PNAS Nexus, 2024, 3, pgae238
https://doi.org/10.1093/pnasnexus/pgae238
Advance access publication 14 June 2024

Research Report

Emergence of bacterial glass
Hisay Lamaa, Masahiro J. Yamamotoa,b, Yujiro Furutac,d, Takuro Shimaya

a,dand Kazumasa A. Takeuchi

a,d,

*

a

Abstract
Densely packed, motile bacteria can adopt collective states not seen in conventional, passive materials. These states remain in many
ways mysterious, and their physical characterization can aid our understanding of natural bacterial colonies and biofilms as well as
materials in general. Here, we overcome challenges associated with generating uniformly growing, large, quasi-two-dimensional
bacterial assemblies by a membrane-based microfluidic device and report the emergence of glassy states in two-dimensional
suspension of Escherichia coli. As the number density increases by cell growth, populations of motile bacteria transition to a glassy
state, where cells are packed and unable to move. This takes place in two steps, the first one suppressing only the orientationalmodes and the second one vitrifying the motion completely. Characterizing each phase through statistical analyses andinvestigations of individual motion of bacteria, we find not only characteristic features of glass such as rapid slowdown, dynamic
heterogeneity, and cage effects, but also a few properties distinguished from those of thermal glass. These distinctive properties
include the spontaneous formation of micro-domains of aligned cells with collective motion, the appearance of an unusual signal in
the dynamic susceptibility, and the dynamic slowdown with a density dependence generally forbidden for thermal systems. Our
results are expected to capture general characteristics of such active rod glass, which may serve as a physical mechanism underlying
dense bacterial aggregates.
Keywords: bacteria, glass transition, active glass, biofilm, dynamic heterogeneity, orientation glass

Significance Statement
Bacteria often live in the form of dense populations, such as biofilms. While diverse approaches have been taken to understand suchaggregates, physical consequences of being dense remained largely unexplored. Here, by using a microfluidic device suitable for a uni­
form culture of dense bacteria, we revealed that bacteria transition from an actively swimming state to jammed states as they pro­liferate, through a pathway analogous to glass transitions of colloidal rods. Through analysis of both single-cell and statisticalproperties, we characterized the observed collective states and transitions, and identified not only similarities but dissimilarities
with usual glass formers including colloids. Our model experiment of dense bacteria may impact broad contexts beyond biofilms,
hinting at general characteristics of such active rod systems.

IntroductionDense bacterial populations offer an exciting frontier of researchfor both physical and microbial sciences. From the biological
viewpoint, dense bacterial populations, especially biofilms,
abound in diverse natural environments and beyond (1, 2), being
also encountered in medicine and industries often as the bane(2–4). It is therefore crucial to characterize their multifaceted as­pects (1, 2), including not only extracellular substances and cell
phenotypes as studied extensively in the literature, but also phys­
ical consequences of being dense aggregates, which have gained
an emerging interest in physical sciences. Indeed, recent physicalstudies on dense bacterial populations unveiled a plethora of col­lective states not seen in conventional passive materials (5, 6),
which however remain in many ways mysterious.

Generally, dense particle systems may undergo glass and jam­ming transitions as the number density is increased, showing dra­
matic changes in both single-particle dynamics and material
properties as suspension (7–11). Even for conventional thermal sys­tems, it is only recently that firm theoretical grounds on glass tran­
sitions started to be built for some idealized cases (12). Therefore, it
constitutes an important challenge in physics to extend this under­
standing to active systems (13–15), i.e. systems made of motile par­ticles akin to cells, or more generally, to athermal systems including
intracellular environments. Experimentally, glassy dynamics has
been reported in cytoplasm and cell extracts (16–18) as well as inmammalian tissues (19–21), posing interesting problems both inphysics and biology (13–15). Concerning bacteria, by contrast,
whereas a few recent studies suggested the relevance of glassy

Competing Interest: The authors declare no competing interest.
Received: November 22, 2023. Accepted: June 3, 2024
© The Author(s) 2024. Published by Oxford University Press on behalf of National Academy of Sciences. This is an Open Access article
distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/), which permits
unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.

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Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
National Metrology Institute of Japan, National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba 305-8560, Japanc
Department of Physics, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji 192-0397, Japand
Department of Physics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan*To whom correspondence should be addressed: Email: kat@kaztake.org
Edited By: Victor Nizetb2 | PNAS Nexus, 2024, Vol. 3, No. 7
a relatively short relaxation time, indicating fast structural relax­
ation. This corresponds to what is called the α-relaxation in the lit­
erature (7–11). However, this α-relaxation time increases rapidly
for ϕ ≳ 0.85, soon exceeding the observation time. To be morequantitative, we fit the data by a stretched exponential function,βQ
Q(Δt) ∼ e−(Δt/τQ ) , well known to describe the α-relaxation of glassy
materials (7, 8), and evaluate the relaxation time τQ thereby(Fig. S4). The result indeed shows a rapid increase of τQ (Fig. 2d,blue circles), by nearly two orders of magnitude in
0.78 ≲ ϕ ≲ 0.88. The observed superexponential growth of τQ indi­cates that our bacterial populations are a fragile glass former (7–9).
It is compatible with typical growth laws documented in the litera­ture, such as the power-law divergence−γQτQ ∼ (ϕQc − ϕ)(2)

predicted by mode-coupling theories (MCT) (7, 8, 11) (Fig. 2d,blue dashed line), as well as the Vogel–Fulcher–Tamman law (7–9),
τ ∼ exp( ϕ cϕ−ϕ ) (Fig. S6). This allows us to evaluate the glass transition
VFT

point; for example, from the MCT power law Eq. (2), one obtains
ϕQ
c = 0.882(4), where the number(s) in the parentheses represents
the uncertainty in the last digit(s) (see Methods).

Two-step transition
At this point, it is worth recalling the spherocylindrical shape ofthe constituting entity, namely E. coli, which has both translation­
al and orientational degrees of freedom. The relaxation of theorientational degrees of freedom can be evaluated by the orienta­
tional correlation functionCθ (Δt) = 〈cos 2[θ(􏿻r, t + Δt) − θ(􏿻r, t)]〉􏿻r,t ,(3)where θ(􏿻r, t) represents the nematic orientation angle. Figure 2cshows Cθ (Δt) for different ϕ. Similarly to Q(Δt), Cθ (Δt) also decays,βθ

Rapid dynamic slowdown
The rapid suppression of motion can be evaluated by the differ­ence of phase-contrast image intensities taken at two different
times, ΔI(􏿻r, t, Δt) = I(􏿻r, t + Δt) − I(􏿻r, t). Figure 1j–m shows that, withincreasing ϕ, the region with ΔI(􏿻r, t, Δt) ≈ 0 (where bacteria hardly
moved during the chosen time interval) expanded, and eventual­ly, near ϕ ≈ 0.88, the entire population became kinetically ar­
rested, i.e. vitrified. We also notice that this kinetic arrest took
place heterogeneously (see Fig. 1k,l and Movie S1), analogously
to glassy systems showing the dynamic heterogeneity (8, 9).
We characterize the observed vitrification by the differential
variance analysis (DVA) (26), which uses the intensity differenceΔI(􏿻r, t, Δt) to analyze the structural relaxation and the dynamic
heterogeneity. The structural relaxation is studied by the overlap
function defined by
Q(Δt) = 1 −

V(Δt)
,
V(∞)

(1)

2

following the stretched exponential form Cθ (Δt) ∼ e−(Δt/τθ )(Fig. S7), with a characteristic relaxation time τθ that increases
rapidly with ϕ (Fig. 2d, red squares). Importantly, we find thatthe orientational relaxation time τθ is larger than that of the over­lap function τQ by an order of magnitude or more, and seems to di­verge at lower ϕ. This is underpinned by the MCT fitting (Fig. 2d,
red dashed line)−γθτθ ∼ (ϕθc − ϕ),(4)which gives ϕθc = 0.852(13) that is significantly smaller thanϕQ
c = 0.882(4). The same conclusion was reached when the data
were fitted with the Vogel–Fulcher–Tamman law (Fig. S6). Fromϕθc < ϕQc , we conclude that the orientational degrees of freedom vit­
rify earlier than the rest, i.e. the translational degrees of freedom,the latter of which essentially governed the relaxation of the over­lap function. In other words, the glass transition in our systemtakes place in two steps, the first being a transition to the orienta­tion glass at ϕθc = 0.852(13) and the second the ultimate transition to
the complete glass at ϕQ
c = 0.882(4) (Fig. 2d).

where V(Δt) = 〈ΔI(􏿻r, t, Δt) 〉􏿻r,t is the intensity variance taken overposition 􏿻r and reference time t, and V(∞) is evaluated by twice
the variance of I(􏿻r, t). The quantity Q(Δt) roughly corresponds toDynamic heterogeneity

the fraction of bacteria that did not move over lag time Δt. Morequantitatively, Q(Δt) was reported to behave similarly to the selfintermediate scattering function (26), a quantity often used tocharacterize the structural relaxation of glassy materials.
Figure 2b shows the result of structural relaxation assessed
through Q(Δt) for different ϕ. For low ϕ, Q(Δt) decays to zero after

Another hallmark of glassy dynamics is dynamic heterogeneity,
which concerns nontrivial spatiotemporal correlation that devel­
ops near the glass transition (8, 9). It is often quantified by the dy­
namic susceptibility χ4 , which is essentially the variance of thestructural correlation function. In DVA (26), it can be evaluatedthrough the variance of Q(t, Δt), defined analogously to Eq. (1)Downloaded from https://academic.oup.com/pnasnexus/article/doi/10.1093/pnasnexus/pgae238/7693663 by guest on 11 July 2024

phenomena to the regulation of motility and three-dimensional
growth in bacterial colonies (22, 23), identification of glassy
states in bacterial populations remains a challenge, especially
under controlled environments that are necessary for the quan­titative investigation. A primary difficulty is to keep uniform
growth conditions for such dense cell populations for a longtime. While microfluidics is generally suitable for controlled ex­
periments, conventional devices that deliver nutrients throughchannels cannot maintain uniform growth conditions for large
and dense populations (24).
Here we overcame past difficulties and report a controlled ex­
periment characterizing emergent glassy phases of dense popula­tions of motile bacteria. We used a membrane-type microfluidic
device developed in (25) (Fig. 1a), named the extensive microperfu­
sion system (EMPS). Delivering growth medium to bacteria througha porous membrane, this device can maintain a uniform and con­stant growth condition for bacteria trapped in a 2D well, even if
the bacterial cells are densely packed (25). The membrane may
also let out substances secreted by cells, thus providing an ideal
platform for studying the physical effect of crowding. In the present
work, we cultured motile bacteria (E. coli, strain RP437, width≈ 1 μm, length varying roughly from 2 to 6 μm; see Fig. S1 for the dis­tribution of cell areas) in a closed 2D well (diameter 71.2 ± 0.5 μm,
depth ≈ 1.4 μm) supplied with growth medium (tryptone broth sup­plemented with surfactant; see Methods), and monitored their
spatiotemporal dynamics in a region near the center. Bacteria
were initially swimming actively. However, as the area fraction ofbacteria, ϕ, increased by cell growth and division at a uniform andconstant growth rate (Fig. 1b–e, Figs. S2 and S3), we found thatthe motion of the bacterial population started to be hampered rap­
idly (Movies S1–5), while their positions and orientations remained
globally disordered in space (Fig. 1f–i). In particular, the static struc­ture factor does not show a significant change in its shape (Fig. 2a) in
the range of ϕ where the bacterial motion slows down.

Lama et al. |amedium inlet

medium outlet

b

c

1

d

e

g

1

h

i

k

1

l

m

3

PDMS pad
frame
seal

PET membrane

cellulose
membraneobservation areastage
fcoverslip
stage

10

objective

observation area40

jcoverslip
20
motile E. coli RP437

0

Fig. 1. Experimental setup and vitrification of the bacterial population. a) Sketch of the experimental system. b–e) Phase-contrast images for different
area fractions φ, taken at different times from a single experimental run (see Fig. S2). f–i) Orientation field (pseudocolor) overlaid on the phase-contrast
images. j–m) Intensity difference ΔI(􏿻r, t, Δt) = I(􏿻r, t + Δt) − I(􏿻r, t) with Δt = 0.053 s.

but with a given t, without taking average over time. Here we
adopt the following definition:
22χQ
4 (Δt) = ϕ[〈Q(t, Δt) 〉t − 〈Q(t, Δt)〉t ],(5)

where 〈· · ·〉t denotes time averaging. The result in Fig. 2e showsQ
that χQ
4 (Δt) develops a peak as the second transition point ϕc =0.882(4) is approached, at the time scale consistent with τQ . Thisis typical of glassy systems (8), providing another support of char­acteristic glassy dynamics in our bacteria. By contrast, Fig. 2e also
shows an unusual peak development for low ϕ, at small Δt. This
will be scrutinized below, through the analysis of the motion ofbacteria and the collectivity. We also evaluated the dynamic sus­
ceptibility associated with the orientational degrees of freedom,
2

defined by χθ4 (Δt) = ϕ[〈Cθ (t, Δt) 〉 − 〈Cθ (t, Δt)〉2 ] (Fig. 2f). In this quan­tity, we only see the peak due to the transition to the orientation
glass, with the profile change controlled by the increase of τθ(inset).

Individual dynamics of bacteria
Now we characterize the observed phases. First, we tracked single
cells and investigated the evolution of their position 􏿻ri (t) andorientation θi (t). Figure 3a displays an example in the orientation
glass phase, shown with time series of the displacement Δ􏿻ri (t) =􏿻ri (t) − 􏿻ri (0) and the orientation θi (t) (Fig. 3b,c, respectively; seealso Movie S6). This cell was initially caged by neighbors (t ≲ 5 s),
but eventually escaped and moved significantly, over 4 μm or soduring 5 s ≲ t ≲ 7 s, until it was caged again. This is the cage effect,
another characteristic of glassy systems (7–9) (see Fig. S8 andMovie S7 for another cage escape event). Moreover, Fig. 3d showsthat the displacement tends to occur along the cell orientation,even in such a dense population where cells are pushed by neigh­bors in all directions. In other words, cells are led to move along
the orientation field θ(􏿻r, t), which is frozen in the orientation glass.
As a result, it is practically only when bacteria move, by escaping
from a cage, that they change the orientation significantly in theorientation glass phase (compare Fig. 3b,c). By contrast, in the ac­tive fluid phase ϕ < ϕθc , the orientation field θ(􏿻r, t) along which bac­teria tend to move evolves in space and time.

Formation of microdomains and collective
motionHere we scrutinize the spatial structure of the orientation field
θ(􏿻r, t), which turned out to guide the motion of bacteria.
Figure 4a,b shows, in their top left corner, θ(􏿻r, t) measured in theentire well, for ϕ = 0.784(7) (active fluid phase) and ϕ = 0.873(4)(orientation glass), respectively (see also Movies S8–11). Both fig­
ures indicate the formation of nematic microdomains, composedof cells that are oriented in similar directions, reminiscent of thosereported earlier for growing colonies of nonmotile bacteria (27). By
plotting |∇θ(􏿻r, t)|2 (main panels of Fig. 4a,b), we find that these do­mains are surrounded largely, if not entirely, by nearly discon­tinuous borders (red; notice the logarithmic scale of thepseudocolor code) with neighboring domains oriented in different
directions. This microdomain structure is considered to be a re­sult of the competition between the steric interaction, whichtends to align the cells locally, and the activity-driven force, which
originates from self-propulsion and cell growth and tends to de­stabilize the ordered alignment. We characterize the distributionof microdomain areas A and find an exponential distribution
e−A/A0 , with characteristic area A0 = 8.3(21) μm2 that hardly de­pends on ϕ (Fig. 4c and Fig. S9). The exponential distribution was
also found for nonmotile bacterial colonies (27), but the character­istic area A0 turned out to be much smaller in our motile bacteria,presumably because of the stronger destabilizing force due to theself-propulsion.
An important consequence of the formation of microdomains
is the emergence of collective motion. Since individual bacteria
tend to move along the orientation field, they attempt to move col­lectively in each microdomain, though the motion is largely ham­
pered in the glassy states. However, in the active fluid phase,bacteria do move in the form of microdomains or clusters(Fig. 5a,b and Movies S8 and 9), more visibly for lower ϕ, similarly
to swarming states of bacteria (28–32). The collective motion isevidenced by the presence of the velocity correlation between
nearby cells (Fig. 5c), within a distance of ≈ 2 μm, which is consist­ent with the typical size of the microdomains reported above.
Note that the velocity correlation is generally absent in thermal
systems, hence another athermal characteristic of our system,

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4 | PNAS Nexus, 2024, Vol. 3, No. 7

b

c

d

e

f

􏿻 ) for different area fractions φ. In theFig. 2. Static structure factor, structural relaxation, and dynamic susceptibility. a) The static structure factor S(q􏿻| by taking the average over all angles in the reciprocal space. b) The overlap function Q(Δt) for different area
main panel, it is shown as a function of q = |qfractions φ (legend). c) The orientational correlation function Cθ (Δt) for different area fractions φ (legend). d) The translational (overlap) and theorientational relaxation times, τ Q (blue circles) and τ θ (red squares), respectively, as functions of φ. The dashed lines indicate the results of the−γ
Qθ
mode-coupling theory fitting, τ ∼ (ϕc − ϕ) , with ϕQ
c = 0.882(4) for τ Q and ϕc = 0.852(13) for τ θ . e) The dynamic susceptibility χ 4 (Δt) associated with theoverlap function, for different area fractions φ (legend). f) The dynamic susceptibility χθ4 (Δt) associated with the orientation modes, for different area
fractions φ (legend). The same symbols indicate the same values of φ in all panels except d.

a

b

d

c

Fig. 3. Glassy dynamics in the motion of individual bacteria. The displayed results are for ϕ = 0.873(4), which is in the orientation glass phase. a)
Trajectory of a single cell for 0 ≤ t ≤ 13.14 s, drawn on the phase-contrast image taken at the last time frame. The positions at t = 0, 3.29, 6.58, 9.87, 13.14 s
are shown by colored disks with labels 1, 2, . . . , 5, respectively. b,c) Time series of the displacement from the initial position, |Δ􏿻ri (t)| b), and that of theorientation θi (t) c) of the cell tracked in panel a. These time series show a cage escape event during 5 s ≲ t ≲ 7 s. d) Histogram of the angle difference
between the cell orientation and the displacement (see the sketch). The cell orientations and the displacements are measured between two times
separated by an interval Δt, with Δt = 0.026 s (blue) and 0.26 s (red). The two histograms are overlaid with semitransparent colors, so that the dark bars
indicate the overlapping part and the light blue and red regions indicate the difference.

and is known to play a significant role in active glassy dynamics(13, 15, 33). In our system, the velocity correlation is formed as aresult of the microdomain structure of the orientations, but it isnoteworthy that the observed velocity correlation indicates thepresence of polar order, despite the essentially nematic natureof the steric interaction. This collective motion produces non­trivial spatiotemporal correlation in the cell positions, which
presumably results in the anomalous peak of the dynamic

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Lama et al. |

a

b

5

c

a

b

c

Fig. 5. Collective motion of bacteria in the active fluid phase for ϕ = 0.784(7). a,b) The displacements 􏿻ri (t + Δt) − 􏿻ri (t) a) and the orientation changes θi (t +Δt) − θi (t) b) of the individual bacteria during a short time interval, Δt = 0.053 s, displayed on top of the image at time t. In a, the displacements areindicated by the white arrows, whose endpoints are placed at the positions of the center of mass at times t and t + Δt. In b, the orientation at time t and􏿻j 〉 as a function of distance rij = |􏿻rj − 􏿻ri |. The distances rij between
􏿻i · vt + Δt is shown by the white and cyan lines, respectively. c) The velocity correlation 〈vcells were divided into bins and the average was taken in each bin. The error bars indicate the standard error, evaluated by regarding all pairs of cells as
independent.

susceptibility χQ
4 found to develop for low ϕ (Fig. 2e). This argument
is also supported by the fact that the anomalous peak is absent in
the dynamic susceptibility of the orientation (Fig. 2f), χθ4 , which is
not affected by the bacterial motion. Interestingly, a similar shorttime peak was also reported in a recent simulation of particles
self-propelling in discrete directions and attributed to the co­operative vibrational motion of active particles (34).

Concluding remarks
To summarize, we report that dense populations of motile bac­teria spontaneously vitrify as the number density increases bycell growth and division. We found that this transition takes placein two steps as sketched in Fig. 2d, first from the active fluid phaseto the orientation glass, where only the orientational degrees of
freedom are arrested, and second to the complete glass where
the remaining translational degrees of freedom are also arrested.
These transitions were found to show characteristic properties ofglass transitions, such as rapid slowdown, fragility, dynamic het­
erogeneity, and cage effects. We also showed that bacteria form
nematic microdomains, leading to collective motion which seems
to result in the unusual signal in the dynamic susceptibility χQ
4 for
low ϕ. These are attributed to the rod shape and self-propulsion ofbacteria, and as such, can be characteristic of active rod systems
in general.

Our analysis has revealed some other aspects that deserve fur­ther investigation. First, regarding the two-step transition, it is nottrivial whether the glass transition should first occur in the orien­
tation modes, in the translation modes, or both simultaneously.
The literature is mixed in this respect; experiments and simula­tions of ellipsoidal colloid glass showed the two-step transitionin the same order (35–38), but an MCT approach to hard ellipsoids(39) as well as simulations of an active dumbbell model (40) exhib­
ited the two transitions in the opposite order, i.e. first translation,then orientation. The two transitions may occur simultaneously
depending on the particle aspect ratio, but to our knowledge, notheory or system has demonstrated a change in the order. It istherefore an interesting open problem to clarify what physicalproperty controls the type of the two-step transition. Second, weremark that our estimates of the MCT exponents for the dynamic
slowdown, γQ = 1.6(3) and γθ = 1.5(13), seem to suggest the athe­rmal nature of our system, because MCT generally gives γ >1.76 . . . for thermal systems (7) (see supplementary material). It
is important to identify what aspect of our active system is re­sponsible for violating this lower bound for thermal systems,
and what the consequence is.
All in all, our experiment serves as a model system for investi­
gating physical properties of dense bacterial populations, withpotential relevance in various contexts such as biofilms. It
also contributes to the understanding of characteristic glassy

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Fig. 4. Formation of microdomains of aligned cells. a,b) The orientation field θ(􏿻r, t) (top left) and its gradient squared |∇θ(􏿻r, t)|2 (main) overlaid on thephase-contrast image, for ϕ = 0.784(7) (a, active fluid) and ϕ = 0.873(4) (b, orientation glass). See also Movies S8–11. The pseudocolor code for theorientation is identical to that used in Fig. 1f–i. c) Histograms of the microdomain area A for different ϕ (legend). The results were shifted vertically for thesake of visibility. The dashed lines are guides for the eyes indicating the exponential distribution e−A/A0 with A0 = 8.3(21) μm2 . The presented results were2
obtained with a threshold |∇θ(􏿻r, t)| ≥ 10−2 (rad/μm) here. Changing this threshold results in a constant vertical shift (Fig. S9), while it hardly affects thecharacteristic area A0 of the exponential distribution.

6 | PNAS Nexus, 2024, Vol. 3, No. 7
dynamics of such active rod systems, a class of active, or athermal
glass, which represents a frontier in the study of the physics ofglass.

Materials and methods
Culture of bacteria

Fabrication of microfluidic device
We performed experiments using a membrane-based microflui­dic device, namely, the EMPS (25) (Fig. 1a). The EMPS comprisesa micropatterned coverslip, a bilayer porous membrane (cellu­
lose and polyethylene terephthalate), and a polydimethylsilox­ane (PDMS) pad with an inlet and two outlets. The coverslip
substrate used in the present work has an array of circular wells(diameter ≈ 70 μm and depth ≈ 1.4 μm) that we microfabricated.
To assemble the device, we first soaked the coverslip substratein 1 wt% solution of 3-(2-aminoethyl aminopropyl) trimethoxysi­
lane (Shin-Etsu Chemical) and then treated it with biotin solu­
tion. We also prepared a bilayer membrane of EMPS, which
comprises a biotin-coated polyethylene terephthalate porous
membrane (taken from Transwell 3450, Corning, with a nominal
pore size of 0.4 μm) and a streptavidin-decorated cellulose mem­brane (Spectra/Por 7, Repligen, Waltham, MA, molecular weight
cut-off 25,000). Before the experiment, we put 1 μL of the bacter­ial suspension (OD600 = 0.1, prepared by the aforementioned
method) on top of wells on the substrate and attached the bi­
layer membrane to confine bacteria in the wells below themembrane, by biotin-streptavidin bonding between the cellu­
lose membrane and the coverslip. Then we placed a doublesided tape (also acting as a spacer) of thickness 100 μm on the
coverslip, enclosing the micropatterned region, and attached a
PDMS pad on the double-sided tape. This completes the fabrica­tion of EMPS.

Observation of bacteria
The assembled EMPS device was placed on the stage of an in­verted optical microscope (Leica DMi8), equipped with a 63x(NA=1.30) oil immersion objective and operated by the software
Leica LasX. During the experiment, bacteria in the microfluidic
wells were kept supplied with TB medium containing 0.02 wt%
of surfactant Tween-20, through the bilayer porous membraneof EMPS. This medium was infused from a syringe by a pump(NE-1,000, New Era Pump Systems), at the flow rate of 60 mL/h
for the first 5 min and 2 mL/h for the rest. As a result, bacteria

Image pre-processing
Pre-processing of the phase-contrast images consists of thefollowing two parts. We corrected the effect of non-uniform
illumination, by normalizing the image intensity with the lo­
cal threshold intensity evaluated by adaptthresh functionof MATLAB. Also, unless otherwise stipulated, we cropped
the images to the region of interest of size 259 × 214 pixels(44.7 μm × 36.9 μm) near the center of the well, to avoid influ­
ence from the well perimeter.

Estimation of the area fraction
The area fraction ϕ, i.e. the ratio of the area occupied by bacteria
to the total area of the region of interest, was evaluated by bi­
narizing the pre-processed phase-contrast images as follows.
The binarization threshold was set by a method called the
3-class fuzzy c-means clustering (42). Then we evaluated thefraction of the darker pixels in the binarized images. Using all
500 images of each data set, we evaluated the mean and thestandard deviation of the fraction of the darker pixels, andused them as the most probable value and the error, respective­
ly, of the area fraction ϕ.

Static structure factor􏿻) is defined as the squared modulus
The static structure factor S(qof the Fourier transform of the image intensity I(􏿻r, t), i.e.
􏿻) = 〈|FT[I(􏿻r, t)|2 ]〉t , where FT[ · · · ] is the 2D Fourier transformS(q􏿻 = (qx , qy ) is the wavenumber vector.
and q

Orientation field
The coarse-grained orientation field of bacteria, θ(􏿻r, t) with􏿻r = (x, y), was obtained by the structure tensor analysis (43).
From the intensity field I(x, y) of a pre-processed phase-contrast
image (here t is omitted from the argument for simplicity), thestructure tensor J(x, y) is defined by⎡⎤2〈(Δσx I) 〉σ〈(Δσx I)(Δσy I)〉σ⎣⎦,
J(x, y) =(6)2〈(Δσy I)(Δσx I)〉σ〈(Δσy I) 〉σ

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We used a motile strain of E. coli, RP437. As one of the stand­ard strains for motility studies, its run-and-tumble behavior iswell documented in the literature (41). First we inoculated
bacteria into a sterile test tube with 5 mL of Luria–Bertani(LB) medium (containing bacto-tryptone 10 g/L, yeast extract
5 g/L, and NaCl 10 g/L). Then we incubated the liquid culture
inside a shaking incubator at 37 ◦ C for 12 h at the shaking
speed of 220 rpm. We resuspended 100 μL of the overnight cul­
ture into 10 mL of fresh tryptone broth (TB, containing bactotryptone 10 g/L and NaCl 10 g/L), and again incubated it for 4 h
in the same culture condition. Finally, we measured the optic­
al density of the liquid culture by a spectrophotometer. The
optical density at wave length 600 nm, OD600 , was 0.4, whichis equivalent to 108 cells/mL. We diluted the liquid culture
to a concentration of OD600 = 0.1 (∼ 107 cells/mL) by resus­
pending it into a fresh TB medium containing 0.02 wt% of sur­factant Tween-20.

grew and proliferated throughout each experiment. We moni­
tored bacterial population in a well (diameter 71.2(5) μm) byphase-contrast microscopy, capturing images (pixel size
0.1724 μm, optical resolution 0.258 μm) by a charge-coupled de­vice camera (DFC3000G, Leica). For the main experiment pre­sented in this work, there were initially three cells in theobserved well, but after roughly five hours, the number in­creased to ≈ 800. We then started to repeat series of acquisitionof 1,000 images at an interval of ≈ 0.0263 s, preceded by auto­
matic focus adjustment (Leica adaptive focus control, singleshot mode). We further grouped the images into sets of 500 con­secutive images and statistical analysis was carried out for eachgroup. Bacteria continued growing and proliferating during thisset of image acquisitions too, leading to an increase of the area
fraction ϕ (Fig. S2). Note that, because the timing of the transi­tion varied a little among different samples, we used a single
biological replicate for the main analysis presented in this pa­
per. For the uninterrupted observation shown in Movie S1,phase-contrast images were acquired at a regular interval of
1 s with automatic focus adjustment (continuous mode).

Lama et al. |where􏽘
〈g(x, y)〉σ =g(x′ , y′ )fσ (x − x′ , y − y′ )

(7)

∂ fσ
(x − x′ , y − y′ )
∂x

(8)

∂ fσ
(x − x′ , y − y′ )∂y(9)x′ ,y′

Δσx I =

􏽘g(x′ , y′ )x′ ,y′

􏽘g(x′ , y′ )x′ ,y′

withaGaussiankernel−1fσ (x, y) = 2πσ2 ex2 +y22σ2acknowledge the useful codes and libraries made available by
S. Panigrahi and L. Espinosa for MiSiC (44), by J. C. Crocker,
E. R. Weeks, D. Blair and E. Dufresne for the particle tracking, by
G. Xiong for the 3-class fuzzy c-means clustering (42), and by
F. Grussu for the structure tensor method.

Supplementary Material
Supplementary material is available at PNAS Nexus online.

Fundingand

σ=6pixels = 1.03 μm. Then, the orientation field θ(x, y, t) was obtainedby􏼠􏼡
2〈(Δσx I)(Δσy I)〉σ1−1θ(x, y, t) = tan
.
(10)
2
2
2
〈(Δσx I) 〉σ − 〈(Δσy I) 〉σThis work is supported in part by KAKENHI from Japan Society for
the Promotion of Science (Grant Nos. JP16H04033, JP19H05800,
JP20H00128, JP21K20350, JP24K00593), by Core-to-Core Program“Advanced core-to-core network for the physics of self-organizing
active matter (JPJSCCA20230002), and by “Planting Seeds for
Research” program and Suematsu Award from Tokyo Instituteof Technology.

Tracking bacteria

Author Contributions

To track the motion of individual bacteria, we first need to carryout cell segmentation of phase-contrast images. This was done
by applying MiSiC (44), a deep learning-based method for the seg­mentation of bacteria, iteratively to each pre-processed phasecontrast image. More specifically, after each application of
MiSiC, we removed the regions where cells were detected, added
small noise to the image intensity, varied parameters that set
the criteria of cell detection slightly and randomly, and applied
MiSiC again, unless cells were already detected in a sufficient frac­tion of the area or MiSiC was already applied sufficiently manytimes (specifically, 300 times). After this iteration, we manuallycorrected the segmentation result if necessary, at least for thecell we focused on and its neighbors for the results presented inFig. 3 and Movie S6, and for all cells in the field of view, except
those on the boundary, for the results in Fig. 5. Then, using thesegmentation results of all images in a given data set, we applied
Blair and Dufresne’s particle tracking code available at https://site.physics.georgetown.edu/matlab/, which is based on the algo­rithm developed by Crocker, Grier, and Weeks (45). For the resultson the active fluid phase shown in Fig. 5, manual correction of the
tracking result was also necessary for bacteria that happened tomove over a long distance through the neighbors. Note that theanalysis shown in Fig. S8 and Movie S7 did not use the method de­scribed here, but is a result of fully manual tracking.

K.A.T. conceived the project and directed the research. H.L. and
T.S. constructed the device. H.L. performed the experiments.
H.L. and K.A.T. analyzed the data. M.J.Y. and Y.F. contributed tothe development of the project. All authors contributed to the in­terpretation of the results. H.L. and K.A.T. wrote the manuscript,
and all authors revised or commented.

Nonlinear fit
All nonlinear fits presented in this work were carried out by using
the Levenberg–Marquardt algorithm, known to solve nonlinear
least-squares problems reliably. The uncertainties of the fitting
results indicate the 95% confidence interval.

Acknowledgments
We are grateful to Y. Wakamoto and R. Okura for their help in theconstruction of a prototype of the experimental device used in thiswork. We thank A. Ikeda for his enlightening discussions on inter­
pretations of the MCT fitting results (supplementary material),
H. Yoshino and A. Ikeda for discussions on glass transitions of an­
isotropic particles, G. Luca for his suggestion to carry out domain
analysis (Fig. 4), Y. Han for his suggestion to measure the displace­ments (Fig. 5), and D. Nishiguchi for frequent discussions. We

Preprints
A preprint of this article is published at DOI:10.48550/arXiv.2205.
10436.

Data Availability
The data that support the findings of this study, as well as relevant
microscope images and scripts, have been deposited in Zenodo athttps://doi.org/10.5281/zenodo.11522483.

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