61978-1-4799-5296-0/14/$31.00 © 2014 IEEE

PROC. 29th INTERNATIONAL CONFERENCE ON MICROELECTRONICS (MIEL 2014), BELGRADE, SERBIA, 12-14 MAY, 2014

Biological Circuits for Signaling and Synchronization in Bacterial Populations

Paul Isaac Hagouel and Ioannis G. Karafyllidis

Abstract - To coordinate their behavior and virulence and to synchronize attacks against their hosts, bacteria communicate by producing and detecting signaling molecules (autoinducers). This communication is controlled by biological circuits called quorum sensing circuits. Recently quorum sensing circuits have been recognized as an alternative target for controlling bacterial virulence and infections without the use of antibiotics. Here we model the quorum sensing process as a state transition graph. Based on this model we develop a simulation tool for the quorum sensing process in open and confined spaces. We perform a number of numerical experiments with various strategies of quorum sensing circuit regulation and we study the effectiveness of quorum sensing inhibitors. We also use network graph theory to model the complete quorum sensing system of Pseudomonas aeruginosa and construct its state space, which turned out to be very large, hierarchical, modular and scale-free.

I. INTRODUCTION

Most bacteria species regulate various functions and especially gene expression in order to synchronize their behavior. To obtain this synchronization they use a signaling process which involves producing and secreting signaling molecules, called autoinducers [1]. These molecules diffuse into the environment and their concentration depends on the density of the bacterial population. Bacteria use a sensing circuit to estimate the autoinducer concentration and, therefore, the density of the bacteria population. When this density exceeds a threshold level, i.e. a critical concentration, bacteria obtain the information that their concentration is large enough to overwhelm host defenses. In this case, a sensing circuit activates the transcription of certain genes in all bacteria and a “quorum” is formed [2]. The bacteria in this quorum produce and secrete into their environment molecules, called exofactors, which usually are virulence factors that break down host macromolecules into a form suitable for uptake. This process of signaling, information gathering and reaction synchronization is called quorum sensing (QS) [3, 4]. QS was first observed in the expression of bioluminescence in the symbiotic system of Vibrio fischeri and Vibrio harveyi [5, 6]. Since then QS signaling circuits

were discovered in both Gram-positive and Cram-negative bacteria. Among others Pseudomonas aeruginosa, Vibrio cholerae, Bacillus subtilis, Streptococcus pneumoniae and Staphylococcus aureus use QS processes to control and synchronize their gene expression [7, 8]. QS signaling circuits have been recognized as targets for a new generation of antimicrobial drugs that can control infection virulence [9-12].

Here the QS process is modeled as a state transition graph with transitions depending on the diffusion and local concentration of the QS molecules (autoinducers). Based on this model a simulation tool has been developed to simulate the QS process in both open and confined spaces. Using this simulation tool a number of numerical experiments has been carried out with various strategies of QS circuit regulation. The results of these experiments showed that regulation of the QS signaling circuit can lead to significantly reduced bacterial virulence. The model and the simulation tool presented here can be used to facilitate the design of new antimicrobial drugs.

We also use Boolean networks to model the complete QS system of Pseudomonas aeruginosa (P. aeruginosa). The state space of the QS system is constructed and it turned out to be very large, hierarchical, modular and scale-free. The model and tools we developed will give to life scientists a deeper insight to the complex QS system.

II. THE QUORUM SENSING SIGNALING CIRCUIT

Various bacteria have developed different QS circuits. Most Gram-negative bacteria secrete acylated-homoserine lactone (HSL) molecules which are used as autoinducers. The circuit is controlled by two regulatory proteins the LuxI and LuxR and is known as the LuxI/LuxR autoinduction system. LuxI is an autoinducer synthase which produces the HSL signaling molecules that are secreted through the bacterial membrane into the surrounding environment. When a critical concentration of HSL is reached these molecules are transported from the environment into the bacteria through their membranes and bound to LuxR proteins. After that, the LuxR-HSL complex activates the transcription of genes, producing thus exofactors such as host cell wall degrading enzymes, which are secreted into the surrounding environment and cause the degradation of host cells so that the bacteria can uptake nutrients [1-3].

P. I. Hagouel is with Optelec, 11 Chrysostomou Smyrnis Street, GR–54622 Thessaloniki, GREECE, E–mail: hagouel@eecs.berkeley.edu

I. G. Karafyllidis is with the Department of Electrical and Computer Engineering, Democritus University of Thrace, 67100 Xanthi, GREECE, E-mail: ykar@ee.duth.gr

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Gram-positive bacteria use oligopeptides as autoinducers which are processed and exported by ABC proteins. As in the case of Gram-negative bacteria, the autoinducer molecules are secreted into the environment and the critical concentration is detected by sensor kinase proteins which activate a two-component phosphorylation cascade, which in turn activates the transcription of target genes and exofactors are produced [2].

Fig. 1. Schematic representation of the quorum sensing system.

The autoinducer production/processing (AP) and autoinducer sensing (AS) circuits are represented as a (yellow) ellipse and a (brown) rectangle respectively. The autoinducer molecules are represented as (blue) circles and the exofactor molecules as (red) stars.

Fig. 2. The structure of the QS signaling circuit. Although different bacteria use different proteins and

molecules for their autoinduction production and sensing circuits, their QS signalling systems have the same structure which is depicted in Figure 1. Each bacterium produces autoinducer molecules using an autoinducer production/processing (AP) circuit which is represented as an ellipse. The autoinducer molecules, represented as

circles, are secreted into the surrounding environment. The critical concentration is sensed by an autoinducer sensing (AS) circuit, represented as a rectangle, and the target genes are activated. The transcription of these genes results in exofactor production. The exofactors, represented as stars are secreted into the surrounding environment [1].

The structure of the QS signaling circuit is shown in Fig. 2. When the signal production gene gI is expressed the protein PI is produced. PI produces the autoinduction signaling molecule A, which is secreted into the environ-ment. In the environment there exist a number of autoin-ducer molecules, the concentration of which reflects the size of the bacterial population. Autoinducer molecules, A, enter the bacterial cell and bind to the signal response protein PR, which is produced by the gene gR, forming an active complex, PR+. PR+ regulates a number of genes some of which produce exofactors. PR+ also binds to the promoter region of the signal synthase gene gI closing the autoinduction loop of the circuit.

III. MODELING AND SIMULATION OF THE

SIGNALING PROCESS

In order to achieve an effective synchronised behaviour, such as an attack against the cells of their host, bacteria must produce and secrete exofactors simultaneously. This is the only way to reach exofactor concentrations that will be effective against their hosts. But exofactors are very expensive to synthesise and bacteria must know if their concentration is large enough before starting exofactor production. To achieve this, bacteria use smaller molecules, the autoinducers, the production of which is significantly less expensive than exofactors. Bacteria produce and secrete into their environment autoinducer molecules and in the same time they continuously monitor the autoinducer concentration in their environment. The autoinducer concentration is related directly to the concentration of bacteria. This way bacteria sense the presence and the number of other bacteria in their neighborhood. In many bacteria species, when the autoinducer concentration becomes larger that a threshold value the autoinducer production rate is increased. When the autoinducer concentration reaches the critical value, all bacteria which sense this increased concentration in their neighborhood form a quorum and start to produce and secrete exofactors.

Bacteria in a QS signaling process can be found in three states. In the normal state, in which they produce and secrete autoinducers in a small constant rate, in the autoinduced state which is reached when autoinducer concentration is larger that a threshold value, in which they produce and secrete autoinducers in a larger constant rate and in the quorum state which is reached when autoinducer concentration becomes larger that the critical value, in which they produce and secrete exofactors. Exofactor production is expensive and bacteria produce exofactors for a limited time. In the neighborhood of bacteria clusters or

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in confined spaces the concentration of autoinducers may exceed the critical value only in small areas resulting in a small number of exofactor producing bacteria and, therefore, to an ineffective attack [2]. In this case after the exofactor production time period bacteria state is changed to normal if the autoinducer concentration is smaller that the first threshold or to autoinduced if the autoinducer concentration is greater that the first threshold. The states and the transitions between them are shown in Figure 3.

Fig. 3. Bacteria state transition graph. Bacteria states are represented as ellipses. ThA is the first autoinducer concentration threshold, ThE is the critical threshold for exofactor production and Tep is the time period during which bacteria produce exofactors.

In Figure 3 bacteria states are represented as ellipses.

ThA is the first autoinducer concentration threshold. When this concentration is reached, bacterium state changes from normal to autoinduced. ThE is the critical threshold for transition from the autoinduced to quorum state in which exofactors are produced for a time period equal to Tep. After this time the state changes to normal or to autoinduced depending on the autoinducer concentration around the bacterium. In the case of a bacteria species in which there is no difference between normal and autoinduced states, i.e. there is only one autoinducer production rate, the state transition model can be adjusted by just setting ThA = ThE.

The transitions between states depend on the local autoinducer concentration. The spatial distribution of bacteria is not homogeneous and, therefore, the autoinducer concentration is not uniform throughout the space of interest. Furthermore, in most cases the space is confined by walls that are impenetrable for autoinducer molecules.

In this case autoinducer concentration varies significantly and it is possible to reach ThA or ThE in parts of the space while in other parts the concentration is smaller than ThA.

The autoinducer concentration is a solution of the diffusion equation in which the bacteria are modeled as autoinducer sources:

( ) ( ) ( ) ( ) ( )tyxaybxbR

ytyxa

xtyxaD

ttyxa

A ,,,,,,,,,2

2

2

2

⋅+

∂

∂+

∂∂

=∂

∂

(1) where a(x,y,t) is the autoinducer concentration at the point with coordinates (x,y) at time t and DA is the diffusivity (or diffusion coefficient) of autoinducer molecules. (xb,yb) are the coordinates of points where bacteria exist. R(xb,yb) is the autoinducer production rate and is zero in all points where a bacterium does not exist. Therefore, the second term in the right side of (1) is nonzero only at points occupied by bacteria. R(xb,yb) can take three values:

( )

=

State dAutoinducein bacteriun aby occupied is yb)(xb,point if,

State Normalin bacteriun aby occupied is yb)(xb,point if,

bacterium aby occupiednot is yb)(xb,point if,0

,

A

N

R

RybxbR

(2)

where RA and RN are the autoinducer production rates at normal and autoinduced states respectively, with RA ≥ RN. RA is set equal to RN in the case of a bacteria species in which there is no difference between normal and autoinduced states. The geometry of the space in which bacteria exist is entered as a set of boundary conditions for equation (1). In the case where the space is confined by (host tissue) walls that are impenetrable for autoinducer molecules, the boundary condition at these walls is:

( ) ( ) 0,,,,=

∂∂

=∂

∂y

tyxax

tyxa (3)

In boundaries through which autoinducer molecules

can diffuse the boundary condition is:

( ) ( ) ry

tyxax

tyxa=

∂∂

=∂

∂ ,,,, (4)

where r is a constant.

Based on the model described previously a simulation tool has been developed. The user of this tool can select to simulate the QS process in open or confined spaces. In the case of confined spaces the user can draw or import the shape of the impenetrable boundaries. Bacteria position coordinates are generated using a random number generator. This way an inhomogeneous bacteria distribution is obtained. The user can determine the approximate number of bacteria that will occupy the simulation space.

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The units in the simulation were chosen so that the diffusion coefficient is equal to one. The simulation tool produces as outputs the distribution of autoinducer concentration, the contour plot of the two isolines where the autoinducer concentrations are equal to ThA and ThE and the number of bacteria in autoinduced and quorum states as a function of time.

Figure 4 shows simulation results for the case of bacteria in open space. Figure 4(a) shows the bacteria positions. Bacteria are represented as circles. Figure 4(b) shows the distribution of the normalized autoinducer concentration and Figure 4(c) the two isolines where the autoinducer concentrations are equal to ThA and ThE. Bacteria included in the contour of the ThA isoline are in the autoiduced state and bacteria included in the contour of the ThE isoline are in the quorum state. The maximum (normalized) autoinducer concentration is 1 and the thresholds ThA and ThE were set equal to 0.3 and 0.5. Figure 4(d) shows the time variation of the number of bacteria in autoinduced and quorum states. Line A (red) represents bacteria in quorum state and line B (blue) bacteria in autoinduced state.

Figure 5 shows the simulation results for the same bacteria distribution in confined space. The impenetrable wall is represented by a black solid line. Figures 5(b) and 5(c) show the distribution of the autoinducer concentration and the two isolines where the autoinducer concentrations are equal to ThA and ThE at the same time as in Figures 4(b) and 4(c). As expected, in confined space the quorum state is reached faster and by an increased number of bacteria (Figure 5(d)). Again, line A (red) represents bacteria in quorum state and line B (blue) bacteria in autoinduced state.

The simulation tool described in the previous section was used to analyze in silico the QS signaling process by conducting a number of numerical experiments. Regulation of the QS signaling circuit can be obtained using autoinducer blockers or inhibitors. It is supposed that these inhibitors are uniformly distributed in the area occupied by bacteria. Figure 6 shows results of numerical experiments for the bacteria distribution shown in Figure 4(a). Autoinducer inhibitors are diffused into the space occupied by the bacteria population starting at time step 3000 and stopping at time step 4000. The autoinducer inhibitor concentration in the case of Figure 6(a) is 20% smaller than the concentration in the case of Figure 6(b). In both cases, during the time of inhibitor action, the number of bacteria in quorum state is reduced and the number of bacteria in autoinduced state is increased. Soon after the inhibitor action is stopped the number of bacteria in quorum state increases and reaches a number which is 10% and 25% less than the number in Figure 4(d), for the cases of Figures 6(a) and (b), respectively. These experiments with varying autoinducer inhibitor concentrations showed that inhibition of the QS process for one time period only, results in reduction of the number of bacteria in quorum states. This reduction becomes more significant as the concentration of

the inhibitor is increased. Since the number of bacteria in quorum state is directly related to exofactor concentration and to infection virulence, the use of inhibitors even for one time only can reduce the virulence.

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Fig. 6. Results of numerical experiments for the bacteria distribution shown in Figure 4(a). Line A (red) represents bacteria in quorum state and line B (blue) bacteria in autoinduced state.

Figure 7 shows results of numerical experiments for the bacteria distribution shown in Figure 4(a) in which autoinducer inhibitors are used periodically. Autoinducer inhibitors were used from time step 2000 to 2500, from time step 3000 to 3500 and from time step 4000 to 4500. Again, the autoinducer inhibitor concentration in the case of Figure 7(a) is 20% smaller than the concentration in the case of Figure 7(b). Periodic use of inhibitors reduces significantly the number of bacteria in the quorum state, but results in increased number of bacteria in autoinduced state. These bacteria as soon as the action of the inhibitor stops, drive themselves and the bacteria in their neighborhood in the quorum state again. The number of bacteria in quorum state fluctuates but their final number is

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25% and 45% less than the number in Figure 4(d), for the cases of Figures 7(a) and (b), respectively.

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Numerical experiments have shown that QS signaling

can not be silenced, because each time autoinducer inhibitors are used and the number of bacteria in quorum state is reduced, the system reacts by increasing the number of bacteria in autoinduced state. As soon as the inhibitor action stops, these autoinduced bacteria drive themselves and the bacteria in their neighborhood in the quorum state again. On the other hand, the numerical experiments showed that the use of autoinducer inhibitors and especially the periodic use of higher inhibitor concentrations can reduce significantly bacterial virulence.

IV. PSEUDOMONAS AERUGINOSA QUORUM

SENSING CIRCUITS

There are three known distinct QS circuits in P. aerugi-nosa. Two of the circuits, named las and rhl, use the

LuxR regulatory proteins LasR and RhlR, respectively, and two AHL autoinducers. The third, named pqs, uses a LysR-type regulatory protein, PqsR (also known as MvfR) and a PQS autoinducer [13, 14]. The las and rhl circuits regulate more that 10% of the P. aeruginosa genome and microarray data showed that there are genes that respond to only one of the AHL autoinducers, genes that respond to either autoinducer, performing thus a logical OR operation and genes that require both autoinducers simultaneously, performing thus a logical AND operation [13, 14].

The most important known parts of the P. aeruginosa QS circuits and the most important known interconnections between them are shown in Figure 8. In this Figure the parts that belong to the las QS circuit are coloured green, the parts of the rhl circuit are coloured blue and the parts of the pqs circuit yellow. The arrow-headed edges present a positive interaction and the T-headed edges a negative interaction.

Fig. 8. The P. aeruginosa QS system. The parts of the las QS

circuit are colored green, the parts of the rhl circuit are colored blue and the parts of the pqs circuit, yellow.

The dynamic behavior of the QS system can be

analyzed by modeling it as a Boolean network and constructing its state space. The state space of a Boolean network comprises nodes and edges. Each node represents a possible state of the network in binary form. For example, a possible state of the P. aeruginosa QS system is: lasR=1, LasR=1, lasI=0, LasI=0, LasR+=1, …, PqsR=1, Pqsr+=1. This state is represented by a node which is labeled with the binary number 11001…11. There are 31 nodes, including the inputs, in the QS Boolean network, each of which may be in state 1 or in state 0, therefore the possible states for the QS system are 231= 2,147,483,648. This is the number of nodes of the state space. Two nodes in the state space are connected with an edge, if the QS system can change its state from the state corresponding to one of the nodes to the state corresponding to the other node. Therefore the state space structure describes the dynamics of transition from one state to another. The state space also

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provides the information about the states that can or cannot be reached from the present state of the system.

Fig. 9. The spate space of the las QS circuit.

Fig. 10. The spate space of the rhl QS circuit.

Fig. 11. The spate space of the pqs QS circuit.

The state space can be analyzed using network techniques such as statistical or spectral analysis [15, 16].

Although the analysis of the state space is beyond the scope of this work, the form and structure of the space may provide valuable information about the dynamic operation of the system. A state space of about two million nodes is very large and its graphic representation is too dense to be of any practical use.

Fig. 12. The QS system with the three QS circuits as blocks.

(a)

(b)

Fig. 13. (a) The spate space of the QS system.

(b) Magnification of the area in the dashed ellipse.

For this reason we constructed the state space of each circuit separately and then we constructed the system’s state space using a block representation of the QS circuits as will be explained later on. The spate spaces of the las, rhl and pqs QS circuits are shown in Figures 9, 10 and 11, respectively. The las and rhl networks are both scale free. There are no attractors that if deactivated would disrupt the

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function of these circuits. There are also no nodes with high centrality. This structure is a strong indication of versatility and adaptation. The las state space which is on top of the QS hierarchy is the most complex one and has only a few unreachable nodes. The pqs state space is modular. Modularity in biological networks is a strong indication of robustness and evolvability [15].

To construct the state space of the QS system we represented the three QS circuits with blocks, as shown in Figure 12. The state space of the block-formed QS system is shown in Figure 13(a). Figure 13(b) shows in magnification the part of the state space included in the dashed ellipse. Each node of this QS system state space includes the three networks of the QS circuits. The system state space is highly modular. Modules in biological networks arise from separated state compartments that act as buffers against mutations and a modular structure is known to facilitate variation.

The state space of the QS system is hierarchical, scale free and modular. The system is dominated by the most complex circuit, the las. Two scale free circuits the las and the rhl are parallel and are connected in series with a modular circuit, the pqs. The structure of the P. aeruginosa state space revealed a robust, adaptable and versatile organism.

V. CONCLUSIONS

We presented a model for the QS process based on a state transition graph where the transitions between states depend on the diffusion and local concentration of autoinducers. The local autoinducer concentration is calculated by solving numerically the two-dimensional diffusion equation with bacteria as distributed sources. The geometry of the environment is entered as a set of boundary conditions. Based on this model, a simulation tool has been developed and presented. Simulation results for bacteria populations in free and confined spaces were also presented. Using this simulation tool a number of numerical experiments has been carried out with various strategies of quorum sensing circuit regulation. Numerical experiments have shown that the use of autoinducer inhibitors and especially the periodic use of high inhibitor concentrations can reduce significantly bacterial virulence. We constructed the state space of the QS system which turned out to be very large, hierarchical, modular and scale free. This state space has been shaped by evolution and gives the bacterium robustness, versatility and adaptability that enable it to survive and infect a variety of hosts. We also developed a gene knock-out simulation tool, which allows the study of the QS system operation when some of the genes do not operate. This tool can be used to study P. aeruginosa QS system gene mutations that cause bacteria to be signal-blind or signal-negative. Our work added nothing new to the biochemistry of the P. aeruginosa QS system, but we believe that the model and simulation tools we developed will help life scientists to better understand this complex QS system.

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