precise sequential activationof HOX genes in relation to the periodic pattern - seemsno longer tenable. In mutants that have a longer oscil-lation frequency, the next HOX gene becomes activatedafter a certain time, not after a particular number of os-cillations [99]. Also both processes take place in differ-ent regions of the developing embryo. New HOX-genesare activated the horseshoe-shaped region around theblastopore excluding the midline and organizer [100].In contrast, oscillations and waves occur at the dorsalmidline, i.e., in a complementary region.

    The sequential promotion model as proposed forthe interpretation of a gradient (Fig. 4) can be extendedin a straightforward manner to achieve a sequential‘promotion’ in the course of time. For the simulation Fig.8 it was assumed that the anterior genes are activatedunder gradient control as described above. For themore posterior genes, each (HOX-) gene produces acomponent that has an activating influence on the sub-

    sequent HOX-gene (BOX 2). It is only produced in theregion where the signal from the AP-organizer is high,i.e., close to the organizer (the restriction to the non-organizer mesoderm is ignored in this one-dimensionalsimulation). While models of this kind can be easilyconstructed, so far it is unknown how both the peri-odic pattern of the somites and the sequential patternof Hox-gene activation can be brought so precisely intoregister.

    What terminates the time-dependent posterioriza-tion? Although mainly involved in the DV patterning bymidline formation, the Spemann-type organizer plays acrucial role also in the AP patterning of the trunk bybeing involved in the termination of the time-dependentposteriorization. This is an unusual function of an orga-nizer since, as the rule, the strength of an organizer-derived signal determines the fate of a cell. In am-phibians, cells of the non-organizer mesoderm movetowards the organizer and join the elongating midline(Fig. 2). Due to this movement, cells leave the zonein which posterior transformation takes place, obtainingin this way their final AP determination. As mentionedabove, after removal of the organizer, the anterior neu-ronal genes were almost normally expressed in fishesmutant for BMP [15]. The AP pattern of the trunk, how-ever, was completely missing. This is in agreement withthe view that, due to the absence of the organizer, cellswere unable to escape from the posteriorization untilthe most terminal determination is reached.

    12. A possible scenario for the evolutionaryinvention of segmentation: giving up complete

    separation during asexual reproductionSegmentation, the metameric repetition of body parts,was certainly a fundamental evolutionary invention, forinstance, to allow rapid swimming. Many proposals forits evolutionary origin has been put forward [101]. Al-though segmentation in insects and vertebrates sharesome common features, it is still controversially dis-cussed whether both processes have a common evo-lutionary origin [102, 103].

    Segmentation emerged and was lost several timesduring evolution, suggesting that segmentation was de-rived from mechanisms that were available early in evo-lution in non-segmented animals for a different pur-pose. Here I propose that one of the preceding mech-anisms was asexual reproduction. Primitive organismare usually organized by two organizing regions, one ateach pole, head/tail or aboral/oral. One way of asex-ual reproduction is the insertion of a new tail (T) - head(H) pair, (T/H), somewhere in the body column, con-verting H—–T pattern into a pattern H—T/H–T pattern,followed by a separation at the new T/H border; leadingtwo organisms with identical polarity. Such a separa-

    17

  • Fig. 9: A hypothetical scenario for the evolutionary invention of segmentation by modification of asexual reproduction. (A) The anteroposterioraxis of ancestral organisms is organized by two organizing regions, one for anterior (head, pink, left) and one for posterior (tail, green), realizede.g., by the WNT-pathway. To reproduce asexually, a new pair of tail/head organizers becomes inserted, followed by a separation that gives riseto two complete animals. (B) For segmentation, the insertion of the Wnt-expressing regions was maintained that forms, not accidentally, themost posterior part of each parasegment. In contrast, the head signal was replaced by a signal ‘beginning of the trunk’ (e.g., engrailed, red). Theseparation into individual animals became replaced by the generation of metameric structures that no longer separate from the parental body.The sequential insertion of Wnt signals in short germ insects [106] follows the proposed scheme. (C, D) A system at the borderline betweenasexual reproduction and segmentation, the strobilation of Aurelia [107]. In the polyp stage (C) a repetitive structures is generated that leads tothe shedding off of juvenile Medusas (D); (figure C and D kindly supplied by Barbara Siefker).

    tion occurs spontaneously, for instance, in the flatwormStenostonum incaudatum [104].

    According to this view, crucial for the transition fromasexual reproduction to segmentation was the replace-ment of the tail/head insertion by another pair that didn’tled to a separation. Wnt is involved in both the forma-tion of the posterior terminal end of animals and in theformation of the most posterior part of parasegments[105]. This suggests that the Wnt pathway was origi-nally involved in the determination of the posterior pole.Whenever asexual reproduction should occur by inser-tion of a new tail-head pair, a Wnt activity has to betriggered somewhere between head and tail (Fig. 9A).The insertion of new Wnt regions during growth of shortgerm insects [106] is proposed to be conserved fromthis ancestral process. It is the expected pattern ofa terminal gene that was once involved in asexual re-production and that became subsequently adopted forsegmentation (Fig. 9). For segmentation, the inser-tion of a new WNT activity occurs whenever sufficientspace is available between the terminal Wnt expres-sion and the already established Wnt regions [106], afeature that is explicable in a straightforward manner byour toolkit of pattern-forming reactions.

    In insects the most anterior part of each paraseg-ment is specified by the engrailed gene. engrailed (see

    [76] for review) has no function in the determination ofthe anterior-most structures in any organism. In verte-brates it is activated at the mid/hindbrain border, i.e.,at a region that can be regarded as the most ante-rior part of the trunk. This suggests that the insertionof tail/head pairs for asexual reproduction became re-placed by pairs of signals for end/begin of primordialtrunks. The physical separation of the animals was re-placed by the formation of metameric units; the integrityof the anteroposterior axis became maintained.

    A possible link between asexual reproduction and asegmentation-like process can be seen in the strobila-tion process of asexual reproduction in some Cnidaria.Aurelia aurata (Scyphozoa) forms first a polyp. Start-ing at the tentacle region a repetitive pattern is formedthat is overtly very reminiscent of a segmented struc-ture (Fig, 9C) [107] A substantial part of the polyparound the foot remains non-segmented. Later, thesemetameric units are released as individual ephyra (Fig.9D), the juvenile form of the medusa (jellyfish). Extrap-olating the situation from hydra [16] the non-segmentedpart around the foot is the anterior part of the organ-ism. It is a common feature of many segmented ani-mals that only the posterior part becomes segmented.The tentacle-bearing part at which the ‘segmentation’starts is posterior. In this case, the segmentation does

    18

  • not take place in a posterior growth zone but, unusu-ally, by trigger of an alternating repetitive pattern at aposterior position that spreads towards anterior.

    Thus, it is proposed that, as sexual reproduction be-came the dominant mode of reproduction, asexual re-production became obsolete and was modified to anincomplete separation as seen in today’s segmenta-tion. The evolutionary advantage is clear. The repet-itive segmental organization can provide the scaffold,e.g., for muscle and neuronal organization to allow acoordinated movement. During further evolution someof the segments could specialize to take over particularfunctions including sexual reproduction.

    13. ConclusionIn pre-molecular times, classical observations provideda very informative set of regulatory features. To findpossible molecular interactions we formulated hypo-thetical molecular interactions that described the pro-duction, spread, removal and the mutual regulatory in-terferences between the components in a mathematicalway. By simulating patterning processes on the com-puter it turned out that the classical observations werevery restrictive. Differences between the observed andmodel-expected regulatory features allowed reformu-lating the hypotheses and checking again; the modelsevolved. If a particular model was then able to describeeven more details than originally envisioned, the mod-els found increasing confidence. These models are, ofcourse, minimum models; they describe what is at leastrequired to accomplish a particular step. The minimummodels however, provide a basis to understand what isgoing on. Self-enhancing reactions combined with an-tagonistic reactions are the driving force in these self-organizing processes, both in spatial patterning and inspace-depending gene activation. With the advent ofthe molecular techniques, it turned out that most ofthese models were close to what is actually realized.An intimate interaction between theory and observationcontributed substantially in most branches of naturalsciences to the progress. Theories and mathematicallyformulated models are now an accepted tool in devel-opmental biology, bridging the gap between the obser-vations on the one hand and underlying principles onthe other. By accepting theories, developmental biol-ogy became a normal branch of science.

    Acknowledgment I wish to express my thanks to AlfredGierer. Much of the basic work on pattern formationemerged from a fruitful collaboration and exchange ofideas over many years.

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