Proc. NatI. Acad. Sci. USAVol. 86, pp. 6973-6977, September 1989Biophysics

Migration of bacteria in semisolid agar(Escherichia coli/motility/chemotais/swarm plates)

ALAN J. WOLFE AND HOWARD C. BERGDepartment of Cellular and Developmental Biology, Harvard University, Cambridge, MA 02138

Contributed by Howard C. Berg, June 26, 1989

ABSTRACT We studied the migration through semisolidagar ofchemotactic and nonchemotactic cells ofEscherichia coli.While swarms of nonchemotactic cells were generally smallerthan those ofchemotactic cells, they varied markedly in size andin structure. Cells that failed to tumble or that tumbled inces-sandy formed the smallest swarms. Cells that tumbled atintermediate frequencies formed much larger swarms, evenwhen deleted for many of the genes known to be required forchemotaxis. Surprisingly, the higher the tumble frequency, thelarger the swarms. Microscopic examination revealed that tum-bles enable cells to back away from obstructions in the agar.Thus, not all cells that swarm effectively need be chemotactic.

When chemotactic cells ofEscherichia coli are inoculated nearthe center of a Petri plate containing semisolid nutrient agar,they swarm outwards in concentric bands. The bands formbecause of chemotactic responses to spatial gradients gener-ated by transport and metabolism. In 1% tryptone (a caseinhydrolysate), the first band (extending from the top to thebottom of the agar) consumes all of the serine and most of theoxygen, the second band (at the top of the agar) consumesmost of the aspartate, and the third band (at the bottom of theagar) consumes all of the threonine (1). In 1% tryptone,swarms produced by motile yet nonchemotactic cells movemuch more slowly and show less structure (2-4). The behavioris complex: swarming involves transport, metabolism, andgrowth, as well as motility in a quasi-rigid environment (5).Swarm plates have been used successfully to study genetransfer (6-8), to distinguish mutants defective for flagellation(6, 9-11) or flagellar function (12, 13), and to isolate a varietyof second-site suppressors (14-16). For a review ofearly workinvolving motility in semisolid media, see ref. 17.Chemotaxis in a fluid environment is well understood.

Cells drift up spatial gradients of attractants by executing abiased random walk. Runs (long, relatively straight segmentsof the walk) that happen to carry a cell up the gradient areextended; tumbles (short segments that give rise to nearlyrandom changes in direction) are not affected (18). Cells takerunning averages ofconcentrations: they compare the resultsobtained for the past second with those obtained for theprevious 3 seconds and respond to the difference (19, 20).For chemotaxis to serine, aspartate, maltose, dipeptides,

or ribose and galactose, the machinery required for thesechemotactic computations includes a specific membrane-spanning receptor (from the set Tsr, Tar, Tap, and Trg, alsocalled transducers or methyl-accepting chemotaxis proteins)and six cytoplasmic proteins (CheA, CheW, CheR, CheB,CheY, and CheZ). The receptor senses changes in theperiplasmic concentration ofan attractant or ofan attractant-binding protein. Four of the cytoplasmic proteins (CheA,CheW, CheY, and CheZ) relay information from the receptorto the flagella by a phosphorylation cascade (21). The othertwo cytoplasmic proteins (CheR and CheB) catalyze receptor

methylation and demethylation. Cells make temporal com-parisons between the recent and earlier past by comparingthe levels of receptor occupancy and receptor methylation.For recent reviews on bacterial chemotaxis, see refs. 22-24.We have reexamined the behavior of wild-type and mutant

cells in semisolid agar by measuring swarm rates and byobserving motion under the microscope. We conclude thatformation of the wild-type band structure requires the com-plete set of chemotaxis proteins listed above. Nonchemo-tactic cells that retain the ability to tumble as well as to runmigrate faster than cells that can only run. Cells of the lattertype tend to get trapped in the agar. For example, cheR cheBmutants, which run and tumble, swarm faster than mutantsthat only run, such as cheR mutants. However, they do notswarm faster than a number ofother nonchemotactic mutantsthat run and tumble.

MATERIALS AND METHODSChemicals. Bacto-agar (lot 763856) and Bacto-tryptone (lot

762166) were purchased from Difco. Ampicillin, isopropylP-D-thiogalactoside (IPTG), and maltose were purchasedfrom Sigma and streptomycin from Nutritional Biochemicals.Chemotaxis assays utilized synthetic amino acids: L-serinefrom K & K and sodium L-aspartate from ICN. Otherchemicals were reagent grade.

Bacteria and Bacteriophage. All strains were streptomycin-resistant derivatives of E. coli K-12 and are listed in Table 1.Generalized transductions used phage Plkc (30). PhageADFB19 carries cheY expressed by the lactose promoter(Plac) (31).Swarm Assays. Cells were grown to mid-exponential phase

at 31°C in broth composed of 1% tryptone and 0.5% sodiumchloride or in M63 minimal salts medium (32) containingglycerol (25 mM) and the amino acids required for growth:threonine, leucine, histidine, and methionine (20 ,ug/mleach). Tryptone swarm plates were 0.20-0.35% agar in broth(as above). Minimal swarm plates were 0.20o agar in M63minimal salts medium containing glycerol (25 mM) and theamino acids required for growth at concentrations (2 ,ug/mleach) well below the chemotactic thresholds observed incapillary assays (33). Synthetic amino acids were used asattractants to avoid responses to contaminants (33). Strep-tomycin (125 ,Ag/ml) was added to both the tryptone andminimal swarm plates to minimize contamination duringextended periods of incubation. IPTG was added to thevarious media, as required. A 5-1,u aliquot of the appropriateculture (106-107 cells) was placed on the surface of a swarmplate near its center, and the plate was incubated at 31°C ina humid environment (a closed box containing a dish ofwater). Duplicate plates were prepared to avoid artifacts dueto changes in temperature that might occur during handling.Once a plate had been removed from the incubator andexamined, it was discarded. The plates were illuminatedobliquely from below and viewed against a dark background.

Abbreviation: IPTG, isopropyl f3-D-thiogalactoside.

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Table 1. Bacterial strains used in this studyChemotaxis

Strain Relevant genotype genes present* Source

HCB294 A(tar-cheB)2234 tsr::TnS-la trg, cheAWYZ RP5723 x RP2896; KnrtHCB436 A(tsr)7021 A(trg)100 zbd::Tn5 cheAWYZ HCB294 x HCB433;

A(tar-cheB)2234 Eda+/Che-tHCB437 A(tsr)7021 A(trg)100 zbd::Tn5 None* Ref. 25

A(cheA-cheZ)2209HCB483 A(tsr)7021 A(trg)100 zbd::Tn5 Nonet Ref. 25

A(cheA-cheZ)2209 fliM(scyA3)HCB626 A(cheY)m60-21 (ADFB19) tsr, tar, trg, tap ADFB19 lysogen of

cheAWRBZ, Piac-cheY RP5232HCB627 HCB437 (ADFB19) Plac-cheYt Ref. 25RP437 Wild-type for chemotaxis All Ref. 26RP1091 A(cheA-cheZ)2209 tsr, trg* Ref. 27RP1273 A(tap-cheB)2241 tsr, tar, trg, cheAWYZ Ref. 28RP2896 A(tar-cheB)2234 tsr, trg, cheAWYZ Ref. 27RP5232 A(cheY)m60-21 tsr, tar, trg, tap, J. S. Parkinson§

cheAWRBZ*Out of the set tsr, tar, trg, tap, cheAWRBYZ.tP1 transduction (parents; relevant selection/screen).tPIus a gene fragment giving rise to two CheA-CheZ fusion proteins (29).§University of Utah, Salt Lake City.

Swarm radii were measured with a ruler. Some swarms werephotographed with Polaroid type 665 positive-negative film.

Microscopy. Swarm plates were also examined with aninverted phase-contrast microscope. Alternatively, plugs ofswarm agar were placed within a grease ring on a microscopeslide, compressed by a coverslip, and observed with anordinary phase-contrast microscope. In the latter case, somecells were squeezed out of the agar and swam in the culturefluid, while others remained within the agar matrix. Tetheredcells were prepared and their rotational behavior was ana-lyzed, as described previously (25, 34).

RESULTSSwarms of Wild-Type Cells. Wild-type cells (strain RP437)

formed concentric bands when inoculated at the center of atryptone swarm plate (Fig. la). Both the number ofbands andtheir displacement increased with time (Fig. 2a). The bandsfirst appeared about 2, 5.5, 6, and 7 hr after inoculation. Thefirst band was broader and traveled far ahead of the rest. Thisleft a large expanse of relatively cell-free medium between itand the second band. The migration rates of the bandsincreased with time, at least initially. This was particularlyclear for the first band, which attained a rate of about 0.8cm/hr after 7 hr (in 0.2% agar). Migration rates were gener-ally lower in harder agar, as shown for the first band in Fig.2b. However, no qualitative differences in the formation ofthe various bands were observed at different concentrationsof agar.

Wild-type cells also formed bands in minimal swarm platescontaining attractant, e.g., L-aspartate. The swarm morphol-ogies (Fig. 3 a-d) and the swarm rates (Fig. 4) depended

strongly on the concentration of the attractant. With 10 AML-aspartate (Fig. 3a) a single band formed with a sharp outeredge and a more diffuse inner edge; at 5 AM (Fig. 3b) twobands formed with similar morphologies; and at 1 ,M (Fig.3c) a faint diffuse outer band formed at the surface of the agarand a more sharply defined inner band formed within theagar. At concentrations of 0.1 ,uM or 1 mM, no bandsappeared and the swarm rates were close to the rate observedwithout attractant. The swarm rate peaked at about 10 ,uML-aspartate (Fig. 4 Inset).Swarms of Mutant Cells. Gutted cells. Most of the

nonchemotactic cells tested were derivatives of a null strain,called "gutted," in which genes for all of the transducers andcytoplasmic chemotaxis proteins were deleted (25). In tryp-tone swarm plates, the gutted cell (strain HCB437) producedan irregular growth pattern of high density (Fig. lb). Nobands were observed. The edge of this swarm moved out-ward at a rate about 2% of that of the first band of thewild-type swarm, as shown by the bottom line in Fig. 5. Cellsof this strain swim smoothly and rotate their flagella exclu-sively counterclockwise (25).Gutted cells with mutant switch components. Occasion-

ally, an arc-shaped band or "bleb" was formed by a group ofcells that traveled ahead of the other cells at the edge of aswarm of gutted cells (Fig. ic). In contrast to cells from theparent swarm, cells removed from the bleb ran and tumbled.Swarms produced by isolates obtained from these blebsmigrated faster than swarms of the parent cells, and theiredges were smooth (data not shown). Cells from blebs weretethered and their rotational behavior was analyzed. Theyexhibited ajerky bidirectional motion reminiscent of mutantsof fliM (formerly flaAII) and fliG (formerly flaBII). These

@0000FIG. 1. Photographs of swarms produced by cells of the wild-type strain (RP437) (a), the gutted strain (HCB437) (b), the gutted strain

(HCB437) showing a bleb (c), the gutted strain containing Plac-cheYinduced with 50,LM IPTG (d), and the methylation/demethylation-deficientstrain that expresses the transducers Tsr, Tar, and Trg (RP1273) (e). Cells were inoculated near the center of tryptone swarm plates containing0.20% agar and photographed after 7.5, 43, 50, 30.3, and 29.5 hr, respectively. The Petri plates were 8.5 cm in diameter; circular regions of eachare shown, 6.4 cm in diameter.

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FIG. 2. (a) Displacement (ra-dius) of bands of wild-type cells(RP437). Cells were inoculatednear the center of tryptone swarmplates containing 0.20% agar.Four bands appeared. (b) Radiusof the first (outermost) band ofwild-type cells (RP437). Cellswere inoculated near the center oftryptone swarm plates containingagar at a concentration of 0.20%O(), 0.25% (9), 0.30% (A), or0.35% (A). The standard errors ofthe mean displacements for dupli-cate plates were less than 0.1 cm.

genes are believed to code for components of the motor thatcontrol its direction of rotation (switch components; ref. 22).Preliminary mapping of these mutants indicated a map posi-tion close to those of fliM and fliG (data not shown). Aderivative of the gutted strain with a mutant flagellar motor(strain HCB483) produced swarms similar to those justdescribed (data not shown). This strain carries a fliM allelethat permits both clockwise and counterclockwise rotation ofits flagella.Gutted cells containing Che Y. In the gutted strain contain-

ing CheY (HCB627), expression of CheY is under control ofthe lactose promoter. The migration rate in tryptone platesfor cells of this strain increased with IPTG concentration, asshown by the dashed lines in Fig. 5. The fraction of time thattethered cells of this strain spun clockwise also increasedwith increasing IPTG concentration (Fig. 5 Inset). So did thefraction of time that cells tumbled, as judged by eye whencultures were viewed under the microscope. Thus, the swarmrate increases with tumble frequency. The swarm morphol-ogy was similar at all IPTG concentrations. The cells pro-duced an irregular growth pattern of moderate density.However, the leading edge of the swarm was complex: adiffuse pattern near the agar surface was superimposed upontwo narrow bands embedded in the agar (Fig. ld; compare tothe more compact swarm of the gutted strain, Fig. lb).

Cells with extreme clockwise bias. It is known the morethat cells spin their flagella clockwise the more frequentlythey tumble (35), up to a limit at which they are able to formright-handed flagellar bundles and swim smoothly (36). Westudied cells of a strain with an extreme clockwise bias(HCB626, induced with 200 AM IPTG). In tryptone plates,swarms of these cells were identical to those of the guttedstrain (HCB437, Fig. lb), except that they had a moreserrated outer edge. No bands were observed. In broth, most

b

of the cells tumbled incessantly, but some swam smoothly,albeit relatively slowly and along meandering paths. It wasevident that the latter cells had right-handed flagellar bun-dles, because they tended to travel in clockwise spirals alongthe under surface of the coverslip and in counterclockwisespirals along the upper surface of the slide-i.e., in a senseopposite to that observed with runs in wild-type cells. Whentethered, the cells spun clockwise nearly 100% of the time.

Cells deficient in methylation and demethylation. Cells ofstrains that express all of the cytoplasmic chemotaxis pro-teins except CheR and CheB and also express some of thetransducers-e.g., Trg (strain HCB294), Tsr and Trg (strainRP2896), or Tsr, Tar, and Trg (strain RP1273)-swarmed intryptone plates at rates in the same range as those of cells ofthe gutted strain containing CheY (HCB627). The larger thenumber of transducers, the greater the swarm rate and thelarger the fraction of time that tethered cells spun clockwise(Fig. 6). So here, also, it appears that the swarm rateincreases with tumble frequency. Swarms of these cells wererelatively homogeneous, and each had a narrow band at theleading edge. The larger the number of transducers the moreprominent the band. However, only one band was observed,even when both Tar and Tsr were present. The swarm forstrain RP1273 is shown in Fig. le. The appearance of thisband required the expression of both the cytoplasmic pro-teins CheA, CheW, CheY, and CheZ and some of thetransducers: a strain expressing CheA, CheW, CheY, andCheZ and no transducers (HCB436) or a strain expressingtransducers and no CheA, CheW, CheY, and CheZ (RP1091)produced swarms identical in size and morphology to thoseof the gutted strain (Fig. lb). However, the formation of theband did not appear to be due to chemotaxis. In minimalswarm plates that contained no attractant, methylation- anddemethylation-deficient cells containing Tsr, Tar, and Trg

d

FIG. 3. Photographs of swarms produced by cells of the wild-type strain (RP437) (a-d) or the methylation/demethylation-deficient strain thatexpresses Tsr, Tar, and Trg (RP1273) (e). Cells were inoculated near the center of minimal swarm plates containing 0.20o agar. The wild-typeswarms were photographed after 15 hr with L-aspartate at an initial concentration of 10 jutM (a), 5 AM (b), 1 ,M (c), or 0 (d). The swarm of strainRP1273 (e) was photographed after 17.5 hr with L-aspartate at an initial concentration of 10 ,uM. The photographs were cropped as in Fig. 1.

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FIG. 4. Displacement of the outermost edge of swarms ofwild-type cells (strain RP437). Cells were inoculated near the centerof minimal swarm plates containing 0.20o agar and L-aspartate at aconcentration of 0 (o), 0.1 ,uM (e), 1 ,uM (A), 5 jM (v), 10 AiM (v),50 AiM (v), 100 jiM (o), or 1 mM (m). The standard errors of the meandisplacements for duplicate plates were less than 0.1 cm. (Inset) Thedisplacement after 20 hr of the edge of these swarms as a function ofthe concentration of L-aspartate. No bands were found at 0.1 jiM or1 mM L-aspartate.

(strain RP1273) migrated at about half the rate of wild-typecells (data not shown). In contrast to wild-type cells, noincrease in migration rates was observed on the addition of

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,)3 Conenratin IPG pM) _ _ ,

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FIG. 5. Displacement of the edge of swarms produced by cellsof the gutted strain (HCB437, open circles) and of the gutted straincontaining Piac-cheY (HCB627, triangles) induced with variousamounts of IPTG. Cells were inoculated near the center of tryptoneswarm plates containing 0.20%o agar and IPTG at a concentration of0 (v), 50 jM (v), or 100 ,uM (v). The standard errors of the meandisplacements for duplicate plates were less than 0.1 cm. (Inset) Thefraction of time that cells of strain HCB627 spun clockwise whentethered, as a function of the concentration of IPTG.

U > H Trg9No. Transducers .01 .. r

----~~~~~ None

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FIG. 6. Displacement of the edge of swarms produced by cellsof methylation/demethylation-deficient strains that express thetransducers Tsr, Tar, and Trg (RP1273), Tar and Trg (RP2896), or Trg(HCB294) or no transducers (HCB436). Cells were inoculated nearthe center of tryptone swarm plates containing 0.20%o agar. Thestandard errors of the mean displacements for duplicate plates wereless than 0.1 cm. (Inset) The fraction oftime that cells spun clockwisewhen tethered, as a function of the number of different transducersexpressed.

attractants (aspartate at a wide range of concentrations orserine at 10 ,uM), nor were any bands formed (Fig. 3e). Cellsof the strain with no transducers (HCB436) migrated at halfthe rate of cells of the strain expressing Tsr, Tar, and Trg(RP1273). A bleb that arose from a swarm ofthe former strainafter about 24 hr migrated at a rate comparable to that of theswarm of the latter strain. A band formed at the edge of thebleb. These cells ran and tumbled, probably because of amutation affecting the flagellar switch components.Motion of Individual Cells. Agar (0.20-0.35%) observed by

phase-contrast microscopy appeared grainy or mottled, withinhomogeneities on a scale of a few micrometers. Cellsswimming in the agar behaved as if they were negotiating athree-dimensional maze. Wild-type cells (strain RP437) exe-cuted both runs and tumbles. Runs ranged from less than oneto several micrometers long. Sometimes a cell appeared toignore the agar, and other times it collided with the agar walls.When this happened, the cell appeared to idle: one could tellthat the flagellar bundle was still working because the cellbody continued to roll about an axis roughly parallel to itslong axis, but there was no translational movement. Asubsequent tumble reoriented the cell, which then swam offin a new direction. Thus, the cells migrated through the agarin a series of runs, stops (idles), and tumbles. Cells that couldrun and tumble-e.g., those of the gutted strain with defec-tive flagellar switch components (HCB483) or of the guttedstrain containing CheY (HCB627)-moved through the agarin a similar manner, except that they tumbled more and, thus,idled less than the wild-type cells. Cells that swam smooth-ly-e.g., those of the gutted strain (HCB437)-invariablycollided with the agar walls; no tumbles were observed.These cells were unable to reorient themselves efficiently andthus spent a large fraction of their time idling. Occasionally,such a cell would work its way free and continue to run, onlyto collide with a wall once again. These cells made little netprogress through the agar.

DISCUSSIONThe major conclusion of this work is that motile cells canmigrate through semisolid agar even though they are missingmany of the genes known to be required for chemoreceptionand chemotactic signal processing. The swarms for such cells

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vary markedly in size and in structure, depending on whetheror not their flagellar motors are able to spin both clockwiseand counterclockwise. In 1% tryptone, bands sometimesform at the leading edges of these swarms, but they do notappear to be due to responses to chemotactic stimuli, at leastto stimuli utilizing the methylation-dependent system. Re-sponses to sugars sensed by the sugar phosphotransferasesystem can be ruled out, because tryptone does not containcarbohydrates (37). Residual effects due to oxygen seemunlikely; Adler (1) was able to demonstrate bands due tooxygen in tubes containing soft agar but not in swarm plates.For mutant cells, plots of swarm size as a function of time

are approximately linear. This is not what one would expectfrom simple diffusion of a fixed number of cells. For diffu-sion, the root-mean-square displacement increases as thesquare root of the time (ref. 38, p. 10). Clearly, one is dealingwith growth as well as with diffusion. Evidently, diffusioncarries cells to nearby virgin territory, which is then popu-lated by cell division and growth.

In an isotropic, homogeneous medium, such as a diluteaqueous buffer, one expects the diffusion coefficient of abacterium to increase linearly with mean run duration, up toa limit set by rotational Brownian movement (ref. 38, pp.93-94). Thus, cells spread more effectively when tumbles arerare. In agar, we find the opposite result for nonchemotacticcells that rotate their flagella both clockwise and counter-clockwise: these cells spread more effectively when tumblesare frequent. The reason for this behavior is clear from themicroscopic observations: cells that do not tumble tend to gettrapped in the agar. However, the cells that tumble inces-santly also fail to spread effectively. Their diffusion coeffi-cient is small, with or without agar.

Cells in a swarm plate transport and metabolize chemicalattractants. As the cells grow and divide, attractants areconsumed and spatial gradients are formed. If the cells arechemotactic, they drift up these gradients at velocities thatallow them to outdistance cells swimming at random. Thedependence of drift velocity on tumble frequency was notdetermined. The attractants must be present at concentra-tions high enough to be sensed, yet low enough that amountsremaining after uptake do not saturate the receptors. Plots ofswarm size as a function oftime are concave upwards; swarmrates increase with time, at least initially. Here, too, dis-placement due to motility appears to be enhanced by celldivision and growth.There is nothing in our data to suggest that cheR cheB

mutants are chemotactic, as formerly supposed (39). Theswarm rates of these strains increase with tumble frequency,as do those of the derivatives of gutted cells. A strain deletedfor cheR and cheB that contains Tsr and Tar swarms in anidentical fashion on glycerol in the presence or absence ofaspartate or serine. Note that E. coli is not chemotactictoward glycerol (40); glycerol acts as a repellent, but only atrelatively high concentrations (41, 42). Thus, the fact thatcheR cheB pseudorevertants of cheR strains swarm fasterthan their parents (43) cannot be taken as evidence forchemotaxis; the double mutants can swarm faster simply byregaining the ability to tumble.

We thank M. M. Dahl and J. S. Parkinson for sharing with us theirknowledge of swarm plates and M. P. Conley, J. S. Parkinson, andB. A. D. Stocker for their comments on the manuscript. This workwas supported by Public Health Service Grant AI16478 from theNational Institute of Allergy and Infectious Diseases.

1. Adler, J. (1966) Science 153, 708-716.2. Armstrong, J. B., Adler, J. & Dahl, M. M. (1967) J. Bacteriol.

93, 390-398.

3. Armstrong, J. B. & Adler, J. (1969) Genetics 61, 61-66.4. Armstrong, J. B. & Adler, J. (1969) J. Bacteriol. 97, 156-161.5. Berg, H. C. & Turner, L. (1979) Nature (London) 278, 349-351.6. Stocker, B. A. D., Zinder, N. D. & Lederberg, J. (1953) J.

Gen. Microbiol. 9, 410-433.7. Stocker, B. A. D. (1956) J. Gen. Microbiol. 15, 575-598.8. Lederberg, J. (1956) Genetics 41, 845-871.9. Iino, T. (1962) J. Gen. Microbiol. 27, 167-175.

10. Enomoto, M. & Iino, T. (1963) J. Bacteriol. 86, 473-477.11. Joys, T. M. & Stocker, B. A. D. (1965) J. Gen. Microbiol. 41,

47-55.12. Enomoto, M. (1966) Genetics 54, 715-726.13. Armstrong, J. B. & Adler, J. (1967) Genetics 56, 363-373.14. Parkinson, J. S. & Parker, S. R. (1979) Proc. Natl. Acad. Sci.

USA 76, 2390-2394.15. Parkinson, J. S., Parker, S. R., Talbert, P. B. & Houts, S. E.

(1983) J. Bacteriol. 155, 265-274.16. Yamaguchi, S., Fujita, H., Ishihara, A., Aizawa, S.-I. &

Macnab, R. M. (1986) J. Bacteriol. 166, 187-193.17. Iino, T. & Enomoto, M. (1971) in Methods in Microbiology,

eds. Norris, J. R. & Robbins, D. W. (Academic, New York),Vol. SA, pp. 145-163.

18. Berg, H. C. & Brown, D. A. (1972) Nature (London) 239,500-504.

19. Segall, J. E., Block, S. M. & Berg, H. C. (1986) Proc. Natl.Acad. Sci. USA 83, 8987-8991.

20. Berg, H. C. (1988) Cold Spring Harbor Symp. Quant. Biol. 53,1-10.

21. Borkovich, K. A., Kaplan, N., Hess, J. F. & Simon, M. I.(1989) Proc. Nati. Acad. Sci. USA 86, 1208-1212.

22. Macnab, R. M. (1987) in Escherichia coli and Salmonellatyphimurium: Cellular and Molecular Biology, ed. Neidhart,F. C. (Am. Soc. Microbiol., Washington, DC), Vol. 1, pp.732-759.

23. Stewart, R. & Dahlquist, F. W. (1987) Chem. Rev. 87, 997-1025.

24. Parkinson, J. S. (1988) Cell 53, 1-2.25. Wolfe, A. J., Conley, M. P., Kramer, T. J. & Berg, H. C.

(1987) J. Bacteriol. 169, 1878-1885.26. Parkinson, J. S. (1978) J. Bacteriol. 135, 45-53.27. Parkinson, J. S. & Houts, S. E. (1982) J. Bacteriol. 151,

106-113.28. Sherris, D. & Parkinson, J. S. (1981) Proc. Natl. Acad. Sci.

USA 78, 6051-6055.29. Kuo, S. C. & Koshland, D. E., Jr. (1987) J. Bacteriol. 169,

1307-1314.30. Silhavy, T. J., Berman, M. L. & Enquist, L. W. (1984) Exper-

iments with Gene Fusions (Cold Spring Harbor Lab., ColdSpring Harbor, NY).

31. Wolfe, A. J., Conley, M. P. & Berg, H. C. (1988) Proc. Natl.Acad. Sci. USA 85, 6711-6715.

32. Miller, J. H. (1972) Experiments in Molecular Genetics (ColdSpring Harbor Lab., Cold Spring Harbor, NY).

33. Hedblom, M. L. & Adler, J. (1983) J. Bacteriol. 155, 1463-1466.

34. Berg, H. C., Block, S. M., Conley, M. P., Nathan, A. R.,Power, J. N. & Wolfe, A. J. (1987) Rev. Sci. Instrum. 58,418-423.

35. Larsen, S. H., Reader, R. W., Kort, E. N., Tso, W.-W. &Adler, J. (1974) Nature (London) 249, 74-77.

36. Khan, S., Macnab, R. M., Defranco, A. L. & Koshland, D. E.,Jr. (1978) Proc. Natl. Acad. Sci. USA 75, 4150-4154.

37. Difco (1984) Difco Manual: Dehydrated Culture Media andReagents for Microbiology (Difco Laboratories, Detroit, MI),10th Ed.

38. Berg, H. C. (1983) Random Walks in Biology (Princeton Univ.Press, Princeton, NJ).

39. Block, S. M., Segall, J. E. & Berg, H. C. (1982) Cell 31,215-226.

40. Adler, J. (1969) Science 166, 1588-1597.41. Oosawa, K. & Imae, Y. (1983) J. Bacteriol. 154, 104-112.42. Oosawa, K. & Imae, Y. (1984) J. Bacteriol. 157, 576-581.43. Stock, J., Borczuk, A., Chiou, F. & Burchenal, J. E. B. (1985)

Proc. Natl. Acad. Sci. USA 82, 8364-8368.

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