dynamics of dpp signaling and proliferation control

8/2/2019 Dynamics of Dpp Signaling and Proliferation Control

1/7

DOI: 10.1126/science.1200037, 1154 (2011);331Science

, et al.O. WartlickDynamics of Dpp Signaling and Proliferation Control

This copy is for your personal, non-commercial use only.

clicking here.colleagues, clients, or customers by, you can order high-quality copies for yourIf you wish to distribute this article to others

here.following the guidelines

can be obtained byPermission to republish or repurpose articles or portions of articles

):March 3, 2011www.sciencemag.org (this infomation is current as of

The following resources related to this article are available online at

http://www.sciencemag.org/content/331/6021/1154.full.htmlversion of this article at:

including high-resolution figures, can be found in the onlineUpdated information and services,

http://www.sciencemag.org/content/suppl/2011/03/01/331.6021.1154.DC1.htmlcan be found at:Supporting Online Material

http://www.sciencemag.org/content/331/6021/1154.full.html#ref-list-1, 15 of which can be accessed free:cites 39 articlesThis article

http://www.sciencemag.org/content/331/6021/1154.full.html#related-urls1 articles hosted by HighWire Press; see:cited byThis article has been

http://www.sciencemag.org/cgi/collection/developmentDevelopment

subject collections:This article appears in the following

registered trademark of AAAS.is aScience2011 by the American Association for the Advancement of Science; all rights reserved. The title

CopyrighAmerican Association for the Advancement of Science, 1200 New York Avenue NW, Washington, DC 20005.(print ISSN 0036-8075; online ISSN 1095-9203) is published weekly, except the last week in December, by thScience
http://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/content/331/6021/1154.full.htmlhttp://www.sciencemag.org/content/331/6021/1154.full.htmlhttp://www.sciencemag.org/content/331/6021/1154.full.htmlhttp://www.sciencemag.org/content/suppl/2011/03/01/331.6021.1154.DC1.htmlhttp://www.sciencemag.org/content/suppl/2011/03/01/331.6021.1154.DC1.htmlhttp://www.sciencemag.org/content/suppl/2011/03/01/331.6021.1154.DC1.htmlhttp://www.sciencemag.org/content/331/6021/1154.full.html#ref-list-1http://www.sciencemag.org/content/331/6021/1154.full.html#ref-list-1http://www.sciencemag.org/content/331/6021/1154.full.html#ref-list-1http://www.sciencemag.org/content/331/6021/1154.full.html#ref-list-1http://www.sciencemag.org/content/331/6021/1154.full.html#related-urlshttp://www.sciencemag.org/content/331/6021/1154.full.html#related-urlshttp://www.sciencemag.org/content/331/6021/1154.full.html#related-urlshttp://www.sciencemag.org/content/331/6021/1154.full.html#related-urlshttp://www.sciencemag.org/cgi/collection/developmenthttp://www.sciencemag.org/cgi/collection/developmenthttp://www.sciencemag.org/cgi/collection/developmenthttp://www.sciencemag.org/content/331/6021/1154.full.html#related-urlshttp://www.sciencemag.org/content/331/6021/1154.full.html#ref-list-1http://www.sciencemag.org/content/suppl/2011/03/01/331.6021.1154.DC1.htmlhttp://www.sciencemag.org/content/331/6021/1154.full.htmlhttp://www.sciencemag.org/about/permissions.dtlhttp://www.sciencemag.org/about/permissions.dtl


2/7

Dynamics of Dpp Signaling andProliferation ControlO. Wartlick,1* P. Mumcu,2* A. Kicheva,1* T. Bittig,2* C. Seum,1 F. Jlicher,2 M. Gonzlez-Gaitn1

Morphogens, such as Decapentaplegic (Dpp) in the fly imaginal discs, form graded concentrationprofiles that control patterning and growth of developing organs. In the imaginal discs,proliferative growth is homogeneous in space, posing the conundrum of how morphogenconcentration gradients could control position-independent growth. To understand themechanism of proliferation control by the Dpp gradient, we quantified Dpp concentration andsignaling levels during wing disc growth. Both Dpp concentration and signaling gradients scalewith tissue size during development. On average, cells divide when Dpp signaling levels haveincreased by 50%. Our observations are consistent with a growth control mechanism based ontemporal changes of cellular morphogen signaling levels. For a scaling gradient, this mechanismgenerates position-independent growth rates.

G

rowth regulation of the Drosophila wingimaginal disc critically depends on the

Dpp morphogen gradient(1

7). Dpp mu-tant imaginal discs fail to grow, and ectopicexpression of Dpp in clones of wing cells or-ganizes growth and elicits the formation of anectopic winglet (7). Growth of imaginal discs isspatially homogeneous. How a graded Dpp sig-nal can control homogeneous tissue growth is anopen question for which a number of modelshave been proposed: For example, it has beensuggested that the steepness of the gradient (5, 8)and/or mechanical feedback (9, 10) control pro-liferation. However, little quantitative data sup-ports these models. To address this, we quantifiedspatial and temporal changes of Dpp concentra-

tion, signaling activity, and disc growth param-eters during development.The Dpp gradient scales with wing size. We

used a functional green fluorescent proteinDpp(GFP-Dpp) fusion (11, 12) expressed in the en-dogenous Dpp source to quantify GFP-Dpp pro-files as a function of distancex from the source atdifferent times t during larval development (Fig.1, A to C), both with and without expression ofthe endogenous Dpp gene (13) (fig. S1). Duringthe growth period, the Dpp gradient expands:Both the gradient amplitude C0 (i.e., the concen-tration at the source boundary) and the decaylength l (the distance l over which the gradientdecays) increase significantly (Fig. 1, D and E).The decay length, l, is proportional to the targettissue width L [the scaling ratio l/L = 0.112 is

constant; Fig. 2, A and B; n = two independentdata sets with l/L = 0.107 (n1 = 98 discs) and

l/L = 0.116 (n2 = 60 discs); table S3]. Furtheranalysis of Dpp gradient profiles, C(r,t), wherer = x/L is the relative distance to the source,revealed that the relative concentration gradient,C(r,t)/C0(t), is invariant during development (Fig.2A); the gradient scales with the growing tissue.Gradient scaling behaviors have been reportedin this and other systems (1417), and possiblemechanisms have been discussed (18, 19) [supporting online material (SOM) text S1.2]. Notethat thegradient of another morphogen, Hedgehog(Hh), does not scale (fig. S2).

Decreasing degradation accounts for gradi-ent expansion. Gradient expansion is not due to

stretching of the gradient by wing growth, be-cause the Dpp degradation rate is much largerthan the disc growth rate; the gradient renewsitself faster than the tissue grows (SOM text S1.1).Hence, gradient expansion is due to changes inDpp production (n), diffusion (D), or degradation(k) (12, 20) (SOM text S1.1). Estimation of theseparameters by fluorescence recovery after photo-bleaching(FRAP) (12) and a reporter assay [SOMquantitative procedures (QP) 3] showed that Dppproduction and diffusion vary only slightly dur-ing the growth phase (Fig. 2, C and D), whereasthe degradation rate decreases substantially ask ~ 1/A with increasing posterior compartmentareaA (Fig. 2E). This decrease of the degrada-tion rate could account for the constant scalingratio l/L, because l = D/kand A ~L2 (12, 21)(SOM text S1.2). Furthermore, the gradient am-plitude, C0, also increases, because of the de-creasing degradation rate and the widening of theDpp source (w) (Fig. 2F) (SOM text S1.1). Thus,changes of the Dpp source width and trafficking(degradation rate) result in Dpp gradient expan-sion during growth.

Cells experience an increase in Dpp concen-tration. Gradient expansion implies that cellularDpp concentration changes over time. Two fac-

tors determine the cellular Dpp concentratichanges of the gradient profile (Fig. 1) achanges in cell position, xcell(t), in the growitissue. Proliferation is approximately homoneous in space (22, 23) (figs. S3A and S4A),the relative position of a cell, rcell = xcell(t)/Lremains constant as the tissue grows (fig. S3SOM QP5). Because rcell is constant and relative concentration gradient C(r,t)/C0(t) is

variant (Fig. 2A), the relative cellular concenttion, C(rcell,t)/C0(t), is constant during developmTherefore, the average cellular Dpp concenttion, Ccell(t) = C(rcell,t), increases proportionato the gradient amplitude, C0(t) (fig. S4C).

The Dpp concentration increases, on avage, by 40% during each cell cycle. Does increase in cellular Dpp concentration correlwith changes in the proliferation rate? We dtermined the proliferation rate (fig. S5; SOMQPfrom the area growth rate, g A=A, where Athe time derivative of the area A. This is a goapproximation for the cellular proliferation rbecause the cell density only shows a minor

crease during wing growth (fig. S5, B and DDuring the growth phase, the growth rate decreases (fig. S5D), which reflects an increascell doubling time q (q ln2/g; SOM QPmostly because of a lengthening of the G2 ph(24) (fig. S6).

We found that area growth correlates with increase of the gradient amplitude by a powlaw (Fig. 2G)

C0(t) ~ A(t)b

where b = 0.59 (n = two data sets; table S3). Taverage cellular Dpp concentration, Ccell, is p

portional to the amplitude C0 (see above) and thefore, Ccell(t) ~ A(t)b. Derivation of this express

with respect to time reveals a correlation of average growth rate (g A=A) with average teporal changes in the Dpp level (Ccell) perceivby cells: Ccell=Ccell C0=C0 bA=A Because the area growth rate and the cellu proliferation rate gcell are approximately eq(see above), it follows that

gcell 1

b

Ccell

Ccell

i.e., the proliferation rate is proportional to rative temporal changes of Dpp.

To estimatethe relative increase of the celluDpp concentration a = DCcell/Ccell during cell cycle time q, we combine Eq. 2 with the aproximations Ccell=Ccell DCcell=q=Ccell aq ln 2/gcell, and obtain the following:

a DCcell

Ccell b ln2

Thus, we find a constanta = 0.41 (n = two dsets; table S3); throughout development, cell vision correlates with an increase of Dpp cocentration by 40%.

RESEARCHARTICLES

1Departments of Biochemistry and Molecular Biology, Facultyof Sciences,GenevaUniversity, 30 QuaiErnest-Ansermet,1211Geneva, Switzerland. 2Max Planck Institute for the Physics ofComplex Systems,Nthnitzer Strasse 38,01187 Dresden, Germany.

*These authors contributed equally to this work.Present address: Developmental Neurobiology, National In-stitute for Medical Research, Medical Research Council, TheRidgeway, Mill Hill, London NW71AA, UK.To whom correspondence should be addressed. E-mail:[email protected] (F.J.), [email protected] (M.G.-G.)

4 MARCH 2011 VOL 331 SCIENCE www.sciencemag.org54
http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/


3/7

Dpp signaling activity parallels Dpp concen-tration. Proliferation depends on Dpp signalingactivity, rather than ligandconcentration(3, 2527).We therefore measured Dpp pathway activity atdifferent levels [reviewed in (28)]: phosphorylatedMad (P-Mad) (29), P-Mad/Medeacomplex forma-tion, and brkand dadtranscription [Fig. 3A andfig. S7; SOM experimental procedures (EP) 1](30, 31). Of these, we systematically analyzed nu-clear redfluorescent protein expressedunder control

of thedadenhancer(dad-nRFP) as a transcriptionalreadout reflecting cellular signaling activity, Scell.

With time-lapse analysis, we confirmed thatDpp signaling increases in living wing discs (Fig.3B and movie S1). Consistent with Eq. 2, relativechanges in signaling, S=S, are larger at earlytimes of development, when growth is faster.Quantification of dad-nRFP profiles, S(r,t) (Fig.3C), in fixed discs showed that (i) the signalinggradient scales (Fig. 3D), i.e., the scaling ratiols/L is constant (Fig. 3E); and (ii) the amplitude

S0 increases with A as a power law (Eq. 1),with bs = 0.69 T 0.02 (SEM) (n = four data sets;table S3), corresponding to as = 48% T 2% (Fig.3F). Invariance (scaling) of the relative signalingprofile, S(r,t)/S0(t) (Fig. 3D), implies that thecellular signaling level is proportional to theamplitude (Scell ~ S0). The power-law relationbetween amplitude S0 and area A (Fig. 3F) in-dicates that the proliferation rate correlates withthe average relative temporal increase of Dpp

signal, S

cell=Scell S

0=S0 (as in Eq. 2):

gcell ln2

as

Scell

Scell4

Here, as = 48% implies that the cellular Dppsignaling level Scell increases by about 50% dur-ing each cell cycle. On the basis of Eq. 4, wepropose a model of growth control where the cellcycle length is determined by how fast an in-crease of cellular Dpp signal by 50% is achieved.

In different growth regimes, as 50%. Dsource and transport parameters contribute to amplitude S0 (SOM text S1.1) and thereforecellular signaling levels Scell. To test how rate of increase of the gradient amplitude affegrowth, we analyzed three conditions with changDpp source and/or transport parameters (SOEP2): (i) haltere discs, where we found that Dproduction, diffusion, and degradation are sma(32, 33) (Fig. 2, C to F; SOM QP3.2); (ii) wi

discs with a Dpp source of haltere histoty(dpp>Ubx) (32, 33); and (iii) wing discs witconstant one-cell-wide source [limiting Hh snaling range to one cell with membrane-tetheHh (Hh-CD2)] (34).

In these tissues, the decay time of the growrate, the growth period, and final size differ frthat of the wild-type wing disc (table S2 and fS8). However, growth and Dpp signaling still related by the same features: (i) Gradients scwith tissue size. The scaling ratio l/L is consta

Fig. 1. Dpp gradient parameters.(A) dpp-Gal4/UAS-GFP-Dpp wing

(Wi), leg (Le), and haltere (Ha) discsat different developmental times;w, source width, L, target width. (B)Images of GFP-Dpp gradients, cor-responding to boxed areas in (A).(C) Quantification of GFP-Dpp con-centration as a function of the dis-tance to the source (x). (D and E)(D) Amplitude, C0 and (E) decaylength, l, over time. At the end ofthegrowth phase, in prepupal discs(t> 140 hours), C0 again decreases.Error bars correspond to standarderrors(SEM) of averages from binneddata, and one data set per graph is

shown. For fit functions, parame-ters, number of data sets, and num-ber of discs per data set, see tablesS1 to S3 and SOM QP1. For ex-tended versions of figure legends,see SOM.

AB C

D E

Fig. 2. The Dpp gradi-ent and growth. (A) Rel-ative Dpp concentrationprofiles C(r, t)/C0 from 48hours to 130hours (span-

ning the whole growthperiod) with density plot(below). Note the datacollapse of gradient pro-files onto a single curve.(B) Decaylength,l, versuscompartment width, L.(C to F) (C) Dpp produc-tion rate, n; (D) diffu-sion coefficient, D; and(E) degradation rate, k,versus posterior compartment area, A; and (F) Dpp source width, w, versus posterior compartment width, L, of wing (black) and haltere (blue) discs during growestimated by FRAP (red rectangles, wing) and a reporter assay (circles) (SOM QP3). (G) Gradient amplitude, C0, versus posterior compartment area, A.

2

A B

E F G

C D

www.sciencemag.org SCIENCE VOL 331 4 MARCH 2011

RESEARCH ART
http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/


4/7

but different, in the different conditions (Fig. 4Aand fig. S9), the relation between decay lengthand area is the same in all conditions except Hh-CD2 (Fig. 4C; SOM text S1.2). This points to a possible role of Hh for scaling. (ii) g andScell=Scell are proportional during growth (Fig.4B). And (iii), as is similar under all these con-ditions (Fig. 4D; mean ofas = 49% T 2%). Thus,cells divide when Dpp signaling levels have in-

creased by about 50%, regardless of histotype(haltere versus wing), Dpp transport dynamics, orHh signaling in the source.

A scaling mutant shows inhomogeneousgrowth while as 50%. In all conditions dis-cussed, the gradient scales, and proliferation isspatially uniform. In contrast, proliferation is nothomogeneous when Dpp is ubiquitously expressed with the C765-Gal4 driver (C765>Dpp):Lateral positions have a larger growth rate (27).We quantified Dpp signaling and growth param-eters in C765>Dpp to determine whetherScell=Scell is related to the local inhomogeneousgrowth rates in a manner consistent with Eq. 4.

In C765>Dpp discs, the spatial signalingprofiles S(r,t) increase over time, but do not scale(Fig. 5, A and B). We quantified the inhomoge-neities of the growth rate, g(r,t), using spatialprofiles of phosphorylated histone H3 (PH3)positive mitotic cells (Fig. 5C andfig. S3B; SOMQP4 and QP5). From g(r,t) and S(r,t), we thenestimated gcell, Scell=Scell, and as for cells at dif-ferent positions, rcell(t) (Fig. 5; SOM QP6). Wenoted that cells divide as they do in wild typewhen Dpp signaling levels have increased byabout 50%, independent of time and cell position(Fig. 5D). Lack of scaling causes position

dependence of Scell=Scell (SOM text S1.3), andthus, higher lateral growth rates are explained bythe fact that the relative increase as is reachedfaster (i.e., Scell=Scell is larger) in lateral positions.

Exogenous manipulation of Scell=Scell re-sults in predictable growth rates. To furthertest whether cells divide when Dpp signaling

levels increase by 50%, we used an establishmethod to conditionally express the consttively active Dpp receptor, TkvQD, in cell clon(5) (Fig. 6). Here, TkvQD transcription is induexogenously, only after adding the progesteroanalog drugmifepristone (RU486) (5) (SOM EPIn our model, exogenous manipulation ofScell=S

Fig. 3. Dpp signaling gradients. (A)Dpp pathway. (B) Average dad-nRFPintensity over time for time-lapse se-ries at 72 and 96 hours of devel-opment (SOM QP6). Below, framesfrom a time-lapse series. (C) dad-nRFPimages with quantification (60-hourand72-hour imagesarecontrasted). (D)Relative signaling profiles,S(r, t)/S0(t),spanning the whole growth period,

with density plot. Profiles collapse on-to a single curve. (E and F) (E) Decaylength, l, versus L and (F) amplitude,S0, versus A.

2

A

D

E F

B C

dad-nRFP 0 h 0.5 h 1 h

Fig. 4. Dpp signaling and growthin different growthconditions. (A and B) (A) dad-nRFP decay lengthversus L and (B) amplitude, S0, versus A for wing and haltere discs (n = four data sets; table S3); haltewing chimera (dpp>Ubx; n = 2); and the one-cell-wide source experiments (Hh-CD2; n = 2). (C and(C) Scaling ratio l/A and (D) coefficient aS.

A

B

C D


RESEARCH ARTICLES
http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/


5/7

in clones should result in clonal growth raquantitatively predicted by Eq. 4.

For an RU486 concentration of 20 mg/mGal4 activity (and, therefore, TkvQD expressiincreases 3.6 times as fast as at 0.2 mg/ml; i.e.these two experiments, Scell is different (Fig. 6The relative increase in signaling levels in clonScell=Scell, therefore, depends on RU486 conctration, as well as on the initial endogenous snaling level: Although exogenously impo

S

cell is the same in medial and lateral regionsthe disc (Fig. 6D), clones in lateral positioexperience a bigger relative increase in signaliupon TkvQD induction because their initial snaling level is lower, i.e., Scell=Scell is dependon clone position (fig. S10). If growth is causacontrolled by Scell=Scell, then RU486 concenttion, clone position, and duration of drug posure should determine the clone area, wheras should be independent of these parameters

The growth rate of clones indeed correlawith the exogenously imposed Scell=Scell; i.e., relative increases in clone area and in signallevel are correlated by a power law (Fig. 6

and E; SOM QP7). The data are remarkaconsistentwithas 50%,independently of RU4concentration, duration of exposure (Fig. 6and C), and clone position (Fig. 6, D and EThus, local exogenous changes of Scell=Scellcally result in proliferationrates predictedby Eq

Simulation of growth control. To further twhether Eq.4 describes a plausiblegrowth meanism, we developed a two-dimensional physdescription of proliferation control [Fig. 7 amovies S2 to S5; SOM simulation (SI)]. implemented Dpp and Hh production, diffusiand degradation in a discrete vertex model thdescribes cells as polygons and accounts for

mechanical properties of the tissue (35). Dsource cells are selected in response to Hh; Dproduction and diffusion are kept constant; athe Dpp degradation rate is dynamically altein response to cell division events, such that average degradation rate in the tissue becominversely proportional to the cell number (cosistent with Fig. 2, C to F). A cell divides whthe relative increase of the local Dpp level reaca threshold a.

Simulations of this model using paramevalues estimated experimentally for wing ahaltere discs result in growth dynamics tquantitatively match the experimental obsertions for wing and haltere discs (Fig. 7, D toand movie S3), although only the initial cell nuber, minimal cell cycle length, and Dpp diffusand degradation are different in the haltere. Fthermore, simulations of our model can accoufor the growth properties of TkvQD clones: Cosistent with previous experimental results (3,simulated lateral TkvQD clones have a biggrowth rate and grow to a larger size than medTkvQD clones (about 4-fold and 2.5-fold as laras simulated wild-type clones, respectively) (F7, G to I), and cells surrounding TkvQD clonoverproliferate (Fig. 7G; SOM text S2). The

2

A C

DB

Fig. 5. Dpp signaling and growth inC765>Dpp. (A) dad-nRFP profiles,S(r,t); blacklines trace three cells during developmentstarting out at three initial relative positions(rcell = 0.1, 0.5, 0.9). (B) Relative signalingprofiles, spanning the whole growth period,

with density plot. Profiles do not collapse onto a single curve. (C) Spatiotemporal growth profile, g(r,t);white arrow traces cell starting out at rcell = 0.5. (D) Growth (g) versus Scell=Scell of cells starting out atdifferent relative positions (rcell = 0.1, , 0.9; different colors).

Fig. 6. TkvQD clones(SOM EP2/QP7). (A) (Left)TkvQD clones marked byGFP;(right) dad-nRFP; rel-

ative position rc, area Acand average signaling lev-el Sc of clones were mea-sured in discs at differenttimes after TkvQD induction[hours after addition ofdrug (h AAD)]. Genotype: y w hsFlp/UAS-p35; dad-nRFP/UAS-GFP; act>y>Gal4:PR/UAS-TkvQD. (B and D)Average GFP intensity, re-flectingTkvQD and p35 ex-pression levelfor(B)differentdrugconcentrations and (D)medial versus lateral clones.

(C and E) Relative increasein clone area with respectto the initial area, Ac/Ai,versus relative increase inDpp signaling levels, Sc/Si(rc). For determination ofAi and Si, see SOM QP7.Symbols in (C) and (E) in-dicate data points at dif-ferent times AAD. Grayline (our model): For everysignaling increase by aS = 50%, clone area is expected to double, i.e., the cell generation numberincreases by 1.

A

B

C E

D

www.sciencemag.org SCIENCE VOL 331 4 MARCH 2011

RESEARCH ART
http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/


6/7

results indicate that growth control by means ofrelative changes in Dpp levels could underliegrowth control during imaginal disc development.

Conclusion. We have shown here that, in thewild type, Dpp concentration and signaling gra-dients scale and that, on average, cells dividewhen Dpp signaling levels have increased byas 50%. A growth mechanism based on rel-ative changes in signaling levels can quantita-tively account for growth dynamics of wing and

haltere discs, for inhomogeneous growth ob-served in scaling mutants, and for growth prop-erties of TkvQD clones. Other growth-controlmechanisms we consideredfor example, mech-

anisms based on spatial differences in Dppconcentration or signalingare less consistentwith our data (SOM text S1.3.2). However, thegrowth rule proposed here remains to be verifiedon the single-cell level.

Would the growth mechanism proposed herework in the entire wing? In wild-type discs, ourDpp concentration and signaling measurementswere only significantly above background inmedial regions. However, the C765>Dpp and

TkvQD

clone experiments show that the S

cell=Scellmechanism also works laterally. Furthermore, inour simulations of wild-type disc growth, Dppmolecule numbers in lateral regions are low but

sufficient to provide enough precision to contproliferation by a temporal growth rule (SOSI8). The simulations indeed capture the mgrowth properties of the complete wing and htere, which indicates that the growth mechanicould in principle operate globally.

How could cells determine relative increain Dpp signaling? Sensitivity of signaling stems to relative changes of input is typical adaptive sensory systems and plays a role in b

terial and sperm chemotaxis and in olfactory avisual transduction, where determination of rative temporal changes is achieved by combinadaptation with a dynamic response (3640). T

4000

3500

3000

2500

2000

1500

1000

500

0

A B C

D E F

G H I

Fig. 7. Simulations of morphogen spreading and growth control(SOM SI). (A to C) Representative sample of simulation results. (A)Simulated Dpp distribution; color intensity code: number of Dppmolecules. (B) Cell cycle state [red, M (M phase); blue, I (constantphase in interphase); black, C(checkpoint phase)]. (C) Cell generationnumber(color-coded). (D to F) Averaged simulation results (red and blue, n = 2 5) withexperimental data (black and gray). (D) Posterior compartment area overtime. (E) Decay length versus posterior compartment width. (F) Gradientamplitude versus posterior compartment area. (G to I) Numerical simulationsof wild-type and TkvQD clones located close to and far from the source

(medial and lateral, respectively). (G) Lateral clone expressing Tkv(black outline; dashed line, AP boundary) with cell generation number (colcoded); note nonautonomous effects on proliferation around the clo(arrowheads). (H) Average growth rates of simulated medial and lateral Tkv(red) and control (black) clones (n=25); vertical dashed line: inductionTkvQD production; I, average simulated clone size at t= 120 hours.


RESEARCH ARTICLES
http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/


7/7

Dpp pathway is a dynamic network and maygenerate adaptive responses by combining feed-forward and feedback elements in its structure.Consistent with this idea, in brkXA mutants, wherethe Dpp network is perturbed, as has a differentvalue (fig. S11) [This mutant is discussed indetail in SOM text S2.4].

Our observations raise the question of whatmolecular mechanisms underlie (i) cell cyclecontrol via relative temporal changes of Dpp

signaling, (ii) gradient scaling via decrease ofDpp degradation, and (iii) final size determina-tion. Although pupariation time and final sizewere different in the different conditions studied,the average cell cycle length at pupariation wasabout 30 hours for all (table S2; SOM textS1.3.4), which suggested that cells could stopdividing when their cell cycle is prolongedbeyond a threshold. Response to this thresholdcould be deregulated in some tumor mutants.

References and Notes1. J. Capdevila, I. Guerrero, EMBO J. 13, 4459 (1994).

2. T. Lecuit et al., Nature 381, 387 (1996).

3. C. Martn-Castellanos, B. A. Edgar, Development 129,

1003 (2002).4. D. Nellen, R. Burke, G. Struhl, K. Basler, Cell 85,

357 (1996).

5. D. Rogulja, K. D. Irvine, Cell 123, 449 (2005).

6. F. A. Spencer, F. M. Hoffmann, W. M. Gelbart, Cell 28,

451 (1982).

7. M.Zecca, K.Basler,G. Struhl, Development121, 2265 (1995).

8. S. J. Day, P. A. Lawrence, Development 127, 2977 (2000).

9. T. Aegerter-Wilmsen, C. M. Aegerter, E. Hafen, K. Basler,

Mech. Dev. 124, 318 (2007).

10. L. Hufnagel, A. A. Teleman, H. Rouault, S. M. Cohen,

B. I. Shraiman, Proc. Natl. Acad. Sci. U.S.A. 104,

3835 (2007).

11. E. V. Entchev, A. Schwabedissen, M. Gonzlez-Gaitn,

Cell 103, 981 (2000).

12. A. Kicheva et al., Science 315, 521 (2007).

13. Materials and methods [experimental procedures (EPs),

quantitative procedures (QPs), and simulations (SIs)]

along with supporting text (including extended figures

legends for text figures), tables, figures, and movies are

available as supporting material on Science Online.

14. D. Ben-Zvi, B. Z. Shilo, A. Fainsod, N. Barkai, Nature

453, 1205 (2008).

15. T. Gregor, W. Bialek, R. R. de Ruyter van Steveninck,

D. W. Tank, E. F. Wieschaus, Proc. Natl. Acad. Sci. U.S.A.

102, 18403 (2005).

16. H. Spemann, H. Mangold, Roux Arch. Entw. Mech. 100,

599 (1924).

17. A. A. Teleman, S. M. Cohen, Cell 103, 971 (2000).

18. N. Barkai, D. Ben-Zvi, FEBS J. 276, 1196 (2009).

19. D. Ben-Zvi, N. Barkai, Proc. Natl. Acad. Sci. U.S.A. 107,

6924 (2010).

20. O. Wartlick, A. Kicheva, M. Gonzalez-Gaitan, Cold Spring

Harbor Perspect. Biol. 1, a001255 (2009).

21. H. G. Othmer, E. Pate, Proc. Natl. Acad. Sci. U.S.A. 77,

4180 (1980).

22. A. Garcia-Bellido, J. R. Merriam, Dev. Biol. 24, 61

(1971).

23. M. Gonzlez-Gaitn, M. P. Capdevila, A. Garca-Bellido,

Mech. Dev. 46, 183 (1994).

24. M. J. Fain, B. Stevens, Dev. Biol. 92, 247 (1982).

25. R. Burke, K. Basler, Development 122, 2261 (1996).

26. E. Moreno, K. Basler, G. Morata, Nature 416, 755

(2002).27. G. Schwank, S. Restrepo, K. Basler, Development

135, 4003 (2008).

28. M. Affolter, K. Basler, Nat. Rev. Genet. 8, 663 (2007).

29. H. Tanimoto, S. Itoh, P. ten Dijke, T. Tabata, Mol. Cell

5, 59 (2000).

30. A. Weiss et al., Nat. Struct. Mol. Biol. 17, 69 (2010).

31. L. C. Yao et al., Development 135, 2183 (2008).

32. M. A. Crickmore, R. S. Mann, Science 313, 63 (2006).

33. L. F. de Navas, D. L. Garaulet, E. Snchez-Herrero,

Development 133, 4495 (2006).

34. M. Strigini, S. M. Cohen, Development124, 4697

(1997).

35. R. Farhadifar, J. C. Rper, B. Aigouy, S. Eaton, F. Jlic

Curr. Biol. 17, 2095 (2007).

36. U. Alon, M. G. Surette, N. Barkai, S. Leibler, Nature 3168 (1999).

37. C. I. Bargmann, WormBook (25 October), 1 (2006).

38. N. Barkai, S. Leibler, Nature 387, 913 (1997).

39. B. M. Friedrich, F. Jlicher, Proc. Natl. Acad. Sci. U.S

104, 13256 (2007).

40. L. Zheng et al., PLoS ONE 4, e4307 (2009).

41. We thank E. Snchez-Herrero, S. Cohen, G. Campbe

and K. Irvine for reagents, and M. Milinkovitch,

A. Martnez-Arias, T. Ferraro, and F. Naef for discussi

A.K. developed and performed the FRAP and P-Mad

assays. O.W. generated all other experimental data a

had a leading role to develop the quantitative method

analyze it. P.M. had a leading role to develop the

theoretical description of growth control, and he

performed computer simulations. P.M. and T.B.

developed a continuum theory of the Dpp gradient

during growth and studied possible growth rules.

C.S. generated reagents. O.W., P.M., A.K., T.B.,

F.J., and M.G.-G. developed the whole project

synergistically and equally and wrote the paper

together. P.M., T.B., and F.J. were supported by the

Max-Planck-Gesellschaft. O.W., A.K., C.S., and M.G.-G

were supported by Geneva University and by Europea

Research Council advanced investigator grant (SARA)

SystemsX (LipidX), Swiss National Science Foundation

(SNF), National Centre of Competence in Research

(NCCR) chemical biology and Frontiers in Genetics an

R'equip grants.

Supporting Online Materialwww.sciencemag.org/cgi/content/full/331/6021/1154/DC1

Materials and Methods

SOM Text

Figs. S1 to S53

Tables S1 to S5

References

Movies S1 to S5

5 November 2010; accepted 6 January 2011

10.1126/science.1200037

Crystal Structure of the DyneinMotor DomainAndrew P. Carter,1,2* Carol Cho,1* Lan Jin,1 Ronald D. Vale1

Dyneins are microtubule-based motor proteins that power ciliary beating, transport intracellularcargos, and help to construct the mitotic spindle. Evolved from ring-shaped hexameric AAA-familyadenosine triphosphatases (ATPases), dyneins large size and complexity have posed challengesfor understanding its structure and mechanism. Here, we present a 6 angstrom crystal structureof a functional dimer of two ~300-kilodalton motor domains of yeast cytoplasmic dynein. Thestructure reveals an unusual asymmetric arrangement of ATPase domains in the ring-shaped motordomain, the manner in which the mechanical element interacts with the ATPase ring, and anunexpected interaction between two coiled coils that create a base for the microtubule binding

domain. The arrangement of these elements provides clues as to how adenosine triphosphatedrivenconformational changes might be transmitted across the motor domain.

The cytoskeletal motor proteins consist ofthe myosin family, which moves along ac-tin filaments, and the kinesin and dynein

families, which move along microtubules. Thesemotors use a common principle to generate move-ment in which they bind to their track, undergoa force-producing conformational change, re-lease from the track, and then return to their orig-inal conformation. These structural changes are

coupled to chemical transitions in the motorsadenosine triphosphatase (ATPase) cycle [adeno-sine triphosphate (ATP) binding, hydrolysis, andproduct release].

The force-generating cycles of kinesins andmyosins are understood in considerable mechanis-tic detail. Even though they interact with differ-ent cytoskeletal polymers, kinesins and myosinsshare a protein fold, reflecting their common evo-

lutionary origin (1). Dyneins, by contrast,

unrelated to kinesins/myosins and instead haevolved from the AAA family of ATPases (The AAA ATPases (ATPases associated wdiverse cellular activities), which are present both prokaryotes and eukaryotes, participatediverse functions, including protein unfoldfor proteolysis, disassembly of stable protcomplexes, and helicase activities (3). The mjority of AAA ATPases self-assemble into hemeric rings that carry out the functional activitof these enzymes (4, 5). Dynein is one of twAAA ATPases that has six distinct AAA mains concatenated within a single polypeptchain [the other being Rea1, an ATPase involvin ribosome biogenesis (6)]. Electron microsco(EM) studies of dynein have shown that theAAA domains fold into a ring-shaped structsimilar to other AAA ATPases (79).

1Department of Cellular and Molecular PharmacoloHoward Hughes Medical Institute, University of CaliforniaFrancisco, 600 16th Street, San Francisco, CA 94158, U2Medical Research Council Laboratory of Molecular BioloHills Road, Cambridge, CB2 0QH, UK.

*These authors contributed equally to this work.To whom correspondence should be addressed. [email protected] (A.P.C.); [email protected].(R.D.V.)

i SCIENCE VOL 331 4 MARCH 2011

RESEARCH ART
http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/http://www.sciencemag.org/

dynamics of dpp signaling and proliferation control

Documents