REVIEW Activator-Inhibitor Dynamics of Vertebrate Limb Pattern … · 2019-08-13 · Defects of the limb skeleton are among the most frequent human congenital anomalies. Mutations

Activator-Inhibitor Dynamics of Vertebrate LimbPattern Formation

Stuart A. Newman* and Ramray Bhat

The development of the vertebrate limb depends on an interplay of cel-lular differentiation, pattern formation, and tissue morphogenesis onmultiple spatial and temporal scales. While numerous gene productshave been described that participate in, and influence, the generation ofthe limb skeletal pattern, an understanding of the most salient featureof the developing limb—its quasiperiodic arrangement of bones, requiresadditional organizational principles. We review several such principles,drawing on concepts of physics and chemical dynamics along with mo-lecular genetics and cell biology. First, a ‘‘core mechanism’’ for precarti-lage mesenchymal condensation is described, based on positive auto-regulation of the morphogen transforming growth factor (TGF)-b, induc-tion of the extracellular matrix (ECM) protein fibronectin, and focalaccumulation of cells via haptotaxis. This core mechanism is shown tobe part of a local autoactivation-lateral inhibition (LALI) system thatensures that the condensations will be regularly spaced. Next, a ‘‘bare-bones’’ model for limb development is described in which the LALI-coremechanism is placed in a growing geometric framework with prediffer-entiated ‘‘apical,’’ differentiating ‘‘active,’’ and irreversibly differentiated‘‘frozen’’ zones defined by distance from an apical source of a fibroblastgrowth factor (FGF)-type morphogen. This model is shown to accountfor classic features of the developing limb, including the proximodistal(PD) emergence over time of increasing numbers of bones. We reviewearlier and recent work suggesting that the inhibitory component of theLALI system for condensation may not be a diffusible morphogen, andpropose an alternative mechanism for lateral inhibition, based on syn-chronization of oscillations of a Hes mediator of the Notch signalingpathway. Finally, we discuss how viewing development as an interplaybetween molecular-genetic and dynamic physical processes can providenew insight into the origin of congenital anomalies. Birth DefectsResearch (Part C) 81:305–319, 2007. VC 2008 Wiley-Liss, Inc.

INTRODUCTIONDefects of the limb skeleton areamong the most frequent humancongenital anomalies. Mutationsand teratogens can dramaticallyaffect the structure of the limbskeleton without otherwise impair-ing survival, reproduction, andother bodily functions. This has ledto the presence of a wide-ranging

set of limb variations throughoutthe human population as well asproviding the opportunity, usingexperimental systems, to explorethe bases of normal and abnormallimb formation. The limb skeleton,an array of jointed bone or carti-lage elements, has a stereotypicalpattern that (as Charles Darwinnoted) is only modestly altered by

adaptations for functions as variedas walking, swimming, flying, andgrasping (Darwin, 1859). Thetransmission and molecular genet-ics of limb variations have beenextensively studied in humans andmice, while the developing appen-dages in embryos of egg-layingspecies have lent themselves toexperimental analysis by surgicalmanipulation. In fishes andamphibians the paired limbs, orrelated structures, exist with vari-ant anatomical characteristics andregenerative properties, enablinginformative comparative studies.Finally, limb bud mesenchymalcells from avian and mammalianspecies can be grown in culture,where they undergo differentiationand pattern formation, thoughsimplified, with a time-course andon a spatial scale similar to that inthe respective embryos. Thesefeatures have made the limb ahighly favorable system for study-ing the generation of multicellularform.Over the past three decades the

protein products of scores ofgenes have been identified as par-ticipating in patterning of the limbskeleton (reviewed in Tickle,2003; Newman and Muller, 2005).Genes and the interactive net-works in which they participate,however, are only part of the storyin the generation of biologicalstructures (Nijhout, 1990; New-man and Comper, 1990; Newman,

REVIE

W

VC 2008 Wiley-Liss, Inc.

Birth Defects Research (Part C) 81:305–319 (2007)

Stuart A. Newman and Ramray Bhat are from the Department of Cell Biology and Anatomy, New York Medical College, Valhalla,New York.

Grant sponsor: National Science Foundation.

*Correspondence to: Stuart A. Newman, Department of Cell Biology and Anatomy, New York Medical College, Valhalla, NY 10595.E-mail: [email protected]

Published online in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/bdrc.20112

2002; Newman and Bhat, in press).Tissue pattern formation and mor-phogenesis involve switching ofcells between alternative physio-logical states, redistribution, rear-rangement and reshaping of cellsand the chemical gradients thatact on them (Forgacs and New-man, 2005). Each of these proc-esses is mediated by chemical dy-namics and/or the physics of con-densed materials. Indeed, physicsand chemical dynamics are themeans by which gene expressionchanges tissue form (Forgacs andNewman, 2005) and the linear in-formation of the genotype isimplemented to construct a three-dimensional (3D) organismal form.In this work, we focus on the

question of whether, given what isknown about the biochemical andcellular bases of limb develop-ment, physical and chemical-dynamic organizational mecha-nisms utilizing these ingredientscan account for the general pat-tern of the skeleton. If so, we willhave a ‘‘universal’’ mechanism oflimb development, in addition to a

plausible scenario for the origina-tion of the limb from the fin-appendage of an ancient fish-likeancestor. We will also haveimproved our understanding of thevulnerabilities of the developinghuman limb to mutational and ter-atogenic disturbances.

SKELETAL PATTERN

FORMATION: THE

CENTRALITY OF

PERIODICITY

The limb buds of vertebrates pro-trude from the body wall, or flank,at four discrete sites—two for theforelimbs and two for the hin-dlimbs. The paddle-shaped limbbud mesoblast, which gives rise tothe skeleton and muscles, is sur-rounded by a layer of simple epi-thelium, the ectoderm. The skele-tons of most vertebrate limbs de-velop as a series of precartilageprimordia in a proximodistal (PD)fashion: that is, the cartilaginouselements destined to be closest tothe body form first, followed, suc-

cessively, by structures more andmore distant from the body. Forthe forelimb of the chicken, forexample, this means the humerus(stylopod) of the upper arm isgenerated first, followed by the ra-dius and ulna (zeugopod) of themid-arm, the wrist bones, andfinally the digits (autopod) (Fig. 1)(Saunders, 1948; reviewed inNewman, 1988). Urodele sala-manders appear to be an excep-tion to this PD progression (Franssenet al., 2005). Cartilage is mostlyreplaced by bone in species withbony skeletons.Much work on limb skeletal pat-

tern formation over the past twodecades has occurred within the‘‘positional information’’ paradigm(Wolpert, 1971, 1989). This viewassumes that limb skeletal ele-ments are established by cellsautonomously responding to asystem of molecular coordinatesalong each of three relatively inde-pendent axes and thereby assum-ing precise roles in the developingstructure. The anteroposterior (AP)coordinate has been proposed tobe concentration values along gra-dients of retinoic acid or its recep-tors (Tickle et al., 1985; Dolleet al., 1989), Hox gene products(Duboule, 1992), or Sonic hedge-hog (Riddle et al., 1993), but eachof these suggestions has encoun-tered disconfirming evidence (seeWanek et al. (1991) for retinoicacid; Luo et al. (1995) for retinoidreceptors; Davis et al. (1995) forHox gene products; Kraus et al.(2001) for Sonic hedgehog). ThePD coordinate has been proposedto be determined by the length oftime cells spend in an apical ‘‘pro-gress zone’’ comprising approxi-mately 300 lm (Summerbellet al., 1973), or specified earlywithin the apical zone by anunknown mechanism (Dudleyet al., 2002). There is no evi-dence, however, for an internalbiochemical clock that stops whencells move out of the progresszone, nor have spatially deter-mined bands of gene expressionbeen identified within the progresszone that are related to skeletalelement identity as postulated bythe early specification model (Dudley

Figure 1. Progress of limb skeletal development in a chicken forelimb (wing) betweenfour and seven days of embryogenesis. The skeletal elements emerge in a proximodis-tal order. Gray represents precartilage condensation and black definitive cartilage.This developmental period corresponds to human limb development between approxi-mately 25 to 50 days of gestation. (Adapted from Newman and Frisch (1979) and For-gacs and Newman (2005)).

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Birth Defects Research (Part C) 81:305–319, (2007)

et al., 2002; Tabin and Wolpert,2007).The positional information notion

implicitly assumes that the identi-ties of cells in the developing limbare specified along separable geo-metric coordinate axes. But, infact, the three limb axes them-selves are not independentlyspecified (Bowen et al., 1989),and factors such as the Hox geneproducts, which clearly influencethe details of the skeletal pattern,do so in a fashion that cannot beaccounted for by the simple com-binatorial codes implied by thepositional information framework(Graham, 1994; Newman, 1996).Most importantly, the positional

information model, devised to rep-resent a recurrently employed setof molecular signals that couldproduce the pattern of a Frenchflag as readily as the whorls of afingerprint, if only the organism’sgenome were capable of providingthe proper readout (Wolpert,1971), is indifferent to the factthat the vertebrate limb, the seg-mental plate, and epithelial appen-dages such as bristles, hairs andfeathers, to take a few examples,have quasiperiodic patterns. Inthe limb the periodicity is two-fold—there is a segmental patternalong the PD axis, where succes-sive elements are separated byjoints, and structural repetitionacross the zeugopod and autopod,where parallel skeletal elementsare separated by intervening softtissue, or by free spaces createdby apoptotic removal.While it is clear that position-

related identities are indeedimprinted on limb skeletal ele-ments by gradients of molecules,including those of retinoic acid,bone morphogenic protein (BMP)-and Wnt-family morphogens, andhomeodomain proteins includingthose of the Hox, Tbx, Prx, andMeis families (reviewed in Tickle,2003; Tickle, 2006), the roles ofsuch determinants vary from spe-cies to species and from oneregion of a developing limb toanother. They can most produc-tively be treated as second-orderfine-tuning effects acting on thestripe- and spot-like elements of

developing cartilage as the skele-ton takes form (Tickle, 2006; New-man, 2007). Indeed, attempts todiscern positional informationalgrids in these patterns of geneexpression independently of anunderlying generator of spatialperiodicities of precartilage pri-mordia is increasingly reminiscentof the pre-Copernican program ofemploying epicycles to account forthe retrograde motion of the plan-ets around the Earth.

A CORE GENETIC NETWORK

FOR PRECARTILAGE

CONDENSATION

The limb mesoblast consists ofmesenchymal cells distributed uni-formly within a hyaluronan richextracellular matrix (ECM). Beforethese cells differentiate into chon-drocytes (cartilage cells), theytransiently condense into tightaggregates at discrete sites wherethe cartilaginous elements will ulti-mately form. Precartilage conden-sations form when the ECMchanges locally in composition,becoming richer in glycoproteinssuch as fibronectin, thus trapping(Frenz et al., 1989; Cui, 2005) thecells and modifying their move-ment. These aggregations are fur-ther consolidated through cell-celladhesive interactions mediated bycell-surface attachment molecules(CAMs), such as N-CAM (Widelitzet al., 1993), N-cadherin (Ober-lender and Tuan, 1994), and pos-sibly cadherin-11 (Luo et al., 2005)(reviewed in Hall and Miyake, 1995,2000; Forgacs and Newman, 2005).Because all the precartilage cells

of the limb mesoblast are capableof producing fibronectin and CAMsbut only those at sites destined toform skeletal elements do so,there clearly must be communica-tion among the cells to divide thelabor in this respect. This is medi-ated in part by secreted, diffusiblefactors of the transforming growthfactor (TGF)-b family of growth fac-tors, which promote the pro-duction of fibronectin (Leonardet al., 1991) and cadherins (Tsoniset al., 1994). Limb bud mesen-chyme also shares with many other

connective tissues (Van Obberghen-Schilling et al., 1988) the autoreg-ulatory capability of producing moreTGF-b upon stimulation with thisfactor (Miura and Shiota, 2000a).The limb bud ectoderm is a

source of fibroblast growth factors(FGFs) (Martin, 1998). Althoughthe entire limb ectoderm producesFGFs, the particular mixture pro-duced by the apical ectodermalridge (AER), a narrow band of spe-cialized ectodermal cells runningin the AP direction along the tip ofthe growing limb bud in birds andmammals, is essential to limb out-growth and pattern formation.FGF8 is the most important ofthese (Mariani and Martin, 2003).The AER affects cell survival(Dudley et al., 2002) and keepsthe precondensed mesenchyme ofthe apical zone in a labile state(Kosher et al., 1979). Its removalleads to terminal truncations ofthe skeleton (Saunders, 1948).The FGFs produced by the ecto-

derm affect the developing limbtissues through three distinct FGFreceptors. The cells of the apicalzone express FGF receptor 1(FGFR1) (Peters et al., 1992; Sze-benyi et al., 1995). Signalingthrough this receptor presumablymediates the suppressive effect ofthe AER in this region of the devel-oping limb. As the chicken limbelongates, a second, ‘‘active,’’ zoneis established at a distance ofapproximately 0.3 mm from theAER, where cells begin to con-dense. In the active zone FGFR1 isdownregulated and cells thatexpress FGFR2 appear at the sitesof incipient condensation (Peterset al., 1992; Szebenyi et al.,1995; Ornitz and Marie, 2002;Moftah et al., 2002). Activation ofthese FGFR2-expressing cells byFGFs induces a laterally acting(that is, peripheral to the conden-sations), inhibitory effect whichsuppresses cartilage differentia-tion (Moftah et al., 2002). Recentwork suggests that Notch signal-ing also plays a part in this lateralinhibitory effect (Fujimaki et al.,2006).The roles of TGF-b, the putative

lateral inhibitor of its effects, andfibronectin in mediating precarti-

ACTIVATOR-INHIBITOR DYNAMICS 307


lage condensation in the limb budmesenchyme can be schematizedin the form of a ‘‘core’’ cell-molec-ular-genetic network (Fig. 2). Thisnetwork is characterized in termsof molecules that directly partici-pate in cell-cell and cell-substra-tum interactions and therebymediate the physical aspects ofpattern formation (Newman andBhat, in press). Transcription fac-tors and coregulators that controlchanges in the levels of these mul-ticellular ‘‘interaction molecules,’’as well as transducers of intracel-lular signals to and from the nu-cleus, are of course essential com-ponents of any complete descrip-tion of such a developmentalnetwork. In the schematic modelsdescribed below, however, wetreat these components implicitly,as complex response functions.

PATTERNING LIMB BUD

MESENCHYME BY A ‘‘LOCAL

AUTOACTIVATION–

LATERAL INHIBITION’’

SYSTEM

Reaction-Diffusion andReactor-Diffusion Systems

Reaction-diffusion systems arenetworks of molecular species in

which positive and negative feed-back in the molecules’ productionand consumption, and disparatediffusion rates, lead to a stableconfiguration in which the chemi-cal composition is nonuniform,rather than uniform, over a spatialdomain. These systems haveattracted interest as biologicalpattern-forming mechanisms eversince Turing (1952) proposedthem as the ‘‘chemical basis ofmorphogenesis’’ more than half acentury ago.For purely chemical systems,

where Turing-type mechanismshave been unambiguously demon-strated (Castets et al., 1990;Ouyang and Swinney, 1991),chemical reactions are the sourcesand sinks of the molecular compo-nents, and diffusion is the classic,Brownian motion-based physicalprocess. In the case of developingtissues, however, ‘‘reaction’’ involvesproduction and consumption ofmolecules by cells, and is an elab-orate, multistep processes. Trans-port through tissues, moreover,while capable of generating molec-ular gradients that attenuate withdistance from the source, is typi-cally a more complex process thansimple molecular diffusion (Kruseet al., 2004; Lander, 2007). Forthis reason, the term ‘‘reactor-dif-fusion’’ has been suggested asbeing more appropriate than reac-tion-diffusion for applications ofthe Turing mechanism to biologicaldevelopment (Hentschel et al., 2004).Reactor-diffusion models have

been gaining prominence in manyareas of developmental biology(reviewed in Forgacs and New-man, 2005; Maini et al., 2006),including the patterning of the pig-mentation of animal skin (Yama-guchi et al., 2007), feather germs(Jiang et al., 2004), hair follicles(Sick et al., 2006), teeth (Salazar-Ciudad and Jernvall, 2002), andthe limb itself (Newman and Frisch,1979; Hentschel et al., 2004;Newman et al., 2007). The Turingscheme stipulates a slowly diffusi-ble, positively-autoregulatory acti-vator and a more rapidly diffusibleinhibitor that is induced by the ac-tivator. For certain developmentalsystems, there is strong evidence

for the identification of both thesefactors with specific molecules. Inother cases, however, only one ofthese components, usually the ac-tivator, has been thus identified.

Morphogen and NonmorphogenMediators of CondensationSpacing

Patterning of the limb skeletonis dependent on molecules of theTGF-b and FGF classes, which aredemonstrably diffusible morpho-gens (Lander et al., 2002; Williamset al., 2004; Filion and Popel,2004). As reviewed in the previoussection (see also Hall and Miyake,1995, 2000; Chimal-Monroy et al.,2003), TGF-b, which initiates acascade of events that leads toprecartilage condensation and chon-drogenesis, is positively autoregu-latory (van Obberghen-Schillinget al., 1988; Miura and Shiota,2000a), and is therefore an excel-lent candidate for the activator ina reactor-diffusion scheme (Newman,1988; Leonard et al., 1991; Miuraand Shiota, 2000a). The molecularidentity of the lateral inhibitor hasbeen elusive, however. Lateral in-hibition can be abrogated byblocking the function of FGF recep-tor 2 (FGFR2), which is localized inthe incipient condensations (Moftahet al., 2002). While this can betaken to imply that the normalfunction of FGFR2 is to mediatethe release of a diffusible lateralinhibitor of chondrogenesis (Moftahet al., 2002), it does not comportwith other evidence that FGFR2scontaining Apert syndrome muta-tions, which lead to expanded,fused skeletal elements (i.e., decreasedlateral inhibition of chondrogene-sis) in humans, are actually hyper-activated (Ibrahimi et al., 2001).Activation of Notch signaling

in vitro and in vivo is also associ-ated with lateral inhibition of con-densation and chondrogenesis. Block-ing of the activated Notch state withthe g-secretase inhibitor N-S-phe-nyl-glycine-t-butyl ester (DAPT),for example, led to fusion of con-densations (Fujimaki et al., 2006).But these results are difficult toreconcile with the known function-ality of the Notch pathway, which

Figure 2. Core network of cell-gene prod-uct interactions leading to limb precarti-lage mesenchymal condensation. The mo-lecular identity of the lateral inhibitor ofcondensation is unknown, but depends oninteraction of ectodermal FGFs with mes-enchymal FGF receptor 2 (Moftah et al.,2002) as well as the Notch signaling path-way (Fujimaki et al., 2006). This inhibitormay act at the level of TGF-b synthesis oractivity (solid inhibitory vector), fibronec-tin synthesis (dashed inhibitory vector), orat some earlier stage. (Adapted from Kis-kowski et al. (2004)).

308 NEWMAN AND BHAT


acts in a juxtacrine fashion, andwould not be an obvious candidatefor a long-range lateral inhibitor ina reactor-diffusion system.

Evidence for Activator-InhibitorDynamics in Limb BudMesenchyme

Despite the complexities men-tioned, a reactor-diffusion-like mech-anism remains the most compel-ling basis for the generic verte-brate limb skeletal pattern for thefollowing reasons: 1) randomizedlimb mesenchymal cells with dis-rupted gradients of Hox proteins,Shh, etc., give rise to digit-likestructures in vivo (Zwilling, 1964;Ros et al., 1994) and of discrete,regularly spaced cartilage nodularor stripe-like arrangements in vitro(Downie and Newman, 1994; Kis-kowski et al., 2004; Christley et al.,2007); 2) the pattern of precartilagecondensations in limb mesenchymein vitro changes in a fashion consist-ent with a reactor-diffusion mecha-nism (and not with an alternativemechanochemical mechanism) whenthe density of the surrounding ma-trix is varied (Miura and Shiota,2000b); 3) exogenous FGF perturbsthe kinetics of precartilage conden-sation in vitro in a fashion consistentwith a role for this factor in regulat-ing the inhibitor in a reactor-diffu-sion-type model (Miura and Maini,2004); 4) the ‘‘thick-thin’’ pattern ofdigits in the Doublefoot mouse mu-tant can be accounted for by theassumption that the normal patternis governed by a reactor-diffusionprocess, the parameters of whichare modified by the mutation (Miuraet al., 2006); 5) simultaneous knock-out of Shh and its inhibitory regu-lator Gli3 in mice yields limbs withnumerous extra digits (Litingtunget al., 2002), suggesting a defaultpropensity of the limb mesen-chyme to generate regularly spacedrepetitive elements of indefinitenumber. A reactor-diffusion-typemechanism is the most plausiblebasis for this.Reaction-diffusion and allied sys-

tems exhibit scale dependence inthat the number of repetitive pat-tern elements that form varies inproportion to the size of the reac-

tive domain. This has sometimesbeen considered to count againstsuch mechanisms for developmen-tal processes which often producethe same pattern over a range oftissue sizes. But scale-dependenceactually represents the biologicalreality in the developing limb. Ex-periments show, for example, thatthe number of digits is sensitiveto the AP (thumb-to-little finger)breadth of the developing limb bud,and will increase (Cooke and Sum-merbell, 1981) or decrease (Alberchand Gale, 1983) over typical valuesif the limb is broadened or nar-rowed. Furthermore, the generallyincreasing number of parallel ele-ments in the proximal to distaldirection in most limbs may, in fact,be a function of dependence of thenumber of morphogen peaks on thechanging spatial dimensions of limbbud domains during pattern forma-tion (see below).A broader category of pattern

forming mechanism that includesreactor-diffusion systems as aspecial case, can be termed ‘‘localauto-activation-lateral inhibition’’(LALI) systems or networks (seealso Meinhardt and Gierer, 2000;Nijhout, 2003). In particular, LALIsystems form patterns by exactlythe same formal means as reac-tor-diffusion systems but need notutilize molecular diffusion or simi-lar mechanisms to propagate acti-vation or inhibitory functions. Liv-ing tissues are ‘‘excitable media’’(Mikhailov, 1990) that can trans-mit signals by means other thanmaterial transport. Consideringthe limb mesenchyme as a LALIsystem, we can entertain alterna-tives to molecular diffusion for thespread of the inhibitor that areconsistent with the molecular find-ings described above.Expression of the Notch tran-

scriptional mediator hes1 is knownto oscillate in time during somito-genesis (Palmeirim et al., 1997),and in the zebrafish there is largescale spatial coordination of theseoscillations through the mecha-nism of synchronization (Giudicelliet al., 2007). Because synchron-ized oscillations of Hes1 expres-sion also appear in early-stagemicromass cultures (Ramray Bhat

and Stuart A. Newman, unpub-lished results), we have been con-sidering LALI networks for limbpattern formation in which lateralinhibition of precartilage conden-sation is mediated by the propaga-tion of coherent states of Notchactivation peripheral to sites of ini-tiation. This framework provides away to understand the apparentlyparadoxical role of FGFR2 signal-ing in mediating both stimulationand inhibition of chondrogenesis.It also suggests a way to ‘‘glob-alize’’ the juxtacrine effect ofNotch signaling.In the next section we provide

motivation for filling out thedetails of a limb-specific LALI net-work by showing that, in the geo-metric context of the growing limbbud, it can reproduce several ofthe important features of this de-velopmental system. We will followthis by presenting a specific modelfor the oscillation-synchronizationmodule in a LALI network for limbskeletal patterning.

A ‘‘BARE-BONES’’ SYSTEM

FOR LIMB SKELETAL

PATTERNING

Modeling MesenchymalPatterning In Vitro and In Vivo

A LALI mechanism based on thecore mechanism for precartilagecondensation formation is fully ca-pable, under realistic assumptions,of generating authentic patterns ofcondensations on a 2D plane (Kis-kowski et al., 2004; Christley et al.,2007). This simulation design is agood representation of the micro-mass culture system, for which agreat deal of experimental data isavailable (Mello and Tuan, 1999;DeLise et al., 2000; Newmanet al., 2007). In the most sophisti-cated of these models the stipu-lated conditions included valuesfor cell dimensions, average dis-tances traveled, initial cell density,and diffusion coefficient of the ac-tivator. The simulations produc-ed condensation patterns (both‘‘spots’’ and ‘‘stripes’’) with aver-age width and spacing statisticsthat were virtually indistinguish-able from experimental values in



the in vitro system (Kiskowskiet al., 2004; Christley et al., 2007).Behavior of the simulated system

under attenuated inhibitor condi-tions indicated that lateral inhibi-tion was critical for realistic pat-terns (Kiskowski et al., 2004). Andalthough, as mentioned, no directevidence exists for a diffusible me-diator of lateral inhibition, the pu-tative inhibitor would have tospread about four times as fast asthe activator for authentic patternsto form, given other constraints(Christley et al., 2007). This is bothphysically and biologically reasona-ble, whatever the actual processmediating lateral inhibition mayturn out to be. It would be useful todetermine the additional assump-

tions needed for this substantiatedin vitro pattern-forming mecha-nism to mediate the generation ofskeletal elements in the appropri-ate number and order in a 3Ddeveloping limb bud.This is an exceedingly difficult

problem, both mathematically andcomputationally, because formalrepresentation and simulation of3D multicomponent dynamicalsystems, of systems with movingboundaries, and of systems withnonstandard shapes, are all formi-dable. Based on informationreviewed in earlier sections wehave modeled the developing limbusing several different idealiza-tions. One such representation is agrowing parallelepiped housing a

continuous-variable (‘‘continuum’’)set of reactor-diffusion equationsdescribing the spatiotemporal evo-lution of AER-derived FGF, activat-ing and inhibitory morphogens, fi-bronectin, and different cell types(defined by expression of differentFGF receptors) (Hentschel et al.,2004). Here the distribution of celltypes was represented by a den-sity, an approximation to inde-pendently acting, physically dis-crete cells. Though inherently a 3Dmodel, we have simulated itsbehavior in two dimensions, i.e.,assuming a negligible thickness inthe dorsoventral dimension (seeFigs. 1 and 3).We have also simulated the

developing limb in 3D, using much

Figure 3. ‘‘Bare-bones’’ mechanism for verte-brate limb development. The interactions of thecore mechanism are superimposed on a 2D sche-matic limb bud organized into zones defined byexperimentally-determined expression patternsof FGF receptors 1, 2, and 3. In the ‘‘apicalzone’’ fibronectin synthesis and precartilage con-densation is suppressed by the FGFs emanatingfrom the AER. In the ‘‘LALI zone,’’ comprisingthe apical zone and an ‘‘active zone’’ just proxi-mal to it, a local autoregulatory-lateral inhibitorysystem sets up peaks of an activator of fibronec-tin synthesis and precartilage condensation (i.e.,TGF-b). The length of the LALI zone, lx, is a func-tion of time. The active zone (a detailed view ofwhich is shown below) is the region in which cellsare sufficiently far from the AER to respond tothe activator and undergo cell condensation.When cells leave the proximal end of the activezone and enter the frozen zone they differentiateinto cartilage and their spatiotemporal patternbecomes fixed, constituting a ‘‘frozen zone.’’ Thelength of the AP axis, ly, is constant duringchicken wing development in which three digitsare generated, but expands during limb develop-ment in mouse and human, where five digitsform. The dorsoventral axis is collapsed to zeroin this simplified model. PD, proximodistal; AP,anteroposterior. In lower panel, curved arrows:positively autoregulatory activator; lines endingin circles: lateral inhibitory effect. (Adapted fromHentschel et al. (2004) and Forgacs and New-man (2005)).

310 NEWMAN AND BHAT


simplified (and therefore less bio-logically founded) equations formorphogen dynamics, but morerealistic discrete, stochastic cell dy-namics (Chaturvedi et al., 2005;Cickovski et al., 2005). In particu-lar, the cells in these 3D represen-tations were modeled as distinct,independently motile, deformable,biosynthetically active entities.These model cells move randomly,consistent with a requirement tominimize their energy of interactionwith the patterns of fibronectininduced by the activator (TGF-b-like) morphogen. The theoreticalframework that permits the simula-tion of cell rearrangement by differ-ential adhesion or, as in this case,haptotaxis, is the Cellular Pottsmodel of Glazier and Graner (1993).Our ultimate aim, of course, is

to incorporate realistic morphogenand cell dynamics into a singlegeometrically realistic framework(Newman et al., 2007), but atpresent this is beyond the limits ofavailable methods. The family ofmodels described (beginning withthe 3D model of Newman andFrisch (1979)), however, containsa shared set of assumptions con-cerning the zonal organization ofthe developing limb. Moreover,despite the different idealizationsemployed, they reproduce a com-mon set of its key features. Wewill focus on the properties of thecontinuum model of Hentschelet al. (2004) in the remainder ofthis section.

Zonal Organization of theDeveloping Limb

Reiterating the description in anearlier section, we take the limbmesoblast to be divided into an ap-ical zone, under the condensation-suppressive effects of the AER, andan active zone consisting of cellsthat, based on distance from theapical source of FGF8, are suscepti-ble to patterning interactions. Themodel also includes a frozen zoneproximal to the active zone wheredifferentiation of the condensedcells into chondrocytes is stipulatedto be irreversible and no additionalpattern changes are possible.

This organization of the limb budmesoblast into tandemly arrangedzones of: 1) unresponsive butunpatterned; 2) responsive to pat-terning signals; and 3) irreversiblypatterned, which was carried overfrom an early simpler version ofthis model (Newman and Frisch,1979), also has similarities to cur-rent models of somitogenesis(Pourquie, 2003; Giudicelli et al.,2007). The similarity extends alsoto the molecule constituting thesuppressive gradient emanatingfrom the terminal region, which isFGF8 in both cases. In the somito-genesis models the patterning sig-nal operating in the equivalent ofthe active zone is a synchronizedbiochemical oscillation, while inthe limb model it is a reactor-diffu-sion, or more generally, LALI sys-tem. We will revisit the possiblerelationships between these pat-terning signals below.For representational and compu-

tational expediency the followinggeometric idealization was em-ployed (Newman and Frisch, 1979;Hentschel et al., 2004): the limbbud is considered to have time-dependent PD length, L(t), takenalong the x-axis, and fixedlengths, ly and lz, along the AP (y-axis) and dorsoventral (z-axis)directions (Fig. 3). Another vari-able, lx(t), represents the lengthalong the PD axis of the domainof the limb bud where activator-inhibitor interactions take place.We refer to the model for limb

development in this growing do-main as ‘‘bare-bones,’’ becausewhile it incorporates the core mes-enchymal cell-morphogen-ECM net-work summarized in Fig. 2, itomits spatiotemporally distributedmodulatory factors such as Hoxprotein gradients, Shh, and so on,that cause the various skeletalelements (e.g., the radius andulna, the different digits) to appeardifferent from one another.As mentioned, the division of

the distal portion of the limb intoan apical and active zone reflectsthe activity of the AER in sup-pressing differentiation of themesenchyme subjacent to it (Ko-sher et al., 1979). The spatialrelationship between the apical

and active zones results from thegraded distribution of FGFs, thepresumed AER-produced suppres-sive factors. The active zone,therefore, is where the mesen-chyme cells no longer experiencehigh levels of FGFs and thereforebecome responsive to the activa-tor, TGF-b, and the factors thatmediate lateral inhibition. Thedynamic interactions of cells andmorphogens in the unpatternedportion of the limb bud give rise tospatial patterns of condensationsin the active zone.

Factors Controlling the Numberof Elements

LALI systems are sensitive tospatial scale. In general, the des-ignated interactions set a charac-teristic ‘‘chemical wavelength,’’but do not determine how manypeaks will form overall. The latternumber is a function of the dimen-sions of the ‘‘LALI domain’’ inwhich the reaction-diffusion orallied process takes place. In em-bryonic tissues this domain is thetissue region in which inductivepatterns of morphogens are estab-lished, independently of whetherthe cells are prepared to respondto these signals by differentiating.There are no experimental data

that directly bear on the bounda-ries of the LALI domain in thedeveloping limb bud; in differentversions of the bare-bones modelthe domain has been consideredto comprise the apical and activezones together (Newman andFrisch, 1979), or only the activezone (Hentschel et al., 2004; Cha-turvedi et al., 2005; Cickovskiet al., 2005). As will be seen be-low, assuming that the LALI domainextends fully to the end of the limbbud (i.e., comprises both the activeand apical zones) brings the modelinto conformity with predictions ofsome classic experiments.In all versions of the model, the

greater the value of the AP (AP)length, lz, the more parallel peakswill form. Thus, whether three dig-its (as in the chicken forelimb),four digits (as in the chicken hin-dlimb), or five digits (as in mouseor human limbs), arise, is pre-



dicted to be positively correlatedwith this distance, and this isborne out in the actual systems.What is somewhat counterintuitiveis the model’s determination of anegative correlation between thePD length of the LALI domain, lx(t),and the number of parallel ele-ments generated. This is a straight-forward mathematical consequenceof the behavior of the LALI systemunder the asymmetric conditionsimposed by the AER-dependentgradient (Newman and Frisch,1979; Hentschel et al., 2004; Cha-turvedi et al., 2005; Cickovskiet al., 2005). Since it appears in anumber of different mathematicalembodiments of the model, it isprobably a robust feature.In the developing chicken wing,

where lz remains constant duringthe period of pattern formation,the length of the unpatterned dis-tal region (encompassing, in ourterminology, both the apical andactive zones) declines progres-sively over the course of develop-ment (Summerbell, 1976). Themodel’s stipulation that lx(t) actsas a ‘‘control parameter’’ influenc-ing the number of parallel ele-ments is thus consistent with(though not compelled by) exist-ing evidence.Cell proliferation enters into this

scheme in the following fashion:cells are recruited into the activezone from the proximal end of theapical zone, as dividing cells moveaway from the influence of theAER. (This is similar to the role ofthe caudal FGF gradient in somito-genesis) (Dubrulle et al., 2001).The active zone loses cells, inturn, to the proximal frozen zone,the region where cartilage differ-entiation has occurred and a por-tion of the definitive pattern hasbecome set. The overall effect ofthis growth and zonal reassign-ment is a time-dependent reduc-tion of lx. The growth of thedomains implies the presence of alocal velocity field and thus cellrearrangement by convection.However, estimates of the Pecletnumber, defined by the mathe-matical relation LV/D, where L isthe characteristic length scale ofthe limb, V the characteristic ve-

locity of the flow, and D themorphogen diffusion coefficient, isrelatively small, meaning that dif-fusion is more important than con-vection, at least for the purposesof our basic model (Newmanet al., 2007).Four main types of mesenchy-

mal cells are involved in chick limbskeletal pattern formation. Theseare represented in the continuummodel by their spatially and tem-porally varying densities. The celltypes are characterized by theirexpression of one of the three FGFreceptors found in the developinglimb. The cells expressing FGFR1,FGFR2 (and cells), and FGFR3 aredenoted, respectively, by R1, R2 1R02, and R3. The apical zone con-

sists of R1 cells, and those of thefrozen zone, R3 cells (reviewed inOrnitz and Marie, 2002). Theactive zone contains R2 cells andthe direct products of their differ-entiation, R0

2 cells. These lattercells secrete elevated levels of fi-bronectin. The R1, R2, and R0

2 cellsare mobile, while the R3 (carti-lage) cells are immobile.Transitions and associations

between the different cell typesare regulated in the model by thegene products of the core mecha-nism (Fig. 2). The model containsterms representing, respectively,the spatially and temporally vary-ing concentrations of FGFs (pro-duced by the AER), TGF-b (pro-duced throughout the mesen-chyme), a diffusible inhibitor ofchondrogenesis produced by R2

cells, and fibronectin, produced byR02 cells. The model thus comprises

eight independent variables, withan equation for the behavior ofeach of them. These eight varia-bles correspond to the core set ofinteractions necessary to describethe development of a basic, bare-bones skeletal pattern.Simulations using the eight-

equation system are computation-ally unfeasible. In Hentschel et al.(2004) a biologically motivatedseparation of time scales wasemployed to reduce the system tofour equations. This involved aver-aging the values of variables thatevolve very rapidly relative to theactivating and inhibitory morpho-

gens and holding constant thosethat evolve more slowly.The mathematical technique of

linear stability analysis was thenused to identify solutions of thefour-equation system on a 2Dplane (i.e., under the simplifyingassumption that the dorsoventralwidth is very small) for LALIdomains of progressively decreas-ing width (Fig. 4). 3D simulationsof the growing limb bud, based onthe model of Hentschel et al.(2004), but using different simpli-fying assumptions for the activa-tor-inhibitor dynamics, and a ‘‘mul-timodel’’ computational frameworkthat permitted representation ofcells as autonomous, discrete enti-ties (Cickovski et al., 2007), alsoaccurately portrayed the PD orderof appearance and increase inthe number of skeletal elements(Fig. 5) (Chaturvedi et al., 2005;Cickovski et al., 2005).

Additional Predictionsof the Model

Several emergent properties ofthe bare-bones model add to itsplausibility as an accurate accountof the cell-molecular basis of limbpattern formation. It has longbeen known, for example, that ex-perimental removal of the AERbefore full elaboration of the pat-tern leads to terminal deletions,which are less extensive the laterthe procedure is performed (Saun-ders, 1948). If the distal source ofFGF is removed as the model limb‘‘develops,’’ the entire distal regionis immediately unsuppressed. Un-der the assumption that the LALIdomain extends to the end of thelimb (one of the possibilities men-tioned above), the full domainwould become ‘‘active,’’ and theactivator pattern currently undergeneration would become the final,albeit terminally incomplete, one.(The alternative assumption, thatthe LALI domain is coextensivewith the active zone, would predicttandem duplications of proximalelements from AER removal, con-trary to experimental findings.)Another unanticipated explana-

tory feature of the bare-bonesmodel concerns predicted devia-

312 NEWMAN AND BHAT


tions from the PD appearance oflimb skeletal elements. Unlikeamniotes (reptiles, birds, andmammals), for which this develop-

mental progression universallypertains, for urodele amphibianssome distal elements may appearbefore some proximal ones (Franssen

et al., 2005). The developing limbsof amniotes and urodeles also dif-fer in that whereas the formerproduce FGF8 only in the apical

Figure 5. 3D simulations of limb development. A: Simulation of distribution of TGF-b (activator) over progressive developmentalstages (time increasing from bottom to top) in a 3D computational model based on the bare-bones mechanism represented in Fig-ure 3 and a simplified version of the core-mechanism equations in Hentschel et al. (2004), using a ‘‘multimodel’’ representation ofautonomous cells (Cickovski et al., 2007). B: Simulation of cell distributions after completion of development into humerus (lower),ulna and radius (middle), and digits (top). C: Simulation of successive stages (top to bottom) of proximodistal development of limbskeleton using the multimodel described in Cickovski et al. (2007) and a different simplification of the core-mechanism equationsthan in (A) and (B). (A) and (B) are from Chaturvedi et al. (2005); (C) is from Forgacs and Newman (2005), based on Cickovskiet al. (2005), courtesy of Trevor Cickovski.

Figure 4. Relationship of size of LALI zone and number of activator morphogen peaks formed. A: Top, graph of change in size ofthe unpatterned distal portion of the embryonic chicken wing between 3.5 and five days of development, based on measurementsby Summerbell (1976); bottom, computational results of activator distribution as a function of the proximodistal length, lx(t), of theLALI zone, which is identified with the unpatterned tissue in above graph. The scale represents the concentrations as a fraction ofthe concentration (5 1.0) at the uniform stationary state. B: A typical developed ‘‘limb skeleton’’ arising from the bare-bones modelrepresented in Figure 3 and the calculations in (A), above, allowing for growth. Specifically, after the cellular condensations formbased on patterns of activator peaks, growth is assumed to occur at a constant rate. Consequently, earlier forming cartilage ele-ments are subject to more growth than later ones. All panels adapted from Hentschel et al. (2004).



ectoderm, the latter produce it inthe mesenchyme as well (Hanet al., 2001). When we performedsimulations using a modified ver-sion of the bare-bones model inwhich both the limb bud tip andthe mesoblast produced suppres-sive FGFs, we obtained two activezones and patterns that developedout of strict PD order (TilmannGlimm and Stuart A. Newman,unpublished results).

OSCILLATION-

SYNCHRONIZATION

AS A MECHANISM FOR

LATERAL INHIBITION

In a study of limb bud mesenchy-mal cells in culture we examinedthe response to perturbation byexogenous TGF-b of several devel-opmental variables (Leonardet al., 1991). These variablesincluded production of fibronectinmRNA, the extent and rate ofappearance of condensations, andlevels of production of the carti-lage-specific sulfated proteogly-can, aggrecan. We found, surpris-ingly, that there was a temporalperiodicity in the dynamics of allthese factors. For example, peaksof fibronectin mRNA or aggrecanproduction appeared at increasingdurations of TGF-b exposure, butexposure durations interdigitatedbetween the ones that elicitedpeaks produced, instead, responseminima (Leonard et al., 1991).It had been known for some

time that processes controlled byan oscillatory mechanism can res-pond to continuously varying exter-nal perturbations by changing inalternating directions, producingso-called type 0 resetting curves(Winfree, 1980). Such indirectdata, though diagnostic of anunderlying oscillator, give no hintof what is actually oscillating. Weconcluded from our experiments,however, that the generation ofprecartilage condensations or theirmolecular determinants may in-volve one or more periodic pro-cesses (Leonard et al., 1991).Since then, evidence has been pre-sented for periodic expression ofhes2 in the chicken limb (Pascoal

et al., 2007) and, as mentionedabove, hes1 has been found to beexpressed in a synchronized, peri-odic fashion during the condensa-tion-forming period in micromasscultures of limb bud mesenchyme(our unpublished results).The synchronization of oscilla-

tions provides a way of propagat-ing a signal that may begin as ajuxtacrine interaction and convertit to a long-range effect (see forexample, Garcia-Ojalvo et al.,2004). This has led us to considera mechanism for lateral inhibitionof precartilage condensation thatis an alternative to one based on adiffusible morphogen. We suggest,instead, that this effect resultsfrom Notch-Delta juxtacrine sig-naling followed by synchronizationof a Notch-activated oscillatorystate. As will be seen, this pro-posed solution to the elusive inhib-itor problem can potentially recon-cile a set of puzzling cell-molecularfindings relating to the spacing ofcondensations discussed earlier.Like the reactor-diffusion mecha-nism described earlier, in whichboth the activator and inhibitorare diffusible morphogens, theoscillation-synchronization-depend-ent system is a LALI mechanismand, as such, can play the samerole in the bare-bones model forlimb development as the reactor-diffusion process considered in earlierversions of this model (Chaturvediet al., 2005; Cickovski et al.,2005; Hentschel et al., 2004).The precartilage mesenchymal

condensation pattern seen inmicromass cultures shows a spa-tial regularity that depends on azone of inhibition forming aroundincipient condensations. Thesezones of inhibition consist of cellswhich have failed to enter thecondensation and thus do notundergo differentiation into carti-lage. In preliminary studies usingquantitative real-time PCR, wehave found that the expression ofhes1, a Notch pathway targetgene, enters into synchronousoscillations in a significant portionof the cells within the first dayof culture, just as the spatial pat-tern of condensations is becomingestablished (Ramray Bhat and

Stuart A. Newman, unpublished;shown schematically in Fig. 6A).Notch is transiently activated in

precartilage mesenchymal cellsas they first enter condensationsand pharmacological abrogation ofNotch activation leads to expansionand fusion of the condensations(Fujimaki et al., 2006). Since theNotch-activated state is transducedby Hes1, the oscillatory nature ofhes1 expression (the ‘‘Hes1 clock’’)implies that the synchronized cellsperiodically cycle through Notch-activated and Notch-inhibitedphases. We assume that when hes1expression is minimal, there is a‘‘phase window’’ during which thecells become permissive to respondto the activator signal (by our earlierassumption, TGF-b) and producemore activator and fibronectin.If the window for activator prop-

agation in the Hes1 clock is short,in a field of cells with randomphases of the Hes1 clock there willbe a low but finite probability ofpropagation of the condensationstate from any point. Therefore,in the absence of synchrony,although the default state for acti-vator propagation is ‘‘mostly inhib-ited,’’ i.e., refractory to activator(indicated by there being morelight blue cells than dark blue cellsin the upper row of panel B in Fig.6), activator/TGF-b expression willeventually percolate through theentire field, leading all the cells tocondense. However, in reality, thecells become largely synchronizedin hes1 expression. This is shownschematically in the upper row ofFig. 6C, where the ‘‘high Hes1’’phase of the clock, nonpermissiveto propagation of activation, isrepresented by the preponderanceof light blue cells.The precartilage mesenchymal

cells, derived from the apical zoneof the limb bud, express FGFR1(Peters et al., 1992; Szebenyiet al., 1995; see discussion in ACORE GENETIC NETWORK FORPRECARTILAGE CONDENSATION,above), a condition that may beconducive to the hes1 oscillatorystate. Once they are removedfrom the influence of the AER inthe developing limb, or are placedin culture, however, some cells

314 NEWMAN AND BHAT


become FGFR2-positive (red cellsin upper row of Fig. 6C), and theseare located at sites of incipientcondensation (Szebenyi et al.,1995; Moftah et al., 2002). SinceTGF-b can induce the functionalactivation of FGFR2 in some celltypes (Kanda et al., 2003), wesuggest that this factor, in con-junction with FGF itself, acts onthe precartilage cells to stop orslow down the Hes1 clock.This implies that there will be an

antagonism between the inducedcessation or slowing of the Hes1clock at the condensation sitesand the self-organizing (probablyNotch-dependent; Giudicelli et al.,2007) synchronization of the clockat a characteristic distance fromthe condensation centers. (See Rie-del-Kruse et al., 2007 for a descrip-tion of how competition between

synchrony and desynchrony setsan analogous ‘‘defect range’’ inperturbed segmental plates).Synchronization thus converts

local juxtacrine signaling intobroad-range lateral inhibition, butwithout the need for a diffusibleinhibitor. FGFR2-positive sites cancontinue to be initiated withinthese synchronized domains onlywhen the synchronized Hes1 oscil-lation is at its trough, but thesmall phase window permissiveto propagation of the activatorensures that two such cell clustershave a low probability of beingnext to each other. Unlike the casewith initially asynchronous fieldthat is mostly inhibited all of thetime, but across which the activa-tor signal will thus always have apathway to propagate (Fig. 6B), inthe synchronized situation the

domains surrounding the initiationsites will be totally inhibited mostof the time (Fig. 6C, upper row).The condensations can expandperiodically but will be limited bythe duration and decay of the acti-vator signal, and the outcome willbe a LALI-mediated pattern (Fig.6C, lower row).The synchrony-based pattern

forming mechanism describedabove, while sufficient to generatepatterns of the regularity seen inlimb bud mesenchymal cultures, ismissing a key element required togenerate the entirely regular pat-terns seen in vivo by a LALI mech-anism: feedback between the con-trol of the initiation sites and thezones of inhibition. This feedbackcircuitry is specified in several pre-viously proposed reactor-diffusion-type LALI mechanisms for limb

Figure 6. Oscillator-synchronization mechanism for lateralinhibition of condensation formation. A: Schematic represen-tation of periodic changes in hes1 (and presumably Hes1 pro-tein) expression over time during the period of pattern forma-tion. Light blue represents the ‘‘high Hes1,’’ TGF-b-refractorystate; dark blue represents the ‘‘low Hes1,’’ TGF-b-permissivestate. B: Upper row, schematic representation of precartilagemesenchymal cells oscillating in hes1 expression over time,with random phases. Lower row, randomly initiated centers ofactivator production (purple) expand with time, becausethere is always a pathway for activator propagation in thephase-randomized field of cells. C: Upper row, cells express-ing FGFR2 (red) appear, possibly induced by local elevation ofactivator. The Hes1 clock is halted or slowed, causing localdesynchrony (scattered light and dark blue cells). Self-organ-ized synchronization continues peripheral to the condensa-tions (mainly light blue cells). Since, by our assumption, mostof the Hes1 cycle is inhibitory to propagation of the activator,the latter fails to spread (lower panel) and pattern formationensues.



mesenchymal pattern formation(Hentschel et al., 2004; Christleyet al., 2007; Alber et al., 2007),but so far these activator-inhibitorinteractions are hypothetical. Someevidence suggests that the amountsand types of ectodermal FGFs towhich the mesenchyme is exposedinfluences the regularity of thecondensation pattern (Moftah et al.,2002). This would be well-regulatedby the surrounding ectoderm in thein vitro context and may mediatethe connection between initiationand inhibitory effects.This oscillation-synchronization

mechanism of lateral inhibition isconsistent with existing experi-mental data and helps explainsome earlier puzzles. TGF-b, forexample, is much more effectivein inducing fibronectin expressionand condensation formation a dayafter cultures are established thanwithin the first day of culture(Leonard et al., 1991). This laterperiod is when FGFR2-positivecells first appear. It is significantin this regard that in osteogeniccells FGFR2 synergizes with TGF-bin inducing the production of fibro-nectin (Tang et al., 2007).The role of juxtacrine Notch sig-

naling in mediating long-range lat-eral inhibition (Fujimaki et al.,2006) becomes understandablewhen synchronization is taken intoaccount. Finally, the paradoxicalrole of FGFR2 mentioned abovecan be explained as follows:FGFR2 promotes condensation for-mation, and thus if it is present ina hyperactivated form (as it is inApert syndrome in humans) (Ibra-himi et al., 2001) condensationswill expand. Nonetheless, withoutFGFR2 present, the mesenchymewill not initiate centers from whichHes1 synchrony can spread. In theabsence of broad inhibitory zones,TGF-b will eventually induce allcells to produce more TGF-b andalso fibronectin. Thus if FGFR2 isknocked down, ectopic condensa-tions are predicted to form, asreported (Moftah et al., 2002).

DISCUSSION

We have presented a combinedphysical and molecular-genetic

approach to limb skeletal patternformation that accounts for anumber of major features of thisprocess. These include: 1) thegeneration of discrete, regularlyspaced precartilage condensa-tions, 2) the PD emergence ofincreasing numbers of parallel ele-ments over time, 3) the depend-ence of successive patterningsteps on the presence of a gradedsignal from the AER, 4) the devia-tion from strict PD development,as in urodele amphibians, when anAER type signal is produced by themesoblast, as it is in urodeles, and5) roles consistent with experi-ment of the following factors:FGF8, FGFR2, TGF-b, fibronectin,and Notch.The general perspective of our

analysis is based on the patternforming capabilities of LALI sys-tems (Meinhardt and Gierer,2000). Such systems, based ondiffusible activators and inhibitors,have been shown to quantitativelyreproduce the pattern characteris-tics of limb bud precartilage mes-enchyme in vitro (Kiskowski et al.,2004; Christley et al., 2007).But while there is strong evidence(reviewed above under A COREGENETIC NETWORK FOR PRECAR-TILAGE CONDENSATION) that thediffusible, positively autoregula-tory morphogen TGF-b plays therequisite role of activator in a limbmesenchymal LALI system (Leon-ard et al., 1991; Miura and Shiota,2000a), the identity of the lateralinhibitor has been more elusive.Moreover, the dependence of long-range lateral inhibition of precarti-lage condensation on FGFR2 (Moftahet al., 2002), which is expressedat sites of condensation and is apositive mediator of chondrogenesis(Ornitz and Marie, 2002), and on theNotch pathway (Fujimaki et al.,2006), which acts in a juxtacrinefashion, suggests that a mechanismother than diffusion may mediatethis process.Drawing on indications from an

earlier study that patterning ofcondensations may involve anunderlying oscillatory process(Leonard et al., 1991), recentfindings that Notch transcriptionalmediators of the Hes family show

oscillatory dynamics in vivo (Pas-coal et al., 2007) and in vitro (ourunpublished results), and evidencethat Notch-based juxtacrine sig-naling can mediate the synchroni-zation of Hes oscillations and thusconvert short-range into long-range signals (Giudicelli et al.,2007), we have here proposed anovel mechanism for the laterallyinhibitory component of the LALIsystem of limb precartilage mes-enchyme.The reformulated LALI system

(with appropriate activator-inhibi-tor feedback; see above) can playthe same role in the bare-bonesmodel for skeletal developmentas the earlier-proposed reactor-diffusion system (Hentschel et al.,2004; Alber et al., 2007). Indeed,the robustness of the morphoge-

netic outcomes of this model tochanges in the molecular detailsof one of its functional modules,the LALI mechanism, is a generalcharacteristic of developmentalsystems. These can often changedramatically at the molecular levelover the course of evolution whileleaving anatomical structures rela-tively unaltered (Muller and New-man, 1999; Felix and Wagner,2006). Further experimentationwill be required to determinewhether one or another version ofa reactor-diffusion system (Newmanet al., 2007; Alber et al., 2007),the oscillator-synchronization LALIsystem proposed here, or a differ-ent category of mechanism, bestaccounts for chondrogenic patternformation in vivo and in vitro.One set of issues not addressed

in the foregoing is the bases of dif-

The spatiallyquasi-periodic nature

of the vertebratelimb skeleton,however, is an

invariant property ofall limb types in alltetrapod species.

316 NEWMAN AND BHAT


ferences in size and shape amongthe limb’s individual skeletalelements. These include fairly dra-matic differences between corre-sponding fore- and hindlimb ele-ments, differences along the PDaxis such as between the humerusand the ulna, more subtle onesalong the AP axis such as betweenthe radius and ulna, or amongthe various digits, and even finerones along the dorsoventral axissuch as between the dorsal andventral aspects of the femur. Theprocesses regulating such differ-ences has been a major concernof research in limb developmentalbiology over the last 35 years, andhas led to information concerning

the influence of Hox and Tbx tran-scription factors, Sonic hedgehogand other molecular determinantson the identities of the skeletalelements. These effects, althoughthey typically vary for a given mol-ecule between limb types and dif-ferent species, are clearly impor-tant, since the limb skeleton is nota tandem arrangement of indistin-guishable elements, as in ourbare-bones model, but a finelyhoned result of evolutionaryforces. It seems likely that modu-latory factors, acting at a varietyof regulatory levels, could fine-tune the morphology of the devel-oping skeletal elements by alteringrelative amounts of common tis-

sue components (Downie andNewman, 1994, 1995). The spa-tially quasi-periodic nature of thevertebrate limb skeleton, how-ever, is an invariant property of alllimb types in all tetrapod species.Indeed, its very ubiquity mayhave led to its relative neglect as ascientific problem. It is this aspectof the vertebrate limb, which iscentral to developmental, evolu-tionary, and clinical concerns, thatthe approach described here isdirected towards understanding.Finally, we note that conceptual-

izing a developmental processsuch as limb skeletal patterning asan interplay between molecular-genetic and physical and physico-chemical mechanisms (Newmanand Comper, 1990) can providenew insight into the genesis ofbirth defects. Because genes andtheir products generate biologicalforms only as participants in dy-namical systems, the properties ofsuch systems, specifically theirnonlinear behaviors and sensitivityto physical (including mechanical)and chemical externalities, needto be taken into account in under-standing their typical and variantmorphological outcomes. Recog-nizing that developing embryosare not genetically programmedmachines, but rather complex, ex-citable systems in interaction withthe physical world, can help deci-pher the often puzzling relation-ships between familial and geneticbackground and environmentalexposure to teratogens and otheragents in the production of con-genital anomalies and disease(Dournon et al., 1998; Ozanneand Constancia, 2007; Godfreyet al., 2007).

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