Proc. Nati. Acad. Sci. USAVol. 84, pp. 4140-4144, June 1987Developmental Biology

Genesis of a spatial pattern in the cellular slime moldPolysphondylium pallidum

(lateral inhibition/reaction-dlffusion/prepaterns/morphogenesis/symmetry breaking)

G. BYRNE AND EDWARD C. COX*Department of Biology, Princeton University, Princeton, NJ 08544

Communicated by J. T. Bonner, March 2, 1987 (receivedfor review January 5, 1987)

ABSTRACT The branches in Polysphondylium pallidumwhorls are arranged in a radial pattern. We have used apattern-specific monoclonal antibody to study branch forma-tion and characterize the origin of this pattern. A quantitativespatial analysis of antibody staining reveals that the branchingpattern arises from a random distribution. This distributionpasses through a series of intermediate stages to yield a radialprepattern. The origins and evolution of this prepattern aresatisfactorily accounted for by models that produce spatialpatterns by short-range autocatalytic and longer-range inhib-itory forces.

The mature fruiting body of Polysphondylium pallidum iscomposed of a central cellulose stalk along which 1-10 ormore sets of branches are arrayed at regular intervals alongthe central stalk. Each branch terminates in a sorus of spores.Formation of the radial branch pattern begins with thesegregation ofa whorl mass from the base ofthe sorogen (Fig.1). Soon after separating from the sorogen, one to eight tipsform in a radial pattern about the equator of the whorl (Fig.LA). Each tip organizes the formation of a branch so that theinitial whorl mass is equally partitioned, with each branchcontaining a similar number of spores (1). The number of tipsthat eventually arises is a function of the surface area of thewhorl (2). It is not related to the number of tips present onneighboring whorls (1), and consequently the formation oftips represents a true symmetry breaking event in which thespheroidal symmetry of the whorl is transformed, by theinitiation of tips, into the radial symmetry of the branchpattern.

In this report, we analyze the spatial distribution oftip-specific antigens over the equatorial surface of a series ofwhorls prior to and after the formation oftips. We use Fourieranalysis to quantify the spatial distribution of antigen andcompare our results to a simple model. Using this unbiasedmeasure of the spatial pattern, we show that initially thespatial prepatterning of tip-specific antigens is randomlydistributed about the equator of the whorl. This randomprepattern subsequently evolves into a periodic radial prepat-tern. The essential features of our results are captured bymodels that form prepatterns of spatio-temporal informationthrough local autocatalysis and long-range lateral inhibition(3-5).

MATERIALS AND METHODSStrain. PN500 was used throughout (1).Antibody Strains. Sorogens were methanol-fixed and incu-

bated overnight with anti-PglOl diluted in phosphate-buff-ered saline (PBS) containing 2% bovine serum albumin, asdescribed (6). The samples were washed with PBS and

incubated overnight with affinity-purified biotin-conjugatedsheep anti-mouse immunoglobulin (Vector Laboratories,Burlingame, CA). Specimens were washed with PBS, incu-bated for 20 min with Texas-red-conjugated streptavidin(Amersham), washed in PBS, and mounted in a solution ofglycerol/PBS (9:1) containing 1.0 mg ofp-phenylenediamineper ml (7).

Quantitative Analysis of Antigen Distribution. Anti-PglOl-stained whorls and sorogens were immersed in glycerol andmounted in a pulled 20-/l capillary (Corning 7099-S; innerdiameter, -85 pum). The capillary was placed on a micro-scope slide in a drop of glycerol, covered with a coverslip,and the free end was attached to a micromanipulator. Whorlswere photographed every 22.5° as the specimen was rotatedabout the axis of the central stalk. Eighteen photographs ofthe proximal whorl surface were taken through a Zeiss x25oil/glycerol/water immersion lens using a constant shutterspeed. A photomontage of the equatorial image was con-structed and scanned with a Perkin-Elmer PDS photodigi-tizer. Image density was measured using a 20 x 20 gtm slit.This typically resolved the negative into 170 x 300 pictureelements and 256 grey levels. To map the antigen density,each picture element was assigned a value of 0, 1, 2, or 4corresponding to background, dim, bright, and very brightpixels. The initial density distribution is the sum of thesevalues for each column of the digitized image. To computethe power spectrum, the density distribution was smoothedwith a running average. Window size was the average celldiameter (3.5 Am for these fixed preparations). Any trend inthe density data was removed by subtracting the best-fitlinear regression line prior to a direct Fourier transformationof the smoothed density profile (8). The highest detectableFourier frequency is limited by the Nyquist theorem (8),which in this case is =-7 ,m, or a frequency equal to half thenumber of cells on the equator of the whorl. The powerspectrum was normalized according to Shimshoni (9).

RESULTSTip Prepatterns. The monoclonal antibody anti-PglOl de-

tects an antigen (PglOl) present at high levels in tips anddistributed as a shallow gradient along the anterior-posterioraxis of the sorogen (6). Whorls stained with anti-PglOl firstdisplay a band of increased fluorescence on their equatorialsurface (Fig. 1B b-e). This band is detected well in advanceof tip formation, usually before the whorl detaches from thesorogen. The fluorescence intensity of the equator is greaterthan the intensity observed in both the off-equatorial surfaceof the whorl, and the most basal section of the sorogen. Overtime, the band fragments into a series of densely clusteredfluorescent spots. These antigen clusters are restricted to thesurface of the whorl, and each cluster generally representsthe position where a new tip will form (6). Anti-PglOl was

*To whom reprint requests should be addressed.

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The publication costs of this article were defrayed in part by page chargepayment. This article must therefore be hereby marked "advertisement"in accordance with 18 U.S.C. §1734 solely to indicate this fact.

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Proc. Natl. Acad. Sci. USA 84 (1987) 4141

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spatial patterns are much more variable. Whorls 7-10 in Fig.3 illustrate the range of patterns we have observed. Whorl 7has two regions of localized anti-PglOl stain and a thirddiffuse area of stain. In its power spectrum (Fig. 4d) thefourth Fourier frequency is just beneath the 5% significancelevel. It appears that this whorl was still regulating itsprepattern, which may ultimately have developed four orpossibly three antigen clusters. Whorl 8 has a uniform levelofanti-PglOl stain about its circumference underlying at least

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FIG. 2. Anti-PglOl-specific stain on a whorl with well-developedtips. (a) Immunofluorescent photomontage of the equatorial whorlsurface. Four brightly stained tips are present. (b) Solid line is thedensity distribution of anti-PglO1 stain about the circumference ofthe whorl. Dotted line is a reconstruction of the original densitydistribution using the Fourier frequencies from the power spectrum.(c) Normalized power spectrum of b. An asterisk indicates theFourier frequency with power significantly above the random ex-pectation (9) (P > 0.05). Over 50% of the power is contained in thefourth and fifth Fourier frequencies. These two frequencies largelydelimit the number and position of the antigen peaks in b. Power inthe other Fourier frequencies is required for accurate determinationof peak shapes. (Inset) Bright-field photomicrograph of the whorlduring rotation. (Bar = 40 um.) The equatorial distribution ofanti-PglOl-specific antigen was recorded by repeatedly photograph-ing stained whorls rotated in thin capillaries (see Materials andMethods).

two and possibly three patches (Fig. 3h). Unlike the otherwhorls in Fig. 3, these PglOl patches are clustered on oneside of the whorl. This clustering gives rise to a powerspectrum with a significant amount of power in a higherharmonic, the sixth Fourier frequency (29 um). The otherstriking aspect of this power spectrum, which is qualitativelysimilar to Fig. 5b (t = 80), is that 52% of the power isuniformly distributed over the first to fifth and seventh toninth Fourier frequencies. Although the power spectrum ofwhorl 8 exhibits a strong sinusoidal component, the PglOlpattern on the whorl (Fig. 3h) shows that this periodicity doesnot extend about the entire circumference. It therefore seemslikely that a period of 29 Am reflects the inhomogeneitiesinitially present in whorl 8 rather than the equilibriumpattern.Whorls 9 and 10 do not exhibit obvious periodic patterns,

although some local regions of dense stain are apparent. Thespatially random nature of this stain is clear in the powerspectra for these whorls (Fig. 4 e and f). The power spectrumfor whorl 9 is broadly distributed among the lower Fourierfrequencies with no statistically significant single frequency.The spectrum for whorl 10 is similar, although there issomewhat greater power in the higher frequencies.

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(a-c) Late whorls with well-established tips. (d-f) Equatorial anti-PglOl staining on whorls prior to tip formation. (k) Hoechst nuclearstaining pattern around the equatorial surface of a whorl prior to tipformation. Numbers in the upper right corner of each panel are usedto identify the whorls throughout this report. The circumference ofeach whorl is listed in Table 1.

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Table 1. Summary of spectral analysisCircumference, Tips Significant Spacing,

Whorl atm (patches)* frequenciest gm1 182 4 (4) 4, 5 (0.543) 41.72 197 5 (5) 5 (0.580) 39.43 123 3 (3) 2, 3 (0.631) 53.44 183 - (5) 4, 6 (0.663) 40.35 211 - (5) 5 (0.412) 42.26 222 - (6) 6 (0.217) 37.07 129 -(3)8 174 - (3) 6 (0.317) 29.09 146 -() -

10 201 -(11 117 ( -A summary of the power spectra for anti-PglOl-stained whorls.

Whorls are numbered according to Fig. 3.*The number of tips, or antigen patches (in parentheses), is given.tThe significant Fourier frequencies were determined using themethods described by Shimshoni (9). The number in parentheses isthe fraction of the total power contained in the significant frequen-cies. When two significant frequencies are present, the spacing is aweighted average of their periods. The average spacing of tips inwhorls 1-3 is 44.8 ,Am (SD = 7.5). The mean spacing of antigenpatches for whorls 4-6 is 39.8 tum (SD = 2.6). Using a two-way ttest, these mean values are not significantly different (P > 0.5).

DISCUSSIONThe Fourier transformation of PglOl density profiles wasparticularly valuable during the initial stages of prepatternformation when periodicities were not obvious (Fig. 3 e andf) or absent (Fig. 3 g-j). A modified version (9) of Fisher'stest (10) was used to determine which frequencies in thepower spectrum were significantly more powerful than therandom expectation. By this test we conclude that tip-specific antigens are initially expressed in a random fashion(Fig. 4 e and f). The subsequent transformation of this initialpattern into a periodic prepattern is not entirely synchronous(Fig. 3 g-j) but, in general, occurs uniformly about thecircumference. We emphasize that the prepattern is estab-lished before tips or their visible precursors can be seen.The transformation of the initial distribution of PglOl into

a periodic prepattern is strikingly similar to the pattern-forming process observed in models first formulated byTuring (3), Gierer and Meinhardt (4), and Oster et al. (5).These models postulate that within a homogenous field of

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cells, small random differences exist. The initial distributionis transformed into a periodic one by autocatalysis and lateralinhibition. To compare model spatial patterns to the PglOlpatterns discussed here, we modeled the whorl equator as aring of cells and simulated tip formation using a set ofreaction-diffusion equations. Although other models, andother formulations of reaction-diffusion theory, could havebeen used to illustrate the general character ofour results, weuse this particular version because it is computationallysimple, and because we have used it in another study toexamine the relationship between the regularity of radialpatterning and the variance in the initial morphogen concen-tration at t = 0. It is also worth pointing out here that for anorganism the size ofP. pallidum, it is realistic to imagine thatdiffusing chemicals can operate over the required distances inthe required time (11).

Fig. 5a illustrates morphogen concentration over time forone such simulation. This example displays a wide variety ofintermediate periodic patterns. There are three morphogenpeaks at equilibrium (Fig. Sb; t = 1600). The initial morpho-gen profile (Fig. Sb; t = 0) was chosen to be statisticallyuniform. As expected, Fourier transformation of this profileresulted in a power spectrum with no favored frequency. Thefirst obvious periodic pattern has seven morphogen peaks(Fig. Sb; t = 80). Each of these peaks is present, though lessevident, in the initial morphogen profile. At this early stage,the periodicities detected by Fourier analysis are oftenrelated to the initial morphogen distribution rather than theequilibrium pattern. Over time several morphogen peaks aresuppressed, and Fourier analysis reveals a consistent selec-tion for lower frequencies. This often leads to a time whenthere is clearly an emerging pattern, yet no single Fourierfrequency in the power spectrum is significant (Fig. 5b; t =400). This stage is inevitably followed by growth of a lowerfrequency, which persists to equilibrium (Fig. Sb; t = 1600).There is significant agreement between this model and the

experimental results. First, the power spectra for whorls 9and 10 reveal no evidence for a radial prepattern, and thus wecan conclude that the very early origins of the tip pattern liein an almost constant distribution of antigen about theequator. This was Turing's postulate (3). Second, during theevolution of the radial prepattern, both in simulation andexperiment, nonequilibrium frequencies grow and then dis-appear, as evidenced by the shift in the power spectra withtime from higher to lower frequencies (Figs. 4 and 5). Andfinally, it is characteristic of our results that the regularity of

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FIG. 5. Simulation of tip formation on a whorl. (a) Morphogenconcentration over time relative to the cell position on a ring of cells.Selected profiles are shown on a different scale on the right. Time ismeasured in relative units. The initial morphogen profile is t = 0 andt = 1600 is the equilibrium pattern. (b) Power spectra for selectedmorphogen profiles. Dotted lines above the morphogen distributionsin a are the sine waves corresponding to the most powerful frequencyin the power spectrum in b. The equator of the whorl was modeledas a ring of40 cells. Equations 1 and 2 from Meinhardt (12) were used.The initial activator concentration (here labeled morphogen) wasrandomly selected from a distribution with mean = 0.5 (SD = 0.1).Initial inhibitor concentration for each cell was set to its activatorconcentration plus 1.0. SDs as low as 0.001 produced similar results.Only the activator concentrations are displayed. The number of cellsin the ring is unchanged throughout the simulation. The constantsused were c = 0.02, /i = 0.025, Da = 0.01, po = S X 1o-4, pi = 0, C'= 0.04, v = 0.035, Dh = 0.45.

the final pattern-the extent to which the radial spacing oftips, arms, and patches ofPglOl deviate from perfect spacing,as judged by nearest-neighbor analysis-exhibits the samedegree of order for both the model and the experiments (ref.1; and results not shown). In sum, the final distribution oftipson whorls, the angle between arms within whorls, thepartitioning of whorl cells into arms, and the distribution oftip-specific antigens throughout the prepatterning stages areaccurately described by generic autocatalysis/lateral inhibi-tion models. We note that many different formulations ofreaction-diffusion systems (13, 14), the chemotactic model ofKeller and Segel (15), and the mechanochemical models ofOster et al. (5) and Odell and Bonner (16) might be expectedto produce broadly similar results.

This study does not attempt to answer the question ofwhether the spatio-temporal signals required for tip forma-tion are derived from diffusing morphogens, as predicted ina reaction-diffusion model, or from the cell-cell and cell-substrate interactions predicted by mechanochemical mod-els. Our observations that a radial prepattern is establishedbefore we see tips or bulges on the whorl mass suggests thatthe prepattern is established by a reaction-diffusion-likemechanism, since in most mechanical models visible changesare expected to accompany symmetry breaking. It is clear,however, that the patterning of tips on whorls cannot beaccurately described by models based on the activities of afew cells (17, 18), growth of crystalline-like precursors (19),or cell-lineage processes. These models all predict that thespatio-temporal signals for pattern formation arise locally, incontrast to the global PglOl patterns we observe.

Patterns with similar origins have been described for theearly expression of two Drosophila segmentation genes(20-22). Transcripts from both the fushi tarazu and hairy

genes are initially expressed in an apparently random man-ner, over a broad region of the Drosophila blastoderm. Overtime this diffuse pattern evolves into the seven abdominalbands with an additional area ofexpression in the head regionfor hairy. The techniques described in this report can be usedto analyze the origins of these patterns and to quantify thespatial characteristics of the evolving prepattern.To determine in detail the patterning mechanism for tip

formation of P. pallidum whorls, several fundamental ques-tions must still be addressed. What contributions do cellularmotion and antigen turnover make in establishing the periodicprepattern? What functions do these antigens have, and whatother tip-specific antigens exist? Is the rapid appearance ofthese antigens the result of new expression or local modifi-cation of existing cell products? We are pursuing answers tothese questions through both a detailed morphological andmolecular analysis of the early patterning stages in hope ofdetermining the character of the initial symmetry breakingevent.

We are indebted to Ed Turner, Bill Seebok, and Gerry Ostriker ofthe Princeton University Astrophysics department for providingfacilities, guidance, and the software used for image analysis. Wealso wish to thank Jim McNally, Garry Odell, and George Oster fortheir advice and helpful discussions. This work was supported byNational Institute of General Medical Sciences Training GrantGM07312, National Cancer Institute Training Grant CA0916, aNational Science Foundation equipment grant (PCM-8115662), andthe Whitehall Foundation.

1. Cox, E. C., Spiegel, F. W., Byrne, G., McNally, J. G. &Eisenbud, L., Development, in press.

2. McNally, J. G., Byrne, G. & Cox, E. C. (1987) Dev. Biol. 119,302-304.

3. Turing, A. M. (1952) Philos. Trans. R. Soc. London Ser. B237, 37-72.

4. Gierer, A. & Meinhardt, H. (1972) Kybernetik 12, 30-39.5. Oster, G. F., Murray, J. D. & Harris, A. K. (1983) J. Embryol.

Exp. Morphol. 78, 83-125.6. Byrne, G. & Cox, E. C. (1986) Dev. Biol. 117, 442-455.7. Johnson, G. D., Davidson, R. S., McNamee, K. C., Russell,

G., Goodwin, D. & Holborow, E. J. (1982) J. Immunol.Methods 55, 231-242.

8. Bloomfield, P. (1976) Fourier Analysis of Time Series: AnIntroduction (Wiley, New York).

9. Shimshoni, M. (1977) Geophys. J. R. Astron. Soc. 23, 373-377.10. Fisher, R. A. (1929) Proc. R. Soc. London Ser. A 125, 54-59.11. Crick, F. H. C. (1970) Nature (London) 225, 420-422.12. Meinhardt, H. (1977) J. Cell Sci. 23, 117-139.13. Prigogine, I. & Nicolis, G. (1971) Q. Rev. Biophys. 4, 107-148.14. Murray, J. D. (1981) Philos. Trans. R. Soc. London Ser. B 295,

473-496.15. Keller, E. F. & Segel, L. A. (1970) J. Theoret. Biol. 26,

399-415.16. Odell, G. M. & Bonner, J. T. (1986) Philos. Trans. R. Soc.

London Ser. B 312, 487-525.17. Wigglesworth, V. B. (1940) J. Exp. Biol. 17, 180-200.18. Stenhouse, F. 0. & Williams, K. L. (1981) Dev. Biol. 81,

139-144.19. Inoue, S. (1982) in Developmental Order: Its Origins and

Regulation, eds. Subtelny, S. & Green, P. B. (Liss, NewYork), pp. 35-76.

20. Hafen, E., Kuroiwa, A. & Gehring, W. J. (1984) Cell 37,833-841.

21. Weir, M. P. & Kornberg, T. (1985) Nature (London) 318,433-439.

22. Kilchherr, F., Baumgartner, S., Bopp, D., Frei, E. & Noll, M.(1986) Nature (London) 321, 493-499.

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