A new direct-viewing chemotaxis chamber

DANIEL ZICHA, GRAHAM A. DUNN* and ALASTAIR F. BROWN

MRC Muscle and Cell Motility Unit, Biophysics Section, King's College London, 26-29 Drury Lane, London WC2B 5RL, UK

* Author for correspondence

Summary

A new form of chamber for studying chemotaxis,similar in principle to the Zigmond chamber, allowsthe behaviour of the cells in a linear concentrationgradient to be observed directly. The chamber wasdeveloped mainly for studying chemotaxis in fibro-blasts using interferometric microscopy and themain design criteria were that it should have betteroptical characteristics, a higher dimensional pre-cision and better long-term stability than the Zig-mond chamber. It is made entirely from glass bygrinding a blind circular well centrally in thecounting platform of a Helber bacteria countingchamber. This procedure leaves an annular 'bridge',approximately lmm wide, between the new innercircular well and the original outer annular well.This bridge fulfils the same function as the linearbridge of the Zigmond chamber but the precise

construction of the counting chamber ensures that agap of 20 fim between bridge and coverslip can beaccurately and repeatedly achieved when thechamber is assembled. It is envisaged that theimproved optical clarity, dimensional accuracy andlong-term stability of the new chamber will beadvantageous in other applications, particularly instudies requiring critical microscopy or a preciseknowledge of the gradient and in studies of cells,such as fibroblasts, that move much more slowlythan neutrophils.

Key words: chemotaxis chamber, visual chemotaxis assay,neutrophil chemotaxis, fibroblast chemotaxis, cell orientation,diffusion theory, chemotactic gradient formation and decay,Helber bacteria counting chamber, FMLP, PDGF.

Introduction

The Boyden chamber has become established as theroutine method for studying chemotaxis in leucocytes(Boyden, 1962) and fibroblasts (Postlethwaite et al. 1976).While it is particularly advantageous for screening largenumbers of cells and putative chemotactic factors, it hasserious limitations for investigating the mechanism ofchemotaxis or even for confirming the occurrence ofchemotaxis. One problem is that the exact nature of theconcentration gradient is unknown: the cells themselvesmay severely modify their local gradient by obstructingthe pores in the filter membrane and the gradient aroundthe entrances and exits of the pores may be dependent onunknown flow conditions within the two wells. Anotherproblem is that the behaviour of the cells cannot beobserved but only deduced from their final distributionand this has led to some false claims of chemotaxis,although such deductions can be improved by using a fullcheckerboard analysis to take account of chemokinesis(Zigmond and Hirsch, 1973). Although the Boydenchamber is still useful as a convenient and sensitivemethod for identifying possible chemotactic responses,unequivocal confirmation of chemotaxis requires directobservation of the cells.

The currently available methods for directly observingchemotaxis include simply applying the cells and thesource of chemotactic factor to a slide and covering themwith a coverslip (Zigmond and Hirsch, 1973; Allan andWilkinson, 1978), the under agarose assay (Nelson et al.1975), and the Zigmond chamber (Zigmond, 1977). OfJournal of Cell Science 99, 769-775 (1991)Printed in Great Britain © The Company of Biologists Limited 1991

these methods, the Zigmond chamber has better opticalproperties than the under agarose assay and has theadvantage that the concentration gradient approaches alinear steady state whereas, with the other two methods,the gradient never reaches a steady state.

In Zigmond's description of the construction of herchamber, ' . . .a I"x3"xi" Plexiglass slide was cut to havetwo wells 1 mm deep and 4 mm wide separated by a 1-mmbridge. A 22 mmx40 mm coverslip over the bridge andwells was held firmly in place with a brass clip screwedinto the Plexiglass at each end' (Zigmond, 1977). Afterassembling the chamber and filling the wells with theappropriate solutions, Zigmond found that the layer offluid over the bridge was generally very thin and sherecommended that only those assembled chambers with agap over the bridge in the range 3-10 [an should be usedfor experiments. But predicting the decay of the gradientthat forms across this bridge requires knowing the exactdimensions of the chamber, particularly the critical gapbetween the bridge and the coverslip. This is by no meanseasy, since the gap over the bridge is not determined by thegeometry of the chamber but by factors such as flexure ofthe chamber, caused by the coverslip clamp springs, whichcannot be duplicated reliably. The range of gaps is so widethat each must be measured individually, not only at onepoint but all along the bridge, if the decay of the gradientis to be predicted. The theory of prediction becomesdifficult and unreliable if the gap varies along the bridgeor, even worse, if it varies with time.

While the Zigmond chamber has acceptable opticalproperties for uncritical forms of microscopy such as low-

769

power phase-contrast, its thickness of greater than 3 mmand construction from polymethyl methacrylate, which isa highly photoelastic polymer, render it unsuitable forcritical microscopy. In particular, for certain quantitativemethods of microscopy such as microinterferometry, it isnecessary to have the chamber made of an opticallyisotropic material, free from strain and with the opticalsurfaces worked to a high standard of flatness. Glass is anobvious choice but construction of a Zigmond chamberfrom glass is difficult, since, if strain must not be used tocreate the gap, the bridge must be optically polished tospecify an exact gap.

A new chamber designed by one of us (Dunn) circum-vents these problems by relying on the precise geometry ofa commercially made counting chamber to specify the gap.Being made of glass only 1 mm thick, this has ideal opticalproperties for microscopy. Further advantages accrue fromthe concentric layout of the bridge and wells, which makesthe chamber less prone to flexure, provides a more positiveseating for the coverslip and avoids the end effectsassociated with a linear bridge. The fact that the centralwell is completely "blind' in this design, rather than beingsealed with wax or left open as both wells are in theZigmond chamber, helps to prevent any forced flow overthe bridge even if the chamber is flexed; but this is at theexpense of not being able to change the medium in theinner well during an experiment.

Materials and methods

Modifying the chambersHelber bacteria counting chambers, type Z3, can be purchasedfrom the manufacturers: Weber Scientific International Ltd., 40Udney Park Road, Teddington, Middlesex, TW11 9BG, UK. Theunmodified chamber consists of a 1 mm thick microscope slidewith a 0.5 mm deep annular well ground into one face to leave acentral platform approximately 7.6 mm in diameter. The face ofthis central platform is optically polished so as to lie precisely20/on below the face of the slide and is ruled for countingpurposes. These precision chambers are generally useful forobserving the behaviour of living cells under ideal opticalconditions. For this they can be obtained without rulings (Z3

special unruled) but this is not necessary for the currentapplication, since the standard Thoma ruling is removedcompletely during modification of the chambers.

The modification consists of grinding a circular well centrally inthe counting platform to leave an annular Tjridge' approximately1 mm wide that fulfils the same function as the linear bridge of theZigmond chamber. In order to prevent chipping of the bridge edgeduring machining of the well, a circular coverslip of approxi-mately 8 mm diameter is cemented onto the central platformusing Glassbond (Loctite UK), a u.v.-curing methacrylate ad-hesive. The chamber is then accurately centred on a rotatingmachine table using a dial test indicator and clamped with cardpacking. The well is excavated to a depth of 0.5-0.6mm and adiameter of approximately 5.6 mm using a cylindrical sintereddiamond burr, 2 mm in diameter, mounted in a high-speedengraving machine with water as a coolant. Concentricity of thewell is ensured if the rotating table drive is used to feed the finalcut round the edge of the well. The coverslip is then removed bysoaking in acetone for an hour or two and the chamber is cleanedand sterilised ready for use.

The dimensions of the commercial chambers are variablebetween batches but we aimed to leave a bridge width ofapproximately 1 mm. Typical volumes for the inner and outerwells are 14/il and 30//I, respectively. The manufacturers arewilling to perform the modification but, unless a large batch isrequired, laboratories with workshop facilities will find it muchmore economical to make their own. Fig. 1 is a photograph of afinished chamber shown in comparison with an unmodifiedHelber chamber and a Zigmond chamber.

Setting up the chambersIn most applications, it is best to set up the chamber with theexperimental factor contained in the outer well. If the factor iscontained in the inner well, it is difficult to avoid subjecting thecells in the bridge region to the maximum concentration and thuspossibly saturating their receptors before the gradient becomesestablished.

The best way that we have found of setting up the chambers isfirst to fill both wells with control medium and then to cover thechamber with a 24 mm x 24 mm no. 3 coverslip carrying theadherent cells. The chamber should be entirely free from bubblesand the coverslip should be offset from centre in order to leave agap just large enough to admit a fine syringe needle at the edge ofthe outer well. The coverslip is then carefully pressed at thesupported edges, using a medical wipe to soak up surplus medium,until low-order interference fringes are visible round all the

Fig. 1. An example of a Zigmond chamber (top left), an unmodified Helber bacteria counting chamber (bottom left) and the newchemotaxis chamber (bottom right).

770 D. Zicha et al.

Fig. 2. Showing how the outer well of the chemotaxis chamberis filled with medium containing the experimental factor.

supported edges. The upper surface of the coverslip and chamberis washed and dried and the coverslip is sealed into place using ahot paraffin wax/beeswax/vaseline mixture (1:1:1, by wt) roundall the edges except for the gap. The outer well is then drained,using a piece of sterile filter paper, to leave the inner well and theregion over the bridge filled with medium and a meniscus aroundthe bridge. With a little practice, the outer well can now berefilled quickly and completely with medium containing theexperimental factor by directing a syringe tangentially as inFig. 2. If performed properly, the meniscus around the bridgeprotects the region over the bridge from becoming contaminatedwith the experimental factor during this procedure. Finally, thegap is sealed with the hot wax mixture and the chamber is readyfor microscopy.

Visualising the gradientThe formation and decay of the gradient were visualised using arhodamine B isothiocyanate-dextran 20S (Sigma R 9006)fluorescent dye of average molecular weight 17 200. Thismolecular weight was chosen to give a similar diffusion coefficientto that of human platelet-derived growth factor (11301), which weintend to use for studying fibroblast chemotaxis. Visualising thegradient in this way serves to check the efficacy of the chamber-filling procedure and to test the assumptions that the onlymechanism of mass transport in the 20 /an gap over the bridge isdiffusion, whereas convection currents keep the bulk contents ofthe two wells stirred.

The inner well was filled with control medium and the outerwell with medium containing approximately 1.5/igml"1 fluor-escent dye as described above. A sector of the bridge region wasexamined using a Zeiss (Oberkochen) IM35 inverted microscopeset up for rhodamine epifluorescence. The microscope stage wasmaintained at 37 °C by means of an air-curtain incubator, whichwas directed at the underside of the chamber in order to stimulateconvection in the wells. Image intensity was quantified using aSony CCD camera (set to gamma=l) with Peltier coolingattachment and frame integrator (Oggitronics Ltd) interfaced to aCompaq Deskpro 386/20 computer. The camera is very sensitiveLn the infrared region and extra infrared barrier filters wereneeded to reduce the background signal.

The short-term formation of the gradient was quantified at5min intervals from 5min to l h after setting up the chamber.Using a 6.3 x objective, each image of the bridge region wasintegrated over 16 video frames and then processed by subtract-ing a background image taken from a non-fluorescent region ofthe chamber. Fluorescence intensity as a function of positionacross the bridge was computed by averaging grey levels withinblocks of 19x60 pixels. A strip, 50 pixels wide, composed of 12adjacent blocks, spanned the bridge from the inner to outer wells.These intensity measurements were normalised to a maximumvalue of 100 and taken directly as measures of dye concentrationin arbitrary units.

Because of the poor long-term stability of the arc source, it wasnecessary to use a different protocol based on measuringintensities in the wells to study the long-term decay of thegradient. This was done in a separate experiment using a 2.5 x

objective to include a portion of each well in the image. At the endof the experiment, intensities obtained from the chamber filleduniformly with fluorescent dye at half concentration were used tocompensate for any difference in well depth. Fluctuations in lampbrightness were compensated by assuming that the total amountof fluorescent dye in the two wells of known volume is conserved.For the backgound subtraction we used the intensity of the innerwell at time zero and also compensated this for lamp fluctuations.Compensated intensities were taken as measures of dye concen-tration in the wells in arbitrary units.

Trial experiments with neutrophilsHuman peripheral blood neutrophils were isolated as describedby Forrester et al. (1983), except that acid citrate dextrose insteadof heparin was used as the anticoagulant. The isolated neutro-phils were resuspended in Hepes-buffered balanced salt solution(HBSS) containing 2 % foetal calf serum (Flow) and 10 000 cellscontained in this solution were allowed to settle on the centralregion of a 24mmx24mm no. 3 coverslip for 20min at roomtemperature. The chemotactic chamber was filled with HBSS andthe coverslip with adherent neutrophils was rinsed in HBSS andinverted onto the chamber as described above. The outer well wasthen drained and refilled with HBSS containing 4xlO~8MN-formylmethionylleucylphenylalanine (FMLP, Miles) and thechamber sealed with wax. Some chambers were maintained at37 °C on the stage of the Zeiss IM35 microscope equipped with a40 x oil-immersion apochromat and regions of the bridge werephotographed in phase-contrast 30min later. Others were usedfor time-lapse video recording on a Zeiss Standard microscopeequipped with a 10 x phase-contrast objective.

Results

Theory of formation and decay of the gradientOne advantage of precise and stable chamber dimensionsis that the establishment and decay of the gradient can beaccurately predicted for substances of known diffusioncoefficient. It is assumed that diffusion is the onlymechanism of mass transport in the bridge region whereasconvection currents keep the bulk contents of the two wellsstirred. The diffusion in the bridge region is thentheoretically equivalent to diffusion within the wall of ahollow circular cylinder and solutions for the steady andnon-steady states are given by Crank (1956). In the steadystate, the concentration as a function of distance, r, fromthe centre of the chamber is:

C W = ln(6/«) '

where C, and Co are the concentrations in the inner andouter wells, respectively, and a and b are the inner andouter radii of the bridge. Because the bridge is annular,this is not a strictly linear concentration gradient but isslightly convex if the higher concentration is in the outerwell. For the actual dimensions of the chamber, however,the deviation from linearity is very small.

If the inner well and the bridge region have initialconcentrations of zero, the concentration profile as afunction of time, t, for a molecule with a diffusioncoefficient, D, is given by:

C ( r f) _ CJn(r/a) " CoU0{ran) ^ _ t

where

Uoirctn) = JoircyJYo^bctJ - J0(ban)Y0(ran) (3)

and the an values are the positive roots of:

U0(aan) = 0 (4)

A new direct-viewing chemotaxis chamber 771

and Jo(x) and Yo(x) are Bessel functions of order zero of thefirst and second kinds, respectively.

Equation (2) is only valid if the concentrations in thetwo wells remain constant during time t. For the actualdimensions of the chamber, it is a very good approximationduring the approach to the steady-state condition, butestimating the long-term decay of the gradient requiresthat we take account of the flux across the bridge and thesubsequent changes in the concentrations of the wells.Since very little of the total material passes from the outerto the inner well during the approach to the steady state, itis adequate to consider only the steady-state flux. The fluxof diffusing substance, dQ/dt, from outer to inner wellthrough the gap of height h over the bridge is given by:

dQdt

2nhD(Co-Ci)(5)

\n(b/a)This equation can be written as a first-order differentialequation in terms of the steady-state gradient G(t)=(Co— CJ/(6—a) and solved to give:

~kDt, (6)

where:

k = (7)

and v, and v0 are the volumes of the inner and outer wells.The steady-state gradient therefore decays exponentiallyand the rate of decay can be characterised by the half-life\n(2)/kD. The constant k is determined by the geometry ofthe chamber and so it is only necessary to calculate thecharacteristic area, ln(2)/&, once for the chamber in orderto predict the half-life of the steady-state gradient of anysubstance of known diffusion coefficient.

Mathematica (Wolfram Research Inc., P.O. Box 6059,Champagne, IL 61826, USA), a computer algebra pro-gram, was used to find the first ten positive roots ofequation (4) for the values a=2.8mm, 6=3.9mm corre-sponding to the dimensions of one of the chambers.Equation (2) was then evaluated numerically for D=13.3xlO~6mm2s"1 at 12 points across the bridge and at5 min intervals for the period 5 min to 1 h. This value for Dwas chosen as the diffusion coefficient in water at 37 °C of atypical globular protein with a molecular weight of 17 200,which is the molecular weight of the fluorescent dye thatwe used to test the performance of the chamber. Thetheoretical evolution of the gradient profile during theperiod 5 min to 1 h is shown in Fig. 3. At the end of 1 h, thegradient has practically reached its steady-state profileand a slight convexity can be seen in the diagram.

The decay of the steady-state gradient was observedexperimentally in a chamber with slightly differentdimensions and so we used these dimensions (a=2.8mm,6=3.8 mm, u,-=14^1, uo=30jul, h=0.02mm) for the theor-etical prediction of gradient decay. The characteristic areaof this chamber is 16.08 mm2 and so the half-life of thegradient for a substance with D=13.3xlO~6mm2s~1 isapproximately 120 000 s or 33.6 h. Fig. 4 shows thetheoretical decay of the steady-state gradient over theperiod 1 to 96 h calculated from equations (1) and (6).

Provided that the chamber being used does not differvery much in dimensions from the above, Figs 3 and 4 canbe used to estimate the formation and decay of thegradient of any substance with known diffusion coef-ficient. It is only necessary to rescale the time axes so thatthe ratio of old to new times is the reciprocal of the ratio ofold to new diffusion coefficients. Thus, for a substance with

3.8

r (mm)

Fig. 3. Theoretical evolution of the gradient during theapproach to the steady state for a hypothetical chemotacticfactor with a diffusion coefficient of 13.3xlO~5mm2s~I.Concentration of the factor (C in arbitrary units) is shown as afunction of radial distance from the centre of the inner well (rin mm, the bridge extends from 2.8 to 3.9 mm) and timeelapsed since setting up the chamber (t in min) with all thefactor initially in the outer well. The evolution during the first5 min is not shown because the numerical approximationrapidly loses accuracy as time zero is approached.

100

Fig. 4. Theoretical decay of the steady-state gradient for ahypothetical chemotactic factor with a diffusion coefficient of13.3xlO~5mm2s~1. Concentration of the factor (C in arbitraryunits) is shown as a function of radial distance from the centreof the inner well (r in mm, the bridge extends from 2.8 to3.8 mm) and time elapsed since setting up the chamber (t in h)with all of the factor initially in the outer well. The approachto the steady state during the first hour, which is shown indetail in Fig. 3, is omitted from this figure.

a diffusion coefficient of 53.2x10" (i.e.4x13.3x10 ), Fig. 3 shows gradient formation duringthe period 75 s to 15 min and Fig. 4 shows gradient decayduring the period 15 min to 24 h. This diffusion coefficientis probably not very different from that of a chemotactictripeptide such as FMLP. If the diffusion coefficient isunknown but the substance is a rigid spherical molecule,

772 D. Zicha et al.

then D can be estimated from the molecular radius r,using:

kTD = (8)

6nnrm

where n is the viscosity of the solvent, k is the Boltzmanconstant (1.38x KT^JK"1) and T is the absolute tempera-ture. For a globular protein, rm may be estimated from themolecular weight M using:

rm = (3MJ/4jt7V)', (9)

where N is Avogadro's number and ~v, the partial specificvolume, is given as differing little from 0.730 for a widerange of proteins by Squire and Himmel (1979). Applyingthese two equations to FMLP (Af=437.6) gives an estimateofZ)=45.2xHr5

very reliable for such small peptides.mm2 s 1 although the method may not be

Formation and decay of the fluorescent dye gradientFig. 5 shows the formation of a gradient of the fluorescentdye during the first hour after setting up the chamber.This is very close to the predicted evolution of the gradientprofile in Fig. 3 except that the high end of the dyegradient takes approximately 20 min to reach the maxi-mum concentration. A likely explanation is that the dye inthe outer well takes some time to mix into the meniscusthat was left surrounding the bridge. The assumption ofrapid and thorough mixing by convection in the wells istherefore not entirely valid but the gradient neverthelessevolves as predicted after the first 20 min.

Fig. 6 shows the decay of the dye gradient during thefirst 4 days after setting up. As described in Materials andmethods, this is based on measurements of the intensitiesin the two wells and the gradient profiles in the figurehave been calculated using equation (1) on the assumptionthat the gradient is in a steady state after lh . Theobserved behaviour is again very close to the predictedbehaviour shown in Fig. 4 and this demonstrates that theassumption of mixing in the wells is valid in the long term.The observed flux allowed us to calculate an experimentalestimate of the diffusion coefficient using equation (5) and

t (min)

100

Fig. 5. Evolution of a gradient of the rhodamine/dextran dyeduring the approach to the steady state. Concentration of thedye (C in arbitrary units) is shown as a function of radialdistance from the centre of the inner well (r in mm, the bridgeextends from 2 8 to 3.9 mm) and time elapsed since setting upthe chamber (t in min) with all of the dye initially in the outerwell.

3.2r (mm)

Fig. 6. Decay of a gradient of the rhodamine/dextran dye.Concentration of the dye (C in arbitrary units) is shown as afunction of radial distance from the centre of the inner well(r in mm, the bridge extends from 2.8 to 3.8 mm) and timeelapsed since setting up the chamber (t in h) with all the dyeinitially in the outer well. This figure is based onmeasurements of the concentrations in the inner and outerwells and the gradient profile is calculated theoretically.

this turned out to be 11.0x10 5mm2s 1 compared withthe theoretical value of 13.3xl0-Bmm2s~1 based on themolecular weight of the dye. This small discrepancy can beexplained by any hydration or lack of sphericity of themolecule or a slightly different partial specific volumefrom the one that we assumed.

To summarise the performance of the chamber, a proteinwith a molecular weight of the order of 10 000 to 20 000will form a close approximation to a linear gradient withinabout 30 min of setting up the chamber and the half-life ofthe gradient (i.e. the time for its slope value to halve) willbe about 30 h whereas a peptide of molecular weight350-750 will form a linear gradient within 10 min anddecay to half its initial value in 10 h. The times of gradientformation and decay are approximately proportional to thecube root of the molecular weight of the substance.

Neutrophil chemotaxis to FMLP in the chamberFig. 7 shows several neutrophils close to the outer edge ofthe bridge 30 min after setting up the chamber with4 X 1 0 ~ 8 M FMLP in the outer well and control medium inthe inner well. In a cursory examination we found morethan half of the total number of non-rounded cells in thebridge region to be oriented in the up-gradient directionquadrant (only 25 % would be expected in this quadrant onthe hypothesis of random orientation). But, since chemo-taxis is more properly defined in terms of the motilityrather than the orientation of cells, we decided on adynamic analysis of cell displacements in order toestablish whether chemotaxis occurs in the new chamber.

Fig. 8 is a vector scatter diagram of the displacements of22 motile neutrophils (from a total sample of 50 of which28 were non-motile) taken from a time-lapse videorecording during the l h period from 30 to 90min aftersetting up a gradient of FMLP as before. The displace-ments are oriented and translated so that each dot in thediagram represents where a cell would be after 90 min if ithad started at the origin at 30 min and the gradient hadbeen directed vertically upwards through the origin. The

A new direct-viewing chemotaxis chamber 773

Fig. 7. Several neutrophils close to the outer edge of thebridge (which can just be seen in the upper left) in a gradientof FMLP 30min after filling the outer well with 4xl(T8MFMLP. Zeiss 40 x phase-contrast apochromat. All the non-rounded neutrophils can be seen to be oriented approximatelyin the direction of the gradient. Bar, 50 /an. Direction ofgradient is indicated by arrow.

+ represents the vector mean migration and it is clear thatthe large majority of cells have tended to migrate in theup-gradient direction. Even in such a small sample, thesignificance of this tendency to migrate up-gradient isvery high and the results of two-tailed i-tests on X- andY-components are given in the figure legend. Only one ofthe 22 motile cells shows a displacement down thegradient and similarly high significance levels wereobtained using the non-parametric Signs test and Wil-coxon signed rank test.

Discussion

The optical properties of the new chamber are close tothose of the ideal microscope slide/coverslip combinationand permit practically all forms of light microscopy. Invery critical work such as microinterferometry (Brownand Dunn, 1989), it may be found that the slightly turneddown edge at the outer rim of the bridge, which is left bythe manufacturer's polishing procedure, needs to beremoved during the modification of the chamber. As with ahaemocytometer, the coverslip needs to be rigid in order tobenefit from the precision of the chamber and we find itbest to use a no. 3 (0.25-0.35 mm thick). This dictates thathigh-power, non-immersion objectives with a fixedcompensation for the standard no. l i coverslips(0.16—0.18 mm) should not be used for critical work.

It is apparent from our fluorescent dye experiments that

200-

100;

-200 -100 100 200

-100

-200

Fig. 8. Vector scatter diagram of displacements of 22 motileneutrophils (from a total sample of 50) during the 1 h periodfrom 30 to 90min after setting up a gradient of FMLP as inFig. 7. Direction of gradient is vertically upwards. Meandisplacement is indicated by + and the mean y-component issignificantly greater than zero at the 0.001% level (two-tailedi-test: *=5.89, d.f.=21, 0.000001<P<0.00001) indicating ahighly significant positive chemotaxis. As a control, the meanre-component was tested and found to be insignificantlydifferent from zero ( £=0.89, d.f. = 21, 0.3<P<0.4).

the gradient in the new chamber can be predicted quitereliably from diffusion theory. This is in contrast toZigmond's experiences with her chamber using fluoresceinisothiocyanate to visualise the decay of the gradient(Zigmond, 1977). In Figure 2 of her paper, the fluoresceingradient at room temperature appears to have reached itsmaximal value after 15min and to have fallen to abouthalf its maximal value after 105 min. She comments that,'Variations among experiments indicated that it was notpossible to predict the exact shape of the gradient at anygiven time; nevertheless, between 30 and 90 min thegradients were usually steep and stable'. This rapid decayof the gradient is remarkable, since basic diffusion theorypredicts that the half-life of the gradient should be at least40h! The volume of each well is 100 /.tl and initially the twowells contain lOnmol and lnmol. The bridge is 25 mmlong by 1 mm wide and, for the maximum recommendedgap of 10 /an, the maximum flux across the bridge shouldbe no more than 0.05 nmol h"1 for a molecule of about400 Mr such as fluorescein isothiocyanate. Even if thisinitial maximum flux were to continue indefinitely insteadof decaying as the gradient decays, only 2 nmol would havepassed over the bridge in 40h: the first well would stillcontain 8 nmol and the second well would contain 3 nmol.

Reliable prediction and long-term stability were notessential for the excellent work on the mechanism ofleucocyte chemotaxis done by Zigmond and others usingthe Zigmond chamber but they are necessary in otherareas of research. Our chamber was designed for studyingchemotaxis in fibroblasts and long-term stability of thegradient is essential for this, since these cells move muchmore slowly than neutrophils, often moving much lessthan their own length during one hour. Being able topredict the gradient accurately also opens up new areas ofstudy on the mechanism of neutrophil chemotaxis,

774 D. Zicha et al.

particularly with regard to such important and contro-versial issues as whether a stable gradient can evokechemotaxis in neutrophils (Vicker et al. 1986). For thesereasons we tried to determine the potential sources ofunpredictability in the Zigmond chamber and to takeparticular precautions to eliminate them from the newdesign and mode of operation.

Small or transient convective flows in the gap over thebridge would distort or destroy the gradient and it seemsfrom Figure 2 in Zigmond's paper that some distortion aswell as decay of the gradient has occurred after 105 min.Boundary layer theory dictates that it is unlikely thatthermal convection currents occur in the narrow gap overthe bridge but convective flow could arise for a variety ofmechanical reasons. Bulk flow across the bridge of theZigmond chamber could arise simply by drainage if theends of the wells are left open and the chamber is not keptperfectly horizontal. Even sealing the wells with wax maynot entirely eliminate this problem, since wax is not verystable mechanically and a change of only 0.25 % in thevolumes of the wells could completely destroy the gradientover the bridge. The new chamber avoids these problemsby relying on the blindness of the inner well and theincompressibility of medium to prevent bulk flow acrossthe bridge. Only one well need be blind for this and so itdoes not matter that the outer well is sealed with wax. Butit is important to guard against trapping bubbles in thechamber, particularly in the inner well, since the contentsof the inner well would not be incompressible if bubbleswere included.

Small changes in the gap height could also havedramatic (but temporary) effects on the profile of thegradient by causing surges of medium to and from the gapregion. These changes could result from thermal expan-sion and contraction of any bubbles trapped in a sealedchamber. They could also arise from flexion of the chamberresulting from differential thermal expansion or mechan-ical creep, or from handling. Our chamber is likely to beless susceptible to these changes because it has a largergap than the Zigmond chamber. Nevertheless, it isdesigned to avoid differential thermal expansion by usingglass throughout and to avoid mechanical creep by notusing spring clips or similar devices that subject thechamber to continual stress. We find that it maintains theplane of focus much better than a Zigmond chamber,which is evidence that we have succeeded in improving themechanical stability.

We investigated the susceptibility to handling of the twotypes of chamber by assembling them without mediumand viewing a diffuse monochromatic light source re-flected from their upper surfaces. A shift of one fringewidth in the interference fringes observable over thebridge indicates a change in the gap of about 0.27 ^m.Even gentle handling of the Zigmond chamber, such aslifting the horizontal chamber by one end, resulted in achange in gap of 0.5 j/m. With the chamber supported at itsends, light finger pressure near the coverslip could resultin a change of 2/.cm or more. Gentle handling couldtherefore be sufficient to distort the gradient significantly,especially if the initial gap is set as low as 3 [im. No effectwas noticeable when applying the same treatments to ourchamber. Even so, any procedure that applies considerablestress to the chamber, such as using strong spring clips toclamp it to a microscope stage, should be avoided.

Another possible explanation of the rapid decay of thegradient that Zigmond observed is that the ambientthermal conditions in her experiments were such that the

wells were not continually being mixed by convectioncurrents. This seems unlikely, since she remarks that, ifthe chamber is set up with Trypan Blue (961 Mr) in onewell and water in the other, a difference in concentrationbetween the two wells is still noticeable after 72 h at roomtemperature. If there were no mixing in the wells, thedifference in concentration would be more than justnoticeable, it would be almost unchanged except near thebridge after 72 h. Yet it is clearly important to be sure thatmixing is occurring in the wells of either type of chamberand, in our experiments, we directed the air flow of theincubator towards the lower surface of our chamber inorder to encourage convection. Our observations indicated,however, that mixing will occur even without taking suchprecautions.

In our preliminary experiments with neutrophils andFMLP in the new chamber, we found levels of orientationconsistent with Zigmond's observations (Zigmond, 1977).Our analysis of cell displacements leaves no doubt thatchemotaxis can occur in the new chamber and ourtheoretical and experimental analysis of gradient forma-tion in the chamber strongly suggests that the gradientwas practically linear and stable during the period ofobserving displacements. This analysis would seem,therefore, to present evidence against the controversialassertion that a stable spatial gradient of FMLP will notinduce chemotaxis in neutrophils (Vicker et al. 1986) butthere is also the possibility that the rapidly changinggradient during the first 10 min could still influence thecells over the period 30 to 90 min. This delayed effectmight conceivably arise from a persistence in cell motilityor in receptor occupancy. Further experiments with thenew chamber and a detailed dynamic analysis will beneeded to decide this issue.

Daniel Zicha is supported by a Wellcome Trust Fellowship.Graham Dunn and Alastair Brown are members of staff of theMedical Research Council.

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(Received IS March 1991 - Accepted 19 April 1991)

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