In Silico Evaluation of the Impacts of Quorum Sensing Inhibition (QSI) on Strain Competition and Development of QSI Resistance

Abstract

As understanding of bacterial regulatory systems and pathogenesis continues to increase, QSI has been a major focus of research. However, recent studies have shown that mechanisms of resistance to quorum sensing (QS) inhibitors (QSIs) exist, calling into question their clinical value. We propose a computational framework that considers bacteria genotypes relative to QS genes and QS-regulated products including private, quasi-public, and public goods according to their impacts on bacterial fitness. Our results show (1) QSI resistance spreads when QS positively regulates the expression of private or quasi-public goods. (2) Resistance to drugs targeting secreted compounds downstream of QS for a mix of private, public, and quasi-public goods also spreads. (3) Changing the micro-environment during treatment with QSIs may decrease the spread of resistance. At fundamental-level, our simulation framework allows us to directly quantify cell-cell interactions and biofilm dynamics. Practically, the model provides a valuable tool for the study of QSI-based therapies, and the simulations reveal experimental paths that may guide QSI-based therapies in a manner that avoids or decreases the spread of QSI resistance.

While the era of antibiotics marks a cornerstone of modern medicine, it has, likewise, triggered the rise of virtually untreatable multidrug-resistant bacteria¹,². As new drug-resistant bacterial strains, such as carbapenem-resistant Enterobacteriaceae (CRE), continue to appear and spread, health officials are raising concern over the future efficacy of traditional antibiotics³. In response, substantial research efforts have shifted focus toward innovative targeted drug development strategies including anti-virulence therapy targeting cellular functions essential for pathogenesis within the human host rather than cellular vitality⁴.

Quorum sensing (QS) is a mechanism used by many bacteria to synchronize their collective behavior when reaching a sufficient high cell density⁵. In this paper, we consider the LasI/R QS system, which belongs to the LusI/R family of Gram-negative QS system. Specifically, members of the LuxI family produce acyl homoserine lactones (AHL) of varying acyl chain length that function as a signal. The signaling molecules bind to the receptors and activate the transcription regulator (LuxR homologs) in a form of LasR − AHL complex. This complex then leads to the transcription of a plurality of genes that are directly involved in bacteria collective behaviors⁶.

QS inhibitors (QSIs) aim at disabling the QS molecular signaling machinery within a bacterial pathogen, effectively rendering cells incapable of sensing the neighboring cell and consequently modifying the regulation of genes⁷. As a consequence, QSI modifies the regulation of genes such as biofilm formation, the production of secondary metabolites, and the expression of disease-causing virulence factors⁸,⁹,¹⁰,¹¹.

Despite the preliminary success of QSIs (see Supplementary Note 1), there remain fundamental issues that may constrain their potential clinical merit. Principally, QS inhibition, since its inception, has been argued to be an “evolution-proof” therapy insofar that it precludes direct pressures on cellular fitness and thereby obviates the explicit selection of drug resistant genotypes⁴,⁸,¹²,¹³,¹⁴. Unfortunately, the validity of this claim has failed to hold true in light of recent accounts of QSI resistant strains found both in clinical and laboratory settings¹⁵,¹⁶,¹⁷. The major issue is that while the QS inhibition does not directly kill bacteria (bactericidal effect) or stop bacteria from growing (bacteriostatic effect) like conventional broad-spectrum antibiotics— it does, however, alter the behavior of targeted pathogens by modifying the expression levels of QS-regulated genes. These changes are likely to influence the intra- and inter-strain interactions. As a result, QS inhibition can introduce changes into the microbiome by redistributing the competitive advantage during the development of a complex community.

A most striking example lies in Pseudomonas aeruginosa, a common human pathogen that can cause infections in cystic fibrosis (CF) patients. In P. aeruginosa, the QSI pressure (in vitro and in vivo) can lead to the selection of QS-negative strains. In patients with CF, loss of QS signaling is associated with chronic infection and increased growth rates¹⁸. On the other hand, QS-regulated virulence determinants such as elastase, rhamnolipids and alginate play a key role in establishing P. aeruginosa colonization in the CF lung¹⁹,²⁰. Thus, the development of QSI-based therapies should consider how the pressure of QSIs selects for QS mutants with modifications not only in their cooperative and competitive behaviors, but also in their virulence potential. However, existing simulation tools (see Supplementary Table 1) are unable to efficiently simulate dense networks of interacting bacteria populations in a complex 3D environment and incorporate both cellular and population level dynamics among bacteria in the meantime.

To investigate the major health problem of the emergence and the spread of QSI resistance, we develop a new computational framework (see Supplementary Fig. 1) to analyze the long-term dynamics of QSI-based therapies on the development and stability of biofilms and emergence of QSI-resistance. Our model uniquely accounts for mutations in different components of the QS machinery, as well as multiple properties of QS-regulated genes. The selective pressures on the QS variable cells will depend on the accessibility of QS-metabolic products to the neighboring cells. To capture this aspect, we model four types of QS outputs: (i) non-beneficial, (ii) private, (iii) quasi-public, and (iv) public goods (detailed modeling specifics are available in Methods). For each scenario, we consider the pathogenic properties of strains and the probability of the emergence of QSI-resistance.

Our proposed simulation framework simultaneously considers both intracellular and intercellular signaling and its effects on biofilm dynamics. We note that the intercellular network approach we propose can quantify various type of interactions and dynamics in populations of bacteria. For conditions where QSI-resistance spreads rapidly, we demonstrate that the metabolic output (i.e., different kinds of goods) of the community can substantially alter the spread of resistance. Specifically, our simulations suggest that the quasi-public goods (e.g., extracellular polymeric substances (EPS)) plays an important role in the spread of QSI resistance. Thus, we also model drugs targeting the quasi-public and public goods, and demonstrate that if resistance to such drugs arises, it will rapidly spread in a population.

Looking through such a quantitative lens at these complex phenomena can open new avenues both in fundamental knowledge and disease treatment. More specifically, from a theoretical point of view, the new network-based approach helps us model and investigate the cell-cell interaction and biofilm dynamics; this can help us estimate how manipulating signaling pathways influences the cell-cell interactions and coordination during biofilm attachment, growth, and detachment. From a practical perspective, our model provides a platform to experiment with the evolutionary outcome of different QSI therapies (alone and in combination) and prioritize testable hypotheses for strategies that will limit the emergence of QSI resistance. Moreover, the “computational microscope”²¹,²² we propose offers the advantages of rapid turnaround (hours instead of days), ability to test theoretical strategies, and high reproducibility of simulations. Taken together, all these contributions help us better understand and model the spread (dynamics) of QSI resistance which is paramount to the long-term success of QSIs in treating human pathogens.

Results

Simulation Environment and Model Calibration

We explain the model of the cell-cell interactions in Methods and define a 3D microfluidic environment as shown in Fig. 1. We note that our 3D simulator accounts for the spatial volume occupied by bacteria. In other words, we can capture the dynamics of interacting particles, while taking into account that a certain spatial volume can be occupied by at most one particle at any given point in time. (The details of various simulation environment configurations are described in Methods).

Figure 1. The simulation environment is modeled as bulk, boundary, and biomass layers.

The chemical concentrations in the bulk layer are invariant over time. To account for the high cell/EPS density, the biomass layer has a diffusion coefficient value roughly half of the boundary layer. More precisely, since the viscosity in high cell/EPS density is lower, we assume that the diffusion coefficient is half compared to the boundary layer. Bacterial cells attach to the substrate and grow upwards with nutrition diffusing from the bulk layer toward the biomass layer. See biofilm formation in Supplementary Videos 1 and 2.

Experiments were performed with a dual labeled Pseudomonas aeruginosa PAO1 strain, generously provided by Michael Givskov²³. The strain encodes a chromosomally integrated lasB-gfp(ASV) reporter system, as well as rfp under the control of a constitutive promoter²³. Thus, the strain produces rfp under all conditions, and gfp when QS is active. The growth condition and strain are described in Methods.

We calibrated our QS and QSI models with experimental data. More precisely, we added Furanone at a concentration of 100 uM at time equal to 24 hr (1 day after biofilm seeded), and imaged biofilms at 25, 27 and 28.5 hr. Images were processed to obtain the percentage of total cells positive for QS signal (see Methods), and this data was used to calibrate the model parameters (see Fig. 2 and Supplementary Table 2).

Figure 2. Simulation-model calibration.

Confocal images where all bacteria expressed red fluorescent protein (red), and only the subset undergoing QS express green fluorescent protein (gfp) were used to measure the influence of C-30 Furanone (an AHL analog) on the ratio of signaling cells in a biofilm (red circles represent measured ratios). The QS signaling decreases over time, and disappears 4 hrs post-treatment. We calibrate our model to these experimental results.

Selection of the Bacterial Genotypes and Regulons

We define three bacterial genotypes: (i) functional QS systems sensitivity to QSI (QS⁺), (ii) deletion of the QS machinery (QS⁻), (iii) or modified QS systems that are functional but resistant to QSIs (QSI-resistant). Additionally, to account for the production of multiple types of goods (Fig. 3), we classify the bacterial regulons into four categories: (i) non-beneficial goods, (ii) private goods, (iii) quasi-public goods, and (iv) public goods. Details are described in Methods.

Figure 3. Simulation roadmap for our initial experiments on QS⁺/QS⁻ competition without QS inhibition.

Each experimental setup (i.e., SE1-4, M1-4) is characterized by the class of goods generated by the QS⁺ strains and/or environmental conditions. Our simulation experiments, which corroborate previously reported wet-lab results, are indicated by green checkmarks.

Simulations without QSI under Different Conditions

The first scenario (Supplementary SE1) we corroborate with simulations is the non-beneficial goods, where QS⁺ cells suffer a metabolic cost and display a growth disadvantage over QS⁻ cells (Supplementary Fig. 2). This has been observed with pathogenic E. coli strains expressing virulence factors, such as Shiga toxins, that do not appear to confer a fitness advantage in human infection²⁴.

Next, we test private goods (Supplementary SE2), which are only available to producing cells. We confirm the relative fitness of QS⁺ cells over QS⁻ cells (Supplementary Fig. 3). It has been reported that, in the presence of the carbon source adenosine, P. aeruginosa is only able to gain access to nutritional benefits if the adenosine is first metabolized by the degradative enzyme nucleoside hydrolase (Nuh) that is positively regulated by LasR. Nuh is considered a private good as it is only available in the periplasm of the producing cell, thus conferring a metabolic gain solely to the individual cells²⁵.

Finally, our simulations correctly capture a case of quasi-public goods (Supplementary SE3). A prime example of quasi-public goods is the EPS secreted during biofilm formation. The QS-mediated production and secretion of EPS provides structural support to the extracellular matrix of a developing biofilm that, in turn, provides insulation from external threats, as well as increased access to nutrients²⁶,²⁷,²⁸. Although metabolically costly to its QS⁺ producers, EPS confers a large competitive advantage due to its hardly exploitable nature beyond the immediate vicinity of the producers. As shown in Supplementary Fig. 4, the biofilm growth trajectories show that the EPS cells (yellow spherical globules) surround QS⁺ and provide biofilm structure support. Additionally, QS⁺ cells gain a competitive advantage by jettisoning themselves and their lineages into higher nutrient rich regions while suffocating QS⁻ cells below. Our simulation results capture the relative fitness of QS⁺ cells over QS⁻ cells if the quasi-public goods are hardly exploitable for non-producer cells (QS⁻ cells).

In the following subsection, we provide three scenarios (M2-M4) where we modify diffusion, decay, and production rates of public goods.

The Effect of Public Good Properties on Biofilm and Network Parameters

Active QS is often associated with pathogenesis, given the QS-mediated production of virulence effectors. The spread of QS⁻ (cheater) cells, in the presence of public goods, decreases QS⁺ cells and has been proposed as an anti-virulence strategy²⁵. In the baseline case, the QS⁻ cells can take advantage of the public goods produced by QS⁺ cells and grow significantly faster after bacteria enter the exponential growth phase (i.e., after time t = 50 hrs), when QS controlled public goods are massively produced (Fig. 4A, M1). The biofilm metrics display the increase in thickness and decrease in roughness that occurs when QS-controlled public goods are massively produced (Fig. 4B, magenta). As the QS⁻ cells gain the growth advantage over QS⁺ cells, they split apart large communities into small communities among QS⁺ cells (Fig. 4C, magenta). The spread of QS⁻ cells has been observed both in vitro²⁹, as well as within hosts in animal-infection models²⁹. More recently, the loss of such social behavior has been identified as a consistent trend in CF lungs chronically infected by P. aeruginosa³⁰,³¹.

Figure 4. The effect of public good properties on biofilm and network parameters.

We have simulated a slower molecular diffusion rate (M2), a faster public goods decay rate (M3), and higher production rate for public goods (M4) and then compared our results against the baseline (M1). Panel (A) shows projections of biofilm growth and the relative ratio of QS⁺ and QS⁻ strains over time. Panel (B) shows the physical metrics that measure the thickness and the roughness of the total biofilm with both strains combined. Panel (C) shows the network metrics that quantify the changes of the biofilm structure. Strains are color coded as red: QS⁺ and blue: QS⁻. Simulations with baseline, different diffusion rates, decay rate, and production rate are color coded as magenta, purple, orange, and cyan, respectively.

We compare the baseline with the influence of decreased diffusion coefficient (Fig. 4A, M2), increased decay rate (Fig. 4A, M3), and increased production rate (Fig. 4A, M4). The two latter modifications have only mild effects on the ratio of strains and the overall biofilm structure, and lead to a decrease in the number of communities (Fig. 4B and C, orange and cyan). In contrast, decreasing diffusion rate leads to an increase in QS⁺ cells (Fig. 4A, M2), and fewer communities of larger size in the population (Fig. 4C, purple). This suggests that environmental changes (e.g., EPS or host immune cells) that result in a decreased diffusion of QS-public goods will increase QS⁺ cells. Early in colonization of CF lungs, such a change would be predicted to increase pathogenesis.

Simulations with QSI Effects and QSI Resistance

We have developed an intercellular network model (see Methods) to understand the emergence and dynamics of QSI-resistance; thus, we explore three QS inhibition strategies, which target different components of the QS system³²,³³,³⁴: (1) signal generation (Fig. 5A, M5); (2) extracellular signal accumulation (Fig. 5A, M6); (3) signal reception (Fig. 5A, M7); as well as all three treatments combined (Fig. 5A, M8). To simulate the long-term QSI treatment expected in clinical settings, the concentration of each QSI in the bulk layer (see Fig. 1) is kept constant after its introduction. Initially, 100 μM of QSI is added at time t = 0 hrs to inhibit QS and subsequent QS-mediated biofilm formation. These simulations assume QS directly regulates the production of private goods, quasi-public goods, and diffusible public goods. The simulations are performed with each type of QSI. We model QSI-resistant cells to intracellular signal reception and generation, but not to extracellular signal degrading enzymes, such as lactonase. We also run experiments to independently target non-beneficial goods, private goods, quasi-public, and public goods (Supplementary Note 2–4, Supplementary Figs 6–8).

Figure 5. Simulations of QSI effects and spread of QSI resistances modeling both quasi-public and public goods.

Four QSI targets are considered: Signal generation (M5), signal accumulation (M6), signal reception (M7), and all three combined (M8). Panel (A) shows the projections of biofilm growth up to 10 days and the dynamics of relative ratio of each strain over time. Panel (B) compares multiple QS and bacteria population measurements. Panel (C) shows the network metrics that quantify the changes of the biofilm structure. Strains are color coded as red: QS⁺, blue: QS⁻, green: QSI-resistant. Simulations with different strategies are color coded as magenta (M5), purple (M6), orange (M7), and cyan (M8).

When the model includes the production of both quasi-public and public goods, QSI spreads if the drug targets either signal generation (Fig. 5A, M5) or signal reception (Fig. 5A, M7). Importantly, this spread is not observed if QS leads only to production of public goods (Supplementary Fig. 8). The QSI-resistant cells begin to generate QS-regulated proteins to boost their growth around time t = 50 hrs (Fig. 5A). At this point in time, the communication between communities increases dramatically and stabilizes over time (Fig. 5C, magenta and orange). In both cases the number of communities stabilizes after t = 150 hrs, the QSI-resistant cells outcompete the other two strains, organize into high number of communities with high connectivity, and become the dominant population (Fig. 5A, M5, M7 day 10 and Fig. 5C).

While the 10-day outcome is very similar for both of these targets, the dynamics are different. More precisely, when targeting signal production, the signal molecules produced by the QSI-resistant cells diffuse out and activate QS⁺ cells nearby. The QS⁺ cells gain an advantage over the QS⁻ cells (Fig. 5, M5 day3). This advantage leads to formation of small clusters of QS⁺ cells (observed as hill-like shape in the number of communities in Fig. 5C, magenta line). In the long-term, this slow quasi-public goods production at boundaries fails to endow a fitness advantage when competing with QSI-resistant cells, and the many communities join the resistant cell communities (observed as drop in the number of communities in Fig. 5C at time t = 150 hrs). In contrast, when targeting signal reception, the QS⁺ cells do not encounter this temporary advantage over QS⁻ (Fig. 5A, M7). In both scenarios, when our model includes EPS, it predicts that targeting signal generation or reception may lead to the spread of QSI resistance.

When using signal degrading enzymes in M6, the QSI-resistant strains do not spread. The intracellular resistance that we model does not rescue cells from the extracellular degradation. In this scenario, we observe similar outcomes for QSI-resistant and QS⁺ cells. The total number of QSI-resistant cells is lower only because it reflects their lower number at time t = 0 hrs (see Supplementary Fig. 10 and Supplementary Note 5 for model robustness). When combining all three drug classes simulations resemble the one observed when signal accumulation is targeted. These simulations suggest targeting signal accumulation could be an effective long-term strategy for infection control.

To our knowledge, this is the first time when simulations have been used to estimate the spread of resistance for QSIs targeting signal production and reception. We observe that resistance to drugs targeting the production and reception of QS spreads rapidly in our models if they include quasi-public (EPS) and public goods in the meantime (Fig. 5, M5 and M7 respectively). In contrast, QSI resistance does not spread in our models that account only for public goods (Supplementary Fig. 8, S11 and S13, respectively). These differences highlight the important role of EPS in the spread of QSI resistance.

Simulations of drugs targeting the production of public or quasi-public goods

Targeting quasi-public goods (i.e., EPS) has been explored as an antimicrobial strategy, given the importance of EPS in biofilms³⁵. Thus we model the spread of resistance to therapies targeting enzymes involved in production of public or quasi-public goods. We test two putative inhibitors, one that targets quasi-public goods such as the biofilm matrix (Fig. 6A, M9) and another that targets public goods (Fig. 6A, M10).

Figure 6. The spread of resistance to inhibitors of QS products.

QS⁺, QS⁻ and drug resistant strains are treated with an inhibitor of quasi-public goods (M9) or an inhibitor of public goods (M10). Panel (A) shows the projections of biofilm growth up to 9 days and the relative ratio of each strain over time. Panel (B) compares multiple QS and bacteria population measurements. Panel (C) shows the network metrics that quantify the changes of the biofilm structure. Strains are color coded as red: QS⁺, blue: QS⁻, green: drug resistant. Simulations with different strategies are color coded as magenta (M9) and purple (M10).

Under both therapies modeled, the drug resistant strains spread rapidly throughout the biofilms (Fig. 6A). The difference between inhibitors specifically targeting quasi-public versus public goods is the fitness of QS⁻ strains, and the rate at which resistant strains expand in the population (Fig. 6A,B). Specifically, when quasi-public goods are inhibited both QS⁻ and QS⁺ cells exhibit similar growth rates, and the spread of resistant strains is higher. When public goods are inhibited, the number of QS⁻ cells is lower than that of QS⁺ cells. This difference is explained by the fitness costs incurred by QS⁻ strains in the absence of access to quasi-public goods. However, in all cases the biofilm structure exhibits similar patterns, defined by a peak in the number of communities at the time point of QS production (t = 50 hrs), and a stabilization of larger resistant communities after 3 days (Fig. 6C). The spread of resistance and the community of resistance strains suggest that once resistance to such inhibitors arises, it will spread rapidly throughout the population.

Discussion

In this paper, we have explored, through comprehensive computational studies, the effects of QSI on multi-strain biofilms consisting of QS⁺, QS⁻, and QSI-resistant cells, and the proliferation of resistance throughout a bacterial population. To this end, we have considered properties of molecules in the QS regulon, including non-beneficial goods, private goods, quasi-public goods, and public goods. Further, we have considered three distinct classes of QSIs targeting signal generation, signal molecule accumulation, and signal reception (Fig. 7).

Figure 7. Simulations summary.

The conditions and factors of each in silico experiment are outlined and labeled with respect to the successful decrease in QS regulated expression, QS⁺ genotype ratio, QSI resistance (SE5-SE11, and M5-M8), and drug resistance (M9 and M10).

One of the main contributions of this paper is the introduction of a network-theoretic framework to describe and analyze the “social” collaboration among bacteria within a population. We have applied network metrics such as the average clustering coefficient and the number of communities to understand the spatial distribution of strains with variation in QS during biofilm development. Specifically, we have used the network clustering coefficient to describe the size and distribution of clusters composed of cells with the same genotypes. By tracking the dynamic status of the network, one can observe how different drugs (see Figs 5 and 6 and Supplementary Figs 6–8), such as QSI with different QS component targets, work on the biofilms in real-time, thus, unveiling the underlying bacterial social interactions. We also note that in contrast to the physical biofilm metrics (e.g., biofilm average thickness and biofilm roughness), the network metrics can best discriminate the spread of QS mutants. Indeed, as shown in Fig. 4C, the number of communities show different behaviors of different biofilm organization based on properties that modify diffusible goods. While these parameters are easily outputted in our model, it is challenging to obtain similar metrics in laboratory experiments.

From a biological standpoint, our work suggests that when the QS regulon controls quasi-public goods (such as EPS), and QSI targets either signal generation or reception, once emerged QSI-resistance will rapidly spread (Fig. 5, M5 and M7). The spread is not observed if network links are completely dissolved by targeting signal accumulation in the absence of QSI (Fig. 5, M6 and M8). Additionally, the spread of QSI is not observed when only public goods are considered (Supplementary Fig. 8). If QSI or inhibitors of QS products are employed separately, both are prone to the spread of resistance (Figs 5 and 6). But, if QSI is combined with an EPS-targeting drug(s), the spread of resistance may be slowed or contained. Currently, EPS targeting can be achieved by expressing the degradation enzymes or adding compounds that act directly on the EPS (e.g., eDNA³⁶). This modeling suggests that the best long-term strategy to avoid QSI resistance while combating virulence associated with QS, is to combine QSIs and EPS targeting drugs. This opens the door for future experiments, testing the spread of QSI resistance in the presence of QSI and anti-EPS drugs, where the drug-induced absence of EPS is predicted to decrease the spread of QSI resistance.

Most QSI resistance mechanisms reported so far are based on multidrug efflux pumps or cellular enzymes³⁷. Resistance to signal degrading enzymes, such as the lactonase that hydrolyzes the ester bond of the homoserine lactone ring of AHLs, has not been reported so far. Thus, the lack or resistance spread observed with lactonase (Fig. 5, M6) and combinations of QSI (Fig. 5, M8) may reflect clinical scenarios. However, it is conceivable that resistance to lactonases will emerge, or is already present in the environment, and will spread to the human microbiome.

The cheater behavior of QS⁻ cells, and their delay on population growth has been reported, consistent with our model for QS in the context of public goods³⁸. However, our simulation results contradict another scenario presented in ref. 38 where resistant strains did not spread in the presence of QSI. However, in this scenario the native QS levels were below the QS activation threshold. Our model represents a scenario where the QS signal is above the activation threshold.

Our computational approaches offer a tool to guide experimental design by generating hypotheses on drug combinations, timing, and conditions that either increase or reduce the spread of drug resistance. The simulation results suggest a combined therapy targeting quasi-public goods and QS. Additionally, with the increasing development of more efficient, accurate, and inexpensive medical technologies (cutting-edge omics technologies such as metagenomics), it is now possible to measure evolution dynamics of biofilm in vitro. To this end, our simulation models can be validated and verified. Overall, this work computationally explores the QSI resistance, and predicts the timing and targets for therapeutics that may decrease or inhibit the spread of QSI resistance.

Methods

Bacteria Strain and Growth Condition

Bacterial Strain: We utilized the dual labeled Pseudomonas aeruginosa, with a QS reporter. The strain, PAO1(wt)::lasB-gfp(ASV)::Plac-lasR::rfp, was generously provided by Michael Givskok²³. Furanone C-30 was acquired from Sigma-Aldrich Co., and used at a final concentration of 100 μM.

P. aeruginosa biofilms: Biofilms were set up on MatTek plates, at 37 °C using Columbia browth. Furanone was added at time of 24 hour after biofilm development. Biofilm images were collected on a Zeis510 Meta Conforcor3 Laser Scanning Microscope at 25, 27, and 28.5 hours post-seeding.

Bacterial Image Processing

We detect the intensity of each bacterial image acquired from the confocal laser. Next, we compute the number of bacteria that express rfp and gfp, respectively. We then compute the relative concentration of the QS signal by using the following formula:

where N_rfp and N_gfp represent the number of bacteria that express rfp and gfp, respectively.

Definition of the Bacterial Genotypes and Regulons

• Bacterial genotypes: Specifically, we make use of three naturally occurring genotypes in regards to QS genes³⁹,⁴⁰ (i) functional QS systems sensitivity to QSI (QS⁺), (ii) deletion of the QS machinery (QS⁻), (iii) or modified QS systems that are functional but resistant to QSIs (QSI resistant). QS⁻ cells that have access to the benefits of QS, but do not incur the metabolic costs of production, should be at an adaptive advantage relative to their QS⁺ counterparts and can be characterized as “cheaters” within the community. We assume that the strains do not differ in other regions, and consequently there are no fitness advantage incurred by variability in other genomic regions.

• Bacterial regulons: Signaling via QS can lead to the production of multiple types of goods (Fig. 3). We separate these into four categories: (i) non-beneficial goods that provide no fitness advantage to producers or neighboring cells; (ii) private goods that provide a fitness advantage to producers but not neighboring, (iii) quasi-public goods that provide a fitness advantage to producers and neighboring cells but remain exclusively accessible to their producers, and (iv) public goods that provide a fitness advantage to producers as well as neighboring cells. The competitive index between QS⁺ and QS⁻ depends the production costs and benefits of QS, and the availability of QS products to QS⁻ cells.

Bacteria Population Model

The intracellular biochemical pathways giving rise to quorum sensing have been well studied from both molecular and systems biological perspectives⁴¹,⁴²,⁴³,⁴⁴. Yet, the endogenous mechanisms of such signaling systems are inextricably bound to exogenous processes, cues, and constraints suggesting that, in isolation, intracellular models are unrealistic⁴⁵,⁴⁶. Consequently, recent efforts have been put forth to contextualize the intracellular signaling mechanisms within the scope of intercellular interactions⁴⁷,⁴⁸,⁴⁹,⁵⁰,⁵¹,⁵²,⁵³,⁵⁴,⁵⁵. Nevertheless, this line of work has, hitherto, been limited to interactions among small groups of cells and has neither considered characterizations of molecular communication at a higher level of abstraction, nor differentiated cell types capable of behavioral variances including cooperation, exploitation, and pathogenesis.

To this end, we present a new computational model for bacterial community dynamics capable of capturing highly emergent behaviors found at the population level. We draw from the paradigm of agent-based modeling whereby each cell is outfitted with its own set of equations governing metabolic and communication processes⁵⁶,⁵⁷,⁵⁸,⁵⁹,⁶⁰. Our model domain consists of a 3-dimensional micro-fluidic environment governed by the laws of diffusion and volume exclusion. The model incorporates molecular signaling, nutrient limited metabolism, exoproduct formation, and virulence processes that are crucial in the development and evolution of mixed biofilm communities (see Supplementary Table 2 for model parameters).

In our model, we assume the QS regulatory network of Pseudomonas aeruginosa has two feedback loops (see Supplementary Fig. 9). The LasR − AHL complex up-regulates the expression of both lasR and lasI genes, generating even more signal molecules (AHL) and receptors (LasR), thereby forming a positive feedback loop. To model the QS system, we use a set of ordinary differential equations proposed in refs ⁴⁷ and ⁶¹, and then extend the ODE system to incorporate the effects of QSI. Particularly, we focus on three components of the QS system that are potential targets for QSI therapy: (1) LasI signal synthase (i.e., signal generation) (2) Extracellular AHL molecules (i.e., signal accumulation) (3) LasR antagonist (i.e., signal reception)³²,³³.

Furthermore, we simulate bacterial growth kinetics based on the classic Monod model⁶² by considering multiple nutrient sources. The production of all inter or intracellular proteins are all constrained by nutrition availability in the ambient microenvironment. Nutrients and drug molecules diffuse across the space following Fick’s low while using different diffusion coefficient for different layers (see Fig. 1). Physical collisions are handled using CUDA platform which is capable of calculating the overlapping area of thousands of particle pairs (i.e., cells and EPS) and shoving them simultaneously.

Quorum Sensing Model

The regulatory network of the LasR/R quorum sensing system has two feedback loops. Based on the ODE-models proposed in refs ⁴⁷ and ⁶¹, we have the following equations for the luxIR QS system:

where [X] denotes the concentration of a particular molecular species X. In our formulation, A stands for AHL, R is LasR homologs, RA is the LasR − AHL complex and C is the dimerized complex. c_A and c_R account for the basal level transcription of A and R, respectively. The values and references of the parameters are adapted from a general LasIR system⁴⁷.

To give some intuition, the first term c_A of Eq.(2) describes the basal level transcription, the second term captures the positive feedback loop regulated by the dimerized complex C and the third and forth terms describe the AHL concentration changes caused by the binding and unbinding reactions of AHL and LasR receptor, respectively. The last term describes the degradation of AHL. Eqs (4) and (5) describe the binding reaction of AHL and LasR receptor, as well as the dimerization process of the binding product [RA], respectively.

Quorum Sensing Inhibition Model

Recently, a large number of chemical compounds have been screened and many of them show QS inhibition effects targeting various components of the QS system. In this paper, we focus on three components of the QS system that are potential targets for QSI therapy: (1) LasI Signal Synthase (i.e., signal generation) (2) Extracellular AHL molecules (i.e., signal generation) (3) LasR antagonist (i.e., signal reception)³²,³³.

(1) Inhibition of LasI signal synthase. AHL synthase catalyses the formation of an amide bond between the homoserine lactone ring from S-adenosylmethionine (SAM) and the acyl chain from the acyl acyl-carrier-protein (acyl-ACP). After catalysed, the product of AHL and by-products of holo-ACP and 59-methylthioadenosine (MTA) are generated and released⁶³. Many chemical compounds have been shown to be effective reducing LasI activity¹⁴. Recently, a new compound trans-cinnamaldehyde, which has no chemical structure similarity to AHLs or AHL analogues, is shown to inhibit AHL synthases by molecular docking studies³⁴. To have a general form in our model, we modify eq. (2) to add the lasI inhibition; also, a new equation for the drug degradation is also added:

where [QSILasI] stands for the concentration of QSI molecules that inhibits luxI expression, k₆ is its degradation rate.

(2) Extracellular AHL: AHL molecules can diffuse in and out of the bacterial cell freely. Therefore, once they appear in the extracellular environment, they are potential targets for destruction or inactivation. The AHL-degrading enzyme, AHL-lactonase (such as AiiA or AiiM), has been reported to deactivate the bacterial virulence through hydrolysis of the lactone ring of AHL⁶⁴. Accordingly, eq. (6) needs to be modified to describe the AHL-degradation by AHL-degrading enzyme; similarly, we also need to add a new equation describing the drug degradation:

where [QSI_d] stands for the concentration of QSI which degrades AHL. In these equations, k_cat represents the maximum rate achieved by the system, at maximum (saturating) substrate concentrations. The Michaelis constant K_M is the substrate concentration at which the reaction rate is half of k_cat, and k₇ is the drug degradation rate.

(3) AHL signal reception: The most promising mechanism for inhibiting LasR activation is achieved through the use of AHL analogues that act as antagonists for the native AHL (i.e., 3O-C12-HSL for LasIR system). These molecules are likely to be similar in structure to the natural AHL and compete for LasR-receptors binding (some can bind covalently). Accordingly, eq. (3) needs to be modified to:

where [QSI_anlg] stands for QSI which inhibits the LasR activation, [RQSI_anlg] is the binding product of LasR and [QSI_anlg]. Also, we need to add two more equations to describe the dynamics of [QSI_anlg]:

where k₁₀ is the degradation rate of QSI_anlg. We assume that the AHL analogues have the twice the affinity as the native AHL to the LasR receptor, therefore, the binding reaction rates satisfy k₈ = 2k₁.

Cell Growth

Monod introduced the concept of single nutrient controlled kinetics to describe microbial growth⁶². The kinetic relates the specific growth rate (μ_X) of a bacterium cell mass (X) to the substrate concentration (S). The kinetic parameters, maximum specific growth rate (k_X) and substrate affinity (K_S), are assumed to be constant and dependent on strain, medium, and growth conditions (e.g. temperature, pH). Also, we consider a second nutrient source, and add a new term Q. On the other hand, when cells are metabolically active, but not growing or dividing, they may still take up substrate. To address this, a maintenance rate (m) is generally used to describe the reduction, and Monod’s model can be improved as follows:

EPS Production

We model the production of EPS as a function of the intracellular dimerized LasR − AHL complex C and incurring a cost on the carbon substrate (S) in Eq. (20):

where k_EPS is the maximum EPS production rate, and represents nutrition limitation. 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 passes a given threshold).

Digestive Enzyme (DGE) Production

We present a simplified and generic model of a diffusible public good motivated the production and utilization of the iron-chelating siderophore, pyoverdine. The production of DGE is also regulated by the intracellular dimerized LasR − AHL complex (C) a maximum production rate (k_DGE),

and the amount of complex Q (e.g., chelated iron) available in the extracellular environment is

where β is the chelation rate, DGE_in and DGE_ex are the intracellular and extracellular DGE concentration, respectively.

Metabolic Burden and Nutrition Consumption

Also, we need to take into account the cost of generating QS-related molecules, EPS, and digestive enzymes. Specially, to balance the limiting nutrition, we introduce utilization coefficients U_X, U_DGE, U_EPS, U_A, U_R to model the metabolic burden and consumption of substrate nutrition to produce general cell mass, digestive enzymes, EPS, AHL molecules, and QS receptors, respectively:

Therefore, higher cell densities can lead to a decreased growth rate as well as production rate of various cellular products in a nutrition-limited environment.

Mass Volume, Radius, and Physical Interactions

Similar to⁶⁰, in our simulation platform, a bacterial cell structure is compartmentalized with inner “biomass” core consisting of all intracellular material, and an outer layer consists of the capsular EPS. For each compartment, a density ρ_i, the mass m_j, and volume V_j is updated at each simulation step according to the following equation:

Then, the radii of the inner biomass and entire cell are calculated using the volumes V_j and V_jtotal respectively. When the volume of a cell grow to be twice of the regular size (division threshold), it divides into two daughter cells. Similarly, when the capsular mass is above a “separate threshold”, the capsular mass fall off and form a new particle, such as the EPS.

Besides chemotaxis, cell growth, division, and shrinking are all the sources of movements. We use a physical collision kernel powered by CUDA technology to resolve any pair-wise agent overlap.

Cell-Cell Interaction Network and QS Signaling Molecules

Our network model considers the intracellular molecular information of the QS system, as well as the extracellular physical diffusion limit.

To replicate cell-cell interactions, in our model, a directed link from bacterium A to bacterium B is established under two conditions (see Fig. 8):

Figure 8. Bacteria QS-based collaboration network.

A directed link is formed from cell A to cell B if cell B lies within the influence range, D_if, of cell A and both cells have activated QS systems. The influence range, D_if, of a cell depends largely on the intracellular concentration of the QS activity regulator complex, C. This is demonstrated by the bacterial color scale which represents intracellular [C]. The arrow from A to B indicates that A can influence B; the blue circles represent the radius of QS influence.

(I) Bacterium B must be within a diffusion-limited signal influence range D_if of bacterium A.

(II) Bacteria A and B must be QS active at the same time.

The first condition accounts for the spatially constrained nature of molecular diffusion. The signaling molecules produced and secreted by bacteria have a strong impact only within a range, D_if, depending on production rate, diffusivity, and decay rate. The second condition ensures that the QS system of both bacteria is active; this is realized by comparing against a concentration threshold of the intracellular QS regulator. To account for different levels of signal production of spreader bacteria, D_if is defined as:

where α is a scaling factor for the overall influential distance, β is the saturation factor for the intracellular QS activity regulator complex C, and is the ratio of the effective diffusion (D) coefficient in the complex extracellular environment normalized to the free diffusion case (D₀). It is important to emphasize that the influence range, D_if, differs across cells as a function of intracellular QS activity regulator complex, C. Fig. 8 illustrates an instance of a collaboration network formed across a small number of cells.

Physical Metrics to Quantity Biofilm Structure

• Biofilm average thickness: The average biofilm thickness is measured based on the distance between the substrate and the outermost cell over the space.

• Biofilm roughness: Biofilm surface roughness is defined by the following equation:

where L_f is the average thickness, L_fi is the ith value of the thickness matrix in the ith grid.

Metrics to Quantify Interaction Dynamics and Parameters

Once the cell-cell interactions are mathematically characterized, we can derive two network metrics to describe the interaction dynamics:

• Clustering coefficient measures the degree to which network nodes are clustered together. In this paper, we consider a global clustering coefficient which is based on triadic network nodes⁶⁵. Since our network links are constrained by the influential distance, a high clustering coefficient means that the network nodes are not only highly active but also in close proximity to one another, without being separated by non-active cells or other particles in the extracellular space.

• Communities are defined as groups of nodes with high clustering coefficient (i.e., densely interconnected) that are only sparsely connected with the rest of the network. Therefore, a cell group may have only a few links across another group, but if the two cell groups have a large impact on one another (e.g, gene expression synchronization.), then they are considered to belong to the same community.

We also define three quantitative parameters:

• QS-regulated expression: As indicated in our QS activity based network definition, the percentage of networked nodes (i.e. QS-activated cells) over the total number of cells (i.e., the sum of QS⁺ cells, QS⁻ cells, and QSI-resistant cells) can be used as a measure of the overall activity of QS-regulated product expression in a biofilm. Given that QS systems commonly up-regulate virulence factors, its expression is generally considered to be positively correlated with the percentage of networked nodes.

• QS⁺ genotype ratio: The ratio of the sum of the number of QS⁺ cells and QSI-resistant cells over the total number of cells. This measure is critical because it indicates how strong the QS activity in the bacteria populations would be once the QSI treatment is reduced or stopped, regardless of how much it is inhibited when QSI is used.

• Resistance: The ratio of the number of QSI-resistant cells over the total number of cells (i.e., the sum of QS⁺ cells, QS⁻ cells, and QSI-resistant cells). Note that QSI resistance is defined as the continuance of QS activity following QSI treatment.

Simulation Environment Configuration

All the scenarios we model bacterial growth in a 3D microfluidic environment (250 μm × 205 μm × 400 μm) is initialized and inoculated with 25 wild-type QS⁺ and 25 QS⁻ mutant cells, all of which are non-overlapping and randomly attached to the substrate, see Fig. 1. A constant nutrition concentration, S = 1 mM, available to both types of cells is maintained in the bulk layer and free to diffuse to the biomass layer. The duration of the growth period is 5 days.

Additional Information

How to cite this article: Wei, G. et al. In Silico Evaluation of the Impacts of Quorum Sensing Inhibition (QSI) on Strain Competition and Development of QSI Resistance. Sci. Rep. 6, 35136; doi: 10.1038/srep35136 (2016).