9
TOPICAL PAPER Modeling the Quorum Sensing Regulatory Network of Human-Pathogenic Pseudomonas aeruginosa Alessandro Usseglio Viretta and Martin Fussenegger* Institute of Biotechnology, ETH Hoenggerberg HPT D74, CH-8093 Zurich, Switzerland The biochemical network underlying quorum sensing in human-pathogenic Pseudo- monas aeruginosa is one of the best characterized. Mathematical modeling is required to untangle the complexity of its architecture and dynamics. We present a qualitative model of the P. aeruginosa quorum-sensing network including interactions between the las and rhl modules, the signaling molecule PQS and the regulatory proteins Mvfr and VfR. Simulations exemplify the model to reproduce natural network behavior and suggest quorum-sensing responses to pharmacological interference. Introduction Pseudomonas aeruginosa is a Gram-negative opportu- nistic pathogen of humans, animals, plants, and lower eukaryotes (1, 2). P. aeruginosa is known to produce a variety of factors enabling colonization of almost any mammalian tissue, which may result in severe infections in (i) burn victims, (ii) immunocompromized and (iii) cystic fibrosis patients, as well as in users of (iv) soft contact lenses, (v) indwelling urethral catheters, and (vi) prosthetic appliances. Control and eradication of P. aeruginosa infections remain a clinical challenge of high importance. The effectiveness of antibiotics, which typi- cally represent the best option to treat bacterial infec- tions, becomes increasingly limited as a result of the increasing prevalence of multi-drug-resistant human pathogenic bacteria. Therefore, novel pharmacologic in- tervention strategies, preferably ones that limit develop- ment and horizontal transfer of resistance mechanisms, are urgently required (3). In most bacterial pathogens, conditional expression of virulence-factor-encoding regu- lons coordinate infection, cell invasion, evasion of the host immune system, and persistence (4-6). Undermining virulence factor regulatory networks may thus be a promising therapeutic strategy. P. aeruginosa produces virulence factors only after having reached a critical population density in the host (4-6). The molecular crosstalk underlying population-wide coordination of host defense breaches is known as quorum sensing (QS), a phenomenon that had first been discovered for biolumi- nescent marine bacteria (4-6). Communication between and among bacterial popula- tions is implemented by molecules known as pheromones or autoinducers since they induce their own production (4-6). Above a critical threshold concentration, quorum- sensing receptors in target bacteria bind the pheromones and translate this signal into a specific target regulon expression readout in a dose-dependent manner (4-6). The P. aeruginosa QS system is one of the best charac- terized and consists of at least two biochemical sub- systems, the las and the rhl modules (7), which are fine- tuned by the homoserine lactone pheromones (HSL) 3-oxo-C12-HSL and C4-HSL, respectively. More recently, another QS pheromone, the Pseudomonas Quinolone Signal (PQS) (8), was discovered. However, PQS’s posi- tion in the P. aeruginosa QS biochemical network re- mains elusive. Several molecules contribute to sensing and regulation of these pheromones in P. aeruginosa; Vfr (9), Mvfr (10), RsaL (11), RpoN (12, 13), QscR (14, 15), and GacA (16) are some examples. Mathematical models have the potential to manage biological knowledge, untangle/interpret complex net- work interactions, and enable simulation-based predic- tion of systems’ behavior, missing parameters, or ambi- guities. The choice of the detail level required for modeling a biological system is not trivial. If the param- eters (kinetic and time constants) are well-known or easy to approximate, the system can be described by a set of differential equations (17-23), mode-switched differential equations (24), or stochastic simulation of the chemical reactions (25-28). Often, system knowledge remains insufficient or incomparable between different experi- mental setups. Modeling strategies will have to consider and integrate such data sets in a comparative manner. Such approaches are known as “qualitative modelling” and include examples by Kauffman (29, 30), Thieffry (31), Shmulevich (32), and de Jong (33) (see also 34-37). Some aspects of prokaryotic QS networks have already been formalized by Dockery et al. (38) and by James et al. (39), who pioneered mathematical models of the P. aeruginosa las and the Vibrio fischeri lux modules, respectively. Both models were based on a set of differential equations the dynamics of which was analyzed. Other works on differ- ent aspects of QS are those by Ward et al. (40), Koerber et al. (41), and Chopp et al. (42). Because integration of novel QS interactions into highly detailed models is * To whom correspondence should be addressed. Tel: +41 1 633 3448. Fax: +41 1 633 1234. E-mail: fussenegger@ biotech.biol.ethz.ch. 670 Biotechnol. Prog. 2004, 20, 670-678 10.1021/bp034323l CCC: $27.50 © 2004 American Chemical Society and American Institute of Chemical Engineers Published on Web 04/23/2004

Modeling the Quorum Sensing Regulatory Network of Human-Pathogenic Pseudomonas aeruginosa

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Page 1: Modeling the Quorum Sensing Regulatory Network of Human-Pathogenic Pseudomonas aeruginosa

TOPICAL PAPER

Modeling the Quorum Sensing Regulatory Network ofHuman-Pathogenic Pseudomonas aeruginosa

Alessandro Usseglio Viretta and Martin Fussenegger*

Institute of Biotechnology, ETH Hoenggerberg HPT D74, CH-8093 Zurich, Switzerland

The biochemical network underlying quorum sensing in human-pathogenic Pseudo-monas aeruginosa is one of the best characterized. Mathematical modeling is requiredto untangle the complexity of its architecture and dynamics. We present a qualitativemodel of the P. aeruginosa quorum-sensing network including interactions betweenthe las and rhl modules, the signaling molecule PQS and the regulatory proteins Mvfrand VfR. Simulations exemplify the model to reproduce natural network behavior andsuggest quorum-sensing responses to pharmacological interference.

Introduction

Pseudomonas aeruginosa is a Gram-negative opportu-nistic pathogen of humans, animals, plants, and lowereukaryotes (1, 2). P. aeruginosa is known to produce avariety of factors enabling colonization of almost anymammalian tissue, which may result in severe infectionsin (i) burn victims, (ii) immunocompromized and (iii)cystic fibrosis patients, as well as in users of (iv) softcontact lenses, (v) indwelling urethral catheters, and (vi)prosthetic appliances. Control and eradication of P.aeruginosa infections remain a clinical challenge of highimportance. The effectiveness of antibiotics, which typi-cally represent the best option to treat bacterial infec-tions, becomes increasingly limited as a result of theincreasing prevalence of multi-drug-resistant humanpathogenic bacteria. Therefore, novel pharmacologic in-tervention strategies, preferably ones that limit develop-ment and horizontal transfer of resistance mechanisms,are urgently required (3). In most bacterial pathogens,conditional expression of virulence-factor-encoding regu-lons coordinate infection, cell invasion, evasion of the hostimmune system, and persistence (4-6). Underminingvirulence factor regulatory networks may thus be apromising therapeutic strategy. P. aeruginosa producesvirulence factors only after having reached a criticalpopulation density in the host (4-6). The molecularcrosstalk underlying population-wide coordination of hostdefense breaches is known as quorum sensing (QS), aphenomenon that had first been discovered for biolumi-nescent marine bacteria (4-6).

Communication between and among bacterial popula-tions is implemented by molecules known as pheromonesor autoinducers since they induce their own production(4-6). Above a critical threshold concentration, quorum-sensing receptors in target bacteria bind the pheromones

and translate this signal into a specific target regulonexpression readout in a dose-dependent manner (4-6).The P. aeruginosa QS system is one of the best charac-terized and consists of at least two biochemical sub-systems, the las and the rhl modules (7), which are fine-tuned by the homoserine lactone pheromones (HSL)3-oxo-C12-HSL and C4-HSL, respectively. More recently,another QS pheromone, the Pseudomonas QuinoloneSignal (PQS) (8), was discovered. However, PQS’s posi-tion in the P. aeruginosa QS biochemical network re-mains elusive. Several molecules contribute to sensingand regulation of these pheromones in P. aeruginosa; Vfr(9), Mvfr (10), RsaL (11), RpoN (12, 13), QscR (14, 15),and GacA (16) are some examples.

Mathematical models have the potential to managebiological knowledge, untangle/interpret complex net-work interactions, and enable simulation-based predic-tion of systems’ behavior, missing parameters, or ambi-guities. The choice of the detail level required formodeling a biological system is not trivial. If the param-eters (kinetic and time constants) are well-known or easyto approximate, the system can be described by a set ofdifferential equations (17-23), mode-switched differentialequations (24), or stochastic simulation of the chemicalreactions (25-28). Often, system knowledge remainsinsufficient or incomparable between different experi-mental setups. Modeling strategies will have to considerand integrate such data sets in a comparative manner.Such approaches are known as “qualitative modelling”and include examples by Kauffman (29, 30), Thieffry (31),Shmulevich (32), and de Jong (33) (see also 34-37). Someaspects of prokaryotic QS networks have already beenformalized by Dockery et al. (38) and by James et al. (39),who pioneered mathematical models of the P. aeruginosalas and the Vibrio fischeri lux modules, respectively. Bothmodels were based on a set of differential equations thedynamics of which was analyzed. Other works on differ-ent aspects of QS are those by Ward et al. (40), Koerberet al. (41), and Chopp et al. (42). Because integration ofnovel QS interactions into highly detailed models is

* To whom correspondence should be addressed. Tel: +41 1633 3448. Fax: +41 1 633 1234. E-mail: [email protected].

670 Biotechnol. Prog. 2004, 20, 670−678

10.1021/bp034323l CCC: $27.50 © 2004 American Chemical Society and American Institute of Chemical EngineersPublished on Web 04/23/2004

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rather difficult and requires heuristic search of param-eters in the parameter space (43), we opted for thequalitative approach pioneered by de Jong (33). Followingde Jong’s approach, a biochemical network is describedby a set of piecewise linear differential equations, whichare qualitatively evaluated but not numerically solved(see Methods).

In the following sections we review current QS knowl-edge and integrate it into a qualitative network model.Then, simulation methods are specified prior to simulat-ing P. aeruginosa’s QS network behavior under bothphysiological and hypothetical conditions.

Network Structure

Because there is no precise or widely accepted defini-tion of a network module available, it is useful to defineone to improve understanding of the network’s architec-ture and dynamics. Network modules are parts of aspecific gene network and consist of functionally relatedmolecules that are involved in similar tasks and oftenact on similar time scales (44). This definition enablesdescription of the QS network as two interconnectedmodules that can mutually influence each other: (i) Thelas module includes the lasI and lasR genes, their proteinproducts LasI and LasR, the pheromone 3-oxo-C12-HSLand the pheromone-bound, activated form of LasR (LasR:3-oxo-C12-HSL). (ii) The rhl module includes the rhlI andthe rhlR genes, their protein products RhlI and RhlR,the pheromone C4-HSL, and the pheromone-bound,activated version of RhlR (RhlR:C4-HSL). The modulechoice influences neither the architecture nor the dynam-ics of the network model since it represents a molecularrather than a logical classification. We also consider PQSas well as the regulatory proteins MvfR and Vfr. Thenatural QS network is even more complex. Severalproteins including RpoN, QscR, GacA, and MvaT modu-late the activity of the specified modules. The QS networkdynamics follows a well-orchestrated series of events,which requires the las module to activate the rhl module.The las module, which is often considered as the “masterswitch” of the QS system, is the first one responding toan increase in pheromone concentration. About 25 bacte-rial species share such global QS network structureincluding similar pheromone molecules (5). Therefore,modeling P. aeruginosa QS regulatory networks willlikely retain a global scope.

The relative transcription-initiation times of genes arekey parameters for all living systems. Therefore, aqualitative gene network model preserving relative tim-ing of global gene expression is expected to providesufficient details even when lacking precise knowledgeon the expression dynamics of individual genes. Thisqualitative manner greatly simplifies the model struc-tures without significant loss in parameter integrationpotential. For example, since mRNA is typically shorter-lived than proteins (38), protein concentration followsmRNA concentration with some delay. Therefore, mRNAconcentrations will not be required in a qualitativenetwork model. Transcription control can be lumped withtranslation control without affecting the qualitativemodel dynamics, provided that neither control levelmodulates the appearance of new active molecules.Concentrations of key QS network players (proteins andmolecules) were discretized by assigning one or severalthreshold values. The impact of each specific networkplayer on synthesis and degradation profiles of all otherswere described in sets of piecewise linear differentialequations (according to de Jong et al. (33)). Choices for

discretization (the number of thresholds) and the natureof the interactions (e.g., activation, repression, andstrength of the interaction) were based on the currentliterature. The P. aeruginosa QS network structure isshown in Figure 1. Detailed descriptions of key networkplayers are provided in the following section.

Interactions and Discretization

LasI, encoded by lasI, is required for the synthesis ofthe pheromone 3-oxo-C12-HSL (45, 46). lasI expressionrequires LasR and 3-oxo-C12-HSL (46, 47). Binding of3-oxo-C12-HSL to LasR (LasR:3-oxo-C12HSL) convertsLasR into a transcriptional activator. This pheromone-mediated functional transition is a common characteristicof LuxR-type proteins, all of which contain an acyl-homoserine lactone (acyl-HSL) binding region. Vibriofischeri’s LuxR is P. aeruginosa’s LasR homologue, whichis one of the best-studied QS systems (39). LasR:3-oxo-C12-HSL activates several genes including lasI itself (45).This positive feedback loop is an important feature of QSnetworks and accounts for the switchlike expressionintegration in response to pheromone concentrationchanges.

• For our qualitative model, the intracellular LasIconcentration was allowed to adopt low, middle, and highlevels. The LasI concentration follows that of LasR:3-oxo-C12-HSL.

3-oxo-C12-HSL is a diffusible molecule produced byP. aeruginosa containing a functional lasI gene (46).When bound to LasR, LasR:3-oxo-C12-HSL activatesseveral virulence genes including aprA (alkaline pro-tease), lasA (elastase A), lasB (elastase B), toxA (exo-toxin), and lasI (45, 48, 49). 3-oxo-C12-HSL is typicallyproduced and secreted at a baseline rate. The intra-cellular 3-oxo-C12-HSL concentration increases with thebacterial population density since secretion of the phero-mone becomes increasingly rate-limiting. After havingreached a specific threshold concentration, 3-oxo-C12-HSL binds to and converts LasR into a transcriptionalactivator, initiating a positive feedback loop via LasIproduction, which results in maximum 3-oxo-C12-HSLexpression (50). Therefore, QS pheromones are also

Figure 1. Schematic representation of the P. aeruginosa QSnetwork. Filled arrows indicate transcription and translation,open arrows complex formation, filled circles modulation, andopen circles enzymatic synthesis.

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referred to as autoinducers. In a steady state, theintracellular 3-oxo-C12-HSL concentration is about 3-foldthe extracellular one, despite active secretion mediatedby the MexAB-OprM pump (51). Because the steady-stateconcentration is reached within 5 min following changesof extracellular pheromone concentrations (51), the in-tracellular concentration can be considered proportionalto the extracellular one (40). 3-oxo-C12-HSL inhibits therhl module by competing with C4-HSL for binding toRhlR. 3-oxo-C12-HSL keeps RhlR in an inactive stateuntil being replaced by C4-HSL at a specific thresholdconcentration. Such a regulation theme was suggestedto enable sequential control of QS-induced genes as wellas steplike induction of C4-HSL (5, 7). Because our QSmodel approximates interactions between molecules withsteplike functions, the competition between 3-oxo-C12-HSL and C4-HSL was not explicitly modeled, as its maineffect on the network dynamics, the steplike inductionof C4-HSL, was already considered in the model.

• The 3-oxo-C12-HSL concentration range was dividedinto three intervals (low, middle, and high concentra-tions). The 3-oxo-C12-HSL concentration is at intermedi-ate levels when either the LasI concentration is middleor the MvfR (see below) concentration is high. The 3-oxo-C12-HSL concentration will only reach high levels ifeither (i) its external concentration is high (high popula-tion densities that limit efficient secretion of 3-oxo-C12-HSL) or (ii) if the external concentration is middle in thepresence of high LasI concentrations (since LasI enhances3-oxo-C12-HSL synthesis). The 3-oxo-C12-HSL concen-tration will be low if none of the two aforementionedconditions are satisfied.

LasR is encoded by the Vfr-activated gene lasR andis the cognate receptor of the pheromone 3-oxo-C12-HSL.LasR is a global regulator of the P. aeruginosa virulencegenes (46). Indeed, Vfr-mediated induction of lasR (9) isan essential component of the QS regulatory networksince lasI requires LasR for maximal expression (45).

• LasR concentration was divided into two intervals(low and high concentrations). Because LasR is up-regulated by both Vfr and PQS (see below), its concentra-tion was never low. The low concentration range, al-though unused, is kept for consistency and clarity.

LasR:3-oxo-C12-HSL is the pheromone-bound formof the LasR receptor. It is the link between the QS systemand the QS-inducible genes and positively regulates lasIand in smaller amounts rhlI (7, 45), as well as thevirulence factors lasA, lasB, aprA, and toxA (see above).The positive feedback loop consisting of LasR:3-oxo-C12-HSL inducing LasI production, which in turn upregulates3-oxo-C12-HSL, represents a central switch mechanismin QS network control (20). Induction of rhlI by LasR:3-oxo-C12-HSL is one of the two major links between thelas and the rhl modules. The second link is LasR-mediated RhlR inhibition (7).

• The concentration range of the LasR:3-oxo-C12-HSLwas divided into 3 intervals (low, middle, and highconcentrations). LasR:3-oxo-C12-HSL concentrations cor-relate with the ones of LasR and 3-oxo-C12-HSL. TheLasR:3-oxo-C12-HSL concentration remains low if theconcentration of either LasR or 3-oxo-C12-HSL is low.At high LasR concentrations the LasR:3-oxo-C12-HSLconcentration follows the one of the pheromone.

RhlI is encoded by the rhlI gene, which shows signifi-cant sequence similarity with the P. aeruginosa lasI gene(47). The position of rhlI in the rhl QS network moduleis equivalent to that of the lasI gene in the las module.Disruption of the rhlI gene impairs synthesis of rham-nosyltransferase and the biosurfactant/hemolysin rham-

nolipid (47). The rhamnosyltransferase synthesis rate canbe restored by addition of N-butyryl-HSL (C4-HSL),whose synthase is encoded by the rhlI gene (47). The rhland the las modules need to be active for elastaseproduction, whereas the rhl module alone is sufficientfor rhamnolipid synthesis (47). The rhlI gene is mainlyregulated by the las module (via LasR:3-oxo-C12-HSL),by the PQS pheromone (see below), and to a lower extentby RhlR:C4-HSL (see below) (52).

• The RhlI concentration range was divided into twointervals (low and high concentrations). RhlI concentra-tion is expected to be high if either RhlR:C4-HSL or LasR:3-oxo-C12-HSL concentration is high or if both PQS andRhlR concentrations are high.

C4-HSL is a rhl module-specific diffusible pheromone(53) belonging to the family of the acylated homoserinelactone molecules. Its synthesis is controlled by RhlI (54,55). The intracellular C4-HSL concentration increases ina population-density-dependent manner. When the C4-HSL concentration exceeds a certain threshold, it bindsto the RhlR receptor. Binding of C4-HSL converts RhlRinto a transactivator, which induces expression/synthesisof a variety of virulence factors including rhamnolipids,pyocyanin, cyanide, and chitinase (47, 56), as well as rhlI.C4-HSL freely diffuses across membranes, and at thesteady-state concentration the intracellular and extra-cellular concentrations are identical (51).

• C4-HSL concentration range was divided into twointervals (low and high concentrations). In either case,it follows the concentration of its synthase RhlI.

RhlR is encoded by the rhlR gene, which exhibits basalexpression even in the absence of 3-oxo-C12-HSL and C4-HSL (7). When bound to C4-HSL, RhlR is a transcrip-tional activator for rhlI and a regulon also controlled byLasR:3-oxo-C12-HSL (47). Module-specific induction ofthe pheromone synthase gene by a cognate regulatorprotein is a common theme in QS regulatory networks(5, 57). Analogously to LasR, RhlR is a homologue of theV. fischeri LuxR protein, and its role in the rhl networkmodule is equivalent to the one of LasR in the las module(57). Synthesis of RhlR is mainly controlled by the lasmodule via LasR:3-oxo-C12-HSL (7) and by PQS (58).RhlR is up-regulated by PQS and required for PQS to beactive (8, 58).

• The concentration range of the RhlR receptor wasdivided into two intervals (low and high concentrations).The RhlR concentration is high if either the activatedform of LasR or PQS and RhlR are available at highconcentrations.

RhlR:C4-HSL is the pheromone-bound form of RhlR.RhlR competes with LasR for C4-HSL. RhlR:C4-HSLactivates several genes encoding virulence factors andcreates a positive feedback loop by inducing the C4-HSL-synthase-encoding gene rhlI.

• The concentration range of RhlR:C4-HSL was sub-divided into two intervals (low and high concentrations).This concentration reaches high levels if both RhlR andC4-HSL concentrations are high.

PQS is the only known QS pheromone that is not amember of the acylated HSL molecule family. PQSactivates the rhl module and, to a lower extent, the lasmodule. PQS requires LasR for synthesis and RhlR foractivity. The nature of PQS’s interaction with RhlR andother molecules remains elusive (8). PQS and C4-HSLwere shown to coinduce lasB (8). Furthermore, PQSstrongly induces rhlI and to a lower extent rhlR and lasR(58). PQS production starts in early stationary phase,reaches a maximum during the late stationary phase,and decreases subsequently (58). The presence of PQS-

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producing P. aeruginosa strains in the lungs of cysticfibrosis patients indicates optimal adaptation to thepathogen’s microenvironment (59).

• The concentration range of the recently discoveredPQS pheromone was set to either low or high levels. PQSconcentration increases if activated LasR and MvfRconcentrations are high. PQS always requires high RhlRconcentrations to become active in the QS system.

MvfR (multiple virulence factor regulator) is a mem-brane-associated protein that induces synthesis of elastase,phospholipase, 3-oxo-C12-HSL, and PQS (10). MvfR isencoded by the mvfR gene. mvfR regulation reachesmaximum levels at late exponential phase and is down-regulated by some of its target gene products. AlthoughMvfR’s relevance for the pathogenesis of P. aeruginosais well-established, its precise position within the QSnetwork remains elusive (10). MvfR is expected to providea redundant control system to ensure execution of QSprograms even following concentration fluctuations of theexternal pheromones.

• The concentration range of the regulatory proteinMvfR was divided into low and high levels. Typically,MvfR concentration was fixed at high levels to prevent anegative feedback loop, which results in non-naturaloscillations.

Vfr was found to be a major regulator of lasR (9). TheQS mechanism critically depends on the presence of Vrf,as it is needed for lasR expression (9).

• As the presence of Vfr is crucial for the functioningof the QS system, its level was supposed to be alwayshigh enough to allow lasR expression.

The aforementioned QS components were assembledinto a mathematical QS model, which is expected tocapture key features of the natural system: (i) stablestates of the network dynamics and (ii) relative timingof gene activation. A stable point of the dynamics is aset of QS component concentrations to which the systemrelaxes following small perturbations (60). Because inputdata were derived from experiments typically covering afew days, we expect model predictions to be valid withinthe same time frame.

Methods

The molecules included in the model were the twopheromones 3-oxo-C12-HSL and C4-HSL and their syn-thases LasI and RhlI, the receptor proteins LasR andRhlR, which are activated by the cognate pheromones,the recently discovered PQS, and the regulatory proteinsMvfR and Vfr. MvfR and Vfr actions were considered,but their concentrations were set at constant levels sincetheir critical interactions with the remainder of the QSnetwork remain elusive. For simplicity, gene transcrip-tion was never set as rate-limiting, so that changes intranscription are immediately converted into translation.A set of variables and thresholds define a set of qualita-tive states, which can be intuitively defined as regionsof the multidimensional concentration space where thebehavior of the system is qualitatively constant (33). Atransition between two qualitative states occurs when thevariables describing the system move from a qualitativestate to another one. The network dynamics is describedas a set of qualitative states and transitions betweenthem. As the model contains no time constants, resultingsimulations provide no quantitative information on net-work kinetics. Starting with an initial qualitative state,the simulation algorithm computes all reachable qualita-tive states and transitions on the basis of provided data.

The network is described as a set of piecewise lineardifferential equations, of the form

where

and

The variables xi correspond to protein concentrations,and fi describe the rates of protein concentration changesas a function of the protein concentrations and a set ofconstant parameters uj, 1 e j e m. Similarly to fi, girepresent the degradation rates of the concentrations xias a function of the concentrations xi and parameters uj.Both fi and gi are defined as linear combinations of stepfunctions sj:Rg0

n f {0,1} (33). Given a qualitative state xiand the parameters uj, the system tends toward anequilibrium state that is a solution of the set of dif-ferential equations

and namely

The values xit are called the system’s target equilibri-

um states for a given qualitative state and set ofparameters. The network interaction matrix is shown inFigure 2. The differential equations that describe thenetwork’s dynamics can be extracted from the interactionmatrix. For example, the equation describing the changein time of LasI concentration can be derived from the firsttwo rows of the matrix displayed in Figure 2. The firsttwo rows indicate that LasI concentration simply followsthe LasR:C12-HSL concentration. The correspondingdifferential equation is

where s+(x, y) ) 1 if x g y (x and y being a moleculeconcentration and a threshold concentration) and s+(x,y) ) 0 otherwise, k1,2 are the LasI synthesis rateconstants, g is its decay rate constant, and t1,2 are C12-HSL threshold concentrations. The target equilibriumstates are defined by means of inequalities involving rateconstants and threshold concentrations. For example, ift1 e [LasR:C12-HSL] e t2 (medium LasR:C12-HSL con-centration), the inequalities k1 > gθ1 and k1 < gθ2 definethe LasI target equilibrium concentration to lie betweenθ1 and θ2, where θ1 < θ2 are LasI threshold concentra-tions.

The simulations were performed using a publiclyavailable software tool called Genetic Network Analyzer(GNA) (33). GNA is written in the Java language andwas run on a G4-processor-based computer running the

dxbdt

fB(xb, ub) - g(xb, ub)xb

dxi

dt) fi(xb, ub) - gi(xb, ub)xi; xi > 0, 1 e i e n

xb ) (x1, ..., xn)′, ub ) (u1, ..., um)′, fB ) (f1, ..., fn),gb ) diag (g1, ..., gn)

dxbdt

) 0

xit )

fi(xb, ub)

gi(xb, ub)

d[LasI]dt

) k1s+([LasR:C12-HSL], t1) +

k2s+([LasR:C12-HSL], t2) - g[LasI]

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Mac OS X operating system (version 10.2.6) and the JavaVirtual Machine version 1.4.1_01.

ResultsMathematical models enable in silice experiments on

the QS gene network. The qualitative simulation methodwe used exploits the experimental information providedto calculate all allowed paths of the biochemical systemin the multidimensional molecule concentration space.The path the real system will take depends on the timeconstants, which are not included in the model. Far frombeing a limitation, the simulation algorithm we usegenerates the number and positions of the system’s stablestates independent of the time constants. The behaviorof the network can be explored by initializing it atdifferent component concentrations. Furthermore, thenetwork’s behavior can be observed and analyzed indifferent conditions. For example, when one or moreconcentrations are fixed at desired values or mutualinteractions of network components are modified. Sincedifferent conditions can be chosen to emulate the actionof therapeutic molecules and predict their impact on theQS network, simulations may speed up discovery of novelanti-infective drugs.

The QS network structure is not known in its entiretyand the magnitude of QS signal integration cannot yetbe unambiguously extracted from the available literature.When needed, in silice experiments can be repeated forseveral similar networks, each one approximating the

“real” network to a different extent. The results ofsimulations may often suggest which gaps in systemknowledge need to be filled and which experiments arerequired to eliminate existing ambiguities in the modelformulation. Reiterated coupling of simulation and ex-perimental readouts will likely render anti-infective drugdiscovery more efficient and speed up drug-functionanalysis. The P. aeruginosa QS network model presentedhere uses a specific algorithm to integrate qualitativenon-numerical component interaction functions and de-termine stable points of the network dynamics. Figure 3shows a graphical representation of the network simula-tion results. The QS system’s final state reflected by thediscrete concentration levels of all considered networkcomponents was simulated using the following initialstates:

Concentrations of all components are low. LasRand MvfR are constitutively expressed, resulting in highintracellular concentrations (LasR is positively regulatedby Vfr, which is supposed to be always present). LasI,3oxo-C12-HSL, and LasR:3-oxo-C12-HSL reach mediumconcentrations, MvfR a high concentration (Figure 3a).

LasR and MvfR concentrations are high, andthose of LasI, 3-oxo-C12HSL, and LasR:3-oxo-C12-

Figure 2. Matrix representation of QS network interactionsconsidered in the model. Discretized concentrations of eachcomponent are assigned to columns and rows of the matrix. Aninteraction symbol at the intersection of column i and row jindicates that component i at the indicated concentration isrequired for component j to reach the indicated equilibriumconcentration. A compound concentration is set low by defaultif no condition for medium and high levels is met. For thisreason, low concentrations are not represented. Interactionsymbols of the same kind in one row indicate the necessity forall (column) molecules to be present at the indicated concentra-tions. Different symbol sets in one row indicate alternative waysto result in the same equilibrium concentration. For example,the row corresponding to the protein RhlR indicates that highconcentration of this protein can either be obtained at highLasR:3-oxo-C12-HSL concentration or in the presence of highRhlR and PQS concentrations.

Figure 3. Schematic representation of QS network simulationresults. The first column indicates extracellular concentrationof the QS pheromone 3-oxo-C12-HSL, which is supposed to beproportional to the intracellular one. The extracellular 3-oxo-C12-HSL concentration is not affected by any model variable.The “start” column describes the state at which the biochemicalnetwork was initialized. The “stop” column indicates the steadystate reached by the network following the simulation. “Fixed”concentrations were kept constant throughout the simulation.Only a selected set of biologically relevant states were consid-ered. (a) The system was initialized to an all-low concentrationstate and relaxed to a stand-by state in which bacteria can reactto changes in the QS pheromone concentration; (b) The stand-by state is actually stable. (c) An over-threshold concentrationof QS 3-oxo-C12-HSL pheromone induces all QS-responsivegenes. (d) The fully activated state of the QS system is stablewith respect to a small decrease of the pheromone concentration.(e) The QS system locks in the stand-by state when the 3-oxo-C12-HSL pheromone concentration drops again to low levels.(f) If the RhlR concentration was fixed at a high value, the rhlmodule remained active when the 3-oxo-C12-HSL pheromoneconcentration became low. (g) Similarly to (f), the rhl moduleremained also active at low 3-oxo-C12-HSL pheromone concen-tration when PQS concentration is fixed at a high value. (h)When lasR was not upregulated (LasR fixed at a low value),the QS system was insensitive to the 3-oxo-C12-HSL phero-mone.

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HSL are medium. When initialized at these values thenetwork remains in the same state (Figure 3b), indicatingthat this network state is a stable point (attractor) of thenetwork dynamics. This stable network configurationcorresponds to a stand-by mode, which is characterizedby reduced pathogenicity resulting from downregulatedvirulence factors. Although P. aeruginosa appears aviru-lent, it produces the receptor protein LasR and releasesthe pheromone 3-oxo-C12-HSL. Intracellular accumula-tion of 3-oxo-C12-HSL in a population-density-dependentmanner will trigger the QS network beyond a certainthreshold pheromone concentration/population density.

The network is in stand-by mode, and the exter-nal 3-oxo-C12-HSL concentration is fixed beyondthreshold. The QS is triggered. The las module reachesthe active state and simultaneously activates the rhlmodule. High LasR concentration increases the synthesisrate of PQS, which requires high RhlR levels to be active.Eventually, the concentrations of all variables includedin the model become high (Figure 3c). In this state, theQS-controlled genes are up-regulated, including severalP. aeruginosa virulence factors.

All component concentrations are high whileextracellular 3-oxo-C12-HSL concentration is set toa medium level. The concentrations of all moleculesremain identical. This result shows that the QS switchingsystem is at least partially insensitive to fluctuations in3-oxo-C12-HSL concentration (Figure 3d). This phenom-enon is usually called hysteresis and occurs in nonlinearsystems (60). When a component’s concentration (in ourcase, 3-oxo-C12-HSL concentration) increases beyond athreshold (3-oxo-C12-HSL concentration must be high)the system’s state will change. However, following de-crease of the component’s concentration below threshold,the system is remains unaffected. A larger decrease ofthe parameter is necessary to restore the system’soriginal state (60). In the las module, hysteresis is causedby upregulation of lasI by LasR:3-oxoC12-HSL. The rhlmodule structure and dynamics are similar to those ofthe las module.

All concentrations are high, and the concentra-tion of external 3-oxo-C12-HSL is set to a low level.The system returns to stand-by mode (Figure 3e). QS-mediated gene expression is basal; bacteria quantify thepheromone concentration and remain ready to trigger theQS circuitry.

The simulation describes normal operation of the QSnetwork. The QS machinery is triggered by above-threshold concentration of 3-oxo-C12-HSL, which resultsin induction of QS-responsive genes and puts P. aerugi-nosa in a highly virulent state. Should the pheromoneconcentration decrease again well below threshold, thevirulence of this pathogen will decline consequently.

DiscussionAlthough the model can reproduce the global scope of

the QS network’s dynamics, it does not include fullcoverage of architecture, dynamics, and characteristics.Nonetheless, even in a situation where knowledge on QSregulatory networks remains incomplete, well-designedmodels may provide/confirm valuable information onbacterial quorum-sensing phenomena. This statementholds particularly true when the system’s dynamics isexplored under non-natural conditions including drug-impact and/or drug-function analyses. Here, models mayprovide important molecular insight and/or suggestcomplementary experiments. Every iteration integratingadditional knowledge into the model renders simulationsmore precise and reliable.

Crosstalk between QS regulatory networks of differentbacterial populations as well as interference of otherorganisms with QS systems is a generally accepted fact,which will lead the way for therapeutic interventions inQS signaling (4, 46, 61, 62). A paradigm of such inter-ference includes the Australian macroalga Deliseapulchra, which produces secondary metabolites of halo-genated furanone class. This class of halogenated fura-nones exhibits high structural homology to acylated HSLpheromones, which control many bacterial QS regulatorynetworks (62, 63). Also, several higher plants such assoybean, rice, tomato (62) and the pea (Pisum sativum(62, 64)) secrete substances that modulate the readoutof prokaryotic QS systems. Will plants represent a sourcefor next-generation non-antibiotic anti-infectives? Designand implementation of therapeutic interference with thebacterial QS system remains a major challenge. Theoverlapping role of QS chemical signals on differentbacteria is a key reason. Also, the same QS signal cantrigger various gene expression profiles in differentbacterial strains (62). The fact that some bacteria producereceptors for QS pheromones belonging to other speciesincreases the complexity of developing QS network-targeted drugs.

Examples of QS-disrupting strategies protecting anorganism from specific bacterial species are limited toplants. The halogenated furanones produced by themacroalga Delisea pulchra interfere with las-analoguemodules of HSL-driven QS regulatory networks (63, 65,66). The interference mechanism seems to involve de-stabilization of the QS receptor protein by heterologousQS analogues as exemplified by recent data about theinteraction of Delisea pulchra halogenated furanones andV. fischeri LuxR protein overproduced in E. coli. (67).Although high expectations are set with respect tointeractions at this level, the P. aeruginosa QS networkmay offer alternative targets.

Using a model to spot drug targets in QS regulatorynetworks and predict the impact of drug candidates willlikely bring QS-targeting anti-infectives into a clinicalreality. Naturally occurring gene regulatory networks areoften error tolerant but easy to attack (68). In any geneexpression network, the most vulnerable nodes aretypically those with the highest degree of interconnection.Visual inspection of Figure 1 reveals that LasR:3-oxo-C12-HSL represents the QS network node with thehighest signal integration potential, consisting of twoincoming and four outgoing connections. Interestingly,the halogenated furanones synthesized by the macroalgaDelisea pulchra affect this part of the generic QS net-work. 3-oxo-C12-HSL analogues are not exclusive waysto interfere with LasR activity. Bacteria of the Bacillusspecies and the soil bacterium Variovorax paradoxusevolved enzymes inactivating HSLs (69). Interfering withQS networks at this level can be considered an effectiveway of preventing bacterial colonization yet may be lesssuccessful once the QS mechanism is in full operation.Let us suppose that the RhlR concentration can be fixedat high levels, independent of LasR:3-oxo-C12-HSL avail-ability, once the QS network has been triggered by anabove-threshold concentration of 3-oxo-C12-HSL. If the3-oxo-C12-HSL concentration is reduced to the minimumin this scenario, the rhl module remains in operation evenafter the las module has become inactive (see Figure 3f).The position of PQS in the QS network is between thelas and the rhl modules (58). High PQS concentrationcan be sufficient to upregulate rhlR independent of LasR:3-oxo-C12-HSL (Figure 1). PQS requires an active lasmodule for synthesis and an active rhl module to become

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active (8). In vitro experiments substantiated that PQSproduction is initiated at the end of log phase anddeclines after 2 days (58). PQS production profiles duringinfection may be radically different. Following airwaysinfection of cystic fibrosis patients, P. aeruginosa pro-duces increased PQS levels (59, 70). This fact suggestsP. aeruginosa adapts expression levels of critical genesin response to microenvironmental changes. In our model,PQS synthesis requires high LasR:3-oxo-C12-HSL levels.During colonization of cystic fibrosis patients’ airways,other proteins may substitute LasR:3-oxo-C12-HSL forupregulation of PQS. In such a scenario, PQS synthesiswould become independent of LasR levels. If PQS levelsremain fixed at a high level, simulations suggest the lasmodule be switched off at external below-threshold 3-oxo-C12-HSL levels but not the rhl one, which can continueto induce production of several virulence factors (57, 58)(Figure 3g). Therefore, PQS was recognized as a possibletarget for pharmaceutical treatment of P. aeruginosainfections (8). Inhibition of PQS production was indeedshown to reduce the virulence of this pathogen (71).

In our model, Vfr levels are considered to always besufficient for production of LasR, even if this only occursin the second half of the log-phase (9). Because of its keyrole in LasR production, Vfr may be considered a primetarget for pharmacologic intervention. Our simulationsconfirm that failure of Vfr to induce lasR expression willprevent the onset of QS-dependent regulation even athigh 3-oxo-C12-HSL concentrations (Figure 3h). AlsoMvfR, which positively regulates 3-oxo-C12-HSL andPQS synthesis as well as several other virulence factors,may be a drug target to consider in the not-too-distantfuture (10).

Conclusions

We have employed qualitative methods to formalizepart of the P. aeruginosa QS biochemical network. Thesimulated network dynamics is in agreement with ex-perimental results. Qualitative modeling represents avalid method for integrating biological information.Inspection of the QS biochemical network structure andsimulation of its dynamics can indicate alternative waysto interfere with the QS system in an efficient and specificway. Drug action can be optimized to minimize thedosage, secondary effects on collateral biochemical net-works or maximize the specificity for a bacterial speciesor strain.

Acknowledgment

We thank Beat P. Kramer for critical comments on themanuscript. This work was supported by the SwissNational Science Foundation (grant 631-065946) and theNovartis Foundation.

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Accepted for publication March 4, 2004.

BP034323L

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