Polymer-induced phase separation in Escherichia coli suspensions

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    View Article Online / Journal Homepage / Table of Contents for this issuePolymer-induced phase separation in Escherichia coli suspensions

    Jana Schwarz-Linek,a Alexander Winkler,b Laurence G. Wilson,a Nhan T. Pham,a Tanja Schillingb

    and Wilson C. K. Poon*a

    Received 7th April 2010, Accepted 25th June 2010

    DOI: 10.1039/c0sm00214cWe studied aggregation and phase separation in suspensions of de-flagellated Escherichia coli (AB1157)

    in phosphate buffer induced by the anionic polyelectrolyte sodium polystyrene sulfonate. We also

    performed Monte Carlo simulations of this system based on the AsakuraOosawa model of colloid

    polymer mixtures. The results of these simulations, as well as comparison with previous work on

    synthetic colloidpolymer mixtures, demonstrate that the role of the polymer is to cause a depletion

    attraction between the E. coli cells. The implication of these results for understanding the role of

    (predominantly anionic) extracellular polymeric substances (EPS) secreted by bacteria in various

    natural phenomena such as biofilm formation is discussed.Introduction

    Understanding the effect of polymers on suspensions of bacteria

    is important in diverse areas of microbiology. In nature, many

    bacteria secrete significant amounts of exopolysaccharides and

    other extracellular polymeric substances (EPS) like proteins and

    DNA into their surroundings.1,2 These polymers are important in

    bacterial aggregation, initial colonization of surfaces as well as

    development, maturation and stability of biofilms.3 Aggregation

    caused by the formation of complex polymeric structures like

    fibriles consisting of polysaccharideprotein mixtures4 is

    involved in spore formation of Myxococcus xanthus5 and plant

    root colonisation by Azospirillum brasilense.6 Industrially, poly-

    meric additives find widespread use, e.g. for concentrating

    bacteria in biotechnology, and for removing them in water


    Since bacteria usually carry a net negative surface charge,8

    synthetic polymeric additives for inducing bacterial aggregation,

    such as polyethylenimine, are mostly cationic polyelectrolytes,

    which can bridge neighbouring cells.9 This is analogous to the

    way synthetic colloids are bridged by oppositely charged poly-

    electrolytes.10 It has been shown that similar electrostatic inter-

    actions may be involved in biofilm formation. Microbially

    synthesized PGA, a homopolymer of b-1,6-linked N-acetylglu-

    cosamine, partly de-acetylated and therefore positively charged,

    can cause cellsurface and cellcell attachment in Staphylococcus

    epidermidis as well as Escherichia coli.11,12

    However, the majority of bacterial exopolysaccharides are

    anionic.1 From the perspective of colloid science, a dispersion of

    bacteria and anionic exopolysaccharides constitutes a mixture of

    like-charge colloids (the bacteria) and polymers (the exopoly-

    saccharides). Three generic mechanisms may be invoked toaSUPA and School of Physics & Astronomy, The University of Edinburgh,Kings Building, Mayfield Road, Edinburgh, EH9 3JZ, UK. E-mail:w.poon@ed.ac.uk; Fax: +44 (0)-131-6507174; Tel: +44 (0)-131-6505297bInstitut fur Physik, Johannes Gutenberg Universitat, 55099 Mainz,Germany

    Electronic supplementary information (ESI) available: Time course ofviable cells in MPB (with stills shown in Fig. 2). See DOI:10.1039/c0sm00214c

    Present address: Universite du Luxembourg, Luxembourg.

    4540 | Soft Matter, 2010, 6, 45404549explain polymer-induced aggregation in such mixtures.

    Consider, for specificity, anionic polyelectrolytes and colloids

    carrying a net negative charge (such as most bacteria).

    First, the colloids may be amphoteric, and display a minority

    of positive charges. On such heterogeneous charged surfaces,

    conditions exist in which the negative polymer segments may

    adopt loopy configurations to contact the positive surface

    patches.13 This could lead to bridging of nearby colloids, and

    hence aggregation.x This mechanism relies on strong electrostaticinteractions, and therefore operates only when there is little salt

    in the solvent to screen the Coulomb interaction. Secondly,

    polyvalent cations can form salt bridges between negatively

    charged bacteria and polymer, once again causing bridging.14

    At high enough salt concentrations and in the absence of

    polyvalent cations, a third mechanism can operate. Here, the

    Debye screening length (k1) may become significantly smaller

    than the size of the colloids and polymers, but is still large enough

    to prevent attractive van der Waals forces from operating. In

    these marginally screened mixtures of anionic polyelectrolytes

    and negatively charged colloids, we have effectively neutral

    particles with the size increased by k1, and slightly expanded

    polymer coils that are non-adsorbing to the particles. It has long

    been understood that the polymers in this situation cause an

    effective interparticle attraction by the depletion mechanism.15

    Exclusion of polymer from the region between two nearby

    particles leads to an unbalanced osmotic pressure pushing them

    together.{ The range of the resulting depletion attractionbetween particles is controlled by the size of polymer coils, while

    its strength increases with the polymer concentration.

    Depletion aggregation is well understood in uncharged

    colloidpolymer mixtures, especially mixtures of hard-sphere

    colloids and near-ideal linear polymers. In such model systems,

    experiments, theory and simulations show satisfactory agree-

    ment, especially in the limit where the polymers are substantiallyx At higher polymer concentration, it is possible that this mechanism mayalso give complete surface covering of the colloids and therefore lead tosteric (re)stabilisation of the suspension.

    { Thus, we require the polymer to be larger than k1. Otherwise, thesurfaces of neighbouring particles never come close enough to excludepolymer from the space between them.

    This journal is The Royal Society of Chemistry 2010


  • Fig. 1 AFM images of viable AB1157 cells harvested in stationary phase

    and washed using the protocol described in the text. Note that most cells

    have lost their flagella; the few flagella that are imaged are not clearly

    attached to cells. The width of the image is 10 mm.



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    View Article Onlinesmaller than the colloids.16 Marginally screened like-charge

    colloidpolymer mixtures display qualitatively identical

    phenomenology,1719 although quantitative explanation needs to

    take account of residual electrostatic repulsive effects.20 Mixtures

    of non-adsorbing polymers and colloidal rods have also been

    studied.21 The depletion attraction between two rods is aniso-

    tropic; being stronger for two rods aligned side by side than end

    on. High enough concentrations of polymer lead to nematic (or

    orientational) ordering if the aspect ratio of the rods is high


    There are few physico-chemical studies of bacterial aggrega-

    tion induced by anionic polyelectrolytes. Recently, however,

    Eboigbodin et al.22 investigated this phenomenon using a non-

    pathogenic laboratory strain of E. coli (AB1157) and the anionic

    polyelectrolyte sodium polystyrene sulfonate (NaPSS). They

    found that sufficient concentrations of NaPSS caused bacteria to

    phase separate out of solution, and suggested that this was due to

    depletion. Interestingly, Eboigbodin et al. found that the

    minimum concentration of NaPSS, c*P, needed for phase sepa-

    ration of bacteria at cell density cC increased with the latter, i.e.

    dc*P/dcC > 0. But depletion is due to crowdingbacteria (or

    other colloids) aggregate to make room for the highly entropic

    polymers, so that less polymer is needed to cause aggregation in

    a more concentrated suspension, i.e. dc*P/dcC < 0 if aggregation is

    depletion induced. An alternative mechanism may therefore be in


    Eboigbodin et al. worked in distilled water. Such low ionicity

    conditions favour the adsorption of an anionic polyelectrolyte onto

    a negatively charged surface with (minority) positive patches.13 As

    bacterial surfaces are indeed amphoteric,23 this mechanism

    could lead to the bridging of neighbouring cells. To bridge

    more cells, more polymer is required, resulting in dc*P/dcC > 0

    as found by Eboigbodin et al. Moreover, consistent with such an

    electrostatic bridging mechanism, these authors reported that more

    negatively charged cells were less aggregated by NaPSS. Thus it is

    likely that electrostatic interactions rather than depletion dominate

    in the system studied by Eboigbodin et al.kTo access depletion-induced phenomena in mixtures of E. coli

    and NaPSS, the electrostatic contribution needs to be significantly

    reduced. In this paper, we present such a study using the same

    bacterial strain as Eboigbodin et al.22 We followed closely their

    preparative protocol, with the important exception that we

    worked in a modified phosphate buffer (MPB) with ionicity in the

    region of 0.1 M rather than distilled water. We used cells with few

    or no flagella in order to access the basic physics first: flagella

    would complicate the colloidal interaction between cells, and the

    associated motility may give rise to new physics (since the

    particles in our colloidpolymer mixture would now be active).

    Our mixture should belong to the marginally screened

    regime. The Debye screening length in our MPB (see below for

    the exact composition) is calculated to be 0.8 nm, much smallerk A further complication in seeking to understand Eboigbodin et al.22 isthat by adding different amounts of NaPSS to distilled water, the pH andconductivity of the solutions are likely to vary. Over the range of thepolymer concentrations used, we measured a decrease in pH from 7.9to 5.3 going from 0.2 wt% to 10 wt% of polymer. Preliminarymeasurements show that the electrophoretic mobility of the cells andthe conductivity of the dispersions also change significantly over thisrange of polymer concentration.

    This journal is The Royal Society of Chemistry 2010than even the smaller of the two polymers we used (radius z 17nm, Appendix 1) or the size of an E. coli cell (Fig. 1). Charge

    effects must therefore be mostly screened out. For NaPSS, this is

    confirmed by literature data24 showing that NaPSS behaves very

    nearly as an ideal, uncharged random coil. On the other hand, we

    know that the screening has not gone so far as to induce aggre-

    gation on its own (salting out), since direct observation of pure

    cell suspensions and polymer solutions over the whole range of

    conditions we used did not detect any instability. The depletion

    mechanism therefore should operate.

    Indeed, we find that our system reproduces the phase separa-

    tion and transient gelation phenomena expected in a mixture of

    neutral colloids and non-adsorbing polymers.25

    We also performed Monte Carlo simulations of spherocy-

    linders and idealized polymers within the framework of the

    AsakuraOosawa model15 with parameters matching our

    experimental system. The shape of simulated and measured

    phase boundaries agree; there is also semi-quantitative agree-

    ment of simulated and measured phase boundaries. We therefore

    conclude that depletion is indeed the dominant mechanism

    causing aggregation and phase separation in E. coliNaPSS

    mixtures in 0.1 M phosphate buffer. Since bacterial exopoly-

    saccharides are predominantly anionic in character, this result

    has implications for a variety of important phenomena in

    microbiology such as biofilm formation.

    Some of our results have been announced before (Fig. 2, the

    high-cell-concentration portion of Fig. 3(A), and Fig. 6) in a brief

    comparative study26 of polymer-induced phase separation in E.

    coli and an unrelated Gram-negative bacterium, Sinorhizobium

    meliloti. We re-presented these results here for completeness.Materials and methods

    Chemicals and media

    All chemicals were of analytical or higher grade and obtained

    from Fisher Scientific (NaCl, H2SO4, H2O2 and ethanol), FlukaSoft Matter, 2010, 6, 45404549 | 4541


  • Fig. 3 Phase diagram for viable (A) and non-viable (B) E. coli AB1157

    in MPB with NaPSS1 (Mw 64700). For calculation of cell and poly-mer volume fraction, fc and hp, see text below. Note all axes are log-

    arithmic. Data points above an initial cell concentration of 5 109 cfuml1 are obtained from time-lapsed video observations (see Fig. 2), and

    indicate three different kinds of behaviour with time: A single phase,+ two-phase coexistence, B transient gels. Data points at cellconcentrations of 109 cells ml1 or lower indicate the position of the

    phase boundary, as estimated by the composition of the upper phase in

    phase coexisting samples with three initial cell concentrations for (A)

    2.2 1010, 5.5 1010, 1.1 1011 cfu ml1 and (B) 1.4 1010,4.5 1010, 9.1 1010 cfu ml1. The dashed line indicates theapproximate position of the equilibrium vapourliquid phase boundary

    according to the two datasets combined. The position of the phase

    boundary estimated from the averaged simulation data plotted in Fig. 7

    is also shown (:).

    Fig. 2 Samples of viable E. coli AB1157 (cell density 9.6 1010 cfuml1, corresponding to a cell volume fraction of 12.5%) dispersed inphosphate buffer with NaPSS1 (Mw 64700). The polymer weightfraction increasing from left to right, with samples 1 to 11 containing 0%,

    0.1%, 0.2%, 0.3%, 0.4%, 0.5%, 0.75%, 1%, 2%, 5% and 10% of NaPSS1.

    Times: (a) t 0, (b) t 30 min, (c) t 100 min, (d) t 24 h. Part (e)shows the lowest portion in samples 25 at 24 h at higher magnification.



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    View Article Online(HK2PO4 and H2KPO4) and Sigma-Aldrich (EDTA dipotassium

    salt, kanamycin and 3-aminopropyltriethoxysilane). Tryptone

    and yeast extract were purchased from Difco (Bacto, BD) and

    bacteriological agar (no. 1) from Oxoid.Bacteria

    The non-pathogenic strain E. coli AB1157 (DSM9036) was used.

    All cultivations were performed in LB medium (tryptone 10.0 g l1,

    yeast extract 5.0 g l1 and NaCl 5.0 g1) using an orbital shaker at

    30 C and 200 rpm. (Note that this differs from Eboigbodin et al.,

    who added 0.5% glucose (w/v) to their growth medium.) A pre-

    culture inoculated from a single colony on LB agar (tryptone 10.0

    g l1, yeast extract 5.0 g l1, NaCl 5.0 g1 and agar 15 g l1) was

    grown for 5 h and used in a 1 : 100 dilution to start an overnight

    culture. After reaching stationary phase (16 h) cells were harvested4542 | Soft Matter, 2010, 6, 45404549by centrifugation (10 min, 2700 g, Hermle Z323K) and preparedfor experiments (see below)). Optical density measurements at 600

    nm (Cary 1E, Varian) normalized by viable plate counts on LB

    agar of serial diluted samples (OD600nm 1 corresponding to 1.55 109 cfu ml1) were used to determine cell densities. Non-viablebacteria were obtained by heating suspensions at 60 C for 3060

    minutes. To confirm cells were non-viable, representative samples

    were serial diluted and plated on LB agar where no growth was

    observed after incubation at 30 C for 48 h.

    P1 phage transduction27 was used to create a non-flagellated

    mutant (AB1157DfliF) using the appropriate E. coli K-12 single

    knockout mutant available from the KEIO collection.28

    Kanamycin (final concentration 30 mg l1) was added to all

    growth media for AB1157DfliF.This journal is The Royal Society of Chemistry 2010


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    View Article OnlineA representative sample of bacteria treated using the standard

    preparation protocol was characterised using tapping-mode

    atomic force microscopy (Multimode Veeco with a NanoScope

    IIIa controller equipped with a J scanner) with silicon canti-

    levers (Veeco, spring constant k z 48 N m1 and resonancefrequency between 130 and 150 kHz). Glass coverslips (Agar

    Scientific, 13 mm diameter, no. 2 thickness) were treated prior to

    experiments using the following protocol. After cleaning in

    a 8 : 2 (v/v) solution of 96% H2SO4 and 30% H2O2 for 20 min,

    coverslips were rinsed with distilled water and dried in a stream

    of nitrogen. Subsequently, they were immersed in a 0.1%

    3-amino-propyltriethoxysilane solution in 95 : 5 ethanol : water

    for 20 min and rinsed with ethanol. 10 ml cell suspensions were

    deposited on a coverslip and left to settle for 5 min after which

    they were then rinsed gently with water and left to dry under

    ambient conditions. Comparison with optical microscopy

    suggests that our protocol did not significantly change cell shape

    or size.Polymer

    Sodium polystyrene sulfonate (Aldrich) of two different molec-

    ular weights was used: NaPSS1 (Mw 64700 g mol1, Mw/Mn 3.1) and NaPSS2 (Mw 620500 g mol1, Mw/Mn 4.6). Themolecular weights and polydispersities were determined by gel-

    permeation chromatography (GPC) against PSS standards.

    Dynamic light scattering returned a hydrodynamic radius of

    rH 8.7 0.1 nm for NaPSS1 in MPB. Polymer stock solutionswere prepared at 20% (w/v) in MPB and filtered through a 0.2 mm

    disposable syringe filter prior to use.Phase behaviour studies

    Cells were prepared using the following standard protocol. After

    harvesting at stationary phase, the cell pellet was washed three

    times with and re-suspended in MPB containing 6.2 mM

    K2HPO4, 3.8 mM KH2PO4, 67 mM NaCl and 0.1 mM EDTA

    (pH 7.0). Between washes centrifugation was carried out for 10min at 2700 g (Hermle Z323K). Vigorous shaking was used tore-suspend cells. By adjusting the final volume bacterial

    suspensions could be concentrated up to 200-fold compared to

    the original overnight culture. Observations were made in closed

    1.6 ml disposable cuvettes with a total sample volume of 1 ml.

    Polymer solution, cell suspension and MPB were mixed in

    different ratios to achieve cell concentrations in the range of

    5 109 cfu ml1 to 2 1011 cfu ml1 (corresponding to volumefractions of 0.5% to 20%, based on a single cell being a2 1 mm spherocylinder, see Fig. 1) and polymer concentrationsin the range of 0 to 10 wt% (with the overlap concentration

    corresponding to 5%, based on using a coil radius of 17.5 nm,see Appendix 1).

    Samples were homogenised by thorough mixing prior to

    incubation at 20 C (MIR-153, Sanyo). OD600nm was measured

    at the start and after a 24 h period. Aggregation was followed

    inside the incubator using a camera (QImaging, Micro-publisher

    3.3RTV) controlled by QCapture pro 5.0 software. Images were

    captured every two minutes for the initial two hours, and

    thereafter for varying periods up to and beyond 24 h. From theseThis journal is The Royal Society of Chemistry 2010images, we created videos using ImageJ (National Institutes of

    Health).Experimental results

    An AFM image of viable AB1157 cells is shown in Fig. 1. It

    illustrates that our preparative protocol removes most, if not all,

    flagella from the majority of cells, so that these can be appro-

    priately modelled as bare spherocylinders. From the images of

    40 cells, we measured the mean cell width and length to be

    D 0.95 0.2 mm and L 1.95 0.5 mm respectively. The meanaspect ratio is L/D 2 0.2. These findings are consistent withprevious data collected under a variety of conditions, showing

    that an aspect ratio of 2 : 1 is a lower bound,29 and that cells are

    smallest and least polydisperse in the stationary phase.30 Images

    of heat-treated, non-viable cells (not shown) reveal that they lose

    all flagella, maintain their overall shape and size, but have rather

    more irregular surfaces.

    Cuvettes containing bacteria and NaPSS dispersed in MPB at

    various concentrations were monitored by time-lapsed imaging.

    Since bacterial suspensions appear turbid in our sample cells

    even at the lowest concentrations studied here (5 109 cfuml1), sedimentation and phase separation are easily visible.

    Over the range of bacteria and polymer concentrations we

    investigated, three types of behaviour were seen irrespective of

    whether viable or non-viable cells were used. Here we show

    time-lapsed stills from experiments using viable cells and

    NaPSS1, Fig. 2 (see also Movie S1). At zero and the lowest

    concentration of added polymer (Fig. 2ad, samples 1 and 2) we

    observed a meniscus that moved down at a few mm within 24 h,

    which is consistent with what is expected for micron-sized

    objects (density z 1.08 g cm3)31 sedimenting in MPB (density z1.00 g cm3).32 In other words, we are seeing essentially single-cell


    At each cell concentration, there was a critical polymer

    concentration above which samples rapidly became optically

    inhomogeneous, with a region denser in bacteria building up

    at the bottom (Fig. 2bd). Eventually this resulted in

    completely phase separated samples. As the polymer concen-

    tration was increased, the phase separation process was found

    to accelerate.

    Three observations suggest that we are seeing thermody-

    namic phase separation into equilibrium coexisting phases.

    First the upper phase, whilst more dilute than the lower phase,

    certainly contains bacteria. This was evident to the naked eye in

    the case of sample 3, Fig. 2(e). Optical density measurements

    (see below) confirmed that this was also the case for other

    phase separated samples (such as 49 in Fig. 2(d)). Secondly, at

    a fixed cell concentration, increasing polymer concentration

    gave rise to upper phases containing decreasing number of

    bacteria. Again, this was evident by visual inspection (compare

    sample 3 with samples 4 and 5 in Fig. 2(e)), but also from OD

    measurements reported below. This is what is expected upon

    moving deeper into a thermodynamic two-phase coexistence

    region. Finally, we should anticipate the volume of the lower

    phase to increase correspondingly. This was indeed observed,

    Fig. 2(e).

    The phase coexistence here is of the vapourliquid kind. Two

    phases with low and high concentrations of colloids coexist, withSoft Matter, 2010, 6, 45404549 | 4543


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    View Article Onlinethe arrangement of particles being disorderly in both cases. This

    is analogous to the coexistence of vapour and liquid states at the

    boiling point of atomic and molecular liquids. Evidence for the

    fluid nature of the lower phase comes from the simple experiment

    of tilting phase separated samples; the meniscus separating the

    two phases remained horizontal in each case.

    Upon further increase of the polymer concentration, the

    acceleration in the phase separation process is abruptly arrested,

    samples 10 and 11 Fig. 2(c). Instead, these samples remained

    uniformly turbid throughout for extended periods before any

    sedimentation became visible. After 24 hours, all the bacteria

    were precipitated out in a solid-like mass. The interface between

    this precipitate and the supernatant was often visibly lumpy,

    and it did not remain horizontal when the sample was tilted.

    These observations are typical of the phenomenon of delayed

    sedimentation, which is widely seen in colloids with strong short-

    range attractions.33 There is an emerging consensus that such

    transient gelation is the result of arrested vapourliquid phase


    All three types of behaviour were found to be reversiblethe

    same observations were made in samples re-suspended by


    A summary of our observations is given in Fig. 3(A) in the

    form of a phase diagram.** Note that we report these results in

    two sets of variables. The experimental variables are the cell

    concentration in cfu per ml and the polymer concentration in

    weight percent. To facilitate theoretical comparison, we also

    show the respective volume fractions which were calculated as

    follows. The cell density in cfu per ml multiplied by a cell volume

    of 1.3 mm3 gives the cell volume fraction, fc, while the polymer

    weight (wp) and volume (hp) fractions are related by eqn (1)

    (see below) using a polymer radius of 17.5 nm (see Appendix 1).

    The latter procedure is appropriate for polydisperse polymers.35

    The lowest cell concentration we could use in these experi-

    ments was limited by the ability to detect phase separation

    visually and distinguish it from slow sedimentation.

    To access the phase boundary at concentrations lower than

    5 109 cfu ml1, a different approach was necessary. Wemeasured the optical density of the dilute, upper phase in samples

    showing two-phase coexistence. Thus, for example starting at

    9.6 1010 cfu ml1 (OD600nm > 3), after 24 h the OD600nm of theupper phase in samples 410 in Fig. 2(d) was measured to be

    0.7797, 0.5969, 0.5277, 0.3193, 0.2332, 0.0868 and 0.0523

    respectively, confirming the presence of cells in each case. Up to

    one unit OD600nm these values are proportional to cell density,

    with OD600nm 1 corresponding to 1.55 109 cfu ml1, thusgiving an estimate of bacterial concentration in the upper phase.

    The polymer concentration in the upper phase in each case will

    be higher than the polymer concentration in the sample as

    a whole, balancing a lower concentration of polymer in the

    coexisting lower phase more concentrated in bacteria. However,

    this difference is small for our samples, because of the small

    volume of lower phase in each case. Indeed, the maximum

    possible underestimate in taking the upper phase polymer

    concentration to be the average concentration is given by the** Note that this terminology is loose. Strictly speaking the reporting oftransient gelation has no place in a phase diagram, which, sensus strictus,only contains equilibrium thermodynamic information.

    4544 | Soft Matter, 2010, 6, 45404549percentage of the sample occupied by the lower phasefrom

    5 wt% in sample 4 to 13% in sample 9. With this proviso, wewere able to calculate the cell density in the upper phase for each

    sample (49). These are plotted in Fig. 3(A), and should give

    a lower bound for the low-bacterial-concentration side of the

    phase boundary. Results obtained by repeating this procedure

    for samples with initial cell densities of 2.2 1010 and 1.1 1011 ml1 are also shown.

    Experiments using non-viable cells gave results that were

    qualitatively identical to those made using viable cells: the same

    three kinds of behaviour were seen as polymer concentration was

    increased. This is not surprising considering the similar cell

    shapes and dimension in both cases. Only very small quantitative

    differences were found, summarized in a second phase diagram,

    Fig. 3(B). Similarly, a limited number of experiments using viable

    cells of the AB1157DfliF mutant unable to synthesize flagella,

    gave results which were identical to viable wild-type cells

    prepared using the vigorous washing procedure (data not


    We repeated our experiments using a higher molecular weight

    sodium polystyrene sulfonate (NaPSS2, Mw 620500). Theresults for viable cells are summarised in Fig. 4 (with hp calcu-

    lated using a polymer radius of 54.2 nm). Results for non-viable

    cells (not shown) are identical within experimental uncertainties.

    Phase separation was observed above a polymer concentration of

    0.05 wt%. The phase boundary was flat but at lower wt%

    compared to NaPSS1.Simulations

    To help elucidate the mechanism for polymer-induced phase

    separation in the bacterial suspensions, we performed Monte-

    Carlo simulations of our experimental system in the spirit of

    what is perhaps the simplest possible model of colloidpolymer

    mixtures, the AsakuraOosawa (AO) model. In the original AO

    model15 both colloids and polymers are modelled as spheres. The

    colloids are hard spheres. The polymers are spheres of radius r

    that are interpenetrable to each other but whose centres cannot

    approach closer than a distance r from the surface of the hard


    The AO model offers a reasonably quantitative account of

    mixtures of nearly monodisperse hard-sphere colloids and

    polymers in nearly q (or ideal) solvents.16 We replace the hard

    spheres by hard spherocylinders. Again, the polymers are

    modelled as spheres that can penetrate each other but cannot

    overlap with the hard spherocylinders,36 Fig. 5.

    Choosing r, the radius of the AO spheres representing the

    polymers, is less straightforward. Finding the best value of r in

    an AO-simulation to represent a particular experimental system

    is beset with experimental uncertainties (e.g. the solvent quality is

    often not precisely known). There is also the theoretical issue of

    how to model the depletion of polymer segments next to

    a particle surface by a single parameter, the depletion layer

    thickness. The issue is nevertheless important. While in the The electrophoretic mobilities of viable and non-viable cells (washedand re-suspended in MPB) of wild type as well as DfliF mutant areidentical to within 5% (data not shown), suggesting that they haveapproximately equal surface charges.

    This journal is The Royal Society of Chemistry 2010


  • Fig. 5 The AsakuraOosawa model for a mixture of polymers and rod-

    shaped bacteria. The bacteria are represented as spherocylindrical

    particles (such as 1, 2 and 3). Each polymer coil is represented as a sphere

    of radius r (inset). These spheres can interpenetrate each other, but the

    centre of a sphere cannot come closer than a distance r to the surface of

    the spherocylinder. Each particle is therefore surrounded by a depletion

    zone (delineated by thin dotted lines). There are no polymers within the

    overlapping depletion zones of two neighbouring particles (hatched); the

    resulting imbalance in osmotic pressure pushes the two particles together.

    This is the origin of the depletion attraction. Consideration of the volume

    of overlapping zones immediately suggests that the depletion attraction

    between particles 1 and 2, in the parallel configuration, will be the

    greatest compared to that between particles in any other mutual orien-

    tation (such as 2 and 3). The dotted background indicates the free

    volume available to the centres of the interpenetrable polymer spheres.

    Fig. 4 Phase diagram for viable E. coli AB1157 in MPB with NaPSS2

    (Mw 620500). Note axes are logarithmic and the same as in Fig. 3. Datapoints above an initial cell concentration of 5 109 cfu ml1 areobtained from time-lapsed video observations, and indicate two different

    kinds of behaviour with time: A single phase, + two-phase coexis-tence. Data points at lower cell concentrations indicate the position of the

    phase boundary, as estimated by the composition of the upper phase in

    phase coexisting samples from samples with three initial cell concentra-

    tions: 1.0 1010, 5.2 1010 and 1.0 1011 cfu ml1. The dashedline indicates the approximate position of the equilibrium vapourliquid

    phase boundary according to the two datasets combined.

    This journal is The Royal Society of Chemistry 2010



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    View Article Onlinesimulations we control the volume fraction of interpenetrable

    spheres, hp, the corresponding experimental variable is the weight

    fraction of polymers, wp. These two parameters are related by

    wp h




    where r0 is the density of the solution (1 g cm3), NA is Avo-gadros constant, and vp is the volume of a polymer coil.

    Crucially, vP (4/3)pr3, so that converting between hp and wpdepends strongly on r.

    Appendix 1 explains why we chose to perform simulations

    using 2r 35 nm, which is the largest possible value of r con-strained by our experimental measurement of the hydrodynamic

    radius using dynamic light scattering and theoretical information

    available from the literature (see Appendix 1). Using the largest

    possible value for r should give a lower bound for the phase

    boundary in a representation where polymer concentration is

    reported in weight fraction. Even with the choice of the largest

    possible value for r, the size ratio D/r z 29 is still large, so thatmany polymers (interpenetrable spheres) are required per

    bacterium (hard spherocylinder). Thus, special simulation

    techniques are necessary and the simulations are restricted to

    a small number of spherocylinders. Configuration space was

    explored by local translation and rotation moves and by cluster

    moves. In order to avoid checking for overlaps with spherocy-

    linders at a distance larger than the range of interaction, we used

    cell systems. Due to the large size ratio we needed two systems of

    different cell size. One was on the order of the spherocylinder

    diameter, D, and it was used for checking cylindercylinder

    overlaps. The second one consisted of very small cells on the

    order of the diameter of the interpenetrable spheres, 2r, and it

    was used for detection of spherespherocylinder overlaps.

    As there is a high probability of generating overlaps with the

    surrounding spheres for every displacement of a spherocylinder

    over a distance on the order of D, standard translation and

    rotation moves lead to very small acceptance probabilities (or to

    very small displacements).

    One possible approach to this problem is to derive an

    approximation to the effective interaction potential between the

    colloids by integrating out the degrees of freedom of the poly-

    mers. Simulations are then performed for the colloids only using

    the effective interactions.37 Another possibility, which explicitly

    includes the degrees of freedom of the polymers, is to apply

    rejection-free schemes.38,39

    However, rejection-free schemes in which a cluster of particles

    is mirror reflected at a pivot point would be computationally

    expensive at our target densities due to the large number of

    particles involved. If a spherocylinder overlaps with another

    spherocylinder or with a polymer sphere, we reject the move.

    These spherocylinder moves are similar to the rejection free

    moves introduced previously.38,39 However, our moves include

    some probability for rejection. For the concentrations studied

    here, the computational cost for the rejections is more than

    compensated by the smaller number of distance computations

    involved in one move.

    We used three different types of cluster moves:

    1. Translate the spherocylinder along the translation vector M.

    Mirror reflect all spheres which overlap with the new position of

    the spherocylinder at the center of M.Soft Matter, 2010, 6, 45404549 | 4545


  • Fig. 7 Simulation results for predicted phase boundaries. Data points

    indicate two different kinds of behaviour: A single phase and + two-phase coexistence.



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    View Article Online2. Rotate the spherocylinder like in the ordinary MC moves.

    Calculate the vector w u + v, where u and v are the directionalvectors of the cylinder before and after the rotation. Detect the

    overlapping spheres and rotate them by p around the axis w.

    3. Detect a cluster of spherocylinders and proceed like in

    cluster move 1 for every individual translation vector of the

    spherocylinders in the cluster.

    Since the size ratio is very large, systems near the phase

    boundary, or binodal, contain very high numbers of spheres. We

    used a box size (measured in units of spherocylinder diameter) of

    9 9 9 for spherocylinder volume fractions between f 5.03% and 9.3% and a box size of 12 12 12 for lower volumefractions. For these system sizes simulations with up to 6 million

    spheres were performed, which were computationally expensive

    (ca. one month of CPU time on a Intel(R) Xeon(R)CPU E5345

    running at 2.33GHz). Therefore, we could not compute free

    energy differences, but rather had to extract an estimate for the

    location of the binodal from visual observation of snapshots and

    from measuring the cluster size distribution, P(S). A cluster

    consists of connected spherocylinders where two spherocylinders

    are called connected if their depletion zones overlap. The size

    of a cluster is the number of spherocylinders which belong to it.

    Typical histograms of P(S) are shown in Fig. 6. The continuous

    distribution in Fig. 6(a) corresponds to a sample that remains

    single phase, while the twin-peaked distribution in Fig. 6(b) we

    take as the signature of phase separation. Note that we cannot

    access spherocylinder volume fractions below 1% because ofthe very large number of polymer spheres such simulations

    would entail.

    Our simulation results are summarized in Fig. 7 plotted in

    terms of the volume fractions of spherocylinders, fc, and poly-

    mer spheres, hP. We estimate the phase boundary (or binodal) toFig. 6 Distribution of cluster sizes. P(S) gives the probability of

    encountering a cluster of size S. Note that the vertical scale is logarithmic.

    (a) Cluster size distribution for a sample that we consider to be in the

    single-phase region of the phase diagram; P(S) is approximately expo-

    nential. (b) Cluster size distribution for a sample in what we consider to

    be a phase separated sample, displaying two peaks.

    4546 | Soft Matter, 2010, 6, 45404549be mid-way between the highest single-phase sample and the

    lowest phase separated sample at each spherocylinder concen-

    tration. To compare with experiments, we convert hP into

    polymer weight fraction using eqn (1), and fC into cell concen-

    tration by dividing by the volume of a 2 1 mm spherocylinder(1.3 mm3). The phase boundary estimated from simulations in

    this way is shown in Fig. 3.Discussion

    The observed phenomenology summarized in Fig. 3 can be

    mapped onto that seen in mixtures of synthetic colloids and non-

    adsorbing polymers, where depletion is known to be operative.

    In a nearly monodisperse suspension with volume fraction

    (40%, adding sufficient polymer leads to fluidcrystal phase

    separation.16 Buried in the fluidcrystal coexistence region of the

    phase diagram, there is a metastable vapourliquid phase

    boundary.16 Particles that are sufficiently polydisperse or non-

    spherical in shape will not be able to crystallize. In such

    a suspension where crystallization is suppressed, increasing

    polymer concentration gives rise to vapourliquid phase sepa-

    ration instead.40 In both cases, the highest concentrations of

    polymer lead to transient gelation.16

    If the particles are sufficiently anisotropic, adding polymer

    leads to coexistence of isotropic and nematic phases of the

    particles. For spherocylinders, this requires an aspect ratio of


    Our E. coli cells may be approximated as somewhat poly-

    disperse spherocylinders of aspect ratio z 2, which is too low forthe occurrence of a nematic phase. If depletion is the dominant

    mechanism in our bacteriapolymer mixtures, we may therefore

    expect that adding polymer should give rise to vapourliquid

    phase separation, which is exactly what we observed, Fig. 2. As the number of spherocylinders in the simulations is rather small, weoverestimate the densities at the binodal due to droplet evaporation.Under conditions in which the bulk would be phase separated it isentropically favourable to break up a cluster of rods into severalsmaller clusters. Therefore one needs a larger density of depletant ina finite system to produce a single droplet than in the bulk.

    This journal is The Royal Society of Chemistry 2010


  • xx We have shown before26 that the phase boundary also moves withpolymer chain stiffness in a way that is consistent with depletion.



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    View Article OnlineQualitatively, this provides direct evidence that phase separation

    in our mixtures is depletion-driven.

    On the other hand, the shape of the directly measured phase

    boundaries in the range of cell concentration between 5 109and 1011 cfu ml1 does not immediately support a depletion

    mechanism. As we have already explained, since depletion is

    a crowding effect, we expect that less polymer should be needed

    to cause phase separation at higher cell densities, i.e. the phase

    boundary should have a negative slope. But the directly

    measured phase boundaries at cell densities between 5 109 and1011 cfu ml1, Fig. 3, appear flat. However, the indirectly

    measured phase boundary at cell densities below 109 cfu ml1,Fig. 3, does have a pronounced negative slope, suggesting that

    the boundary at higher concentrations should indeed have

    a negative slope, but of such small magnitude as to be hardly

    measurable. Importantly, the simulated phase boundary at

    higher cell densities is also essentially flat. Depletion therefore

    remains the most likely mechanism in operation.

    Our data obtained using the higher molecular weight polymer

    NaPSS2, Fig. 4, provide further support for this claim. Within

    the AO model, the depletion potential at contact between two

    spherical particles of radius a induced by polymers of radius r, so

    that x r/a, is given by41

    U contactdep

    kBT 3




    where kBT is the thermal energy and hfree is the concentration of

    polymers in the free volume left by the spherical particles

    (dotted region in Fig. 5). In the limit of x 1, hfree z h/(1 f),where f is the volume fraction of particles, and h is the volume

    fraction of polymer in the total sample volume. The weight

    fraction (wp) of a polymer with molecular weight Mw has already

    been given in eqn (1). If we assume that the depletion potential at

    the phase boundary at any given f is constant, then eqn (1) and

    (2) together give the result that the weight fraction of polymer

    needed to cause phase separation should scale as Mw/r2. In an

    ideal solvent, r z M1/2w , so that we expect the phase boundary inthe (f, wp) plane to be independent of molecular weight. In

    a good solvent, r z M0.588w , so that we expect the phase boundaryto scale as M0.176w ; in other words, a 10-fold increase in molecular

    weight should drop the phase boundary in the (f, w) plane by

    about one third. Experimentally, we find that the phase bound-

    aries in Fig. 3A and B lie within the range 0.1% < w < 0.2%, while

    the boundary in Fig. 4 lies within 0.05% < w < 0.1%. This

    observed small shift downwards is consistent with depletion

    operating with the polymers being in a slightly better-than-q

    solvent. A theoretically better justified procedure, matching

    second virial coefficients for the two cases rather than Ucontactdep (see

    Appendix 2), does not change this conclusion.

    Quantitatively, the simulated boundary occurs for NaPSS1 at

    a polymer weight fraction (w z 0.03%) that is about a factor of5 lower than the measured ones (at w z 0.15%). There aretwo reasons why we may expect the simulated boundary to be

    lower than the measured ones. First, recall that we used the

    largest justifiable diameter for the polymer spheres,

    r 1:8rH2=ffiffiffiffip

    p 17:5 nm, in our AO simulations. So the

    simulated boundary plotted in Fig. 3 should represent a lower

    bound. We can estimate an upper bound for the AO phase

    boundary by using the smallest possible r 8.7 nm rH. If, as weThis journal is The Royal Society of Chemistry 2010have argued above, the phase boundary scales at least approxi-

    mately as Mw/r2, then we may expect the boundary to shift from

    w z 0.03% to w z 0.03 (17.5/8.7)2 0.12%. The apparentlynear-perfect agreement of this value with the observed position

    of the phase boundary is no doubt fortuitous. Indeed, we expect

    that in reality, 8.7 nm < r < 17.5 nm, so that the AO boundary

    will still be somewhat lower than the observed ones. Again,

    matching second virial coefficients rather than contact potentials

    (Appendix 2) does not change this conclusion.

    The polyelectrolyte nature of NaPSS constitutes a second

    reason why the observed phase boundaries may be expected to lie

    above the simulated one. Each polymer molecule gives rise to

    a large number of Na+ counter ions when it is dissolved. In MPB

    preliminary conductivity measurements showed an increase from

    10 to 30 mS cm1 for polymer samples of 0.1 and 10% respec-

    tively. This leads to increased screening of the polystyrene

    sulfonate backbone and therefore shrinking of the polymer coils.

    This decrease in r would again lead to an experimental phase

    boundary at higher wP then predicted by a model in which

    individual polymer coils remain at a constant size irrespective of

    the polymer concentration.

    We should mention that due to the finite system size and the

    use of the canonical ensemble in the computer simulations, we

    overestimate the location of the binodal. Such effects have been

    observed in several other systems before,42 and were always on

    the order of a few percent. We therefore assume that the finite

    size correction in our case is also weak. But we have no

    knowledge of the relevant interfacial energies to give a precise


    We used sodium polystyrene sulfonate, an anionic poly-

    electrolyte, to induce phase separation and transient gelation in

    suspensions of stationary phase grown, deflagellated E. coli

    AB1157 suspended in modified phosphate buffer. We have

    argued that under our experimental conditions, the polymer and

    bacteria should both be marginally screened. Thus, the deple-

    tion mechanism should operate, whereby the polymer induces an

    effective attraction between bacteria. The phase separation and

    transient gelation phenomenology we observed are analogous to

    similar phenomena seen and extensively studied in mixtures of

    non-adsorbing polymers and spherical colloids, where depletion

    is undoubtedly the responsible mechanism. The phase boundary

    was observed to move with polymer molecular weight in

    a manner that is consistent with depletion.xx We thereforesuggest that depletion is the dominant mechanism causing phase

    separation in our system. Simulations of depletion-induced phase

    separation using the AsakuraOosawa model provided further

    support for this.

    Previous studies22 of mixtures of NaPSS and E. coli used

    distilled water as the suspension medium. We argued that the

    phenomenology in this distilled-water-based system was domi-

    nated by electrostatics. In particular, the positive slope of the

    observed phase boundary led us to suggest that depletion was not

    the operative mechanism. The experiments and simulationsSoft Matter, 2010, 6, 45404549 | 4547


  • {{ This is defined as I P

    z2i ci. The summation is over all N species ofions. The i-th species has charge zi (in units of the electronic charge) and(molar) concentration ci. In MPB, the main contributing species are 0.01M potassium phosphate and 0.067 M NaCl.



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    View Article Onlinereported here strengthen the plausibility of this suggestion. As

    a consistency check, we performed a limited number of experi-

    ments in distilled water and the resulting phase diagram also

    showed a positive slope for the phase boundary (data not

    shown). Whether other mechanisms contribute to aggregation

    and phase separation in the distilled water system remains

    unknown and intriguing. The recent prediction13 of the possible

    adsorption of anionic polyelectrolytes onto negative surfaces

    that also carry a minority of positive charges at low ionicity offer

    an interesting possibilitythe adsorbed polymers can then

    bridge neighbouring bacteria.

    The majority of bacterial exopolysaccharides are anionic. Our

    experiments suggest that such exopolysaccharides can induce

    depletion attraction between bacteria irrespective of any specific

    chemical or biochemical effects they may have (such as adhesion,

    recognition by receptors, etc.) at physiological ionicity (0.1 M).In the microbiology literature, appeal is almost invariably made

    to these latter, specific, effects to explain experimental observa-

    tions, with depletion almost never considered. This is no longer

    tenable in view of our results. Since depletion is generic, its role

    must always be taken into account.43 Experiments using the

    nitrogen-fixing bacterium S. meliloti and a variety of anionic

    polyelectrolytes of biological and chemical origin confirm this

    conclusion, since depletion was also shown to be the operative

    mechanism in these mixtures.44 Since depletion also operates

    between a bacterium and a surface,45 it may also play a role in the

    initial stages in biofilm formation. Note that the non-motile state

    of our cells may be of particular relevance: the biofilm phenotype

    of several bacteria, for instance S. meliloti, E. coli and Pseudo-

    monas aeruginosa is often associated with down-regulation of


    Finally, we comment on how the presence of flagella may

    affect the phenomenology. Passively, if the flagella are not

    bundled, they may provide a degree of steric stabilization,

    hindering the surfaces of neighbouring bacteria from coming

    close enough for depletion to take effect. Actively, flagella enable

    motility which could also have a large effect. We can see this by

    calculating the depletion force holding two bacteria together,

    a lower bound of which can be estimated by

    FdepzU contactdep


    This comes to 0.5 pN at the phase boundaries shown inFig. 3, which is comparable to the hydrodynamic drag on a 1mm sphere moving at 2030 mm s1 (typically E. coli swimming

    speed). We therefore expect motility to affect very significantly

    the phenomenology reported here. Experiments to test and

    quantify these predictions are underway in our laboratory.

    Appendix 1: estimation of polymer radius in the AOmodel

    In the AO model, polymers are treated as interpenetrable spheres

    of radius r, such that the centre of a polymer cannot approach

    closer than distance r to the surfaces of the hard particles present

    in the system. It is clear that below the concentration at which

    polymer coils overlap (the overlap concentration), r should scale

    as the dimension of single coil. But there is no unique recipe for

    mapping the various possible dimensional measures of polymers4548 | Soft Matter, 2010, 6, 45404549to r. Theory suggests that the thickness of the layer depleted of

    polymer segments for an ideal and athermal polymer next to a

    flat hard wall is given by r 2=ffiffiffiffip

    prgz1:13rg49 and r 1.074rg50

    respectively, where rg is the radius of gyration of the individual

    polymer coils. The athermal result applies only at zero polymer

    concentration; the prefactor decreases as the concentration

    increases. NaPSS1 has a hydrodynamic radius of rH 8.7 0.1 nm and behaves like a neutral polymer in a good solvent

    in 0.1 M NaCl, but becomes progressive more ideal at higher salt

    concentrations.23 Our experiments are performed using poly-

    disperse polymers (Mw/Mn 3.1) in MPB with a total ionicstrength{{ of I z 0.18 M. For linear monodisperse polymers ingood solvents rg/rH 1.6, while in q solvents rg/rH 1.5 and1.7 for monodisperse and polydisperse coils with Mw/Mn 2,respectively.51 For our (larger) polydispersity, we may then

    expect rg/rH > 1.7. Using r/rg 1.13, rH 8.7 nm and rg/rH 1.8(since we have Mw/Mn > 2), we estimate 2r z 35 nm.

    In the simulations, we vary the volume fraction of the poly-

    mers, h 4/3pr3r, where r is the number density of inter-penetrable spheres. We convert h into weight fraction for

    comparing with experiments using eqn (1). Theory suggests that

    Mw is the appropriate average to use when the polymer is poly-

    disperse.35Appendix 2: mapping phase boundaries viacorresponding states

    For soft and hard spheres interacting with a variety of attractive

    potentials, a law of corresponding states exists. In particular, the

    critical volume fraction, fc, and a reduced second virial coeffi-

    cient, b2c, at the critical point, stay remarkably constant as the

    details of the interaction potential are varied.52 The second virial

    coefficient of a system of particles with interparticle potential

    U(r) is given by

    B2 2pN


    dr r21 eUr=kBT

    For attractive hard spheres (diameter s), the reduced second

    virial coefficient is given by

    b2 B2


    whereBHS2 2/3ps3 is the second virial coefficient of the hardspheres without attraction. For many different interparticle

    potentials, fc z 0.2 and b2c z 1.5.53 A similar result likelyholds for hard spherocylinders interacting via an attractive

    square well.52 We can use these results to predict how the phase

    boundary should move when the polymer molecular weight is

    changed, or if a different AO polymer radius is used to convert

    the simulations to experiments. The reduced second virial coef-

    ficient of spherocylinders of length L and diameter D (aspectThis journal is The Royal Society of Chemistry 2010


  • Publ


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    View Article Onlineratio a L/D) interacting via a square well attraction of depth 3and range lD is given by52

    b2 B2




    l3 1


    l2 1


    4a2l 1

    e3=kBT 1

    23 a 1


    We can make use of this result if we approximate the depletion

    attraction between bacteria by a square well with the same

    contact energy, and have a means to estimate this contact value.

    As an approximation, we replaced the spherocylinders by spheres

    with the same volume, and then used the AO model for spherical

    particles and polymers given in eqn (1) in the main text to esti-

    mate 3. We first calculated the reduced second virial coefficient

    along the experimental boundary in Fig. 3 (with 1 cfu ml1

    corresponding to f 1.3 1012) and then assumed that thesame b2(f) to be the phase boundary also for the larger polymer.

    Converting this back into polymer weight fraction using eqn (2),

    we find that the weight fraction of polymer to cause phase

    separation should drop by 25% and 50% under ideal andgood solvent conditions respectively. Next we calculated the

    second virial coefficient along the simulated phase boundary

    (Fig. 3(A), calculated using an AO polymer radius of

    r 17.5 nm), and used a similar procedure to predict wherethis boundary would be located if an AO polymer radius of

    r rH 8.7 nm was used instead. This gives a 4.6-fold rise in theboundary in the (f, wp) plane, only slightly different from the

    4-fold change predicted by matching contact potentials rather

    than second virial coefficients.Acknowledgements

    We thank Gail Ferguson and Graham Walker for providing the

    E. coli strain (AB1157) used in this work. The EPSRC funded

    WCKP and JSL (EP/D071070/1), LGW and NTP (EP/E030173)

    and GD (studentship). We thank Catherine Biggs for intro-

    ducing us to the subject. NaPSS molecular weight and poly-

    dispersity analysis were funded by the EPSRC and performed at

    Rapra Technology.References

    1 I. W. Sutherland, Microbiology (UK), 2001, 147, 39.2 J. Wingender, T. R. Neu and H.-C. Flemming, Microbial Extra-

    Cellular Polymeric Substances: Characterization, Structure andFunction, Springer, 1999.

    3 L. Hall-Stoodley and P. Stoodley, Curr. Opin. Biotechnol., 2002, 13,228233.

    4 H. C. Flemming, T. R. Neu and D. J. Wozniak, J. Bacteriol., 2007,189, 79457947.

    5 R. M. Behmlander and R. Dworkin, J. Bacteriol., 1994, 176, 62956303.

    6 S. Burdman, E. Jurkevitch, M. E. Soria-Diaz, A. M. G. Serrano andY. Okon, FEMS Microbiol. Lett., 2000, 189, 259264.

    7 O. Bayat, V. Arslan, B. Bayat and C. Poole, Biochem. Eng. J., 2004,18, 105110.

    8 V. P. Harden and J. O. Harris, J. Bacteriol., 1953, 65, 198202.9 R. H. Harris and R. Mitchell, Annu. Rev. Microbiol., 1973, 27, 2750.

    10 S. Barany and A. Szepesszentgyorgyi, Adv. Colloid Interface Sci.,2004, 111, 117129.This journal is The Royal Society of Chemistry 201011 S. Amini, H. Goodarzi and S. Tavazoie, PLoS Pathog., 2009, 5,e1000432.

    12 C. Vuong, S. Kocianova, J. M. Voyich, Y. Yao, E. R. Fischer,F. R. DeLeo and M. Otto, J. Biol. Chem., 2004, 279, 5488154886.

    13 N. Hoda and S. Kumar, J. Chem. Phys., 2008, 128, 164907.14 J. A. Libera, H. Cheng, M. O. de la Cruz and M. J. Bedzyk, J. Phys.

    Chem. B, 2005, 109, 2300123007.15 S. Asakura and F. Oosawa, J. Chem. Phys., 1954, 22, 12551256.16 W. C. K. Poon, J. Phys.: Condens. Matter, 2002, 14, R859R880.17 P. R. Sperry, J. Colloid Interface Sci., 1982, 87, 375384.18 P. R. Sperry, J. Colloid Interface Sci., 1984, 99, 97108.19 P. R. Sperry, H. B. Hopfenberg and N. L. Thomas, J. Colloid

    Interface Sci., 1981, 82, 6276.20 A. P. Gast, W. B. Russel and C. K. Hall, J. Colloid Interface Sci.,

    1986, 109, 161171.21 P. G. Bolhuis, A. Stroobants, D. Frenkel and H. N. Lekkerkerker,

    J. Chem. Phys., 1997, 107, 15511564.22 K. E. Eboigbodin, J. R. A. Newton, A. F. Routh and C. A. Biggs,

    Langmuir, 2005, 21, 1231512319.23 Y. Hong and D. G. Brown, Colloids Surf., B, 2006, 50, 112119.24 L. X. Wang and H. Yu, Macromolecules, 1988, 21, 34983501.25 W. C. K. Poon, A. D. Pirie and P. N. Pusey, Faraday Discuss., 1995,

    101, 6576.26 J. Schwarz-Linek, G. Dorken, A. Winkler, L. G. Wilson, N. T. Pham,

    C. E. French, T. Schilling and W. C. K. Poon, Europhys. Lett., 2010,89, 68003.

    27 J. H. Miller, Experiments in Molecular Genetics, Cold Spring HarborLaboratory Press, 1972.

    28 T. Baba, T. Ara, M. Hasegawa, Y. Takai, Y. Okumura, M. Baba,K. A. Datsenko, M. Tomita, B. L. Wanner and H. Mori, Mol.Syst. Biol., 2006, 2, 111.

    29 F. J. Trueba and C. L. Woldringh, J. Bacteriol., 1980, 142, 869878.30 T. Akerlund, K. Nordstrom and R. Bernander, J. Bacteriol., 1995,

    177, 67916797.31 J. E. Bailey and D. F. Ollis, Biochemical Engineering Fundamentals,

    McGraw Hill, 2nd edn, 1986.32 J. E. Schiel and D. S. Hage, Talanta, 2005, 65, 495500.33 W. C. K. Poon, L. Starrs, S. P. Meeker, A. Moussaid, R. M. L. Evans,

    P. N. Pusey and M. M. Robins, Faraday Discuss., 1999, 112, 143154.34 E. Zaccarelli, J. Phys.: Condens. Matter, 2007, 19, 323101.35 P. B. Warren, Langmuir, 1997, 13, 45884594.36 S. Jungblut, R. Tuinier, K. Binder and T. Schilling, J. Chem. Phys.,

    2007, 127, 244909.37 S. V. Savenko and M. Dijkstra, J. Chem. Phys., 2006, 124, 234902.38 C. Dress and W. Krauth, J. Phys. Chem., 1995, 28, L597L601.39 J. Liu and E. Luijten, Phys. Rev. Lett., 2004, 92, 035504.40 D. J. Fairhurst, PhD thesis, School of Physics, University of

    Edinburgh, 1999.41 J. Bergenholtz, W. C. K. Poon and M. Fuchs, Langmuir, 2003, 19,

    44934503.42 H. L. Vortler, K. Schafer and W. R. Smith, J. Phys. Chem. B, 2008,

    112, 46564661.43 K. E. Eboigbodin and C. A. Biggs, Biomacromolecules, 2008, 9, 686

    695.44 G. Dorken, J. Schwarz-Linek, L. G. Wilson, G. P. Ferguson and

    W. C. K. Poon, in preparation.45 R. P. Sear, Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat.

    Interdiscip. Top., 1998, 57, 19831989.46 S. Y. Yao, L. Luo, K. J. Har, A. Becker, S. Ruberg, G.-Q. Yu, J.-B. Zhu

    and H.-P. Cheng, J. Bacteriol., 2004, 186, 60426049.47 C. Prignet-Combart, O. Vidal, C. Dorel and P. Lejeune, J. Bacteriol.,

    1999, 191, 59936002.48 E. S. Garrett, D. Perlegas and D. J. Wozniak, J. Bacteriol., 1999, 181,

    74017404.49 H. Dehek and A. Vrij, J. Colloid Interface Sci., 1982, 88, 258273.50 A. Hanke, E. Eisenriegler and S. Dietrich, Phys. Rev. E: Stat. Phys.,

    Plasmas, Fluids, Relat. Interdiscip. Top., 1999, 59, 68536878.51 M. Rubinstein and R. H. Colby, Polymer Physics, Oxford University

    Press, 1st edn, 2003.52 D. C. Williamson and Y. Guevara, J. Phys. Chem. B, 1999, 103, 7522

    7530.53 M. G. Noro and D. Frenkel, J. Chem. Phys., 2000, 113, 29412944.Soft Matter, 2010, 6, 45404549 | 4549


    Polymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214c

    Polymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214c

    Polymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214cPolymer-induced phase separation in Escherichia coli suspensionsElectronic supplementary information (ESI) available: Time course of viable cells in MPB (with stills shown in Fig.nbsp2). See DOI: 10.1039/c0sm00214c


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