Generic oscillation patterns of the developing systems and their role in the origin and evolution of ontogeny

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ARTICLE IN PRESSG ModelIO 3478 1–17

BioSystems xxx (2014) xxx–xxx

Contents lists available at ScienceDirect

BioSystems

jo ur nal home p age: www.elsev ier .com/ locate /b iosystems

eneric oscillation patterns of the developing systems and their rolen the origin and evolution of ontogeny

ladimir G. Cherdantsev ∗

epartment of Biological Evolution, Faculty of Biology, Moscow State University, Moscow, Russia

r t i c l e i n f o

rticle history:eceived 5 March 2014eceived in revised form 13 April 2014ccepted 14 April 2014vailable online xxx

eywords:orphogenesis

volutionelf-oscillationsariabilityctive shells

a b s t r a c t

The role of generic oscillation patterns in embryonic development on a macroscopic scale is discussed interms of active shell model. These self-oscillations include periodic changes in both the mean shape ofthe shell surface and its spatial variance. They lead to origination of a universal oscillatory contour in theform of a non-linear dependence of the average rudiment’s curvature upon the curvature variance. Thealternation of high and low levels of the variance makes it possible to pursue the developmental dynamicsirrespective to the spatiotemporal order of development and characters subject to selection and geneticcontrol. Spatially homogeneous and heterogeneous states can alternate in both time and space being theparametric modifications of the same self-organization dynamics, which is a precondition of transform-ing of the oscillations into spatial differences between the parts of the embryo and then into successivestages of their formation. This process can be explained as a “retrograde developmental evolution”, whichmeans the late evolutionary appearance of the earlier developmental stages. The developing system pro-gressively retreats from the initial self-organization threshold replacing the self-oscillatory dynamics by
a linear succession of stages in which the earlier developmental stages appear in the evolution after thelater ones. It follows that ontogeny is neither the cause, nor the effect of phylogeny: the phenotype devel-opment can be subject to directional change under the constancy of the phenotype itself and, vice versa,the developmental evolution can generate new phenotypes in the absence of the external environmentaltrends of their evolution.
© 2014 Published by Elsevier Ireland Ltd.

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. Introduction

A hypothesis that ontogenesis originates from self-organizationGoodwin, 1994; Cherdantsev et al., 1996; Beloussov, 1998, 2012)

eans that structuring is an egoistic process comparable to origi-ating of the new self-reproduction modes at the intra-individual

evel having neither adaptive value nor inheritance on a scale ofhe organism. The only way in which self-organization can refer tovolution is in that the increase in complexity of the structural pat-erns generates in the developing system new variation canals and,onsequently, evolutionary trends which persist irrespective of anyhange in specific directions of selection. By definition, the devel-ping system arising from self-organization has no developmentalistory, which is certainly not the case for any extant developing

Please cite this article in press as: Cherdantsev, V.G., Generic oscillatioand evolution of ontogeny. BioSystems (2014), http://dx.doi.org/10.10

rganism. It follows, if we assume the self-organization hypothesis,hat what we call the developmental history of a structure arisesfter the structure has emerged (Cherdantsev et al., 1996).

∗ Tel.: +7 84994320425.E-mail addresses: [email protected], [email protected]

ttp://dx.doi.org/10.1016/j.biosystems.2014.04.004303-2647/© 2014 Published by Elsevier Ireland Ltd.

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In dominating view, self-organization is a matter of reaction-diffusing systems (Turing, 1952; Meinhardt, 1982). The inconsis-tence of the theory is quite evident, because of the “interpretationproblem” (Beloussov, 1998). Cells should know what the “local acti-vators” and “distant inhibitors” mean, but how can they do thatbefore selection has taught them to interpret concentrations ofthese substances? In his ingenious work, Turing (1952) emphasizedthat the point of self-organization is in that characters, which in theinitial state could be actualized everywhere in the system, becomerestricted to only a part of this system. This is the only way in whicha part of the system — but not the characters of this part — becomes anew structural domain. The only feasible connection with develop-mental evolution consists in the origination of a domain separationboundary and, consequently, new variation canal emerging on amacroscopic scale. The developing system becomes susceptible tochanges that shift the domain-separation boundary irrespectivelyto the interpretation of characters that distinguish the domain from

n patterns of the developing systems and their role in the origin16/j.biosystems.2014.04.004

its surrounding.It follows from this that self-organization is not compatible with

a mainstream thesis of developmental biology that cells appreci-ate their positions in the developing system with no respect to its

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dx.doi.org/10.1016/j.biosystems.2014.04.004


http://www.sciencedirect.com/science/journal/03032647

http://www.elsevier.com/locate/biosystems

mailto:[email protected]

mailto:[email protected]


ARTICLE IN PRESSG ModelBIO 3478 1–17

2 V.G. Cherdantsev / BioSystems xxx (2014) xxx–xxx

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ig. 1. Scheme illustrating two opposite approaches to morphogenesis, one basing

n the geometry of mass cell movements (B). DV – conventional dorsoventral axoundary, blue arrows – cell movements toward the blastopore dorsal pole, red do

eometry (Wolpert, 1969; De Robertis, 2006). The true seems to beonverse (Cherdantsev, 2006): cells may have different positionsecause, and only because, the shape of the embryo is not uni-orm. The behavior of a cell seems to depend on its position onlyn an extent in which the form and, consequently, morphogeneticotencies of a given area differ from that of neighboring areas. Para-oxically, the closest to self-organization was an ancient conceptf mosaic development considered the embryo as a mosaic of frag-ents, not in the sense of their early commitment but, rather, in the

ense that their commitment, in its initial form, was not a stepwiseierarchical process taking place in the same referent coordinateystem.

To illustrate this point, compare two manners of matching ofhe parts of the embryo to their positions taking as an examplehe idealized gastrulation in Chordates (Fig. 1). If we assume thathe initial shape is uniform (in particular, at the initiation of gas-rulation the blastopore boundary has a uniform curvature), thene get a scheme of gastrulation movements shown in Fig. 1A. In

he absence of geometric differences, values of the cell movementectors can differ only because of different positions of cells withespect to an axis conventionally denoted as the DV (dorsoventral)xis of the embryo. The initial symmetry provides two mass cellows, one (big red arrows) directed to the blastopore boundary, andhe other (blue arrows) directed along the blastopore boundary tohe dorsal pole. These flows do not interact having, instead, a com-

on dependence on the DV polarity. The local concentration of cellsshown by dots) increases at the dorsal and decreases at the ventralide with no change in the blastopore shape, except the blasto-ore closer. The outlined model inspired by modern versions of theositional information theory (see, for example, De Robertis, 2006)asily dispenses with morphogenesis and even physical forces.

In the geometric model, inferred from studies of gastrulationn amphibian (Cherdantsev, 2006; Scobeyeva, 2006) and teleostCherdantseva and Cherdantsev, 2006) embryos the initial shape isot uniform, the curvature of the dorsal blastopore boundary beingmaller than that of the ventral one (Fig. 1B). Therefore, there is no


eed in referent coordinate axes because the DV polarity is a nat-ral consequence of the geometric differences. The point is thatne cannot inscribe the blastopore boundary into a single circum-erence and the consequences of this simple fact are mighty. First,

igning of the cell positions in a referent coordinate system (A), and the other basinghe embryo, Bl – blastopore, red arrows – cell movements toward the blastoporenes – the dorsal blastopore lip contour, dots – local cell concentrations.

local shape differences predict and explain shaping trends – thisbasic idea was first stated by Gurwitsch (1914) almost exactly ahundred years ago. The form itself provides a vector field to changethis form, as shown in Fig. 1B by the small red arrows convertingthe dorsal blastopore boundary into the dorsal blastopore lip. Notethat this is not the case in Fig. 1A where the small red arrows havea normal orientation with respect to the dorsal blastopore bound-ary. Second, the system tending to inscribe the unequal parts into asingle circumference becomes subject to mechanical stress open-ing doors to the interplay of active and passive mechanical forces(Beloussov, 2012). Third, the dependence on geometry leads to adecrease in the number of variables being necessary for a descrip-tion of the dynamics. Bending of the cell flows toward the regionwith a minimal curvature of the blastopore boundary shown inFig. 1B by the big red arrows converts the two-parametric systemof cell flows shown in Fig. 1A into one-parametric one.

Not denying and even emphasizing that the developing systemsclose to those shown in Fig. 1A do exist, there is a good likeli-hood to consider that, in the evolutionary view, these are secondarysystems evolved from the systems shown in Fig. 1B. This hypothe-sis means, first, that the so-called primary embryonic axes haveevolved from a mosaic of areas in which the shape differencesamong the areas were of more importance than the areas them-selves including their positions. Then the hierarchical commitmentof the embryonic rudiments is also a secondary phenomenon orig-inating from inserting of the additional (intermediate) stages oftheir formation. Second, what we call the developmental stagescould have evolved from self-oscillations by turning of the initiallyalternative states of embryonic areas into successive developmen-tal stages of the whole embryo. In Fig. 1B, the ventral counterpartis subject only to a secondary shaping adjusting in to that of thedorsal counterpart. Then, in the evolutionary course, its forma-tion, shifting to an earlier stage of the development and extendingto the overall blastopore boundary, becomes a new stage of thedorsoventral differentiation.

Earlier we have shown that, in order to get both a separation of


new structural domains and oscillatory dynamics it is sufficient tohave a single geometric variable being an analog of the inhibitorin reaction-diffusion systems, while its spatial variance workslike the activator of morphogenesis (Cherdantsev and Grigorieva,

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Fig. 2. Self-oscillation cycle (A–D) in the early epiboly in loach: the arrows showtransitions between the oscillation phases. The blue color – blastoderm, the yellowcolor – yolk cell. The solid lines are referent normals X , dotted lines Ri are normalradii of the outer blastoderm surface whose intersection points (red dots) with theradii Ri constitute referent coordinates Xi permitting to calculate the mean surface

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ARTICLEIO 3478 1–17

V.G. Cherdantsev / Bio

012; Cherdantsev and Scobeyeva, 2012). The intimate connec-ion between the self-organization dynamics and variance suggestshat the well-known alternation of variable and invariable (“phylo-ypic”) developmental stages (Goodwin, 1994) simply reflects thelternation of spatially homogeneous and spatially heterogeneoustates inherent to the self-organization process, and so the gener-lly accepted view that it is a reflection of the evolutionary historyeeds revision. It is likely that the converse is true and persistingf the stages with different variation scales in normal developmentrgues its self-organization origin.

As for a question concerning with the role of selection in thisrocess, one needs to make a clear cut distinction between the evo-

ution of morphogenesis per se and ecologically conditioned trendsf developmental evolution. Some impressive transformations inleavage or gastrulation patterns are obviously connected withccumulation of the yolk (Arendt and Nübler-Jung, 1999), whichs a clear example of the ecological adaptation at early develop-

ental stages. The same is true for the so-call embryonization ofevelopment leading to a formation of extraembryonic tissues. Inontrast to that, there exists at least one “eternal” trend of the devel-pmental evolution persisting irrespective to particular directionsf selection operating on fitness components.

This trend is the origination of stable developmental pathwaysformation of Waddington’s chreods) leading, other things beingqual, to a canalization of variability and ordering of developmen-al successions. Stabilizing or directional forms of selection are theenerally accepted explanation of this phenomenon (Waddington,940; Schmalhausen, 1946; Shishkin, 1984) basing primarily on theact that canalization is a property of the wild type. However, evenor the allocation of scutellar bristles in Drosophila considering toe a classical example of canalization (Waddington, 1972), therexists an alternative explanation of the pattern stability, whichppeals not to selective forces but, rather, to morphogenesis itselfCherdantsev et al., 1996). Attempts to connect the morphogeneticvolution with fitness are not convincing since in most cases it isuestion of a random choice between impressively different, butelectively neutral variation patterns. Long ago the determinativeleavage was believed to lead to a loss (or decrease) of regula-ive capacities at early developmental stages. If this were the case,ne could have considered non-determinative cleavage being moredaptive. According to the current view (Biggelaar and Guerrier,979; Lambert, 2010), the determinative and non-determinativeleavages differ not in regulative capacities or variation scales, but,ather, in subjects of variation. In determinative cleavage, this is

choice of a blastomere becoming an ancestor of a given cell lin-age, and in non-determinative cleavage this is a choice of cellseing included in the same anlage irrespective of their lineages.

A hypothesis considered in this work is that the formation ofhe chreods exists independently on net fitness dynamics. In theight of originating of the development from self-organization, this

eans that the developing system progressively retreats from theelf-organization threshold replacing the self-oscillatory dynamicsy the developmental program in the form of a determined succes-ion of developmental stages. Simultaneously, the embryo evolvesrom a mosaic of parts, each having its own spatiotemporal scalef development, to the formation of referent points and axes com-on to different parts of the embryo and different developmental

tages.

. The active shells: a generalizedscillation-differentiation model


In this work, we consider the cell surface being an active shellhat shares basic properties of stretched elastic shells and, inddition, is capable of active growth owing to recruiting of the

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curvature, C∗ = 1/ Xm, and its spatial variance, Cvar = 1/ Sum (Xi–Xm)2 , where Xmis the mean of Xi. For other explanations, see text.

new surface elements (Cherdantsev and Grigorieva, 2012). Passiveforces allowing for the shell surface expansion and leading to adecrease in the surface/volume ratio arise from the intrinsic pres-sure inside the cells, or epithelial sheet cavities. Active forces of thelateral pressure inside the shell leading to an increase in the sur-face/volume ratio arise, at a single cell level, from inserting of thenew surface elements into the cell surface or, at an epithelial sheetlevel, from intercalating of the cells. In the limiting case of a single-layered sheet, the shaping concerns with an apical enlargementand basal narrowing of free cell surfaces, which, at the apical sheetsurface, generates forces of the lateral pressure being indistinguish-able from those arising with the intercalation of cells (Cherdantsev,2006).

In order to illustrate how the active shells work in morpho-genesis, we consider the epiboly in loach embryos studied inexperiments with the time-lapse recording of individual develop-mental pathways (Cherdantsev and Tsvetkova, 2005; Cherdantsevand Grigorieva, 2012). In each individual embryo, the blasto-derm shape alternates in time the forms with high and lowsurface/volume ratios, which means the smaller segments of thespheres with greater radii alternating with larger segments of thespheres with smaller radii. These periodic shape changes concernwith changing of the symmetry, because the forms with a highsurface/volume ratios are asymmetrical, in contrast to radially sym-metrical forms with a low surface/volume ratio (Fig. 2). Insofar asthe asymmetry implies an increase in the within-individual shapedifferences, we observe periodic changes in both the mean blas-toderm shape and its spatial variance, which is the main principleof the active shell behavior. In fact, these changes are strictly peri-odic only in respect to the blastoderm surface shaping because, ateach oscillation loop, the proportion of cells accumulated at theblastoderm edges increases (Cherdantsev and Grigorieva, 2012).

We assume that this behavior is a matter of changing of the meansurface curvature, C*, against its spatial variance, Cvar (Cherdantsevand Scobeyeva, 2012). For a rough definition and practical measur-ing of the C* and Cvar, it is sufficient, in a plane curve correspondingto a cut through the shell surface fragment, to drop, at equal angu-lar distances, a few normal radii, Ri, up to their intersections witha referent normal radius, X (see the red dots in Fig. 2). The refer-


ent normal radii should be dropped from a referent point being atequal distances from the blastoderm edges that may, or may not,correspond to the maximum of the outer surface curvature. We

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Fig. 3. Scheme illustrating the work of the active shell model generating self-oscillation patterns: the ordinate ( C∗) is the mean outer surface curvature, abscissa( Cvar) is its spatial variance, the figures are the same that in the previous figure. Thesmooth third order curve is that of F(C*, Cvar), the red arm corresponding to unsta-bcs

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Fig. 4. Scheme illustrating the parametric transition from an oscillation pattern toa choice between alternative stationary states, one corresponding to the spatiallyhomogeneous shape of the outer blastoderm surface with a high mean curvature andlow spatial variance (A), and the other corresponding to the spatially differentiatedblastoderm shape with a lower mean curvature and higher spatial variance (B). Insome teleosts, for example, in zebrafish, the transition to the second stationary stateis anticipated by an asymmetry (C) arising from differences in the active surface

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le, the blue arms corresponding to stable arms, the straight line intersecting theurve is C∗ = kCvar. For an explanation of the movement in different cycle phases,ee text.

et a one-parametric set of the points Xi falling on the referentormal radius in which the mean distance the referent point pro-ides a measure of the C*, while the dispersion of distances permitso estimate the C* variance, Cvar, in a standard way, as shown inig. 2. If the shell is closed, then the Cvar value can be estimated byeasuring of the maximal diameter of an area of the intersection

f different normal radii dropped from the shell circumference.It is important to emphasize that we are considering shap-

ng subject to the spatial unfolding principle (Cherdantsev, 2006),hich means the identity of moving of the shell surface elements

nd shaping of the surface along which they move. In particular,e assume that relationships between the points Xi correspond-

ng to the radii of the local shell surface curvature do not go beyondhe equation dXi/dt = (RI − R*) 2Xi (see Cherdantsev and Grigorieva,012), where RI is a local and R* is a mean radius of the curvature.his means that the surface/volume ratio increases with the mini-al access of the new surface, which permits to consider shaping

ectors being along the gradients of the local shell surface curva-ure.

The C* provides a macroscopic analog of the inhibitor whilevar acts like the activator in reaction-diffusion systems and theequirements to the dependence of C* on Cvar are not analyticeing common to all robust non-linear dynamical systems capa-le of self-organization (Belintsev, 1990). It is sufficient that theurve F(C*, Cvar) correspond to a smooth third order curve havingwo stable and one unstable arm between the stable ones (Fig. 3).he stable arms (blue in Fig. 3) mean that C* and Cvar are neg-tively connected, which, in turn, means that the passive stretchf the shell is equilibrated by the active growth of the surface,nd vice versa. At these arms, the active and passive forces actn mutually opposite directions, the passive stretch leveling sur-ace swellings created by the active surface growth. The unstablerm (red in Fig. 3) corresponds to a positive feedback between thective growth and passive stretch of the surface, because bending ofhe surface attended by an increase in the surface area (and, conse-uently, decrease in the surface curvature) attenuates its resistanceo passive stretching.

The beginning and the end of each loop of the shape oscilla-ion cycle correspond to radially symmetrical forms whose outerontours are close to those of the spherical segments (Fig. 3A).


xhausting of the surface/volume ratio switches the active surfacerowth leading to an increase in this ratio at the expense of decreas-ng of the outer surface curvature and, consequently, increasingf the spatial heterogeneity of the outer surface shape (Fig. 3B).

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tension at opposite edges of the blastoderm/yolk separation boundary (the blackarrows).

At the bending of the curve, the negative connection between thesurface curvature and its variance should have turned into the pos-itive one, which would have meant that the blastoderm had triedto decrease its surface/volume ratio at the expense of increasing ofthe spatial heterogeneity of the form. Such a movement is not sta-ble, because compressing of the blastoderm surface (increasing ofthe surface curvature) promotes the surface arching making thesystem to travel to one of the stable arms of the curve. There-fore, when reaching the first bending point, the system jumps tothe second stable arm, which means the areas with different sur-face curvature being subject to spatial segregation (with furtherincreasing of the variance) under the constancy of the mean surfacecurvature (Fig. 3C). Then the system moves over the second stablearm increasing the mean curvature at the expense of decreasing ofthe variance until it reaches the second bending point at which,if the system had continued to move over the curve, its move-ment would have become unstable (Fig. 3D). Therefore, the systemjumps back to the first bending point the curve completing the cycleloop.

Oscillations persist until the line C* = kCvar (purple in Fig. 3)intersects the curve F(C*, Cvar) at the unstable arm of the curve,that is, until the k value is close to unity. Insofar as the mean curva-ture is indicative to a contribution of passive stretches arising fromthe intrinsic pressure while its spatial variance is indicative to thatof active forces of the lateral pressure inside the shell arising fromthe active growth of its surface area, this means the contributionsof passive and active forces being roughly equal. Given that we donot consider the limiting cases in which passive or active forcesare negligibly small, the oscillatory behavior turns into the spa-tial differentiation when the slope of the C* = kCvar is essentiallymore or less than unity. In the first case, when the line intersectsthe first stable arm of the curve, we get a stationary state corre-sponding to the spatially homogeneous and radially symmetricalblastoderm form being close to the minimal surface/volume ratio(Fig. 4A). In the second case, when the line intersects the secondstable arm, we get a stationary differentiation of the opposite blas-toderm edges (Fig. 4B). In loach, and in other teleost embryos, theinflated edge whose surface/volume ratio is close to the minimal


feasible value anticipates the dorsal while the deflated edge witha reverse surface/volume ratio anticipates the ventral blastodermedge (Cherdantseva and Cherdantsev, 2006).

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It is easy to see that differences between the dorsal and ventraldges are essentially the same that between the successive blasto-erm shapes within a single loop of the oscillation cycle. One canay that the dorsal and ventral edges adopt morphological statesorresponding to the opposite phases of the oscillatory regime.he next step of turning of the oscillations into the succession ofevelopmental stages is quite simple and consists in replacing ofhe differences between alternative states of the dynamical sys-em by the parametric ones. The normal epiboly of loach embryosegins with the radially symmetrical blastoderm shape, then passeshrough one or two oscillation loops and, at last, differentiates thepposite blastoderm edges. This perfectly corresponds to a gradualecrease in the value of the parameter k, which, in turn, means thathe contribution of active forces increases as compared to that ofassive forces. However, it is not sufficient for obtaining of the trueevelopmental succession, because, in the course of these genericscillations, the dorsal form of a given edge can become ventral athe next loop of the cycle, and vice versa. The only feasible decisiononsists in bestowing of the asymmetry shown in Fig. 4A on thembryo shown in Fig. 4B, to get the embryo shown in Fig. 4C. Thesymmetry cannot be the same that originates at later stages, butt can borrow geometric differences that become initial conditionsor future oscillations attaching the “dorsal geometry” to the samelastoderm sectors. In zebrafish, these differences are those in thective tension of a separation boundary between the blastodermnd the yolk shown in Fig. 4C by the black arrows (Cherdantsevand Cherdantsev, 2006). In this, and only in this sense, the ear-ier developmental stages are the later stages of the developmentalvolution.

. Replacing of the metagenetic life cycle by the ontogenyt the origin of metazoans

The developmental evolution of metazoans starts from therimary metamorphosis in which the alternating forms are notevelopmental stages of the organism but, rather, different lifeorms whose alternation is only one feasible form of theirelf-reproduction. Strictly speaking, what we call the metazoanntogeny originates not from the life cycle but rather from aypercycle being a series of nested cycles, each being capablef the egoistic self-reproduction. The point of the evolution is

conversion of nested cycles into a single cycle being capa-le only to the self-reproduction of its own, which is the mainrerequisite of origination of the developmental schedule. This

ncludes, first, restricting of their autonomous self-reproductionBuss, 1987) and, second, originating of the new self-reproduction

ode, which refers to a whole series of the nested cycles. What weall ontogeny is, in a sense, a new self-reproduction mode whoseharacteristic feature is a reproduction of the developmental path-ays.

A state that one could consider being closest to the ancestralne, we find in primitive Sponges whose development preservesetamorphosis similar to that observed in the life cycles of the Pro-

ozoans (Ereskovsky, 2010). The egg, after a period of the intenserowth followed by fertilization, passes through a series of pal-ntomic (without G1 phase) cell divisions that form ciliated cellsf the blastula, the first generation of ciliated cells. The palintomyeans a timely break between proliferation and self-reproduction

t the cell level, and this is the reason why Haeckel’ blastea couldot exist in the form of an adult organism (Zakhvatkin, 1949).astrulation is the same that primary metamorphosis – the epithe-


ial to mesenchymal transition (EMT) in which ciliated cells drophe cilia, and so the spherical epithelial sheet turns into a solid

ass of mesenchymal cells. In this primitive state, the conti-uity of developmental information between the preceding and

PRESSs xxx (2014) xxx–xxx 5

subsequent phase is out of place. After metamorphosis, cell divi-sions become monotomic (with G1 phase) restoring a connectionbetween the proliferation and self-reproduction. A second gener-ation of ciliated cells arises in the form of choanocytes, which cangive rise to the germ cells. Thus, a characteristic feature of themetazoan life cycle first noted by Zakhvatkin (1949) is the pres-ence of two generations of ciliated cells in the same organism.The principal scheme of developmental succession in metazoans– fertilization → blastulation (palintomic period) → gastrulation(metamorphosis, restoration of monotomy) → organogenesis – iscertainly subject of modifications, but at the heart of a process itproves to by strikingly stable.

It is easy to infer this succession from protozoan life cyclesbeing the hypercycles consisting of two nested cycles (Fig. 5). Acell marked in Fig. 5A by the asterisk belongs to different cyclesbeing an analog of a saddle point of the dynamical system. It isready to continue its development by both palintomy (the red cyclein Fig. 5A) and monotomy (the blue cycle in Fig. 5A). Palintomicdivisions cease with a formation of the blastula analog – a sphereconsisting of small ciliated cells. The sphere dissociates into singlecells and each cell begins to grow without division until it acquiresa capacity of monotomic divisions. Alternatively, a cell marked bythe asterisk can become a large ciliated cell with a monotomiccycle (the blue cycle). Dropping of the cilia before each divisionis obligatory, because Metazoans could originate only from Pro-tozoans having only one center of the formation of microtubules(Buss, 1987).

Red and blue counterparts of the described hypercycle alter-nate in time (though not regularly), which permits to denote theseas successive generations, N and N + 1, as shown in Fig. 5A. Onecan say that these counterparts compete for recruiting of the “sad-dle point cell” shown by the asterisk in Fig. 5B and the competitiondrops, together with the saddle point, when two cycles, N and N + 1,fuse, which is equivalent to a “mirror duplication” of the cycle N,as shown in Fig. 5C. We get a cycle containing, in the form of asuccession, all homologs of the future evolutionary stable stages ofmetazoan development. Thus, the alternation of cycles that initiallyhave corresponded to successive generations becomes a succes-sion of forms alternating within the single cycle and, consequently,within the same generation.

These open doors to what we call heterochronies, which simplymeans a redistribution of the investments of different develop-mental stages in the overall ontogeny (including the time of thegerm cells formation) basing entirely on their investments into netfitness. In contrast to that, the main evolutionary event consist-ing in eliminating of the saddle point refers not to selection, butrather to self-organization, insofar as the saddle point, being themost “hot” point of the dynamical system, should vanish becauseof a unidirectional response of the system to bidirectional fluctua-tions. Corresponding equations tracing back to Delbruck and Szilardare those of the cross-inhibition, and so the self-organization isa mere result of the instability of a state in which two mutuallyexclusive pathways have similar likelihood to continue. The sys-tem is non-holonomic because the accuracy of self-reproductionof a hypercycle having the saddle point yields to that of a sin-gle cycle with no saddle points. Yet, even after originating ofthe single life cycle, the continuity of developmental informationbetween the alternating life forms lacks because of the absenteeof causal relationships between the developmental trends of pre-vious and subsequent forms. The continuity of information beingnot a prerequisite but rather a sum of the developmental evolu-tion arises gradually by adjusting of the variation pattern inherent


to a given developmental state to that of a subsequent state.This general evolutionary trend considering in the next sectionsis principally the same that we have briefly considered in Section2.

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Fig. 5. Scheme of origination of the primary life cycle in metazoan animals: A – the initial cycle in the form of alternating generations N and N + 1 in a protozoan ancestor, 1– m ando egg, It sis), 3

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age: the blastomeres acquire a standard tetrahedral configuration(not shown in Fig. 6) opening doors to a repetition of the oscillationcycle in pairs of sister blastomeres.

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palintomic divisions, 2 – growth, 3 – formation of the ciliated free-swimming forrigination of a saddle point (asterisk); C – the basic life cycle of Metazoans. I – thehe mature somatic cell (choanocyte); 1′ – cleavage, 2′ – gastrulation (metamorpho

. Evolution of the cleavage by adjusting to the epithelialattern of the blastula

From the very beginning of the evolution of multicellular ani-als, the transition from a single cell to a solid mass of cells

morula) encounters an obvious conflict between two oppositeodes of postmitotic cell movements, one inherent to free-living

ells and the other – to cells of the organism. In a freely moving sin-le cell, its anterior end is a source, while the posterior one is a sinkf the free surface, and so are relationships between the free polend equatorial zone of a dividing cell. The free pole is homologouso the anterior, the equatorial zone (that of the division furrow) –o the posterior end of a free moving cell. This is natural for singleells, but not for cells fated to develop together.

As a result, in low invertebrates, at least in first cleavageivisions, we observe oscillations of the cell shape. The whole oscil-

ation cycle persists only in those groups in which the first cell (thegg) has no polarity of its own, for example, in a free-living marineematode Pontonema vulgare (Cherdantsev, 2003). After the firstleavage, the sister cells have reduced contact surfaces, which is

reminiscence of division of free-living cells. In order to describehe first loop of the cleavage cycle in terms of the active shell modelsee Section 2), we assume that shape changes occurring in the sis-er cells are mirror-symmetrical, so that it is sufficient to describehat happens with one of these cells. We are describing the C* and

var in the same manner that in Section 2 using as a referent nor-al radius the line perpendicular to the contact cell boundary or

eing its projection into the plane (Fig. 6).At the start, the outer blastomere surface has a shape being

lose to that of the spherical segment (Fig. 6A) and the movementver the first stable branch of the curve F(C*, Cvar) consists in thenlargement of contact cell surfaces at the expense of decreasingf the mean outer surface curvature. The greater segment of themaller sphere becomes a smaller segment of the greater sphere,hich means an increase in the surface/volume ratio and shift of

he geometric center of the cell toward the contact surface. Thisccurs at the background of increasing of the Cvar, as it followsrom an increase of the area of intersection of local radii of the


uter surface curvature. At the bending point of the curve, the twoells have a common geometric center dispersed around their con-act zone center (Fig. 6B). By the reasons described in Section 3,he system becomes instable and jumps to the second stable arm

growth, 4 – dropping of the cilia; B – the integration of branches of the cycle withI – the blastula, III – the cell having passed the metamorphosis (gastrulation), IV –′ – organogenesis, 4′ – ovogenesis. For other explanations, see text.

of the curve at the expense of further increase in the spatial het-erogeneity of the outer cell surface under a constancy of the C*value (Fig. 6C). The contact surface splits into convex and flat areas,which means blastomeres moving one over another into mutuallyopposite directions. The blastomere twisting is an invariant featureof different types of the early cleavage, particularly of the spiralcleavage, and, in most cases, this occurs before a formation of thenext cleavage spindles. The coincidence between the asymmetry ofthe blastomere shape and that of the loach blastoderm in the mor-phogenetic cycle of epiboly (see Fig. 3) is striking suggesting thatthe active shell model fits in well to both cellular and supracellularlevels of morphogenesis.

Having jumped to the second stable arm of the curve, the system,because of exhausting of the resources for a further active growthof the blastomere surfaces, begins a backward movement increas-ing the C* value with decreasing of the Cvar (Fig. 6D). The backwardjump to the first stable arm corresponds to the next (second) cleav-


Fig. 6. Scheme of morphogenetic self-oscillations in the cleavage cycle of a free-living marine nematode, Pontonema vulgare. The designations of the axes arestandard; C∗ and Cvar refer to the outer surface of one (arbitrary chosen) of thesister blastomeres, the solid and dotted lines having the same meaning that in Fig. 2.Only the shape dynamics of a pair of sister cells is shown, for other details, see text.


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Fig. 7. The normal cleavage pathways in Pontonema vulgare (arrows) until thedegenerated (equifinal) eight-cell stage. The spindles are shaded. Configurations in

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Passing through the whole cycle is only in the range of k val-es in which the line C* = kCvar intersects the curve F(C*, Cvar) athe unstable arm. If this is not the case, stationary points appearrresting the blastomere movements at a low (small contact zone)r high (large contact zone) surface/volume ratio. In fact, variationsn k values are the independent variations owing to the indepen-ence of blastomere movements upon the proceeding of a cell cycleithin each of the blastomeres. The meaning of the cleavage cycle

hown in Fig. 6 is in providing of the algorithm of pre- and postmi-otic movements of sister blastomeres whose dynamic behavior isree from any impact of the egg polarity and interactions betweenon-sister blastomeres.

In most invertebrates including parasite nematodes, the oscil-ations persist only in the form of modifications of the initial cycleirected to adjusting of the cleavage to subsequent developmen-al stages. This, together with oscillations, allows for the diversityf cleavage pathways observed in Pontonema (Fig. 7). Configura-ions shown in shaded squares in Fig. 7 are those deviating fromhe standard cycle and being indicative to different groups of par-site nematodes (for example, to Rhabditidae and Ascaridae). Inhese groups, we observe a connection between the main axesf the embryo and those of the egg. The question is whether thearly cleavage pattern adjusts to the egg axes, or to those axeshat arise by self-organization at later developmental stages. Therst possibility is obviously out of place because in Nematodes theelationships between the egg poles and those of the embryonicnteroposterior axis are not distinct (Guerrier, 1967). On the otherand, it is easy to trace how geometric differences that arise in free-

iving nematodes at the 8-cell stage bypass into cell differences thatrise in parasite nematodes at earlier cleavage stages.

In Pontonema (Fig. 8A–D), all cleavage pathways converge to theame 8-cell configuration whose geometry leads to a separationf blastomeres allocated at geometric poles of the configuration


nd having four neighbors from an equatorial ring of blastomeresshown by red in Fig. 8C) each having five neighbors. Differences inhe number of neighbors use to trigger topological rearrangementsIsaeva et al., 2012) and, in fact, one of the equatorial blastomeres

ig. 8. Matching of the primary to secondary cleavage forms in Nematodes. In Pontonemour-cell configurations, C – the eight-cell configuration having no polar axes of symmetry,Ems) blastomere, D – one of these cells becomes the Ems cell (red) thus bestowing on a

he Ems blastomere is discernable in the T-shaped configuration of four blastomeres by ieferent axis common for all cells of the rhomb-shaped four-cell configuration. Ant – ante

shaded squares are those deviating from the standard cycle shown in the previousfigure.

Source: Modified from Cherdantsev (2003).

(to the unpublished observations of the author, their choice isarbitrary) invaginates inside the embryo to become the entome-sodermal blastomere EMS (shown by red in Fig. 8D). If we assumethat among configurations shown in Fig. 9B, the evolution adoptsthose being most similar to subsequent developmental stages, thenit should select a rhomb whose central zone anticipates the equa-torial ring of the 8-cell stage. This is exactly the case in parasiticnematodes (Fig. 8, in the frame) added by the differences betweenanterior and posterior, and between dorsal and ventral sides of theblastomere configuration. The DV differences are essentially the


same that originate in free-living nematodes after invagination ofone of the equatorial ring cells, because the EMS blastomere is thatwhose geometric center is closest to the geometric center of thewhole blastomere configuration. Thus, the DV polarity, being at

a (A–C); A – the initial two-cell configuration, B – a sample of set of intermediate each of the cells shown by red having equal chances to become the entomesodermalcell configuration both dorsoventral and anterior-posterior polarity. In Ascaris (E),ts maximal adjacency. Note, that in Ascaris, and not in Pontonema, the DV axis is arior. Post – posterior poles, ect – ectoderm, P – germ stem cell.

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Fig. 9. A general scheme of relationships between the polarity of single cells and polarity of a spherical epithelial sheet (A) and infeasibility of inscribing of the whole sheeti rces ot le, ANs

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nto a single sphere (B). The red arrowheads are anterior single cell ends being souhe surface, the dotted blue arrows are cell surface flows on an epithelial sheet scapheres maximally approached to anterior and posterior halves of the embryo.

he start the effect of separation of the EMS blastomere becomes aause of its separation in earlier development, which occurs at latertages of the developmental evolution.

Note that the establishment of an unequivocal connectionetween the form and its developmental history does not leado decreasing of the variation. In fact, when a variable cleavageecomes the determinative one, the shape differences of individuallastomeres repeat those arising in different types of configurationsonsisting of equally shaped blastomeres. In the four-cell configura-ion in parasite nematodes (Fig. 8E), the dorsal and ventral types ofells differ in the same way that upper (“loose”) and lower (“dense”)our-cell configurations in Pontonema shown in Fig. 8B. The evo-ution of cleavage from free-living to parasite nematodes selectsonfigurations deviated from those going to the self-oscillationycle namely because of their deviation from the initial cleavagelgorithm in which contact interactions of cells occur only betweenhe sister cells. This selection operates not on fitness components:mong a variety of changes in preceding developmental stages, itxtracts those that, first, are in causal connection with subsequenttages and, second, have no negative effects on fitness.

. Origination of the main body axes

.1. Origination of the AP polarity

The second conflict in the development of multicellular organ-sms is that between the polarity of single cells and polarity of apherical epithelial sheet of the blastula. Cells in the epithelial blas-ula are polarized so that their apical (outer) ends are homologouso anterior, and their basal (inner) ends to posterior ends of freely

oving single cells (Cherdantsev, 2006). It follows not only fromorphological evidences (such as apical positions of the nuclei), but

lso from a well-known fact that isolated epithelial sheet fragmentsend basal side inward, each cell being subject to an outward move-ent enlarging the apical and narrowing basal cell surfaces. As in

ree moving cells, the anterior end should be a source, while theosterior one a sink of the surface. The polarity on a scale of a closedpithelial sheet should be the same that in single cells, but the flow


rom the source to the sink of the sheet outer surface is a lateral flowith respect to single cell polarity vectors (Fig. 9A). It follows, first,

hat the primary difference between anterior and posterior ends of sheet is independent on a choice of a referent coordinate system

f the new surface, the blue arrows are posterior single cell ends being the sinks ofT – anterior, POST – posterior ends of the blastula, the purple and blue circles are

(“positional information”) and, second, that, with superimpositionof surface flows on the cellular and supracellular scales, the vectorfield has a saddle point in the posterior sheet region. This is a pointat which the closed epithelial sheet should be unstable providing anopportunity of initiating of the EMT. Moreover, it follows that theclosed epithelial sheet inevitably consists, all things being equal,of spherical fragments belonging to the spheres of different radii(Fig. 9B), which explains, first, why the blastula geometry cannotbe uniform and, second, why it is a transient morphological statewith no evolutionary trends on its own. The idea that the spheri-cal epithelial sheet is topologically “a sphere with a hole” (Presnovet al., 2010; Isaeva et al., 2012; see also Cherdantsev and Kraus,1996) is almost true, but, in order to infer the origination of primaryembryonic axes, one needs to add a consideration of both evolution-ary and developmental dynamics of mass cell movements. In thestrict sense, the “holes in a sphere” are not topological holes, butsingularities of mapping of the plane into the plane (Cherdantsev,2006) that arise simply because maintaining of the spherical formis the active process.

Two mentioned above (see Section 2) surface movement modespersist in epithelization allowing to consider the epithelial sheetas being a multicellular active shell (Cherdantsev and Grigorieva,2012). One of these modes is a planar one being a source of thenew free (outer) surface connected with deviating of the contactcell surfaces from normal orientation, and the other is a radial one,which normalizes their orientations at the expense of an increase inthe outer sheet surface curvature. The presence of two movementmodes means that any movement vector includes planar (tangen-tial) and radial (normal) components, which permits to apply tothe system Brouwer’s fixed-point theorem (cf. Isaeva et al., 2012)stating that in the closed surface there will be at least one point atwhich the planar vector is zero. Insofar as epithelization includesthe planar component, from the physical point of view this meansa presence of an area with the lack or delay of epithelization (Krausand Cherdantsev, 1999; Cherdantsev, 2003). Planula, a nodal stageof the development in Cnidarians, is a degenerate form because itcan arise by both fusing of the epithelial sheet fragments omittingthe blastula stage (Fig. 10A and B) and immigrating of the cells from


a blastula pole being deficient for epithelization (Fig. 10C). Invari-ably, in both individual variations and taxonomic differences, theplanula posterior pole (Fig. 10D) is a pole at which the vectors ofthe outer surface planar movement (red arrows in Fig. 10) tend to

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V.G. Cherdantsev / BioSystems xxx (2014) xxx–xxx 9

Fig. 10. Epithelization of cells and formation of the AP axis in cnidarian embryos: A–C – epithelization of cells in a marine hydroid Dynamena pumila (individual variations),D – preplanula. Red arrows – fields of the planar cell surface flows, asterisks – their stationary points (“holes in the sphere” in Brouwer’s sense), ANT – anterior, POST –posterior ends of the planula. The blue cells (presumptive ectoderm) are matters of primary, yellow cells (presumptive endoderm) – of secondary epithelization. The lastp ositio

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epithelial sheet, which leads to a formation of the blastopore andits circumference in the form of a torus that surrounds invaginatingcells (Fig. 11D).

Fig. 11. Alternations in the outer and inner curvatures of the vegetal epithelial sheetduring the blastulation (A–C) and in the beginning of gastrulation in sea urchin

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oint of the outer sheet closure is an evolutionary primer of the blastopore whose p

ource: Modified from Kraus and Cherdantsev (1999).

ero thus corresponding to a fixed point in the sense of Brouwer’sheorem (see asterisks). Degeneracy means that the primary APor oral-aboral) axis persisting, with secondary modifications, inll multicellular organisms arises from self-organization. It followsrom this that internalization of cell, which we call gastrulation, isot a consequence, but rather a starting point of the blastula evolu-ion following from an attempt to make a sphere from an epithelialheet consisting of different counterparts.

If the epithelial blastula were spherical, then the orientationsf cell contact surfaces would be normal projecting into a singleeometric center of the epithelial sheet. This is never observedn morphogenesis of real blastulas. The early blastula of Echino-erms consists of two epithelial sheets having different surfaceurvatures in animal and vegetal counterparts, because the orig-nation of a “sphere with a hole” shifts to the early cleavage, to atage of separation of the micromeres, or even to a stage of orig-nation of the egg animal-vegetal polarity (Presnov et al., 2010).he subsequent development tends to make a sphere with a sin-le geometric center, but it proves to be a patchwork initiating aew loop of oscillations on supracellular scale (Fig. 11). At initia-ion of the epithelial blastula, the orientation of contact surfaces ofegetal cells is not normal, and so, in order to normalize their orien-ations and adjust the outer surface curvature to that of the animalemisphere, the contact cell surfaces become matters of additionallongation inevitably attended by planar cell flows (Fig. 11A, seeed arrows). The overall outer surface shape approaches to thatf a sphere, but this occurs at the expense of attenuating of theell anteroposterior (apical-basal) polarity because of decreasingf the difference in the curvature between the outer and inner veg-tal sheet surfaces (Fig. 11B). At a point at which the inner surfaceecomes almost flat, the vegetal half becomes an area of a sink of theree outer surface inward the embryo, which is equal to the inver-


ion of the initial anteroposterior polarity of single cells followed byheir immigration into the blastocoel (Fig. 11C, see blue arrows). Ifhis had not gone beyond the immigration of cells, as it occurred in

majority of Cnidarians, this would have meant that, in a course of

n on a posterior pole of the planula is not stable (see text).

the blastulation, the developing system had returned to what hadbeen a starting point of its evolution. However, in echinoderms andmost invertebrates, the immigration is added by invagination of the


embryos (D) following from unsuccessful attempts to inscribe the embryo into asingle sphere. The blue and red circles are geometric centers of animal an vegetalhalves, red arrows – cell flows over the outer sheet surface, blue arrows – inversionof the individual cell polarity. Yellow – archenteron, red – the circumferential rolleraround the blastopore.


ARTICLE ING ModelBIO 3478 1–17

10 V.G. Cherdantsev / BioSystem

Fig. 12. Faint self-oscillations alternating the tapering and flattened shapes of thevts

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egetal plate before the beginning of gastrulation in sea urchin embryos. Designa-ions at the graph are standard, the C∗ and Cvar refer to the outer vegetal plateurface.

Yet the oscillations on a single cell scale (see Fig. 6) extinct whenhe dynamics of the surface/volume inside the cells becomes neg-igibly feeble as compared to that on an epithelial sheet scale, thenteractions between active and passive forces remain the same, thentra-blastocoel pressure becoming a source of the passive forces.he generic oscillatory behavior emerges on a supracellular scalef different epithelial sheet parts have different radii of their meanurvature. Their equalization, if it includes an active shell surfacerowth at least in one part of the sheet, leads to the formation of

“pseudospherical” sheet consisting of two spherical fragmentsf similar radii being segments of different spheres (see Fig. 11B).ecause of the difference in surface/volume ratios of animal andegetal counterparts, the animal counterpart being a greater seg-ent of a smaller sphere, such equilibrium is not stable.According to the active shell model this should lead, before the

eginning of the gastrulation, to oscillations in which the vegetalactive) part of the blastula alternates tapering and flattening ofhe epithelial sheet (Fig. 12). At least one loop of such oscillations iseally observed in the normal development of sea urchin embryosetween the midblastula and late blastula stages (E. G. Ivashkin,ersonal communication). The dynamics should depend on bothhe shape of the curve F(C*, Cvar) and slope of the line C* = kCvar. Its reasonable to assume that the oscillations occur under a little con-ribution of active surface flows (shown in Fig. 11 by red arrows),hich means the unstable arm of the curve F(C*, Cvar) having a

aint slope, while the k value is close to unity, as shown in Fig. 12.n this figure, both C* and Cvar refer only to a vegetal epithelialheet whose tapering means the preponderance of passive whileattening means the preponderance of active forces.

With further accession of the active lateral pressure inside thisheet, which is one of the effects of an increase in the cell den-ity owing to cell elongation, the contribution of the active forcesncreases, and so does the slope of the unstable arm of the curve(C*, Cvar). The active shell model predicts origination of twoteady states, one when the line C* = kCvar intersects the first sta-le arm of the curve, and the other when it intersects the secondtable arm. In the first case, the passive forces overcome the activene, which obviously corresponds to a dominating in Cnidariansituation of the absentee of invagination and tapering of the polet which cells immigrate inside the embryo (Fig. 13A and A′). In theecond case, when the k value decreases so that the line intersects


he second stable arm, this leads to a replacement of cell immigra-ion by an invagination of the epithelial sheet (Fig. 13B, B′), becausef the increase of a contribution of active forces of the lateral pres-ure. The increase in the spatial variance realizes in alternating of

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the mutually opposite cell polarity vectors equilibrated by oppo-site signs of the curvature of the same (inner or outer) surfaces.Mechanically, this corresponds to equilibrium of mutually oppo-site active forces, one tending to make a sphere from the blastoporebottom, and the other tending to make its mirror image from theblastopore circumference (see black arrows in Fig. 13B′). This equi-librium inevitably leads to origination of a flex that separates thetorus from the archenteron.

Yet the blastula evolution is primarily a translation of gastrula-tion movement patterns to a closed epithelial sheet, this does notmean that this evolution does not influence the gastrulation itself.Before the line C* = kCvar has intersected a second stable arm ofthe curve F(C*, Cvar), it should intersect this curve at a bendingpoint between the stable and unstable arms, which corresponds toa metastable state of the developing system (Belintsev, 1990). Thisstate shown in Fig. 13B by an intersection between the dotted lineand the curve (Fig. 13B1) is stable to small random fluctuations, butnot to those having finite amplitude, such as a collective immigra-tion of cells in cnidarian or echinoderm embryos (Fig. 13B2). In thebeginning of developmental evolution, the bundle of invaginatingcells persists irrespective to their inward movements acting like ananchor to prevent the emigration of single cells from the epithelialsheet and thus accumulating the active stresses inside the sheet. Onthe evolutionary scale, this leads to the origination of a correlationbetween the archenteron and circumferential torus that proves tobe evolutionary stable. It is remarkable that fragments of the cir-cumferential torus, and not those of the archenteron bottom, arecapable of inducing of the new AP axis in cnidarian embryos (Krauset al., 2007), while in higher organisms the capacity of inductionprogressively spreads to bottle cells (Gerhart, 2001). Thus, origi-nated at earlier developmental stages, the bottle cells acquire thecapacity of induction later than the circumferential torus does.

Moreover, the outlined evolutionary scenario explains why theactivation of a canonical Wnt pathway is an evolutionary stablemark of a posterior pole of the embryo (Angerer et al., 2011).There are no reasons to reject a simplest hypothesis that the Wntpathway turns on in the fragments consisting of loosely packedcells irrespective to their fates and immediate causes of loosening.Given that we evaluate the scalar values, cells going to lose theepithelial phenotype are indistinguishable from those that havenot succeeded to acquire it. In the light of the evolution of basicmetagenetic cycle of multicellular organisms, withdrawal of cellswith distinctly epithelial phenotype from metamorphosis means areplacement of the successive life cycle phases common to all cellsof the individual by intra-individual differences. Surprisingly, thisconfirms the idea of a separation “by default” of the proper (ini-tially anterior) ectoderm capable of formation of only ciliated andneural cells (Hemmati-Brivanloue and Melton, 1997). Summing up,in spite of originating of the intermediate developmental stagesshifting the AP polarity to the very beginning of development andtransforming it into one of the referent embryonic axes, this doesnot go beyond the limits of a primary difference between “the holein the sphere” and the sphere itself.

5.2. Origination of the DV polarity

As we have been trying to argue, the AP polarity is not a ref-erent coordinate axis, but simply a consequence of separation ofa domain whose symmetry order is lower than in the rest of thedeveloping system. Certainly, there is no room to coordinates com-mon to parts with different symmetry orders and, consequently,different ranges and directions of variation. The same is true for


the DV polarity, which is also not a coordinate axis. The first, inthe evolutionary sense, signs of DV polarity are distinct in Cnidar-ians at a planula stages when the embryo starts to elongate alongthe AP axis (Kraus and Cherdantsev, 1999). Yet the epithelial sheet

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Fig. 13. Originating of the cnidarian (A, A′) and deuterostome (B, B′) gastrulation patterns: the designations on the graphs A and B are standard, C∗ and Cvar refer primarilyto the outer surface shapes of the posterior embryonic poles marked in A′ and B′ by the asterisks. The endoderm and the anlage of gastral invagination are shown by yellow;the circumferential torus around the blastopore is shown by red. The black arrows show the counterbalance of forces at the archenteron flex, where the archenteron itselfand adjacent epithelial sheet of the torus fragment tend to bend in mutually opposite directions, which follows from the opposite directions of the cell polarity vectors. Foro

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ther explanations, including that for B1 and B2 figures, see text.

losure point is initially on a pole of the sphere, for the reasonsonsidered above the spherical symmetry is not stable. The pos-erior half of the embryo is a matter of longitudinal elongation athe expense of planar cell intercalation, which means originating ofhe positive feedback between the elongation of a given meridian,ts stretch and further elongation in order to attenuate stretchingCherdantsev, 2003; cf. Beloussov, 1998). This leads to the origina-ion of a variety of forms in which one lateral side of a planula islongated and convex while the remnant of the epithelial sheetlosure site shifts to an opposite, flat or even concave side (seeig. 10D). One cannot say, which of these sides is dorsal or ven-ral, insofar as planula develops into a radially symmetric organism,ut it is quite evident that differences between its opposite lateralides are the same that in the embryos of bilaterally symmetricrganisms. In common with phonological systems, in which theppositions among phonemes are of more importance than thehonemes themselves, the differences between counterparts of theeveloping system precede to an acquisition by these counterpartsf a definite and evolutionary stable meaning. Moreover, a part ofhe system can have no meaning at all except being necessary forhe development of another part.

In those Cnidarians whose gastrulation anticipates the truenvagination, the loss of radial symmetry occurs at earlier devel-pmental stages, namely with a formation of the circumferentiallastopore roller (torus) (Fritzenwanker et al., 2004). It is strikinglyimilar to what occurs with a formation of the primary AP axis. Theoller forms by a fusion of its fragments, marked by expression oforkhead or brachyury genes, and so, at intermediate developmen-


al stages, many embryos have a roller in only one sector of thelastopore circumference being, by definition, bilaterally symmet-ic embryos. The roller becomes radially symmetric only with thelastopore closure, after a fusion of all the roller fragments, when

the blastopore itself shifts to one of lateral sides of the embryomaking it bilaterally symmetric, as shown in Fig. 10D.

Thus, prerequisites to the origination of a true DV polarity basedon self-organization are, first, the planar (tangential) movementof a suprablastoporal circumferential torus, and, second, shapingof the torus followed by differentiation of its sectors. As usedherein, one should expect that the first process arising at laterdevelopmental stages should occur in evolution earlier than thesecond one. However, one can say that the DV polarity acquiresdevelopmental mechanism of its own only after originating of thecorrelation between shaping of the blastopore circumference andits lateral displacement (Cherdantsev, 2006). Such a correlationlacks in low invertebrates, in both protostome Plathelmithes orNemathelminthes, and deuterostome Echinoderms (Beklemishev,1969) and Hemichordates (Gerhart, 2001). It appears, in differ-ent ways, in higher Protostomes (especially in Spiralians), and inChordates.

For our purposes, it is sufficient to consider a radially symmetriccircumferential torus (CT) being a toroidal active shell. To be defi-nite, we consider a CT corresponding to an ideal ring-like blastoporelip being close to what one can observe in Amphioxus after invagi-nation of the blastula vegetal plate (Holland and Holland, 2013).Involution, the main component of gastrulation movements, con-cerns with generic oscillations (Cherdantsev and Scobeyeva, 2012).The CT surface alternates inflating, when recruiting new cells fromthe outer germ layer, and deflating, when pushing recruited cellsinwards, into the inner layer. If we confine ourselves by consid-ering of the cell flows in the CT meridian plane, these oscillations


result from the lack of equilibrium between accumulation of cellsat the CT edge and their exit from the CT zone (for details, seeCherdantsev and Scobeyeva, 2012). Self-maintenance of oscilla-tions follows from the movement geometry whose main feature

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Fig. 14. Self-oscillations attending the main gastrulation movement (involution): A– in the meridian CT plane, B – in the three-dimensional CT . (A) Shaded contoursare those of the dorsal blastopore lip in the course of its development alternatingincreasing (I, III) and decreasing (II, IV) of the curvature of the CT surface, red arrowsshow cell flows over the CT surface while blue arrows show shape changes in thissod

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Fig. 15. Two stages (A, B) of gastrulation in its primitive form (for example, in Echin-oderms), whose characteristic feature is the feeble accumulation of cells in the CTregion yielding to the epiboly rates and, which means the absentee of the red (unsta-

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urface itself. (B) Oscillations of differences in the planar curvature between thepposite CT poles with alternating of the convergence and divergence of longitu-inal (red arrows) and latitudinal (blue arrows) cell flows.

s the alternation of inflation and deflation of the CT edge outerurface in the process of meridian elongation of the blastopore lipFig. 14A). With inflation, which means the preponderance of thelanar movement mode (red arrows in Fig. 14A), the CT surfaceecreases its surface curvature and becomes less resistant to pas-ive stretching by the intrinsic pressure. This triggers the radialurface movement (blue arrows in Fig. 14A), which leads to anncrease in the surface curvature, which makes the surface moreesistant to passive stretching and turns on the planar cell move-ents. This leads to a decrease of the surface curvature and initiates

new loop of the oscillation cycle.In three-dimensional space, recruiting of the cells into a given

T sector is in both meridian and equatorial planes. Insofar that thequatorial convergence of cells decreases, while equatorial diver-ence of cells increases the equatorial radius, this is a prerequisitef both alternating in time and separating in space of the “big end”nd “little end” CT sectors. It is also evident that the big end for-ation promotes inflating while the little end formation promotes

eflating of the CT edge thus introducing a correlation between lon-itudinal (anteroposterior) and latitudinal cell flows (Fig. 14B). Thisenerates a variety of dynamic regimes that seems to comprehendll extant modes of metazoan gastrulation.

Their choice, in common embryological terms, depends on aroportion of epiboly to involution. If, for instance, one compareshe gastrulation in echinoderms, amphioxus and low vertebratesanamniotes), the main difference will be in spatiotemporalynamics of the CT radius (blastopore radius). In echinoderms, it

s a matter of monotonous decreasing (Angerer et al., 2011), inmphioxus it decreases after a slight increase (Holland and Holland,013), and, in amphibians, it increases until the midgastrula stageScobeyeva, 2006). Decreasing means the epiboly preponderancen the sense that recruiting of the cells into the CT zone does noteep pace with pushing of these cells inwards into the inner germ


ayer, which inevitably leads to the CT zone tapering. In terms of thective shell model, this means the absentee of a positive feedbacketween passive and active forces and, as the result, the absenteef the unstable arm in the curve F(C*, Cvar), where C* and Cvar

ble) arm of the curve F(C*, Cvar). Gastrulation goes on only by means of increasingin the slope of the line C∗ = kCvar (purple).

refer only to meridians of the CT surface. We get a monotonouscurve for which both spatial differentiation and alternation in timeof “big end” and “little end” of the CT are absent so that the blasto-pore dynamics is no more than an increase in the slope of theline C* = kCvar (Fig. 15). From the beginning (Fig. 15A) to the end(Fig. 15B) of gastrulation the CT zone to which refer the C* andCvar values is subject to gradual tapering with an elongation ofthe archenteron and decrease of the blastopore diameter. Insofaras all the points of intersection between F(C*, Cvar) and C* = kCvarare stationary points, the system moves over the curve only “para-metrically”, that is, at the expense of increasing in the k value(see the arrow in Fig. 15), which corresponds to exhausting of theactive forces with elongating of the archenteron and closing of theblastopore. This fits in well to all types of gastrulation in whichthe blastopore lateral displacement and mesoderm formation donot correlate with the CT shaping. In Echinoderms, the mesodermdevelops from an anterior part of the archenteron while DV polar-ity originates from an asymmetry of the epiboly, and not from thedifferentiation of CT sectors (Angerer et al., 2011).

The unstable arm seems to appear when the influx of cells intothe CT exceeds their inward outflow. In meridian planes, this meansthat accumulation of cells in the CT region (inflation) alternateswith their migration to the archenteron roof (deflation), which forthe whole torus corresponds to alternating of the decreasing andincreasing of its circumferential (planar) curvature, as shown inFig. 14B. In our model, this occurs when, after originating of theunstable arm of the curve F(C*, Cvar), the slope of the line C* = kCvardecreases up to an intersection with the unstable arm. The corre-sponding oscillations are well documented in teleost (Cherdantsevand Tsvetkova, 2005; Cherdantseva and Cherdantsev, 2006) andamphibian (Cherdantsev and Scobeyeva, 2012) embryos by quanti-tative morphological data. Yet such data are absent for Amphioxus,differences in the planar curvature of dorsal and ventral CT sectorsare quite evident (Fig. 16).

Origination of the unstable arm opens doors to two main typesof gastrulation that one could call “big Ender” and “little Ender”types (Fig. 17). For simplicity, assume that, as shown in Fig. 17,the boundary of a light shaded part containing the CT is near theembryo equator. In the little Ender type (Fig. 17A), the axial meso-derm arises from a CT edge having the greatest circumferential(planar) curvature, which, in the active shell model, correspondsto an increase in the slope of the line C* = kCvar intersecting the


first stable arm of the curve F(C*, Cvar). In a meridian section of theembryo not shown in Fig. 17 this means the dorsal blastopore lipadopting a deflated state as being the stationary one. Originating ofthe axial mesoderm at the CT “little end” is the most characteristic

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ARTICLE ING ModelBIO 3478 1–17

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ig. 16. Differentiation of the CT planar curvature in gastrulation of amphioxusmbryos (D – dorsal, V – ventral sector).

ource: Modified from Holland, Holland, 2013.

eature of gastrulation in higher protostomes, which presumes aositive connection between the epiboly and involution, becausehe both processes act against the accumulation of cells in the dor-al blastopore lip. Yet the further dorsal lip movement is beyond thecope of the graph shown in Fig. 17, it is easy to predict that the dor-al lip should move over the embryonic surface at a pathway showny the curved dotted arrow in Fig. 17A outlining the main body axis.iven that the blastopore (dark shaded) closes only from the dorsalnd lateral sides while the opposite blastopore edge remains at itsnitial place, the main body axis turns out to dispose at a ventralide of the embryo, or, better to say, a side of its eventual dispo-ition becomes the ventral one. Splitting (diverging) of the flowsf cells emigrating from the dorsal lip in the involution processnto two bilaterally symmetrical “armlets” shown in Fig. 17A byhe red arrows is the only way in which the epiboly can help invo-ution, and vice versa. In Spiralians, this corresponds to a splittingf the primary mesoblast into two bilaterally symmetrical anlages


roducing two bilaterally symmetric bands of the somites.In the big Ender type, the axial mesoderm originates at a “big” CT

nd corresponding to a sector having the smallest circumferentialurvature, which means the line C* = kCvar intersecting the curve at

ig. 17. Cell movement geometry in two types of gastrulation – “little Ender” typeA) and “big Ender” type (B). Designations on the graphs are standard, C∗ and Cvareferring to the circumferential (planar) curvature of the dorsal CT sector. The lat-tudinal contours of a part of the embryo containing the CT are light shaded. Theed arrows are cell flows diverging from (A) or converging to (B) a place of the dor-al lip origin, the red spots–axial mesoderm. The blastopore is dark shaded, for anxplanation of the dotted curved and straightened arrows showing the movementathways of the CT edges in a meridian plane, see the text.

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the second stable arm (Fig. 17B). In this case, the epiboly and invo-lution are in a negative connection, which makes the gastrulationproceed by a convergence of the flows of CT cells to a place of themain body axis formation, as shown by the red arrows in Fig. 17B. Asthe result, the dorsal lip movement straightens its movement path-way turning the sphere meridian into a generatrix of the cylindricalsurface (the straight dotted line in Fig. 17B). In contrast to the littleEnder type, the opposite (ventral) blastopore edge participates inthe blastopore closure and moves, as it follows from its initial pla-nar curvature, over the sphere meridian (the curved dotted line inFig. 17B), just like the dorsal blastopore lip does in the little Endertype. In spite of a seemingly tempted hypothesis that the ventralside of protostomes is homologous to the dorsal side of Chordates(Arendt and Nübler-Jung, 1997; Arendt et al., 2001), the differencesin movement pathways between the opposite blastopore edges inthe big Enders are not homologous to those in the little Enders.

Yet, at the outset of evolution, protostomes and deuterostomesare similar in that the embryo is a mosaic of two parts of differ-ent symmetry orders (radial anterior and bilateral posterior parts).Considering of the embryonic poles as being not referent points,but rather differential entities of the form, makes it clear that inboth little and big Enders the anterior and posterior poles are thoseof the whole embryo, while the dorsal and ventral sides are thoseof its posterior half containing the CT. In both types, the separationboundary between anterior and posterior parts is a canonic singu-larity of mapping of the plane into the plane corresponding to theabove mentioned transition from increasing to decreasing of the CTradius (for details see Cherdantsev, 2006). The further evolution isa matter of transformations being almost identical in the little andbig Enders. In little Enders, this is a well-known transition from arandom choice of the dorsal blastomere among four equally shapedand sized cells to differentiation of these cells and then to differen-tiation of the corresponding egg quadrants (Biggelaar and Guerrier,1979; Lambert, 2010). The evolution is exactly in the same direc-tion in which the dorsal blastopore margin (little CT end) moves inits normal development. In higher insects being at the top of the lit-tle Ender evolution the cleft-like blastopore forms immediately atthe ventral side of the embryo. Such a blastopore is widespreadin many invertebrates with spiral cleavage (Beklemishev, 1969;Lambert, 2010), and in nematodes (see above). One could have con-sidered this being a reversion to the ancestral state, if both AP andDV polarities had not refer to the CT.

In amphioxus, early in the big Enders evolution, the oscillationperiod continues until the end of gastrulation with a feeble con-vergence of CT flows to the body axis so that the DV difference inthe epithelial surface curvature become quite distinct only withthe blastopore closure (Holland and Holland, 2013). The vectors ofthe AP and CT polarity are only slightly deviate from the orthogo-nal orientation, which means their correlation being only in statusnascendi. The embryo consists of radially symmetrical anterior andbilaterally symmetrical posterior parts arising at different gastru-lation stages, one at the epithelial invagination and the other at theCT formation stage (Yasui et al., 2001). The evolution of chordategastrulation being also toward smoothing of the initial mosaic issophisticated by a directional influence of the yolk accumulation(Arendt and Nübler-Jung, 1999).

The early CT of lamprey embryos is ring-shaped but it appearson the dorsal pole of the yolk circumference. The reason is simplythat the yolk accumulation is in the vegetal egg half, which is notuniform being at higher rates at the ventral side and thus trans-lating to earlier developmental stages an asymmetry that arisesat later developmental stages of the ancestral forms. In fact, this


leads to a “reduplication” of the blastopore: one copy (“archi-blastopore”) is homologous to that of Amphioxus (Fig. 18A), andanother (“neoblastopore”) is an innovation originating at the yolkplug circumference. In lamprey and urodelan amphibians, these

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ig. 18. The blastopore evolution from amphioxus to anamniotes: A – amphioxus,lastopore is shaded by gray and the neoblastopore is shaded by yellow. The bl

nvolution.

lastopore counterparts behave independently, the involution ofells that form axial structures being almost entirely a matter ofhe archiblastopore shaping until the end of gastrulation (Fig. 18B).n anuran and teleost embryos, the neoblastopore forces out therchiblastopore in the beginning of gastrulation (Fig. 18C). Inso-ar as data concerning with fates of different neoblastopore sectorsn lamprey are contradictory, we have no choice but to make usef data concerning with gene expressions (Takeuchi et al., 2009).ccording to these data, mesodermal markers are only in the cellsigrating through the archiblastopore lip up to its fusion with

he neoblastopore circumference, which occurs only in the endf gastrulation. In amphibian (anuran) and teleost embryos, thesearkers are throughout of the yolk plug circumference beginningith the appearance of the dorsal blastopore lip.

Thus, the evolution mainstream consists simply in that cells ofhe neoblastopore circumference, instead of moving in the initialP direction, turn dorsally toward the big CT end. This process aris-

ng from an inherent to the big Enders correlation between thelongation of the main body axis and convergence of cell flows pro-ressively spreads into the neoblastopore circumference repeating,n the evolutionary scale, a direction in which the dorsal blasto-ore lip moves in its normal development. At a point at which thispreading reaches a pole of the blastopore circumference opposingo that from which it has started, the DV axis of the embryo becomests AP axis, in full agreement with revised fate maps and those forene expressions obtained for Xenopus (Kumano and Smith, 2002)nd zebrafish embryos (Myers et al., 2002). In fact, in Amphioxushe DV axis also becomes AP, which occurs, however, only afterhe convergence of all mesodermal cells to the dorsal side of thembryo. The only difference in evolutionary trends of big and littlenders is that immediately following from the initial conditions ofheir gastrulation. In big Enders, the DV axis adjusts its orientation


o the AP axis on a scale of the whole embryo preserving the initialonnection between the AP axis and that of the egg animal-vegetalolarity. In contrast to that, the AP axis of little Enders adjusts itsrientation to that of the DV axis leaving aside the connection with

mprey, C – amphibians and teleosts; I–III – developmental successions. The archi-re boundary shown by dotted lines means an epiboly of the yolk plug with no

the egg polarity. This explains why the extraembryonic tissues arisein little Enders at the initially dorsal side of the embryo being a placeof the outflow of embryonic cells, while in big Enders this occurs atthe initially ventral side (Arendt and Nübler-Jung, 1999).

One of the evident, though often omitted, consequences of thisprocess is an expansion of given morphogenetic potencies beyondthe limits of an area in which these should be actualized in nor-mal development. This is not a precondition but, rather, a resultof developmental evolution having no adaptive value of its own.This explains, first, why the evolution of development does notlead to decreasing of the capacity of regulation and, second, whythe networks of positive and negative molecular signals becomemore and more sophisticated, because of the necessity to sup-press the development of a given structure at an inappropriateplace. This problem arises only with replacing of self-organizationby causal relationships between successive developmental stages,because self-organization itself makes no distinction between dif-ferentiation and morphogenesis. Just as in the case of AP polarity,originating of the additional earlier stages of development makingfrom the DV polarity a fake of the referent polar axis remains inthe limits of basic binary opposition between the convergence anddivergence of mass cell flows initially corresponded to oppositephases of the generic oscillation regime.

6. Evolution of variability

Controversies concerning with orientation of the primary bodyaxis even in the species being model objects of developmental biol-ogy (for example, in Xenopus laevis, see Keller and Shook, 2004) canbe a mere consequence of a prejudice that these axes are referentand, consequently, cannot be matters of individual variations. Inloach development, whose developmental mechanics is very simi-


lar to that of zebrafish embryos, changes in orientation of the axis,which, in a sense, is the AP but traditionally denoted as DV axis,are in the range of normal variability of the early development.Presence of reliable morphological markers makes these changes

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ig. 19. Stepwise determination of the DV polarity in loach morphogenesis (A–D). Thhow the differences in local cell concentrations. The succession A–D is most frequector allowing for specification of the dorsal side.

bvious with permanent observations of individual embryos with-ut using of artificial marks (Cherdantseva and Cherdantsev, 2006).

From the start of the blastoderm epiboly, and until the forma-ion of the embryonic shield (ES, the dorsal blastopore lip analog),he shape of the blastoderm outer surface is a matter of regularscillations described in Section 2. At initiation of the epiboly, thelastoderm has a more or less distinct polar axis originating fromifferences in the outer surface circumferential curvature between

ts opposite poles–at one of these poles (big Ender’s pole) the radiusf the curvature is significantly smaller (Fig. 19A). With the epibolyrogress, these differences vanish bypassing into those in local celloncentrations and separating an area of densely packed cells athe circumference of one of the blastoderm sectors, which is thenlage of the embryonic ring (ER), the CT analog in teleost embryosFig. 19B). The differences in the outer surface shape emerge againith completing of the ER formation (Fig. 19C) to bypass again into

he difference in cell concentrations, which leads to the formationf ES in one of the ER sectors (Fig. 19D).

In most embryos, the ER arises at the initial big Ender pole and ESt a pole of the ER initiation, which means decreasing in the blasto-erm outer curvature being a positive signal to further dorsalizationf the corresponding sector. However, distribution frequencies ofhe angle between the previous and subsequent positions of theorsal pole have more than one mode, the additional one corre-ponding to a reversal in the orientation of the DV axis with respecto that at previous developmental stages. In the same living embryo,ne can look after how the initial big Ender pole (Fig. 20A) vanishesecause the blastoderm circumference becomes an ellipse with noolar axes (Fig. 20B), how the blastoderm circumference looks for

new place for a singularity (Fig. 20C), and how it finds it form-ng the ES (Fig. 20D). Insofar as this ES dispenses with prepatterns


oth in the forms of big Ender poles or points of the ER initia-ion, one can say that development regresses to self-organizationn the range of normal developmental variability. However, this isot self-organization in the strict sense, because morphogenesis

toderm is shaded: ER – embryonic ring, ES – embryonic shield. Differences in filling normal development, repeating of the shape oscillations in the same blastoderm

starts in the blastoderm having an elliptic, not around circum-ference, so that the ES allocating is a biased choice excluding apossibility of its origination at the poles of the ellipse. In total, theamount of developmental information obtained from positive sig-naling is equal to that obtained from its failure, which emphasizesthat the differences between the parts are more important than theparts themselves. In the same way, an extirpation of a fragmentof the ventral blastoderm circumference followed by the woundhealing can create at the former ventral side a new dorsalizationcenter surpassing that at the initial dorsal side (Cherdantseva andCherdantsev, 2006).

This illustrates how the developmental pathways can evolve inspite of their degeneracy. In fact, the elliptic form of the blasto-derm circumference is a stage of the formation of DV polarity atwhich the blastoderm has neither dorsal nor ventral sides, but,instead, it has two symmetry planes, one becoming that of thebilateral symmetry. Yet its formation is not self-organization, it iscloser to the self-organization threshold than in embryos havingthe DV axis from the very beginning of the epiboly. It follows thatself-organization and “deterministic” development are not differ-ent developmental paradigms because the both can be in the rangeof normal individual variability of morphogenesis. One can imaginea hypothetical situation in which the ES can originate by self-organization from any ER sector. Among morphological variantsafforded by arbitrary variations at earlier developmental stages,only those variants that can be in a causal connection with laterstages will be reproducible on the developmental scale. The ellip-tic form of the blastoderm circumference is convenient becauseit turns the arbitrary choice of dorsal ER sector into the biasedone. The same repeats with variations of the elliptic form of theblastoderm circumference, insofar as only the “egg-like” differen-


tiation can be in a causal connection with the ES formation. As theresult, we get a sequence of events whose developmental orderis the mirror image of the order in which they have appeared inevolution.

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ig. 20. The reversal of the DV axis in normal development of loach embryos: the

he red arrows show the initial, while the blue arrows show the new position of th

Each step of translating of the given form to earlier develop-ental stages is a heterochrony by definition, because the subject

f translation is not the form itself, but its differential charac-ers allowing for the continuity of developmental information. Ineneral, as in the above-mentioned example, the form becomesubject to dissembling – the shape differences initially connectedith ES become those of the ER and then those of the blastoderm

ircumference having no ER at all. This is the same that a hete-ochrony arising between the developments of different parts ofhe embryo at a given developmental stage. The main thing is thathe developing system is susceptible only to acceleration of theevelopment of one of its parts being recognizable by increasingf the variability in a corresponding area. This constitutes a novelevelopmental vector, whose direction is the same that under self-rganization, except that self-organization itself is absent and thescillation cycle reduces to a branch at which the system decreasests variance. The spatially homogeneous state restores at the costf intrinsic differentiation, just as, in the development of teleostmbryos, differences in the outer ER curvature vanish transformingo those in cell concentrations in different ER sectors.

In mathematical terms, the spatial differences, being initially inhe values of dynamic variables, become parametric ones. Advert-ng to the active shell model, it is reasonable to suppose thatt one of the circumferential poles, being ventral in big Enders,he curve F(C*, Cvar) becomes the monotonous curve (such ashown in Fig. 15) with no positive feedback between an increasen the surface curvature and that in its variance. This means thereponderance of passive stresses at the ventral side being a nat-ral consequence of the active cell convergence to the dorsal side


Beloussov, 2012). What is remarkable is that in the course of gas-rulation the developing system “encircles a sphere” in both spacend time, because in the end of gastrulation the ventral poles ofhe amphibian and teleost gastrula are matters of the same cell

graphs A–D refer to individual developmental pathway of the same living embryo.al center.

movements that their dorsal poles in the beginning of gastrula-tion (Cherdantsev and Scobeyeva, 2012). This, however, leads notto repetition, but to completion of the gastrulation at the ventralpole because most cells have migrated to the dorsal side. Given thatthe deficiency of the active surface flow is a property of the primi-tive gastrulation, this explains why the loose mesenchyme arisingat the overall CT in the primitive gastrula arises at the CT posteriorpole of gastrula in vertebrate gastrulation.

7. Conclusion

The principal difference between development and self-organization is that the equations of physical interactions includingthose for self-organization are symmetrical in time, which makesus to infer basic properties of developmental dynamics from pos-tulated ad hoc differences in the initial and boundary conditions(Belintsev, 1990). Earlier (Cherdantsev and Scobeyeva, 2012) wesuggested a hypothesis, ascending to Goodwin’s ideas (see, forreview, Goodwin, 1994), that at the heart of both temporal andspatial organization of the development lies the alternation ofspatially homogeneous and non-homogeneous states and, respec-tively, periods of increasing and decreasing of variability. In fact,the spatial variance is the only macroscopic variable permitting thedeveloping system to estimate its developmental potencies with norespect to referent spatiotemporal axes, which reverses the tradi-tional view on the origin of spatiotemporal developmental order.Originating of the definite developmental pattern of structuring inwhich the fate of the parts depends on their position and devel-opmental history becomes feasible only after the structuring itself.


Thus, what we call the pattern formation is not a cause of mor-phogenesis, but rather the effect of its evolution beginning withself-organization and passing through a series of generic oscilla-tions, which anticipates the developmental succession in which

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Zakhvatkin, A.A., 1949. Comparative Embryology of Low Invertebrates. Nauka,Moscow (in Russian).

Yasui, K., Saiga, H., Wang, Y., Zhang, P.J., Semba, I., 2001. Early expressed genes

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he earlier stages of development appear in evolution after theater ones. Thus, the ontogeny is neither a cause, nor an effect ofhylogeny. Rather, spatiotemporal differences arising within theeveloping system from the generic oscillations specify directions

n which the system could evolve. By definition, such a system ison-holonomic being capable, other things being equal, of unidi-ectional drift under arbitrary fluctuations including fluctuationsf selective forces. This explains why the trends of developmentalvolution are perfectly the same in different groups with no respecto phylogeny. The identity of gene expressions is not an argumentavoring the opposite view being a clear-cut example of the “mis-laced concreteness”, because, for most of these genes, it does notatter what kind of morphogenesis they control.The evolution of morphogenesis is not the only subject to “ret-

ograde evolution”. The same effect can arise in the evolution ofhe catalytic reaction chains being far from thermodynamic equi-ibrium (Pattee, 1967). All that is needed is that changes in oneirection would depend on a given component of the chain whilehose being in the opposite direction would depend on the chain as

whole. This is almost the same that in developmental successionsn which the earlier stages can vary independently from the laternes, but not vice versa. The difference consists only in that thenzyme evolution is under strong selective control, which is nothe case of the evolution of morphogenesis (Cherdantsev, 2003).he developmental evolution considered in this paper is that of thetructures generating new mechanisms of their self-reproductionn a macroscopic (in a sense, geometric) scale, which cannot beubject to selection on fitness (Cherdantsev et al., 1996). Moreover,he causal relationships between previous and subsequent statesre not a precondition of development, but rather a result of theevelopmental evolution.

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Generic oscillation patterns of the developing systems and their role in the origin and evolution of ontogeny