Molecular Tweeting: Unveiling the Social Network Behind
Heterogeneous Bacteria Populations
Guopeng Wei, Connor Walsh, Irina Cazan, Radu Marculescu
{danielwei,connorw,icazan,radum}@cmu.edu
Department of Electrical and Computer Engineering
Carnegie Mellon University
Pittsburgh, PA 15213
ABSTRACT
It is well established that bacteria engage in social behavior
and form networked communities via molecular signaling.
However, most studies published to date focus on the intracellular molecular networks rather than the intercellular
networks formed across strains and species. Therefore, in
this paper, we define for the first time a bacteria intercellular network and describe its dynamics and contribution
to biofilm formation. We apply our methods to a heterogeneous bacteria population consisting of strains that are often
identified from clinical isolates, namely, the wild-type (cooperator), and its signal-blind and signal-negative (cheater)
mutants. We analyze the network dynamics and biofilm
metrics, showing that our method can effectively reveal the
underlying intercellular communication process and community organization within the biofilm. We claim that the application of social and network sciences to understanding
bacteria population dynamics can aid in developing better
drugs to control the many pathogenic bacteria that use social interactions to cause infections.
Categories and Subject Descriptors
J.3 [Life and Medical Sciences]: Biology and genetics;
J.4 [Social and Behavioral Sciences]: Sociology; B.4.3
[Interconnections (Subsystems)]: Topology
General Terms
Theory
Keywords
Biofilm, Dynamic network evolution, Quorum sensing
1.
INTRODUCTION
Despite their size, bacteria hold an overwhelmingly significant influence over earth’s biota [41], playing both beneficial
Permission to make digital or hard copies of all or part of this work for personal or
classroom use is granted without fee provided that copies are not made or distributed
for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than
ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission
and/or a fee. Request permissions from permissions@acm.org.
BCB’15, September 9–12, 2015, Atlanta, GA, USA.
Copyright 2015 ACM 978-1-4503-3853-0/15/09 ...$15.00.
http://dx.doi.org/10.1145/2808719.2808757.
[6] and pernicious [12, 7] roles in human health. Until relatively recently, the prevailing notion of bacterial behavior
was one in which individual cells coexisted within a population but acted independently with respect to their neighbors. However, over the past two decades, it has become
widely acknowledged that bacteria, in fact, communicate
and organize to perform a broad range of collective behaviors through a form of molecular signaling called quorum
sensing (QS) [40, 21]. Consequently, a substantial share of
research has been devoted to elucidating the mode, mechanisms, and effects of intercellular organization [36]. Empirical evidence suggests that the intracellular production and
secretion of signaling molecules, known as autoinducers, are
controlled by a positive feedback genetic pathway dependent on the ambient environmental concentration of autoinducer surrounding a cell [38, 27]. This genetic machinery
facilitates the increase of intracellular concentration of autoinducer within local cells until a molecular consensus, or
quorum, is met. Thus the QS system equips individual bacteria with the ability to detect and measure local cell density
by proxy, enabling group level coordination for carrying out
population sensitive collective behaviors including, but not
limited to, the production of a variety of virulence factors,
digestive enzymes, and extracellular polymeric substances
(EPS) used in biofilm formation [31, 35, 37]. Moreover, these
population level behaviors are vital to the fitness, community coherence, and drug resistance of a bacterial species at
newly colonized infection sites, highlighting the critical role
QS plays in pathogenesis.
Although the intracellular biochemical pathways which
give rise to QS have been well studied from both molecular
and systems biological perspectives [32, 30, 9, 10], a higher
level description of intercellular communication—one capable of capturing population level patterns—has yet to be explored. To this end, we adopt a network centric description
of intercellular signaling in which we draw from canonical
network models as a basis of abstraction for communication
among agents [29]. Figure 1 depicts several phases throughout the development of a bacterial network as described by
our methods.
Biofilms rarely exist as pure, homogenous colonies, rather,
hundreds or even thousands of distinct bacterial species tend
to coexist in cooperation or conflict with one another at a
single site. Within microbiomes, distinct types of bacteria
can establish molecular communication networks, compete
for resources, and collaborate towards common goals in similar ways as in macroscale societies. The interactions among
different types of bacteria within the community—each hav-
Nutrition
Bulk layer
Boundary
layer
Signal molecules
Biofilm and virulence
Bacteria
Biomass
layer
Figure 1:
Four phases of network formation in chronological order. (a) Planktonic state bacteria which swim freely
in the environment. (b) Bacteria attach to surfaces and lose
motility. (c) Bacteria communicate with each other through
Figure 2:
production, transmission, and sensing of signal molecules and
lular DNA, polymers, various obstacles, and cell waste,
biomass layer has a diffusivity value about half of that of
boundary layer. Bacterial cells attach to the surface at
bottom and grow upwards with nutrition diffusing from
bulk layer towards the biomass layer.
form networked communities. The blue lines indicate the
molecular communication links. (d) Connected bacteria produce various virulence as well as extracellular polymeric substance to form a biofilm.
ing distinct behavioral properties—have a critical influence
on the subsequent population dynamics of a developing community, as well as biofilm formation. For example, three
types of pathogenic bacterial strains often found in clinical studies [22, 18, 4]—wild-type (WT) cooperators, signalblind (SB), and signal-negative (SN) mutant cheaters—belong
to the same species but differ in their QS behavior, leading
to dramatically different population evolution outcomes.
The communication network dynamics among the three
strains can be easily understood using a terminology adopted
from social networks. The WT cooperators compose molecular tweets such as “generate public goods like EPS or virulence”, and broadcast them to others through molecular
diffusion. Upon receiving these messages, nearby WT cooperators retweet the message immediately, while starting
to produce goods following the instructions in the message.
However, the SB cheater strain tweets cooperative messages
but ignores the messages it receives, saving resources for its
own growth rather than producing public goods. The SN
cheater strain, on the other hand, does not tweet or retweet
messages; instead, they keep the message secret and produce
the goods silently. In these cases, it is clear that variations in
communication behavior can allow certain types of bacteria
to exploit the behaviors of others. More precisely, bacterial cheaters do not cooperate to produce public goods, but
gain the benefit from those who do, would gain a growth
advantage and be able to take over the population—an instantiation of the “tragedy of the commons” [15]. However,
if this were the case, what would be the evolutionary drive
for cooperative behaviors [14, 13]?
In this work we investigate the population dynamics of
simple heterogeneous biofilms consisting of WT, SB, and SN
strains. We show that molecular social network dynamics
track closely to biofilm dynamics, and that the production
of important exoproducts such as EPS and virulence factors can be largely predicted from these network dynamics.
Furthermore, we offer an explanation of how the tragedy of
the commons is avoided in the experimental cases via the
conversion of public goods to private goods. We argue that
The environment is modeled as three layers, i.e.,
bulk, boundary, and biomass. The chemical concentrations
in the bulk layer do not change over time. The biomass layer
is where bacteria are located; due to secretion of extracelthe
the
the
the
abstracting the complex interactions of cellular communication into a representation readily treated with methods from
network science will not only further our understanding of
complex microbial societies, but also aid the discovery of
effective alternative therapeutics in the fight against multidrug resistance [5, 33, 16, 3].
In the following subsections, we first describe the LuxI/R
QS system used by most gram-negative bacteria, including how signal molecules are generated, how they bind to
receptors, and how the binding product-receptor complexregulates the public goods production. Then, we derive a
single substrate growth model used in our biofilm simulation environment with a constant nutrition concentration at
the top bulk layer (Figure 2). Last but not least, we define a
QS-based bacteria network by identifying the signal spreaders, receivers, and responders in bacterial communities.
2.
BIOFILM MODEL
As computers become more and more powerful, a “bottomup” agent-based approach to study the evolution of pathogen
populations is the next milestone towards understanding
their social behaviors and for treating the infectious diseases
they cause [24], especially for chronic infections. Therefore,
we adopt a “bottom-up” approach and develop a mixed celland ordinary differential equation based model for the cellto-cell/cell-EPS physical interactions and molecular dynamics of a QS system, respectively. In the cell-based model,
bacteria are considered as spheres, and physical interaction
among various agents is explicitly modeled.
2.1
2.1.1
Cellular Dynamics Model
Quorum Sensing
Using the LuxI/R system as a basis for the QS model
is relevant for describing species such as the opportunistic
pathogen Pseudomonas aeruginosa [32, 8]. The LuxI/R
system is mediated by autoinducer signal molecules, such
as acylated homoserine lactone (AHL), produced by the
synthase luxI homologs. The signal molecule AHL binds
bial growth as substrate-controlled [28]. The kinetics relate
the specific growth rate (µ) of a bacterium cell mass (X) to
the substrate concentration (S):
luxI
luxR
µ = µmax ·
EPS
virulence
Figure 3:
Gram-negative bacteria, such as P. aeruginosa, use
largely homologous QS networks, where the AHL molecules
are detected and regulated via genetic circuits. Specifically,
to LuxR receptors and activates the transcription regulator
(LuxR homologs). This LuxR − AHL complex leads to the
transcription of a plurality of genes that are directly involved
in bacterial metabolism and collective behavior.
The molecular network of the LuxI/R QS system has two
positive feedback loops. More precisely, as shown in Figure
3, the LuxR − AHL complex upregulates the expression
of both luxR and luxI genes, which generate more AHL
molecules and LuxR receptors. Based on the ODE-models
proposed in [25, 42], we have the following equations to describe the time-varying dynamics of the luxIR QS system:
d[A]
dt
d[R]
dt
= cA +
kA [C]
KA +[C]
= cR +
kR [C]
KR +[C]
d[RA]
dt
− k0 [A] − k1 [R][A] + k2 [RA]
(1)
− k3 [R] − k1 [R][A] + k2 [RA]
(2)
= k1 [R][A] − k2 [RA] − 2k4 [RA]2 + 2k5 [C]
(3)
= k4 [RA] − k5 [C]
(4)
d[C]
dt
2
where [X] denotes the concentration of a particular molecular species X, t represents time. In our formulation, A is
AHL, R is LuxR homologs, RA is the LuxR − AHL complex, C is the dimerized complex. cA and cR account for
the basal level transcription of A and R, respectively. The
values and references of these parameters (see Table 1) are
adapted from a general LuxIR system [25] and reflect those
used to characterize P. aeruginosa.
To give some intuition, the first term of Eq.(1) describes
the basal level transcription, the second term captures the
positive feedback loop regulated by the dimerized complex
C, the third and forth terms describe the AHL concentration changes caused by the binding and unbinding reactions
of AHL and LuxR receptor, respectively. Eq.(2) and Eq.(4)
describe the binding reaction of AHL and LuxR receptor,
as well as dimerization process of the binding product [RA].
Therefore, to model the SB mutant strain, based on the
WT cooperator model parameters in Table 1, we set cR = 0
and kR = 0 to make sure LuxR molecules are never produced. Similarly, we set cA = 0 and kA = 0 to make sure
SN mutants do not generate any molecular message.
2.1.2
Cell Growth Model
For simplicity, we consider a single nutrient controlled kinetics; Monod introduced this concept to describe the micro-
(5)
The kinetic parameters, maximum specific growth rate
(µmax ) and substrate affinity (Ks ), are assumed to be constant, but dependent on strain, medium, and growth conditions, such as temperature and pH. When cells are metabolically active, but not growing or dividing, they may still take
up substrate. This effect is not considered in the original
model in Eq.(5) [28]. To address this, a maintenance rate
(m) is generally used to describe the reduction, hence Eq.(5)
is modified to:
LuxI is an AHL synthase, LuxR is a receptor which can bind
the AHL molecules, and the LuxR − AHL complex regulates
the transcription of the downstream operon, including EPS
and various virulence factors shown in red.
S
S+Ks
µ = µmax ·
S
S+Ks
−m
(6)
To balance the limiting substrate S, we introduce a utility parameter UX to model the consumption of substrate
nutrition due to cell growth:
d[S]
dt
= −UX · µ · X = −UX d[X]
dt
(7)
Therefore, higher cell densities can lead to a decreased growth
rate µ in a nutrition-limited environment.
Also, we need to take into account the cost of generating
QS-related molecules; therefore, we modify the consumption
equation to be:
d[S]
dt
= −UX d[X]
− UAHL d[A]
− ULuxR d[R]
dt
dt
dt
(8)
where utility parameters UAHL and ULuxR model the consumption of substrate nutrition due to the production of
AHL and LuxR receptors, respectively.
2.1.3
EPS Production
We model the production of EPS as a function of the intracellular dimerized LuxR − AHL complex C while incurring
a cost on the carbon substrate (S) in Eq.(7):
d[EP S]
dt
d[S]
dt
[C]
= kEP S [C]+K
C
= −UX d[X]
− UAHL d[A]
dt
dt
d[EP S]
−ULuxR d[R]
−
U
EP
S
dt
dt
(9)
(10)
where kEP S is the maximum EPS production rate and UEP S
is the utility of EPS production. Using this model, we expect a maximum rate of EPS production once cells reach a
quorum through communication (i.e. the level of AHL in
the extracellular environment exceeds a given threshold).
2.2
Intercellular Network Model
The QS-based bacteria network is significantly different
from traditional networks in several aspects:
• The signal molecules do not have specific destinations
encoded in the information (e.g. the address in the
IP packet); they simply diffuse in the environment.
Therefore, information cannot be precisely “routed” to
target recipients in a network.
• The diffusion of molecules is spatially limited and is
significantly slower than the kinetic dynamics of bacteria. In other words, each bacterium has a limited
influence range in space; for efficient communication,
bacteria need to stay close to each other.
• Bacterial networks based on QS use signaling molecule
concentrations to represent information that is generated collectively by a large number of bacteria; each
bacterium contributes minimally to the overall extracellular AHL concentration.
Based on the above observations, we propose a QS-based
network definition that considers both intracellular and extracellular factors. More specifically, a directed link from
bacterium A to bacterium B is established under three conditions (Figure 4):
• Bacteria A and B must be within a diffusion-limited
signal influence range TD .
• The autoinducer signal concentration inside bacterium
A is larger than that of the bacterium B. Therefore,
there is a descending AHL gradient from A to B.
• The concentration of the signal receptor (e.g., LuxR)
of bacterium B is above an activation threshold TR .
Figure 4:
Bacteria network links. (a) WT bacteria can
connect to its peers and SN mutants. (b) SB mutants can
connect to WT and SN ones, but cannot receive any signals.
(c) SN mutants cannot connect to any of its peers, but can
receive signals. (d) Influence range (TD ) of a signal spreader
is limited by the molecular diffusion rates and gradients.
The first condition represents the fact that molecular diffusion is relatively slow and distance limited, thus the AHL
produced and secreted by a bacterium has direct impact only
within a range TD depending on AHL production rate, properties of the signal molecules and their diffusion medium.
The second condition specifies the link direction, while the
third ensures that bacterium B is able to receive QS signals.
To account for different AHL productivity of spreader
bacteria, we classify them into four categories based on intracellular AHL production rates PA . More precisely, the
first category includes spreaders with PA < 14 PAmax , where
PAmax = cA + kA is the maximum production rate, and cells
have an influence rage TD = 5µm. Similarly, TD = 10µm for
the second category: 14 PAmax < PA ≤ 12 PAmax ; TD = 20µm
for the third category: 12 PAmax < PA ≤ 34 PAmax . Finally,
TD = 40µm for the super spreader category: 34 PAmax < PA .
3.
RESULTS
Using an open-source simulator [39], we set up a 3D environment of size (300µm, 300µm, 500µm) in which 1000
non-overlapping (generic) bacterial agents are randomly attached to the surface at the bottom. To support the survival
and growth of bacteria cells, we assume a constant nutrition
concentration S = 100µM in the bulk layer such that the
cells can get more nutrition as they grow upwards from the
attachment surface towards the bulk layer (Figure 2).
A cell is considered to be a receiver if its intracellular
LuxR concentration is above a threshold TR = 0.2µM . A
cell divides into two daughter cells when its radius is above
Tdiv = 2µm, and dies when the value goes below Tdiv =
0.5µm. Dead cells are not removed, but exist as cell debris.
To show the social dynamics in the formation of heterogeneous biofilms, we consider four scenarios, namely, (S1)
pure WT; (S2) half WT and half SB mutant; (S3) half WT
and half SN mutant; (S4) 1/3 WT, 1/3 SB mutant, and 1/3
SN mutant. In the following subsections, we discuss these
four cases from different perspectives.
3.1
Biofilm Evolution
To give some intuition, let us first see the 24-hour biofilm
evolution dynamics for all scenarios (videos are available at
http://goo.gl/hyrMol). As it can be seen from Figure 5, we
take the snapshots of the biofilm development at time t =
0.2hrs, t = 1.5hrs, t = 10hrs, and t = 24hrs, which capture
the most significant changes of the system as a result of the
social evolution [26]. In our simulations, we use particles
to represent both cells and EPS; SB cells are represented
as red particles, SB mutants are blue, and SN mutants are
yellow. Small green particles represent EPS which provides
structural support to the biofilm. Both WT and SN bacteria
generate EPS particles while SB mutants do not. Note that
the boundary is periodic, which is why some cells appear to
be floating without support (they are actually connected to
the other side of the world.)
As shown in Figure 5, in all scenarios WT cooperators
start tweeting and retweeting the message of producing EPS
around t = 1.5hrs. In scenario S1, where the WT cooperator
is the only strain present, all bacteria participate in tweeting
and retweeting the message of producing EPS, and the EPS
generation process quickly spans the spatial domain. In the
other three scenarios, EPS generation only takes place in
locations with high density of WT cooperators.
Like macro-scale evolution, the evolution of microbes given
certain environmental conditions converges to only a few
cases. At time t = 10hrs, S1 develops a thick biofilm uniformly supported in space by EPS particles. Surprisingly, in
S2, the SB mutant cheaters do not replicate as much as the
WT cooperators. On the contrary, they suffocate at the bottom, losing the ability to compete for nutrition coming from
the top bulk layer. Similar dynamics can be observed in S4.
On the other hand, the SN strain, which does produce EPS
particles to support its growth towards upper layer, survives
the competition in both S3 and S4. However, due to the fact
that the SN strain does not tweet or retweet any chemical
message, the overall AHL concentration within the spatial
domain is lower than the S1 and S2 cases, resulting in lower
EPS and virulence production rates.
These simulation results can explain how pathogenic bacteria are able to avoid the “tragedy of the commons”. More
precisely, due to the nature of immobile EPS, it cannot provide structural support to cheaters that are too far away,
therefore, the cheaters cannot efficiently exploit these exoproducts. From this perspective, a locality principle seems
to govern when “public goods” ought to be more suitably
considered “private goods”. Therefore, it is this locality
Figure 5: Biofilm evolution in four different cases, (S1) pure WT; (S2) half WT and half SB mutant; (S3) half WT and half SN mutant; (S4)
1/3 WT, 1/3 SB mutant, and 1/3 SN mutant. In our simulations, we use particles to represent both cells and EPS; WT cells are represented
as red particles, SB mutants are blue, and SN mutants are yellow. Small green particles represent EPS which provide structural support to the
biofilm; both WT and SN bacteria generate EPS particles while SB mutants do not. Note that the boundary is periodic, which is why some
cells appear to be floating without support (they are actually connected to the other side of the world.)
Figure 6:
Bacteria network evolution for S4 case. (a) t = 0 hrs. (b) t = 12 hrs. (c) t = 24 hrs. Communities emerge in regions
with the highest WT cooperator densities, which means that AHL accumulation in the initial stage is carried out by the WT
cooperators. This is because SN mutants do not generate AHL and SB mutants do not have the AHL positive feedback loop
involving the LuxR receptor (The video is available at http://goo.gl/hyrMol).
and population structure which prevents the “tragedy of the
commons” in bacterial society. Note that EPS as the sole
public good is an extreme case; many other types of public
goods are diffusible in the extracellular space and therefore
can be exploited to a larger extent by the cheaters. However, the locality/population structure still plays a major
role here in constraining the cheaters.
3.2
Biofilm Metrics
To get a deeper understanding of the bioflim formation
process, we characterize some network metrics as well as
classic biofilm measurements. Figure 8.a shows that the
maximum biofilm thickness for the WT cooperators is about
40µm more than all other cases. This is confirmed by Figure 5 where the S1 biofilm at t = 24hrs has several large
mushroom-like structures separated by water-filled channels,
which are often observed in wet-lab experiments [34].
On the other hand, biofilm roughness-the standard deviation of the thickness distribution divided by mean thicknessshows some interesting behaviors (Figure 8.b). At the beginning, the roughness coefficients in all cases are high as a
result of the random spatial attachment of the initial 1000
cells. Then the S1 (green) and S3 (blue) mixed cases dip
down to almost a homogenous flat film due to the generation
of EPS which quickly fills the free extracellular space. As
the biofilm develops, both the S1 (green) and S4 (red) cases
end up with a high roughness for different reasons. In S1,
the emergence of mushroom- or pillar-like structure induced
the rise of roughness while the spatial imbalance caused by
the genotype heterogeneity is the roughness source in S4.
To be clinically relevant, we are focused on virulence production, as it has direct consequence on patient survival rate.
In this work, we assume virulence is positively related by QS
system as supported by experimental evidence [19], and virulence is measured indirectly through the concentration of
LuxR − AHL complex. As shown in Figure 8.c, the cases
producing the highest levels of virulence are S1 (green) and
S2 (pink). This outcome is clear in Figure 5, where the WT
becomes the dominant strain as the most virulent genotype.
However, to get a deeper understanding of the evolution
dynamics, we need to change our view to a network perspective; this is discussed in the following sections.
3.3
Zooming in the Biofilm Formation
To see more clearly the network communication process
and its relationship to biofilm formation, we study in detail
scenario S4, in which we have 1/3 WT, 1/3 SB mutant, and
1/3 SN mutant in the initial population. As can be seen
from Figure 6, individual network communities emerge in
the regions that have the highest WT cooperator density.
The small communities consisting of tens or hundreds of
cells (Figure 7) then expand to have a few thousand cells
within them. However, the spatial population structures and
genotype segregation clearly prevent them from merging into
one large network component. From this perspective, the
bacterial communication networks are distributed networks
without a clear center.
Figure 7:
A small region at t = 10hrs for S4. It is clear that
WT cooperators form densely-knit individual communities.
The purple lines represent the network links.
In Figure 7, we focus on a small region of the biofilm to get
a better sense of how bacterial networks form in our simulations. The snapshot is taken at t = 10hrs, when most of the
network links exist among the WT cooperators and some
links are formed from WT cooperators to SN mutants. Accordingly, EPS particles are produced inside and around the
network communities. As the AHL accumulation/diffusion
process continues, most of the SN cells join the communities
and generate EPS to support their growth upwards.
Figure 8:
Biofilm evolution dynamics. (a) Maximum biofilm thickness. WT cooperators form mushroom-like structures that
are much thicker than others. (b) Biofilm roughness measures the heterogeneity of a biofilm. Spatial irregularities and genotype
segregation result in a rough surface. (c) Virulence production. In this paper, virulence production is assumed to be positively
regulated by the LuxR−AHL complex, thus the amount of virulence being produced is proportional to the complex concentration.
(d)(e) Number of network communities and the diameter evolution in time. Bacteria form small to medium sized communities
consisting of a few thousand cells. (f ) The relatively high clustering coefficient shows that bacteria are tightly connected in
communities. (g) Number of links saturates after an initial exponential growth phase. (h) and (i) show the percentage of WT
(most virulent) cells and the number of networked cells over the total number of cells in the biofilm, respectively.
3.4
Network Metrics
The first metric we calculate is the number of communities
in the bacterial society. As shown in Figure 8.d, the communities emerge around t = 1.5hrs, followed by the transition period during which cells replicate very fast in a relatively nutrient rich environment, then communities form,
merge, and recombine with each other until t = 10hrs. After the transition period, the number of communities stabilizes and the difference among the four cases becomes clear.
Specifically, the S1 and S4 cases have the most independent
network communities; we find a strong correlation between
the community number and the biofilm roughness coefficient
(Figure 8.b). Indeed, more independent communities result
in a higher roughness coefficient of the biofilm.
We also note that the number of communities does not decrease as the biofilm matures, even in scenario S1 where WT
is the only strain. This implies that distributed groups do
not merge into a few strongly connected giant components
as one would have expected. In fact, due to genotype segregation, AHL diffusion constraints, and various 3D spatial
structures formed across the biofilm, bacterial cells always
stay in small to medium size communities, usually consisting
of a few thousand interacting bacteria and having a diameter of 20-40 links (Figure 8.e). Therefore, trying to find and
attack the “central control” of a bacteria population in order
to cure infections may not be a wise strategy.
As shown in Figure 8.f, the average clustering coefficient
spikes to its maximum as communities initially form locally due to proximity and initial local AHL accumulation
and decreases monotonically thereafter as community expansion ensues. However, the average clustering coefficient
of around 0.5 indicates that the cells have tight connections
with each other inside individual communities; this is also
clearly shown in Figure 7. The high clustering coefficients
Figure 9:
Early and advanced stage network degree distributions are depicted for each population combination. Early development stages (red) are best fitted by a normal distribution, showing the homogeneity in incipient structure. Fully developed
networks (blue) start showing differentiation. (a) The WT population maintains its homogeneity in degree distribution, as shown
by the normal fit. (b), (c) and (d) show that, when combining the WT with signal-deficient strains, the bacterial population
degree distribution gains a bias towards overall lower degrees, best fitted by a gamma distribution. (e) CDFs for both early
and later development stages across the population types. Although in the early phase there is not much distinction between
populations, the long-term behavior shows a clear differentiation as the initial WT frequency drops from 100% to 33%, an effect
mirrored by the percentage of networked cells and virulence production.
observed in the mixed strain cases are induced by more
structured bacteria population due to genotype segregation.
In Figure 8.g, the early “explosion” of links can be noticed
immediately following QS activation (t = 2hrs), after which
the link count increases monotonically, approaching a saturation level constrained by the limited nutrition availability.
As mentioned before, the number of links is directly correlated with information propagation efficiency in the network.
An efficient network can lead to a much higher virulence production as observed in Figure 8.c. Figure 8.h, on the other
hand, shows the strain composition in the biofilm which can
better explain the evolution in Figure 5. For example, in
the S2 case the WT cooperators clearly become the dominant species and take up to nearly 90% of the entire population at t = 24hrs; this confirms the evolution advantage
of cooperators against the SB cheaters. On the contrary,
the WT cooperators do not have a clear growth advantage
compared to the SN cheaters; this is because although SN
cheaters do not tweet or retweet any message, they do receive and follow the instructions in the messages sent by
others and generate EPS particles to help them get nutrition. Note that the cooperators have a growth advantage
at early stages (t < 10hrs) because the AHL concentration is much higher in the cooperator clusters, resulting in a
higher EPS production rate; this advantage becomes negligible as AHL continuously diffuses across the space, making
the concentration landscape more homogeneous.
Figures 8.i and g show that virulence production correlates
not only with biofilm thickness/roughness - physical prop-
erties - but also with the percentage of networked cells in a
bacteria population and the number of network links - network metrics. The highest virulence is produced in the WT
(pure) strain case, the second highest being in the WT and
SB mixed case. Similar to other correlations, our network
metrics always identify the trend in advance, showing its predictive power for key biofilm factors such as thickness and
virulence, based on the underlying communication process.
Given such observations, it is desirable for some of our in silico characterization techniques to be implemented in vitro,
analyzing clinical samples in the lab. Possible approaches
include adding fluorescence flags to the luxR receptors or
synthesizing “probe” bacteria with genes of fluorescence proteins fused to the downstream of its QS system to measure
the AHL concentration level [11, 1]; such approaches can
easily measure overall network activities in the biofilm and
help physicians understand the underlying dynamics.
3.5
Degree Distribution
The degree distributions in the four scenarios are indicative not only of the impact that mutant phenotypes have
on connectivity from a network perspective, but also of the
biological implications of reaching a quorum.
Figure 9 shows the degree distributions of the different
mutant frequency cases in the incipient network formation
stage (red) and advanced development (blue), under the
same environment conditions. Early stages of network formation are uniform across all cases due to bacteria initializing connections only with the closest neighbors, thus we
see consistent normal fits in node degree distributions. The
advanced development stage is characterized by significantly
higher cell density, thus elevated quantities of AHL in the
extracellular medium. In the wild type case (Figure 9.a),
the degree distribution maintains a normal shape throughout the network development stages, mirroring the population homogeneity. In contrast, mutants are characterized by
a deficiency in forming links, either on the incoming (SB) or
outgoing (SN) direction; this limitation explains the lower
average degree and skew towards lower degrees, which is well
fitted by a gamma distribution in all three mutant cases.
Also, we notice that although there are some high degree
nodes and the networks show small world network properties, the physical diffusion limit constrains the formation of
super hubs in the networks. This is also confirmed by the
clustering coefficient and the network diameter as shown in
Figure 8. Thus, unlike scale-free or small world networks,
diffusion-based QS networks consist of many small size communities with a few thousand cells each, a network structure
resilient against a hub-targeted attack strategy [29, 2].
It is noteworthy that the node degree distribution skew
exhibited in each of the mutant cases is reflected directly in
the amount of virulence they produce. Generally speaking,
the imbalance in the network degree distribution is caused by
inefficiencies in the information propagation process. Therefore, it is natural to come up with strategies to cut the connections in the molecular social network. Indeed, researchers
recently developed compounds that can inhibit the LuxR receptors or hydrolyze the AHL signal molecules in the extracellular space [5, 33, 16, 3]. Initial experiments have shown
that these compounds can quickly and significantly reduce
the pathogen virulence and make pathogens more susceptible to conventional antibiotics as well as the immune system
due to the lack of EPS protection [23, 20, 17]. In the future, we plan to evaluate the efficiency of these compounds
in inhibiting the QS network through our network analysis.
4.
CONCLUSION
Much of the population dynamics of heterogeneous bacterial colonies can be explained by intercellular communication. Yet, a high level description of such communication
has not previously been explored. In this paper, we have
provided four in silico scenarios in which we analyze biofilm
population dynamics using a network-centric approach. We
have shown that the network metrics correlate well with
many traditional biofilm metrics and can thus be used as
measures of population level behavior. In addition, we have
emphasized the importance of spatial locality for microbial
populations in overcoming the “tragedy of the commons.” In
future, we plan to explore the evolutionary dynamics involving diffusive public goods and the effects of QS inhibition.
With the rise of bacterial resistance to standard drugs, as
well as a plethora of unanswered questions regarding emergent properties in population evolution, we aim to inspire
researchers to adopt a network-centric perspective in future
investigations.
5.
ACKNOWLEDGMENTS
This work was supported in part by the US National Science Foundation (NSF) under Grant CPS-1135850 and in
part by Highmark under Award A016107.
APPENDIX
A.
SUPPLEMENTARY VIDEOS
The biofilm evolution videos for the four scenarios discussed in the paper can be accessed at http://goo.gl/hyrMol.
B.
PARAMETERS
The parameters used in our QS and growth model are
listed here. The QS parameters are adapted from a general
LuxIR system [25]. Other parameters used in our model,
such as nutrition concentration S and influence range TD are
variables, and are described in the main body of the paper.
Parameter
cA , cR , m
kA , kR , µmax
KA , KR
KQSI
k0 , k3 , k9
k1 , k2 , k4 , k5 , k7 , k8
KS , KEP S
UX
UAHL ,ULuxR
UEP S
Value
1e-4
2e-3
1e-9
1e-6
1e-2
1e-1
1
0.6
2e-2
10
Table 1: Model parameters
C.
REFERENCES
[1] J. B. Andersen, C. Sternberg, L. K. Poulsen, S. P.
Bjørn, M. Givskov, and S. Molin. New unstable
variants of green fluorescent protein for studies of
transient gene expression in bacteria. Applied and
environmental microbiology, 64(6):2240–2246, 1998.
[2] A.-L. Barabasi and Z. N. Oltvai. Network biology:
understanding the cell’s functional organization.
Nature reviews genetics, 5(2):101–113, 2004.
[3] T. Bjarnsholt, T. Tolker-Nielsen, N. Høiby, and
M. Givskov. Interference of pseudomonas aeruginosa
signalling and biofilm formation for infection control.
Expert Rev. Mol. Med, 12:e11, 2010.
[4] S. Cabrol, A. Olliver, G. B. Pier, A. Andremont, and
R. Ruimy. Transcription of quorum-sensing system
genes in clinical and environmental isolates of
pseudomonas aeruginosa. Journal of bacteriology,
185(24):7222–7230, 2003.
[5] A. E. Clatworthy, E. Pierson, and D. T. Hung.
Targeting virulence: a new paradigm for antimicrobial
therapy. Nature chemical biology, 3(9):541–548, 2007.
[6] H. M. P. Consortium et al. Structure, function and
diversity of the healthy human microbiome. Nature,
486(7402):207–214, 2012.
[7] J. Costerton, P. S. Stewart, and E. Greenberg.
Bacterial biofilms: a common cause of persistent
infections. Science, 284(5418):1318–1322, 1999.
[8] T. De Kievit. Quorum sensing in pseudomonas
aeruginosa biofilms. Environmental microbiology,
11(2):279–288, 2009.
[9] T. R. De Kievit, R. Gillis, S. Marx, C. Brown, and
B. H. Iglewski. Quorum-sensing genes in pseudomonas
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
aeruginosa biofilms: their role and expression
patterns. Applied and environmental microbiology,
67(4):1865–1873, 2001.
J. D. Dockery and J. P. Keener. A mathematical
model for quorum sensing in pseudomonas aeruginosa.
Bulletin of Mathematical Biology, 63(1):95–116, 2001.
J. Gomes, N. Huber, A. Grunau, L. Eberl, and
K. Gademann. Fluorescent labeling agents for
quorum-sensing receptors (flaqs) in live cells.
Chemistry-A European Journal, 19(30):9766–9770,
2013.
L. Hall-Stoodley, J. W. Costerton, and P. Stoodley.
Bacterial biofilms: from the natural environment to
infectious diseases. Nature Reviews Microbiology,
2(2):95–108, 2004.
W. D. Hamilton. The evolution of altruistic behavior.
American naturalist, pages 354–356, 1963.
W. D. Hamilton. The genetical evolution of social
behaviour. ii. Journal of theoretical biology,
7(1):17–52, 1964.
G. Hardin. The tragedy of the commons. science,
162(3859):1243–1248, 1968.
M. Hentzer, M. Givskov, et al. Pharmacological
inhibition of quorum sensing for the treatment of
chronic bacterial infections. Journal of Clinical
Investigation, 112(9):1300–1307, 2003.
M. Hentzer, H. Wu, J. B. Andersen, K. Riedel, T. B.
Rasmussen, N. Bagge, N. Kumar, M. A. Schembri,
Z. Song, P. Kristoffersen, et al. Attenuation of
pseudomonas aeruginosa virulence by quorum sensing
inhibitors. The EMBO Journal, 22(15):3803–3815,
2003.
L. R. Hoffman, H. D. Kulasekara, J. Emerson, L. S.
Houston, J. L. Burns, B. W. Ramsey, and S. I. Miller.
Pseudomonas aeruginosa lasr mutants are associated
with cystic fibrosis lung disease progression. Journal of
Cystic Fibrosis, 8(1):66–70, 2009.
P. N. Jimenez, G. Koch, J. A. Thompson, K. B.
Xavier, R. H. Cool, and W. J. Quax. The multiple
signaling systems regulating virulence in pseudomonas
aeruginosa. Microbiology and Molecular Biology
Reviews, 76(1):46–65, 2012.
V. C. Kalia and H. J. Purohit. Quenching the quorum
sensing system: potential antibacterial drug targets.
Critical reviews in microbiology, 37(2):121–140, 2011.
L. Keller and M. G. Surette. Communication in
bacteria: an ecological and evolutionary perspective.
Nature Reviews Microbiology, 4(4):249–258, 2006.
T. Köhler, A. Buckling, and C. Van Delden.
Cooperation and virulence of clinical pseudomonas
aeruginosa populations. Proceedings of the National
Academy of Sciences, 106(15):6339–6344, 2009.
B. LaSarre and M. J. Federle. Exploiting quorum
sensing to confuse bacterial pathogens. Microbiology
and Molecular Biology Reviews, 77(1):73–111, 2013.
H. C. Leggett, S. P. Brown, and S. E. Reece. War and
peace: social interactions in infections. Philosophical
Transactions of the Royal Society B: Biological
Sciences, 369(1642):20130365, 2014.
P. Melke, P. Sahlin, A. Levchenko, and H. Jönsson. A
cell-based model for quorum sensing in heterogeneous
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
bacterial colonies. PLoS computational biology,
6(6):e1000819, 2010.
L. Meng, T. Milenković, and A. Striegel. Systematic
dynamic and heterogeneous analysis of rich social
network data. In Complex Networks V, pages 25–37.
Springer, 2014.
M. B. Miller and B. L. Bassler. Quorum sensing in
bacteria. Annual Reviews in Microbiology,
55(1):165–199, 2001.
J. Monod. The growth of bacterial cultures. Annual
Review of Microbiology, 3:371–394, 1949.
M. Newman. Networks: an introduction. Oxford
University Press, 2010.
M. R. Parsek and E. Greenberg. Acyl-homoserine
lactone quorum sensing in gram-negative bacteria: A
signaling mechanism involved in associations with
higher organisms. Proceedings of the National
Academy of Sciences of the United States of America,
97(1):8789–8793.
L. Passador, J. M. Cook, M. J. Gambello, L. Rust,
and B. H. Iglewski. Expression of pseudomonas
aeruginosa virulence genes requires cell-to-cell
communication. Science, 260(5111):1127–1130, 1993.
E. C. Pesci, J. P. Pearson, P. C. Seed, and B. H.
Iglewski. Regulation of las and rhl quorum sensing in
pseudomonas aeruginosa. Journal of Bacteriology,
179(10):3127–3132, 1997.
D. A. Rasko and V. Sperandio. Anti-virulence
strategies to combat bacteria-mediated disease. Nature
Reviews Drug Discovery, 9(2):117–128, 2010.
T. Romeo. Bacterial biofilms. Springer, 2008.
K. P. Rumbaugh, J. A. Griswold, and A. N. Hamood.
The role of quorum sensing in the in vivo virulence of
pseudomonas aeruginosa. Microbes and infection,
2(14):1721–1731, 2000.
A. Shklarsh, G. Ariel, E. Schneidman, and
E. Ben-Jacob. Smart swarms of bacteria-inspired
agents with performance adaptable interactions. PLoS
Comput. Biol, 7(9):e1002177, 2011.
R. S. Smith and B. H. Iglewski. P. aeruginosa
quorum-sensing systems and virulence. Current
opinion in microbiology, 6(1):56–60, 2003.
C. M. Waters and B. L. Bassler. Quorum sensing:
cell-to-cell communication in bacteria. Annu. Rev.
Cell Dev. Biol., 21:319–346, 2005.
G. Wei, P. Bogdan, and R. Marculescu. Efficient
modeling and simulation of bacteria-based
nanonetworks with bnsim. Selected Areas in
Communications, IEEE Journal on, 31(12):868–878,
2013.
S. A. West, A. S. Griffin, A. Gardner, and S. P.
Diggle. Social evolution theory for microorganisms.
Nature Reviews Microbiology, 4(8):597–607, 2006.
W. B. Whitman, D. C. Coleman, and W. J. Wiebe.
Prokaryotes: the unseen majority. Proceedings of the
National Academy of Sciences of the United States of
America, 95(12):6578–6583, June 1998.
J. W. Williams, X. Cui, A. Levchenko, and A. M.
Stevens. Robust and sensitive control of a
quorum-sensing circuit by two interlocked feedback
loops. Molecular systems biology, 4(1), 2008.