††thanks: Email address

# Tubulation and dispersion of oil by bacterial growth on droplets

Vincent Hickla Gabriel Juarezb<EMAIL_ADDRESS>aDepartment of Physics,
University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
bDepartment of Mechanical Science and Engineering, University of Illinois at
Urbana-Champaign, Urbana, Illinois 61801, USA

###### Abstract

Bacteria on surfaces exhibit collective behaviors, such as active turbulence
and active stresses, which result from their motility, growth, and
interactions with their local surroundings. However, interfacial deformations
on soft surfaces and liquid interfaces caused by active growth, particularly
over long time scales, are not well understood. Here, we describe experimental
observations on the emergence of tubular structures arising from the growth of
rod-shaped bacteria at the interface of oil droplets in water. Using
microfluidics and timelapse microscopy, the dimensions and extension rates of
individual tubular structures as well as bulk bio-aggregate formation are
quantified for hundreds of droplets over 72 hours. Tubular structures are
comparable in length to the initial droplet radius and are composed of an
outer shell of bacteria that stabilize an inner filament of oil. The oil
filament breaks up into smaller microdroplets dispersed within the bacterial
shell. This work provides insight into active stresses at deformable
interfaces and improves our understanding of microbial oil biodegradation and
its potential influence on the transport of droplets in the ocean water
column.

###### pacs:

XX.xx.xx

##  I Introduction

Active matter refers to systems that exchange energy with their surroundings,
leading to behaviors that are unlikely at thermal equilibrium. Active systems
consisting of simple building blocks can give rise to complex and emergent
phenomena. Examples range across many scales, from actin microfilaments and
clusters of cells Doostmohammadi  _et al._ (2018); Copenhagen and Gopinathan
(2016) to flocks of birds Bialek  _et al._ (2014) and schools of fish Herbert-
Read  _et al._ (2011). The study of active materials shows promise for
uncovering new physics, with potential applications in a variety of
disciplines, including statistical and biological physics Bechinger  _et al._
(2016); Ramaswamy (2010), soft matter Doostmohammadi  _et al._ (2018);
Marchetti  _et al._ (2013), biomedicine Wang and Gao (2012), materials science
Needleman and Dogic (2017), and traffic engineering Helbing (2001).

Active particles confined to interfaces form a rich subset of active systems
of particular interest to physical and biological research communities. Both
living and non-living interfacial systems can exhibit complex behaviors far
from thermal equilibrium including collective motility, swarming, and active
turbulence Copenhagen and Gopinathan (2016); Metselaar  _et al._ (2019);
Guillamat  _et al._ (2017). These emergent behaviors are believed to play an
important role in biological phenomena such as cellular transport Sanchez  _et
al._ (2012); Woodhouse and Goldstein (2012), self-assembly of microtubules and
motor proteins Kruse  _et al._ (2004); Surrey  _et al._ (2001), clusters of
sperm or epithelial cells Creppy  _et al._ (2015); Blanch-Mercader  _et al._
(2018), and bacterial or algal colonies Lauga  _et al._ (2006); Berke  _et
al._ (2008).

Because of their simplicity, single-celled bacteria are an especially useful
model organism to explore how complex behavior emerges in collections of
simple components Aranson (2022). Studies have explored the ways in which
monolayers of motile bacteria give rise to active behavior Cisneros  _et al._
(2007). Other researchers have created artificial micro- or nanoswimmers to
mimic the self-propulsion observed in living cells Gompper  _et al._ (2020);
Tsang  _et al._ (2020). Rod-shaped bacteria in particular are known for their
tendency to align and self-organize at interfaces Doostmohammadi  _et al._
(2018). The orientational ordering of such bacteria can greatly increase the
magnitude of the stresses exerted on the substrate by either motility or
growth of the cells. However, self-organization of bacterial colonies has
mostly been studied on rigid interfaces, where interfacial deformations can be
neglected. In many systems this assumption does not always hold, and possible
re-organization of the active material’s environment must be considered
Bechinger  _et al._ (2016).

Other active systems have been studied for the interfacial deformations that
can result from the collective motion of active particles. For example, self-
propelled particles enclosed within giant vesicles can induce a variety of
non-equilibrium shapes in the membrane Vutukuri  _et al._ (2020); Alert
(2022). A common deformation mode in active systems is tubulation: the
emergence of high-aspect-ratio tubular structures from an interface. This
process has been studied extensively of liposomes or vesicles, where a
phospholipid bilayer folds onto itself to form a protrusion from the cell
Lamazière  _et al._ (2007); Roux  _et al._ (2002); Osawa  _et al._ (2009).
Tubulation can also be driven by a layer of filaments, such as FtsZ or
microtubules, that coat the surface of the vesicle Keber  _et al._ (2014);
Kumar  _et al._ (2019). Recently, generic models have been developed to
describe how active nematics, such as collections of rod-shaped particles,
produce tube-like deformation on deformable interfaces Metselaar  _et al._
(2019); Hoffmann  _et al._ (2022). To verify the generality of these results,
it is important to determine experimentally whether other model active
nematics such as rod-shaped bacteria can produce similar morphologies.

The study of bacteria at oil-water interfaces is important because of its
relevance to oil spill remediation research. After a deep-sea oil spill, oil-
degrading bacteria such as _Alcanivorax borkumensis_ Yakimov  _et al._ (1998)
play a crucial role in removing oil from marine ecosystems Head  _et al._
(2006); Passow and Hetland (2016); Passow and Overton (2021). The process of
biodegradation has primarily been studied using in situ samples and batch
reactors Kleindienst  _et al._ (2015); Brakstad  _et al._ (2014); Prince and
Butler (2014), which cannot reveal the underlying physics at the oil-water
interface. Many open questions remain, particularly regarding how microscopic
droplets of oil in sub-surface plumes can be biodegraded Hazen  _et al._
(2010); McFarlin  _et al._ (2014).

The effect of droplet size on degradation rates (including the effect of
surfactants and chemical dispersants) is especially contentious Kleindienst
_et al._ (2015); Prince (2015). Recent studies have examined how oil-degrading
bacteria attach to oil droplets and form aggregates such as biofilms at the
interface Bookstaver  _et al._ (2015); Abbasi  _et al._ (2018); Omarova  _et
al._ (2019). However, none have considered the complex deformations to the
oil-water interface that can arise as a result of cell growth. Studies of
individual droplets under environmentally relevant conditions are needed to
better understand the fate of spilled oil Lee  _et al._ (2013); White  _et
al._ (2019). In particular, direct observation of individual droplets with
high spatial and temporal resolution can shed light on the biomechanics of oil
biodegradation.

The self-organization and collective behavior of growing bacteria at liquid
interfaces has recently been shown to lead to the colonization and buckling of
oil droplets Fernandez  _et al._ (2022); Hickl and Juarez (2022). Here, we
describe the extreme deformations of the oil-water interface and dispersion of
oil caused by the growth of bacteria on spherical droplets. Using
microfluidics and timelapse microscopy, hundreds of oil droplets of sizes $5$
µm $\leq R\leq 100$ µm are observed simultaneously and continuously over 72
hours. Confined cell growth leads to tubulation at the interface. We describe
the underlying structure and composition of the tubes, which can form a dense
bio-aggregate in which oil is dispersed as smaller droplets. Image analysis is
used to measure the tube and bio-aggregate extension rate, bio-aggregate size,
and size distribution of micro-dispersed droplets. These phenomena demonstrate
how the growth of simple, non-motile active particles on an interface can lead
to the emergence of complex interfacial deformations. The ability to visualize
these processes has important benefits for the study of bacterial
biodegradation of oil and, more generally, the interactions between fluid
interfaces and active matter.

##  II Experimental methods

The species used in experiments was Alcanivorax borkumensis, a known anaerobic
oil-degrading bacterium. Cells are rod-shaped which average length $2.7$ µm
and width $0.7$ µm. Cells were grown in a culture medium consisting of 37.4
g/L 2216 marine broth (BD Difco) and 10 g/L sodium pyruvate in an orbital
shaker at 180 rpm and $30^{\circ}$C. At the start of each experiment, a cell
culture in the late exponential phase is diluted in culture medium to an
optical density $OD=0.18$, measured using a Biowave CO8000 cell density meter.
Then, the suspension was further diluted $50\times$ in artificial seawater
(ASW). This process ensures that the initial cell concentration in all
experiments is the same. The mean buckling time of the cells in culture medium
was measured to be $1.6$ hours.

A custom microfluidic chamber was constructed to visualize the time evolution
of oil droplets colonized by bacteria Hickl and Juarez (2022). To create
droplets on a glass microscope slide, a thin film of $10$ µL of either
unweathered MC252 crude oil or mineral oil was formed. MC252 is a light sweet
crude oil with a density of $0.83$ g/mL, an interfacial tension of $20$ mN/m,
and a viscosity of $3.9$ mPa s at $32^{\circ}$C Daling  _et al._ (2014). Then,
$450$ µL of the dilute A. borkumensis suspension was dripped on top of the
oil. This aqueous solution initiated the formation of spherical caps pinned to
the glass slide. The droplet size range was $1$ µm $<R<200$ µm. The caps
contained $93\pm 3\%$ of the volume of a sphere with the same diameter, on
average. Then, inlets and outlets made of polyethylene tubing were attached to
both ends of the device. Lastly, the chamber was sealed using silicone rubber
sheets (McMaster-Carr) and epoxy. The chamber dimensions ($L\times W\times H$)
were $3\times 1\times 0.15\text{ cm}$.

To maintain cultures within the chamber for 72 hours, a syringe pump was used
to continuously inject a solution of diluted culture medium and ASW (1:9). In
the experiments where bacteria cells were stained, a solution of 5 mM SYTO 9
nucleic acid stain (Sigma Aldrich) was added to the solution of diluted
culture medium and ASW. These solutions were injected into the chamber at a
flow rate of $0.01$ mL/min, generating an average flow speed of $11$ µm/s and
a Reynolds number of $\textrm{Re}=\rho UD/\mu=0.03$. Here, $\rho$ is the fluid
density, $U$ is the mean flow speed, $D$ is the equivalent diameter of the
channel, and $\mu$ is the fluid viscosity. Experiments were performed at a
room temperature of $20^{\circ}$C.

Using timelapse phase contrast and epi-fluorescence microscopy, images of over
$100$ droplets were taken every 10 minutes in each experiment. Image capture
of each droplet was performed at 40X magnification using a Nikon Ti Eclipse
equipped with an automated motor-controlled stage and an Andor Zyla 4.2 sCMOS
camera.

##  III Results

###  III.1 Oil droplet evolution

Prolonged growth of bacteria on oil droplets leads to extreme deformations of
the interface. The mechanism driving this process is the competition between
the effects of cell growth and the surface tension of the oil-water interface.
Images of the time evolution of two droplets of radii $R_{0}=16$ µm and
$R_{0}=51$ µm are shown in Fig. 1A and 1B, respectively (see also
Supplementary videos 1 and 2). Buckling of the interface occurs shortly after
bacteria fully cover the droplet surface, shown in Fig. 1A, $t=15$ h and Fig.
1B, $t=17$ h. Then, tube-like structures emerge from the interface, extending
outward from the droplet surface. For droplets with initial radius $R\lesssim
15$ µm, individual tubes remain distinct, as shown in Fig. 1A, $t=30$ h. By
contrast, for droplets with $R\gtrsim 15$ µm, tubes become densely packed,
forming a continuous bio-aggregate around a droplet, shown in Fig. 1B, $t=36$
h . These deformations are qualitatively the same for both crude oil and
mineral oil.

To visualize the rich dynamics of the system, including the expansion of the
bio-aggregate, vertical slices were taken through the center of each image in
a timelapse of a droplet’s evolution. These slices were then arranged next to
one another to form a spacetime plot showing bio-aggregate expansion over
time. For example, the spacetime plot of the expansion of the bio-aggregate
around a droplet with $R_{0}=51$ µm is shown in in Fig. 1C. Over 1–2 days
after tubes and bio-aggregates stop growing, oil within the tubes breaks up
and coalesces into spherical droplets, shown in Fig. 1A, $t=65$ h.

###  III.2 Bio-aggregate composition

To determine the composition of the bio-aggregate, fluorescence microscopy was
used to visualize the distribution of crude oil after droplets were deformed,
since the crude oil used is autofluorescent in the visible spectrum. In other
experiments, cells were dyed with SYTO 9 nucleic acid stain to visualize the
distribution of bacteria around deformed droplets. To visualize only the
bacteria, non-fluorescent mineral oil was used in experiments with SYTO 9.
Phase contrast microscopy was also used to observe all parts of the system
simultaneously regardless of the type of oil. Thus, the distribution of both
oil and bacteria around deformed droplets was determined.

The tubes protruding from the oil-water interface contain both oil and
bacteria. An example of a deformed crude oil droplet of $R_{0}=15$ µm after 50
hours is shown in Fig. 2A. The orange (false color) corresponds to crude oil
when visualized using fluorescence microscopy. Oil is present throughout the
tube of length 60 µm, which extends from the droplet surface in Fig. 2B1. When
visualized using phase contrast, the oil (black) can be seen in sharp contrast
against the surrounding bacteria (grey) and device background (white), as in
Fig. 2B2. A mineral oil droplet of initial radius $R_{0}=18$ µm after 48 hours
is shown in Fig. 2C. Bacteria can be seen in green (false color) around both
the original spherical droplet and a tube of length $74$ µm protruding from
the surface in Fig. 2D1. As before, phase contrast images show the dark crude
oil present within the tube shown in Fig. 2D2. Together, these images show
that the tubular structures in our experiments are tubes of oil surrounded and
stabilized by a shell of bacteria.

###  III.3 Tube extension

Having determined the composition of the tubes, the dynamics of their
extension from the droplet surface over time are now described. The contour
length $l(t)$ of a tube is represented by the blue line in Fig. 2D, where
$l(t)=74$ µm. The contour length was measured in successive frames of the
timelapse for tubes that remained in focus throughout the experiment. The
extension of ten representative tubes from different droplets over 4-7 hours
is shown in Fig. 3A, inset. Here $t=0$ corresponds to the time when each tube
begins to extend from the droplet surface. For the first few hours, $l(t)$
appears to increase exponentially with time. Final tube lengths are in the
range $10$ µm $\leq l\leq 75$ µm with a mean of $l=33\pm 1$ µm based on 125
different tubes.

###  III.4 Bio-aggregate expansion

Next, the expansion over time of bio-aggregates, which consist of many densely
packed tubes of oil and bacteria, is described. The bio-aggregate expansion
from a point on a droplet with $R_{0}=18$ µm at $t=0$, $11$, and $17$ h after
buckling is shown in Fig. 3B. A spacetime plot was created by taking a
vertical slice of each frame in the timelapse and arranging them next to one
another, as in the bottom half of Fig. 3B. This plot shows the expansion of
the bio-aggregate. The colored arrows show the edge of the bio-aggregate,
which was used to measure the radial extent of the aggregate from the droplet
surface in each frame of the timelapse. As with individual tube length, the
initial aggregate expansion over time is exponential. An exponential curve
fitted to the data is shown Fig. 3B, red line. Here the doubling time of the
aggregate is $3.78$ hours.

The expansion rate is, on average, independent of initial droplet radius. The
expansion rate was measured at 5–10 different points along the perimeter of 42
different droplets with $10\text{ \textmu m}\leq R_{0}\leq 100$ µm, giving a
total of 323 measurements of the expansion rate, shown in Fig. 3C, grey
points. Averaging the measurements from each droplet gives the mean expansion
rate for that droplet, shown in Fig. 3C, blue points. Mean expansion rates
range from 1.3 h to 7.5 h (including outliers), with 88% of measurements
ranging from 2 h and 5 h. For all droplets, the mean is $3.2\pm 1.1$ h, as
shown in Fig. 3C, blue dashed line. The expansion rate does not depend on the
initial droplet size ($p>0.05$).

The emergence of a bio-aggregate caused by interfacial growth of bacteria
significantly increases the effective size of oil droplets. A side-by-side
comparison of a droplet of crude oil with $R_{0}=51$ µm before ($t=0$) and
after ($t=43$ h) it is colonized and deformed by bacteria is shown in Fig. 4A.
The bio-aggregate size $\Delta R$ is defined as the distance between initial
surface of the droplet at $t=0$ and the edge of the aggregate at the end of
the experiment. This distance is measured radially at many points along the
droplet’s perimeter. The mean aggregate size for this droplet is $\Delta R=30$
µm, or $60\%$ of the initial droplet radius, as shown in Fig. 4A, red line. In
fact, $\Delta R$ is approximately equal to the mean final tube length of
$l=33$ µm, shown in 3A, inset.

The relative increase in droplet size due to aggregate expansion is larger for
small droplets. The quantity $\Delta R/R$ for 131 droplets is shown in Fig.
4B. Error bars represent the variation in bio-aggregate size along the
droplets’ perimeters. The change in size varies from $8\%$ to $156\%$, with a
mean value of $46\%$. The value of $\Delta R$ itself ranges from $3$ µm to
$49$ µm. Power law fitting (red line) shows that $\Delta R/R\propto
R^{-1.20\pm 0.23}$, suggesting that $\Delta R$ is, on average, independent of
the initial droplet radius $R$, and that tube length is independent of droplet
size. Consequently, the relative increase in total size tends to be greater
for smaller droplets.

###  III.5 Secondary droplet formation

Finally, the changes in oil morphology within tubes are examined, which occur
over 1–2 days after tubes and bio-aggregates form. The oil within each
cylindrical tube coalesces into one or more spheres, or secondary droplets. An
extremely deformed droplet with $R_{0}=17$ µm after 21 hours is shown in Fig.
5A. Insets show the evolution of the oil (dark) within a tube of length $l=33$
µm over 36 hours. Initially the oil fills the entire length of the tube, but
then shrinks toward the base of the tube and coalesces into a spherical
droplet of radius $r=4.9$ µm at 36 hours (see Supplementary video 3). A
spacetime plot qualitatively describes the evolution of oil coalescing within
this tube, shown in Fig. 5B. Colored arrows show the edge of the oil within
the tube at different times. The oil in different tubes can break up into
between 1 and 7 smaller droplets. A spacetime plot of oil breaking up and
coalescing into 2 distinct droplets of radii $r=1.9$ µm and $r=2.1$ µm,
respectively, is shown in 5C (see also Supplementary video 4).

After the system reaches a steady state, fluorescence microscopy was used to
observe the secondary droplets embedded in the bio-aggregate, as shown in Fig.
5D. Using a z-stack with height increments of 2 µm, all secondary droplets
within the bio-aggregate were identified and their sizes measured. A histogram
of the radii of secondary droplets ($N=753$) is shown in Fig. 5E. These data
were taken from tubes and bio-aggregates surrounding many different droplets
with $10\text{ \textmu m}\leq R_{0}\leq 100\text{ \textmu m}$. Secondary
droplet radii are in the range $0.25\text{ \textmu m}\leq r\leq 6\text{
\textmu m}$ with a mean of $\bar{r}=1.48\pm 0.03\ $µm — more than an order of
magnitude smaller than the original droplet sizes. The secondary droplets’
size appears to follow a lognormal distribution:

$f(r)\propto\frac{e^{-(\ln{(r)}-\mu)^{2}/(2\sigma^{2})}}{\sigma r\sqrt{2\pi}}$
(1)

with parameters $\mu=0.21\pm 0.02$ and $\sigma=0.53\pm 0.01$, shown in Fig.
5E, black line.

###  III.6 Model of tube extension

Since tube and bio-aggregate expansion are exponential, and bacteria appear to
cover the oil-water interface throughout the experiment, we suggest that the
emergence of these complex structures is driven solely by the growth and
division of cells confined to the interface. Here we present a mechanistic
model of tube formation to quantify the relationship between cell growth and
tubulation.

We assume that tubes begin to extend from a droplet when bacteria have formed
a complete monolayer of cells at the interface. To continue to grow at the
interface, cells must deform the oil droplet to increase the surface area.
Assuming that the density of cells at the interface remains constant, and that
cells remain as a monolayer, the interfacial area must increase proportionally
to the number of cells:

$A(t)=4\pi R_{0}^{2}\ e^{\ln(2)t/T_{d}}\text{,}$ (2)

where $T_{d}$ is the cell doubling time, and $R_{0}$ is the initial radius of
the droplet. At $t=0$, tubes of oil begin to emerge from the interface. We
assume that the total volume of oil remains constant (i.e., the oil is
incompressible and loss of volume from degradation is negligible):

$V(t)=V(0)=\frac{4}{3}\pi R_{0}^{3}$ (3)

Over time, the total surface area and volume of the oil-water interface is
given by

$A(t)=4\pi R(t)^{2}+2\pi r\ l(t)N$ (4) $V(t)=\frac{4}{3}\pi R(t)^{3}+N\pi
r^{2}\ l(t)\text{,}$ (5)

where $N$ is the number of tubes, $r$ is the tube radius, and $R(t)$ and
$l(t)$ are the time-varying droplet radius and tube contour length,
respectively. Combining Eqns. (3), (4) and (5) gives

$A(t)=4\pi
R_{0}^{2}\left[1-\frac{3N}{4}\frac{l(t)r^{2}}{R_{0}^{3}}\right]^{2/3}+2\pi
rl(t)N\text{.}$ (6)

For values of the parameters pertaining to this system, the second term in
brackets is much less than unity. That is, up to a constant, the volume of oil
in the tubes is much less than the total volume, which is in qualitative
agreement with observations. So, to first order in $l(t)r^{2}/R_{0}^{3}$, we
find that:

$A(t)\approx 4\pi R_{0}^{2}+2\pi Nr\left(1-\frac{r}{R_{0}}\right)l(t)\text{.}$
(7)

Finally, we substitute Eqn. (2) and $N=4\pi R_{0}/d^{2}$, where $d$ is the
mean separation of tubes at the interface, to find:

$l(t)=\frac{d^{2}}{2\pi
r\left(1+\frac{r}{R_{0}}\right)}\left(e^{\frac{\ln(2)t}{T_{d}}}-1\right)\text{.}$
(8)

Thus, the model predicts that, because of the exponential growth of bacteria
at the interface, the tube length plus a constant increases exponentially with
time:

$l(t)+A=Ae^{\frac{\ln(2)t}{T_{d}}}\text{,}$ (9)

where

$A=\frac{d^{2}}{2\pi r\left(1+\frac{r}{R_{0}}\right)}.$ (10)

To test the predictions of Eqn. (7), $l(t)+A$ is plotted on a semilog scale,
shown in Fig. 3A. The following experimental values were used to compute $A$:
$d=5.9$ µm, $r=1$ µm, and $5\leq R_{0}\leq 100$ µm. The quantity $l(t)+A$
increases exponentially with time, as predicted by the model, with a mean
doubling time of $3.1$ h and a standard deviation of $0.35$ h, shown in Fig.
3A. Fitting is performed only for the time range when tubes are increasing in
length. The hypothesis that tube extension is driven by cell division is
further supported by the fact that no dependence was found between the tubes’
extension rate and initial droplet size.

##  IV Discussion

The deformations of the oil-water interface are the result of the complex
interactions between surface tension and the growth of surface-attached
bacteria. Without bacteria, interfacial deformations are energetically
unfavorable, and droplets remain spherical. The attachment and growth of
bacteria leads to multiple effects that promote deformations.

First, attachment of bacteria to the interface reduces the energy of the
system by reducing the oil-water surface area. This effect exists for any
colloidal particle attached to a liquid-liquid interface. Bacterial attachment
being energetically favorable is consistent with our observation of no
detachment of cells from the interface before droplets buckle of the
experiments. The energy cost of increasing the area of the oil droplet can be
mitigated significantly if the surface is covered by bacteria. The magnitude
of the reduction in energy depends on the wettability of the cells, which
could not be determined in our experiments. Other oil-degrading bacteria, such
as Pseudomonas putida, have been shown to reduce the oil-water surface tension
by more than half as a result of cell hydrophobicity Rühs  _et al._ (2014).

Second, the growth of surface-attached cells produces mechanical forces on the
interface that oppose surface tension. This effect is similar to what happens
when a droplet or bubble covered in colloidal particles shrinks, leading to
buckling of the interface Datta  _et al._ (2010); Poulichet and Garbin (2015);
Xu  _et al._ (2005). In these systems, a fluid-to-solid transition (jamming)
of the colloidal shell occurs because of an increase in the density of
particles on the surface. In our system, a similar increase in particle
density results from the growth of bacteria. Additionally, as a form of active
matter, growing monolayers of rod-shaped bacteria produce collective stresses
as a result of their orientational order, particularly at a bounded interface
You  _et al._ (2018, 2021). After the oil-water interface buckles, continued
growth of bacteria causes tubular structures to emerge.

Third, _A. borkumensis_ is known to produce biosurfactants at the oil-water
interface Omarova  _et al._ (2019); Yakimov  _et al._ (1998), further
facilitating interfacial deformations by reducing surface tension. Further
research is needed to construct a model that accurately describes the
bacteria’s collective behavior, including the fluid-to-solid transition that
leads to buckling and tubulation. Such a model would include the competing
effects of surface tension and active growth stresses, which can be tuned to
give rise to the droplet morphologies observed in our experiments.

###  IV.1 Tubulation and bio-aggregate expansion

In our experiments, tubulation is observed around droplets of crude or mineral
oil covered in rod-shaped bacterial cells. One key difference between the
system we describe and those in other studies is that the activity of cells at
the oil-water interface is caused solely by cell growth and division, rather
than motility.

Our experimental results on the dynamics of tube growth are consistent with
the mechanistic model described in § III D, suggesting that tube extension is
driven by an exponentially growing monolayer of cells confined to the
interface. Additionally, the average extension rate of individual tubular
structures from the interface ($3.1\pm 0.4$ h) was found to be roughly the
same as the mean expansion rate of the bio-aggregate ($3.2\pm 1.1$ h). This
result supports the hypothesis that bio-aggregate expansion is driven by tube
extension. Thus, fundamentally, the emergent phenomena observed in our
experiments are driven by by the division of densely packed, rod-shaped cells
at a deformable interface. In our previous work, the doubling time of dilute
cells on a flat oil-water interface was measured to have a mean of $1.8\pm
0.1$ h Hickl and Juarez (2022). The slower doubling times observed here
suggest that cells at the interface divide more slowly when they are densely
packed (such as during tube formation) than when they are dilute.

For many droplets, the expansion rates measured at different points on the
droplet’s surface differ by several hours (Fig. 3C). This observation is
consistent with the variation in $\Delta R$ around individual droplets (error
bars in Fig. 4B) and can be explained by differences in the direction of tube
extension. Images of tubes of oil show that tubes are highly non-linear such
as in Fig. 2. Measured values of both the aggregate expansion rate and its
size $\Delta R$ are larger where tubes extend directly radially outward,
compared to where they extend from a droplet’s surface at an angle. Thus,
variation in the experimental values of these variables is consistent with the
relatively uniform values of tube extension rate ($3.1\pm 0.35$ h) and the
cell doubling time ($1.8\pm 0.1$ h) observed.

These results show that a growing colony of rod-shaped bacteria confined to a
liquid interface can produce morphologies similar to those observed in other
active nematic systems. Tube-like protrusions like the ones described here are
often associated with topological defects in the orientational order of an
active nematic, both in general models Hoffmann  _et al._ (2022) and in
specific realizations such as deformable vesicles Kumar  _et al._ (2019) or
regenerating epithelial tissues Mar (2020). To our knowledge, we are the first
to show that tubulation can occur as a result of growing bacterial colonies.
Notably, the tubes described here can remain stable for many hours after they
form, unlike tubes around deformable vesicles which tend to disappear and
retract quickly Keber  _et al._ (2014); Metselaar  _et al._ (2019) because of
surface tension. Additionally, tube-like protrusions are commonly associated
with $+1$ topological defects, whereas the defects in 2D bacterial colonies
typically have charges of $\pm 1/2$. More work is required to determine how
the orientational order of the cells is related to the deformations we
observe. By rigorously quantifying both the shape and dynamics of these
deformations, we hope to pave the way towards more precise quantitative
comparisons between models and experiments of active nematic systems.

###  IV.2 Implications for oil spill research

The deformations observed in these experiments could affect the fate of marine
spilled oil by increasing the bio-availability of oil to bacteria and
influencing the transport of oil droplets. The droplet radii studied here ($5$
µm $\leq R_{0}\leq 100$ µm) fall in the range observed in deep-sea plumes of
oil following the Deepwater Horizon spill in 2010 (approximately $3$ µm $\leq
R_{0}\leq 160$ µm) Li (2015). Such plumes of oil have been studied in situ
Camilli  _et al._ (2010) and in computational models of oil transport North
_et al._ (2015); Paris  _et al._ (2012); Lindo-Atichati  _et al._ (2016), with
mean droplet radii typically given on the order of 10 µm. However, to our
knowledge, models of oil transport have not considered the interfacial
deformations or the expansion of a bio-aggregate that can result from the
colonization of the interface by bacteria. Models that attempt to account for
oil biodegradation simply treat droplets as shrinking spheres North  _et al._
(2015).

Our experiments show that the growth of bacteria on the droplet surface
greatly increases the area of the oil-water interface, thereby increasing the
bioavailability of oil to bacteria. Based on the average dimensions and
density of tubes measured in experiments, the total area of the interface
increases by a factor of 6, on average. Additionally, the formation of a bio-
aggregate can increase the effective droplet size by as much as a factor of 2.
Such expansion would significantly impact the droplet’s buoyancy and increase
the drag force on it White  _et al._ (2020). Thus, the effects of bacterial
growth must be taken into account to accurately assess the fate of spilled oil
White  _et al._ (2019). The formation of a dense bio-aggregate was observed
only for droplets with $R_{0}\gtrsim 15$ µm, demonstrating that droplet size
is crucial in determining how the oil is colonized and deformed. Further
research is currently being done to assess these effects precisely, both
through models of oil transport and laboratory experiments of rising droplets.

Oil can be further dispersed within tubes as it breaks up and coalesces into
smaller droplets of average radius $r=1.48$ µm — more than an order of
magnitude smaller than the mean initial droplet radius $R_{0}$. Mechanically,
the breakup of tubes is likely the result of a Plateau-Rayleigh or pearling
instability Bar-Ziv  _et al._ (1999); Nelson  _et al._ (1995); Alstrøm  _et
al._ (1999), which causes periodic perturbations in the tube radius to grow
over time. In general, surface tension drives droplets to become spherical to
minimize the size of the interface, while interfacial cell growth and
biosurfactant production drive deformations such as tube formations. After
tube extension ends, the oil in the tubes slowly breaks up to form spherical
drops embedded in the bioaggregate. This observation suggests that, over time,
biosurfactant production by A. borkumensis is reduced, and that existing
biosurfactant molecules do not remain at the interface indefinitely. Thus,
surface tension once again becomes the dominant effect, causing a reduction in
the surface area of the oil-water interface. The biological reason for the
cessation of biosurfactant production is not know, but could be related to
nutrient depletion in the bioaggregate. This phenomenon needs further
investigation as it could have important implications for the degradation of
these secondary droplets.

##  V Conclusions

We conducted experiments to describe the deformations of oil-in-water droplets
caused by the active growth of bacteria. As active stresses overcome surface
tension, tubes of oil stabilized by bacteria extend exponentially from the
interface in order for surface-bound cells to continue dividing. These tubes
form a dense bio-aggregate around the droplets, enlarging the droplets
significantly. The emergence of tubes and bio-aggregates is highly non-linear,
but can be modeled accurately with simple statistical arguments and minimal
assumptions. Finally, oil in tubes undergoes breakup into smaller spherical
droplets as a result of an instability driven by surface tension. This
dispersion of oil significantly increases the surface area of the oil and its
bio-availability to the bacteria.

This system is a novel example of active matter physics in a biological
system, displaying emergent phenomena that arise from the collective behaviors
of a large number of cells far from thermodynamic equilibrium. Our analysis
demonstrates how direct visualization combined with models of the system’s
basic properties can shed light on the underlying physics of complex systems.
This research also improves our understanding of the biophysical mechanisms
underlying bacterial biodegradation of spilled oil. To our knowledge, the
precise deformations of oil droplets due to growth of oil-degrading bacteria
had not been described precisely to date. These phenomena are believed to
affect both oil degradation rates and transport of droplets through the ocean.
Thus, this work can be a stepping stone towards significant improvements in
our understanding of the fate of spilled oil in the open ocean.

##  VI Conflicts of Interest

There are no conflicts of interest to declare.

##  VII Acknowledgments

This material is based on work supported by the Oil Spill Recovery Institute
under Contract No. 20-10-06. We thank Seppe Kuehn and Karna Gowda for useful
conversations on cell culturing techniques and Mark Levenstein for useful
conversations on data analysis and presentation.

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Figure 1:  (A) The evolution of an oil droplet ($R_{0}=16$ µm) as it is
deformed by the confined growth of bacteria. Colonization occurs ($t\leq 10$
h) as bacteria grow and divide at the droplet surface. Buckling occurs
($t\approx 15$ h) after the droplet surface is completely saturated by
bacteria. Tubulation occurs ($15\leq t\leq 35$ h) as the oil-water interface
continues to deform because of the growth of bacteria. Secondary droplet
formation and dispersion of oil occurs at later times ($35\leq t\leq 72$ h).
See supplementary material for example timelapse videos. (B) The evolution of
a larger droplet ($R_{0}=51$ µm) is qualitatively similar. However, tubes form
a dense bio-aggregate around the droplet. (C) The evolution of the droplet in
(B) plotted as a spacetime plot, showing the expansion ($18\leq t\leq 36$ h)
of the bio-aggregate from the interface.

Figure 2: Bio-aggregate structure and oil dispersion. (A) Epifluorescence
microscopy shows crude oil (orange false color) at the center of a deformed
droplet ($R_{0}=15$ µm), and contained within the tube structures surrounding
the droplet. Magnified views of a tube containing crude oil with (B1)
epifluorescence and (B2) phase contrast microscopy, show oil within the tube
and the surrounding bio-aggregate, respectively. (C) A mineral oil droplet
($R_{0}=18$ µm) colonized by bacteria stained with SYTO 9 appears bright at
the center and along the tube structures (green false color) surrounding the
droplet. Magnified views of a tube structure with (D1) epifluorescence (D2)
phase contrast microscopy show fluorescent bacteria along the tube and the
mineral oil droplets contained within the same tube, respectively. The contour
length of the tube $l(t)=74$ µm is shown in blue in panels D1 and D2. All
scale bars are $20$ µm.

Figure 3: (A) Inset: Tube length for 10 representative tubes extending over
time from different droplets. Main panel: fitting of experimental data
according to mechanistic model of tube extension. The quantity $l(t)+A$ is
plotted over time on a semilog scale. Solid red line shows mean exponential
fit: $l(t)+A\propto e^{\ln{(2)}t/3.1\text{h}}$. (B) Measurements of bio-
aggregate size at three different times (top), and corresponding spacetime
plot (bottom) showing aggregate expansion from the surface of a crude oil
droplet with $R_{0}=18$ µm. Expansion rates are measured by fitting an
exponential curve (red line) to the boundary of the aggregate during the
initial outward increase in size. Scale bar is 10 µm. (C) The aggregate
expansion rates for a representative sample of crude oil droplets of varying
initial radius. Gray points represent individual expansion rate measurements
(as shown in panel (B)) at different positions along a droplet’s surface. Blue
points represent the average expansion rate ($N=41$) for $5-10$ positions
around a single droplet. The dashed line shows the mean expansion rate for all
droplets. The shaded area shows the mean $\pm 1.5$ standard deviations as a
function of droplet radius. Above $R_{0}=70$ µm, insufficient data were
obtained to calculate these statistics. The expansion rate does not depend on
the initial droplet size ($p>0.05$). Figure 4:  Bio-aggregate formation and
increase in droplet size caused by tubulation. (A) Comparison of a crude oil
droplet before ($t=0$ h) and after ($t=43$ h) it has been colonized and
deformed by bacteria. Here, $R_{0}=51$ µm and the emergent tubes have
increased the final bio-aggregate radius by an amount $\Delta R=30$ µm. (B)
The final bio-aggregate radius with respect to the initial droplet radius for
$131$ droplets. Each point represents the average value of $\Delta R$ for a
single droplet, and the error bar shows the variation along the droplet
perimeter. The best power law fit to the data (red line) corresponds to a
slope of $-1.2$ and the shaded area indicates the 95% confidence interval for
the fit.

Figure 5:  Secondary droplet formation in the bio-aggregate. (A) Droplet with
initial radius $R_{0}=17$ µm after tube formation. Four snapshots ($\Delta
t=0$, 12, 24, and 36 h) of secondary droplet formation inside a single tube
are shown. Colored arrows show the furthest extent of the oil within the tube
in each frame. (B) Movement of oil within the tube above, plotted as a
kymograph, as it coalesces into a single spherical droplet of $R=4.9$ µm. The
data points from the inset of panel A are indicated by the corresponding
arrows. (C) Kymograph showing the movement of the oil in a different tube.
Here, the oil breaks up and coalesces into two secondary droplets of radii
$r=1.9$ µm and $r=2.1$ µm, respectively. (D) Secondary droplets embedded in a
bio-aggregate surrounding the primary droplet visualized using fluorescent
microscopy. (E) Size distribution of secondary droplet radii measured for
$753$ secondary droplets at the end of the 72 hours of droplet evolution. The
lognormal fit to the data with $\mu=0.21$ and $\sigma=0.53$ is shown (black
line). The dashed black line shows the mean secondary droplet radius $r=1.48$
µm.