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Supplementary Information accompanies the paper on Nature’s website (http://www.nature.com).

Acknowledgements We thank H.-S. V. Chen for discussions and T. Ciabarra and M. Forcina for preliminary work. Monoclonal antibody K35/40 was made in collaboration with J. S. Trimmer and N. J. Sucher. NR1 and NR2A cDNAs were gifts of S. F. Heinemann and S. Nakanishi, respectively. This work was supported in part by grants from the National Institutes of Health. S.A.L. and D.Z. are co-senior authors.

Competing interests statement The authors declare competing financial interests: details accompany the paper on Nature’s website (http://www.nature.com).

Correspondence and requests for materials should be addressed to S.A.L. (e-mail: [email protected]) or D.Z. (e-mail: [email protected]). The rat NR3B sequence has been deposited in GenBank under accession number AF440691.

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Establishment of developmental precision and proportions in the early Drosophila embryo Bahram Houchmandzadeh*†, Eric Wieschaus* & Stanislas Leibler*‡§ * Howard Hughes Medical Institute, Department of Molecular Biology, Princeton University, Princeton, New Jersey 08544, USA † CNRS, Laboratoire de Spectrometrie Physique, BP87, 38402, St-Martin D’Heres Cedex, France ‡ Department of Physics, Princeton University, Princeton, New Jersey 08544, USA

a good example of an error-prone process. The morphogen gradient model1 is the most widely accepted model describing how cells in early embryos acquire their positional information: because the concentration of a morphogen decreases with the distance from one pole, measuring this concentration informs a cell of its position inside the embryo. In Drosophila embryos, the maternal gene bcd possesses many properties of a prototypical morphogen2 – 4. In such models, downstream genes, such as hb, are activated by a ‘threshold’ mechanism: only cells that measure concentrations of Bcd above a certain level switch on the hb gene. It is hard to imagine how precision could be achieved in this simple threshold model. To produce exactly the same concentration profile of Bcd in each embryo, the mother would have to control the exact amount of messenger RNA deposited in each embryo, its localization, and the amount of protease responsible for the morphogen degradation. Any error in these parameters modifies the morphogen gradient and induces error in the positional information delivered to downstream genes5. Even if these parameters were precisely controlled, the gradient profile would still be sensitive to environmental conditions such as temperature. Another limitation of a simple gradient is conservation of proportions: an exponential gradient has its own length scale l (depending on the diffusion coefficient D and the protein degradation rate q, l2 = D/q), which is independent of the length of the embryo. We address here both the issue of the error in the positional information of the Bcd gradient and the establishment of the spatial proportions in the embryo. To quantify the precision of gene expression, we measured protein profiles at cycle 14 by immunofluorescence staining (Fig. 1, see Methods). The Bcd protein profiles in about 100 wild-type embryos during early cycle 14 (before significant membrane invagination) are shown in Fig. 2a. The profile displays a high embryo-to-embryo variability. To quantify this variability, we measured the position (xBcd) along the embryo at which each curve crosses a certain threshold (t), chosen here as 0.23 of the maximal intensity (see Methods). These positions are spread over 30% of the embryonic length (EL) (Fig. 2b), and have a standard deviation (jBcd) of 0.07 EL. This means that the positional error of the Bicoid gradient is greater than five nuclei in 50% of embryos. Another way to quantify the variability, which is not sensitive to the normalization of the Bcd protein profile, is to measure the slope of the exponential decay of each curve, l (Fig. 2c). The standard deviation of l is 0.045 EL, which corresponds to the

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§ Present address: Laboratory of Living Matter, Rockefeller University, 1230 York Avenue, Box 34, New York, New York 10021, USA

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I(x)

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During embryonic development, orderly patterns of gene expression eventually assign each cell in the embryo its particular fate. For the anteroposterior axis of the Drosophila embryo, the first step in this process depends on a spatial gradient of the maternal morphogen Bicoid (Bcd). Positional information of this gradient is transmitted to downstream gap genes, each occupying a well defined spatial domain1 – 4. We determined the precision of the initial process by comparing expression domains in different embryos. Here we show that the Bcd gradient displays a high embryo-to-embryo variability, but that this noise in the positional information is strongly decreased (‘filtered’) at the level of hunchback (hb) gene expression. In contrast to the Bcd gradient, the hb expression pattern already includes the information about the scale of the embryo. We show that genes known to interact directly with Hb are not responsible for its spatial precision, but that the maternal gene staufen may be crucial. Development is a precise process. All biochemical phenomena are prone to variation; at each level, correcting mechanisms should exist to avoid the transmission of errors and their amplification to downstream genes. The establishment of a morphogen gradient is

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26. Soloviev, M. M. & Barnard, E. A. Xenopus oocytes express a unitary glutamate receptor endogenously. J. Mol. Biol. 273, 14 –18 (1997). 27. Ishimaru, H. et al. A unitary non-NMDA receptor short subunit from Xenopus: DNA cloning and expression. Receptors Channels 4, 31 –49 (1996). 28. von Euler, M., Li-Li, M., Whittemore, S., Seiger, A. & Sundstro¨m, E. No protective effect of the NMDA antagonist memantine in experimental spinal cord injuries. J. Neurotrauma 14, 53–61 (1997). 29. Palecˇek, J., Abdrachmanova, G., Vlachova´, V. & Vyklicky´, L. Jr Properties of NMDA receptors in rat spinal cord motoneurons. Eur. J. Neurosci. 11, 827–836 (1999). 30. Souverbie, F., Mo, L.-L., Liu, Y., von Euler, G. & Sundstro¨m, E. Pharmacological characterization of [3H]MK-801 binding in the rat spinal cord. Eur. J. Pharmacol. 307, 347–353 (1996).

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Figure 1 Typical image of Bcd staining, and the profile of the extracted curve. For Bcd, profiles are fitted well by an exponential decay. Right axis, intensity in a linear scale; left axis, background-subtracted intensity in log scale. The size of the area used to compute the intensity is exaggerated (see Methods).

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NATURE | VOL 415 | 14 FEBRUARY 2002 | www.nature.com

letters to nature same variability we measured for xBcd (jBcd = jlln(1/t)). In contrast to Bcd, the Hb protein profile displays an extreme reproducibility from embryo to embryo. The Hb profile in about 100 embryos from early to late cycle 14 is shown in Fig. 2d. We quantified the hb distribution using the point (xHb) at which each profile crosses the 0.5 threshold (Fig. 2b). The standard deviation of xHb (jHb) is 0.01 EL, meaning that two-thirds of embryos have Hb boundaries defined more precisely than the size of one nucleus. The information about the embryo scale is also revealed at hb expression level. As discussed above, the Bicoid exponential profile should not be affected by embryo length. When xBcd is plotted against EL (Fig. 2e), the correlation coefficient is indeed negligible (P = 0.40). A similar lack of correlation is observed between the values of l and EL. In contrast to Bcd, however, the position of the Hb boundary displays a strong correlation with the embryo length (Fig. 2f). The linear (r) and Spearman’s rank (rs) correlation coefficients between xHb and EL are 0.84 and 0.82, respectively (P , 10-20; all P-values are computed for rs). hb mRNA displays the same precision and conservation of proportions as Hb protein. The spatial position of the hb mRNA boundary in early cycle 14 embryos has a standard deviation of 0.01 EL, and displays a high correlation with the egg length (rs = 0.88, P , 10-8). The precision of the Hb boundary compared with the variability of the Bcd gradient could seem at odds with experiments where Bcd dosage has been modified. However, when the Hb boundary position as a function of Bcd dosage is compared with the expected value from a simple threshold model (Table 1), the measured shift is significantly smaller than that expected, even when the reduced efficiency we measure for the bcd transgenes is taken into consid-

Figure 2 Positional information of Bcd and Hb gradients. a, Bcd gradient in about 100 embryos. b, Distribution of positions at which each gradient crosses a given threshold: 0.23 for Bcd, 0.5 for Hb. c, Distribution of slope of exponential decay for each Bcd profile. NATURE | VOL 415 | 14 FEBRUARY 2002 | www.nature.com

Table 1 Hb boundaries in different bcd backgrounds Background

Measured Expected if efficiency is 50% Expected if efficiency is 100%

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xHb (bcd 1 £ ) xHb (bcd wild type) xHb (bcd 4 £ ) xHb (bcd 6 £ )

0.41 0.49 0.56 0.59

NA NA 0.60 0.68

0.30 NA 0.68 0.79

............................................................................................................................................................................. The measured and expected values for the position of the Hb boundary are shown for different bcd dosages. The expected shift of Hb boundary is lln(n/n0), where n is the number of copies of bcd compared with the wild type (n0 = 2). The jHb is 1% for the wild-type embryos and bcd 1 £ , 1.5% for bcd 4 £ , and 2% for bcd 6 £ . The statistical significance of the differences between the expected and measured xHb, P , 10-16. For 4 £ and 6 £ , flies carrying two copies of a bcd transgene on chromosome X were used. Heterozygous mothers have four copies of bcd (bcd 4 £ ) and homozygous ones possess six copies (bcd 6 £ ). For 1 £ , mothers heterozygous for bcdE1 were used. bcd wild-type flies are 2 £ . NA, not applicable.

eration. The shift cannot be explained quantitatively if hb were activated only by Bicoid. In mid-embryo, the Hb concentration decreases from the highest to the lowest value across about 0.1 EL. The corresponding change in Bcd concentration in this region is only 30% (corresponding to 1 - exp(-0.1/0.27)). If Bcd were the only source of cooperative activation of hb, this small change in the Bcd concentration would necessitate a Hill coefficient of more than 10. Such strong cooperative activation would be very sensitive to temperature variations6. To measure the temperature sensitivity of the Hb profile, we collected embryos for 1 h at 25 8C, and then allowed them to reach cycle 14 at different temperature (9 –29 8C). The developmental time varies strongly as a function of temperature, and ranges from 2 h at 25 8C to 20 h at 9 8C. The induced changes in the Bcd and Hb profiles are shown in Fig. 3c and d. The Bcd profile is sensitive to temperature: this could be expected from a simple diffusing

d, Hb gradient in about 100 embryos. e, f, Position at which each gradient crosses the given threshold versus embryo length (EL) for Bcd (e) and Hb (f).


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Figure 3 Influence of temperature variation on Bcd and Hb gradients. a, Average profiles of Bcd gradients at different temperatures (9–29 8C). b, The corresponding average profiles of Hb gradients. c– f, Detail of individual Hb profiles at each temperature.

Coordinates of the frame correspond to the rectangle shown in b. c, 9 8C, j = 0.016; d, 18 8C, j = 0.013; e, 25 8C, j = 0.01; f, 29 8C, j = 0.011. The average profiles are computed from 18–32 curves.

morphogen model, in which the protease rate, and thus l, should strongly depend on temperature. However, no change in the position and variability of Hb was observed. Thus, variations due to temperature changes are also compensated at the level of hb expression. To determine when Hb precision arises, we measured gene expression patterns of bcd and hb in the early embryo from cycle 12 to 14. No significant change was observed in the Bcd pattern during this period: its variability remained extremely high (jBcd = 0.07 EL) and its amplitude remained constant throughout early cycle 14. The first trace of zygotic Hb protein was detected at cycle 13, where the amplitude of the signal increased by a factor of 1.5 above that achieved in unfertilized eggs or in embryos at cycle 11 or 12. At cycle 14, the relative amplitude (compared with cycle 12) of the signal is 3.7 (see Methods for fluorescence quantification). The variability of Hb boundary position (jHb) during cycle 13 is 0.015 EL, only slightly higher than that observed during cycle 14, and clearly lower than that of Bcd at any stage in development. The scaling of the Hb boundary position relative to the egg length also appears at cycle 13: no significant correlation existed between the Hb boundary and the size of the egg at cycle 12 (rs = 0.3, P = 0.1). At cycle 13, rs rose to 0.7 (P = 0.00015), and further increased to 0.8 during cycle 14. All the genes downstream of hb that we have measured (Kr, kni, gt, eve) display the same spatial precision as hb. We have used various Drosophila mutants to identify additional genes involved in the fine regulation of Hb. Our search assumed that the removal of such genes would increase the variability of Hb to reflect the variability of Bcd itself (note that some genes such as gt induce a shift in Hb position, but not in its variability). The best candidate for a maternal posterior gradient is nanos (nos). The removal of nos induces a slight shift in Hb boundary, but the variability at this new position is not significantly changed (Table 2). Moreover, the simultaneous removal of maternal hb and nos cancels this shift. Hence, the induced shift by nos can be attributed to auto-activation of hb7,8. The removal of nos does not abolish the scaling property, and the Hb boundary and EL remain tightly correlated (r = 0.71, rs = 0.64, P , 10-5). Thus nos mutations can modify the average position of the Hb boundary without affecting its precision or scaling. The natural candidate for zygotic control of Hb is Kruppel (Kr). Double staining for these two gene products shows a strong

correlation between the position of their boundaries (r = 0.90, rs = 0.89, P , 10-20), and regulation of Kr by Hb has been previously demonstrated9. Repression of hb expression by Kr has also been reported10. However, Hb boundary position and its low embryo-toembryo variability are not affected in Kr mutants (Table 2). These results hold even if we consider very late cycle 14 embryos in which other members of gap gene class are active. They seem not to be responsible for the precision of the Hb boundary (Table 2). To test the existence of another, unidentified gene contributing to this process, we removed genes corresponding to about 80% of the Drosophila genome by using compound chromosomes, but we observed no effect on the precision of the Hb boundary. The auto-activation of hb by its gene products can be important for the sharpness of the Hb boundary and its average position, but this mechanism alone cannot provide any spatial clue for the precision and scaling. To further investigate this issue, we used embryos homozygous for the hb6N mutation. These embryos make detectable protein, even though phenotypically the alleles behave as null11,12. The boundary of gene expression for these embryos is shifted towards the anterior, reflecting a role for Hb in amplification of its own expression, presumably by the P1 enhancer8. The precision and scaling of the Hb boundary in this background,

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Table 2 Variability of the Hb boundary Mutation

xHb

j

0.49 0.52 0.54 0.47 0.51 0.52 0.50 0.51 0.49 0.48 0.46 0.45 0.43 0.49 0.47 0.50

0.010 0.016 0.016 0.014 0.020 0.025 0.014 0.017 0.011 0.010 0.010 0.011 0.014 0.015 0.014 0.020

n

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Wild type oskar6 nosBN hbmat nosBN exuPJ42 swa1 torsoPM51 spg Kr1 kni(del) gtYA82 hb6N X2R2L3L-

110 40 16 31 21 17 30 9 29 11 16 17 40 19 16 39

............................................................................................................................................................................. The average position of the Hb boundary in different zygotic and maternal backgrounds is shown. Anterior = 0; posterior = 1. n, number of embryos sampled. Compound chromosomes were used to generate embryos deficient for the X chromosome and individual autosomal arms18.



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Figure 4 Hb profiles in staufen background. a– c, Hb profiles for about 100 embryos in stauHL (a), stauD3 (b) and staur9 (c). d, Average profile of Hb gradient in stauHL background, for populations shifted forwards and backwards of the average. e, The

corresponding average Bcd profile for these populations. The average maximum Bcd intensities for these two populations are 1,800 ^ 80 (^j) and 1,750 ^ 100.

however, is equal to that of the wild type. Among all the mutations we have studied, the only ones that affect Hb boundary precision are certain alleles of the maternal gene staufen (stau). In embryos from mothers homozygous for either stauHL or staur9, the Hb boundary position shows a variability of 6%, comparable to the observed Bcd variability (Fig. 4a, c). Surprisingly, this variability is largely reduced (to 2%) in another strong allele of stau, D3 (Fig. 4b). Mutations in stau disrupt bcd and osk RNAs and decrease Bcd protein level about twofold. We tested whether the effect of stau on Hb was simply an indirect effect of its variable effect on bicoid. From the pool of embryos in stauHL background that were double stained for Bcd and Hb, we selected two populations: one that displayed an anterior Hb boundary shift, and one that displayed a posterior shift (Fig. 4d). The corresponding average Bcd profiles for these two populations are very similar, both in the Bcd level and in its spatial distribution (Fig. 4e). Thus, the observed variability in the Hb boundary position may reflect an activity of staufen independent of bcd. The disruption of Hb precision in stauHL is transmitted to downstream genes, and is not corrected before gastrulation. For instance, double staining for Hb and Kr (data not shown) shows that the variability of the Kr boundary in the stauHL background is similar to that of the Hb boundary. Moreover, the positions of these two boundaries remain tightly correlated, as in the wild type. By quantitatively analysing the protein profiles of maternal morphogens and zygotic gap genes in numerous wild-type and mutant embryos, we have demonstrated two phenomena that take place in the early Drosophila development. First, at a very early stage, noise associated with the maternal gradient of Bcd is filtered out, and at the same time the genetic network, which includes the Hb

gap gene, establishes spatial proportions (scaling) in the embryo. It is potentially significant that staufen, the one gene affecting the process, makes a product that localizes to both poles of the egg13,14. More work is needed to establish the mechanisms that control the spatial scaling and precision. It would be then interesting to investigate whether similar phenomena are present in other developmental processes in Drosophila and other organisms. A


Methods Immunostaining of embryos Embryos were collected at 25 8C (except when temperature variations were studied), heat fixed and labelled with fluorescent probes following previously published protocols15. All antibodies used were a gift of J. Reinitz and D. Kosman16.

Image analysis High-resolution digital images (1,317 £ 1,015 pixels, 12 bits per pixel) of stained embryos at the same developmental stage and oriented in a lateral projection were taken. Images were focused at mid-embryo to avoid geometric distortion. Intensity profiles were extracted by sliding a rectangle (the size of a nucleus) perpendicular to the embryo along its edges, and computing the average intensity of its pixels, while projecting the coordinates of its centre on the two (anteroposterior and dorsoventral) axes of the embryo. Two curves, corresponding to dorsal and ventral sides of the embryo, were constituted. For consistency, we compared only dorsal profiles. To normalize the intensity profiles, for each curve the minimum and maximum intensity were computed by the average of the 20 lowest- and highest-intensity pixels (corresponding to the size of one nucleus), and the profiles are linearly mapped to a [0,1] interval. The x-axis (when needed) was normalized by the embryo length. At mid-embryo, the concentration of Hb drops from a high value (normalized to 1) to a low one (normalized to 0). We therefore chose the threshold 0.5 to quantify the spatial position of this boundary. The same threshold is used for the quantification of other gap genes studied. To characterize Bcd profiles (which are exponential), we chose the threshold for thisprotein (t ¼ 0:23) such that, on average, xBcd ¼ xHb . The measured variability of


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letters to nature Bcd does not depend on the particular choice of t, and other values (such as 0.5) give the same results.

Competing interests statement The authors declare that they have no competing financial interests.

Profile quantification Fluorescence antibody staining can be used to determine the relative concentration of a protein in a given background compared to the wild type, if a statistical approach is taken: the typical standard deviation for the maximum fluorescence intensity is about 20%. For intensity calibration, we used 20– 30 embryos, so the average maximum intensity displays p a standard error of 4% (0.2/ 25). When a background was compared to wild-type embryos, both mutant and wild-type embryos were stained at the same time and in the same conditions. We used Student’s t-test to decide whether two averages were different. The position at which the Bcd gradient crosses a given threshold is subject to an error in the normalization process, which we could easily estimate. Supposing that the real concentration in normalized coordinates is y real ¼ f ðxÞ, where f varies between 0 and 1, x0 is computed by solving the equation f ðx0 Þ ¼ t, where t is a given threshold. The measured function, using immunofluorescence staining, is y meas ¼ A0 f ðxÞ þ B0 , where B0 is the background due to nonspecific attachment, and A0 depends on the efficiency of probe– target interaction. The normalization procedure transforms ymeas(x) into a normalized function ynorm ðxÞ ¼ ðy meas ðxÞ ÿ BÞ=A. xBcd is computed using ynorm(x). The error in the measurement of xBcd due to error in estimation of A and B is Dx ¼ ð1=df =dxjx¼x0 Þð1 ÿ tÞDB=A0 , where df =dxjx¼x0 is the slope of f(x) at the defining point, and DB is the absolute error in estimating B. The key to reducing the error in the measurement of xBcd is to have a high signal-tobackground ratio (A=B h 8 in our case). Using the above equation, we find DxBcd h 1%. The real variability of xBcd, Dr, is related to the measured one Dm and to error due to normalization Dnorm through ½Delta2r ¼ D2m ÿ D2norm . Hence, given the precision of our procedure, the error of normalization has a negligible effect on the measured variability of bcd gradient. A more robust way of measuring the bcd variability is to use the exponential decay of Bcd concentration. Bcd profiles have a peak at about 35 mm (this peak is variable from embryo to embryo) and display a perfect exponential decay after twice this distance. Raw data of immunofluorescence for Bcd are fitted by I ¼ A expðÿx=lÞ þ B for abscissae beyond twice the peak position. A nonlinear Levenberg – Marquardt fit procedure was used to estimate the parameters. The slope of the exponential, l, for each embryo was then computed from all values of the raw curve, and did not depend on normalization parameters. The confidence limit of l in each fitted curve was determined by the curvature matrix of the x2 function at its minimum17, and is smaller than 1 mm (jl for betweenembryo variability is 20 mm). Received 28 August; accepted 4 December 2001. 1. Wolpert, L. Positional information and the spatial pattern of cellular differentiation. J. Theor. Biol. 25, 1–47 (1969). 2. Driever, W. & Nusslein-Volhard, C. The bicoid protein determines position in the Drosophila embryo in a concentration-dependent manner. Cell 54, 95– 104 (1988). 3. Driever, W. & Nusslein-Volhard, C. A gradient of bicoid protein in Drosophila embryos. Cell 54, 83 –93 (1988). 4. Struhl, G., Struhl, K. & Macdonald, P. M. The gradient morphogen bicoid is a concentrationdependent transcriptional activator. Cell 57, 1259 –1273 (1989). 5. Lacalli, T. C. & Harrison, L. G. From gradient to segments: models for pattern formation in early Drosophila. Semin. Dev. Biol. 2, 107–117 (1991). 6. Segel, I. H. Enzyme Kinetics (Wiley, New York, 1975). 7. Treisman, J. & Desplan, C. The products of the Drosophila gap genes hunchback and Kruppel bind to the hunchback promoters. Nature 341, 335–337 (1989). 8. Wimmer, E. A., Carleton, A., Harjes, P., Turner, T. & Desplan, C. Bicoid-independent formation of thoracic segments in Drosophila. Science 287, 2476–2479 (2000). 9. Struhl, G., Johnston, P. & Lawrence, P. A. Control of Drosophila body pattern by the hunchback morphogen gradient. Cell 69, 237–249 (1992). 10. Jackle, H., Tautz, D., Schuh, R., Seifert, E. & Lehmann, R. Cross regulatory interactions among the gap genes of Drosophila. Nature 324, 668–670 (1986). 11. Simpson-Brose, M., Treisman, J. & Desplan, C. Synergy between the hunchback and bicoid morphogens is required for anterior patterning in Drosophila. Cell 78, 855–865 (1994). 12. Hulskamp, M., Lukowitz, W., Beermann, A., Glaser, G. & Tautz, D. Differential regulation of target genes by different alleles of the segmentation gene hunchback in Drosophila. Genetics 138, 125–134 (1994). 13. St Johnston, D., Beuchle, D. & Nusslein-Volhard, C. Staufen, a gene required to localize maternal RNAs in the Drosophila egg. Cell 66, 51–63 (1991). 14. Ferrandon, D., Elphick, L., Nusslein-Volhard, C. & St Johnston, D. Staufen protein associates with the 3’UTR of bicoid mRNA to form particles that move in a microtubule-dependent manner. Cell 79, 1221– 1232 (1994). 15. Roberts, D. B. (ed.) Drosophila, A Practical Approach (Oxford Univ. Press, Oxford, 1998). 16. Kossman, D., Small, S. & Reinitz, J. Rapid preparation of a panel of polyclonal antibodies to Drosophila segmentation proteins. Dev. Genes Evol. 208, 290– 294 (1998). 17. Press, W. H., Teukolsky, S. A., Vettering, W. T. & Flannery, B. P. Numerical Recipes in C (Cambridge Univ. Press, Cambridge, 1992). 18. Merrill, P., Sweeton, D. & Wieschaus, E. Requirements for autosomal gene activity during precellular stages of Drosophila melanogaster. Development 104, 495–509 (1988).

Acknowledgements Drosophila alleles were a gift from C. Desplan (FRT-hb,nosBN), E. Gavis (stauD3) and Nusslein– Volhard lab stock (staur9). This work has been partially supported by grants from the National Institutes of Health and the Howard Hughes Medical Institute. Discussions with C. Desplan, J. Grosshans, T. Lecuit, J. Reinitz and S. Small are here acknowledged.

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Correspondence and requests for materials should be addressed to E.W. (e-mail: [email protected]).

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Activation-induced cytidine deaminase turns on somatic hypermutation in hybridomas Alberto Martin*, Philip D. Bardwell*, Caroline J. Woo*, Manxia Fan*, Marc J. Shulman† & Matthew D. Scharff* * Department of Cell Biology, Albert Einstein College of Medicine, 1300 Morris Park Avenue Chanin 403, Bronx, New York 10461, USA † Immunology Department, Medical Sciences Building, 1 King’s College Circle, University of Toronto, Toronto, Ontario M5S 1A8, Canada .............................................................................................................................................................................

The production of high-affinity protective antibodies requires somatic hypermutation (SHM) of the antibody variable (V)region genes. SHM is characterized by a high frequency of point mutations that occur only during the centroblast stage of B-cell differentiation. Activation-induced cytidine deaminase (AID), which is expressed specifically in germinal-centre centroblasts1, is required for this process, but its exact role is unknown2. Here we show that AID is required for SHM in the centroblastlike Ramos cells, and that expression of AID is sufficient to induce SHM in hybridoma cells, which represent a later stage of B-cell differentiation that does not normally undergo SHM. In one hybridoma, mutations were exclusively in G·C base pairs that were mostly within RGYW or WRCY motifs, suggesting that AID has primary responsibility for mutations at these nucleotides. The activation of SHM in hybridomas indicates that AID does not require other centroblast-specific cofactors to induce SHM, suggesting either that it functions alone or that the factors it requires are expressed at other stages of B-cell differentiation. Three human B-cell lines (namely Ramos, BL-2 and CL-01) undergo SHM3 – 5, thus opening the possibility of studying this process in vitro. We found previously6 that V-region mutation rates in different Ramos clones were correlated with the level of their AID messenger RNA, suggesting that AID is important in SHM in Ramos cells. Specifically, both the rates of mutation and the mRNA levels of AID for Ramos clones 6 and 7 were higher than those for Ramos clone 1 (Fig. 1a and ref. 6). To determine whether low AID expression was itself responsible for the low mutation rates in Ramos clone 1, this clone was stably transfected with either a vector expressing human AID (hAID) or an empty vector control. Mutation rates of typical transfected clones were then determined by sequencing unselected V regions after 1 or 2 months in culture (Table 1). Clones expressing low levels of AID (that is, clones C.1 and A.1) had very few mutations in the V region, whereas clones that expressed ,25-fold higher levels of AID mRNA (that is, clones A.2 and A.5) had many more V-region mutations (Fig. 1b and Table 1). Table 2 summarizes the mutational features of all the Ramos clones that expressed elevated levels of AID and shows that the rates and characteristics of the mutations in all of these clones were similar: there was a targeting bias of G/C nucleotides, transitions were slightly favoured over transversions, and ,35% of mutations were in G or C nucleotides within RGYW (A/G, G, C/T, A/T) or WRCY hot-spot sequences, motifs that are frequently targeted in SHM both in vivo and in vitro7,8. These results indicate that AID is required for



letters to nature internal solution containing 140 mM KCl, 2 mM MgCl2, 10 mM EGTA, 10 mM HEPES at pH 7.2. The external solution was Leibovitz’s L-15 (Gibco) containing 136 mM NaCl, 5.8 mM NaH2PO4, 5.4 mM KCl, 1.3 mM CaCl2, 0.9 mM MgCl2 at pH 7.2. Osmolarity was adjusted to 300 mosM l21. Motility was measured and calibrated using an electro-optical method in which the cell’s ciliated pole was imaged through a rectangular slit onto a photodiode29.

Acknowledgements We thank K. Cullen for technical assistance; T. Curran, B. Fritzsch, C. A. Shera and D. Freeman for comments on the manuscript; and B. Kachar, T. Hasson and P. Gillespie for antibodies. This work is supported in part by NIH grants to M.C.L., Z.Z.H. and J.Z., NIH Cancer Center Support CORE grant, and the American Lebanese Syrian Associated Charities (ALSAC).

In vivo functional assays For ABR, DPOAE and CM measurements, mice were anaesthetized with xylazine and ketamine. ABRs and DPOAEs were obtained from one set of animals; CMs from a second set. For ABR, needle electrodes were inserted at vertex and pinna. ABR and CM were evoked with 5-ms tone pips (0.5-ms rise–fall, with a cos2 envelope, at 35 per s). The response was amplified ( £ 10,000), filtered (0.1–3 kHz), and averaged with an A/D board in a PC-based data-acquisition system. Sound level was raised in 5-dB steps from 0 to 90 dB SPL. At each level, 1,024 responses were averaged (with stimulus polarity alternated) after ‘artefact rejection’. Threshold was determined by visual inspection. For CM a silverwire electrode was placed on the round window membrane. Responses to alternating pip polarities were subtracted, and the resultant waveform was digitally high-pass filtered to remove residual uncancelled neural potentials. The DPOAE at 2f 1 2 f 2 was recorded in response to two primary tones: f 1 and f 2, with f 2 =f 1 ¼ 1:2 and the f 2 level 10 dB lower than the f 1 level. Ear-canal sound pressure was amplified and digitally sampled at 4-ms intervals. Fast-Fourier transforms were computed from averaged waveforms of ear-canal sound pressure, and the DPOAE amplitude at 2f 1 2 f 2 and surrounding noise floor were extracted. Iso-response contours were interpolated from plots of amplitude versus sound level, performed in 5-dB steps of f 1 level. Threshold is defined as the f 1 level required to produce a DPOAE at 0 dB SPL. Received 29 May; accepted 12 August 2002; doi:10.1038/nature01059. Published online 28 August 2002. 1. Gold, T. Hearing. II. The physical basis of the action of the cochlea. Proc. R. Soc. Lond. B 135, 492–498 (1948). 2. Dallos, P. & Harris, D. Properties of auditory nerve responses in absence of outer hair cells. J. Neurophysiol. 41, 365–383 (1978). 3. Brown, M. C., Nuttall, A. L. & Masta, R. I. Intracellular recordings from cochlear inner hair cells: effects of stimulation of the crossed olivocochlear efferents. Science 222, 69–72 (1983). 4. Dallos, P. The active cochlea. J. Neurosci. 12, 4575–4585 (1992). 5. Brownell, W. E., Bader, C. R., Bertrand, D. & de Ribaupierre, Y. Evoked mechanical responses of isolated cochlear outer hair cells. Science 227, 194–196 (1985). 6. Kachar, B., Brownell, W. E., Altschuler, R. & Fex, J. Electrokinetic shape changes of cochlear outer hair cells. Nature 322, 365–368 (1986). 7. Ashmore, J. F. A fast motile response in guinea-pig outer hair cells: the cellular basis of the cochlear amplifier. J. Physiol. 388, 323–347 (1987). 8. Ashmore, J. F. Cochlear Mechanisms (eds Wilson, J. P. & Kemp, D. T.) 107–116 (Plenum, London, 1989). 9. Santos-Sacchi, J. Reversible inhibition of voltage-dependent outer hair cell motility and capacitance. J. Neurosci. 11, 3096–3110 (1991). 10. Zheng, J. et al. Prestin is the motor protein of cochlear outer hair cells. Nature 405, 149–155 (2000). 11. Belyantseva, I. A., Adler, H. J., Curi, R., Frolenkov, G. I. & Kachar, B. Expression and localization of prestin and the sugar transporter GLUT-5 during development of electromotility in cochlear outer hair cells. J. Neurosci. 20, RC116 (2000). 12. Oliver, D. et al. Intracellular anions as the voltage sensor of prestin, the outer hair cell motor protein. Science 292, 2340–2343 (2001). 13. Forge, A. Structural features of the lateral walls in mammalian cochlear outer hair cells. Cell Tissue Res. 265, 473–483 (1991). 14. Dallos, P. & Fakler, B. Prestin, a new type of motor protein. Nature Rev. Mol. Cell Biol. 3, 104–111 (2002). 15. Bohne, B. A. & Rabbitt, K. D. Holes in the reticular lamina after noise exposure: implication for continuing damage in the organ of Corti. Hear. Res. 11, 41–53 (1983). 16. Holt, J. R. et al. A chemical-genetic strategy implicates myosin-1c in adaptation by hair cells. Cell 108, 371–381 (2002). 17. Kros, C. J. et al. Reduced climbing and increased slipping adaptation in cochlear hair cells of mice with Myo7a mutations. Nature Neurosci. 5, 41–47 (2002). 18. Dallos, P. & Wang, C. Y. Bioelectric correlates of kanamycin intoxication. Audiology 13, 277–289 (1974). 19. Kemp, D. T. Stimulated acoustic emissions from within the human auditory system. J. Acoust. Soc. Am. 64, 1386–1391 (1978). 20. Johnstone, B. M., Patuzzi, R. & Yates, G. K. Basilar membrane measurements and the travelling wave. Hear. Res. 22, 147–153 (1986). 21. Ruggero, M. A. & Rich, N. C. Application of a commercially-manufactured Doppler-shift laser velocimeter to the measurement of basilar-membrane vibration. Hear. Res. 51, 215–230 (1991). 22. Sellick, P. M., Patuzzi, R. & Johnstone, B. M. Measurement of basilar membrane motion in the guinea pig using the Mossbauer technique. J. Acoust. Soc. Am. 72, 131–141 (1982). 23. Kiang, N. Y. & Moxon, E. C. Tails of tuning curves of auditory-nerve fibers. J. Acoust. Soc. Am. 55, 620–630 (1974). 24. Ruggero, M. A. Responses to sound of the basilar membrane of the mammalian cochlea. Curr. Opin. Neurobiol. 2, 449–456 (1992). 25. Manley, G. A. Cochlear mechanisms from a phylogenetic viewpoint. Proc. Natl Acad. Sci. USA 97, 11736–11743 (2000). 26. Fettiplace, R., Ricci, A. J. & Hackney, C. M. Clues to the cochlear amplifier from the turtle ear. Trends Neurosci. 24, 169–175 (2001). 27. Hudspeth, A. J. Mechanical amplification of stimuli by hair cells. Curr. Opin. Neurobiol. 7, 480–486 (1997). 28. Ehret, G. The Auditory Psychobiology of the Mouse (ed. Willott, J. F.)) 169–200 (Charles Thomas, Springfield, Illinois, 1983). 29. He, D. Z., Evans, B. N. & Dallos, P. First appearance and development of electromotility in neonatal gerbil outer hair cells. Hear. Res. 78, 77–90 (1994).

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Competing interests statement The authors declare that they have no competing financial interests. Correspondence and requests for materials should be addressed to J.Z. (e-mail: [email protected]).

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Robustness of the BMP morphogen gradient in Drosophila embryonic patterning Avigdor Eldar*†, Ruslan Dorfman*, Daniel Weiss*†, Hilary Ashe‡, Ben-Zion Shilo* & Naama Barkai*† * Department of Molecular Genetics and † Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel ‡ School of Biological Sciences, University of Manchester, Manchester M13 9PT, UK .............................................................................................................................................................................

Developmental patterning relies on morphogen gradients, which generally involve feedback loops to buffer against perturbations caused by fluctuations in gene dosage and expression1. Although many gene components involved in such feedback loops have been identified, how they work together to generate a robust pattern remains unclear. Here we study the network of extracellular proteins that patterns the dorsal region of the Drosophila embryo by establishing a graded activation of the bone morphogenic protein (BMP) pathway. We find that the BMP activation gradient itself is robust to changes in gene dosage. Computational search for networks that support robustness shows that transport of the BMP class ligands (Scw and Dpp) into the dorsal midline by the BMP inhibitor Sog is the key event in this patterning process. The mechanism underlying robustness relies on the ability to store an excess of signalling molecules in a restricted spatial domain where Sog is largely absent. It requires extensive diffusion of the BMP–Sog complexes, coupled with restricted diffusion of the free ligands. We show experimentally that Dpp is widely diffusible in the presence of Sog but tightly localized in its absence, thus validating a central prediction of our theoretical study. Graded activation of the BMP pathway subdivides the dorsal region of Drosophila embryos into several distinct domains of gene expression. This graded activation is determined by a well-characterized network of extracellular proteins2,3, which may diffuse in the perivitelline fluid4 that surrounds the embryo (Fig. 1a). The patterning network is composed of two BMP class ligands (Scw and Dpp), a BMP inhibitor (Sog), a protease that cleaves Sog (Tld) and an accessory protein (Tsg), all of which are highly conserved in evolution and are used also for patterning the dorso-ventral axis of vertebrate embryos5. Previous studies have suggested that patterning of the dorsal region is robust to changes in the concentrations of most of the crucial network components. For example, embryos that contain only one functional allele of scw, sog, tld or tsg are viable and do not show any apparent phenotype. Misexpression of scw or of tsg also renders the corresponding null mutants viable6–8. To check whether robustness is achieved at the initial activation gradient, we monitored signalling directly by using antibodies that recognize specifically an activated, phosphorylated intermediate of

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letters to nature the BMP pathway (pMad)9,10. Prominent graded activation in the dorsal-most eight cell rows was observed for about 1 h, starting roughly 2 h after fertilization at 25 8C (ref. 11 and Fig. 1b). We quantified this activation gradient in heterozygous mutants that were compromised for one of three of the crucial components of the patterning network, Scw, Sog or Tld. Whereas homozygous null mutants that completely lack the normal gene product have a deleterious effect on signalling11, the heterozygotes, which should produce half the amount of the gene product, were indistinguishable from wild type (Fig. 1c). Similarly, overexpression of the Tld protein uniformly in the embryo did not alter the activation profile (Fig. 1c). The activation profile at 18 8C was the same as that at 25 8C (Fig. 1d). This robustness to temperature variations is marked, considering the wide array of temperature dependencies that are observed in this temperature span. By contrast, the profile of pMad was sensitive to the concentration of Dpp11 (Fig. 1d). The dosage sensitivity of Dpp is exceptional among morphogens and is singled out as being haploid-insufficient12. No apparent transcriptional feedback, which might account for

the robustness of dorsal patterning, has been identified so far. Robustness should thus be reflected in the design of interactions in the patterning network. To identify the mechanism underlying robustness, we formulated a general mathematical model of the dorsal patterning network. For simplicity, our initial analysis was restricted to a single BMP class ligand (Scw or Dpp), a BMP inhibitor (Sog) and the protease (Tld). The general model accounted for the formation of the BMP–Sog complex, allowed for the diffusion of Sog, BMP and BMP–Sog, and allowed for the cleavage of Sog by Tld, both when Sog is free and when Sog is associated with BMP. Each reaction was characterized by a different rate constant. The three reaction–diffusion equations that define this model are given in the Methods. We carried out extensive simulations to identify robust networks. At each simulation, a set of parameters (rate constants and protein Box 1 Mechanism underlying robustness We consider an idealized patterning network that consists of a single BMP (Scw for simplicity), Sog and Tld. Robustness will be manifested in the steady-state distribution of Scw. We assume that free Scw does not diffuse and that free Sog is not cleaved. The set of reaction–diffusion equations defining this network is obtained from equations 1–3 (Methods), by setting DBMP ¼ aS ¼ k 2b ¼ 0: At steady-state, the system can then be reduced to a single equation: 0 ¼ 7 2 ð½Scw21 Þ 2 2l22 b

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where ¼ 2DS =k b ; D S is the diffusion coefficient of Sog and k b is the binding rate of Sog to Scw. Thus, although free Scw does not diffuse, the system is tuned for providing it with an effective diffusion. Two processes govern this effective diffusion: the shuttling of Scw by Sog from the circumference of the embryo into the dorsal midline, and the degradation of Sog by Tld in the dorsal region. Although both processes depend on the amounts of the respective proteins, those concentrations do not appear in the effective Scw diffusion. The key to this quantitative adjustment is the fact that both processes are mediated by the complex Sog–Scw: only the complex, and not free Scw, can diffuse, and only the complex is subject to degradation by Tld. The concentrations of the network components, Scw, Sog and Tld could still affect the steady-state activation gradient through the boundary conditions. The solution of equation (1) is given by Figure 1 Robustness of the pMad activation profile. a, Cross-section of an early Drosophila embryo (,2 h after egg lay) showing the three distinct domains of gene expression. Starting at stage 5, the dorsal domain, which comprises about 50 cells, is subdivided to form the amnioserosa and the dorsal ectoderm. Shown are the genes of the patterning network: Scw and Dpp are two activating BMP class ligands; Sog is an inhibitor of both ligands; Tsg is required for Sog inhibition of Dpp; and Tld is a protease that cleaves Sog. Note that dpp, tld and tsg are expressed only in the dorsal region (DR), whereas expression of sog is restricted to the neuroectoderm (NE) and scw is expressed by all cells. M, mesoderm. b, Activation of the BMP pathway, which induces different cell fates in the dorsal region, visualized by antibodies against pMad. The activation profile is shown in a dorsal view of a wild-type embryo at stage 5. Activation is graded and peaks at the dorsal midline. The pattern of pMad widens at the termini of the embryo, possibly owing to edge effects that modify patterning. Our analysis is focused on the centre of the embryo, where the variability between different embryos is limited (,2 cells). c, Normalized activation profile of wild-type embryos (averaged over n ¼ 11 embryos) compared with that of three sets of heterozygous mutants containing half the amount of Scw (n ¼ 23), Sog (n ¼ 14) and Tld (n ¼ 11). The activation profile of embryos overexpressing the Tld protein uniformly around the embryo, using the Mata4–Gal4 driver, is also shown (n ¼ 33). All embryos were collected at 25 8C. d, Activation profiles at 25 8C and 18 8C (n ¼ 41). This temperature variation is biologically significant, as development is about two times slower at 18 8C than at 25 8C. Embryos were collected at different times but at the same developmental stage for the two temperatures. Shown also is the activation profile of an embryo carrying three copies of the dpp gene. NATURE | VOL 419 | 19 SEPTEMBER 2002 | www.nature.com/nature

l2b ð2Þ þ 12 where x ¼ 0 at the dorsal midline and 1 is an integration coefficient. In general, the value of 1 will depend on most parameters of the system, including the concentrations and the production rates of the network components Scw, Sog and Tld, leading to a nonrobust distribution of Scw. Examining equation (2), however, we note that the only way to accommodate high concentrations of Scw is by placing Scw in a small region surrounding the dorsal midline where Sog is absent, in other words, by setting 1 to 0. Thus, for large enough concentrations of Scw, 1 vanishes and we obtain a robust Scw profile: ½ScwðxÞ ¼

x2

l2b ð3Þ x2 for every position of x that is far enough from the dorsal midline, in other words, x . . 1. Indeed, the concentrations of network components have disappeared from this equation of the activation profile, which reflects the robustness of the system. Finally, we note that the same mechanism generates the gradient of the second BMP (Dpp). We assume, however, that Dpp binds Sog only when the latter is bound to Tsg. Thus, the same formalism is applied but with the molecular entities Dpp, Sog–Tsg (instead of Sog) and the complex Dpp–Sog–Tsg (instead of Scw–Sog). The details and precise conditions necessary for robustness are given in the Supplementary Information.


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letters to nature concentrations) was chosen at random and the steady-state activation profile was calculated by solving equations (1) to (3) numerically. A set of three perturbed networks representing heterozygous situations was then generated by reducing the gene dosages of sog, tld or the BMP class ligand by a factor of two. The steady-state activation profiles defined by those networks were solved numerically and compared with the initial, nonperturbed network. A threshold was defined as a given BMP value (corresponding to the value at a third of the dorsal ectoderm in the nonperturbed network). The extent of network robustness was quantified by measuring the shift in the threshold for all three perturbed networks. Over 66,000 simulations were carried out, with each of the nine parameters allowed to vary over four orders of magnitude. As expected, in most cases (97.5%) the threshold position in the perturbed networks was shifted by a large extent (.50%; see Fig. 2a). In most of those nonrobust cases, the BMP concentration was roughly uniform throughout the dorsal region (Fig. 2c). By contrast, Sog was distributed in a concentration gradient with its a

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Figure 2 Patterning mechanism emerges from the features of the robust networks. The general model of the dorsal patterning network was solved numerically for 66,000 different choices of parameters, with each parameter ranging over four orders of magnitude. a, A typical, nonrobust network. The profile of free BMP (unbroken curves) is shown for the nonperturbed network and for three perturbed networks representing heterozygotes for sog, tld and BMP (see Fig. 1c for a key to the lines).The total concentration of BMP (free plus Sog-associated) is indicated by the grey line (arrow). The broken grey line (T) indicates the threshold where robustness was measured. b, A typical robust system. c–f, Statistical distribution of various features in the robust (black) and nonrobust (white) networks. The analysis was restricted to the 22,000 networks that showed at least twofold spatial variation of free BMP concentration. Each feature was calculated for each of the networks, and the histograms were normalized to account for the different numbers of robust (198) and nonrobust (22,000) networks. c, The extent of BMP confinement to the dorsal midline was quantified by measuring the ratio between total BMP concentration (free plus Sog-associated) at the centre and its average concentration. In all of the robust cases, a high ratio (.10) was observed. By contrast, the low ratios observed in the nonrobust cases indicated that BMP was distributed approximately uniformly. d, The steady-state profile of free BMP was fit to a power-low distribution, x 2n. Nearly all robust profiles corresponded to n ¼ 2, indicating the uniqueness of the robust solution. By contrast, a wide range of exponents were found for the nonrobust solution. The fitting error vanished in the robust cases, but was high in the nonrobust cases (not shown). e, Ratio between the diffusion coefficient of free BMP (D BMP) and the complex BMP–Sog (D BMP–Sog). Note that complex formation significantly enhances BMP diffusion in all robust cases. f, Ratio of the degradation rate of free Sog (a) to that of BMP-associated Sog (l). Note that complex formation greatly enhances Sog degradation in all robust cases. 306

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minimum in the dorsal midline, defining a reciprocal gradient of BMP activation. Thus, the key event in this nonrobust patterning mechanism was the establishment of a concentration gradient of Sog, which was governed by diffusion of Sog from its domain of expression outside the dorsal region, coupled with its cleavage by Tld inside the dorsal region. Although such a gradient has been observed13, it is also compatible with other models (see below). We identified a small class of networks (198 networks, 0.3%) in which a twofold reduction in the amounts of all three genes resulted in a change of less than 10% in the threshold position (see Fig. 2b). Notably, in all of these robust cases, BMP was redistributed in a sharp concentration gradient that peaked in the dorsal midline (Fig. 2c). In addition, this concentration gradient decreased as a powerlow distribution with an exponent n ¼ 2, which indicated the uniqueness of the robust solution (Fig. 2d). In these cases, Sog was also distributed in a graded manner in the dorsal region (data not shown). Analysis of the reaction rate constants of the robust networks showed a wide range of possibilities for most parameters. But two restrictions were apparent and defined the robust network design. First, in the robust networks the cleavage of Sog by Tld was facilitated by the formation of the complex Sog–BMP (Fig. 2f). Second, the complex BMP–Sog was broadly diffusible, whereas free BMP was restricted (Fig. 2e). To identify how robustness is achieved, we considered an idealized network by assuming that free Sog is not cleaved and that free BMP does not diffuse. The steady-state activation profile defined by this network can be solved analytically (Box 1), which reveals the two aspects that are crucial for ensuring robustness. First, the BMP– Sog complex has a central role, by coupling the two processes that establish the activation gradient: BMP diffusion and Sog degradation. This coupling leads to a quantitative buffering of perturbations in gene dosage. Second, restricted diffusion of free BMP enables the system to store excess BMP in a confined spatial domain where Sog is largely absent. Changes in the concentration of BMP

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Figure 3 Properties of the robust model. a, b, The steady-state concentrations of receptor-bound Scw and Dpp. Six altered systems were obtained from a reference system by reducing to half the amounts of scw, sog, tld (see Fig. 1c for a key to the lines), dpp (unbroken grey line), Scw receptor (dotted line), tsg (superimposed on the solid line) and by increasing by 50% the amount of dpp (grey dashed line). The level and position of the threshold used in c and d are indicated. c, d, The positions of the activation thresholds of Scw (c) and Dpp (d) for a series of altered systems, obtained by changing a single parameter by the indicated fold amount. e, Time to reach steady state as a function of the fold change in parameter values. Time is initiated with the onset of ligand production.



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Figure 4 Dpp diffusion requires Sog and Tsg. Dpp was expressed orthogonal to the dorsoventral axis by the eve st2 enhancer in a stripe of about 12 cells at early cleavage cycle 14 (a), which refines to about 6 cells by late cycle 14 (lateral views, b). Note that ectopic amounts of dpp were greater than the endogenous transcripts in the dorsal region, which under these exposures were not visible. c, Normal pattern of race in wild-type embryos. Note the AP bias in the anterior positions (arrowheads). d, Normal pattern of pMad in wildtype embryos. e, Expression of st2–dpp in wild-type embryos leads to an expanded expression of race, which forms a wedge shape with its broadest region at the position of st2–dpp (arrow) and ranges about 25 cells posteriorly (asterisk). The normal pattern of race shows an AP bias at the anterior positions (arrowheads). f, st2–dpp in wild-type embryos also leads to a broader dorsal distribution of pMad, which extends throughout the AP axis. g, In sog 2/2 embryos, the anterior race domain expands (arrowheads), whereas posterior expression is diminished and detected only sporadically as a punctate staining. Some expansion of race was observed in sog þ/2 embryos, probably due to the higher threshold of race induction compared with pMad. h, In sog 2/2 embryos, pMad expands in the dorsal domain, but does not reach the ventral domain. i, Expression of st2–dpp in sog 2/2 embryos leads to a corresponding stripe of race of about 10–12 cells (arrow). j, st2–dpp in sog 2/2 embryos generates a corresponding stripe of pMad (arrow), which extends to the ventral region. The ventral expansion of pMad versus the restricted dorsal expansion of race in embryos of the same genotype indicates that a lower threshold of activation can induce pMad even in the ventral domain, which is devoid of endogenous Dpp. Main view is ventral, inset is lateral. k, l, The patterns of race and pMad in tsg 2/2 embryos are similar to sog 2/2 embryos. m, n, st2–dpp in tsg 2/2 generates a corresponding stripe of both race and pMad, similar to that observed on expression of st2–dpp in sog 2/2 embryos. Main view in n is ventral, inset is lateral. Except where stated otherwise, a dorsal view is shown with anterior to the left. NATURE | VOL 419 | 19 SEPTEMBER 2002 | www.nature.com/nature

alter the BMP profile close to the dorsal midline but do not change its distribution in most of the dorsal region (Box 1). We next examined the complete system, comprising Sog, Tld, Tsg, both Scw and Dpp, and their associated receptors (Supplementary Information). Two additional molecular assumptions were required to ensure the robustness of patterning. First, Sog can bind and capture the BMP class ligands even when the latter are associated with their receptors. Second, Dpp can bind Sog only when the latter is bound to Tsg. Indeed, it has been shown that, whereas Sog is sufficient for inhibiting Scw, both Tsg and Sog are required for inhibiting Dpp6,14,15. This last assumption implies that Tsg functions to decouple the formation of the Scw gradient from the parallel generation of the Dpp gradient, ensuring that Scw and Dpp are transported to the dorsal midline independently by two distinct molecular entities (Supplementary Information). The complete model was solved numerically for different choices of rate constants. In particular, we assessed the effect of twofold changes in gene dosage. The steady-state activation profiles can be superimposed, indicating the robustness of the system (Fig. 3a, b). In addition, with the exception of Dpp, the expression of all other crucial network components can be altered by at least an order of magnitude before an effect on the position of a given threshold is observed (Fig. 3c, d). In the model, the lack of robustness to Dpp stems from its insufficient dosage. Note that the time taken to reach steady state is sensitive to these concentrations of protein (Fig. 3e). For the wide range of parameters that we have used, however, the adjustment time does not exceed the patterning time. Flexible adjustment time thus facilitates the buffering of quantitative perturbations. As discussed above, our analysis identified two principle molecular features that are essential for robust network design: first, free Sog is not cleaved efficiently—an assumption that is supported by the in vitro finding that Sog cleavage by Tld requires BMP6,16; second, the diffusion of free BMP is restricted. This is the central prediction of our theoretical study, namely, that Scw diffusion requires Sog, whereas Dpp diffusion requires both Sog and Tsg. Although several reports suggest that in wild-type embryos both Dpp and Scw are widely diffusible6,17, their ability to diffuse in a sog or tsg mutant background has not been examined as yet. To monitor the diffusion of Scw or Dpp, we used the even-skipped (eve) stripe-2 enhancer (st2) to misexpress Dpp or Scw in a narrow stripe perpendicular to the normal BMP gradient. In transgenic embryos, dpp or scw RNA was detected in a stripe just posterior to the cephalic furrow. Initially the stripe was about 12 cells wide at early cleavage cycle 14, but refined rapidly to about 6 cells by late cycle 14 (Fig. 4a, b). The st2–dpp and st2–scw embryos were viable, despite the high expression of these proteins as compared with their endogenous counterparts. The activation of the BMP pathway was monitored either by staining for pMad or by following dorsal expression of the target gene race, which requires high activation. Scw is a less potent ligand than is Dpp. This experimental setup could not be used to study Scw diffusion properties because expressing st2–scw did not alter the pattern of pMad or race expression in wild-type or sog 2/2 embryos (data not shown). By contrast, expression of st2–dpp led to an expansion of both markers in a region that extends far from the st2 expression domain, indicating a wide diffusion of Dpp in a wildtype background (compare Fig. 4c, d with 4e, f). Conversely, on expression of st2–dpp in sog 2/2 or in tsg 2/2 embryos, both markers were confined to a narrow stripe in the st2 domain (compare Fig. 4g, h and k, l with 4i, j and m, n, respectively). The width of this stripe was comparable to that of st2–dpp expression, ranging from 6 to 12 cells, indicating that Dpp does not diffuse from its domain of expression in the absence of Sog or Tsg. Taken together, these results show that both Sog and Tsg are required for Dpp diffusion, as predicted by the theoretical analysis. The computation ability of biochemical networks is striking when one considers that they function in a biological environment


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letters to nature where the amounts of the network components fluctuate, the kinetics is stochastic, and sensitive interactions between different computation modules are required. Studies have examined the effect of these properties on cellular computation mechanisms18–20, and robustness has been proposed to be a ‘design principle’ of biochemical networks18,21. We have shown the applicability of this principle to morphogen gradient patterning during early development. Quantitative analysis can be used to assess rigorously the robustness of different patterning models and to exclude incompatible ones. The remaining, most plausible model points to crucial biological assumptions and serves to postulate the central feedback mechanisms. Applying the same modelling principles to other systems might identify additional ‘design principles’ that underlie robust patterning by morphogen gradients in development. A

Methods Fly strains We used the following strains: screw12, sog6, tolloid2, tolloid7, UAS–tld (provided by M. O’Connor), Mata4–Gal4 VP16 (provided by D. St. Johnston) and tsg XB56 (provided by L. Marsh). For altering the number of copies of dpp, we used the strain dpp 1846 sp cn bw/ CyO 23P[dpp þ] (provided by S. Roth), which was crossed to wild-type flies. The mutant chromosomes were maintained over a balancer chromosome. When each strain is crossed to itself, two-thirds of the embryos not showing the null phenotype should be heterozygotes for scw and tld, and a third for sog. The st2–dpp strain has been described17. We constructed st2–scw by inserting a scw cDNA fragment into plasmid 22FPE (ref. 22).

Antibodies and staining Rabbit antibodies against pMad were kindly provided by P. ten Dijke. Freshly collected embryos were fixed in 7% formaldehyde. The remaining steps of staining were done according to standard procedures. We used Cy2-conjugated secondary antibodies against rabbit IgG (Jackson ImmunoResearch).

Data analysis The dorso-ventral activation profile was quantified by using image processing tools written in Matlab. The mean intensity was measured at the middle of the anterior– posterior (AP) axis in a swath that was 20 cells wide in the direction of the AP axis. We then averaged the results over the indicated number of embryos.

4. Stein, D., Roth, S., Vogelsang, E. & Nusslein-Volhard, C. The polarity of the dorsoventral axis in the Drosophila embryo is defined by an extracellular signal. Cell 65, 725–735 (1991). 5. DeRobertis, E. M. & Sasai, Y. A common plan for dorsoventral patterning in Bilateria. Nature 380, 37–40 (1996). 6. Nguyen, M., Park, S., Marques, G. & Arora, K. Interpretation of a BMP activity gradient in Drosophila embryos depends on synergistic signaling by two type I receptors, SAX and TKV. Cell 95, 495–506 (1998). 7. Arora, K., Levine, M. S. & O’Connor, M. B. The screw gene encodes a ubiquitously expressed member of the TGF-b family required for specification of dorsal cell fates in the Drosophila embryo. Genes Dev. 8, 2588–2601 (1994). 8. Mason, E. D., Williams, S., Grotendorst, G. R. & Marsh, J. L. Combinatorial signaling by Twisted Gastrulation and Decapentaplegic. Mech. Dev. 64, 61–75 (1997). 9. Persson, U. et al. The L45 loop in type I receptors for TGF-b family members is a critical determinant in specifying Smad isoform activation. FEBS Lett. 434, 83–87 (1998). 10. Tanimoto, H., Itoh, S., ten Dijke, P. & Tabata, T. Hedgehog creates a gradient of DPP activity in Drosophila wing imaginal discs. Mol. Cell 5, 59–71 (2000). 11. Dorfman, R. & Shilo, B.-Z. Biphasic activation of the BMP pathway in the Drosophila embryonic dorsal region. Development 128, 965–972 (2001). 12. Wharton, K. A., Ray, R. P. & Gelbart, W. M. An activity gradient of decapentaplegic is necessary for the specification of dorsal pattern elements in the Drosophila embryo. Development 117, 807–822 (1993). 13. Srinivasan, S., Rashka, K. E. & Bier, E. Creation of a Sog morphogen gradient in the Drosophila embryo. Dev. Cell 2, 91–101 (2002). 14. Neul, J. L. & Ferguson, E. L. Spatially restricted activation of the SAX receptor by SCW modulates DPP/TKV signaling in Drosophila dorsal–ventral patterning. Cell 95, 483–494 (1998). 15. Ross, J. J. et al. Twisted gastrulation is a conserved extracellular BMP antagonist. Nature 410, 479–483 (2001). 16. Marques, G. et al. Production of a DPP activity gradient in the early Drosophila embryo through the opposing actions of the SOG and TLD proteins. Cell 91, 417–426 (1997). 17. Ashe, H. L., Mannervik, M. & Levine, M. Dpp signaling thresholds in the dorsal ectoderm of the Drosophila embryo. Development 127, 3305–3312 (2000). 18. Barkai, N. & Leibler, S. Robustness in simple biochemical networks. Nature 387, 913–917 (1997). 19. Barkai, N. & Leibler, S. Circadian clocks limited by noise. Nature 403, 267–268 (2000). 20. von Dassow, G., Meir, E., Munro, E. M. & Odell, G. M. The segment polarity network is a robust developmental module. Nature 406, 188–192 (2000). 21. Hartwell, L. H., Hopfield, J. J., Leibler, S. & Murray, A. W. From molecular to modular biology. Nature 402, C47–C52 (1999). 22. Kosman, D. & Small, S. Concentration-dependent patterning by an ectopic expression domain of the Drosophila gap gene knirps. Development 124, 1343–1354 (1997). 23. Swaminathan, R., Hoang, C. P. & Verkman, A. S. Photobleaching recovery and anisotropy decay of green fluorescent protein GFP–S65T in solution and cells: cytoplasmic viscosity probed by green fluorescent protein translational and rotational diffusion. Biophys. J. 72, 1900–1907 (1997).

Supplementary Information accompanies the paper on Nature’s website (http://www.nature.com/nature).

Numerical simulations For the general patterning model we considered a single BMP, which is denoted here as Scw. The model was defined by the following set of reaction–diffusion equations: ›½Sog ð1Þ ¼ DS 7 2 ½Sog 2 kb ½Sog½Scw þ k2b ½Sog–Scw 2 a½Tld½Sog ›t

›½Scw ¼ DBMP 7 2 ½Scw 2 kb ½Sog½Scw þ l½Tld½Sog–Scw þ k2b ½Sog–Scw ›t

ð2Þ

›½Sog–Scw ¼ DC 7 2 ½Sog–Scw þ kb ½Sog½Scw 2 k2b ½Sog–Scw 2 l½Tld ›t ½Sog–Scw

ð3Þ

The equations were solved in the region 21 , x , 1. The parameters in this model include the diffusion coefficients of Sog, Scw and the complex Scw–Sog, (DS, DBMP and D C), binding and unbinding of the Scw–Sog complex (k b and k 2b), cleavage of Sog by Tld (a when Sog is free, l when Sog in associated with Scw), a constant flux of Sog on the boundaries (h s) and the total Scw concentration ([Scw]av). DC is DBMP–Sog in Fig. 2e. We solved the equations for 66,000 different sets of random parameters. Each parameter was allowed to vary over four orders of magnitude. The parameters defining the centre of this distributions are (in arbitrary units): DS ¼ l1 ¼ ½Scwav ¼ 1; D BMP ¼ 0.1, D C ¼ 1, k b ¼ 10, k 2b ¼ 1, l[Tld] ¼ 10, a[Tld] ¼ 10, h S ¼ 10. Equations were solved with Matlab. Each run took less than 1 min. The parameters of the systems shown in Fig. 2 are specified in the Supplementary Information. For the parameters of the full model (Fig. 3), we chose diffusion rates that reflected the rapid in vivo patterning time and corresponded to the measured diffusion time in the perivitelline fluid4. This measured diffusion coefficient is similar to that of green fluorescent protein (GFP) in water23. It is possible that mixing processes in the perivitelline fluid contribute to the equilibration process. For simplicity, we approximate such processes as an effective diffusion. This approximation does not affect our conclusions. No biochemical data restricting the values of the other parameters are available. The parameters of the reference system are within the realistic biochemical range and obey the robustness conditions. The parameter choice is specified and rationalized in detail in the Supplementary Information. Received 11 April; accepted 27 July 2002; doi:10.1038/nature01061. 1. Freeman, M. Feedback control of intercellular signalling in development. Nature 408, 313–319 (2000). 2. Podos, S. D. & Ferguson, E. L. Morphogen gradients: new insights from DPP. Trends. Genet. 15, 396–402 (1999). 3. Raftery, L. A. & Sutherland, D. J. TGF-b family signal transduction in Drosophila development: from Mad to Smads. Dev. Biol. 210, 251–268 (1999).

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Acknowledgements We thank P. ten Dijke for the pMad antibody; L. Marsh, M. O’Connor, S. Roth, D. St. Johnston and the Umea and Bloomington Fly Centers for strains; and S. Leibler and S. Roth for comments and criticism. This work was funded by the Israel Science Foundation (B-Z.S.) and the Israel Science Foundation and the Minerva Foundation (N.B). H.A. is a Lister Institute Research Fellow. B-Z.S. is the incumbent of the Hilda and Cecil Lewis professorial chair in Molecular Genetics. N.B. is the incumbent of the Soretta and Henry Shapiro career development chair.

Competing interests statement The authors declare that they have no competing financial interests. Correspondence and requests for materials should be addressed to N.B. (e-mail: [email protected]).

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Molecular basis of seasonal time measurement in Arabidopsis Marcelo J. Yanovsky & Steve A. Kay The Scripps Research Institute, 10550 N. Torrey Pines Road, La Jolla, California 92037, USA .............................................................................................................................................................................

Several organisms have evolved the ability to measure daylength, or photoperiod, allowing them to adjust their development in anticipation of annual seasonal changes. Daylength measurement requires the integration of temporal information, provided by the circadian system, with light/dark discrimination, initiated by specific photoreceptors. Here we demonstrate that in Arabidopsis this integration takes place at the level of CONSTANS

