Escherichia coli as a model active colloid: a practical introduction

Jana Schwarz-Linek∗, Jochen Arlt∗, Alys Jepson∗, Angela Dawson∗, Teun Vissers∗, Dario Miroli∗†,Teuta Pilizota†, Vincent A. Martinez∗(‡) and Wilson C. K. Poon∗(‖)

∗SUPA and School of Physics & Astronomy, The University of Edinburgh, James Clerk Maxwell Building, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK, and†School of Biological Sciences, Darwin Building, Max Born Crescent, Edinburgh EH9 3BF, UK. (‡)vincent.martinez@ed.ac.uk, (‖)w.poon@ed.ac.uk

Abstract

The flagellated bacterium Escherichia coli is increasingly used experimentally as a self-propelled swimmer. To obtain meaningful,quantitative results that are comparable between different laboratories, reproducible protocols are needed to control, ‘tune’ andmonitor the swimming behaviour of these motile cells. We critically review the knowledge needed to do so, explain methods forcharacterising the colloidal and motile properties of E. coli cells, and propose a protocol for keeping them swimming at constantspeed at finite bulk concentrations. In the process of establishing this protocol, we use motility as a high-throughput probe ofaspects of cellular physiology via the coupling between swimming speed and the proton motive force.

Keywords:Escherichia coli, active colloids, motility, differential dynamic microscopy, metabolism, bioenergetics, proton motive force

Some time ago, our lab wanted to culture motile bacteria as‘model active colloids’. We obtained a strain of Escherichiacoli with the full complement of motility genes and a cultur-ing protocol from a local microbiologist. For some time, wethought we were experimenting with motile E. coli, until oneday we checked in the microscope. Few, if any, of the cells wereswimming! So we set out to learn how to modify the standardprotocol to optimise motility by collating literature, talking toother researchers and trial and error; we also implemented dif-ferential dynamic microscopy (DDM) to quantify motility.

This article reviews what we have learnt. Some of the ma-terial is previously known, but seldom critically discussed inone place. We have explained some basic bacterial bioener-getics and genetics, because physical scientists can use E. coliand collaborate with biologists more effectively if these top-ics are understood. Much of the materials is new, arising fromusing DDM to quantify motility. While we aim primarily at re-searchers working on active colloids [1], this article should alsobe useful to others studying motility biophysics [2].

From the outset, we refer to various culture media (BMB,TB, LB) and protocols, and freely use terminology related tomolecular biology (plasmid, gene names, etc.) and measure-ment techniques (OD, DDM, etc.). Readers should refer to Sec-tion 5 on matters of cell culture, Sections 3 and 4 for methodol-ogy, and Section 10 and Appendix C for biological jargon. Wealso provide a table of symbols in Appendix F.

1. E. coli as a model active colloid

An ‘active colloid’ [1] is a suspension of ≈ 5 nm-5 µm par-ticles that consume ‘fuel’ to propel themselves, such as motilebacteria or various synthetic ‘colloidal swimmers’ [3, 4]. Ac-

tive colloids are out of thermal equilibrium even without exter-nal driving. Unusual phenomena displayed by such systems,such as ‘negative viscosity increment’ [5] and ‘rectification’[6], pose a ‘grand challenge’ to statistical mechanics [7, 8]. Theself assembly of active colloids, possibly mixed with passiveparticles, may provide routes to new ‘smart materials’ [9].

Progress in this new area will be greatly facilitated by exper-imental data from ‘model systems’ that can most ‘cleanly’ con-front theory and simulations. Historically, well-characterisedmodel passive colloids have enabled progress at critical points,from sedimentation equilibrium [10, 11] to hard-sphere crys-tallisation [12] and sticky-sphere glass transitions [13]. Theminimal requirements for a ‘model passive colloid’ includereproducible synthesis/preparation, known particle size/shapedistributions, quantifiable and ‘tuneable’ interparticle interac-tions and accurate particle volume fractions [14, 15, 16, 17].For model active colloids, we also need propulsion mechanismsthat are understood and ‘tuneable’, and knowledge of motility-specific interparticle interactions, e.g., via hydrodynamics. Bythese criteria, there is as yet no ideal model active colloid.

Escherichia coli is widely used in active colloids research.Its self propulsion is understood in essence [18, 19, 20], whilepropulsion mechanisms in many synthetic swimmers are stilldebated [21, 22]. However, for E. coli to become a fully-fledged model, reproducibility, control and characterisationneed to be improved. We address these issues in this article.

2. E. coli as a bacterium

Escherichia coli [23] is the best understood living organismon earth today. It is often the model of choice for understandingmolecular biological processes: ‘Tout ce qui est vrai pour leColibacille est vrai pour l’elephant.’ [24]

Preprint submitted to Colloids and Surfaces B June 16, 2015

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Table 1: Average length and standard deviation of 30 cell bodies of E. coliAB1157 grown in LB/TB at 30 C/37 C to late-exponential (OD = 0.5) or sta-tionary (16 hours growth) phase. Note that these cells have not been washed inBMB. Washing, however, makes little difference.

LB30,stat TB30,stat LB37,stat TB37,statl (µm) 1.7 1.5 1.6 1.7δl (µm) 0.4 0.3 0.3 0.5δl/l 0.24 0.2 0.19 0.29

LB30,0.5 TB30,0.5 LB37,0.5 TB37,0.5l (µm) 4.4 2.3 4.4 2.4δl (µm) 1.2 0.6 1.0 0.6δl/l 0.27 0.26 0.23 0.25

The cytoplasm of E. coli is enclosed by two lipid bilayermembranes. Between them is a peptidoglycan ‘cell wall’(or ‘periplasmic space’), a network of poly-sugars (‘glycans’)linked by short peptides. Within the species known as E. colithere are many genetic variants, or ‘strains’ (so that ‘bacterialspecies’ is a problematic concept [25]). The genome of strainMG1655 was first to be sequenced [26]; today, the genome of2085 strains are available in GenBank [27], although & 30% ofthe genes remain of unknown function. The best single sourceof information on E. coli (and its close relative Salmonella) isa two-volume ‘bible’ [28] now updated digitally [29].

Each cell carries multiple helical flagella [30, 31] powered byrotary motors [2, 18] embedded in the membranes and cell wall[32]. When all flagella rotate counterclockwise (CCW) (viewedfrom behind), they bundle to propel the cell forward. Whena motor reverses to clockwise (CW), its flagellum unbundlesand the cell tumbles. Wild-type (WT) cells run (≈ 1 s), tumble(≈ 0.1 s), and run, the latter in a direction that is more or less un-correlated with the run before the tumble [33]. When successivesensings of the environment return an increasing concentrationof an ‘attractant’, intracellular signals reduce the rate of CCW→ CW→ CCW switching (i.e. the tumbling rate). This biasedrandom walk up an attractant gradient constitutes chemotaxis.

A number of E. coli strains used for active colloids and re-lated research are listed in Table B.2, Appendix B. Many ofthese were derived from K-12, a ‘debilitated’ laboratory strain[34, 35] that does not normally infect humans. It is deemed safefor laboratory use and classified as a category 1 biohazard [36].Mutants in which one or more key chemotaxis genes have beendeleted, e.g. ∆cheY, lose the ability to tumble. These ‘smoothswimmers’ simply swim forward, with a persistence time setby their inverse rotational diffusivity D−1

r = 2πηLσ2/kBT ≈ 5 s,where we have modelled a cell body with its flagella bundle asan ellipsoid of major and minor axes L ≈ 10 µm and σ ≈ 1 µm.

3. E. coli as a colloid

The cell body of an E. coli bacterium is a net negativelycharged spherocylinder (diameter σ, pole-to-pole length l).1

1For physicochemical ‘vital statistics’ of E. coli, see [37, 38, 39]

Figure 1: Visualisation of both body and flagella bundle of swimming E. colifrom a real-time movie. Flagella are fluorescently labelled using Alexa546and the body with a plasmid expressing GFP (AD1 pHC60, Table B.2). Us-ing epi-fluorescence microscopy these can be imaged into separate channelsat high enough frame rates to avoid motion blurr. Image part of a 100 fpsmovie acquired using an Orca Flash 4.0 camera on a Nikon Ti microscope withPA60x/1.4 OIL objective using a Cairn Optosplit II.

For mostly unknown reasons [40, 41], bacterial shapes arehighly conserved:2 shape mutations tend to be lethal. In thissection, we review the single-particle ‘colloidal’ properties ofE. coli and how to estimate cell concentrations.

3.1. Shape and size3.1.1. Microscopy

The shape and size of E. coli cell bodies can be obtained us-ing microscopy and scattering (compared in [43]). Measuringcell bodies using phase-contrast microscopy of strain AB1157harvested using our standard protocol and washed into BMBgave 〈l〉 = 2.4 ± 0.6µm, where the uncertainty is a polydis-persity. At mid-cell, 〈σ〉 = 0.86 ± 0.07µm, where the uncer-tainty represents measurement errors. Importantly, these ‘vitalstatistics’ depend on strain, growth conditions and the time ofharvest, Table 1. Time of harvest is important because bac-teria grow in well defined stages: from rapid division in anexponential phase (cell number density n grows exponentiallywith time), through a stationary phase (n = constant), to a deathphase (n decreases with time). Our data show that stationary-phase cells tend to be less polydisperse in length than mid-exponential cells, as found previously [44]. There may alsobe some dependence of σ on l [45].

It is often desirable to visualise the flagella bundle, because itrenders the cell highly anisotropic and introduces strong stericeffects [46, 47]. If the cell body and flagella are labelled withthe same dye [48, 49], fluorescence from the former will dom-inate. To visualise the flagella alone, the fliC gene3 can be mu-tated to facilitate binding to Alexa Fluor C5 maleimide (e.g.,Alexa546) [50]. If cells carry GFP-plasmid pHC60 (Table B.2),then the cell body and flagella can visualised simultaneously,Fig. 1. Note that such mutants should always be checked forpotential changes to their motility and other phenotypes.

3.1.2. ScatteringCell shape and size can also be studied by static light scatter-

ing (SLS) either averaged over cell populations [51, 52, 53, 54,

2It is possible to turn bacteria into silica colloids [42], opening up a novelroute to synthetic colloids with many shapes [40].

3This encodes flagellin, the protein units used to build up flagella filament.

2

55, 56] or individually in flow cytometry [57]. Given informa-tion on the refractive index [58], models can fitted to scatteringdata. Typically, an E. coli cell with cytoplasm surrounded bya cell wall is modelled as a core-shell ellipsoid [51, 59, 60],giving interference fringes that survive polydispersity in l be-cause there is very little variation in either σ or periplasm thick-ness [52, 61]. How optical inhomogeneities due to the chromo-some affect dynamic light scattering, which can also give in-formation on size and shape, has been studied [62]. Polarisedscattering gives extra information [63, 64].

3.2. Sedimentation

The (mass) density of E. coli cells, 1.08 . ρ . 1.16 g cm−3,depends on media and conditions [65, 66, 67]. The density dif-ference with the solvent, ∆ρ . 0.1 g cm−3, causes cells to sedi-ment. The distribution of particles in a suspension in sedimen-tation equilibrium defines the colloidal length scale [16]. In thisdynamic equilibrium, concentration-driven diffusive flux fromthe bottom is balanced by a sedimentation flux from the top, sothat when the suspension is dilute enough to neglect interparti-cle interactions, the number density profile with height is

n(z) = n(0)e−z/`g , (1)

where the gravitational height `g is given by

`g =D0

vs. (2)

Here, D0 is the free-particle diffusivity, and vs is the single-particle sedimentation speed. A colloid is suspendable againstgravity, so that `g has to be larger than its characteristic size.

The friction coefficient for motion parallel to the long axis ofa prolate ellipsoid with major and minor axes l and σ is [68]

ξ‖ =2πηl

ln(

2lσ

)− 1

2

, (3)

where η is the solvent viscosity. For E. coli in typical motilityexperiments, l/σ ≈ 2 to 3, so that ξ‖ ≈ 2πηl, from which

vs ≈∆ρgσ2

12η. (4)

Translational diffusion along the long axis is governed by

D‖ =kBTξ‖

, (5)

so that the gravitational height of a non-motile cell is

`(coli)g ≈

6kBT

πσ2l∆ρg≈ 4 µm ≈ 2l. (6)

Thus, the cell body of non-motile E. coli is just colloidal.Motile E. coli should have significantly higher `g [69]; andmotility coupled with growth can display rich phenomena [70].

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Figure 2: Fraction of bacteria sticking to the lower capillary wall in a ≈ 4 cellwidth layer at different concentrations of TWEEN 20 surfactant in BMB with0.72 mM glucose for WT AB1157 at ≈ 6 × 107 cells/ml. Points are averagesover 0−30 minutes, 30−60 minutes and 60−90 minutes after loading. Arrows:adhering fractions with no surfactant.

3.3. Interactions: stability and surface adhesion

The surface properties of E. coli [71, 72, 73] are strain de-pendent [74]. Interpreting electrophoretic mobilities (µ) is non-trivial because surface macromolecules [72, 74, 73] and theperiplasm are ion-permeable. Even with a ‘soft’ electrokinetictheory allowing for this [75, 76], relating µ to zeta potentialsand surface structures is fraught.

Nevertheless, E. coli definitely carries a net negative chargeunder physiological conditions (−3 . µ . −2µm cm V−1 s−1)largely due to ionised carboxylate and phosphate groups [74,71]. This charge is normally sufficient to confer colloidal stabil-ity in growth media or in BMB.4 However, a strain that has be-haved stably for many months may suddenly start aggregatingdue to ‘phase variation’ in the expression of the surface proteinAg43 (antigen 43) [77]. Each generation, there is an O(10−3)probability that a cell switches between ‘on’ and ‘off’ states ofAg43 expression. ‘On’ renders cells ‘sticky’ and leads to ‘au-toaggregation’. The expression state is heritable and reversible.

For active colloids work using E. coli close to surfaces [78,79, 80, 81], it is important to minimise adhesion, which is farfrom understood. Various non-ionic surfactants prevent E. colifrom sticking to untreated glass [48, 81]. Figure 2 quantifiesthis effect for a popular surfactant used for this purpose.

We imaged AB1157 cells in BMB within an optical sliceof ≈ 4 cell width next to the bottom surface of an untreatedglass capillary using a Mikrotron MC1362 camera and a NikonTi microscope with 60× phase contrast objective (PF60×/0.7).Automated software for identifying [82] and tracking rods wasused to analyse movies, classifying cells into ‘free’ (diffus-ing or swimming) and ‘adhering’ (stuck). The average frac-tion of adhering cells, extracted from many movies, droppedabruptly to & 0 at a TWEEN 20 concentration of ≈ 10−2 wt.%.Note that concentrations up to 0.2% have been used previously[81]. Preliminary DDM data suggest that commercial TWEENmay contain impurities rapidly metabolisable by E. coli, so that

4The screening length in BMB is . 1 nm.

3

high enough concentrations of TWEEN may significantly alterswimming behaviour.

3.4. Cell concentration

The definition of cell concentration and its determination arenon-trivial. The cell body volume fraction, φ, gives a better in-tuitive feel for the degree of ‘crowding’ than the number densityof cells, n. The effective volume fraction, which takes into ac-count the cell consists (body length l) and flagella bundle withtotal length L . 10 µm is φeff ∼ (L/l)3φ & 102φ if the cells arerandomly oriented, so that they reach ‘overlap’ at φ . 0.01.

The standard way to obtain n is from the spectrophotometricoptical density (OD) of cell suspensions, which is proportionalto n for n . 109cells/ml (corresponding to φeff ≈ 0.2).5 Cali-bration is by ‘viable plate counting’ (Section 5.3), and is foundto depend on growth stage and other conditions.

4. Characterising E. coli motility

We turn next to characterising E. coli as self-propelled par-ticles. The average swimming speed, v, and the fraction, β, ofnon-swimmers that only diffuse,6 can be measured using a high-throughput technique, differential dynamic microscopy (DDM)[84, 85, 86]. Application to swimming algae [86] and passivemagnetic rods [87] can be found elsewhere. Here we focus onpractical aspects of using DDM to characterise motile E. coli.

We take a low-magnification movie of a cell population, andcalculate the squared modulus of the Fourier transform (F.T.,reciprocal vector q) of the difference of two images separatedby τ in time, and averaged over starting times:

g(q, τ) =

⟨∣∣∣F.T.[I(x, y; t + τ) − I(x, y; t)

]∣∣∣2⟩ . (7)

If the image intensity I(x, y; t) at pixel position (x, y) at time t islinearly related to the cell density at the corresponding sampleposition and time, then g(q, τ) is directly related to the density-density time correlation function, f (q, τ), of the system, withq = |q| ∼ 2π(image size)−1 to π(pixel size)−1 being experimen-tally accessible. Indeed, under appropriate conditions,

g(q, τ) = A(q)[1 − f (q, τ)

]+ B(q), (8)

Sometimes called the normalised dynamic structure factor orintermediate scattering function (ISF), f (q, τ) is in principle(but not in practice [85]) also measurably by dynamic light scat-tering. We assume isotropy, so that g and f only depend on q.In Eq. 8, A(q) is related to the form and (static) structure factorsof the bacterial suspension, and B(q) is instrument noise.

The ISF can be modelled once we know how cells move. Forsmooth-swimming E. coli in 3D mixed with non-motile cells,

f (q, τ) = βe−q2Dτ+ (1 − β)e−q2Dτ

∫v

P(v)sin(qvτ)

qvτdv, (9)

5The OD depends on the wavelength used; we use 600 nm throughout.6Note that the bulk diffusion is enhanced by the swimmers [83].

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Figure 3: (a) Fitting DDM data g(q, τ), Eq. 7 and 8, using the ISF given byEq. 9 at one q for WT AB1157 at 5 × 108cells/ml. Main plot: data for bacteriaswimming fast enough for ballistic and diffusive motions to show up clearly astwo processes, separated by a point of inflection at τ ≈ 0.4 s. Inset: the bacteriahave slowed down to the extent that swimming and diffusion are no longer wellseparated. (b) Fitted speed v (main plot) and non-motile fraction β (inset) forthe data shown in the main part of (a) (black) and in the inset of (a) (red).

where P(v) is the speed distribution of the swimmers, and Dis the free translational diffusion coefficient, which is mainlydetermined by the diffusivity of the non-motile cells (but seefootnote 6). We have ignored polydispersity in cell size (whichinduces a distribution in D) for simplicity.

Self consistency demands that for straight swimmers mixedwith diffusers, the dynamical quantities obtained by fitting Eq. 9to data, in particular v =

∫ ∞0 vP(v)dv, β and D, should be q-

independent. Residual q dependence is nevertheless observedin practice, Fig. 3(b), e.g. due to tumbling7 [86]; such q depen-dence is the main source of experimental uncertainties in thefitted parameters from DDM quoted in this work.

The average body rotation angular frequency, Ω, can be de-termined using another high-throughput technique, dark-fieldflicker microscopy (DFM) [89]. Essentially, the lowest peak inthe Fourier transform of the time-dependent image intensity of asingle cell in dark-field microscopy is Ω. In the low-Reynolds-number limit, v/Ω depends solely on the geometry of the swim-mers, and not on viscosity, provided that the medium is a New-tonian fluid [1]. Thus, non-constancy of v/Ω indicates eitherchanging cell geometry or non-Newtonian effects [89].

Note that the relative merits of DDM and real-space trackingfor obtaining v and β has been discussed in depth before [86].

4.1. Imaging protocol

We use d ≈ 400 µm deep flat glass sample cells filled with≈ 150 µl of suspension and rendered air tight with petroleumjelly to prevent drift due to evaporation and stop replenishmentof O2 after it is exhausted by respiring bacteria.8 DDM showsthat contact with petroleum jelly does not change (v, β).

Movies in phase-contrast illumination (PF10×/0.3 at 100frames/s, ∼ 4000 images at 512×512 pixels ⇒∼ 40 s movies)are recorded in an inverted microscope (Nikon Ti) with aMikrotron high-speed camera (MC 1362) and frame grabber

7Calculations of the effects of tumbling on the ISF exist [88].8See Section 8, especially Fig. 10(b), to see why we want no O2 supply.

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Figure 4: Average swimming speed v (main) and non-motile fraction β (inset)vs. time at three heights from bottom wall for WT AB1157 at 5 × 108 cells/ml.

(Inspecta 5, 1 Gb memory) at 22 ± 1C. Custom LabVIEWrecording software controlling the microscope stage allowsscanning of many samples (giving good averages) repeatedly(giving time resolution), giving data such as Figs. 4, 9 and 10.

4.2. Observational complications

The majority of experiments to date using synthetic swim-mers produced data at or near surfaces. Escherichia coli cellscan swim in the bulk for extended time, although cells en-countering a wall tend to be trapped there [90, 91]. If per-formed sufficiently far from walls, DDM yields a genuine threedimensional speed distribution [85, 86] via fitting an ISF toEq. 8. Near a wall, the swimming is two-dimensional, andthe sin(qvτ)/qvτ in Eq. 8 is replaced by J0(qvτ), the zeroth-order Bessel function. However, it may not be possible to dis-tinguish between these functional forms unless P(v) is suffi-ciently narrow. Moreover, E. coli swims in circles [92], givingq-dependent fitted dynamical quantities if the circle radii arecomparable to the accessible range of 2π/q. The complex mo-tion of cells ‘tethered’ to walls further complicate data analysis.We therefore typically image at 100 µm away from the bottomof our capillaries (cf. total cell length L . 10 µm).

The sedimentation height of non-motile cells, Eq. 2, can beenhanced by 50% or more because swimmers enhance theirdiffusivity [83]. Nevertheless, lg ≈ O(10 µm), so that non-swimmers will accumulate on the bottom on a time scale ofd/vs . 70 min (using vs ≈ 0.1 µm s−1, Eq. 4). Measurement ofWT swimmers 10 µm from the bottom capillary surface, Fig 4inset, shows that β increases with time, until it saturates justover an hour (≈ d/vs) into the measurement. All non-motilecells have now sedimented into a layer of thickness ≈ lg. Cor-respondingly, β is constant at any single bulk position (e.g., 50or 100 µm from the bottom, Fig. 4 inset) until the sedimentationfront passes (at some fraction of d/vs), whereupon β drops.

Measurement of WT swimming E. coli in a sealed capillaryat our standard height of 100 µm from the bottom shows thatv decrease with time, Fig. 4. A priori, it is conceivable thatthis is because fast swimmers encounter surfaces and becometrapped [90, 91] more rapidly, thus leaving slower swimmers in

the bulk. However, measurements at three heights, Fig. 4, giveessentially identical results,9 so that the observed decreasingv(t) is not due to gradual kinematic accumulation at surfaces.

Drift gives ballistic motions that masquerade as swimming.Evaporative drift can be eliminated by proper sealing, but un-avoidable drift occurs at short times due to loading. These tran-sients decay on a time scale & ρL2/η for a liquid with viscosityη and density ρ, where L is a characteristic length [93]. We useda 5 cm×8 mm×0.4 mm capillary throughout. The 8 mm dimen-sion leads to resolvable speed changes in our time window onthe ≈ 1 min time scale, which probably accounts for the initialfast decay in v(t), Fig. 4. We find that decreasing this dimensiongives faster initial decay.

4.3. Fitting loreThe decay of the ISF, Eq. 9, is due to diffusion (parameterised

by D) and ballistic motion (parameterised by v). Satisfactoryfitting of the data in the form of g(q, τ) using Eq. 9 and Eq. 8 toobtain D and v depends on convincingly decoupling these con-tributions, which is straightforward when the two decays havewell-separated characteristic times, Fig. 3. Overlap of these twocontributions occurs when their relaxation times approach, i.e.v → qD, which, for WT E. coli in bulk, D & 0.3 µm/s, andq . 2.2 µm−1 (using a 10× objective), occurs at v . 1 µm/s.However, due to the distribution of speeds, this limit is under-estimated. In practice, we can resolve v down to 2 to 3 µm s−1

in BMB, Fig. 3. Note also that if β→ 0 or 1, the fitted value ofD or v respectively will be subject to large errors.

4.4. Motility platesWhen chemotactic strains are inoculated into ‘soft agar’

(& 0.2 wt%), they spread out in rings [94]. Non-chemotacticmutants [94] and the chemotactic WT when the agar is &0.3wt% [95] spread out instead as solid discs. The diametersof these rings or solid discs are often used to assay motility.

We inoculated 5 µl drops of OD = 0.3 TB-grown E. coli into0.3wt% LB agar plates, measured the diameter of the solidcolony discs after 22 h of incubation at 30 C, and comparedthese with v measured from DDM in three different media,Fig. 5(a). For chemotactic WT cells, there is reasonably cor-relation between motility plates and DDM measurements in allthree media, but especially glucose-supplemented BMB.

The non-chemotactic spreading of growing cells can be mod-elled using the Fisher equation [96]. This predicts a front speedof u ∼ 2

√Dα, where α is the growth rate, and D is the cells’

effective diffusivity. The latter is ≈ v2τ/3, with τ being theaverage time between tumbles [97]. The colony diameter af-ter time ∆t is d = u∆t ∼ 2v∆t

√ατ/3 ∝ v. Using the value

of τ ∼ 1 s in bulk media [33] and the glucose-BMB data forHCB1, Fig. 5(a), we find α ≈ 0.0003 s−1, or a doubling time ofα−1 ln 2 & 30 min, which is reasonable under our conditions.

Two caveats are in order. First, if the agar concentration al-lows chemotaxis, the dependence of the speed of the front (nowa ‘ring’) on v becomes more complex [95]. Secondly, we find

9Note the longer time axis here than those shown later in Figs. 9 and 10.

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washed (BMB)

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Figure 5: (a) Average swimming speed v (left axis) and (b) non-motile fractionβ for selected E. coli coli strains, from one batch culture in each case, beforewashing (in TB, white) and after washing (in BMB+1.5 mM glucose, grey or inBMB, black) at a cell density of 5 × 108cells/ml. Red bars in (a) are diametersof solid, circular colonies in 22-hour LB motility plates (right axis). Note thatfor HCB437, the cells did not penetrate the agar but stayed on the surface.

that HCB437, a smooth swimmer, did not penetrate the agar;its minimal spread on the plate surface does not reflect v in bulkmedia. Thus, motility plates must only be used with caution.

5. Preparing motile E. coli

We turn now to culturing bacterial swimmers. Readers need-ing to learn generic microbiological protocols should use stan-dard manuals [98, 99] and consult a microbiologist. We focuson extra procedures for obtaining motile cells.

5.1. Culturing cellsOur protocol is based on that of H. C. Berg (Harvard), and in-

volves Luria broth (LB, originally ‘lysogeny broth’ [100]) andtryptone broth (TB). TB is a mixture of amino acids from hy-drolysing milk casein proteins; LB is tryptone broth plus yeastextract, the latter containing various carbohydrates not in TB.

We grow single colonies from frozen stocks on LB agarplates at 30 C overnight. A single colony is transferred froma plate to 10 ml of liquid LB and incubated overnight (≈ 16 h)at 30 C10, shaken (for aeration) at 200 rpm. Finally, cells arediluted 100-fold into 35 ml of TB and grown for ∼ 4 h at 30 Cshaken at 200rpm. DDM shows that transferring to TB fromLB results in higher v. As cell sizes (Table 1) and other proper-ties change with growth phase, it is important that growth timesfor different experiments should be kept constant.

10Growth is optimal at T = 37 C, but lower T promotes swimming [18, 101].

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otile

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ctio

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43210

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filtration into BMB TBcentrifugation into BMB TB

(b)

Figure 6: (a) Average swimming speed v and (b) non-motile fraction β duringa washing process from TB to BMB (black) and from TB to TB (red) of WTAB1157, using filtration (filled) or centrifugation (open) at final cell densityof 5 × 108cells/ml. Inset: measured (symbols) and fitted (line) f (q, τ) of thesecells in TB before washing (turquoise, lower) and in BMB after 4 washing steps(purple, upper). Data sets are from one batch culture.

5.2. Washing cells

The next step is to transfer cells from TB to a ‘minimalmedium’ with no exogenous nutrients. This prevents growth,which is an unwanted complication in the long run. More im-portantly, we find that cells use oxygen very quickly in TB, andonce oxygen is exhausted, v decreases dramatically. For WTAB1157 at OD = 0.3, this occurs within 10 min, which is notlong enough for experiments. We therefore wash (by filtration)and transfer cells into Berg’s motility buffer (BMB), containing6.2 mM K2HPO4, 3.8 mM KH2PO4, 67 mM NaCl, and 0.1mMEDTA. Cells undergo 4 successive filtrations (= 3 washes, seeAppendix D) until the concentration of TB is diluted 103-foldby BMB. After the last wash, the suspension on top of the filteris removed and transferred to a 50ml centrifuge tube togetherwith the filter, where cells are carefully suspended by rolling thetube. This yields 1-3 ml of highly concentrated cells (OD ∼ 10),allowing the preparation of many dilute samples.

Transfer from TB into BMB decreases v and increases β forall strains studied, Fig. 5. This change in cellular motility isreflected in the ISF measured by DDM, Fig. 6(a) inset. In TB,the population of mostly motile cells (a single decay) has a nar-row speed distribution (oscillations). In BMB, two processesare clearly visible: a sizeable fraction of non-motile (diffusive)cells coexists with (ballistic) swimmers, whose speed distribu-tion is now considerably wider (no oscillations).

Figure 6 also shows that washing by filtration has non-trivialeffects on v and β, probably due to a combination of mechanicaldamage to flagella, regrowth (possible in TB) and change ofmedium. Pipetting may also have an effect. After 20 pipettingcycles in BMB using a 0.6 mm tip at normal expulsion speeds,

6

1.0x109

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0.0x109

pla

te c

ount

(ml-1

)

1.00.80.60.40.20.0

OD600nm

Figure 7: Example of viable plate count vs. OD used for calibrating the latter.These values are typical for our culture protocol.

we find that v drops by ≈ 50% and β increases by a factor of. 3. It is not until the tip diameter has been increased to ≈2 mm that the effect on (v, β) begins to saturate. Such flow-driven damage of E. coli flagella has been noted before [102].

If low cell concentrations are required or many strains need tobe processed simultaneously, we use a bench-top centrifuge towash small volumes (. 2 ml) 3 times at moderate speeds (2 minat 8000 rpm) to produce ≈ 1 ml of OD ≈ 0.3 cell suspension.Figure 6 shows that this procedure produces populations withhigher β in TB, but it is considerably faster than filtration.

5.3. Counting cells

The most common protocol for relating OD to cell numberis the ‘viable plate count’ [98, 99]. Briefly, a sample is dilutedto the relevant OD range (say, 0.05-1) using phosphate bufferedsaline (PBS).11 One part of the sample is used to measure OD;another part is used to prepare tenfold serial dilutions (down to10−6) by transferring 100 µl sample to 900 µl PBS with vigor-ous mixing between each dilution. 100 µl of the final two dilu-tions are spread on replicate LB plates and incubated at 37 Covernight. Next day, individual colonies can be seen. Each ofthese has arisen from a ‘colony forming unit’ (CFU), a short-hand for ‘probably but not certainly a single cell’. These arecounted to arrive at the viable plate count in units of CFU/ml.The cell density of the original sample is then calculated takinginto account the dilution. Plotting the OD vs the cell densityfrom plate counting, Fig. 7, gives the desired calibration.

6. E. coli energetics

Self-propulsion requires energy. The energetics of syntheticswimmers is partially understood [103, 104]. Here we give asimplified introduction to E. coli bioenergetics. Details can befound in textbooks [105, 106, 107, 108, 109, 110].12

Bioenergy comes from transferring electrons from high-energy to low-energy bonds through a sequence of molecules.

11PBS = 137 mM NaCl, 2. mM KCl, 10 mM Na2HPO4 and 2 mM KH2PO4.12An unusual, ‘coarse-grained’ introduction is given by Nobel laureate

Christian de Duve [111]. See also tutorials at [112] under ‘The Microbe’ tab.

Figure 8: Schematic of E. coli bioenergetics, with high-energy compounds ATPand NADH picked out in bold. Glycolysis breaks down glucose (C6) into twopyruvates (C3), producing 4 ATP by substrate-level phosphorylation. Pyruvateis reduced to acetyl co-A with the emission of CO2. (Pyruvate is catabolisedto acetate when glucose is abundant.) Acetyl co-A enters the tricarboxylic acid(TCA) cycle to produce 12 NADH per glucose. Each NADH donates it high-energy electron pair, 2 e–, to respiratory enzymes in the inner membrane, whichpass them to a terminal acceptor, here O2, which is reduced to water, regen-erating NAD+ (oxidised NADH) for glycolysis (dotted arrow). The drop inenergy as 2 e– passes along the respiratory enzyme chain is used to pump H+

out of the cytoplasm, generating a proton motive force (PMF), which drivesprotons through rotary flagella motors and through F1F0ATPase to make ATPfrom ADP (chemiosmotic oxidative phosphorylation).

The energy is used to pump protons out of the cell, giving rise toa proton motive force (PMF), which powers swimming. In aer-obic respiration, the electron donors are various reduced foodsrich in C−H bonds, while the final electron acceptor is typicallyoxygen. The electron pair in the C−H bond lowers its energy asit is transferred (notionally as : H−) to an O−H bond (in water),where, because O is more electronegative than C, the electronpair interacts more strongly with positively charged nuclei thanin C−H, and therefore has lower energy. The cell harnesses theenergy released for chemical work. The ‘favourite’ supplier ofhigh energy electrons for E. coli is α-D-glucose (C6H12O6).13

The full oxidation of this molecule in aerobic respiration gen-erates ≈ 2.8 MJ mol−1 under physiological conditions

HO

OH

OHOH

O

HO

+ 6 O2 −−−→ 6 CO2 + 6 H2O ∆G ≈ −103kBT,

(10)Figure 8 summarises the aerobic catabolism (break down)

of glucose, a C6 compound. First, glycolysis via the Embden-Meyerhof-Parnas (EMP) pathway14 breaks glucose into twoC3-halves, pyruvates (CH3COCOO–), a key metabolic interme-diate. Then, pyruvate is oxidised to acetyl coenzyme A (acetyl

13Glucose polymers constitute > 50% of dry terrestrial biomass [108].14When glucose is the sole carbon and energy source for E. coli, ≈ 75% of

it channels into the EMP pathway; the rest feeds into the hexose monophos-phate (HMP) pathway, which mainly provides precursors for biosynthesis, i.e.

7

co-A), another key metabolic intermediate, and fed into the ‘tri-carboxylic acid cycle’ (TCA = Krebs or citric acid cycle) to befurther broken down. After glycolysis, CO2 is produced with-out molecular O2 through the progressive enzymatic dehydro-genation of fragments of catabolised glucose.

During glucose catabolism, the energy released is stored inhigh-energy compounds, mainly adenosine triphosphate (ATP)and (reduced) nicotinamide adenine dinucleotide (NADH).ATP is generated from adenosine diphosphate (ADP) by the ad-dition of an inorganic phosphate group:

ADP + Pi −−→ ATP. (11)

NADH comes from reducing NAD+, the oxidised form of thiscompound, partly via CO2-producing dehydrogenations:

NAD++ H+

+ 2 e–COOH CO2

NADH. (12)

The generation of 4ATP per glucose en route to pyruvate isknown as ‘substrate level phosphorylation’ (SLP), where phos-phate groups are added to ADPs without using molecular O2.The 12 NADH generated in glycolysis and the TCA cycle giverise to up to 96 ATPs through the process of ‘oxidative phospho-rylation’. NADH donates its energetic electron pair to respira-tory enzymes in the inner membrane, ultimately passing them toO2 as ‘terminal electron acceptor’, producing H2O and regen-erating NAD+ for glycolysis and the TCA cycle. Without suchregeneration, e.g., because respiratory enzymes are poisoned orbecause O2 runs out, the TCA cycle falters.

The energy released as 2 e– drops down the potential energyladder of respiratory enzymes pumps between 2 to 8 H+ out ofthe cell (8 at high [O2]) [113], generating a proton motive force(PMF) of ≈ 150 mV. Driven back to the cellular interior by thePMF, protons do work in active solute transport, turning flagellamotor and making ATP in ‘rotary enzyme’ F1F0-ATP synthase(‘chemiosmosis’, requiring ≈ 4 H+ per ATP).

When glucose is plentiful, it is incompletely oxidised to ac-etate (CH3COO–) via pyruvate:

C6H12O6 + 2 O2− > 2 CH3CO−H+

O+ 2 CO2 + 2 H2O. (13)

Such ‘overflow metabolism’ (or the ‘Crabtree effect’) generatesless energy, and excretes acetate for potential later reabsorptionand further oxidation when glucose is less plentiful [114, 115].

How E. coli adapts to decreasing [O2] in its environment iscomplex [116, 117, 118]. At [O2] = 0 and without other ter-minal electron acceptors, E. coli ferments glucose into acetate,formate, lactate and succinate, using metabolic intermediatesas electron acceptors and producing ATP by SLP, with acetate

anabolism [109]. However, the HMP pathway can also feed pyruvate into theTCA cycle [109]. A fraction of TCA intermediates supplies anabolic precur-sors. Such ‘anabolic syphons’ together with overflow metabolism, reaction 13,mean that the stoichiometry in reaction 10 is never satisfied on average.

120

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5.55x109

(a)

Figure 9: (a) Average swimming speed v vs. time for the capillary protocol inBMB at cell densities indicated in the legend (cells/ml). Lines guide the eye.The ‘crash’ in v in each case is due to O2 exhaustion. Data sets from one batchculture. (b) Corresponding O2 exhaustion time as a function of inverse of celldensity. Error bars relate to the accuracy of measuring the ‘crash’ time.

production generating most ATP [116, 119]. In such ‘mixed-acid fermentation’, respiratory enzymes are inactive, and otherpathways maintain the PMF, including F1F0-ATPase workingin reverse, hydrolysing ATP to ADP and using the energy topump protons out of the cell [107, 110, 117]. The PMF powersflagella motors. Within a wide range, the motor speed is pro-portional to the PMF [120]. If the PMF is short circuited (e.g.by making the membrane permeable to protons) [121], or dropsto zero when ‘fuel’ runs out, swimming ceases.

Under starvation conditions (i.e., no exogenous nutrients),such as occurs in BMB, E. coli obtains energy by metabolis-ing intracellular resources. Such ‘endogenous metabolism’ iscomplex [122, 123] and poorly understood. For starved cellsgrown in TB, catabolism of free amino acids and free or RNA-derived ribose (a sugar) feeds into the TCA cycle [108], so thatO2 or other terminal acceptors are needed.

7. E. coli swimming powered by endogenous metabolism

Escherichia coli and other bacteria [124, 125, 126] can swimpowered entirely by endogenous metabolism. We now probethe time dependence of v. All data are obtained from DDM withWT AB1157 in BMB prepared using our standard protocol.

7.1. Observations and practical implications

Figure 9(a) shows the average swimming speed as a functionof time, v(t), in sealed capillaries at various cell densities, n.Cells slow down, approximately linearly with time. If ≈ 10%slowing down is tolerable, then there is a useable window of≈ 1 h at n = 2 × 109 cells/mL, which ends in a ‘crash’.

The time of this ‘crash’, tc, drops with n; we suggest that itis due to O2 depletion. Quantitatively, ntc ≈ constant, Fig. 9(b),as expected if the initial [O2] and the O2 consumption rate percell, Q, are invariant with n. Assuming that the BMB was ini-tially saturated with O2, and using literature solubilities [127],which are only very weakly dependent on ionicity [128], weestimate Q at each cell density, Fig. 9(b) inset, which isweakly dependent on n, rising from Qendo ≈ 2 amol/min/cellat n = 1.67 × 109 cells ml−1 to Qendo . 4 amol/min/cell at

8

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10-6 10

-3 100 10

3

concentration (mM)

(d)

glucose

L-lactate

sucrose

I

VI

V

IIIII

IV

Figure 10: Effect of glucose on time-dependent average swimming speed v(t)for WT AB1157 at 5 × 108 cells/ml. (a) At low [Glu], glucose depletes first,causing the rapid drop (III) in v. Inset: a longer run at [Glu]=0.07 mM reveals asubsequent sharp drop (IV) due to O2 depletion. (b) At high [Glu], O2 depletesfirst, causing the first sharp drop (V) in v. The second, larger sharp drop (VI) inv is due to glucose depletion. Datasets are from one batch culture. (c) Deple-tion time of glucose in aerobic condition versus glucose concentration. Inset:aerobic glucose consumption rate versus [Glu]. (d) Speed v versus moleculeconcentration normalised to the speed in BMB, v0, for three small molecules,measured ≈ 5 min after mixing and filling the capillary. Filled symbols are con-centration markers for Fig. 12. Error bars in (c) and (d) are standard deviationsfrom averaging data from two and three independent batch cultures.

n = 5.55 × 109 cells ml−1 (‘a’ ≡ ‘atto’ = 10−18). These val-ues are comparable to those measured before using a differentstrain and under somewhat different conditions [122].15

The highest density data in Figs. 9 were obtained at n ≈5×109 cells/ml, or φ ≈ 0.5% of cell bodies. Extrapolating fromQ at this n, tc ≈ 1 min at φ ≈ 5%; this is an upper bound, sinceQ probably increases with n. Oxygen exhaustion therefore pre-cludes experimentation at φ & 1% under these conditions.

7.2. Physiological interpretation

The observed slowing down in v at t . 1 h is probably notdue to substrate exhaustion, as extrapolated literature data [122,123] suggests this happens in ≈ 10 h. That dv/dt is identical atdifferent n, Fig. 9(a), supports this suggestion.

The ubiquitous signalling molecule cyclic di-guanylate (c-di-GMP) can slow down bacterial rotary motors by binding to theprotein YcgR to form a molecular ‘brake’ [129]. However, wefound that a ∆YcgR mutant behaved identically to the WT insealed capillaries; so c-di-GMP is unlikely implicated. Instead,we infer a slow decrease in the PMF driving the rotary motors.The adaptive value and mechanism of this putative starvationresponse is unknown, but it can affect many PMF-dependentcellular functions, e.g. ATP synthesis by F1F0-ATPase.

15Qendo ≈ 10 − 20 ml/h/mg dry cell mass [122] → 2-4 amol/min/cell usingO2 molar volume = 24 dm3 and dry cell weight ≈ 0.3 × 10−9 mg/cell [105].

20

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50

0

[O2 ] (

µM

)

3025201510

50

6040200

nÅ5x108 cells/ml

nÅ109 cells/mlII

VI

II V

I

Figure 11: Simultaneous measurements of average swimming speed v (, leftaxis) and [O2] (, right axis), using fluorescence lifetime imaging microscopy(FLIM) vs. time in a sealed capillary for WT AB1157 at ≈ 109 cells/ml and[Glu]=0.5 mM. For FLIM, 47 mM of the O2-sensitive dye ruthenium tris(2,2’-dipyridyl) dichloride hydrate (RTDP) was added to BMB (which did not affectthe cells’ motility). RTDP was excited using sub-ps pulses (λ = 450nm, ∼1mWat 1MHz repetition rate) and its fluorescence imaged using a gated intensifiedCCD camera (Picostar HR-12QE, LaVision GmbH, Germany). The data wasfitted with a single exponential decay yielding a (homogeneous) fluorescencelifetime map, which was averaged to estimate [O2]. Inset: v at 5×108 cells/ml tobetter show the saturation before O2 depletion. Data sets are from independentbatch cultures with v(t = 0) ≈ 12 µm s−1 and ≈ 15 µm s−1, respectively.

8. E. coli swimming powered by glucose

If glucose is present, E. coli utilises it first, and suppressesthe expression of enzymes for processing other nutrients [130].

Glucose increases the swimming speed of E. coli [101] (seealso Fig. 5(a)) and other enteric bacteria [131]. We now demon-strate how to use glucose to enable E. coli AB1157 (cultured bystandard protocol) to swim at a constant v for extended time.

8.1. Observations and practical implications

Figure 10(a) and (b) show v at n = 5 × 108 cells/ml of WTAB1157 sealed in a capillary in BMB supplemented with lowand high glucose concentrations respectively. At 0.03 mM ≤

[Glu] ≤ 0.07 mM, Fig. 10(a), v rises gradually with time (II) af-ter initial transients (I), until it drops suddenly (III). Thereafter,it decreases slowly with time. A longer run at [Glu] = 0.07 mM,Fig. 10(a) inset, reveals a second rapid drop (IV) that is sharperand of larger amplitude. The long, slow decrease with time andthe final sudden drop are reminiscent of ‘endogenous propul-sion’, Fig. 9. Thus, the data suggest that glucose is consumedaerobically until it is depleted, whereupon cells revert to en-dogenous metabolism until O2 is, in turn, depleted.

Consistent with this, the time of the first sharp drop (III) isproportional to [Glu], Fig. 10(c), and the deduced specific glu-cose consumption rate, inset, is nearly independent of [Glu],averaging to G ≈ 6.9 ± 0.5 amol/min/cell. We also measured Gover a range of [Glu] biochemically (Appendix E), and founda comparable value of G ≈ 5 ± 0.6 amol/min/cell.

Figure 10(c) implies that there will be a [Glu] at which O2depletion will occur before glucose depletion. This indeed hap-pens at the higher [Glu] explored in Fig. 10(b). Now, the verysharp, first ‘crash’ (V) in v is due to O2 depletion, at whichpoint there is still plentiful glucose in the medium. Consistent

9

1.5

1.0

0.5

0.0

w0 =

v /

v0

2 3 4 5 61

2

osmolarity (Osm)

0.180.16

glucose

L-lactate

sucrose

Figure 12: Normalised average swimming speed, v/v0, from Fig 10(b) as afunction of the osmolarity. Note the bottom split axis with a linear scale from150 to 190 mOsm (bottom left) and a log-scale from 200 to 2000 mOsm (bottomright). Filled symbols corresponds to markers in Fig. 10(d).

with this interpretation, the time of the first abrupt speed de-crease (V) is independent of [Glu]. Again using literature O2solubilities [127, 128], we find an average O2 utilisation rate ofQGlu = 22.6 ± 0.6 amol/min/cell, which, as expected, is consid-erable higher than the Qendo ≈ 2-4 amol/min/cell reported by us(Section 7.1) and others [122] for endogenous metabolism.

Independent evidence for O2 depletion comes from monitor-ing the fluorescence life time τ of an O2-sensitive dye [132].By measuring τ and using our experimentally derived calibra-tion [O2] = 568.1 µM (604ns/τ− 1) (consistent with [133]), wecan assay [O2] in our sealed samples, Fig. 11, which drops to≈ 0 precisely at the point of the abrupt decrease (V) in v.

Subsequent swimming powered by anaerobic glucosemetabolism shows v constant to ±1 µm s−1 until glucose deple-tion and v abruptly drops by a factor of 3 or more, Fig. 10(c)(VI). Thus, cells in initially aerated BMB supplemented withenough glucose will swim at approximately constant averagespeed after O2 depletion and before glucose depletion.

The period of constant-v swimming can, at first sight, be ar-bitrarily extended by increasing [Glu], Fig. 10(b), up to sat-uration (≈ 5 M at 25 C). However, a practical limit exists.Figure 10(d) plots w0, the average swimming speed at vari-ous [Glu] normalised to the average speed at [Glu] = 0, bothmeasured immediately after loading into sealed capillaries. At[Glu] . 10−3 mM, glucose depletion occurs before measure-ments could begin, so that w0 = 1. At [Glu] & 50 mM, w0catastrophically drops. Repeating using L-lactate, which E. colican metabolise, and sucrose, which it cannot, also shows thesame abrupt drop, which we believe is due to osmotic shock.

Figure 12 replots our data against solution osmolarity (deter-mined using an Osmomat30, Genotec, Germany), showing thatv always starts to decrease at an osmolarity between 0.2 and0.4 Osmom, comparable to the osmolarities needed to start de-creasing cell volumes in previous studies [134]. Thus, there is alimit to the highest useable [Glu] for maintaining constant v.16

16As expected from previous work [134], the results in Fig. 12 were timedependent: waiting longer produced partial recovery in the ‘crashed’ speed.Nevertheless, a definite upper limit exists at ≈ 100 mM small-molecule solutes.

14

12

10

8

6

4

2

0

sp

ee

d v

(µm/s)

100806040200

intensity (mW/cm2)

Figure 13: Average steady-state swimming speed v of E. coli MG1655 (n =

109 cells/ml) expressing SAR86 γ-proteorhodopsin at different intensities of in-cident green light (λ = 510− 540 nm) after O2 depletion; data obtained startingfrom the highest intensity.

8.2. Physiological interpretation

Reaction 10 for complete glucose oxidation requires an oxy-gen to glucose stoichiometry of QGlu/G = 6. We measureQGlu/G ≈ 3.3 ± 0.33, i.e. about 50% of the glucose consumedis fully oxidised. A combination of overflow metabolism and‘anabolic siphon’ (footnote 14) probably explains this finding.

Figure 11 shows the early-time portion of v(t) on an ex-panded time axis. After initial transients (I), v(t) rises (II) andthen saturates (this is particularly clear in the inset) before thecrash (V) due to O2 exhaustion. Immediately before these ex-periments, our cells have been harvested from TB, which con-tains little carbohydrates. While the operon of genes neces-sary for glucose transport (pts) is constitutively expressed irre-spective of whether glucose is present, exposure to glucose canincrease the expression of some pts genes by up to threefold[135, 136], which probably causes the rise (II) of v(t).

Averaging over data sets, the ratio of the average speeds be-fore and after the O2 ‘crash’ (V) in the range 1.3 to 1.6. ThePMF of K-12 E. coli (strain AN387) grown aerobically on glyc-erol and fermentatively on glucose was previously measured tobe −160 mV and −117 mV respectively [137]; 160/117 = 1.36is remarkably close to our speed ratio.

8.3. How much energy does swimming use?

The detailed mechanics of a peritrichous swimmer (= manyflagella distributed over the cell body) is not yet understood[49], so that the vast majority of the literature on E. coli iscouched in terms of propulsion by a single ‘effective flagellum’.The power developed by the ‘effective motor’ turning this ‘ef-fective flagellum’ has been estimated to be P ≈ 4× 10−16 W forswimming in minimal medium [138]. Each H+ driven into thecell by a PMF of ≈ 150 mV [137] can perform w = 2.4×10−20 Jof work. If we assume that flagella motors extract work with100% efficiency from the protons, then P/w . 2 × 104 H+ s−1

is needed to power the ‘effective motor’. In reality, of course,a somewhat higher flux would be needed, because the motor isnot 100% efficient in harnessing energy from the PMF.

On the other hand, full oxidation of one glucose gives 12NADH; each NADH can export up to 8 H+, Thus, G/2 ≈

10

Figure 14: A non-motile Keio knockout [141], ∆(fliC)::kan, where the flagellaprotein gene fliC (red) is replaced by the kanamycin resistance gene kan (blue),flanked by DNA sequences (purple) that allow its easy excision.

4 amol/min/cell ≡ 4 × 104/s/cell fully-oxidised glucose

molecules export up to 384 × 104H+/s/cell. This is in large ex-

cess of the ∼ 104H+/s/cell we estimate as needed to power the

≈ 50% increase in v upon addition of glucose. Thus, swimmingaccounts for only a small part of a cell’s energy budget.

8.4. Other small moleculesWe have also studied swimming powered by acetate (C2),

glycerol and lactate (C3), xylose (C5), galactose (C6), and mal-tose and lactose (C12), which can be expected to generate dif-ferent amounts of energy per molecule. Interestingly, however,the maximum increase in speed in each case is approximatelythe same as observed for glucose (about 50%, see Fig. 10(d)for L-lactate). This suggests that the flagellar motor speed satu-rates at high PMF (as observed for Bacillus subtilis [139]), andsupports our conclusion that swimming uses only a small frac-tion of metabolic energy. At high enough concentration of thesealternative carbon sources, we find that the post-O2-exhaustionspeed drops to zero (for lactate, cf. [140]), rather than to someintermediate, constant level as observed for glucose. This isbecause E. coli cannot ferment these substrates.

9. E. coli swimming powered by light

Some micro-organisms directly harvest energy from light.Thus, photosynthesizers use photons to split water to generatehigh energy electrons. Alternatively, light is harvested directlyto pump protons using proton pumps such as proteorhodopsin(PR). PR, first discovered through the genomic sequencing ofmarine bacteria [142], has been incorporated into E. coli [143].

Most PRs identified to date can generate PMF up to orslightly above WT levels [144]. To enable illuminated PR totake over PMF generation, other sources need to be deactivated.This has been demonstrated on single cells using poisons for therespiratory enzymes (cf. Fig. 8) or by O2 exclusion. As the mo-tor, and therefore flagellum rotation speed, is proportional tothe PMF, illuminating poisoned cells expressing PR leads to acontrolled increase in flagellum rotation speed [143].

Here, we demonstrate this effect in a cell population usingMG1655 transformed with plasmid pBAD-HisC-PR express-ing PR when induced by arabinose (DM-4). We already knowthat O2 is exhausted after a period when swimmers are sealed incapillaries, Fig. 9. After our transformed cells have exhaustedO2, their swimming is wholly powered by PR-generated PMF.The initial increase in speed with incident intensity, Fig. 13, sat-urates at high intensities, in agreement with previous measure-ments of the rotation rate of individual flagellar motors [143].This and other PR mutants therefore enable simple external

Figure 15: Schematic of transposon mutagenesis. See text for details.

control of their swimming speed, making it feasible to changethe samples activity both in time and space. They are livinganalogues of light-driven synthetic swimmers [9, 145].

10. E. coli – the genetic toolbox

A great attraction of E. coli is the availability of many mu-tants and a versatile genetic ‘tool box’. Thus, e.g., the FliCflagella protein could be mutated to include a cysteine residue tomake disulphide bonds with dyes, or the cheY chemotaxis genecould be deleted to give smooth (non-tumbling) swimmers. Webriefly introduce two ‘off the shelf’ mutant libraries and twomethods for mutagenesis to illustrate principles and introduceterminology. Details can be found in the textbooks, e.g. [146].

A major resource is the Keio collection [141] of ‘sin-gle knockout’ mutants of strain BW25113 (closely related toMG1655 but more amenable to molecular biology), availableon a non-profit making basis to academics. Each non-essentialgene was precisely deleted and replaced with an excisablekanamycin resistance gene, Fig. 14.

Many mutagenetic methods use plasmids, extrachromoso-mal pieces of DNA that can be ‘transformed’ into bacteria andmaintained independently. Figure 15 illustrates one strategy tocarry out ‘transposon mutagenesis’. It relies on a temperature-sensitive plasmid, which is only maintained within the cell atthe ‘permissive’ temperature, and is lost at a (higher) ‘restric-tive’ temperature. This ‘suicide’ plasmid acts as a ‘vector’ (car-rier) for a transposon, a piece of genetic code that can ‘jump’between DNA locations. Here, the plasmid carries transposonTn5, which confers resistance to the antibiotic kanamycin.

When the transposon jumps, or transposes, from the plasmidonto the bacterial chromosome, it may insert into a gene, gener-ating a mutation. Following a shift of the E. coli from the per-missive to the restrictive temperature, the plasmid will be lost.Then, all kanamycin-resistant cells carry a chromosomal copyof the Tn5 element transposed onto the chromosome, where itcan be stably maintained. Crucially, the transposon jumps intorandom chromosomal locations, and so can generate mutationsin any gene. A particular mutation can be selected by a changein phenotype and the insertion site mapped by sequencing.

P1 transduction is another popular mutagenesis technique.Here DNA is transferred from a donor to a recipient cell us-

11

Figure 16: Schematic of P1 phage transduction. 1 Phage attaches to cell. 2Phage injects DNA (black) into cell and uses its machinery to replicate as wellas fragment cell’s genome (red). 3 DNA is packaged into viral particles, someof which contain fragments of the cell’s DNA, giving a ‘Trojan’ phage. 4 Celllyses, releasing all viral particles. 5 ‘Trojan’ phage infects target cell. 6Donor DNA fragment is incorporated into target cell genome by recombination.

ing the P1 bacterial virus (a bacteriophage). When P1 infectsa host cell, it not only packages its own genome into the virusparticle, but also can package fragments of the host chromo-some. When these virus particles are purified and used to infectthe target strain of E. coli, DNA homology between the donorDNA packaged in the virus particle and the recipient chromo-some can generate insertion of the donor DNA.

More generally, plasmids constitute a vital resource for in-troducing new genes into E. coli, e.g. transforming with a plas-mid carrying the GFP gene will render cells fluorescent. Eachmember in another useful library, the ASKA collection [147],consists of an E. coli strain containing a plasmid in which asingle gene from E. coli strain W3110 has been cloned. TheDNA encoding each gene has been fused to sequences that per-mit precise temporal control of the expression of the associatedprotein and its fluorescent tagging with GFP.

We end with two ‘health warnings’. First, genetic modifica-tion in motility-related work typically starts with parent strainsselected for motility (e.g. HCBxx or RPxx, Table B.2). Many ofthese retain wild-type features not optimised for DNA manip-ulation. Moreover, the genome of many ‘motility favourites’remains less well characterised compared to ‘canonical’ strainssuch as MG1655 [26]. Sequencing and annotating the genomeof some of these strains is a desirable future step.

Secondly, care must be taken in obtaining a good reliablestarter culture of the strain that one chooses to work with, ei-ther from the originating author or from a national culture col-lection, e.g. ATCC [148] and CGSC [149] in America; NCIMB[150] in the UK; DSMZ [151] in Germany; and CGMCC inChina [152]. Bacterial genomes are changeable, so that strainsdeposited at the back of freezers twenty years ago whose prove-nance is uncertain are not good starting points.

11. Summary and conclusions

Escherichia coli is increasingly used in active colloids ex-periments as an alternative to or to contrast with synthetic col-loidal swimmers. We have reviewed, explained and proposeda set of procedures that, together, should enable the collection

of data from such experiments between different laboratoriesthat can be quantitatively compared. At the heart of these pro-cedures is the use of a new, high-throughput method to charac-terise E. coli motility, differential dynamic microscopy (DDM),which delivers the average swimming speed and motile fractionaveraged over ≈ 104 cells in a matter of minutes [85, 86]. Us-ing DDM, we have established that E. coli swims at constantspeed when motility is powered by mixed-acid fermentation,Fig. 10(b). Along the way, we have explored the use of DDMto interrogate aspects of cellular physiology via the dependenceof swimming speed on PMF. Our results suggest that E. colicells powered by endogenous metabolism actively reduce theirPMF with time. It appears that about 50% of the glucose un-der our conditions is used for generating energy, and that a verysmall fraction (maybe ≈ 1%) of this energy is used for motility.

Whether our proposed procedures, or something similar, arefollowed, it is important that sufficient information is recordedin publications using E. coli as a model active colloid to enablefaithful reproduction of experiments. We therefore propose a‘checklist’ of what needs to be reported in Appendix A.

More needs to be done before E. coli can become an idealmodel for active matter experiments. Biologically, it would bedesirable to sequence the genomes of some favourite motilitystrains. Armed with accurate genomic information, it should bepossible to design bespoke swimmers that have ideal character-istics for different aspects of active matter research, e.g., a strainthat does not depend on either poison, or O2 depletion, or lightto display constant swimming speed over extended time. Theo-retically, it would be useful to construct coarse-grained modelsthat take into account the flagella bundle. Predictions from suchtheoretical models confronted with data from experiments us-ing increasingly well-characterised E. coli suspensions shouldpropel the subject of active colloids significantly forward.

Acknowledgements

WCKP initiated work with E. coli under an EPSRC Se-nior Research Fellowship (EP/D071070). He and JSL, JA, ADand VAM are now funded by an EPSRC Programme Grant(EP/J007404/1) and an ERC Advanced Grant (ADG-PHYAPS).VAM’s was also supported by Marie Curie Fellowship ‘Active-Dynamics’ FP7-PEOPLE (PIIF-GA-2010-276190). AJ held anEPSRC studentship. TV is funded through Marie Curie fel-lowship ‘Living Patchy Colloids’ (LivPaC, 623364) under theFP7-PEOPLE-2013- IEF program. TP is supported by an Edin-burgh Chancellor’s Fellowship and the BBSRC/EPSRC/MRCSynthetic Biology Research Centre grant (BB/M018040/1).

Many past lab members contributed to our knowledge ofE. coli motility, especially Otti Croze (who cultured our firstE. coli) and Laurence Wilson (who performed the first DDM).We thank Howard Berg (Harvard), Ian Booth (Aberdeen) andGail Ferguson (Edinburgh, then Aberdeen) for educational andilluminating discussions, and all the authors represented in Ta-ble B.2 for providing strains and plasmids.

12

Appendix A. Protocol reporting checklist

To facilitate reproducing and comparing results, we suggestthat published methods should always include:

• Strain name and details of any genetic modifications

• Growth conditions (temperature, growth medium compo-sition, cell density of harvest)

• Washing procedure (method: filtration or centrifugation,number of washing steps, exact composition of motilitymedium)

• Conditions for motility experiments (cell concentrationand how determined, sample cell details: material anddimensions, sealing, position and conditions for im-age/video acquisition)

• Details for image analysis and data processing

Appendix B. Strains

Table B.2 summarises a number of strains of E. coli that havebeen used by us and others in active colloids and related motil-ity work. Note that publication in a journal carries the obli-gation of curating and sharing the strains used in a publishedwork.However, one should not give away a strain obtained fromanother laboratory; instead the protocol is to direct enquiries tothe strain originator. Note that intra-strain variability can ariserapidly because certain genetic elements (called insertion se-quences, IS) can ‘jump’ into regions of the genome controllingflagella gene expression, enhancing the motility [? ].

Appendix C. Nomenclature for bacterial genetics

Researchers working with bacteria, especially if they collab-orate with biologists, need some facility in the shorthand usedto described genotypes [157, 158], which in turn requires someknowledge of molecular genetics [146]. Here we give a verybrief introduction based on ‘worked examples’ from Table B.2.

Each gene is given a three-letter, lower-case italicised name(possibly followed by an extra capital letter for different mem-bers of a gene family), often suggestive of its function; differ-ent versions of a gene (alleles) are distinguished by numbers.Thus, tsr7021 is allele 7021 of the tar gene in E. coli codingfor part of a receptor system for sensing L-serine and relatedamino acids. Deletion of this allele in HCB427 is indicatedby ∆(tar)7021. The protein product of a gene is denoted bythe same three letters unitalicised and capitalised. Thus, in thefliC(S353C) mutation carried by AD1, residue 353 of the FliCprotein used to build flagella filaments has been mutated fromserine (S) to cysteine (C).17 Sometimes, a different gene is in-serted in place of a deleted gene. Thus, in JSL1, a cassetteof genes conferring resistance to the antibiotic kanamycin hasbeen inserted in place of the deleted cheY gene for chemotaxis

17See the textbooks, e.g. [106], for single-letter abbreviations of amino acids.

– ∆(cheY::kan); the advantage is that such mutants can be eas-ily selected by growth in the presence of kanamycin. Finally,many bacteria carry plasmids, such as plasmid pHC60, whichcarries tetracycline resistance (TetR) and expresses green fluo-rescence protein (GFP) constitutively (i.e. continuously ratherthan subject to environmental control).

Genotype of strains can be found from various onlinedatabases, including the various culture collections [148, 149,150, 151, 152]. Information on individual genes are availablefrom appropriate databases, e.g. [159].

Appendix D. Filtration

To transfer the bacteria from TB growth media to BMB, weuse a sterile Nalgene filtration unit consisting of two compart-ments separated by a Milipore 45 µm HATF filter [160]. The fil-ter is soaked in BMB for ≈ 5 min before being placed centrallyon the unit with sterile tweezers. After screwing tight the up-per and lower halves of the unit, 35 ml of cell culture is slowlypoured onto the filter. A tap-powered suction pump is used toenhance the flow rate, with a 70% Ethanol bath between theunit and the suction tap to prevent water supply contamination.

When the level of TB had fallen to ≈ 3 mm above the filter,leaving ≈ 3 ml of liquid, 35 ml of BMB is pipetted into the unit.Ensuring that the filter does not run dry during the procedureminimises the number of non-motile cells. This washing step isrepeated 3 times. The water flow is adjusted to maintain a con-stant filtration rate so that each wash step takes 10 min. When∼ 1 to 3 ml of filtrate remains after the third wash, a sterilecut pipette tip is used to transfer the filtrate to a plastic 50mlpolystyrene test tube (Greiner). (Smaller tubes are not wideenough for next step.) The filter is removed from the unit usingsterile tweezers and deposited on the side of the tube. By gen-tly rolling the liquid over the filter, bacteria were resuspendedto reach a final OD between 5 and 15, depending on the volumeof liquid left on-top of the filter after the final washing step.

Appendix E. Glucose assay

We used a Sigma GAGO20 glucose assay kit. Hydrogen per-oxide from the oxidation of glucose by glucose oxidase reactswith o-dianisidine in the presence of peroxidase to form a col-ored intermediate, which further reacts with sulfuric acid toform a more stable, pink final product. The OD measured at540 nm is proportional to the original glucose concentration.Calibration runs showed that in our equipment, the linear rangefor OD540 vs glucose concentration extended to ≈ 600 µM.

Bacterial cells were grown using the standard motility pro-tocol, washed and OD adjusted to 0.3 as for motility exper-iments, except that the buffer here lacks EDTA, which inter-fered with glucose oxidase. Cells and glucose were mixed andsamples taken at different time points, put on ice and filtered(0.22 µm pore size) as quickly as possible. The filtered super-natant was used according to manufacturer’s protocol to mea-sure glucose concentration. Glucose utilization rates were cal-culated using glucose and time difference as well as wet or dry

13

Table E.3: Glucose utilisation rate

Initial [Glu] (mM) rate (µmol/min/g wet cells)0.50 4.9 ± 1.00.20 5.2 ± 0.90.10 6.1 ± 1.60.05 4.7 ± 0.8

weight of cells in 1ml of OD = 0.3 suspension. Results are re-ported as averages and standard deviations using different timeperiods measured in one set of experiments. There is no sys-tematic trend. We therefore average the value determined atdifferent [Glu] to give an estimated glucose utilisation rate of5.2 ± 0.6 µmol/min/g wet cells, or ≈ 5 ± 0.6 amol/min/cell.

Appendix F. List of symbols

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Symbol Typical units Brief definition[. . .] µM or mM concentration of . . .x or 〈x〉 – average of xLatinc µM or mM small molecule conc.D µm2 s−1 diffusion coefficientd mm colony diameterG amol/min/cell glucose consumption rateg m s−2 gravitational accelerationL µm cell body + flagellum lengthl µm cell body length`g µm gravitational lengthn cells/ml cell densityn – refractive indexQ amol/min/cell O2 consumption rateq µm−1 scattering vectorT K or C temperaturet s or min timetc s or min time of speed crashesu(t) – v(t)/v0

V µm3 volumev µm s−1 average speedv0 µm s−1 v(t = 0) ≡ v(0)vs µm s−1 sedimentation speedw0(c) – w0(c) = v0(c)/v0(c = 0)Greekα s−1 or min−1 growth rateβ – non-motile fractionγ – l/ση mPa s viscosityλ µm wavelength in vacuoµ µm cm V−1 s−1 electrophoretic motilityν – number of protons (H+)ξ pN s µm−1 friction coefficientρ g cm−3 (mass) densityσ µm cell body diameterτ s delay time, run time, life timeφ – cell body volume fraction

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Table B.2: E. coli strains and plasmids

Name Motility genotype/relevant characteristics SourceE. coli strainsMG1655 motility WT Laboratory strain [26]AB1157 motility WT Laboratory strain [153]RP437 motility WT J. Parkinson [154]HCB1 motility WT H. C. Berg [155]BW25113 Parent strain of Keio collection, motile [141]

HCB437∆(tsr)7021 ∆(trg)100 ∆(cheA-cheZ)2209Defective in chemotaxis, a smooth swimmer H. C. Berg

DM4 MG1655 + proteorhodopsin-expressing pBAD-HisC-PR This work

JSL1AB1157 ∆(cheY::kan)Smooth swimmer This work

AD1AB1157 fliC(S353C)Motility WT with FliC mutation to bind to Alexa dye This work

AD2AD1 ∆(cheY::kan)Smooth swimmer with FliC mutation to bind to Alexa dye This work

AD3AD1 ∆(ycgR::kan)Motility WT, unable to ‘brake’ This work

PlasmidspHC60 TetR, GFP constitutive [156]pBAD-HisC-PR AmpR, arabinose inducible proteorhodopsin [144]

18