Smectic-like bundle formation of planktonic bacteria upon nutrient starvation
Takuro Shimaya1, ∗ and Kazumasa A. Takeuchi1, 2, †1

arXiv:2407.05031v1 [physics.bio-ph] 6 Jul 20242

Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Institute for Physics of Intelligence, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan(Dated: July 9, 2024)
Bacteria aggregate through various intercellular interactions to build biofilms, but the effect ofenvironmental changes thereupon remains largely unexplored. Here, by using an experimental device
that overcomes past difficulties, we observed the collective response of Escherichia coli aggregatesagainst dynamic changes in the growth condition. We discovered that nutrient starvation caused
bacterial cells to arrange themselves into bundle-shaped clusters, developing a structure akin tothat of smectic liquid crystal. The degree of the smectic-like bundle order was evaluated by a deeplearning approach. Our experiments suggest that both the depletion attraction by extracellularpolymeric substances and the growth arrest are essential for the bundle formation. Since theseeffects of nutrient starvation at the single-cell level are common to many bacterial species, bundle
formation might also be common collective behavior that bacterial cells may exhibit under harshenvironments.
I.

INTRODUCTION

Under favorable environments, bacteria may proliferate by self-replications and eventually build densely organized communities, in particular biofilms [1]. Biofilms
are widely distributed in various habitats, e.g., ocean,soil, kitchens, and also we humans grow bacteria in ourintestines to live in harmony with each other [2]. Biofilms
are also involved in our daily lives and industries, helping
to degrade organic waste and produce fine chemicals [3].
While biofilms benefit humanity in this way, they also
cause a variety of problems in, e.g., medical equipment[4] and industrial products [5]. Therefore, understanding the physiology of biofilms is a crucial mission acrossdiverse disciplines.
During the typical biofilm formation process, bacteria aggregate through a variety of cell-cell interactions[6]. While cell adhesion to material surfaces is regarded
as one of the most crucial events in biofilm formation[7, 8], cell-cell interactions mainly promote aggregationof planktonic cells that are not attached to the surface,which has also been shown to be important for biofilm
construction [9]. In the case of Escherichia coli, the Ag43
antigen protein plays a major role in the aggregation
process [6, 10–12] via protein-protein interactions [13].
Extracellular polysaccharides and other debris also contribute through depletion attraction [14–19]. Type I pili
are also known to be important in some cases [12, 20, 21].
The expression state of extracellular molecules involved in cell-cell interactions, including Ag43, is generally highly dependent on the environment. Interestingly,
it was reported that the relative importance of Ag43 andtype I pili in aggregation depends on the environment:
Ag43 has less effect on aggregation in Luria–Bertani (LB)
broth than in minimal medium such as M9 [12]. Besides,∗ t.shimaya@noneq.phys.s.u-tokyo.ac.jp† kat@kaztake.org

the secretion of proteins and polysaccharides, known as
extracellular polymeric substances (EPS), is known to besensitive to environmental changes such as nutrient starvation [22–25].

Because of the sensitivity of cell-cell interactions to
the environment, aggregates of planktonic cells maycollectively respond to environmental changes. However, planktonic aggregates under time-dependent environments have been hardly investigated. A major difficulty is the necessity to change the environment in acontrolled manner, maintaining spatial uniformity without adding hydrodynamic perturbations, which may influence the aggregates [26–28] and even destroy in somecases.

Here, we overcome the difficulty by a membranetype microfluidic device that we developed previously,
namely the extensive microperfusion system (EMPS),
which can uniformly change the environment surrounding bacterial populations without hydrodynamic perturbations [29]. With this device and using several strains ofE. coli, we observed how planktonic aggregates respondagainst abrupt nutrient starvation. We discovered that,upon starvation, nematically ordered planktonic cells arranged themselves into bundle-shaped clusters, developing a structure akin to that of smectic liquid crystal. By
employing a machine learning technique, we quantified
the degree of this smectic-like bundle order. Moreover,
we found that these bundles were destroyed if cell growth
was resumed by switching back to the nutritious condition. We also found that inhibition of EPS secretion hampered the bundle formation significantly. These results
suggest that both depletion attraction between cells, mediated by secreted EPS, and the arrest of cell elongation
are involved in the bundle formation.

2

a

b

porous membrane

Check valve

Incubation box

MediumSilicon Tube

medium flow

EMPS

Stage
Objective
Syringe pump

Waste medium

FIG. 1. Experimental setup. (a) A cross-sectional illustration of EMPS. Bacterial cells were captured in wells (depth 11 µm
and diameter ϕ). The wells were covered by a rigid porous membrane, through which fresh medium was uniformly supplied.
See Ref. [29]. (b) Overall setup of the experimental system. Liquid medium was constantly supplied from a syringe by a pumpand drained into a waste container. By using another syringe with non-nutritious buffer, connected by a three-way junction
with check valves, we can abruptly change the environment during observation.

II.
A.

RESULTS

Experimental setup and observations understeady growth conditions

Using EMPS (Fig. 1), we observed planktonic aggregates of non-motile E. coli (strain W3110 [30]), formedin microfabricated wells on the substrate of the device.
The absence of motility is important to prevent motilityinduced dispersion of cells. The wells are circular and11 µm deep, with diameters ϕ ranging from 110 µm to
330 µm (Fig. 1a), fabricated on a coverslip by the method
described in Ref. [29]. Bacteria were confined in thosewells by a porous membrane, attached to the substrate
via the biotin-streptavidin bonding. By supplying fresh
medium through the porous membrane, we can control
the culture condition in a spatially uniform manner, without hydrodynamic perturbations [29]. The device wasplaced in an incubation box maintained at 37 ◦ C, andfresh medium was automatically supplied by a syringe
pump (Fig. 1b).
We first observed the formation of planktonic aggregates under steady growth conditions (see Materials andMethods). When the wild-type E. coli W3110 (denotedby WT; see Table I for the list of strains used in this work)
was cultured in M9 minimum medium with glucose andamino acid [denoted by M9(glc.+a.a.); see Table II for
the list of measurements], we observed planktonic aggregates, as well as chains of cells that apparently divided
but remained connected (Fig. S1 and Movie 1). Similar chains were also observed in earlier studies [31, 32]
and are known to be maintained by Ag43 localized on
the pole of the cell [31]. Using a strain W3110 flu::kan(hereafter called flu::kan mutant), for which the flu geneproducing Ag43 was replaced with a kanamycin-resistantgene (kan), we confirmed that chain formation hardly
appeared in this case and planktonic aggregates weremainly produced (Fig. S1b and Movie 2). This indeed
indicates the relevance of Ag43 to the chain formation.
We also observed that some cells adhered to the sub-strate in both the WT and flu::kan strains (see, e.g.,
Movie 2). To focus on planktonic aggregations withoutadhesion of cells, here we attempted to use a strain without flagella, which are known to be an important factor
for adhesion of E. coli cells to surfaces [33–35]. Specifically, we used a mutant W3110 ∆fliC (hereafter called∆fliC mutant), for which the fliC gene producing flagella was deleted, and confirmed that adhesion of cells tothe surface was significantly prevented (Fig. S1c) whileplanktonic aggregates appeared to be almost identical tothose of the WT and the flu::kan mutant (Movie 3). We
also found that chain formation was significantly suppressed in this case (Fig. S1c). Note that, to our knowledge, the relevance of flagella to chain formation has notbeen discussed. Our result implies that flagella and Ag43
may jointly cause chain formation, though further validations are needed for a more decisive conclusion. In any
case, since we can avoid both surface adhesion and chain
formation, in the following we will mainly use the ∆fliC
mutant. With this strain, we measured the time evolution of the total area of aggregates in microscope images
and verified that the growth rate of the aggregate size
is comparable to the single-cell growth rate (Fig. S1d).
This indicates that the presence of aggregates does notdeteriorate local growth conditions in the EMPS.

B.

Bundle formation under nutrient starvation

We then observed how planktonic aggregates respondto nutrient starvation. We first grew bacteria (the ∆fliC
mutant) in a nutritious condition to produce aggregates,
then replaced the growth medium with non-nutritious
phosphate-buffered saline (PBS) while observing the aggregates (see Materials and Methods). Then we found, as
shown in Fig. 2a,b and Movie 4, the formation of bundle
clusters, where multiple cells clumped together next toeach other. Such bundle clusters may also gather and develop a structure similar to that of the smectic A phase of
liquid crystal (Fig. 2b). Bundle clusters can be observed

3

a clusterof bundles

FIG. 2. Bundle formation upon nutrient starvation. (a) Observation of the ∆fliC mutant grown in M9(glc+a.a.) and starved
in PBS. t′ = 0 is the time at which the environment was switched. The well diameter ϕ is 150 µm. Bundle clusters wereobserved in all 30 wells with various diameters ϕ recorded in a single experiment (“∆fliC starvation” in Table II). See also
Movie 4. (b) Enlargement of the regions outlined by the dotted rectangles in (a) at t′ = 0 min (i) and t′ = 320 min (ii). In (i),cells were nematically aligned. In (ii), these cells arranged themselves next to each other, and bundle clusters were formed. (c)A fluorescent image of bundles of the ∆fliC (venus) mutant grown in M9(glc+a.a.) and starved in PBS. The well diameter ϕ is
330 µm. (d) Observation of the ∆fliC mutant grown in LB and starved in PBS. The two snapshots were taken from the same
position. Some regions with bundles are emphasized by dotted lines. The well diameter ϕ is 110 µm. Bundle clusters wereobserved in 23 out of 30 wells with various diameters recorded in a single experiment (“∆fliC starvation (LB)” in Table II).
See also Movie 7. (e) Observation of the WT in the case of M9(glc+a.a.) → PBS. The two snapshots were taken from thesame position. Some regions with bundles are emphasized by dotted lines. The well diameter ϕ is 150 µm. Bundle clusters
were observed in 15 out of 18 wells with various diameters recorded in a single experiment (“WT starvation” in Table II). See
also Movie 8.

4

a

c
b

10 μm

ΔfliC

b

structuretensord

ΔfliC starvationeΔfliC starvation (LB)WT starvation

deep
learning

FIG. 3. Quantitative evaluation of the bundle formation. (a) Illustrations of the definition of the density correlation director(R) and the cell orientation (N ). (Left) When bundles are formed, R is oriented along the bundle axis, so that R and N are
perpendicular. The dotted circle illustrates the approximate range of the Gaussian kernel used in Eq. (2). (Right) Without
bundles, R is along the long axis of cells, parallel to N . (b) Estimation of R and N . The image is enlargement of therectangle region in (c). The density correlation director R is obtained by the structure tensor method [Eq. (2)]. The cellorientation is obtained by the deep learning model which we trained in this study. See Materials and Methods and Figs. S2 andS3. (c) The evaluated bundle order parameter field SB . The image is from the ∆fliC starvation shown in Fig. 2a,b. (d) The
spatially-averaged bundle order parameter in the regions where aggregates exist, ⟨SB ⟩, for the ∆fliC starvation. Each timeseries represents the data in a separate well (ϕ = 150 µm). The inset shows enlargement of the data before. The observation
shown in b,c, Fig. 2a,b, and Movies 4, 5, and 6 corresponds to the purple curve. The error is shown by the shaded bands,
which was evaluated as the mean absolute error of the trained deep learning model compared to the ground truth by manual
annotation (see Materials and Methods for details). (e) The spatially-averaged bundle order parameter ⟨SB ⟩ for the ∆fliC
starvation (LB) and the WT starvation. The former corresponds to the observation shown in Fig. 2d and Movie 7, and thelatter to Fig. 2e and Movie 8.

more clearly by fluorescent microscopy (Fig. 2c) by using
a strain with a fluorescent protein Venus [36]. Also, thebundle formation was not limited to the specific condition and strain chosen here. We observed similar bundle
clusters when we grew cells in LB medium (Fig. 2d andMovie 7; “∆fliC starvation (LB)” in Table II) and when
we used the WT expressing flagella (Fig. 2e and Movie 8;“WT starvation” in Table II). This indicates the robustness of our finding of the bundle formation upon starvation, regardless of detailed conditions and cellular states.
To quantify the degree of the smectic order, we define
the bundle order parameter SB by
SB = SN (1 − |N · R|).

(1)

Here, N denotes the coarse-grained field of the cell orientation, R the orientation of the density correlation, andSN the nematic order parameter evaluated from the cellorientation N (Fig. 3a). The two orientations R and N
were evaluated by the structure tensor method [37] andby a supervised deep neural network method, U-Net [38],respectively (see Materials and Methods for details). The
bundle order parameter SB takes a large value when thenematic order is strong and N and R are nearly per-pendicular. The latter condition is set because, whenbundle clusters are formed, bacterial cells arrange themselves next to each other, in the direction of their shortaxis (Fig. 3b), similarly to the smectic A phase. We also
observe that, when no bundles are formed, cells are typically located along their long axis, resulting in stronger
density correlation in that direction, R ∥ N . Thus, ourbundle order parameter SB can evaluate the degree ofbundle formation and its smectic order, as demonstrated
in Fig. 3c and Movies 5 and 6. In the past, a similar order parameter was adopted in Ref. [39] to evaluate thesmectic order of colloidal rods.
To evaluate the bundle formation process, we measured
the time evolution of the spatially-averaged bundle orderparameter, ⟨SB ⟩. The spatial average was calculated over
the regions where aggregates exist, which were also obtained by the deep neural network (see Materials andMethods). We found that ⟨SB ⟩ increases significantly after the starvation, in all cases described so far [the ∆fliC
starvation (Fig. 3d), the ∆fliC starvation (LB) and the
WT starvation (Fig. 3e)].
We should note, however, that the value of the bundle order parameter is sensitive to subtle differences in5aDepletion attraction ?

bc
PBS + BisBAL

EPSd

ΔfliC starvation (BisBAL) #1

PBS + BisBAL

ΔfliC

ΔfliC

15 μm

15 μm

c
b

bacteria

entropic
force

FIG. 4. Investigation of the relevance of EPS. (a) Illustration of the hypothesis that the depletion attraction is relevant tothe bundle formation. The dotted lines around the bacterial cells represent the excluded region which large molecules suchas EPS cannot enter. Cells may form bundles to minimize the excluded volume and increase the entropy of large molecules.
(b,c) Two examples of starvation response of the ∆fliC mutant grown in M9(glc+a.a.) + 2 µM BisBAL and starved in PBS+ 2 µM BisBAL. The well diameter ϕ is 150 µm. t′ = 0 is the time at which the environment was switched. The bundle
formation was not observed at all (b and Movie 9) in 16 out of 30 wells with various diameters recorded in a single experiment(∆fliC starvation (BisBAL) #1 in Table II), while it was observed (c and Movie 10) in the other wells. We also conducted
a technical replicate (∆fliC starvation (BisBAL) #2 in Table II) and found no bundle formation in 9 out of 13 wells. These
indicate that comprehensive reduction of EPS secretion by BisBAL significantly inhibits the bundle formation, suggesting thepossible relevance of depletion attraction mediated by EPS. (d) The spatially-averaged bundle order parameter ⟨SB ⟩ for thecases where bundles were formed and not formed.

experimental conditions, such as the weakly heterogeneous image background due to the porous membrane.
For example, in another measurement of the ∆fliC mutant strain from M9(glc.+a.a.) to PBS (specifically“∆fliC starvation-recovery” in Table II, to be described
below), the bundle order parameter during the starvation(Fig. 5b) was significantly smaller than that of the ∆fliC
starvation (Fig. 3d). Therefore, we compare the valuesof the bundle order parameter only within each technicalreplicate, to characterize the structure before and after
starvation.
C.

The relevance of extracellular molecules

Here we consider what changes in cell-cell interactions
occur upon starvation and result in the bundle formation. In the literature, qualitatively similar bundles ofrod-shaped cells have been observed in the presence of a
sufficient amount of polymer [14, 16, 40, 41]. This wasinterpreted as a result of depletion attraction between
cells. A similar effect has also been reported for mixturesof rod-shaped and spherical colloids [39, 42–45], resulting
in the smectic A phase similar to our observation. Since
the secretion of some EPS is known to be promoted under
external stresses [22–25], we hypothesize that the EPSinduced depletion attraction may be the mechanism of
the bundle formation upon starvation (Fig. 4a).
To test this hypothesis, we observed the starvation response of aggregates in the presence of a reagent thatcomprehensively inhibits EPS secretion. Specifically. weused bismuth dimercaprol (BisBAL), which has been reported to comprehensively reduce EPS secretion roughly
by a factor of 10 under appropriate concentrations, without significantly affecting cell growth [46, 47]. We cul-

tured, in the presence of BisBAL, populations of the∆fliC mutant forming aggregates in M9(Glc+a.a.) and
exposed them to starvation in PBS (“∆fliC starvation(BisBAL)” in Table II). In contrast to the case without
BisBAL, where bundles were formed in all monitored
wells (∆fliC starvation), with BisBAL we observed thatbundles were not formed (Fig. 4b and Movie 9) in morethan half of the observed wells in two technical replicates(#1 and #2 in Table II), while in the other wells bundles
were formed relatively weakly (Fig. 4c and Movie 10);see also the bundle order parameter for those two cases(Fig. 4d). This indicates that the reduction of EPS secretion by BisBAL significantly, albeit not completely,
inhibits the bundle formation. Our results suggest therelevance of depletion attraction by EPS.
While the comprehensive inhibition of EPS secretion
by BisBAL allowed us to know that EPS is involved in
the bundle formation process, it is useful to identify specific substances that serve as depletants of this depletion attraction. There are several candidate substances,whose secretion is known to increase during starvation
and whose size is large enough to cause depletion attraction between cells. First, E. coli is known to promote
the secretion of cellulose under environmental stresses[48, 49]. However, we can immediately rule out its relevance because the W3110 strain used in this study does
not produce cellulose [49]. Second, curli, polymeric amyloid fibers which usually extend from and attach to cellsurfaces [50], is known to be produced more actively under environment stresses [50, 51]. It was reported that its
major subunit protein, CsgA, can polymerize in medium
being detached from cell surfaces [52], which may induce depletion attraction. Third, outer membrane vesicles (OMVs) have a diameter of 20–250 nm, which contain, e.g., misfolded proteins and toxic substances, and6
are discharged from cells [53]. It has been reported thatthe secretion of OMVs is promoted under external stress[53, 54] and that they can induce depletion attraction
to particles on the scale of tens of micrometers [15, 18].
Therefore, we tested the possible influence of curli and
OMVs on the bundle formation.
We first tested the possibility of curli, by using a mutant W3110 ∆fliC csgA::kan (“∆fliC csgA::kan” mutant
in Table I) for which the gene expressing CsgA protein
was replaced by a kanamycin-resistant gene kan. On
an agar plate of LB broth containing congo red, which
selectively stains amyloid fibers including curli [55], we
confirmed that the ∆fliC csgA::kan mutant does notproduce curli (Fig. S4a). We then observed aggregatesof the mutant grown in M9 (glc+a.a.) and starved
in PBS (“∆fliC csgA::kan starvation” in Table II) andfound bundle clusters in most wells (Table II, Fig. S4band Movie 11). These indicate that curli may not be themain depetant, at least not the only one, for the bundle
formation upon starvation that we observe.
Next, we investigated the influence of OMVs. If OVMs
are main depletants, a significant amount of OVMs need
to be released in the medium. Since OVMs are producedby cells, their density is expected to be higher insidebundle clusters, between individual bundles (region between dashed rectangles in the sketch of Fig. 2b(ii)). We
attempted to inspect this, by staining cell membranes
and OVMs with FM 4-64 dye, which selectively labelhydrophobic cell membranes including OMVs [56, 57](Fig. S5). By using the W3110 ∆fliC intS ::venus-kan
mutant (“∆fliC (venus) mutant” in Table I), the cellbodies were also visualized by the fluorescent protein
Venus. We observed aggregates of this strain grown inM9(glc.+a.a.) and starved in PBS (“∆fliC (venus) starvation” in Table II). However, the results in Fig. S5 did
not show an appreciable amount of OVMs in the medium,even between individual bundles inside clusters (compare
the fluorescence intensities of Venus and FM 4-64). Thissuggests that OMVs may not be the main depletant thattriggers the bundle formation.
As another test, we attempted to induce bundle formation by promoting the secretion of OMVs by antibiotics,
instead of starvation. Specifically, we used polymyxin B,
known to increase the OMV secretion by several times totenfold at sub-minimum inhibitory concentrations (subMIC) [58]. We cultured the ∆fliC mutant in growth
medium (either M9(glc.+a.a.) or LB) containing subMIC polymyxin B for long time, without starvation, but
no bundle clusters were observed at all (“∆fliC growth(PMB)” and “∆fliC growth (LB, PMB)” in Table II,
Fig. S6a,b and Movies 12 and 13).
We also attempted to induce the bundle formation by
an external addition of a standard depletant, namely xanthan gum, an extracellular polysaccharide produced by
Xanthomonas campestris [59], which was used in the literature to introduce depletion attraction between cells[14]. Following Refs. [60, 61], we supplemented xanthan gum to medium, at a concentration sufficient toreproduce the viscosity due to EPS secreted by E. coli.
We observed aggregates of the ∆fliC mutant grown inM9(glc.+a.a.) (“∆fliC growth (xanthan)” in Table II).
In the early stage while the cell density was low, we observed a few small bundles containing 2-3 cells that seemto be induced by the depletion attraction (see Movie 14).
However, the small bundles immediately disappeared afterward, and no bundle formation was finally realized inany of the observed wells (Table II and Fig. S6c). An
interpretation of these observations under growth conditions with depletants will be given in the next subsection.
Our series of experiments suggest that, while depletion attraction via EPS seems to contribute significantly
to the bundle formation upon starvation, the presenceof depletant solely is not sufficient to induce the bundle
formation.

D.

The relevance of growth arrest

Now we consider the possibility that the arrest of cell
growth by nutrient starvation may also have a significant
effect on the bundle formation. We hypothesize that,even if a sufficient amount of depletants are diffused between cells, perturbations due to cell elongation and division may overcome the depletion attraction and prevent
bundle formation.
To test this hypothesis, we attempted to switch backfrom the non-nutritious to nutritious conditions, after
bundle clusters were formed upon starvation. Specifically, we first prepared bundle clusters of the ∆fliC,grown in M9(glc.+a.a.) and starved in PBS, as in the∆fliC starvation, then resumed cell growth by switching
it back to M9(glc.+a.a.) (“∆fliC starvation-recovery” inTable II; Fig. 5a and Movie 15). We measured the time
evolution of the bundle order parameter in three independent wells, as well as the total size of aggregates inthose wells (Fig. 5b). During the starvation stage (PBS),
the bundle order parameter increased, and the total aggregate size slows down after a lag time (red dotted line).
Then, after the growth condition was recovered, the aggregate size started to grow again, while the smectic-likebundles were destroyed and the bundle order parameter decreased. Therefore, not only the depletion attraction induced by EPS but also growth arrest is necessary
for the bundle formation we observed. This may also
be the reason why bundle clusters were not formed in
the aforementioned ∆fliC growth (PMB), ∆fliC growth(LB, PMB), and ∆fliC growth (xanthan) experiments,
where an increased amount of depletants was present but
growth was not arrested.

III.

CONCLUSIONSIn this study, using the EMPS we developed previously,
we realized observations of planktonic aggregates of nonmotile E. coli under time-dependent starving conditions.

7

M9 (glc + a.a.)bswitchPBS

M9 (glc + a.a.)ΔfliC starvation-recovery
M9(glc+a.a.)PBS

M9(glc+a.a.)( )switch

( )

a

ΔfliC

10 μm
FIG. 5. Investigation of the relevance of cellular growth arrest. (a) Observations of the ∆fliC mutant grown in M9(glc+a.a.),starved in PBS, then grown again in M9(glc+a.a.). t′ = 0 is the time at which the environment was switched to PBS, andthe switch back to M9(glc+a.a.) was at t′ = 180 min. The well diameter ϕ is 150 µm. Bundle clusters were observed in 25
out of 27 wells with various diameters recorded in a single experiment (∆fliC starvation-recovery in Table II). Those bundles
were destroyed after the recovery of cell growth by M9(glc+a.a.) in all wells. The displayed snapshots were taken from thesame position. See also Movie 15. (b) The spatially-averaged bundle order parameter over the region where aggregates exist,⟨SB ⟩, in the ∆fliC starvation-recovery experiment. Each time series represents the data in a separate well (ϕ = 230 µm). The
observation shown in (a) and Movie 15 corresponds to the blue curve. The definition of the errors (shades) is the same asthat for Fig. 3d. We also plot the aggregation size, summed over the three wells (red dotted line). The displayed error for theaggregation size is the sum of the errors of the individual aggregate sizes. The error of each aggregate size was estimated tobe the aggregate perimeter × 5 pixels (∼ 0.85 µm), which we consider to be the range of uncertainty in the edge location of
the segmented region. The sudden decrease of the total aggregation size may be because of a weak hydrodynamic disturbancecaused by the medium switch.

We discovered that nutrient starvation altered the structure of aggregates, resulting in the appearance of smecticlike bundle clusters, where cells arranged themselves next
to each other along their short axis. By utilizing the deeplearning method, we successfully quantified the degree ofsmectic order of the bundle clusters. We revealed that
EPS produced by cells is involved in the bundle formation, by showing that comprehensive reduction of EPS
secretion prevented the bundle formation. We also foundthat the smectic-like bundles were destroyed by resumption of growth after recovery of nutrients. Our results
indicate that both the depletion attraction via EPS andgrowth arrest of cells are relevant to the bundle formation
we observed.
Further investigation is required for elucidating what
specific substances are most relevant to the depletion attraction involved. In this work, we inspected two specificsubstances, curli and OMVs, but could not determine
their relevance conclusively. We also remark that it isprobably difficult to validate the relevance of OMVs byinhibition, because complete inhibition of OMVs seems
to be unrealistic for living cells. It is worthwhile to visualize spatial distribution of OMVs in the presence ofbundle clusters, by selectively labeling OMVs with, e.g.,curvature-sensing peptides [62]. In the literature, it isalso known that changes in cell surface conditions may
also affect the formation of similar bundle clusters. For P.
aeruginosa populations, it was observed that decreasing
the hydrophobicity of O-specific antigen on the cell surface resulted in the reduction of the hydrophobic attrac-

tion between cells, which facilitated the bundle formation
by polymers added in the environment [40]. In the caseof E. coli, it was reported that cells in the stationary
phase develop heterogeneous charge distribution on theouter membranes, reducing the electrostatic repulsions
between cells and surfaces [63]. It may also be importantto seek for the possible existence of unidentified processes
underlying the bundle formation we observed. We also
note the apparent similarity to the rouleaux formation of
red blood cells [64].
The physiological significance of the bundle formationneeds to be investigated in future. For the case of thenematic ordering of anisotropic cells, previous studies[65, 66] proposed its effect on the diffusion efficiency ofsmall molecules, such as nutrients and signal molecules
produced by cells, in the intercellular gaps. Specifically,in the case of dense E. coli populations, it has been experimentally suggested that the transport efficiency along
the director of the nematic order can be enhanced [66].
It may be interesting to consider an analogous effect in
the presence of the smectic order as we observed in thiswork. If the bundle formation is beneficial for, e.g., an
uptake of nutrients from the external environment understarvation, our finding may be a behavioral adaptationof bacterial populations.
Finally, our findings may also be relevant to other bacteria, because the elevated EPS secretion and the growtharrest by starvation are not unique to E. coli. Further
elucidation of the mechanism of the bundle formationand its biological significance is an important future task,

8which may also contribute to understanding the physicalmechanisms underlying biofilm development.
IV.

MATERIALS AND METHODSA.

Strains and culture media

We used a wild-type (WT) E. coli strain W3110 andmutant strains W3110 ∆fliC, W3110 flu::kan, W3110∆fliC csgA::kan, and W3110 ∆fliC insS ::venus-kan (seeTable I for the strain names and their genotypes). We
used the ∆fliC mutant prepared in Ref. [67]. By P1transduction, the genes flu::kan and csgA::kan weretransferred to the WT and the ∆fliC mutant, respectively, from the Keio collection of E. coli through National BioResource Project (NBRP) of National Instituteof Genetics, Japan. Concerning the strain ∆fliC (venus)
mutant, we used a strain that was previously prepared bya method similar to that in Ref. [68]. The protein Venus
was developed in Ref. [36] and provided by the RIKEN
BRC through NBRP of the MEXT/AMED, Japan.
Table II is a list of the experiments conducted in thisstudy. The media we mainly used were M9(glc.+a.a.)(glucose 0.2 wt% and MEM Amino Acids solution(M5550, Sigma) 1 wt% in the M9 medium), LB broth(tryptone 1 wt%, sodium chloride 1 wt% and Yeast extract 0.5 wt%), and the phosphate-buffered saline (PBS).
B.

Evaluation of the loss of curli by congo red

We verified the loss of curli in the ∆fliC csgA::kanmutant as follows. We first inoculated the strain froma glycerol stock into 2 ml LB in a test tube and shookit overnight at 37 ◦ C. We then inoculated 10 µl of the
incubated suspension to an LB agar containing 25 µg/ml
of congo red, by an inoculation loop. We then obtained colony images of the ∆fliC mutant and the ∆fliC
csgA::kan mutant, confirming the absence of dye fluorescence from the latter mutant, due to the loss of curli(Fig. S4a).

Ref. [29] for more details on the fabrication process of
the EMPS.
To prepare bacterial suspensions, we first inoculated
the strain from a glycerol stock into 2 ml fresh medium
in a test tube and shook it overnight at 37 ◦ C. We usedeither M9(glc+a.a.) or LB broth, chosen accordingly to
the growth medium used in the main experiment (seeTable II). We then transferred 20 µl of the incubated suspension to 2 ml fresh medium (the same medium as thatused in the main observation) and cultured it until the
optical density (OD) at 600 nm wavelength reached 0.1–
0.5. The cell suspension was finally diluted to OD = 0.05
before the inoculation on the substrate.
The device was placed on the microscope stage, in the
incubation box maintained at 37 ◦ C (Fig. 1b). We useda Leica DMi8 microscope equipped with a 63x (N.A.
1.30) oil immersion objective lens and operated by Leica
LasX. A syringe filled with the nutritious medium wasconnected to the device, and another syringe filled with
non-nutritious buffer was also connected via a three-way
junction with check valves when observing the starvation response. Each syringe was set to a syringe pump(NE-1000, New Era Pump Systems). To fill the device
with the nutritious medium, we first injected the medium
stored at 37 ◦ C at the rate of 60 ml/hr for 5 min. During the observation, first the nutritious medium was constantly supplied at the rate of 2 ml/hr (flow speed approximately 0.2 mm/sec above the membrane). Whenchanging the environment, the syringe pump for the nutritious medium was stopped, and the other pump forthe non-nutritious buffer was turned on to replace themedium inside the device. The flow rate was set to be
60 ml/hr for the first 5 min, then returned to 2 ml/hr.
Throughout the experiment, the device was always
in the microscope incubation box, maintained at 37 ◦ C.
Cells were observed by phase-contrast microscopy focusing near the bottom of the wells and recorded at the timeinterval of 2 min. Images were taken from several wells(stated in the figure captions and Table II) in each experiment. The fraction of the wells showing bundle clusters
presented in Table II is based on visual assessment.

D.
C.

Time-lapse observations

Time-lapse observations were conducted by using theextensive microperfusion system (EMPS) previously developed by us and coworkers [29].
We fabricated
11 µm deep circular wells with varying diameter ϕ =110, 150, 230, 330 µm on a coverslip (Fig. 1a). After introducing cell suspension, these wells were covered by a rigid
porous membrane, attached by biotin-streptavidin bonding. The porous membrane is a bilayer of a streptavidindecorated cellulose membrane (Spectra/Por 7, Repligen,
Waltham, MA, molecular weight cut-off 25,000) and a
biotin-decorated PET membrane (taken from Transwell
3450, Corning, NY, nominal pore size 0.4 µm). See

Fluorescence labeling of cellular membranes by
FM 4-64

For the observation shown in Fig. 1c and Fig. S5, we
first inoculated the strain from a glycerol stock into 2 ml
M9(Glc+a.a.) in a test tube and shook it overnight at
37 ◦ C. We transferred 20 µl of the incubated suspension
to 2 ml fresh M9(Glc+a.a.) and cultured it until OD
reached 0.1–0.5. The cell suspension was finally diluted
to OD = 0.05 before the inoculation on the device substrate.
Preparation of the device and the microscope, and induction of nutrient starvation were conducted similarly
as for the time-lapse observations. 150 min after the onset of starvation, when smectic-like bundle clusters ap-

9
TABLE I. E. coli strains used in this study.
Genotypes
Characteristics
Strains
WT
The wild-type of W3110
flu::kan mutant
W3110 flu::kanno Ag43
W3110 ∆fliCno flagella∆fliC mutant∆fliC csgA::kan mutant W3110 ∆fliC csgA::kanno flagella nor curli∆fliC (venus) mutant W3110 ∆fliC intS ::venus-kan no flagella, expressing the fluorescent protein Venus

TABLE II. List of measurements in this study. The column “Bundle fraction” indicates the fraction of the wells where thebundle formation was observed, showing the number of such wells as the numerator and the total number of the monitored
wells as the denominator.
Measurement
Strains
Conditions
Bundle fraction Note
WT growthWT
M9(glc+a.a.)Fig. S1a, Movie 1
flu::kan growth
flu::kan
M9(glc+a.a.)Fig. S1b, Movie 2∆fliC growth∆fliC
M9(glc+a.a.)Fig. S1c, Movie 3∆fliC starvation∆fliC
M9(glc+a.a.) → PBS
30/30
Fig. 2a,b, Movie 4∆fliC (venus) starvation ∆fliC (venus) M9(glc+a.a.) → PBS
Fig. 2c, Fig. S5
for fluorescence imaging∆fliC starvation (LB)
∆fliC
LB → PBS
23/30
Fig. 2d, Movie 7
WT starvation
WT
M9(glc+a.a.) → PBS
15/18
Fig. 2e, Movie 8
expressing flagella∆fliC starvation (BisBAL) ∆fliC
M9(glc+a.a.) + 2 µM BisBAL
14/30
Fig. 4, Movies 9 and 10#1→ PBS + 2 µM BisBAL
reducing EPS production∆fliC starvation (BisBAL) ∆fliC
M9(glc+a.a.) + 2 µM BisBAL
4/13
technical replicate#2→ PBS + 2 µM BisBAL∆fliC csgA::kan starvation ∆fliC csgA::kan M9(glc+a.a.) → PBS
15/19
Fig. S4, Movie 11
deleting curli∆fliC growth (PMB)∆fliC
M9(glc+a.a.)0/6
Fig. S6a, Movie 12+ 250 ng/ml polymyxin B
promoting OMVs production∆fliC growth (LB, PMB) ∆fliC
LB + 250 ng/ml polymyxin B
0/15
Fig. S6b, Movie 13
promoting OMVs production∆fliC growth (xanthan)∆fliC
M9(Glc+a.a.)0/6
Fig. S6c, Movie 14+ 0.03 wt% xanthan gum∆fliC starvation-recovery ∆fliC
M9(Glc+a.a.)
25/27
Fig. 5, Movie 15→ PBS → M9(Glc+a.a.)peared, PBS containing 5 µg/ml of FM 4-64 was introduced. The medium flow was set to be 60 ml/hr for the
first 5 min and left for 10 min without flow to stain cellular membranes. We then washed unbound FM 4-64 by
supplying PBS without FM 4-64 at the rate of 60 ml/hr
for 3 min, stopped the flow, and obtained fluorescence
images.

E.

Image analysis

We employed image analysis to evaluate the smectic
order of bundle clusters, in terms of the bundle orderparameter SB [Eq. (1)] as follows. The entire pipeline of
the image analysis is illustrated in Fig. S2.
First we detected the regions where planktonic aggregates existed. We utilized the deep neural network,
U-Net [38], to automate this process. For training andevaluating the model, we extracted 144 frames from all
experiments at approximately constant time intervals.
Each image consists of 648 × 483 pixels, with pixel size
≈ 0.18 µm. To prepare the teacher label, the target re-gion was manually annotated by using painting software.
We also performed data augmentation through the horizontal and/or vertical flip and separated the data into fivegroups for cross-validation. After normalizing the image
intensity distribution by contrast limited adaptive histogram equalization (CLAHE), U-Net was trained using
the binary cross entropy loss. The segmentation accuracyof the trained model, evaluated by the Dice similarity coefficient (DSC), was 0.577.
We then detected the two orientation fields, namely
the density correlation director R and the cell orientation
N , separately. For R, we employed the structure tensor
method [37]. We calculated the structure tensor J(r) ata given pixel r = (x, y) by[∆x I, ∆x I]r , [∆y I, ∆x I]r
J(r) =,(2)[∆x I, ∆y I]r , [∆y I, ∆y I]rwith the image intensity I(x, y), ∆x I ≡ I(x + 1, y) −I(x − 1, y),I(x, y − 1), andP ∆y I ≡ I(x, y′ +′ 1) −′ ′ σ ′ ′[g, h]r ≡
g(x
,
y
)h(x
,
y
)fr (x , y ). Theℓ(x′ ,y ′ )∈ROIr
summation is taken over the region of interest ROIℓr ,10which is a square of size ℓ ≈ 7.2 µm (40 pixels) centered at r, and frσ (xh′ , y ′ ) is the Gaussian
kernel definedider parameter ⟨SB ⟩ over the regions with planktonic aggregates, detected by the segmentation model. The mean
absolute error of ⟨SB ⟩ per image was ±0.013 and shownas the shaded bands in the figures.

For the cell orientation N , we employed the U-Net
again. To obtain the teacher label, we manually annotated the long axis of cells by painting black straightlines (see Fig. S2). We then calculated the structure
tensor from the painted images to acquire the groundtruth of the cell orientation, N̂ = ±(cos ψ̂, sin ψ̂) with(−π/2 ≤ ψ̂ < π/2). The U-Net was trained to predict
N = ±(cos ψ, sin ψ) for each pixel in the CLAHE processed image, with the following nematic L2 loss function:

AUTHOR CONTRIBUTIONS

′

′

2

2

+(y −y)by frσ (x′ , y ′ ) ≡ exp − (x −x) 2σ2with σ ≈ 1.8 µm(10 pixels). Then R(r) is given by the eigenvector of J(r)associated with the smallest eigenvalue.

ℓNL2 (ψ, ψ̂) = min(|ψ − ψ̂|, |π − |ψ − ψ̂||)2 .

(3)

During training, the loss function was evaluated only inthe regions with planktonic aggregates obtained by thesegmentation model. The nematic L2 loss was then spatially averaged over all regions with planktonic cells, andthe mini batch training with batch size 8 was carried out.
The angle measurement accuracy of the trained model,
evaluated by the mean absolute error of ψ, was ±20.9◦ .
Using the predicted N , we also evaluated the nematicorder parameter by
SN (r) = ⟨sin 2ψ⟩2ROIℓ + ⟨cos 2ψ⟩2ROIℓ ,
r

r

(4)

where ⟨·⟩ROIℓr denotes the spatial average within ROIℓr .

T.S. and K.A.T. designed research. T.S. performed
all bacterial experiments and analyzed data. T.S. and
K.A.T. discussed the results and wrote the manuscript.
CONFLICTS OF INTEREST

There are no conflicts to declare.
ACKNOWLEDGEMENTS

We are grateful to F. Yokoyama for useful discussions
that motivated us to investigate the influence of OMVs.
We thank Y. Wakamoto and R. Okura for sharing the P1
phage to prepare the flu::kan mutant. We also acknowledge discussions with D. Nishiguchi, Y. Okada, and M.
Yanagisawa. This work is supported in part by KAKENHI from Japan Society for the Promotion of Science(JSPS) (No. JP19H05800, JP20H00128, JP24K00593),
KAKENHI for JSPS Fellows (No. JP20J10682), andthe JSPS Core-to-Core Program “Advanced core-to-core
network for the physics of self-organizing active matter(JPJSCCA20230002)”
DATA AVAILABILITY

Finally, using all these data, we calculated the bundle order parameter SB [Eq. (1)] for each pixel (see also
Fig. S2). We obtained the spatially-averaged bundle or-

The code and data that support the findings of thisstudy will be available at Zenodo.

[1] H. Flemming, J. Wingender, U. Szewzyk, P. Steinberg,
S. A. Rice, and S. Kjelleberg, “Biofilms: an emergent
form of bacterial life,” Nat. Rev. Microbiol. 14, 563–575(2016).
[2] W. M. de Vos, “Microbial biofilms and the human intestinal microbiome,” NPJ Biofilms Microbiomes 1, 15005(2015).
[3] B. Halan, K. Buehler, and A. Schmid, “Biofilms as living catalysts in continuous chemical syntheses,” Trends
Biotechnol. 30, 453–465 (2012).
[4] M. Shirtliff and J. G. Leid, The Role of Biofilms in
Device-Related Infections (Springer, Berlin, Heidelberg,2009).
[5] T. Mattila-Sandholm and G. Wirtanen, “Biofilm formation in the industry: A review,” Food Rev. Int. 8, 573–
603 (1992).

[6] T. Trunk, H. S. Khalil, and J. C. Leo, “Bacterial autoaggregation,” AIMS Microbiol. 4, 140–164 (2018).
[7] T Romeo, Bacterial Biofilms (Springer, Berlin, Heidelberg, 2008).
[8] J. Palmer, S. Flint, and J. Brooks, “Bacterial cell attachment, the beginning of a biofilm,” J. Ind. Microbiol.
Biotechnol. 34, 577–588 (2007).
[9] K. N. Kragh, J. B. Hutchison, G. Melaugh, C. Rodesney,
A. E. L. Roberts, Y. Irie, P. Ø. Jensen, S. P. Diggle, R. J.
Allen, V. Gordon, T. Bjarnsholt, and D. K. Newman,“Role of multicellular aggregates in biofilm formation,”mBio 7, e00237–16 (2016).
[10] H. Hasman, T. Chakraborty, and P. Klemm, “Antigen43-mediated autoaggregation of Escherichia coli isblocked by fimbriation,” J. Bacteriol. 181, 4834–4841(1999).

11[11] K Kjærgaard, M. A. Schembri, H. Hasman,
andP. Klemm, “Antigen 43 from Escherichia coli induces
inter- and intraspecies cell aggregation and changes incolony morphology of Pseudomonas fluorescens,” J. Bacteriol. 182, 4789–4796 (2000).
[12] P. N. Danese, L. A. Pratt, S. L. Dove, and R. Kolter,“The outer membrane protein, Antigen 43, mediates
cell-to-cell interactions within Escherichia coli biofilms,”
Mol. Microbiol. 37, 424–432 (2000).
[13] B. Heras, M. Totsika, K. M. Peters, J. J. Paxman, C. L.
Gee, R. J. Jarrott, M. A. Perugini, A. E. Whitten,
and M. A. Schembri, “The antigen 43 structure reveals
a molecular velcro-like mechanism of autotransportermediated bacterial clumping,” Proc. Natl. Acad. Sci.
USA 111, 457–462 (2014).
[14] G. Dorken, G. P. Ferguson, C. E. French, and W. C. K.
Poon, “Aggregation by depletion attraction in culturesof bacteria producing exopolysaccharide,” J. R. Soc. Interface 9, 3490–3502 (2012).
[15] P. Amimanan, R. Tavichakorntrakool, K. Fong-ngern,
P. Sribenjalux, A. Lulitanond, V. Prasongwatana,
C. Wongkham, P. Boonsiri, J. U Welbat, and V. Thongboonkerd, “Elongation factor Tu on Escherichia coli isolated from urine of kidney stone patients promotes calcium oxalate crystal growth and aggregation,” Sci. Rep.
7, 2953 (2017).
[16] P. R. Secor, L. A. Michaels, A. Ratjen, L. K. Jennings,
and P. K. Singh, “Entropically driven aggregation of bacteria by host polymers promotes antibiotic tolerance inPseudomonas aeruginosa,” Proc. Natl. Acad. Sci. USA
115, 10780–10785 (2018).
[17] M. K. Porter, A. Preska Steinberg, and R. F. Ismagilov, “Interplay of motility and polymer-driven depletion
forces in the initial stages of bacterial aggregation,” Soft
Matter 15, 7071–7079 (2019).
[18] R. Kanlaya, O. Naruepantawart,
and V. Thongboonkerd, “Flagellum is responsible for promoting effectsof viable Escherichia coli on calcium oxalate crystallization, crystal growth, and crystal aggregation,” Front. Microbiol. 10, 2507 (2019).
[19] P. R. Secor, L. A. Michaels, D. C. Bublitz, L. K. Jennings, and P. K. Singh, “The depletion mechanism
can actuate bacterial aggregation by self-produced exopolysaccharides and determine species distribution andcomposition in bacterial aggregates,” bioRxiv (2021),
10.1101/2021.05.11.443568.
[20] L. A. Pratt and R. Kolter, “Genetic analysis of Escherichia coli biofilm formation: roles of flagella, motility, chemotaxis and type I pili,” Mol. Microbiol. 30, 285–
293 (1998).
[21] M. A. Schembri, G. Christiansen, and P. Klemm,“FimH-mediated autoaggregation of Escherichia coli,”
Mol. Microbiol. 41, 1419–1430 (2001).
[22] K. Myszka and K. Czaczyk, “Characterization of adhesive exopolysaccharide (EPS) produced by Pseudomonas
aeruginosa under starvation conditions,” Curr. Microbiol. 58, 541–546 (2009).
[23] K. Myszka and K. Czaczyk, “Effect of starvation stresson morphological changes and production of adhesive exopolysaccharide (EPS) by Proteus vulgaris,” Acta. Sci.
Pol. Technol. Aliment. 10, 305–312 (2011).
[24] W. Zhang, A. Seminara, M. Suaris, M. P. Brenner, D. A.
Weitz, and T. E. Angelini, “Nutrient depletion in Bacillus subtilis biofilms triggers matrix production,” New J.

Phys. 16, 015028 (2014).
[25] O. Y. A. Costa, J. M. Raaijmakers, and E. E. Kuramae,“Microbial extracellular polymeric substances: Ecological function and impact on soil aggregation,” Front. Microbiol. 9, 1636 (2018).
[26] A. Karimi, D. Karig, A. Kumar, and A. M. Ardekani,“Interplay of physical mechanisms and biofilm processes:
review of microfluidic methods,” Lab Chip 15, 23–42(2015).
[27] F. Wu and C. Dekker, “Nanofabricated structures andmicrofluidic devices for bacteria: from techniques to biology,” Chem. Soc. Rev. 45, 268–280 (2016).
[28] M. Pousti, M. P. Zarabadi, M. Abbaszadeh Amirdehi,
F. Paquet-Mercier, and J. Greener, “Microfluidic bioanalytical flow cells for biofilm studies: a review,” Analyst
144, 68–86 (2019).
[29] T. Shimaya, R. Okura, Y. Wakamoto, and K. A.
Takeuchi, “Scale invariance of cell size fluctuations in
starving bacteria,” Commun. Phys. 4, 238 (2021).
[30] M Jishage and A Ishihama, “Variation in rna polymerase
sigma subunit composition within different stocks of escherichia coli w3110,” J. Bacteriol. 179, 959–963 (1997).
[31] R. M. Vejborg and P. Klemm, “Cellular chain formationin Escherichia coli biofilms,” Microbiology 155, 1407–
1417 (2009).
[32] U. Frömmel, A. Böhm, J. Nitschke, J. Weinreich, J. Groß,
S. Rödiger, T. Wex, H. Ansorge, O. Zinke, C. Schröder,D. Roggenbuck, and P. Schierack, “Adhesion patterns ofcommensal and pathogenic Escherichia coli from humans
and wild animals on human and porcine epithelial celllines,” Gut Pathog. 5, 31 (2013).
[33] C. Prigent-Combaret, G. Prensier, T. T. Le Thi, O. Vidal, P. Lejeune, and C. Dorel, “Developmental pathway
for biofilm formation in curli-producing Escherichia coli
strains: role of flagella, curli and colanic acid,” Environ.
Microbiol. 2, 450–464 (2000).
[34] R. S. Friedlander, N. Vogel, and J. Aizenberg, “Roleof flagella in adhesion of Escherichia coli to abiotic surfaces,” Langmuir 31, 6137–6144 (2015).
[35] T. E. P. Kimkes and M. Heinemann, “How bacteria
recognise and respond to surface contact,” FEMS Microbiol. Rev. 44, 106–122 (2019).
[36] T. Nagai, K. Ibata, E. S. Park, M. Kubota, K. Mikoshiba,
and A. Miyawaki, “A variant of yellow fluorescent protein with fast and efficient maturation for cell-biologicalapplications,” Nat. Biotechnol. 20, 87–90 (2002).
[37] Bernd Jähne, Spatio-Temporal Image Processing: Theory
and Scientific Applications, Lecture Notes in Computer
Science, Vol. 751 (Springer Berlin Heidelberg, Berlin,1993).
[38] O. Ronneberger, P. Fischer, and T. Brox, “U-Net:
Convolutional Networks for Biomedical Image Segmentation,” in Medical Image Computing and ComputerAssisted Intervention – MICCAI 2015 (2015) pp. 234–
241.
[39] H. E. Bakker, S. Dussi, B. L. Droste, T. H. Besseling,
C. L. Kennedy, E. I. Wiegant, B. Liu, A. Imhof, M. Dijkstra, and A. van Blaaderen, “Phase diagram of binary
colloidal rod-sphere mixtures from a 3D real-space analysis of sedimentation–diffusion equilibria,” Soft Matter
12, 9238–9245 (2016).
[40] S. Azimi, J. Thomas, S. E. Cleland, J. E. Curtis,
J. B. Goldberg, S. P. Diggle, and M. S. Trent, “Ospecific antigen-dependent surface hydrophobicity medi-

12
ates aggregate assembly type in Pseudomonas aeruginosa,” mBio 12, e00860–21 (2021).
[41] F. J. Lobo-Cabrera, A. Patti, F. Govantes, and A. Cuetos, “Polymer-induced microcolony compaction in earlybiofilms: A computer simulation study,” Phys. Rev. E
103, 052407 (2021).
[42] T. Koda, M. Numajiri, and S. Ikeda, “Smectic-A phaseof a bidisperse system of parallel hard rods and hard
spheres,” J. Phys. Soc. Jpn. 65, 3551–3556 (1996).
[43] M. Adams and S. Fraden, “Phase behavior of mixtures ofrods (Tobacco Mosaic Virus) and spheres (polyethyleneoxide, bovine serum albumin),” Biophys. J. 74, 669–677(1998).
[44] M. Adams, Z. Dogic, S. L. Keller, and S. Fraden, “Entropically driven microphase transitions in mixtures ofcolloidal rods and spheres,” Nature 393, 349–352 (1998).
[45] X. Ye, J. A. Millan, M. Engel, J. Chen, B. T. Diroll,S. C. Glotzer, and C. B. Murray, “Shape alloys ofnanorods and nanospheres from self-assembly,” Nano
lett. 13, 4980—4988 (2013).
[46] A. R. Badireddy, S. Chellam, S. Yanina, P. Gassman,and K. M. Rosso, “Bismuth dimercaptopropanol (bisbal)
inhibits the expression of extracellular polysaccharides
and proteins by Brevundimonas diminuta: Implications
for membrane microfiltration,” Biotechnol. Bioeng. 99,
634–643 (2008).
[47] A. R. Badireddy, B. R. Korpol, S. Chellam, P. L.
Gassman, M. H. Engelhard, A. S. Lea, and K. M.
Rosso, “Spectroscopic characterization of extracellularpolymeric substances from Escherichia coli and Serratia marcescens: Suppression using sub-inhibitory concentrations of bismuth thiols,” Biomacromolecules 9, 3079–
3089 (2008).
[48] L. Gualdi, L. Tagliabue, S. Bertagnoli, T. Ieranó,C. De Castro, and P. Landini, “Cellulose modulates
biofilm formation by counteracting curli-mediated colonization of solid surfaces in Escherichia coli,” Microbiology 154, 2017–2024 (2008).
[49] D. O. Serra, A. M. Richter, and R. Hengge, “Cellulose as an architectural element in spatially structured
Escherichia coli biofilms,” J. Bacteriol. 195, 5540–5554(2013).
[50] M. M. Barnhart and M. R. Chapman, “Curli biogenesis
and function,” Annu. Rev. Microbiol. 60, 131–147 (2006).
[51] E. Brombacher, A. Baratto, C. Dorel, and P. Landini,“Gene expression regulation by the curli activator CsgD
protein: Modulation of cellulose biosynthesis and control of negative determinants for microbial adhesion,” J.
Bacteriol. 188, 2027–2037 (2006).
[52] X. Wang, D. R. Smith, J. M. Jones, and M. R. Chapman,“In Vitro polymerization of a functional Escherichia coliamyloid protein,” J. Biol. Chem. 282, 3713–3719 (2007).
[53] C. Schwechheimer and M. J. Kuehn, “Outer-membrane
vesicles from Gram-negative bacteria: biogenesis andfunctions,” Nat. Rev. Microbiol. 13, 605–619 (2015).
[54] S. Roier, F. G. Zingl, F. Cakar, S. Durakovic, P. Kohl,
T. O. Eichmann, L. Klug, B. Gadermaier, K. Weinzerl,
R. Prassl, A. Lass, G. Daum, J. Reidl, M. F. Feldman,
and S. Schild, “A novel mechanism for the biogenesisof outer membrane vesicles in Gram-negative bacteria,”
Nat. Commun. 7, 10515 (2016).
[55] C. Reichhardt, A. N. Jacobson, M. C. Maher, J. Uang,
O. A. McCrate, M. Eckart, and L. Cegelski, “Congo redinteractions with curli-producing E. coli and native curli
amyloid fibers,” PLoS ONE 10, e0140388 (2015).
[56] M. Toyofuku, G. Cárcamo-Oyarce, T. Yamamoto,
F. Eisenstein, C.-C. Hsiao, M. Kurosawa, K. Gademann,
M. Pilhofer, N. Nomura, and L. Eberl, “Prophagetriggered membrane vesicle formation through peptidoglycan damage in Bacillus subtilis,” Nat. Commun. 8,481 (2017).
[57] P. K. Mandal, G. Ballerin, L. M. Nolan, N. K. Petty,
and C. B. Whitchurch, “Bacteriophage infection of Escherichia coli leads to the formation of membrane vesicles via both explosive cell lysis and membrane blebbing,”
Microbiology 167, 001021 (2021).
[58] A. J. Manning and M. J. Kuehn, “Contribution of bacterial outer membrane vesicles to innate bacterial defense,”
BMC Microbiol. 11, 258 (2011).
[59] A. Palaniraj and V. Jayaraman, “Production, recovery and applications of xanthan gum by Xanthomonas
campestris,” J. Food Eng. 106, 1–12 (2011).
[60] S. Y. Khan, M. Yusuf, and N. Sardar, “Studies on rheological behavior of xanthan gum solutions in presence ofadditives,” Pet. Petro. Chem. Eng. J. 2, 000165 (2018).
[61] X. Yang, T. Xu, P. Cao, K. Qiao, L. Wang, T. Zhao, andJ. Zhu, “The viscosity behaviors of bacterial suspensions
or extracellular polymeric substances and their effects on
aerobic granular sludge,” Environ. Sci. Pollut. Res. 26,
30087–30097 (2019).
[62] K. Kawano, F. Yokoyama, J. Kawamoto, T. Ogawa,
T. Kurihara, and S. Futaki, “Development of a simple
and rapid method for In Situ vesicle detection in cultured
media,” J. Mol. Biol. 432, 5876–5888 (2020).
[63] S. L. Walker, J. E. Hill, J. A. Redman, and M. Elimelech, “Influence of growth phase on adhesion kineticsof Escherichia coli D21g,” Appl. Environ. Microbiol. 71,
3093–3099 (2005).
[64] C. Wagner, P. Steffen, and S. Svetina, “Aggregation of
red blood cells: From rouleaux to clot formation,” C. R.
Phys. 14, 459–469 (2013).
[65] J. Hrabe, S. Hrabĕtová, and K. Segeth, “A model of effective diffusion and tortuosity in the extracellular spaceof the brain,” Biophys. J. 87, 1606–1617 (2004).
[66] H. Cho, H. Jönsson, K. Campbell, P. Melke, J. W.
Williams, B. Jedynak, A. M. Stevens, A. Groisman, andA. Levchenko, “Self-organization in high-density bacterial colonies: Efficient crowd control,” PLoS Biol. 5, e302(2007).
[67] M. Hashimoto, T. Nozoe, H. Nakaoka, R. Okura,
S. Akiyoshi, K. Kaneko, E. Kussell, and Y. Wakamoto,“Noise-driven growth rate gain in clonal cellular populations,” Proc. Natl. Acad. Sci. USA 113, 3251–3256(2016).
[68] Y. Koganezawa, M. Umetani, M. Sato,andY. Wakamoto, “History-dependent physiological adaptation to lethal genetic modification under antibiotic exposure,” bioRxiv , 2021.09.05.459045 (2021).

Supplementary Material for“Smectic-like bundle formation of planktonic bacteria upon nutrient starvation”
Takuro Shimaya1 and Kazumasa A. Takeuchi1, 2
1

2

Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
Institute for Physics of Intelligence, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

arXiv:2407.05031v1 [physics.bio-ph] 6 Jul 2024

SUPPLEMENTARY FIGURESab

M9 (glc + a.a.)M9 (glc + a.a.)aggregateschains

500 minE. coli W3110
WTc

flu::kanmin600

sessileM9 (glc + a.a.)

d

ΔfliC

ΔfliC

FIG. S1. Aggregation processes of planktonic E. coli cells in steady growth environments. (a) Populations of the wild-type
W3110 (WT) in a well (diameter ϕ = 110 µm) cultured with M9(glc+a.a.) for 500 min since the observation was started.
Initially there were 5 cells in the well. The appearance of chains and aggregates was confirmed in all 30 wells of various
diameters recorded in a single experiment (WT growth in Table II). See also Movie 1. (b) Aggregates of the flu::kan mutant(without Ag43 expression), in a well (ϕ = 150 µm) cultured with M9(glc+a.a.) for 600 min since the observation was started.
Initially there were 10 isolated cells in the well. No chain formation was observed in 23 out of 28 wells with various diameters
recorded in a single experiment (flu::kan growth in Table II). In the other 5 wells, chain formation was observed, which may be
due to flagella as mentioned below. In this image, cells adhering to the substrate (slightly out of the focus) can be seen. See also
Movie 2. (c) An aggregation process of the ∆fliC mutant (without flagella) in a well (ϕ = 110 µm) cultured with M9(glc+a.a.).
t = 0 is the time at which the observation was started. Initially there were 8 cells in the well. No chain formation was observedin 28 out of 30 wells with various diameters recorded in a single experiment (∆fliC growth in Table II). In the other 2 wells,
chain formation was observed. This suggests that both flagella and Ag43 are important for chain formation, though they cansometimes complement each other. While the adhesion of cells to the substrate was found in 27 out of 30 wells for the WT
and in 23 out of 28 wells for the flu::kan mutant, this happened only in 8 out of 30 wells for the ∆fliC mutant. See also
Movie 3. (d) Time evolution of the aggregate size of the ∆fliC mutant. Each time series represents the data in a separate well(ϕ = 110 µm). The error was estimated to be the perimeter × 5 pixels (∼ 0.85 µm), which we considered to be the range of
uncertainty in manual detection of the edge of the regions. From the slope of the semi-log plot, we evaluated the growth rate
at 0.009(3) min−1 .

only for training

2

manualannotation
BCE loss

Input
U-Net

Segmentation

Output

CLAHE

structuretensor

CLAHE

U-Net

only for training

Nematic L2 loss
manualannotation

structuretensor

FIG. S2. The entire pipeline of the image analysis. A deep neural network, namely the U-Net, was employed in two places,
specifically for the segmentation of the regions with planktonic aggregates and for the estimation of the cell orientation N .
Note that entire images were given as the input of the U-Net for estimating N while the figure shows a small part of the images
for visibility. See also Materials and Methods in the main text for details.

Density correlation

Cell orientation

3

ΔfliC

ΔfliC

Bundle order

ΔfliC

FIG. S3. Cell orientation N , density correlation director R, and the bundle order parameter SB , overlaid on the microscope
images. These are the results for the ∆fliC mutant grown in M9(glc+a.a.) and starved in PBS (∆fliC starvation in Table II).
N and R are perpendicular if bundles are formed. The spatially-averaged bundle order parameter is shown in Fig. 3d by the
purple curve. See also Movies 5 and 6.

4

a

b
ΔfliC ΔfliC csgA::kanPBS
ΔfliC csgA::kan

10 μm

0.5 mmFIG. S4. Investigation of the relevance of curli to the bundle formation. (a) Confirmation of the loss of curli in the ∆fliC
csgA::kan mutant, by congo red. This dye selectively stains amyloid fibers including curli, as confirmed for the ∆fliC strain(left). No signal was detected for the ∆fliC csgA::kan strain (right). (b) Starvation response of the ∆fliC csgA::kan mutant
grown in M9(glc+a.a.) and starved in PBS. Bundle clusters are indicated by the dashed rectangles. The well diameter ϕ is
230 µm. t′ = 0 is the time at which the environment was switched. The bundle formation was observed in 15 out of 19 wellswith various diameters recorded in a single experiment (∆fliC csgA::kan starvation in Table II). See also Movie 11.

PBS

a

b

c

ΔfliC (venus)

phase-contrast

Venus

FM 4-64

FIG. S5. Multi-channel observation of the bundle formation of the ∆fliC (venus) mutant, 150 min after the environment was
switched from M9(glc+a.a.) to PBS. (a) Phase-contrast image. (b) Venus fluorescence image, which visualizes the entire cellbodies. (c) FM 4-64 fluorescence image, which visualizes the cell membranes and OMVs.

5a

M9 (glc + a.a.) + PMB

ΔfliC

b
ΔfliC

LB + PMBc M9 (glc + a.a.) + xanthan
ΔfliC

FIG. S6. Steady growth measurements intended to test the relevance of depletion attraction. t = 0 is the time at which theobservation was started. (a) Observation of the ∆fliC mutant grown in M9(glc+a.a.) with 250 ng/ml polymyxin B. The welldiameter ϕ is 230 µm. Bundle clusters were not observed in all 6 wells with various diameters recorded in a single experiment(∆fliC starvation (PMB) in Table II). See also Movie 12. (b) Observation of the ∆fliC mutant grown in LB with 250 ng/ml
polymyxin B. The well diameter ϕ is 110 µm. Bundle clusters were not observed in all 15 wells with various diameters recorded
in a single experiment (∆fliC starvation (LB, PMB) in Table II). See also Movie 13. (c) Observation of the ∆fliC mutant
grown in M9(glc+a.a.) with 0.03 wt% xanthan gum. The well diameter ϕ is 150 µm. Bundle clusters were not observed in all
6 wells with various diameters recorded in a single experiment (∆fliC starvation (xanthan) in Table II). See also Movie 14.

6
MOVIE DESCRIPTIONS

Movie 1:
Growth of the wild-type W3110 (WT) in M9(glc.+a.a.). The diameter of the well is 110 µm. The movie is played
1200 times faster than the real speed.
Movie 2:Growth of the flu::kan mutant in M9(glc.+a.a.). The diameter of the well is 150 µm. The movie is played 1200 times
faster than the real speed.
Movie 3:Growth of the ∆fliC mutant in M9(glc.+a.a.). The diameter of the well is 110 µm. The movie is played 1200 times
faster than the real speed.
Movie 4:
Starvation response of the ∆fliC mutant. The environment was switched from M9(glc.+a.a.) to PBS at t = 480 min.
The diameter of the well is 150 µm. The movie is played 1200 times faster than the real speed.
Movie 5:The density correlation director R (top) and the cell orientation N (bottom) overlaid on Movie 4. The pseudo-color
indicates the angle (see Fig. 3b, Fig. S2 or Fig. S3 for the definition). N and R are perpendicular in the regions where
smectic-like bundles are formed.
Movie 6:The bundle order parameter SB overlaid on Movie 4. The pseudo-color indicates the value of the bundle orderparameter. See Fig. 3c for the color bar.
Movie 7:
Starvation response of the ∆fliC mutant. The environment was switched from LB to PBS at t = 225 min. The
diameter of the well is 110 µm. The movie is played 1200 times faster than the real speed.
Movie 8:
Starvation response of the wild-type W3110 (WT). The environment was switched from M9(glc.+a.a.) to PBS at
t = 480 min. The diameter of the well is 150 µm. The movie is played 1200 times faster than the real speed.
Movie 9:Starvation response of the ∆fliC mutant, grown in M9(glc.+a.a.) + 2 µM BisBAL and starved in PBS + 2 µM
BisBAL. Bundles did not appear in this movie. The environment was switched at t = 480 min. The diameter of thewell is 150 µm. The movie is played 1200 times faster than the real speed.
Movie 10:
Starvation response of the ∆fliC mutant), grown in M9(glc.+a.a.) + 2 µM BisBAL and starved in PBS + 2 µM
BisBAL. Bundles appeared in this movie. The environment was switched at t = 480 min. The diameter of the well is
150 µm. The movie is played 1200 times faster than the real speed.
Movie 11:
Starvation response of the ∆fliC csgA::kan mutant. The environment was switched from M9(glc.+a.a.) to PBS at
t = 480 min. The diameter of the well is 230 µm. The movie is played 1200 times faster than the real speed.
Movie 12:Growth of the ∆fliC mutant in M9(glc+a.a.) + 250 ng/ml polymyxin B. The diameter of the well is 230 µm. The
movie is played 1200 times faster than the real speed.
Movie 13:Growth of the ∆fliC mutant in LB + 250 ng/ml polymyxin B. The diameter of the well is 230 µm. The movie isplayed 1200 times faster than the real speed.
Movie 14:Growth of the ∆fliC mutant in M9(Glc+a.a.) + 0.03 wt% xanthan gum. The diameter of the well is 150 µm. The
movie is played 1200 times faster than the real speed.
Movie 15:
Response against starvation and growth recovery of the ∆fliC mutant. The environment was switched fromM9(glc.+a.a.) to PBS at t = 480 min, and from PBS to M9(glc.+a.a.) at t = 660 min. The diameter of thewell is 230 µm. The movie is played 1200 times faster than the real speed.