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CCS THE UNIVERSITY OF NEW SOUTH WALES Thesis/Dissertation Sheet

Surname or Family name: Fagerlind

First name: Magnus Other name/s: Gert

Abbreviation for degree as given in the University calendar: PhD

School: The School of Biotechnology and Biomolecular Sciences Faculty: science The Centre for Marine Bio-Innovation

Title: Mathematical modelling of bacterial quorum sensing and biofilm formation

Abstract To date, bacterial resistance to antibiotics is an increasing problem and there is a growing appreciation that biofilm formation is a significant contributor to antibiotic resistance. This has led to increased research on ways to reduce/control biofilm formation. One such target is bacterial cell-cell communication that allows bacteria to co- ordinate gene expression, and that has been shown to be involved in biofilm formation and production of virulence factors. By interfering with this communication system it should be possible to control gene expression and thus inhibit production of virulence factors as well as the formation of biofilms. However, these processes are multi- factorial, which make it a very complicated task to experimentally identify key parameters that subsequently could guide the development of cell-cell communication strategies to control bacterial virulence and biofilm formation. However, by using mathematical modelling, it is possible to study complex processes and to identify those parameters that are most important for these processes.

The focus of this thesis was to develop mathematical models of bacterial cell-cell communication systems and biofilm formation to identify key parameters that could subsequently guide the development of cell-cell communication strategies to control bacterial virulence and biofilm formation.

It was found that the cell-cell communication system in the model bacterium Pseudomonas aeruginosa works by hysteretic switching between two stable steady states, reflecting low and high rates of signal production, respectively. It was also shown that this bacterium uses different regulators to adjust the cell density required for switching the system on or off. Moreover, it was also demonstrated that signal antagonists have the capacity to switch the system from an induced state to the lower, uninduced state. However, it was also shown that this blocking behaviour is extremely dependent on the properties of the AHL antagonists, since even very small differences could greatly affect the outcome. Finally, accumulation of damage was predicted to be the main cause of cell death during the formation of biofilms. In addition, a strong relationship between nutrient availability and damage accumulation (and consequently cell death) was also found.

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Date Mathematical modelling of bacterial quorum sensing and biofílm formation

Magnus Fagerlind

A thesis submitted in fulfilment of the requirements for the degree of

Doctor of Philosophy

School of Biotechnology and Biomolecular Sciences Faculty of Science The University of New South Wales Sydney, Australia

August 2008 Table of Contents

Table of Contents ü Acknowledgements v Abstract vii List of Publications x List of Figures xi List of Tables xvi Chapter 1. Quorum sensing dynamics and bioHlm formation: a literature review 1 1.1. Introduction 1 1.2. Pseudomonas aeruginosa 3 1.3. Quorum sensing 4 1.4. Pseudomonas aeruginosa and quorum sensing 9 1.5. Inhibition of quorum sensing 12 1.6. Biofilms 14 1.7. Biofilms and quorum sensing 19 1.8. Modelling of quorum sensing 21 1.9. Biofilm modelling 26 1.10. Why mathematical modelling? 31 1.11. Aims of the thesis 32 1.11.1. ModelHng of quorum sensing 32 1.11.2. Biofilm modelling 33 Chapter 2. The role of regulators in the expression of quorum sensing signals in Pseudomonas aeruginosa 35 2.1. Introduction 35 2.2. Model theory 40 2.2.1. R-protein/AHL complexes 41 2.2.2. LasR 41 2.2.3. RhlR 42 2.2.4. RsaL 43 2.2.5. 30-C12-HSL 43 2.2.6. C4-HSL 44 2.2.7. Steady State and Stability Analysis 45 2.3. Results 48 2.3.1. Quorum sensing dynamics 48 2.3.2. Influence of RhlR/30-C12-HSL complex formation on the activation of the rhl system 49 2.3.3. The role of RsaL as an inhibitor 52 2.3.4. Vfr as a modulator of quorum sensing 54 2.3.5. Signal production by Pseudomonas aeruginosa 59 2.4. Discussion 63 2.5. Experimental procedure 69 2.5.1. Bacteria, media and growth conditions 69 2.5.2. Collection of signal-containing supematants 69 Ill

2.5.3. Determination of AHL concentration from Pseudomonas aeruginosa. 70 Chapter 3. Modelling the effect of acylated homoserine lactone antagonists in Pseudomonas aeruginosa 71 3.1. Introduction 71 3.2. Model theory 77 3.2.1. R-protein/AHL complexes 81 3.2.2. Simplifying assumptions 82 3.2.3. LasR 83 3.2.4. RhlR 84 3.2.5. RsaL 84 3.2.6. Intracellular 30-C12-HSL 84 3.2.7. Extracellular 30-C12-HSL 85 3.2.8. Intracellular C4-HSL 85 3.2.9. Extracellular C4-HSL 86 3.2.10. Extracellular 30-C12-HSL antagonist 86 3.2.11. Intracellular 30-C12-HSL antagonist 86 3.3. Results 89 3.3.1. Effect of increasing affinity between LasR and the 30-C12-HSL antagonist 89 3.3.2. Effect of increasing 30-C 12-HSL antagonist induced degradation of LasR 91 3.4. Discussion 94 Chapter 4. Modelling the effect of cell death in the formation of microbial biofilms 100 4.1. Introduction 100 4.2. Model theory 105 4.2.1. Simulation domain 105 4.2.2. Substrate diffusion and reaction 106 4.2.3. Damage production 108 4.2.4. Cellular automata rules 108 4.2.5. Parameter values 112 4.2.6. Model simulation 112 4.3. Results 115 4.3.1. Death rule 1 - bacteria die if they have been in stationary phase for a specific number of hours 115 4.3.2. Death rule 2 - bacteria die as a function of the ratio between biomass formation and endogenous metabolism 119 4.3.3. Death rule 3 - bacteria "die" as a function of damage accumulation... 123 4.3.4. Influence of substrate concentration on cell death within laboratory experimental biofilms 129 4.4. Discussion 131 4.4.1. Death rule 1 - bacteria die if they have been in stationary phase for a specific number of hours 131 4.4.2. Death rule 2 - bacteria die as a function of the ratio between biomass formation and endogenous metabolism 133 4.4.3. Death rule 3 - bacteria "die" as a function of damage accumulation... 135 4.4.4. Differences and similarities between the outcomes of the three tested death rules 137 4.4.5. Comparisons of cell death in the modelling system and within laboratory experimental biofilms 138 4.5. Laboratory experimental biofilms 140 Chapter 5. Summary and general discussion 141 5.1. Summary of results 141 5.2. QS dynamics and regulation 143 5.3. Inhibition of QS 148 5.4. Biofihns 152 5.5. Cell death during biofilm development 154 References 161 Acknowledgements

There are many people who have guided and supported me throughout my PhD studies.

Thanks to Prof Staffan Kjelleberg, my main supervisor, for giving me the opportunity to work experimentally in his laboratory, for his support and help when writing my papers and thesis.

Thanks to Dr Scott Rice, my co-supervisor, for biological expertise, support, guidance and help when writing my papers and thesis.

Thanks to Dr Patrie Nilsson, my co-supervisor, who made the whole project possible, helped me with international contacts and writing of my papers.

Thanks to Dr Mikael Harién, my cD-supervisor, for sharing his mathematical expertise and for critical reading of the mathematical parts of my papers.

Thanks to Dr Jeremy Webb, for providing the experimental data on cell death in biofilms at two carbon concentrations, general discussions and for critical reading of manuscripts.

Thanks to my colleagues Andreas and Simon L, for fruitful discussions and help with

C++ programming.

To all other colleagues at University of Skovde, especially the Molecular biology group, for friendship and the supportive and positive atmosphere you all are a part of. Thanks to Julie and Adam, who helped me with accommodation and other matters

during my stays in Australia.

Thanks to all other members of CMBB that have been involved in my project; Tim,

Sally, Nic, Carsten and Diane (for fruitful discussions and help when writing the

papers).

Finally, many thanks to my wife Pernilla, mother of my two children Fanny and Tova,

for great support and patience during my studies. Vll

Abstract

Bacteria, both in natural and pathogenic settings, are found mainly within surface associated cell assemblages, or biofilms. To date, bacterial resistance to antibiotics is an increasing problem and there is a growing appreciation that biofilm formation is a significant contributor to antibiotic resistance. Biofilms are currently considered as a significant medical problem and according to a public announcement from the US

National Institute of Health, more than 80 % of all microbial infections involve biofilms. This has led to increased research on ways to reduce/control biofilm formation and resistance. One such target is bacterial cell-cell communication that allows bacteria to co-ordinate gene expression, and that has been shown to be involved in biofilm formation and production of virulence factors. By interfering with this communication system it should be possible to control gene expression and thus inhibit production of virulence factors as well as the formation of biofilms. To date, most studies of inhibition of bacterial cell-cell communication have been based on empirical approaches, and have not taken advantage of theoretical guidance to identify key parameters that are essential for the regulation of biofilm formation or cell-cell communication based gene expression. This may be due to the fact that bacterial communication and biofilm formation are multi-factorial processes and may involve multiple regulatory circuits, sensitivity to growth conditions etc. This makes it difficult to predict which of these processes and parameters will be they key parameters involved in the inhibition of cell- cell communication and to do so by relying solely on experimental approaches may be intractable due to this complexity. Therefore, such studies can benefit from mathematical modelling. By using mathematical modelling, it is possible to study complex systems, such as bacterial cell-cell communication and biofilm formation, and to identify those processes and parameters that are most important for these systems. vili

Therefore, the focus of this thesis was to develop mathematical models of bacterial cell- cell communication systems and biofilm formation to identify key parameters that could subsequently guide the development of strategies to control bacterial virulence and biofilm formation based on the inhibition of cell-cell communication. Because of its wide distribution, relevance to a broad range of infections, use of cell-cell communication to control production of virulence factors as well as biofilm formation, Pseudomonas aeruginosa served as a model bacterium for the studies.

Analysis of the mathematical model systems revealed that the cell-cell communication system in P. aeruginosa displayed hysteresis based dynamic behaviour, i.e. the system has two stable steady states (reflecting low and high rates of signal production, respectively) separated by an unstable steady-state and that signal production switches on at a higher concentration of signals (reflecting a high population density or population growth in a diffusion limited environment) than at which it switches off. It was further shown that this bacterium uses different regulators to adjust the cell density required for switching the system on or off (presumably as a response to different environmental influences). Further, it was also demonstrated that signal antagonists have the capacity to switch the system from an induced state to the lower, uninduced state. However, it was also shown that this blocking behaviour was extremely dependent on the parameter values used, since even very small differences greatly affect the outcome. Most notably, it was shown that the ability of the signal antagonist to mediate degradation of the receptor protein was a core parameter for successful inhibition of the cell-cell communication system. Finally, accumulation of damage within developing biofilm microcolonies was predicted to be the main cause of cell death during the formation of microbial biofilms. Moreover, a strong relationship between nutrient availability and cell death was also found, as lower bulk phase nutrient concentrations resulted in more and/or earlier cell death during biofilm development, presumably due to the accumulation of higher amounts of damage. This latter finding was supported by in vitro studies of biofilm formation, which demonstrated that biofilms grown in the presence of lower glucose concentrations showed greater cell death than biofilms grown at higher concentrations. List of Publications

Peer review

Fagerlind MG, Rice SA, Nilsson P, Harlen M, James S, Charlton T, Kjelleberg S.

2003. The Role of Regulators in the Expression of Quorum-Sensing Signals in

Pseudomonas aeruginosa. J. MoL Microbiol. Biotechnol. 6:88-100.

Fagerlind MG, Nilsson P, Harlen M, Karlsson S, Rice SA, Kjelleberg S. 2005.

Modelling the effect of acylated homoserine lactones in Pseudomonas aeruginosa.

Biosystems. 80:201-213.

(In preparation)

Fagerlind MG, Webb J, Barraud N, McDougal D, Jansson A, Nilsson P, Harlen M,

Kjelleberg S, Rice SA. Modelling the effect of cell death in the formation of microbial

biofilms. Manuscript. List of Figures

Figure 1-1. Bioluminescence in Vibrio fischeri. At low cell densities, the luxICDABE genes (luxCDABE gene products make up the enzymatic machinery that is responsible for the production of bioluminescence, i.e. production of light) are transcribed at constitutively a low level and the small amounts of 30-C6-HSL (shown as green diamonds), produced diffuse out of the cell and are significantly diluted in the marine environment. At high cell densities (or low cell densities in diffusion limited environments), 30-C6-HSL accumulates in the local environment. The signal molecules subsequently accumulate within the cell and form complexes with the transcriptional activator LuxR, which serves to activate LuxR (shown in blue). The activated LuxR/30-C6-HSL complex binds to a region of the DNA called the lux box, resulting in an increased transcription of luxICDABE. In this way 30-C6-HSL autoinduces its own synthesis and thereby amplifies the signal cascade 8

Figure 2-1. The cell-to-cell signalling hierarchy in P. aeruginosa. LasI, an autoinducer synthase synthesizes 30-C12-HSL, Rhll is an autoinducer synthase that synthesizes C4- HSL, LasR and RhlR are transcriptional activators, OdDHL is an autoinducer, also called 30-C12-HSL, BHL is also an autoinducer molecule that is alternatively named C4-HSL, RsaL is a LasI inhibitor, and Vfr is a LasR inducer 39

Figure 2-2. The steady state concentration of the LasR/30-C12-HSL complex as a function of increasing concentration of extracellular 30-C12-HSL (which is annotated here as OdDHL). When the concentration of extracellular 30-C12-HSL is below a specific value, there exists only one low stable steady state in the system. When the concentration of extracellular 30-C12-HSL exceeds this specific value, another higher stable steady state, as well as an unstable steady state, will be formed. The unstable steady state is a saddle point that separates the two steady states from each other. When another specific concentration of extracellular 30-C12-HSL is reached, the lower of the two stable steady states will cease to exist and only the high stable steady state will remain. The arrows in the figure show the movement pattern in the system. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were KI = 0.17 (l/|xM s), K2 = 0.25 (1/s), KS = 0.17 (1/îM s), k4 = 0.25 (1/s), ks = 0.17 (l/|iM s), k6 = 0.25 (1/s), bm = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), bA2 = 0.2 (1/s), Tm = 0.004 (|iM/s), Tr2 = 0.004 (jiM/s), Ts = 0.004 (iiM/s), TAI = 0.004 (^M /s), TAI = 0.004 (îM /s), VM = 0.6 (îM /s), VR2 = 0.6 (|xM/s), V5 = 0.9 (jiM/s), VAI = 1.2 {[IM/s), VA2 = 1 (^M/s), KRI = 4 (|iM), KR2 = 1.2 (|XM), Ks = 1 (|iM), Kai = 0.4 (|iM), Ka2 = 1 (l^M), Ksi = 2.5 (^M), dj = 0.2 (1/s), J2 = 0.4 (1/s), and A2.X = 0 ()iM) 50

complex formation between 30-C12-HSL and RhlR. To see the influence from this complex formation, the parameter ks was varied, ks is the rate constant of binding reaction between RhlR and 30-C12-HSL. The model with influence from RhlR/30- C12-HSL complex formation consists of the differential equations 2-1, 2-2, 2-3, 2-4, 2- 5, 2-7, 2-8 and 2-10. The other model, i.e. without influence from RhlR/30-C12-HSL complex formation consists of the differential equations 2-1, 2-2, 2-4, 2-5, 2-7, 2-9 and 2-10. The parameter values used were ki = 0.17 (1/jiM s), k2 = 0.25 (1/s), ks = 0.17 (l/|iM s), k4 = 0.25 (1/s), ks = [0.2, 0.4, 0.6] (1/jiM s), ke = 0.25 (1/s), BM = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), bA2 = 0.2 (1/s), Tri = 0.004 (jiM/s), Tr2 = 0.004 (jiM/s), TS = 0.004 (^M/s), TAI = 0.004 (|iM /s), TA2 = 0.004 (|iM /s), VRI = 0.6 (jiM /s), VR2 = 0.6 (^iM/s), = 0.9 (^M/s), VAI = 1.2 (jiM/s), VAI = 1 (|iM/s), KRI = 4 (^M), Kr2 = 1.2 (|iM), Ks = 1 (|iM), KAI = 0.4 (^M), KA2 = 1 (|iM), Ksi = 2.5 (^iM), DI = 0.2 (1/s), D2 = 0.4 (1/s), ALEX = 4 (ixM) and A2.;c = 0 (|iM) 51

Figure 2-4. The steady state concentrations of the LasR/30-C12-HSL complex are shown as a function of increasing concentration of extracellular 30-C12-HSL (marked as OdDHL in the figure). Line a, no RsaL production; line b, basal production is then same for RsaL, 30-C12-HSL and LasR; and line c, basal production is 100 times higher for RsaL (compared with both LasR and 30-C12-HSL). For each line, the solid lines correspond to two stable steady states whereas the dotted line corresponds to an unstable steady state. The concentration of extracellular 30-C12-HSL needed to induce a system is higher in a system where 30-C12-HSL production is influenced by RsaL (lines b and c), compared with a system in which the 30-C12-HSL production is independent of RsaL (line a). The figure also demonstrates that basal production of RsaL (compared with LasR and 30-C12-HSL) has a major impact on the level of this concentration (lines b and c). Both models (with and without influence of RsaL) used the differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10). However, the model without influence of RsaL, used a modified version of equation 2-8, in which "1 + {SIKsiy\{ i.e. the influence of RsaL) was deleted from the equation. The parameter values used were ki = 0.17 (1/jiM s), k2 = 0.25 (1/s), ks = 0.17 (l/|iM s), k4 = 0.25 (1/s), ks = 0.17 (1/^M s), ke = 0.25 (1/s), bRi = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), BA2 = 0.2 (1/s), TRI = 0.004 (|iM/s), TR2 = 0.004 (|iM/s), TS = [A = no RsaL production, b = 0.004, c = 0.4] (|iM/s), Tai = 0.004 (}xM /s), Ta2 = 0.004 (|iM /s), VRJ = 0.6 (|iM /s), VR2 = 0.6 (|iM/s), = 0.9 (îM/s), Va; = 1.2 (îM/s), = 1 (i^M/s), KRJ = 4 (|IM), Kr2 = 1.2 (^M), Ks = 1 (|iM), KAI = 0.4 (|iM), KA2 = 1 (îM), Ksi = 2.5 (|iM), DI = 0.2 (1/s), D2 = 0.4 (1/s) and = 0 (jiM) 53

Figure 2-5. The concentration of extracellular 30-C12-HSL (marked as OdDHL in the figure) required to induce the system at different affinity values between RsaL and the las I promoter. Ksi is the parameter that determines this affinity. When the affinity between RsaL and the lasi promoter increases, so will the concentration of extracellular 30-C12-HSL needed to induce the system increase. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were: ki = 0.17 (l/|iM s), k2 = 0.25 (1/s), kj = 0.17 (l/|iM s), k4 = 0.25 (1/s), ks = 0.17 (l/îM s), k6 = 0.25 (1/s), BRI = 0.2 (1/s), BR2 = 0.2 (1/s), BS = 0.25 (1/s), BAI = 0.2 (1/s), BA2 = 0.2 (1/s), TRI = 0.004 ()iM/s), TR2 = 0.004 (îM/s), 7^5 = [a = 0.004, b = 0.4] (|iM/s), TAI = 0.004 (^M /s), TA2 = 0.004 (^M /s), VRI = 0.6 (|iM /s), y/?2 = 0.6 (îM/s), V5 = 0.9 (|iM/s), Va; = 1.2 (^M/s), VA2 = 1 {[IM/s), KRI = 4 (îM), KR2 = 1.2 (îM), KS = Xlll

1 (^M), KAI = 0.4 (^M), KA2 = 1 (|iM), Ksi = varied (jiM), dj = 0.2 (1/s), d2 = 0.4 (1/s), and A2ex = 0 (}xM) 56

Figure 2-6. The steady state concentration of the LasR/30-C12-HSL complex is shown as a function of increasing concentration of extracellular 30-C12-HSL (marked as OdDHL) (at different affinity values between the LasR/30-C12-HSL complex and lasR). Line a, KRI = 3.0 |iM; line b, KRI = 3.5 |iM; and line c, KRI = 4 }xM. A low KRJ value indicates a high affinity. This example clearly indicates that when this affinity increases, the concentration of extracellular 30-C12-HSL required to induce the system decreases. For each line, the two solid lines correspond to two stable steady states, whereas the dotted line corresponds to an unstable steady state. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were: ki = 0.17 (l/|iM s), = 0.25 (1/s), ks = 0.17 (l/|iM s), k4 = 0.25 (1/s), ks = 0.17 (l/|iM s), ke = 0.25 (1/s), Òri = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), ÒAi = 0.2 (1/s), bA2 = 0.2 (1/s), Tri = 0.004 (}xM/s), Tr2 = 0.004 (^M/s), Ts = 0.004 (|iM/s), Tai = 0.004 (|iM /s), Ta2 = 0.004 (|iM /s), VRI = 0.6 (|iM /s), VR2 = 0.6 (liM/s), Vs = 0.9 (|iM/s), VAI = 1.2 (^M/s), VA2 = 1 (|iM/s), Kri = [a = 3.0, b = 3.5, c = 4.0] (^M), Kr2 = 1.2 (^M), Ks = 1 (^iM), Kai = 0.4 (|iM), KA2 = 1 {[iM), Ksi = 2.5 (}iM), di = 0.2 (1/s), d2 = 0.4 (1/s), and A2.;c = 0 (|iM) 57

Figure 2-7. This figure visualizes the concentration of extracellular 30-C12-HSL (marked as OdDHL) needed to induce the system as a function of KRJ. KRI is the parameter that determines the affinity between the LasR/30-C12-HSL complex and the lasR promoter. It is shown that the lower KRJ value, the lower is the concentration of extracellular 30-C12-HSL needed to induce the system. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were: ki = 0.17 (l/jiM s), k2 = 0.25 (1/s), k3 = 0.17 (l/|iM s), k4 = 0.25 (1/s), ks = 0.17 (l/îM s), k6 = 0.25 (1/s), ÒRI = 0.2 (1/s), BR2 = 0.2 (1/s), BS = 0.25 (1/s), BAI = 0.2 (1/s), bA2 = 0.2 (1/s), TRI = 0.004 (|iM/s), TR2 = 0.004 (jiM/s), TS = 0.004 (îM/s), Tai = 0.004 (|iM /s), TA2 = 0.004 (|iM /s), VRI = 0.6 (|iM /s), VR2 = 0.6 (|iM/s), = 0.9 (jiM/s), VAI = 1.2 (\iM/s), VA2 = 1 (^M/s), KRJ = varied (îM), KR2 = 1.2 (^M), KS = 1 (^M), KAI = 0.4 (jiM), KA2 = 1 (jiM), KSI = 2.5 (^M), DI = 0.2 (1/s), D2 = 0.4 (1/s), and A2e. = 0 (|iM) 58

Figure 2-9. To separate individual signals produced by the three strains, the wild type, the vfr mutant and the vfr mutant carrying pSB299.15A (encoding a wild-type vfr), the samples were chromatographed on CI8 reverse phase TLC plates. To visualize the spots, the plates were overlaid with the Agrobacterium tumefaciens A136 monitor. The results indicated that P. aeruginosa produced three different signals, corresponded to 30-C12-HSL (marked as OdDHL and A), as compared with a 30-C12-HSL standard and two other signals (marked as B and C, respectively), probably 30-C8-HSL and 30- C6-HSL 62 Figure 3-1. The cell-to-cell signalling hierarchy in Pseudomonas aeruginosa. Solid lines indicate the known QS systems within P. aeruginosa. Antagonist items are marked as dashed lines. LasI is an autoinducer synthase which synthesizes the autoinducer 30- C12-HSL; Rhll is an autoinducer synthase which synthesizes the autoinducer C4-HSL; LasR and RhlR are transcriptional activators; RsaL is a LasI inhibitor; Vfr acts to induce LasR expression and 30-C12-HSL antagonist is an inhibitor of 30-C12-HSL regulated reactions 73

Figure 3-2. The concentration of 30-C12-HSL antagonist required to silence the AHL- system (drive the system to the lower stable steady state) is shown as a function of increasing affinity between LasR and the 30-C12-HSL antagonist. The figure also compares three different rates of 30-C12-HSL antagonist induced degradation of LasR (¿7m3)- The parameter values used in this example are: «2, «i, «5 = 0.16 = varied, Si, Ò2, S3, S4, S5 = 0.25 s~\ ÒRI, bR2 = 0.15 bs = 0.2 bAi , bAi , bAiEX ,

BAIEX , BMI. BM2, bM4 = 0.12 BM3 = [0.03, 0.05, 0.1] TRI, TR2, TS = 0.004 ^Ms'^

TAU TA2 = 0.0036 |LIMS-\ VRI , Vj^ = 0.7 ¡xMs-', Vs = 0.9 ^Ms'^ VAI , VA2 = LO liMs'^

KRI , KR2 = 1.2 nM, Ks =1.0 |iM, KAI = 0.4 |uM, KA2 = 0.7 ^iM, Ksi = 1 |iM, di, ds = 0.2 s-\d2 = 0.4 s"^ 90

Figure 3-3. The concentration of 30-C12-HSL antagonist required to silence the system (drive the system to the lower stable steady state) is shown as a function of increasing 30-C12-HSL antagonist induced degradation of LasR. The figure also compares three different affinity values between LasR and the 30-C12-HSL antagonist. Note, the affinity between 30-C12-HSL and LasR is 0.64 The parameter values used in this example are: a2, as, as = 0.16 jiM"^ s~\ a4 = [0.10, 0.16, 0.50] Si, S2, S3, S4, Ss = 0.25 bRi, bR2 = 0.15 , bs = 0.2 bAi , bAi , bAiEx , bA2Ex , ^M/, bMi, BM4 = 0.12 s"^ BM3 = varied s"\ TRI, TR2, TS = 0.004 |iMs"\ TAI, TA2 = 0.0036 \xMs~\ VRI , VR2 = 0.7 \iMs-\ Vs = 0.9 ^Ms'^ VAI , = LO ^iMs'S KRI , KR2 = 1.2 |iM, Ks =

1.0 [xM, KAI = 0.4 |iM, KA2 = 0.1 ^M, Ksi = 1 |iM, di, ds = 0.2 d2 = 0.4 s"^ 92

Figure 4-1. Flow-chart of the biofilm cell death model, describing the sequence of processes during a typical simulation. For a more comprehensive description, see the "model simulation" section 114

Figure 4-2. A simulation in which bacteria (green), growing in a bulk phase (black) substrate concentration {Sc bulk) of 3 g m ^ die after 72 hours in stationary phase (NH). The simulation shows a growth cycle consisting of biofilm growth, bacterial death at the bases of the microcolonies (after 150 hours of growth), sloughing of microcolonies (between 150 and 250 hours) and re-growth of the biofilm (after 300 hours). The domain size is 750 ^m (width) by 450 |im (height) 116

Figure 4-3. A simulation in which bacteria (green), growing in a bulk phase (black) substrate concentration {Sc bulk) of 5 g m ^ die after 72 hours in stationary phase {NH). The simulation shows a growth cycle consisting of biofilm growth, bacterial death at the bases of the microcolonies (after 150 hours of growth), sloughing of microcolonies (between 150 and 250 hours) and re-growth of the biofilm (after 300 hours). The domain size is 750 jim (width) by 450 jim (height) 118

Figure 4-4. A simulation in which bacteria, growing with a bulk phase substrate concentration {Scbuiù of 5 g m ^ die if their R value decreases below or equal 0.15. (A- D) R values of the individual bacteria, as indicated by the colorbar, at four different time steps; 50 hours (A), 100 hours (B), 200 hours (C) and 300 hours (D). Dark red bacteria are the ones with an R value above 1 (bacteria exhibiting net growth). Void spaces indicate areas of cell death, and the white arrow indicates an area of cell death within the interior of the microcolony as opposed to cell death occurring at the base of the biofilm. (E-H) Substrate concentration in g m"^, as indicated by the colorbar, at the four presented time steps; 50 hours (E), 100 hours (F), 200 hours (G) and 300 hours (H). The domain size is 750 |im (width) by 450 }im (height) 121

Figure 4-5. A simulation in which bacteria, growing with a bulk phase substrate concentration (Scbuik) of 3 g m'^, die if their R value decreases below or equal 0.15. (A- D) R values of the individual bacteria, as indicated by the colorbar, at four different time steps; 100 hours (A), 200 hours (B), 300 hours (C) and 400 hours (D). Dark red bacteria are the ones with an R value above 1 (bacteria exhibiting net growth). Void spaces indicate areas of cell death. (E-H) Substrate concentration in g m"^, as indicated by the colorbar, at the four presented time steps; 100 hours (E), 200 hours (F), 300 hours (G) and 400 hours (H) The domain size is 750 jim (width) by 450 jim (height) 122

Figure 4-6. Simulation of biofilm growth in a bulk phase substrate concentration (Sc bulk) of 3 g m'^. The parameter a (damage production rate) is 0.01 m^ whereas P (damage removal rate) is 0 The colorbar indicates damage amount. The domain size is 750 |j.m (width) by 450 |im (height) 125

Figure 4-7. Simulation of biofilm growth in a bulk phase substrate concentration (Scbuik) of 5 g m" . The parameter a (damage production rate) is 0.01 m whereas ^ (damage removal rate) is 0 The colorbar indicates damage amount. The domain size is 750 |im (width) by 450 jim (height). The yellow arrow is pointing at a "fast" growing microcolony, whereas the red arrows are pointing at "slow" growing colonies 126

Figure 4-8. Simulation of biofilm growth in a bulk phase substrate concentration {Sc bulk) of 3 g m'^. The parameter a (damage production rate) is 0.1 m^ whereas P (damage removal rate) is 0.001 The colorbar indicates damage amount. The domain size is 750 |im (width) by 450 jim (height) 127

Figure 4-9. Simulation of biofilm growth in a bulk phase substrate concentration (Scbuik) of 3 g m"^. The parameter a (damage production rate) is 0.1 m^ whereas p (damage removal rate) is 0.01 hThe colorbar indicates damage amount. The domain size is 750 jim (width) by 450 |im (height) 128

Figure 4-10. Epifluorescence micrographs (magnification x400) of cell death in P. aeruginosa biofilms growing at two different glucose concentrations, 0.9 g m"^ (5 mM) and 3.6 g m'^ (20 mM), respectively. The biofilm was stained with the BacLight, Live- Dead fluorescent stain and shows Syto9 stained live cells in green (left panels) and Propidium iodide stained dead cells in red (right panels) 130 List of Tables

Table 1-1. Structure of A^-acylated homoserine lactones (AHLs) 5

Table 2-1. Definition of variables and parameters 46

Table 3-1. Definition of variables and parameters 79

Table 3-2. The dependency on LasR degradation of the stoichiometric ratio of 30-C12- HSL antagonist to 30-C12-HSL required for successful inhibition of the model system 93

Table 3-3. Inhibitory activity of QS blockers with different structures 97

Table 4-1. Definition of variables and parameters 110 XVll

List of Abbreviations

ID one-dimensional 2D two-dimensional 3D three-dimensional 30-C6-HSL 3-Oxo hexanoyl homoserine lactone 30-C12-HSL 3-Oxo dodecanoyl homoserine lactone 4Qs 4-quinolones AHL acylated homoserine lactone AIDS acquired immune deficiency syndrome AMP adenosine monophosphate BHL N-butyryl-L-homoserine lactone C Celsius C4-HSL butyryl homoserine lactone CA cellular automata CaCl2 calcium chloride CF cystic fibrosis EPS extracellular polymeric substance Eq equation FeCl2 iron(II)chloride h hour H2O2 hydrogen peroxide HSL homoserine lactone IBM individual based model KH2PO4 potassium phosphate LB Luria-Bertani M molar MgCl2 magnesium chloride mRNA messenger ribonucleic acid NaCl sodium chloride Na2HP04 sodium hydrogen phosphate (NH4)2S04 ammonium sulphate NIP no inhibition possible NO nitric oxide NO2 nitrite NO3 nitrate O2 oxygen ONOO peroxyni trite PAI-1 Pseudomonas autoinducer 1 PAI-2 Pseudomonas autoinducer 2 PCO2 potential of carbon dioxide pK potential of hydrogen PMN polymorphonuclear leukocytes PO2 potential of oxygen PQS Pseudomonas quinolone signal OdDHL N-3-oxododecanoyl-L-homoserine lactone QS quorum sensing ROS reactive oxygen species Rpm revolutions per minute xvm

s second SDS sodium dodecyl sulphate t time tRNA transfer ribonucleic acid UV ultraviolet OD optical density TLC thin layer chromatography Wt wild type Chapter 1. Quorum sensing dynamics and

bioHlm formation: a literature review

1.1. Introduction

Bacterial resistance to antibiotics is an increasing problem and there is a growing

appreciation that biofilm formation is a significant contributor to antibiotic resistance.

Biofilms are not only resistant to antibiotics, but also to a range of stresses, such as UV

light, chemical disinfection (e.g. bleach), heavy metals and other antimicrobial agents

(Anwar et al 1989, 1990; Allison et al 1993; Donlan and Costerton, 2002; Drenkard,

2003; Teizel and Parsek, 2003). Biofilms develop on virtually all surfaces immersed in

aqueous environments, including both biotic and abiotic surfaces (Slusher et al. 1987;

Prince, 1992; O'Toole and Kolter, 1998a, 1998b; Hogan and Kolter, 2002). Biofilms are

also a major problem in medicine where according to a public announcement from the

US National Institute of Health more than 80 % of all microbial infections involve biofilms (Costerton et al. 1999). This has led to increased research on ways to reduce/control biofilm formation and resistance. One such target, bacterial communication which allows bacteria to co-ordinate gene expression, has been shown to be involved in biofilm formation (Davies et al 1998; de Kievit et al. 2001; Huber et al. 2001; Lynch et al. 2002; Labbate et al. 2004), and controls the production of several virulence factors (van Delden and Iglewski, 1998; Rumbaugh et al. 2000; Winzer and

Williams, 2001; Hentzer et al. 2003; Schuster et al. 2003; Wagner et al. 2003; Vasil,

2003; Juhas et al. 2005; Rasmussen et al. 2005b). By interfering with their communication system it should be possible to control gene expression and thus inhibit the production of virulence factors as well as the formation of biofilms. Indeed, the control of bacterial communication has been recognized as a strategy for the control of bacterial infections and biofilm formation. At present there are several promising approaches to block cell communication, including: 1) inhibiting signal production; 2) degradation of the signal molecule or receptor protein; and 3) blocking perception of the signal molecule by its cognate receptor protein (reviewed in Rasmussen and Givskov,

2006). However, most studies of inhibition of communication are typically based on empirical, laboratory based approaches, and have not taken advantage of theoretical guidance to identify key parameters that are essential for the regulation of biofilm formation or communication based gene expression. This may be due to the fact that bacterial communication and biofilm formation are multi-factorial processes and may involve control by multiple regulatory circuits, sensitivity to growth conditions etc. This makes it a complicated task to evaluate all of these processes and parameters by wet-lab experiments to identify an ideal inhibitor of cell communication systems. Therefore, such studies can benefit from mathematical modeUing. By using mathematical modelling, it is possible to study complex systems, such as bacterial communication and biofilm formation, and to identify those processes and parameters that are most important for the systems. Hence, mathematical modelling can be regarded as a tool that can be utilized to guide subsequent wet-lab experiments. Therefore, the focus of this thesis was to develop mathematical models of bacterial cell-cell communication systems and biofilm formation to identify key parameters that could subsequently guide the development of cell communication strategies to control bacterial virulence and biofilm formation. 1.2. Pseudomonas aeruginosa Pseudomonas aeruginosa is a Gram-negative aerobic bacterium in the y subclass of proteobacteria. These bacteria are straight or slightly curved rods, 0.5 to 1.0 |Lim by 1.5 to 5.0 |im in length, and are motile by one or several polar flagella. They are non- fermentative bacteria, capable of growing without O2 if arginine or NO37NO2" are available as alternative electron acceptors (Lu et al. 1999; Hassett et al. 2002). P. aeruginosa lives in most environments, including, soil, costal marine habitats, plants, as well as mammalian tissues (Stover et al. 2000). In hospitals, it grows in moist reservoirs such as food, flowers, sinks, toilets, mops, dialysis equipment, and catheters and even in disinfectant solutions (Murray et al. 2002). P. aeruginosa is the most common Gram- negative bacterium found in nosocomial infections. It causes infections in immunocompromised patients, such as patients with AIDS, patients undergoing chemotherapy and those with breaches in normal barriers caused by bums, indwelling medical devices or the prolonged use of antibiotics (Douglas et al 1998; van Delden and Iglewski, 1998; Pesci et al. 1999; Lyczak et al. 2000; Stover et al. 2000). It is also the predominant cause of chronic lung infection in patients with cystic fibrosis (CF) (Koch and H0iby, 1993; Frederiksen et al 1997; Douglas et al 1998; Lyczak et al 2002). Two other key features of P. aeruginosa are that it uses a conserved cell communication system, quorum sensing, to regulate virulence factor expression and it rapidly forms biofilms. Because of its wide distribution, relevance to a broad range of infections, use of quorum sensing to control virulence factor production and biofilm formation, P. aeruginosa serves as a model bacterium for experimental studies. 1.3. Quorum sensing

Until recently, bacteria were studied predominantly in liquid culture and were treated as collections of individual cells growing and behaving independently. Thus, it was expected that bacteria only responded, as individuals, to their local physical (e.g. temperature or UV) and chemical (e.g. carbon, nitrogen, or chemical stressors) stimuli.

However, approximately 30 years ago, it was discovered that the Gram-negative marine bacterium Vibrio fischeri controls its ability to luminesce by producing a small, diffusible molecule called an autoinducer (Nealson et al 1970; Eberhard, 1972). This autoinducer was later identified as an acylated homoserine lactone (AHL) (Eberhard,

1981). Today it is known that many Gram-negative bacteria produce varying types of

AHLs that differ in acyl chain length and substitution at the third position of the acyl side chain (Table 1-1). Many of these AHLs are freely diffusible across the cytoplasmic membrane while others are dependent on export systems (Kaplan and Greenberg, 1985;

James et al. 1999). In the general and most accepted model of AHL mediated signalling, the signals diffuse (or being transported) out of the cell and into the surrounding milieu.

At low cell density, the concentration of signal that accumulates extracellularly is insufficient to mediate an effect on the bacteria. However, as the cell density increases, the concentration of AHLs increases in the surrounding milieu and consequently, the diffusion gradient is reversed and the AHLs start to diffuse back into the cell. It has been hypothesized that because the concentration of AHLs is cell density dependent, this system enables individual cells to determine population density. An alternative model of AHL mediated signalling has suggested that bacteria use the AHL concentration as a measure of diffusion limitation in the local environment (Redfield,

2002). Table 1-1. Structure of A^-acylated homoserìne lactones (AHLs). Type of AHL/Abbreviatíons Structure N-butanoyl (butyril)-HSL/ BHL/C4-HSL/PAI-2 Î ^

0 N-hexanoyl-HSL/ HHL, Cô-HSL,

0 N-heptanoyl-HSL/ HPHSL, C7-HSL

H 0 N-octanoyl-HSL/ s ^ OHL, Cg-HSL, VAI-2 0 N-decanoyl-HSL/ DHL, Cio-HSL

0 N-dodecanoyl-HSL/ DDHL, C12-HSL 0 N-tetradecanoyl-HSL/ TDHL,Ci4-HSL 0

N-(3-oxo-butanoyl)-HSL/ S 8 r^^ OBHL, 3-OXO-C4-HSL N H 0 N-(3-oxo-hexanoyl)- HSL/ OHHL, 3-0X0-C6-HSL, VAI-1 Î S

0 N-(3-oxo-octanoyl)-HSL/ s s ^ OOHL, 3-0X0-C8-HSL, AAI-1 0 N-(3-oxo-decanoyl)-HSL/ ODHL, 3-oxo-Cio-HSL

N-(3-oxo-dodecanoyl)- HSL/ OdDHL, 3-0X0-C12-HSL, PAI-1 N-(3-oxo-tetradecanoyl)-L- HSIV OtDHL, 3-0X0-C14-HSL N-(3-hydroxy-butanoyl)-HSL/ HBHL, 3-hydroxy-C4-HSL, HAI-1 N-(3-hydroxy-hexanoyl)-HSL/ HHHL, 3-hydroxy-C6-HSL

N-(3-hydroxy-octanoyl)-HSL/ HOHL, 3-hydroxy-C8-HSL

N-(3-hydroxy-decanoyl)-HSL/ HDHL, 3-hydroxy-Cio-HSL

N-(3-hydroxy-dodecanoyl)- HSL/ HdDHL, 3-hydroxy-Ci2-HSL N-(3-hydroxy-7-cis- tetradecanoyl)-HSL/ HtDHL, 3-hydroxy-Ci4-HSL, RLAl Table adapted from Rice et al (2004). In this model, the concentration of AHL can increase in the surrounding milieu of a low density population if diffusion is limited, e.g. in a closed, limited space, such as the light organ of the squid. However, independent of the model assumed, it is accepted that when the AHL concentration reaches a threshold value it is perceived by the receptor and this interaction induces the expression of target genes that regulate specific phenotypes, depending on the species. This phenomenon is termed quorum sensing

(QS). Many of the QS regulated functions involve bacterial-host interactions, such as symbiosis and pathogenicity and it has been suggested that these functions are most effective if a large number of bacteria are present (Miller and Bassler, 2001).

As described above, the earliest known example of QS is the regulation of bioluminescence (production of Ught) by the symbiotic marine bacterium V. fischeri

(Figure 1-1). When free living and at low cell density, cultures of V. fischeri appear dark. Upon reaching a critical cell density (e.g. when in symbiosis with a squid) the population emits light. In this relationship between the squid and V. fischeri, it is beneficial for the bacterium to generate light when at high density in the light organ.

However, light production is energetically expensive and not productive at low cell density, when the amount of light produced from a single cell would be imperceptible, and thus, it can be dispensed with at low cell density, such as well the bacteria are outside of the squid's light organ. In V. fischeri bioluminescence is dependent upon the accumulation of a low molecular weight molecule termed 30-C6-HSL (Table 1-1), which is synthesized by the AHL synthase Luxl. The signal binds to its receptor, LuxR, which acts as a transcription factor to induce or repress QS controlled gene expression

(Figure 1-1). Luxl and LuxR are the protein products of the luxl and luxR genes respectively. Low cell densities iuxR lux box iuxl

High cell densities fuxR fuxbox fuxl C^ D^ A^ B^ E

Figure 1-1. Bioluminescence in Vibrio fischeri. At low cell densities, the luxICDABE genes {luxCDABE gene products make up the enzymatic machinery that is responsible for the production of bioluminescence, i.e. production of light) are transcribed at constitutively a low level and the small amounts of 30-C6-HSL (shown as green diamonds), produced diffuse out of the cell and are significantly diluted in the marine environment. At high cell densities (or low cell densities in diffusion limited environments), 30-C6-HSL accumulates in the local environment. The signal molecules subsequently accumulate within the cell and form complexes with the transcriptional activator LuxR, which serves to activate LuxR (shown in blue). The activated LuxRy30-C6-HSL complex binds to a region of the DNA called the lux box, resulting in an increased transcription of luxICDABE. In this way 30-C6-HSL autoinduces its own synthesis and thereby amplifies the signal cascade. 1.4. Pseudomonas aeruginosa and quorum sensing

It has been speculated that QS helps bacteria to avoid the host immune system by delaying the production of virulence factors until the number of bacteria is sufficient to overwhelm the immune system (Mekalanos, 1992). In this way, QS is thought to be part of a "stealth mechanism" which helps the bacteria to avoid recognition by the host immune system when they are at low cell density and unable to make a productive infection. The quorum sensing response of P. aeruginosa is probably the most intensively studied due to the environmental and medical significance of the organism.

It has been suggested that six to ten percent of the chromosomal genes of P. aeruginosa are regulated by QS (Arevalo-Ferro et al. 2003; Schuster et al. 2003; Wagner et al

2003). It has also been shown that these genes are distributed throughout the whole chromosome, rather than appearing as a cluster of genes, which supports the hypothesis that QS is an ancient regulatory mechanism and is not present due to recent acquisition by horizontal gene transfer (Gray and Garey, 2001; Manefield and Turner, 2002). It has been suggested that approximately one third of the QS regulated genes in P. aeruginosa encode virulence factors. Among these are many secreted factors, including, alkahne protease, chitinases, cyanide, elastase, lectins, phenazines, siderophores, rhamnolipids as well as a large number of proteins with unknown functions (van Delden and

Iglewski, 1998; Rumbaugh et al 2000; Winzer and Williams, 2001; Hentzer et al 2003;

Schuster et al 2003; Wagner et al 2003; Vasil, 2003; Juhas et al 2005; Rasmussen et al 2005b). It has also been shown that QS is involved in the development of biofilms

(Winson et al 1995; Passador et al 1996; Davies et al 1998; Hentzer et al 2003).

Additionally, quorum sensing negative mutants display reduced virulence in animal models of infection compared to the parental strain. These include chronic lung infections (Wu al 2001), bum wound infections (Rumbaugh et al 1999) as well as acute pulmonary infections (Pearson et al 2000; Lesprit et al. 2003). Moreover, AHLs have been detected in the sputum of cystic fibrosis (CF) patients infected with P. aeruginosa, suggesting that QS is active during infection in the CF lung (Favre-Bonte et al. 2002; Middleton et al. 2002).

The QS system of P. aeruginosa is responsive to two chemically different signal molecules, one based on AHLs and the other based on 4-quinolones (4Qs). The AHL- based circuits are encoded by the lasRI and rhlRI genes, each of which encodes homologues of luxR and luxl genes of V. fischeri. LasI is an autoinducer synthase that synthesizes 30-C12-HSL (Table 1-1), whereas LasR is the receptor for 30-C12-HSL and is a transcriptional activator (Pesci et al 1999). The LasR/30-C12-HSL complex controls the expression of multiple virulence genes and also plays a role in biofilm formation (Winson et al. 1995; Passador et al. 1996; Pearson et al. 1997; Davies et al.

1998; Pesci et al. 1999; Hentzer et al. 2003). In addition, the LasR/30-C12-HSL complex also binds to the lasi promoter and allows an initial rapid rise in autoinducer synthesis, which increases the concentration of 30-C12-HSL available to bind to LasR

(Seed et al. 1995). The Rhl system is composed of the transcriptional activator RhlR and Rhll, the autoinducer synthase that synthesizes the cognate autoinducer, C4-HSL

(Table 1-1). The Rhl system also regulates the expression of several virulence genes and some genes not directly involved in virulence. It has been suggested that the LasR/30-

C12-HSL complex induces the expression of rhlR placing the Las system above the Rhl system in the cell-to-cell signalling hierarchy (Latifi et al. 1996; Pesci et al. 1997,

1999). Moreover, 30-C12-HSL can bind to RhlR and thereby block the binding of C4-

HSL to its transcriptional activator protein. This binding hierarchy is hypothesized to allow P. aeruginosa to delay the induction of genes controlled by Rhl quorum sensing (Pesci et al. 1997). Other regulatory systems have also been shown to be involved in the control of the Las system in P. aeruginosa. For example, Vfr, a cyclic AMP receptor protein homologue, influences the expression of lasR and it has been proposed that the P. aeruginosa quorum sensing cascade begins with the production of Vfr (Albus et al. 1997). It has been shown that Vfr is required for lasR expression, and that there is a putative cyclic AMP receptor protein consensus binding site in the lasR promoter (Pesci et al. 1999). Vfr is believed to induce conformational changes in the promoter region, which may increase the affinity between the promoter region and the LasR/30-C12- HSL complex (Albus et al. 1997; Pesci et al. 1999). An inhibitor, RsaL, also affects the Las system. This inhibitor is beUeved to repress expression of lasi thereby blocking activation of the P. aeruginosa quorum sensing cascade. At low cell densities, RsaL competitively inhibits the transcription of lasI by binding to the lasI operator region. As the cell density increases, the intracellular concentration of 30-C12-HSL increases, which enables sufficient LasR/30-C12-HSL complex formation to out compete RsaL for binding to the lasI operator region (de Kievit et al. 1999). In addition, the Las and Rhl systems have been identified as being hierarchically ordered, with the Las systems in control of the Rhl system (Pesci et al. 1997). The recently discovered 4Qs-based system, the PQS system, acts as an intermediary signal between the Las and the Rhl system (McKnight et al. 20(X); Pesci et al. 2000). The Las system induces production of PQS whereas PQS (together with the AHLs) induces the production Rhll, elastase, rhamnolipids, the galactophilic lectin LecA, pyocyanin, the MexGHI-OpmD multidrug efflux pump and influences biofilm formation (Diggle et al. 2003, 2006; Allesen-Holm et al. 2006). Recently, it has also been demonstrated that PQS acts as an immune modulator, by inhibiting human T-cell proliferation (Hooi et al. 2004). 1.5. Inhibition of quorum sensing The high infection and mortality rates observed for P. aeruginosa in cystic fibrosis patients and other chronic infections make it imperative to identify appropriate therapeutic interventions against P. aeruginosa infections, especially in light of the development of resistance to many of the available antibiotics. The selection pressure created by antibiotic mediated killing is probably the leading cause of development of antibiotic resistance (Drenkard and Ausubel, 2002; Huang et al 2002; Loureiro et al 2002). The observation that P. aeruginosa uses QS to regulate virulence factor production, as well as biofilm formation which is important in chronic infections makes this system an ideal target for control strategies. For example, it has been suggested that QS blockers (QSBs), would interfere efficiently with the QS system in P. aeruginosa (Passador et al 1993; Pearson et al 1994; Finch et al 1998) and potentially abrogate virulence in this pathogen. Since QS regulates non-essential traits, inhibition of QS is not assumed to create the same strong selection pressure seen with antibiotics. Since bacteria and eukaryotes have coexisted for millions of years, it would not be surprising if, at least some, eukaryotes have developed defence-systems based on QSB. Indeed, recent studies have demonstrated that both plants (Teplitski et al 2000; Daniels et al 2002; Gao et al 2003; Mathesius et al 2003; Sanchez-Contreras et al 2007) as well as algae (de Nys et al 1993; Givskov et al 1996; Teplitski et al 2004) are able to interfere with QS in bacteria by secreting compounds that mimic the signal molecules. The first natural QSBs discovered were the halogenated furanones produced by the Australian marine macroalga Delisea pulchra (de Nys et al 1993; Givskov et al 1996). This macroalga produces a number of halogenated furanones that are structurally very similar to the AHL molecules found in bacteria (Givskov et al 1996). These autoinducer antagonists have been demonstrated to disrupt bacterial cell-cell communication and are thought to be used by the alga to prevent colonization of, or biofilm formation on, its surface (Kjelleberg et al. 1997). The inhibitory activity of autoinducer antagonists has been demonstrated in a range of bacteria, including V. fischeri (Milton et al. 1997), Serratia liquefaciens (Givskov et al. 1996; Lindum et al.

1998; Manefield et al. 1999; Rasmussen et al. 2000), Erwinia carotovora (Manefield et al. 2001) and P. aeruginosa (Hentzer et al. 2002, 2003). It has recently been reported that the naturally derived furanone compounds have a rather limited effect on P. aeruginosa when tested individually (Hentzer et al. 2002). However, the furanone compounds can be modified through combinatorial chemistry to generate a large number of analogues. Such exercises, using natural furanones as scaffold molecules has identified synthetic furanone derivates, C-30 and C-56, which displayed stronger inhibitory properties than those of the natural furanone compounds (Manefield et al.

2002). In addition, transcriptomic analysis demonstrated they have high target specificity for QS-controlled gene expression and very specific mode of action (Hentzer et al. 2003). As noted above, one phenotype that is QS controlled biofilm formation, and hence, QSBs could be used to control biofilm formation. This is supported by the observation that furanones reduce bacterial colonisation of the surface of D. pulchra. 1.6. Biofilms As described above, biofilms are today a major problem in both medical, as well as in industrial systems. Hence, it is vital to be able to control biofilm formation. However, in the biofilm mode of life, bacteria are protected from numerous harmful agents such as UV light, antibiotics, heavy metals and other antimicrobial agents. It has been reported that as much 1000-fold more (relative to their planktonic counterparts) antibiotic or heavy metal is required to kill biofilm cells compared to planktonic cells (Anwar et al 1989, 1990; Allison et al 1993; Donlan and Costerton, 2002; Drenkard, 2003; Teizel and Parsek, 2003). In relation to antibiotics, this level often exceeds the highest deliverable doses, making treatment impossible (Costerton et al 1987, 1999; Hoiby et al 2001; Drenkard, 2003). Recent findings suggest that bacteria employ multiple strategies, both active as well as "passive", to acquire increased resistance against drugs, such as antibiotics. As an active strategy P. aeruginosa has several efflux pump systems, MexAB-OprM, MexXY-OprM, MexJK-OprM, MexCD-OprJ and MexEF- OprN (Schweizer, 2003). This bacterium also produces compounds which interact directly with some antimicrobial compounds. Examples are: p-Lactamase that cleaves and inactivates p-Lactam antibiotics (Bagge et al 2004a, 2004b); periplasmic glucans that sequester tobramycin and prevent this antibiotic from reaching the site of action by entrapping it in the periplasm (Mah et al 2003; and catalases which prevent penetration of H2O2 into the biofilm cells (Elkins et al 1999; Stewart et al 2000). Several "passive" strategies have also been suggested. For example, it has been suggested that the biofilm matrix itself can act as a diffusion barrier, slowing down penetration of antimicrobial agents. It has also been shown that biofilms increase the tolerance of the biofilm- embedded cells to a number of heavy metals (Teizel and Parsek, 2003). Moreover, several studies indicate that the majority cells within the biofilm matrix are undergoing slow growth or are in stationary phase. Because most antibiotics only affect actively

growing cells, these non-growing biofilm cells are protected from the effects of such

antibiotics (Hoyle and Costerton, 1991; Donlan and Costerton, 2002; Hall-Stoodley et al. 2004). The microenvironment of biofilms, for example different pH, pCOj, p02, etc., may also influence the efficacy of some antimicrobial agents, such as macrolides and tetracyclines that are inactive at low pH (Dunne, 2002; Walters et al 2003). The development of subpopulations of resistant cells, often referred to as persister cells, has been suggested as another mechanism to increase resistance of the biofilm (Spoering

and Lewis, 2001; Keren et al 2004). Taken together, there is no question that biofihn mediated tolerance to antimicrobial compounds is a multifactorial phenomenon. The resistance of biofilms to antimicrobial agents undoubtedly has serious medical consequences. For instance, insertion of a prosthetic device into the human body frequently results in the formation of biofilms on the surface of the device. Often the only way to treat patients in this situation is by removing the implant or infected area by surgery (Holman, 2007). Biofilms are also a major problem in cystic fibrosis patients

(Gómez and Prince, 2007; Murray et al 2007) who tend to have intractable, life-long P. aeruginosa infections.

Biofilms can form different types of structures, with varying complexity. It was previously thought that biofilms were flat, homogenous structures. However, discoveries in the beginning of the 1990's revealed that biofilms are frequently composed of microcolonies interspersed with open water channels (Lawrence et al

1991). It is now currently accepted that biofilms, in response to varying environmental conditions, can adopt different structures which can range from homogenous monolayers, to heterogeneous structures including mushrooms, ripples, and filamentous streamers (de Beer et al 1994; Costerton et al 1995; Stoodley et al 1999, 2002a; Labbate et al 2004). The current model of biofilm development is a cycle of three steps (which can further be divided into several substeps); attachment, growth of colonies/microcolonies and detachment (sloughing or dispersal) (Figure 1-2) and a range of processes have been suggested to contribute to the development of biofilms, and consequently affect biofilm structure. These include, for example: adhesion (Cramton et al 1999; Froeliger and Fives-Taylor 2001; Gavin et al 2002; Tsuneda et al 2003); detachment (Alison et al 1998; Sawyer and Hermanowicz, 1998; Hentzer et al 2002); mass transport (Characklis and Marshall, 1990; de Beer et al 1994); hydrodynamics (Stoodley et al 1999, 2002b), EPS production (Nielsen et al 1996; Tsuneda et al 2003), cell motility (OToole and Kolter, 1998a; Klausen et al 2003), QS (Davies et al 1998; de Kievit et al 2001; Huber et al 2001; Lynch et al 2002; Labbate et al 2004); cell death (Webb et al 2003; Mai-Prochnow et al 2004, 2006; Barraud et al 2006), DNA excretion (Petersen et al 2005; Allesen-Holm et al 2006) and active dispersal (Barraud et al 2006; Prochnow et al 2006; Koh et al 2007). Attachment Growth Detachment a

Figure 1-2. The biofilm development cycle in three steps: 1) bacteria attach to a surface; 2) growth of colonies/microcolonies; 3) detachment (sloughing or dispersal). The detached bacteria are free to colonize new surfaces and the cycle can be repeated again. Image credit. ©Center for Biofilm Engineering at Montana State University, Bozeman One of the least understood processes, and how it effects biofilm development, is cell death. To date, only a few studies addressing this process have been published. Webb, et al (2003) observed that killing and lysis occur in localized regions in wild-type P. aeruginosa biofilms, inside microcolonies by a mechanism that involves a genomic Pfl like phage of P. aeruginosa. They also found evidence that the generation of reactive oxygen species (ROS) was essential for prophage activation and subsequent superinfection and lysis. These findings were recently supported by Barraud et al

(2006), who described peroxynitrite (ONOO ) dependent cell death in mature P. aeruginosa biofilms. In addition, a correlation between ONOO" accumulation, cell death and dispersal was observed. Prochnow et al (2004) observed a similar death pattern in biofilms formed by the marine bacterium Pseudoalteromonas tunicata. An autotoxic protein designated AlpP, was found to induce cell death in this organism. Later it was speculated that self-lysis in P. tunicata biofilms increases the ability of the surviving cells to disperse from the biofilms and colonize new surfaces (Prochnow et al 2006).

More recently, a similar pattern of cell death and dispersal has also been identified in the pathogen Serratia marcescens (Koh et al 2007). Hence, several studies indicate a strong relationship between cell death and dispersal in microbial biofilms. It is interesting to note that the production of NO has been linked to QS (Yoon et al 2002).

Combined with the observations above that QS is important for biofilm formation, it is an attractive target for control of bacteria and biofilm formation. 1.7. Biofilms and quorum sensing

The first report on the involvement of QS in biofilm formation and differentiation was published by Davies et al (1998) who argued that biofilm development, including formation of the well-known mushroom structures, required a functional QS system

(Davies et al 1998). However, several other groups have subsequently shown that the

QS requirement for microcolony development is media dependent, and depending on growth conditions, QS mutants can make biofilms that are indistinguishable from the wild-type (Heydom et al 2002; Bjamsholt et al 2005). Even though the details of the specific pathways that QS controls to co-ordinate biofilm formation and differentiation is not fully understood, several groups have shown a link between biofilms, QS and resistance against many antimicrobial compounds as well as the host immune system.

Thus, it is clear that QS plays a role in biofilm formation in multiple bacteria and that

QS not only contributes to biofilm formation, but also to the inherent resistance of the biofilm. For instance, Bjamsholt and colleagues (Bjamsholt et al 2005) showed by viability staining and by determination of viable counts that the biofilms formed by QS deficient strains of P. aeruginosa are much less tolerant of tobramycin treatment compared to the wild-type. Similar results have also been demonstrated with kanamycin

(Shih and Huang, 2002). Moreover, Hentzer and co-workers (Hentzer et al 2003) showed that P. aeruginosa biofilms grown in the presence of furanones C-30 and C-56 were susceptible to antimicrobial killing (tobramycin and SDS), in contrast to biofilms grown in the absence of furanones. Several QS-inhibitors have also proven effective at rendering biofilms susceptible to grazing by polymorphonuclearcytes (PMNs)

(Bjamsholt et al 2005; Rasmussen et al 2005a; de Nys et al 2006) as well as attenuating the virulence of P. aeruginosa in a pulmonary mouse model (Hentzer et al 2003). Taken together the accumulated data suggest that there is great potential to use interference with QS in bacteria to control the biofilm mode of growth. 1.8. Modelling of quorum sensing

One of the first models related to QS described the regulation of bioluminescence in V. fischeri (James et al. 2000), i.e. the system illustrated in Figure 1-1. In their single cell model, the author's described the change in intracellular concentrations of AHL, R- protein and the AHL/R-protein complex (described by three ordinary, non-linear differential equations) when exposed to different concentrations of extracellular AHL (a parameter in the model), which was an attempt to investigate the dynamics of the system as a function of population density. The model predicted that the QS system in this species had two stable steady states, corresponding to a non-luminescent phenotype

(zero AHL/R-protein complex concentration) and a luminescent phenotype (high

AHL/R-protein complex concentration). A related model was proposed by Dockery and

Keener (2001). Their model, which was based on mass action laws, described the Las system in P. aeruginosa (which is similar to the quorum sensing system in V. fischeri).

However, they also incorporated spatial effects by including expression of a simple homogenous biofilm in their model system. Hence, their QS model was composed of both ordinary as well as partial differential equations. This approach enabled them to investigate the effect of a non-homogeneous distribution of the AHLs in the extracellular space. In their model they focused on the production and diffusion

(between the intracellular and the extracellular spaces) of AHLs. They concluded that

QS worked by a hysteretic switching (AHL production switches on at a different

(higher) AHL level than it switches off) between two stable steady-state solutions, reflecting low and high rates of AHL production. In addition, they also demonstrated that increasing biofilm depth or population density (parameters in the model) caused the shift from low to high AHL production rates. In both James et al. (2000) and Dockery and Keener, (2001) the population density was described by a fixed parameter value. In contrast, Ward at el, (2001) used a dynamic population approach to model QS in V. fischeri which was comprised of a system of non-linear ordinary differential equations coupled to AHL production and dynamic cell-population growth. Cells were assumed to be in one of two states; down-regulated (producing low amounts of AHL) or up- regulated (producing high amounts of AHL), and down-regulated cells become up- regulated by AHL. This model generated similar results to those of the models of James et al. (2000) and Dockery and Keener (2001), which demonstrated that increasing cell density caused an increase in AHL production. However, the dynamics behind this behaviour were mathematically quite different for the three models. In James at el. (2000) and Dockery and Keener (2001), the increase in AHL production (as cell density increased) resulted from moving along and eventually jumping between stable steady- states; steady states reflecting low versus high production rates of AHL. In Ward et al. (2001) by contrast, the same behaviour occurred due to the cumulative effect of increased AHL concentration, with an associated increase in the up-regulation of signal production as the population increased. This resulted in a rapid increase of AHL concentration, which was faster than the population growth rate. In Nilsson et al. (2001) a similar modelling approach to the one adopted in Ward et al. (2001) was considered, where a dynamic cell population growth was coupled with AHL production by a system of non-linear ordinary differential equations. By varying three different rate parameters (population growth rate, AHL diffusion rate and rate of AHL autoinduction) these authors investigated the temporal changes of AHL concentration, both intracellular and within a biofilm, as cell density increased. Their model showed that the intracellular AHL concentration had a non-trivial behaviour over time, and often showed a rapid increase early in population growth. This rapid increase was followed by a plateau, followed by another rise in the concentration of AHLs, to a second plateau. Moreover, the model also demonstrated that high concentrations of intracellular AHLs can be reached at very low population densities. This result was promoted by slow AHL diffusion rates out of the cell and the biofilm, slow bacterial growth rates and fast AHL autoinduction. In both Nilsson et al (2001) and Ward et al. (2001), no spatial variation in AHL concentration was considered. However, it has been shown experimentally that AHL concentration can vary significantly through the biofilm (de Kievit et al 2001). Accordingly, the model developed in Ward et al. (2001) was updated to consider spatial variation in the AHL concentration (Koerber et al 2002). The main aim in Koerber et al (2002) was to investigate the affect of increasing the rate of signal (AHL) degradation, and when analyzing the model it was demonstrated that an increased rate of signal degradation slowed or prevented the onset of QS. It was further speculated that QS would be a possible target for novel therapy, presumably by introducing a hypothetical AHL degrading agent into the system. In Ward et al (2003) the QS model developed used a complex growth model (described by a system of nonlinear partial differential equations), in which it was assumed that bacterial growth generated movement within the growing biofilm. Analysis of this model system showed that there was a phase of biofilm development in which the bacteria remain in an uninduced (producing low amounts of AHL) state, but as the concentration of AHL increased in the biofilm, up-regulation (producing increasing amounts of AHL) of bacteria occurred throughout almost the entire biofilm, over a very short period of time. Another contemporary QS model was developed by Chopp et al (2003). Their model described a growing P. aeruginosa biofilm, in which the biofilm was separated in two various constituents, active cells and inert biomass (EPS and water). In addition, this QS model also considered consumption of a growth limiting substrate as well as production of AHL, and was similar to the P. aeruginosa QS models described previously where only the Las system was considered. When analyzing the model system, they showed that increased AHL production rapidly induces QS in the entire biofilm, a finding that was in agreement with Ward et al. (2003). Moreover, it was also demonstrated that the onset of quorum sensing was determined by the depth of the biofilm and that increased AHL degradation slowed or prevented the onset of quorum sensing, a finding that was in agreement with Koerber et al. (2002). Ward et al. 2004, was the first model that included QS repression of gene expression. Their model analysis showed that QS repression had the highest impact on populations during exponential growth, and in particular, on the saturation levels of QS molecules, as well as the proportion of QS induced cells (e.g. in a biofilm). The authors suggested that the main advantage of this repression process was the prevention of superfluous production of QS molecules, which fits with the biological model, where QS is uninduced at low population densities. In Anguige et al. (2004) a model of the Las system in P. aeruginosa was developed. This QS model was a based on the QS model developed by Dockery and Keener (2001). However, in contrast to Dockery and Keener (2001), in which population density was set by a fixed parameter value, these authors assumed logistic growth of a spatially homogenous (batch-culture) P. aeruginosa population, an approach that was similar to the one adopted in Nilsson et al. (2001). In addition, QSBs, which degraded either LasR or AHL, were also incorporated in their model system. Similar to the results presented in Dockery and Keener (2001), the model of Anguige et al. (2004) showed that the QS system in P. aeruginosa works by hysteretic switching between two stable steady states, one with low concentrations of AHL and one with high concentrations of AHL. As a consequence of these dynamics, it was shown that the timing of treatment (addition of QSB) was important. If the treatment is not initiated early enough (during population growth), then it will only be possible to reduce the AHL concentration to the higher of the two stable steady states, but it is not possible to shift the system back to the uninduced state. It was also demonstrated that the qualitative response to QSB treatment was heavily dependent on the parameter values used, and that the critical concentration of QSB ("for inactivation") increased linearly with increasing population density. These authors extended their model (Anguige et al. 2005) with a more complex growth function, which, instead of assuming a spatially homogenous planktonic population, a population growing on a flat surface was assumed with growth dynamics similar to those used in Chopp et al (2003) and Ward et al (2003). This surface based population, i.e. biofilm, was further exposed to treatment with topically applied, diffusible QSBs. Interestingly, numerical solutions of the model equations revealed that the response to QSB treatment was similar to their previous model based on a planktonic culture (Anguige et al 2004). In contrast, the critical QSB concentration (for inactivation of the QS system) increased exponentially with biofilm thickness, which can be compared with the linear increase experienced in the planktonic model. In addition, in the biofilm setup the critical concentration also decreased exponentially with the diffusivity of the QSB. In Anguige et al (2006) their previous model (Anguige et al 2005) was extended to include QS regulated EPS production, as well as entrainment of water as the biofilm developed. As expected, model analysis demonstrated that the application of a QSB on top of a growing biofilm reduced EPS production, which consequently resulted in much thinner, uniform and closely packed biofilms. Moreover, this behaviour was also speculated to have medical implications since this flat biofilm morphology is more susceptible to conventional antibiotics or surfactants, as well as to attack by the immune system. 1.9. Biofilm modelling

In some of the QS models described above, simple biofilms were also incorporated.

However, in those models the focus was on understanding the QS dynamics and the biofilms were incorporated mainly to determine if a structured community affected the

QS dynamics. Hence, the process of biofilm development and its dependence on QS was not considered in those models. However, others have specifically developed biofilm models that examine biofilm development and the formation of two and three- dimensional structures in an attempt to elucidate key parameters that drive the formation of the observed biofilm structures.

Previously it was assumed that biofilms where flat homogenous structures. This

assumption was also reflected in the first biofilm models developed. In those early

models, biofilms were represented as homogenous single-species films, governed only by one-dimensional (ID) mass transport and biochemical changes (Atkinson and

Davies, 1974; Harris and Hansford, 1976; Williamson and McCarty, 1976; Rittmann

and McCarty, 1980). Subsequently, more complex biofilm models were constructed

(Kissel et al 1984; Wanner and Gujer, 1986; Wanner and Reichert, 1996). However,

even though these dynamical models were able to describe complex multispecies

interactions within the biofilms, they were not able to generate complex biofilm

morphologies. The reason for this outcome was that those models required the biofilm

morphology as an input (determined by the user), i.e. the biofilm morphology was not

generated as a model output. Thus, new modelling approaches were necessary which

could reproduce the types of 3D structures observed for biofilms (de Beer et al. 1994;

Costerton et al. 1995). A computational approach that revolutionized biofilm modelling

during the 1990's was the cellular automata (CA) approach (Wimpenny and Colasanti, 1997; Hermanowicz, 1998, 1999, 2001; Picioreanu étal. 1998a, 1998b, 1999; Noguera et al 1999; Pizarro et al 2001; Chang et al 2003; Hunt et al 2003, 2004; Laspidou and Rittman, 2004; Chambless et al 2006). CA models are discrete models, in which space, time and properties of the system only can have a finite number of possible states. The model space (domain) is composed of elements organized in a regular spatial lattice/grid (2D or 3D) for which the state of the elements is updated synchronously according to local rules. A common feature of CA biofilm models is their inherent ability to generate a wide range of observed biofilm morphologies. Thus, in CA biofilm models the biofilm morphology is not a model input (as in previous biofilm models). Instead, local interactions (governed by the rules) between the bacteria in the CA results in biofilm morphologies that are observed as model output. Since the rules in CA biofilm models often are stochastic in nature, the output from different simulations will not be identical. However, even though the output differs between different CA simulations, general trends are often possible to identify by analyzing the results from multiple simulations. A related discrete modelling approach is individual based modelling (IBM), which also is widely used in biofilm research (e.g. Kreft et al 1998, 2001; Kreft and Wimpenny, 2001, Xavier et al 2004, 2005, 2007; Alpkvist et al 2006; Picioreanu et al 2007). The major difference between CA biofilm models and IBM biofilm models lays in the biomass distribution and the biomass spreading mechanism. As described above, in CA biofilm models the biomass is located in grids (squares or cubes of biomass), and hence biomass spreading can only occur in a finite number of grid directions, as well as distances (discrete biomass spreading). IBM biofilm models, on the other hand, are gridless and hence the biomass can take any position in the modelling domain and consequently biomass spreading can occur in a continuous set of directions and distances (continuous biomass spreading). This is achieved by minimizing the overlap of the cells, which will relax the pressure that has been build-up through the increase in biomass. Another strong feature associated with IBMs (a feature that indeed can be incorporated in CA biofilm models as well) is that the agents/individuals (e.g. bacteria) are treated individually, i.e. as independent entities with there own state and behaviour.

The individuals/agents interact with one another and with the environment, and these interactions often give rise to complex global dynamics and patterns. This closely reflects the behaviour of individual bacteria as well, where each cell would respond to its specific local microenvironment, based on chemical and physical stimuli, as well as its interactions with other cells. Thus, this individual based feature is particularly useful for studying global complex systems in which individual heterogeneity is important.

However, from a computational point of view, individual heterogeneity can also be a disadvantage since many details requires more computational effort (compared to non individual CA models with the same spatial resolution). One way to circumvent this is to allow the presence of larger biomass particles (usually 10 - 20 jim in diameter). This approach, termed as particle-based modelling, gives up the individual cell representation while still keeping the IBM associated shoving or pushing principle for biomass spreading (Picioreanu et al. 2004). As described, both CA biofilm models as well as

IBM biofilm models represent biomass as discrete units/particles. This is in contrast to the continuum biofilm models, which assume no discrete representation of individuals

(Wanner and Gujer, 1986; Dockery and Klapper, 2001, Eberi et al. 2001; Alpkvist et al.

2004; Alpkvist and Klapper, 2007). Instead, these models regard the biomass as a continuum medium, thus applying partial differential equations for biomass balance to describe its development in time. In these models, shapes, sizes and local interaction between individual cells are not directly taken into account. Instead they assume that concentrations/densities of biomass may be adequately described by one or more density fields and that these density fields obey some sort of conservation law, e.g. conservation of mass or momentum. The main advantage with this modelling approach (compared to the discrete CA and IBM approaches) is the use of well known partial differential equations (e.g. describing biomass developing in time). Model simulations are therefore a matter of solving equations governed by a frame-work of numerical analysis, which today is well developed. Moreover, continuum based models generate deterministic solutions (one solution for each given initial condition), which is in contrast to the solutions generated by stochastic CA models and IBMs (often infinite possible solutions for each given initial condition). Thus, only one simulation (for each initial condition) is necessary for continuum based models, while CA models and IBMs require multiple simulations (for each initial condition) before any conclusions can be postulated. However, formulation and derivation of continuum based models requires a comprehensive mathematical skill, making this approach less accessible for most biofilm researcher.

Some of the processes usually included in biofilm models are computationally intense, which has lead to the development of a method called pseudo-steady state modelling to alleviate this problem. In this modelling approach, fast processes are separated from slow processes according to their characteristic calculation times. For example, in a biofilm system the process of diffusion and substrate uptake are fast compared with the process of microbial growth, decay and spreading (Kissel et al. 1984; Wanner and Gujer, 1986; Picioreanu et al. 2000). When using the concept of pseudo steady state in biofilm modelling, diffusion and substrate uptake are continued until a stationary substrate concentration profile is reached. Then the growth, decay and spreading processes are evaluated (but often with much larger time steps), assuming that the substrate concentration gradient does not change over time. The computational

efficiency of this separation of fast and slow processes results from the elimination of

the computational time that would otherwise be required to evaluate very small changes in biofilm thickness (biomass) when the two processes (fast and slow) are solved using the smaller time steps. This modelling approach has allowed for biofilm models to incorporate more parameters, thus increasing the complexity of the models allowing them to advance beyond the previous models describing biofilms at a fixed moment in time, to models capable of simulating the transient behaviour of biofilms. 1.10. Why mathematical modelling?

Mathematical modelling can be regarded as an additional tool to inform and make predictions about wet-lab experiments. More specifically, mathematical models can be used for a number of applications such as;

o for systems that are affected by several processes acting simultaneously, e.g.

biofilm formation, mathematical models can be used to study the

interdependence of these processes, and also to identify those processes that are

most important for the system,

o evaluate the importance of different parameters within a system and how they

effect the system,

o investigate, and possibly explain, biological processes that would be impossible

to study by wet-lab experiments,

o test hypotheses,

o design experimental protocols. 1.11. Aims of the thesis

This thesis is presented as two separate sets of models that treat bacteria as complex communities that interact with each other or as multicellular entities. The models presented are related to: 1) modeUing of quorum sensing; and 2) biofilm modelling.

1.11.1. Modelling of quorum sensing

As described above, the QS modelling work performed so far has focused on individual

QS systems, e.g. the lux system in V. fischeri and the Las system in P. aeruginosa.

Given that most regulatory circuits do not act in isolation, as is the case for the AHL regulatory network in P. aeruginosa, we were interested in how the Las/Rhl systems and global regulators interact to control QS in P. aeruginosa. Therefore, to explore these interactions, a mathematical model of the AHL regulatory network in P. aeruginosa was developed. This model embraced both the Las system as well as the Rhl system, which have been described by a system of ordinary differential equations. In addition, the regulators RsaL and Vfr were also included in the model system. The model was analyzed by steady state calculations and a systematic evaluation of each interaction and parameter incorporated in the model system.

Moreover, as described previously, QS has been suggested as a potential target for control strategies. For example, it has been speculated that AHL antagonists, i.e. QS blockers (QSBs), would interfere efficiently with the QS system in P. aeruginosa. To explore this possibility, the QS model developed was furthered to also incorporate AHL antagonists. This enabled us to investigate the dynamics of the QS system in P. aeruginosa when disturbed by AHL antagonists. 1.11.2. Biofilm modelling

It is currently appreciated that there are many fundamental processes that interact in a complex manner during biofilm formation. The first objective of this part of the thesis was to develop an individual based CA biofilm model that includes fundamental processes, such as the diffusion of substrate, substrate consumption, bacterial growth, spreading and detachment. This individual based CA biofilm model is expected to serve as a framework to explore biofilm development, with the possibility to expand the model by the addition of other processes that are thought to be important during biofilm development.

The second objective of the biofilm modelling was to use the individual based CA biofilm model developed to identify and test key aspects of biofilm development that lead to cell death during biofilm development. Several hypotheses (death rules) were tested and compared with wet-lab experiments.

Taken together, this thesis includes four different aims:

1. Develop a mathematical model of the hierarchical quorum sensing system in P.

aeruginosa. This model will be used to investigate how the las and rhl systems

along with RsaL and Vfr interact to control quorum sensing in P. aeruginosa.

2. The model developed in (1) will be modified to also incorporate quorum sensing

blockers. This model will be used to investigate the dynamics of the quorum sensing

system in P. aeruginosa when disturbed by AHL antagonists. In addition, the effect

of different AHL antagonists will also be tested.

3. Develop an individual based CA biofilm model that includes the some of the key

metabolic parameters involved in biofilm formation. 4. Use the model developed in (3) to investigate the implications of cell death during

biofilm development. Chapter 2. The role of regulators in the

expression of quorum sensing signals in Pseudomonas

aeruginosa

2.1. Introduction

Pseudomonas aeruginosa is a Gram-negative, opportunistic human pathogen that

infects immunocompromised individuals, such as cystic fibrosis (CF) patients, or those

having breaches in normal barriers caused by bums, indwelling medical devices or

prolonged use of antibiotics (Douglas et al 1998; Pesci et al 1999). The capacity of P.

aeruginosa to induce severe infections is due to the coordinated expression of an arsenal

of virulence factors, many of which are controlled by a mechanism that monitors

bacterial cell density (Pesci et al 1999). The coordinated expression of virulence genes

allows P. aeruginosa to secrete virulence factors only when they can be produced at

sufficiently high levels to overcome host defences (Pearson et al 1997; Pesci et al

1999). The ability of an individual bacterium to sense and respond to its population

density is called quorum sensing (QS). This phenomenon is widespread in Gram-

negative as well as Gram-positive bacteria. In some Gram-negative bacteria, the QS

system utilizes small signal molecules called acylated homoserine lactones (AHLs) or autoinducers. At low cell density, autoinducers are believed to be synthesized at basal levels. These autoinducers are able to diffuse out of the cell into the surrounding media, as well as into the cell, resulting in equilibrium between the extracellular space and the intracellular space. As the cell density increases, so does the intracellular level of the autoinducer until it reaches a threshold concentration. At this threshold concentration, it has been proposed that the autoinducer helps to trigger the induction of the QS dependent genes (Douglas et al 1998; Pesci et al 1999). P. aeruginosa has two overlapping AHL producing circuits; the las system and the rhl system. The las system is composed of LasI and LasR. LasI is an autoinducer synthase that synthesizes N-3- oxododecanoyl-L-homoserine lactone (also known as PAI-1, OdDHL or 30-C12-HSL). LasR works as a transcriptional activator in the presence of the autoinducer 30-C12- HSL (Pesci et al. 1999). The LasR/30-C12-HSL complex controls the expression of several virulence genes and also plays a role in biofilm differentiation (Pearson et al. 1997; Davies et al. 1998; Pesci et al. 1999). In addition, the LasR/30-C12-HSL complex also binds to the lasi promoter and allows an initial rapid rise in autoinducer synthesis, which increases the concentration of 30-C12-HSL available to bind to LasR (Seed et al. 1995). The rhl system is composed of the transcriptional activator RhlR and Rhll, the autoinducer synthase that synthesizes the cognate autoinducer, N-butyryl-L- homoserine lactone (also known as PAI-2, BHL or C4-HSL). The rhl system also regulates the expression of several virulence genes and some genes not directly involved in virulence. It has been suggested that the LasR/30-C12-HSL complex induces the expression of rhlR placing the las system above the rhl system in the cell-to-cell signalling hierarchy (Latifi et al. 1996; Pesci et al. 1999). Moreover, 30-C12-HSL can bind to RhlR and thereby block the binding of C4-HSL to its transcriptional activator protein. This autoinduction hierarchy is suggested to allow P. aeruginosa to delay the induction of genes controlled by rhl QS (Pesci et al. 1997). Recently, other regulatory systems have been shown to be involved in the control of the las system in P. aeruginosa. For example, Vfr, a cyclic AMP receptor protein homologue, influences the expression of LasR and it has been suggested that the P. aeruginosa QS cascade begins with the production of Vfr (Albus et al. 1997). It has been shown that Vfr is required for lasR expression, and that there is a putative cyclic AMP receptor protein consensus binding site in the promoter of lasR (Pesci et al 1999). Vfr is believed to induce conformational changes in the promoter region, which may increase the affinity between the lasR promoter and the LasR/30-C12-HSL complex (Albus et al 1997; Pesci et al 1999). An inhibitor, RsaL, also affects the las system. This inhibitor is believed to repress lasi expression thereby blocking activation of the P. aeruginosa QS cascade. At low cell densities, it has been suggested that RsaL competitively inhibits the transcription of lasI by binding to the lasI operator region. As the cell density increases, the intracellular concentration of 30-C12-HSL increases, which enables sufficient LasR/30-C12-HSL complex formation to outcompete RsaL for binding to the lasI operator (de Kievit et al 1999). For a summary of the QS system in P. aeruginosa, see Figure 2-1 (adopted, with some small changes, from van Delden and Iglewski, 1998). Most of the modelling work performed so far has focused on individual signalling systems, e.g. the lux system in Vibrio fischeri (James et al 2000) and the las system in P. aeruginosa (Dockery and Keener, 2(X)1). Given that most regulatory circuits do not act in isolation, as is the case for the AHL regulatory network in P. aeruginosa, we were interested in how the las/rhl systems and the regulators RsaL and Vfr interact to control QS in P. aeruginosa. To explore these interactions, we have developed a theoretical model for the AHL regulatory network in this organism. Our results indicate that the system as a whole has two stable steady states, and when a specific threshold concentration of extracellular 30-C12-HSL (with a corresponding concentration of intracellular 30-C12-HSL) has been reached, the system will suddenly switch from a low steady state to a high steady state. In biological terms, this high steady state corresponds to an induced phenotype. The level of this threshold concentration is greatly dependent on the regulators RsaL and Vfr. RsaL will increase the concentration of extracellular 30-C12-HSL required to induce the system, whereas Vfr will decrease the concentration of extracellular 30-C12-HSL required to induce the system. We have also demonstrated this dependency of the system on Vfr experimentally by monitoring signal production in the wild type and a vfr mutant of P. aeruginosa. Virulence genes

Virulence genes

Cell membrane Figure 2-1. The cell-to-cell signalling hierarchy in P. aeruginosa. LasI, an autoinducer synthase synthesizes 30-C12-HSL, Rhll is an autoinducer synthase that synthesizes C4- HSL, LasR and RhlR are transcriptional activators, OdDHL is an autoinducer, also called 30-C12-HSL, BHL is also an autoinducer molecule that is alternatively named C4-HSL, RsaL is a LasI inhibitor, and Vfr is a LasR inducer. 2.2. Model theory In the model system, a single bacterium exposed to various concentrations of extracellular 30-C12-HSL is envisaged. In addition, it is assumed that there is no change in bacterial cell volume over time (e.g. during changes from logarithmic to stationary growth phase). The model is based on the las and rhl genes and their products in P. aeruginosa, and it includes only those components considered as central to the dynamics of the system. The model is a system of eight coupled differential equations, following the rate of change in the concentration of LasR, RhlR, RsaL, 30-C12-HSL, C4-HSL, the LasR/30-C12-HSL complex, the RhlR/ C4-HSL complex and the RhlR/30-C12-HSL complex. To simplify the model system, a number of assumptions were made. First, it was envisaged that protein turnover is slower than the degradation of mRNA and that there is no significant post-transcriptional regulation. Therefore, in the model system, binding of the R-protein/autoinducer complex to a promoter directly results in protein synthesis. Second, it was also assumed that there is no shortage of substrate for autoinducer synthesis. As a consequence, there is no need to explicitly model the biosynthesis of 30-C12-HSL and C4-HSL by the LasI and Rhll synthases. Third, production of LasR, RhlR, RsaL, 30-C12-HSL, and C4-HSL are assumed to follow Michaelis-Menten kinetics. In such systems, the rate of production has an upper limit determined by Vmax, whereas Km determines the affinity between a particular complex and a promoter (Fersht, 1999). Fourth, both 30-C12-HSL and C4-HSL are assumed to diffuse freely across the bacterial cell membrane. This seems to be biologically correct for C4-HSL. However, there is evidence that 30-C12-HSL requires the MexA-MexB-oprM encoded efflux pump for its extrusion (James et al. 1999). Since the model is focused on the genetic regulation of the QS system, the subtleties of active efflux vs. diffusion have been ignored, and this model assumes free diffusion of both

C4-HSL and 30-C12-HSL.

2.2.1. R-protein/AHL complexes

At the molecular level, this model takes into consideration the formation of three

different kinds of complexes. First, 30-C12-HSL is allowed to form a complex with

LasR, C/. Second, 30-C12-HSL can associate with RhlR, Cs, and finally, C4-HSL can

form a complex only with RhlR, C2. Complex formation proceeds according to the law

of mass action, i.e. when two or more reactants are involved in a reaction step, the rate

of reaction is proportional to the product of their concentration. C; associates at rate ki

and dissociates at rate kz, respectively. Similarly, C2 and C3 are formed at rates ks and

ks, respectively, and dissociate at rates k4 and kó, respectively. Mathematically, it is now

possible to formulate the rate of change in the formation of these complexes as:

= (Eq.2-1) at

= (Eq.2-2) at

^ = (Eq.2-3)

where Rj and R2 are the cellular concentrations of LasR and RhlR, respectively, and A;

and A2 are the cellular concentrations of 30-C12-HSL and C4-HSL, respectively.

2.2.2. LasR

The production of LasR is determined by C;, VRI, and KRJ. LasR has a maximum rate of production that is determined by VRI. KRJ is a constant that determines the affinity between the LasR/30-C12-HSL complex (C;) and the lasR promoter. In the absence of C;, LasR is assumed to be constitutively expressed at rate TRI and that LasR is degraded proportionally to its own concentration and that this proceeds at rate ÒRI. In this model system, the rate of change for LasR is also positively influenced by the dissociation of Cj. Ci dissociates at rate fo- Finally, there is a loss of LasR due to its association with 30-C12-HSL which proceeds at rate kj. dR = + - + —C ^ + T,,. (Eq. 2-4) at

2.2.3. RhlR The maximum rate of production of RhlR is determined by Vr2, whereas the affinity between C; and the rhlR promoter is determined by Kr2. The production of RhlR is also positively affected by C;. In the absence of C;, RhlR is expressed at a basal production rate, Tr2. Further, the degradation of RhlR is considered to be proportional to its own concentration and it proceeds at rate bR2. The concentration of RhlR increases due to the dissociation of C2 and C3. This is supposed to proceed at the rates k4 and ke for C2 and Ci, respectively. However, there is also a loss of RhlR due to RhlR association with autoinducers. With respect to RhlR, two different scenarios exist, depending on whether or not RhlR forms a complex with 30-C12-HSL. If RhlR forms a complex with 30- C12-HSL, the system corresponds to:

^ = -R,A,k, + C,k, - R,A,k, + C,k, - + ^ + (Eq. 2-5) at where ks and ks are rates at which RhlR {R2) and C4-HSL (A2), and RhlR and 30-C12- HSL (A/) associate, respectively. If the possibility that RhlR and 30-C12-HSL can form a complex is disregarded, then the system simplifies to: dR = + - + C ^ + T,,. (Eq. 2-6)

2.2.4. RsaL The rate of change for RsaL depends on C;, V5 and Ks. This is in accordance with the above assumptions regarding LasR and RhlR. Likewise, Ks is an affinity parameter determining the affinity between Cj and the rsaL promoter, and Vs is the maximum rate of RsaL production. It is also assumed that RsaL is constitutively produced at a basal level determined by the basal production rate Ts, and that RsaL is degraded proportionally to its own concentration which proceeds at rate bs. dS , o T r C*, ^

2.2.5. 30-C12-HSL The production of 30-C12-HSL is assumed to be not only positively influenced by the LasR/30-C12-HSL (C;) complex but also negatively affected by RsaL. In the model system, RsaL is assumed to work as a competitive inhibitor, and therefore the Michaehs-Menten formula for competitive inhibition is used. In equation 2-8 below, VAI is the maximum rate at which 30-C12-HSL is produced due to the interaction between Ci and the to/promoter (the '30-C12-HSL promoter' in the model), and KAI depicts the affinity between Ci and the lasi promoter. In contrast, Ksi determines the affinity between RsaL and the lasI promoter. In the absence of Ci, 30-C12-HSL is constitutively expressed at rate TAI- It is also assumed that 30-C12-HSL is degraded at rate BAI in proportion to the concentration of 30-C12-HSL, A;. In the model, the concentration of 30-C12-HSL is positively influenced by the dissociation of C; and Q, which is assumed to take place at rates k2 and ke, respectively. It is further assumed that there is a loss of 30-C12-HSL due to its association with LasR and RhlR. This occurs at rates ki and ks for C; and C3, respectively. In this model system, 30-C12-HSL is assumed to diffuse freely across the bacterial cell membrane. This is assumed to occur at rate dj, in proportion to the concentration of 30-C12-HSL. The parameter Aiex determines the concentration of extracellular 30-C12-HSL available for the cell. In addition, as was the situation for RhlR, we envisage two plausible scenarios. First, the situation in which 30-C12-HSL, A;, is allowed to form complex with RhlR is considered. In such a situation, the rate of production for 30-C12-HSL corresponds to:

^ = -RAK + C,k, - + C,k, - + V,, ^^ — + T,, + d, - A,)

(Eq. 2-8) Second, it is assumed that 30-C12-HSL does not form a complex with RhlR. Hence, Eq. 2-8 simplifies to:

dA = + - + C ^ — + r„ + d, (A,„ -A,). (Eq. 2-9) ^51

2.2.6. C4-HSL The production of C4-HSL, A2, follows the same principles as for the production of 30- C12-HSL. Va2 is the maximum rate for C4-HSL production, and Ka2 is the affinity between C2 and the rhll promoter (the 'C4-HSL promoter' in the model). The concentration of C4-HSL is also dependent on C2. At low levels of C2, C4-HSL is constitutively expressed at rate Ta2- It is also assumed that C4-HSL is degraded at rate bA2 proportionally to its own concentration. Further, there is a loss of C4-HSL due to its association with RhlR. This proceeds at rate ks. The concentration of C4-HSL, however, is positively affected by the dissociation of C2, which takes place at rate k4. C4-HSL is supposed to diffuse freely over the bacterium cell membrane at rate dz. The parameter A2ex determines the concentration of extracellular C4-HSL available for the cell. In summary, the rate of change for C4-HSL is defined as:

^ = + - + —^ + T,, + d, (A,,, - A,). (Eq. 2-10)

For a summary of the variables and parameters used in the model system, see Table 2-1.

2.2.7. Steady State and Stability Analysis One of the objectives of this study was to understand the dynamics of the AHL regulatory network in P. aeruginosa, and particularly investigate whether the system equilibrates, oscillates or behaves chaotically. The term 'steady state' implies a condition where the rate of change in the concentrations of the variables included in the model is equal to zero (Edelstein-Keshet, 1987). The steady states are obtained by solving the system of coupled differential equations simultaneously. Moreover, the qualitative behaviour of the steady states was also of interest. Biologically speaking, it is of interest to understand what happens to the dynamics if the system is disturbed. In biological systems, this is essential since bacterial cells constantly have to adapt and respond to different environmental conditions. The stability of the steady states is determined by analyzing the eigenvalues of the linearization of the system. If all the eigenvalues have negative real parts then the steady state is locally stable (Edelstein- Keshet, 1987). Table 2-1. Definition of variables and parameters Variable/ Unit Description parameter A; ^iM Cellular concentration of autoinducer 30-C12-HSL A2 jiM Cellular concentration of autoinducer C4-HSL Alex |iM Extracellular concentration of 30-C12-HSL Alex ^iM Extracellular concentration of C4-HSL bAi 1/s Degradation constant for 30-C12-HSL bA2 1/s Degradation constant for C4-HSL bRi 1/s Degradation constant for LasR bR2 1/s Degradation constant for RhlR bs 1/s Degradation constant for RsaL Ci jiM Cellular concentration of LasR/30-C12-HSL complex C2 |iM Cellular concentration of RhlR/C4-HSL complex Cs |iM Cellular concentration of RhlR/30-C12-HSL complex di 1/s Diffusion constant of 30-C12-HSL through the cell membrane d2 1/s Diffusion constant of C4-HSL through the cell membrane ki 1/jiMs Rate constant of binding reaction between LasR and 30- C12-HSL k2 1/s Rate constant of dissociation reaction of LasR and 30-C12- HSL ks y|iMs Rate constant of binding reaction between RhlR and C4-HSL k4 1/s Rate constant of dissociation reaction of RhlR and C4-HSL ks 1/^Ms Rate constant of binding reaction between RhlR and 30- C12-HSL ks 1/s Rate constant of dissociation reaction of RhlR and 30-C12- HSL KAI jiM A constant that deteimine the affinity between the LasR/30- C12-HSL complex and the promoter KA2 jiM A constant that determine the affinity between the RhlR/30- C12-HSL complex and the rhll promoter KRJ jiM A constant that determine the affinity between the LasR/30- C12-HSL complex and the lasR promoter KR2 jiM A constant that determine the affinity between LasR/30- C12-HSL complexes and the rhlR promoter Ks A constant that determine the affinity between the LasR/30- C12-HSL complex and the rsaL promoter Ksi A constant that determine the affinity between RsaL and the lasi promoter Ri |iM Cellular concentration of LasR R2 |iM Cellular concentration of RhlR S |iM Cellular concentration of RsaL TAI |liM/S Rate constant for basal transcription of 30-Cl 2-HSL TA2 |iM/s Rate constant for basal transcription of C4-HSL TRI |iM/s Rate constant for basal transcription of LasR TR2 |iM/s Rate constant for basal transcription of RhlR Ts )iM/s Rate constant for basal transcription of RsaL VAI jxM/s The maximum rate at which 30-Cl 2-HSL is produced |iM/s The maximum rate at which C4-HSL is produced VRI )iM/s The maximum rate at which LasR is produced VR2 |iM/s The maximum rate at which RhlR is produced Vs |iM/s The maximum rate at which RsaL is produced 2.3. Results

2.3.1. Quorum sensing dynamics The central component in the AHL regulatory network is the LasR/30-C12-HSL complex. In addition to its role as an inducer of several virulence genes, it also induces the transcription of lasR, lasi and rhlR. Therefore, it was postulated that the concentration of LasR/30-C12-HSL is an indication of the induction of the whole AHL system. In Figure 2-2, the steady state concentration of the LasR/30-C12-HSL complex is shown as a function of increasing concentrations of extracellular 30-C12-HSL (extracellular 30-C12-HSL can either be added experimentally or produced by other cells in the population). At low levels of extracellular 30-C12-HSL (below 1.171 |iM in this example), the dynamics of the system are characterized by one locally stable steady state. In this situation, the system equilibrates at low concentrations of the LasR/30- C12-HSL complex. This steady state is believed to correspond to an uninduced phenotype. In contrast, at high levels of extracellular 30-C12-HSL (above 2.057 )iM in this example) the system equilibrates at a much higher level of the LasR/30-C12-HSL complex. This steady state is suggested to correspond to an induced phenotype. Between these two levels of extracellular 30-C12-HSL, the dynamics of the system exhibit a complex behaviour of changes characterized by two locally stable steady states (solid lines) and one locally unstable steady state (dotted lines). Here, the bacteria can switch from an uninduced phenotype represented by the lower level of the LasR/30- C12-HSL complex to an induced state represented by the higher concentration of the LasR/30-C12-HSL complex. The unstable steady state is a saddle point that separates the two locally steady states from each other. For a given set of parameters, the system will end up either in an induced phenotype or in an uninduced phenotype depending on the initial values of the components in the las system (the arrows indicate the movement of the system at different concentrations of the LasR/30-C12-HSL complex). If the initial concentrations of the components are low, the dynamics of the system are characterized by an uninduced phenotype. Here, a relatively high concentration of extracellular 30-C12-HSL is required to induce the system. On the other hand, if the initial values of the components are high, the concentration of extracellular 30-C12- HSL required to induce the system are much lower. Thus, once the system has reached a critical threshold concentration, the dynamics of the system are characterized by a jump from the low steady state to the high steady state, and the concentration of the LasR/30- C12-HSL complex will increase rapidly.

2.3.2. Influence of RhlR/30-C12-HSL complex formation on the activation of the rhl system Two scenarios are considered in the present model (Figure 2-3). First, RhlR and 30- C12-HSL are assumed to not form a complex. In such a situation, the concentration of the RhlR/ C4-HSL complex equilibrates at 1.9 )iM, and this equilibration occurs relatively fast (solid line). In the second scenario, it is assumed that RhlR and 30-C12- HSL can form a complex. By varying the rate at which they associate, denoted by ks, it is not only possible to investigate how the final concentration of RhlR/C4-HSL is affected but also the relative time it takes for RhlR/C4-HSL to form a complex (broken lines). In general, the higher the ks value, the longer it takes for the RhlR/C4-HSL complex to accumulate inside the bacterial cell. Interestingly, the final concentration of the RhlR/C4-HSL complex is not affected by the ks value. 4.5-|

4.0-

3.5-

i 3.0- 3, X^ 2.5- Q "O O 2.0- ^w m 1.5-

1.0-

0.5- i iYrtrc 0- 0.5 1.0 1.5 2.0 2.5 3.0 Extracellular OdDHL {\iM)

Figure 2-2. The steady state concentration of the LasR/30-C12-HSL complex as a function of increasing concentration of extracellular 30-C12-HSL (which is annotated here as OdDHL). When the concentration of extracellular 30-C12-HSL is below a specific value, there exists only one low stable steady state in the system. When the concentration of extracellular 30-C12-HSL exceeds this specific value, another higher stable steady state, as well as an unstable steady state, will be formed. The unstable steady state is a saddle point that separates the two steady states from each other. When another specific concentration of extracellular 30-C12-HSL is reached, the lower of the two stable steady states will cease to exist and only the high stable steady state will remain. The arrows in the figure show the movement pattern in the system. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were ki = 0.17 (1/jiM s), fe = 0.25 (1/s), k3 = 0.17 (1/)J.M s), k4 = 0.25 (1/s), ks = 0.17 (l/|iM s), k6 = 0.25 (1/s), bRi = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), bA2 = 0.2 (1/s), Trj = 0.004 (jiM/s), Tr2 = 0.004 (^M/s), Ts = 0.004 (|iM/s), Tai = 0.004 (jiM /s), Ta2 = 0.004 (jiM /s), Vri = 0.6 (jiM /s), = 0.6 (liWs), Vs = 0.9 (^iM/s), Va; = 1.2 (|iM/s), yA2 = 1 (^M/s), KRJ = 4 (|iM), KR2 = 1.2 (|lM), Ks = 1 (^M), Kai = 0.4 (^iM), Kai = 1 (|iM), Ksi = 2.5 (|lM), dj = 0.2 (1/s), d2 = 0.4(l/s), andA2ex = 0(jiM). V . i

No RhIR/OdDHL complex k5 = 0.2 l/^mol s ks = 0.4 l/pmol s ks = 0.6 l/iimol s

T 100 200 300 400 500 600 700 800 Trme (s}

Figure 2-3. The concentration of the RhlR/C4-HSL complex as a function of time. C4- HSL is abbreviated here as BHL. 30-C12-HSL (abbreviated as OdDHL) can delay activation of the rhl system by binding to RhlR. In the solid line, there is no formation of RhlR/30-C12-HSL complexes. The other lines originate from a system allowing complex formation between 30-C12-HSL and RhlR. To see the influence from this complex formation, the parameter ks was varied, ks is the rate constant of binding reaction between RhlR and 30-C12-HSL. The model with influence from RhlR/30- C12-HSL complex formation consists of the differential equations 2-1, 2-2, 2-3, 2-4, 2- 5, 2-7, 2-8 and 2-10. The other model, i.e. without influence from RhlR/30-C12-HSL complex formation consists of the differential equations 2-1, 2-2, 2-4, 2-5, 2-7, 2-9 and 2-10. The parameter values used were ki = 0.17 (l/|iM s), k2 = 0.25 (1/s), ks = 0.17 (l/jiM s), k4 = 0.25 (1/s), ks = [0.2, 0.4, 0.6] (1/îM s), ke = 0.25 (1/s), bRi = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), Z?a2 = 0.2 (1/s), Tn = 0.004 (|iM/s), Tr2 = 0.004 (jiM/s), Ts = 0.004 (}iM/s), Tai = 0.004 (jiM /s), Tai = 0.004 (jiM /s), Vri = 0.6 (îM /s), = 0.6 (jiM/s), V5 = 0.9 (|iM/s), Vî = 1.2 (îM/s), Va2 = 1 (^M/s), Kri = 4 (îM), Kr2 = 1.2 (jiM), Ks = 1 (|iM), Kai = 0.4 (jiM), Ka2 = 1 (|iM), Ksi = 2.5 (|iM), di = 0.2 (1/s), d2 = 0.4 (1/s), Alex = 4 (|iM) SindA2ex = 0 (liM). The formation of the RhlR/30-C12-HSL complex also influences the las system, but not to the same extent as is observed for the rhl system. The explanation for this behaviour is that the las system is active before RhlR is being produced (not shown). As recently demonstrated by de Kievit et al (2002), the LasR/30-C12-HSL complex is the dominant regulator of Rhll. This assumption was incorporated into the model by modifying Eq. 2-10. However, incorporating this assumption into the model only had minor quantitative effects on the induction of the rhl system (not shown).

2.3.3. The role of RsaL as an inhibitor This model allows one to explicitly analyze the effect of RsaL on the formation of the LasR/30-C12-HSL complex. Here it is assumed that RsaL is a competitive inhibitor of the LasR/30-C12-HSL complex in binding to the to/promoter. Hence, the basal rate of RsaL production as well as the affinity of RsaL for the lasi promoter has to be taken into consideration. In Figure 2-4, a comparison is made between a system in which no RsaL production takes place (Figure 2-4, line a) with a system in which the basal production rates of RsaL are varied (Figure 2-4, lines b - where the basal production rates of RsaL, LasR and 30-C12-HSL are the same- and c - where the basal production rate of RsaL is 100 times higher). The model analysis clearly demonstrated that the AHL regulatory system in P. aeruginosa is very sensitive to changes in the basal production rate of RsaL. In the system without any production of RsaL (Figure 2-4, line a), a much lower concentration of extracellular 30-C12-HSL is required to induce the system (switch from an uninduced phenotype to an induced phenotype), compared with the system with production of RsaL (Figure 2-4, lines b and c). 5.0 n 4.5 4.0-

- 3.0-

i 2.5 Q W 1.5H 1.0- 0.5-

0 , , p- 0.5 1.0 1.5 2.0 2.5 3.0 Extracellular OdDHL (\LM) Figure 2-4. The steady state concentrations of the LasR/30-C12-HSL complex are shown as a function of increasing concentration of extracellular 30-C12-HSL (marked as OdDHL in the figure). Line a, no RsaL production; line b, basal production is then same for RsaL, 30-C12-HSL and LasR; and line c, basal production is 100 times higher for RsaL (compared with both LasR and 30-C12-HSL). For each line, the solid lines correspond to two stable steady states whereas the dotted line corresponds to an unstable steady state. The concentration of extracellular 30-C12-HSL needed to induce a system is higher in a system where 30-C12-HSL production is influenced by RsaL (lines b and c), compared with a system in which the 30-C12-HSL production is independent of RsaL (line a). The figure also demonstrates that basal production of RsaL (compared with LasR and 30-C12-HSL) has a major impact on the level of this concentration (lines b and c). Both models (with and without influence of RsaL) used the differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10). However, the model without influence of RsaL, used a modified version of equation 2-8, in which "1 + (S/Ksiy\( i.e. the influence of RsaL) was deleted from the equation. The parameter values used were ki = 0.17 (l/|iM s), fe = 0.25 (1/s), ks = 0.17 (l/jiM s), k4 = 0.25 (1/s), ks = 0.17 (1/îM s), ks = 0.25 (1/s), bRi = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), Z?a2 = 0.2 (1/s), TRI = 0.004 (|iM/s), TR2 = 0.004 (|LiM/s), Ts = [a = no RsaL production, b = 0.004, c = 0.4] (|iM/s), TAI = 0.004 (^M /s), TA2 = 0.004 (|iM /s), Vri = 0.6 (jiM /s), y/?2 = 0.6 (îM/s), Vs = 0.9 (|aM/s), VAI = 1.2 (|iM/s), VAI = 1 (^M/s), Kri = 4 (îM), Kr2 = 1.2 (^M), Ks = 1 (îM), Kai = 0.4 (îM), KA2 = 1 (|iM), Ksi = 2.5 (jiM), DI = 0.2 (1/s), D2 = 0.4 (1/s) and A2ex = 0 ([IM). Furthermore, if the basal production rate of RsaL is increased, the concentration of extracellular 30-C12-HSL required to induce the system will increase further (Figure 2-

4, lines b and c). These comparisons assumed a value of Ksi = 2.5 jiM (affinity between

RsaL and the lasi promoter) and of KAI = 0.4 |iM (affinity between the LasR/ 30-C12-

HSL complex and the lasI promoter). Thus, the affinity between the signal-receptor complex and the promoter is much higher than between RsaL and the promoter.

Therefore, emphasis was placed on how the affinity between RsaL and the lasI promoter affects the concentration of extracellular 30-C12-HSL needed to induce the system (Figure 2-5). As expected, a decrease in the Ksi value (increased affinity of RsaL for the lasI promoter) will increase the concentration of extracellular 30-C12-HSL needed to induce the system. Furthermore, if the basal production rates are higher for

RsaL (compared with LasR and 30-C12-HSL), the increase in requirement for will be of greater magnitude. In line a, the basal production rates are the same for RsaL, LasR and 30-C12-HSL and in line b, the basal production rate for RsaL is 100 times higher then for LasR and 30-C12-HSL.

2.3.4. Vfr as a modulator of quorum sensing

In the model system, it is hypothesized that Vfr increases the affinity between the

LasR/OdDHL complex and the lasR promoter. In Figure 2-6, the steady-state concentration of the LasR/OdDHL complex is shown as a function of increasing concentration of extracellular OdDHL. In addition, three different affinity values were also compared. KRI is the parameter determining the affinity between the LasR/OdDHL complex and the lasR promoter. In line a, KRI = 3 |iM; in line b, KRJ = 3.5 |iM, and in line c, KRI = 4.0 |iM. A low KRI value indicates a high affinity. As can clearly be seen in

Figure 2-6, an increase in this affinity will decrease the concentration of extracellular OdDHL required to induce the system, i.e. the opposite effect of RsaL. Thus, it seems that this parameter is a significant factor for the induction of the whole QS circuit in P. aeruginosa. To identify the relationship between this affinity and the concentration of extracellular 30-C12-HSL needed to induce the system, a comparison was made between these two parameters (Figure 2-7). In Figure 2-7, the concentration of extracellular 30-C12-HSL needed to induce the system is presented as a function of

KRI. The model clearly shows that as Km decreases (increasing affinity) the concentration of extracellular 30-C12-HSL required to induce the system decreases in a linear fashion. 3.2-

3.0-

% 2.8-

i 2.6- O • fc v ^ . • : CO • 3 2.4-

2.0-

1.8 10 15 20 KS1 {\iM)

Figure 2-5. The concentration of extracellular 30-C12-HSL (marked as OdDHL in the figure) required to induce the system at different affinity values between RsaL and the las I promoter. Ksi is the parameter that determines this affinity. When the affinity between RsaL and the las I promoter increases, so will the concentration of extracellular 30-C12-HSL needed to induce the system increase. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were: ki = 0.17 (l/|iM s), fo = 0.25 (1/s), ks = 0.17 (l/jiM s), k4 = 0.25 (1/s), fe = 0.17 (l/|iM s), k6 = 0.25 (1/s), bm = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), bA2 = 0.2 (1/s), Tri = 0.004 (|iM/s), Tr2 = 0.004 (jiM/s), Ts = [di = 0.004, b = 0.4] (|iM/s), TAI = 0.004 (iiM /s), TA2 = 0.004 (|iM /s), Vri = 0.6 (^M /s), = 0.6 (îM/s), = 0.9 (jlM/s), Va; = 1.2 (liM/s), = 1 (^M/s), Kri = 4 (îM), Kr2 = 1.2 (îM), KS = 1 (|iM), KAI = 0.4 (îM), = 1 (^M), KSI = varied (jiM), DJ = 0.2 (1/s), i/2 = 0.4 (1/s), and A2ex = 0 (jiM). 5.5-1 5.0- 4.5- 4.0- 3.5 3.0 XQ §T3 2.5 (0 2.0 1.5 1.0 0.5 0 1 1 1 =n 0 0.5 1.0 1.5 2.0 2.5 3.0 Extracellular OdDHL ([iM)

Figure 2-6. The steady state concentration of the LasR/30-C12-HSL complex is shown as a function of increasing concentration of extracellular 30-C12-HSL (marked as OdDHL) (at different affinity values between the LasRy30-C12-HSL complex and lasR). Line a, Krj = 3.0 |iM; line b, Krj = 3.5 |iM; and line c, Kri = 4 |iM. A low Kri value indicates a high affinity. This example clearly indicates that when this affinity increases, the concentration of extracellular 30-C12-HSL required to induce the system decreases. For each line, the two solid lines correspond to two stable steady states, whereas the dotted line corresponds to an unstable steady state. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were: ki = 0.17 (l/}iM s), fe = 0.25 (1/s), fe = 0.17 (l/|iM s), k4 = 0.25 (1/s), k5 = 0.11 (1/jiM s), ks = 0.25 (1/s), Òri = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), bAi = 0.2 (1/s), Z?a2 = 0.2 (1/s), Tri = 0.004 (|iM/s), Tr2 = 0.004 (|iM/s), Ts = 0.004 (îM/s), Tai = 0.004 (|iM /s), Tai = 0.004 (|iM /s), Vri = 0.6 (^M /s), y/i2 = 0.6 (jlM/s), = 0.9 (jiM/s), Vaì = 1.2 (îM/s), Va2 = 1 (|iM/s), Kri = [a = 3.0, b = 3.5, c = 4.0] (jiM), Kr2 = 1.2 (|iM), Ks = 1 (|iM), Kai = 0.4 (jiM), Kai = 1 (|iM), Ksi = 2.5 (îM), di = 0.2 (1/s), d2 = 0.4 (1/s), and = 0 (jiM). 3.5-

3 4 Kri {\iM) Figure 2-7. This figure visualizes the concentration of extracellular 30-C12-HSL (marked as OdDHL) needed to induce the system as a function of KRI. KRI is the parameter that determines the affinity between the LasR/30-C12-HSL complex and the lasR promoter. It is shown that the lower Kri value, the lower is the concentration of extracellular 30-C12-HSL needed to induce the system. In this example, differential equations (2-1, 2-2, 2-3, 2-4, 2-5, 2-7, 2-8 and 2-10) were used and the parameter values used were: kj = 0.17 (1/^M s), k2 = 0.25 (1/s), ks = 0.17 (1/jiM s), k4 = 0.25 (1/s), ks = 0.17 (l/jiM s), k6 = 0.25 (1/s), ÒRI = 0.2 (1/s), bR2 = 0.2 (1/s), bs = 0.25 (1/s), Òai = 0.2 (1/s), bA2 = 0.2 (1/s), Tri = 0.004 (|iM/s), Tr2 = 0.004 (|iM/s), Ts = 0.004 ()i.M/s), Tai = 0.004 (^M /s), Ta2 = 0.004 (^M /s), Vri = 0.6 (\iM /s), Vr2 = 0.6 (îM/s), = 0.9 (^M/s), Vaì = 1.2 (\IM/s), Va2 = 1 (|iM/s), KRJ = varied (îM), KR2 = 1.2 (|iM), KS = 1 (^M), KAI = 0.4 (jiM), KA2 = 1 (jiM), KSI = 2.5 (|iM), dj = 0.2 (1/s), d2 = 0.4 (1/s), and A2.. = 0 (îM). 2.3.5. Signal production by Pseudomonas aeruginosa To experimentally test the model, signal production in the P. aerugionsa wild-type, a vfr mutant and the vfr mutant complemented with a plasmid encoded copy of vfr were compared. There was no significant difference in the growth of the three P. aeruginosa strains in Luria-Bertani broth as determined by spectrophotometry (Figure 2-8). Analysis of the AHL bioassay results indicated that P. aeruginosa produced detectable quantities of AHLs at all time points, with the exception of hours 1 and 2 where there was no detectable signal produced for any of the three strains (Figure 2-8). The amount of signal increased with cell density over the growth cycle of the organism. Interestingly, the vfr mutant strain produced less signal during the early phase of growth (OD610 0.06-0.27), but during the latter phases of growth, and in particular during the transition and stationary phases (ODeio 0.5 and later), there was no detectable difference in signal production between the three strains (Figure 2-8). Notably, the vfr mutant produced approximately half the amount of signal as the wild type (ODeio 0.06-0.27). For example, at 4 h after inoculation (ODeio 0.14), the mutant produced the same amount of signal (diameter 1.15 cm) as the wild type did at 3 h after inoculation (OD610 0.06). A similar difference in signal production between the wild type (diameter: from 2.1 to 3.0 cm) and mutant (diameter: from 1.15 to 2.35 cm) was observed for hours 4 and 5 (ODeio: from 0.15 to 0.3). The vfr mutant was also delayed in the initiation of signal production (t = 4 h) compared with the wild type (t = 3 h). This would suggest that the presence of Vfr significantly increases signal production during the logarithmic phase of growth (t = 3-6 h). Time ih)

Figure 2-8. Signal production in P. aeruginosa wild type and vfr mutant. The relative amount of signal produced by the three strains, the wild type, the vfr mutant and the vfr mutant carrying pSB299.15A (encoding a wild-type vfr) was determined using an agar diffusion assay with the monitor strain A. tumefaciens A136. The growth of the strains is shown on the left-hand axis and the amount of signal produced is shown on the right- hand axis, wt = Wild type. The complemented strain produced levels of signal that were similar to that of the wild type. Because P. aeruginosa produces several AHL signals, we chromatographed the samples on TLC plates (CI8, reverse phase) to separate individual signals, and overlaid the TLC plate with the Agrobacterium tumefaciens A136 monitor. The results indicated that P. aeruginosa produced three distinct signals (Figure 2-9). One signal corresponded to 30-C12-HSL (Figure 2-9, marked as A), as compared with a 30-C12-HSL standard.

The other two signals (Figure 2-9, marked as B and C, respectively) are probably 30-

C8-HSL and 30-C6-HSL, although standards were not included for those AHLs. The results from the TLC analysis suggest that there is no preferential inhibition of either of the three detected signals. This would be expected as these signals are all produced through the activity of LasI (Pearson et al 1994) and thus suggests that loss of Vfr leads to a reduction in the amount of LasI present in the cells in the early phase of growth or at low cell densities. Figure 2-9. To separate individual signals produced by the three strains, the wild type, the vfr mutant and the vfr mutant carrying pSB299.15A (encoding a wild-type v/r), the samples were chromatographed on CI8 reverse phase TLC plates. To visualize the spots, the plates were overlaid with the Agrobacterium tumefaciens A136 monitor. The results indicated that P. aeruginosa produced three different signals, corresponded to 30-C12-HSL (marked as OdDHL and A), as compared with a 30-C12-HSL standard and two other signals (marked as B and C, respectively), probably 30-C8-HSL and 30- C6-HSL. 2.4. Discussion

The AHL regulatory system in P. aeruginosa exhibits a complex behaviour as the

concentration of extracellular 30-C12-HSL increases (Figure 2-2). The results

presented here will remain qualitatively the same for a wide range of parameter values.

This is an important result since most of the parameter values used in the model system

have not been experimentally defined. It is, however, important to stress that it is the

relationship between the different parameters rather than the actual values of the

parameters that determines the behaviour of the system. The parameter values used in

the figures were chosen to match steady state concentrations of 30-C12-HSL reported

in the literature (e.g. Pearson et al 1994). At low concentrations of extracellular 30-

C12-HSL, the system has one locally stable equilibrium. However, as the concentration

of extracellular 30-C12-HSL increases, the behaviour of the system changes

dramatically and a second steady state appears. At this new steady state, the system

equilibrates at a much higher level of the LasR/30-C12-HSL complex inside the cell. In

such a situation, the system will switch from the uninduced state to an induced state if

the concentration of extracellular 30-C12-HSL reaches a specific threshold value.

Interestingly, if the concentration of extracellular 30-C12-HSL increases further, the

lower steady state ceases to exist and the system equilibrates at a high level of the

LasR/30-C12-HSL complex. This result is in agreement with earlier analyses

performed on LasR/LasI in P. aeruginosa (Dockery and Keener, 2001). James et al.

(2000) also arrived at a similar conclusion regarding the LuxR/LuxI system in V. fischeri.

This model is not only the first to consider the interaction between the las and rhl

systems, but also the first study to theoretically address the role of regulators on the expression of QS signals in P. aeruginosa. The results suggest that these regulators play important roles in the control of QS phenotypes. The model predicts that RsaL will raise the concentration of extracellular 30-C12-HSL required to induce the system (Figures

2-4, 2-5). Without RsaL, the system would be induced earher, i.e. at a lower cell density. These findings are in accordance with the suggestion by de Kievit et al. (1999) who speculated that in an rsaL mutant (no RsaL produced), lasi would be turned on earlier than in a wild-type bacterium. The model predicts that this occurs under decreased concentrations or in the absence of RsaL in the cell. Furthermore, if the influence of RsaL is considered, the basal production of RsaL is the parameter that most profoundly affects the threshold concentration of extracellular 30-C12-HSL required to induce the system (Figure 2-4). In the uninduced state, RsaL and LasRy30-C12-HSL complexes in the cell are derived from the basal production. If there is a relatively high rate of production of RsaL (compared with LasR and 30-C12-HSL), there is a need for a high concentration of LasR/30-C12-HSL complexes to overcome the blocking effect of RsaL. At high concentrations, LasR/30-C12-HSL complexes will outcompete RsaL for binding to the lasI promoter and the system is consequently induced. Another parameter that will influence the concentration of extracellular 30-C12-HSL needed to induce the system is the affinity between RsaL and the lasI promoter, i.e. Ksi (Figure 2-

5). As the affinity between RsaL and the lasI promoter increases, the concentration of extracellular 30-C12-HSL required to induce the system will also increase. The inhibitory effect of RsaL can be overcome if the concentration of the LasR/30-C12-

HSL complex increases, which is dependent on a higher concentration of extracellular

30-C12-HSL. The other parameters that influence the concentration of RsaL in the cell, i.e. V5 (the maximum RsaL production rate) and Ks (the affinity of RsaL for the lasI promoter), do not significantly influence the concentration of extracellular 30-C12-HSL needed to induce the system (data not shown). Based on the results presented in this study, it is suggested that RsaL is a key element in the inhibition of the QS system at low cell densities (as speculated by de Kievit et al. (1999)). However, RsaL is also induced by the QS system. The reason for this is not clear, but it may be that later in the stationary phase, the Vfr expression decreases which in turn will increase the concentration of the LasR/30-C12-HSL complex required to maintain the system in an induced state. This, together with the high concentration of RsaL present, will ensure that the system rapidly shuts off in the late stationary phase. If this is true, RsaL also works as an inhibitor at higher cell densities or during nutrient exhaustion. Interestingly, the signal data (Figure 2-8) indicate that signal production may have peaked around 11 h after inoculation and then began to decline, suggesting that the system has begun to switch back towards the uninduced state.

The model also predicts that the change in affinity between the LasR/30-C12-HSL complex and the lasR promoter caused by Vfr will have a significant impact on the behaviour of the system. Importantly, Vfr decreases the concentration of extracellular 30-C12-HSL required to induce the system (Figures 2-6, 2-7). There are several situations when this scenario would be an advantage in a population of cells. For example, it would be beneficial to switch to a communal lifestyle at low nutrient availability and when the population is still at low cell densities. Such conditions may involve the production of Vfr. Because of changes in affinity between the LasR/30- C12-HSL complexes and the lasR promoter, Vfr will decrease the concentration of extracellular 30-C12-HSL required to induce the system. Since the concentration of extracellular 30-C12-HSL is a measure of the cell density, Vfr allows the bacteria the ability to induce the AHL system also at lower cell densities. Thus, when nutrient levels become insufficient to sustain planktonic growth, induction of the QS system through Vfr could lead to initiation of biofilm formation. Thus, the model predicts that there exist two ways to induce the AHL system, either through the production of high concentrations of extracellular 30-C12-HSL and/or production of Vfr. The experimental data would also support this outcome of the model, where signal production is delayed in a vfr mutant, especially in the early phase of growth. Indeed, the cell density of the vfr mutant must be almost double that of the wild type to produce the same relative signal activity (Figure 2-8, t = 3 and 4 h). In contrast, the vfr deletion did not appear to affect signal production in the latter phases of growth (e.g. t = 5 h, mid-logarithmic phase), which suggests that signal production becomes independent of Vfr. This contrasts with results published by Albus et al. (1997), who demonstrated that Vfr is required for production of LasR. Those results would imply that signal production should also be similarly dependent on Vfr, if LasR is required for expression of LasI, the signal synthase. It should be noted, however, that the latter study only measured LasR expression after 24 h of growth and did not measure expression earlier. Thus, it could be that Vfr plays a role in maintaining signal production in the late stationary phase as well as in the early phases of growth, although the data in this study on signal production at 24 h does not seem to support this. It is also possible that differences in media (Luria-Bertani vs. tryptic soy broth) may account for the two different results.

The results presented in this work lead to the conclusion that the AHL system in P. aeruginosa will be induced once a threshold concentration of intracellular 30-C12-HSL has been reached. This actually means that the system jumps from a low steady state to a high steady state at this threshold concentration of intracellular 30-C12-HSL. The threshold concentration is very much dependent on the concentration of RsaL and Vfr in the cell. Increasing concentrations of RsaL requires a higher concentration of extracellular 30-C12-HSL (higher cell density) to reach the threshold concentration (outcompete the blocking effect from RsaL). In contrast, higher concentrations of Vfr will decrease the concentration of extracellular 30-C12-HSL needed to reach the threshold concentration, and the system will be induced despite the relatively low 30- C12-HSL concentration. If the 30-C12-HSL concentration reflects cell density, then it can be understood that increasing expression of this regulator would lead to induction at a 'lower' cell density than without it. Once the system is induced, the formation of RhlR/30-C12-HSL complexes together with induction of rhlR by the LasR/30-C12- HSL complexes ensures that the rhl system is induced after the las system. Recently, de Kievit et al (2002) have shown that, although the rhl system (the RhlR/C4-HSL complex) will induce rhll, the las system (the LasR/30-C12-HSL complex) is the dominant inducer of rhll. However, this most interesting finding does not change the conclusions presented in this study. The results presented here are mostly dependent on the las system only, and the finding by de Kievit et al. (2002) mainly affects the induction of the rhl system. Therefore, the conclusions here still hold true despite this latter finding. Indeed, when this observation was taken into account, the effect on rhl expression was negligible (data not shown). The results from this study also highlight the need of theoretical analyses in order to understand complex behaviour of interconnected processes at the molecular level. A dynamic molecular system is often characterized by positive as well as negative feedback loops. In such a system, it is difficult to experimentally disentangle the role of individual regulatory molecules (e.g. LasR, Vfr), as they themselves are part of the regulatory system in concern. By the use of mathematical modelling, we may in fact improve our understanding of quite complex systems such as the las and rhl system in P. aeruginosa. Other advantages of models are that they not only allow us to analyze a wide range of parameter values but also allow us to postulate different scenarios based on theoretical predictions.

Future studies of the modelling of the AHL system in P. aeruginosa could involve factors that either prevent induction of the system or 'inactivate' the system if it is already induced. The identification of such a factor would be very helpful in the treatment of patients infected with P. aeruginosa. A possible factor would be a 30-C12-

HSL antagonist such as a furanone (Givskov et al. 1996; Rasmussen et al. 2000).

Furanones are a class of compounds that have been demonstrated to inhibit AHL- mediated QS by inhibiting the association of the signal with the receptor protein, as exemplified in this model by the 30-C12-HSL/LasR complex formation. It has been demonstrated that such signal antagonists are potent inhibitors of QS processes

(Givskov et al. 1996; Rasmussen et al. 2000). The effects of a QS inhibitor are modelled in Chapter 3. Similarly, factors that effect the expression of regulators such as

Vfr and RsaL would be potential targets for the modulation of QS phenotypes. The present study indicates that these two regulators can have a major impact on the induction of the system. For example, a bacterium with high concentrations of RsaL and low concentrations of Vfr would have to produce significantly more 30-C12-HSL to induce the AHL system compared with a bacterium producing low concentrations of

RsaL and high concentration of Vfr. During the course of this study, it has been identified that there are potentially two steady states associated with 30-C12-HSL production. One steady state represents an induced state and the other an uninduced state. Furthermore, the data suggest that regulators such as Vfr and RsaL may play key roles in the control or expression of QS phenotypes. 2.5. Experimental procedure

2.5.1. Bacteria, media and growth conditions

The bacterial strains used in this study include: P. aeruginosa PAOl (ATCC 15692), the Vfr mutant, PAOlv/r (Beatson et al 2002), PAOlv/r carrying pSB299.15A which carries a wild-type copy of Vfr (Beatson et al 2002), and A. tumefaciens A136 (Fuqua

et al. 1996). P. aeruginosa strains were kindly provided by the laboratory of J. Mattick

(University of Queensland).

Bacteria were routinely grown and maintained on Luria-Bertani medium with 1% NaCl

(Bertani, 1951). ABT medium was used for the measurement of AHLs in culture

supematants using the A. tumefaciens strain (ABT: 0.3 M (NH4)2S04, 0.34 M

Na2HP04, 0.22 M KH2PO4, 0.51 M NaCl, 1 mM MgCh, 0.1 mM CaClz, 0.01 mM

FeCl2, 2.5 mg thiamin supplemented with 0.5% glucose and 0.5% casamino acids)

(Clark and Maaloe, 1967). Tetracycline (6 |ig/ml) was used to maintain plasmid

selection for A. tumefaciens A136, and ampicillin (150 }ig/ml) was used to maintain pSB299.15A in P. aeruginosa.

2.5.2. Collection of signal-containing supematants

P. aeruginosa strains were grown overnight in LB at 37° C with shaking (180 rpm) and were diluted 1:100 the following morning into fresh medium. Three separate cultures were grown for each strain. Samples, 3 ml, were collected, the optical density (610 nm) was measured to determine growth, and the cells were removed by centrifugation and subsequent filtration through 0.2-|im filters (0.2-|im Supor Acrodisc filters, Pall Gelman Laboratories). The supematants were stored at -20° C. Supematants were extracted 3 times using ethyl acetate, and the organic phases for each sample were pooled and taken to dryness. The dried supematants were resuspended in 0.1 ml of ethyl acetate.

2.5.3. Determination of AHL concentration from Pseudomonas aeruginosa Supernatant extracts, 50 |il, were added to wells that had been made in agar plates seeded with the AHL monitor strain A. tumefaciens A136 as described (Fuqua et al 1996). The plates were incubated at 30° C for 24 or 48 h and the amount of signal were quantified by measuring the diameter of the induced zone (the monitor strain produces 6-galactosidase in the presence of AHLs which hydrolyzes X-gal in the medium (75 |ig/ml)). The concentration of AHLs in the supernatant extract was determined by measuring the diameter of the induced zone; at least 3 measurements of the diameter were averaged for each sample and the average of the 3 repHcates for each strain is presented. Separation and identification of individual AHL molecules were achieved by using the monitor strain in combination with TLC separation of the signals, as described in Shaw et al. (1997) and Ravn et al (2001). Chapter 3. Modelling the effect of acylated

homoserine lactone antagonists in Pseudomonas

aeruginosa

3.1. Introduction

Pseudomonas aeruginosa is a Gram-negative bacterium capable of forming biofilms, which offers protection from environmental stresses. Indeed, biofilms of P. aeruginosa are more resistant to antibiotics, disinfectants as well as host defences compared to planktonic cells (Costerton et al. 1999; Davey and O'Toole, 2000). Furthermore, the ability of P. aeruginosa to cause severe illness is due in part to the density dependent expression of an arsenal of virulence factors. This phenomenon, termed quorum sensing

(QS), allows P. aeruginosa to coordinate the expression of virulence factors once they have reached high cell numbers (de Kievit and Iglewski, 2000). For a more thorough description of QS in Gram-negative bacteria, see Chapter 2.1.

The QS system in P. aeruginosa consists of two circuits (Figure 3-1), the las and the rhl systems (Pesci et al 1997; Pesci and Iglewski, 1999). The las system is composed of

Las I, an autoinducer synthase that synthesizes the autoinducer A^-3-oxododecanoyl- homoserine lactone (30-C12-HSL), and LasR which operates as a transcriptional activator in the presence of 30-C12-HSL. The LasR/30-C12-HSL complex induces several virulence genes as well as lasi itself, creating a positive feedback loop (Pesci and Iglewski, 1999). This autoinduction hierarchy is responsible for a dramatic increase in the expression of virulence genes once a critical cell density has been reached (Seed etal 1995). The rhl system works in a similar way as the las system (Pesci et al. 1997; Pesci and

Iglewski, 1999). It is composed of the transcriptional activator RhlR, and Rhll, the autoinducer synthase that synthesizes the autoinducer A^-butanoyl-homoserine lactone

(C4-HSL). The rhl system also regulates the expression of several virulence genes. It has been shown that the LasR/30-C12-HSL complex induces the expression of rhlR placing the las system in a cell-to-cell signalling hierarchy above the rhl system (Pesci et al 1997). Moreover, 30-C12-HSL can bind to RhlR and thereby block the binding of

C4-HSL to its transcriptional activator protein. In this way, 30-C12-HSL works as an inhibitor of the rhl system (Pesci et al 1997). I have previously modelled this system, and demonstrated that the QS system in P. aeruginosa works as a biochemical switch between two stable steady states, one with low levels of autoinducers and one with high levels of autoinducers (Fagerlind et al 2003), Chapter 2). It was also shown that the system could switch from the steady state with low levels of autoinducers to the steady state with high levels of autoinducers when a specific threshold concentration of intracellular autoinducer has been reached. These findings were in agreement with earlier theoretical studies of the lux system in Vibrio fischeri (James et al 20(X)) and the las system in P. aeruginosa (Dockery and Keener, 2(X)1). The high infection and mortality rates observed for P. aeruginosa make it imperative to identify appropriate therapeutic interventions against P. aeruginosa infections, especially in light of the development of resistance to many of the available antibacterial drugs (Drenkard and

Ausubel, 2002; Huang et al 2002; Loureiro et al 2002). Thus, the finding that QS controls biofilm formation and the production of virulence factors in P. aeruginosa makes this system an interesting target for control strategies. 30-C12-HSL ^, ^ Cms RT-'-Ì ^ ^ antagonist

30-C12-HSL Viruienee genes n

C4-ftSL Viruience genes O

rhfl' Ceil membrane Figure 3-1. The cell-to-cell signalling hierarchy in Pseudomonas aeruginosa. Solid lines indicate the known QS systems within P. aeruginosa. Antagonist items are marked as dashed lines. LasI is an autoinducer synthase which synthesizes the autoinducer 30- C12-HSL; Rhll is an autoinducer synthase which synthesizes the autoinducer C4-HSL; LasR and RhlR are transcriptional activators; RsaL is a LasI inhibitor; Vfr acts to induce LasR expression and 30-C12-HSL antagonist is an inhibitor of 30-C12-HSL regulated reactions. For example, it has been suggested that a QS blocker (QSB), would interfere efficiently with the QS system in P. aeruginosa (Passador et al 1993; Pearson et al. 1994; Finch et al. 1998) and potentially abrogate virulence in this pathogen. The Australian marine macroalga Delisea pulchra produces a number of halogenated furanones that are structurally very similar to the AHL molecules found in bacteria (Givskov et al 1996). These autoinducer antagonists have been demonstrated to disrupt bacterial cell-cell communication and are thought to be used by the alga to prevent colonization of, or biofilm formation on, its surface. The inhibitory activity of autoinducer antagonists has been demonstrated in a range of bacteria, including Vibrio fischeri (Milton et al 1997), Serratia liquefaciens (Givskov et al 1996, Lindum et al 1998; Manefield et al 1999; Rasmussen et al 2000), Erwinia carotovora (Manefield et al 2001) and P. aeruginosa (Hentzer et al 2002, 2003).

Recent studies on autoinducer antagonists, including the halogenated furanones, have given rise to several models with respect to the properties and mode of action of these molecules. These include the proposal that antagonists work by displacing autoinducers from their cognate R-protein and hence prevent activation of the R-protein (Manefield et al 1999; Hentzer et al 2002). Moreover, Manefield et al (2002) suggested that halogenated furanones induce a rapid degradation of the LuxR protein in V. fischeri. These authors showed that the half-life of the LuxR protein was reduced as much as 100-fold in the presence of halogenated furanones. In contrast, Zhu and Winans (2001) demonstrated that TraR, in the presence of autoinducers, has a half-life of 70 min whereas TraR in the absence of AHLs has a half-life as short as 2 min. Thus, it appears that autoinducers protect its cognate R-protein against degradation whereas halogenated furanones increase the degradation of the R-protein. Recently, Hentzer et al (2002) reported that the naturally derived furanone compounds have a rather limited effect on

P. aeruginosa when tested individually. However, the furanone compounds can be modified through combinatorial chemistry to generate a large number of analogues.

Such an exercise has identified synthetic furanones that displayed stronger inhibitory properties than those showed by the natural furanone compounds and also demonstrated the utility of QSBs as treatments of biofilms, a finding that suggests QSBs have significant potential as a biofilm control strategy (Hentzer et al 2002).

In this study, I was interested in: (a) the dynamics of the QS system in P. aeruginosa when disturbed by a 30-C12-HSL antagonist and (b) whether QSB properties can be enhanced by altering the 30-C12-HSL antagonists. It was hypothesized that an alteration of a 30-C12-HSL antagonist will influence the affinity between the 30-C12-

HSL antagonist and the R-proteins, i.e. LasR and RhlR, and its ability to enhance degradation of the R-proteins. To disentangle these outcomes, I extended the QS model of P. aeruginosa (Fagerlind et al 2003), Chapter 2) by introducing, in silico, different

30-C12-HSL antagonists. The 30-C12-HSL antagonists differed with respect to the properties discussed above, i.e. (1) different affinity values between the 30-C12-HSL antagonist and the R-proteins and (2) different rates of 30-C12-HSL induced degradation of the R-proteins. The 30-C12-HSL antagonists introduced into the system were assumed to bind to, but not activate the R-proteins (Figure 2-1). The simulation results indicate that 30-C12-HSL antagonists represent a potential therapeutic approach for P. aeruginosa infections. Under certain conditions, the 30-C12-HSL antagonists will drive the system to the low steady state, which will serve to inactivate the expression of phenotypes in an otherwise induced QS system. The two properties tested were also shown to play significant roles for the dynamics of the system. Most importantly, the model predicted that the 30-C12-HSL antagonist induced degradation of LasR is the core parameter for successful QSB based inhibition of the QS system in P. aeruginosa. 3.2. Model theory In Fagerlind et al. (2003), Chapter 2), a mathematical model of the two overlapping QS systems in P. aeruginosa was developed in order to capture the dynamics of these systems in response to changes in the concentration of extracellular 30-C12-HSL. In addition, RsaL and Vfr were included as modulators of the QS response to determine their effects on the dynamic behaviour of the QS system. This model used a nonhnear system of eight coupled ordinary differential equations to study the concentrations of LasR, 30-C12-HSL, LasR/30-C12-HSL complex, RhlR, C4-HSL, RhlR/C4-HSL complex, RsaL, and the RhlR/30-C12-HSL complex.

In order to model non-spatial dynamics there are three well-established methods, systems of ordinary differential equations, systems of recurrence equations and agent based models. For all of these models, the dynamics are given by an updating-rule, which describes how the variables change. In this section, a brief description of updating-rule, mathematical theory and numerical tools will be given for these three kinds of models. When modelling dynamics using a system of recurrence equations, it is assumed that the time is discrete and the time step is constant. Values of variables are dependent on earlier values and are given by functions, i.e. usually a straightforward calculation. The mathematical theory for this is well developed, where there exists a number of efficient methods for finding steady states and there exists useful criteria for deciding stability of a steady state. It is rather simple to simulate a system of recurrence equations on a computer. If the system is stiff, i.e. the system has a large variation in its time-dependent response, then one has too choose a very small time step in order to achieve accuracy. In this case, the computation will take long time. A system of recurrence equations is efficient to use for non-stiff problems with straight forward updating rule. When modelling the dynamics by a system of agents it is assumed that the time is discrete and the time step is constant. Values of variables are dependent on earlier values and may be presented in complex ways. Mathematical issues such as finding steady states and deciding stabiUty could be difficult with this approach. As with a system of recurrence equations, it is rather easy to simulate agents on a computer but for stiff problems it may take a long time for computation. Agent based models can be used and have advantages for spatial modelling or for systems with complex updating rule. When modelling the dynamics of a system described by a system of ordinary differential equations, it is assumed that the time is continuous. The system updates continuously, and the derivatives are given by smooth functions. For this approach, the mathematical theory is also well developed, and stability criteria are almost the same as for a system of recurrence equations. Using commercial numerical procedures, it is not a hard task to simulate a system of ordinary differential equations.

Even stiff problems may be handled with high accuracy. Now consider the two overlapping QS systems in P. aeruginosa modelled by Fagerlind et al. (2003) and also consider the present chapter. From a biological point of view, it is rather natural to assume continuous time and suspect stiffness, therefore the appropriate modelling tool here would be to use systems of ordinary differential equations.

In this chapter, I extend the model developed by Fagerlind et al. (2003), (Chapter 2) to also include 30-C12-HSL antagonists. It is assumed that this antagonist is able to diffuse through the cell membrane and competitively bind to both LasR and RhlR

(Figure 3-1). A thorough description of the model is presented below. For easier understanding of the model description, all variables and parameters used by the model are denoted in Table 3-1. Table 3-1. Definition of variables and parameters Variable/ Unit Description parameter Oil ^M"^ s"^ Rate constant of binding reaction between LasR and 30- C12-HSL ^ s-^ Rate constant of dissociation reaction of LasR and 30-C12- HSL 0C2 Rate constant of binding reaction between RhlR and C4-HSL s-^ Rate constant of dissociation reaction of RhlR and C4-HSL (Xi Rate constant of binding reaction between RhlR and 30- C12-HSL ^ s-^ Rate constant of dissociation reaction of RhlR and 30-C12- HSL Ot Rate constant of binding reaction between LasR and 30- C12-HSL antagonist 1 S4 s"^ Rate constant of dissociation reaction of LasR and 30-C12- HSL antagonist Os Rate constant of binding reaction between RhlR and 30- C12-HSL antagonist S5 s-^ Rate constant of dissociation reaction of RhlR and 30-C12- HSL antagonist Ai Intracellular concentration of autoinducer 30-C12-HSL AIEX |iM Extracellular concentration of autoinducer 30-C12-HSL AIA Intracellular concentration of 30-C12-HSL antagonist AIAE îM Extracellular concentration of 30-C12-HSL antagonist A2 |iM Intracellular concentration of autoinducer C4-HSL A2EX jiM Extracellular concentration of autoinducer C4-HSL bRi s-^ Degradation constant for LasR bR2 s-^ Degradation constant for RhlR bs s-^ Degradation constant for RsaL bAi s-^ Degradation constant for intracellular 30-C12-HSL bAlEX s-^ Degradation constant for extracellular 30-C12-HSL bA2 s-^ Degradation constant for intracellular C4-HSL bA2EX s-^ Degradation constant for extracellular C4-HSL bMl s-^ Degradation constant for intracellular 30-C12-HSL antagonist bM2 s-^ Degradation constant for extracellular 30-C12-HSL antagonist bM3 s-^ Degradation constant for LasR/30-C12-HSL antagonist complex (only LasR is degraded) bM4 s-^ Degradation constant for RhlR/30-C12-HSL antagonist complex (only RhlR is degraded) Ci Cellular concentration of the LasR/30-C12-HSL complex C2 Cellular concentration of the RhlR/C4-HSL complex C3 jiM Cellular concentration of the RhlR/30-C12-HSL complex C4 Cellular concentration of the LasR/30-C12-HSL antagonist complex Cs Cellular concentration of the RhlR/30-C12-HSL antagonist complex di Diffusion constant of 30-C12-HSL through the cell membrane d2 Diffusion constant of C4-HSL through the cell membrane ds Diffusion constant of 30-C12-HSL antagonists through the cell membrane KAI |iM A constant that determines the affinity between the LasR/30-C12-HSL complexes and the /izs/promoter. KA2 |iM A constant that determines the affinity between the RhlR/30-C12-HSL complex and the r/i//promoter. KRI A constant that determines the affinity between the LasR/30-C12-HSL complex and the lasR promoter. KR2 A constant that determines the affinity between LasR/30- C12-HSL complexes and the MR promoter. Ks jiM A constant that determines the affinity between the LasR/30-C12-HSL complex and the rsaL promoter. KSI |iM A constant that determines the affinity between RsaL and the /as/ promoter RI îM Concentration of LasR R2 Concentration of RhlR s Concentration of RsaL TAI Rate constant for basal transcription of 30-C12-HSL TA2 îMs'^ Rate constant for basal transcription of C4-HSL TRI jiM s'^ Rate constant for basal transcription of LasR TR2 Rate constant for basal transcription of RhlR Ts îMs"^ Rate constant for basal transcription of RsaL VRI jiM s"^ The maximum rate at which LasR is produced

YR2 The maximum rate at which RhlR is produced Vs The maximum rate at which RsaL is produced VAI jiM s"^ The maximum rate at which 30-C12-HSL is produced

VA2 The maximum rate at which C4-HSL is produced 3.2.1. R-protein/AHL complexes In the model system, the rate of change in formation of five different complexes are considered: C; (LasR/30-C12-HSL); C2 (RhlR/C4-HSL); Cj (RhlR/30-C12-HSL); C4 (LasR/30-C12-HSL antagonist); and C5 (RhlR/30-C12-HSL antagonist). All complexes are assumed to be formed according to the law of mass action, i.e. when two or more reactants are involved in a reaction step, the rate of reaction is proportional to the product of their concentration. The law of mass action has been used in several other papers when modelling the formation of different complexes (e.g. Dockery and Keener, 2001; FagerUnd et al 2003; James et al 2000). Each equation below contains an association constant, a, (/=1, 2,. . ., 5), as well as a dissociation constant. Si (/=1, 2,. . ., 5). First, the rate of change for the LasR/30-C12-HSL complex is considered:

^at = (Eq.3-1) where Ri and Ai are the concentrations of LasR and 30-C12-HSL, respectively. Similarly, an expression for the rate of change for the RhlR/C4-HSL complex is derived: ^ = (Eq.3-2) dt where R2 and A2 are the concentrations of RhlR and C4-HSL, respectively. In the model system, 30-C12-HSL is also allowed to form a complex with RhlR. The rate of change for the RhlR/30-C12-HSL complex is expressed as: ^ = (Eq.3-3) dt ^ As mentioned before, a 30-C12-HSL antagonist will be included in the system. This compound is assumed to form a complex with LasR according to:

^ = - <^4^4 -¿>«3^4 (Eq. 3-4) dt where Ay^ is the concentration of the 30-C12-HSL antagonist. It is also assumed that the antagonist induces degradation of the LasR/30-C12-HSL complex at rate BMS. However, this degradation is assumed for the LasR part of the complex only, i.e. the antagonist will not be degraded during this reaction. Finally, it is assumed that the 30- C12-HSL antagonist also competes with C4-HSL in binding to RhlR and, as for LasR, also induces degradation of the R-protein. In such a situation, the rate of change of RhlR/30-C12-HSL antagonist complex is described by the equation: dC = ^S^IAA - - . (Eq. 3-5)

3.2.2. Simplifying assumptions Next, expressions for the rate of change in the concentration of LasR, RhlR, RsaL, 30- C12-HSL, and C4-HSL are derived. However, since complex model systems usually are very difficult to analyze, it is necessary to make some assumptions to simplify the model system. These assumptions/simplifications were also made in the model system developed in Fageriind et al (2003), (Chapter 2). First, it is presumed that protein degradation is slower than the degradation of mRNA and that there is no significant post-transcriptional regulation. Therefore, in the model system, binding of the R- protein/autoinducer complex to a promoter, results in protein synthesis directly. Second, it is also assumed that there is no shortage of substrate for autoinducer synthesis. Therefore, there is no need to explicitiy model the biosynthesis of 30-C12-HSL and C4-HSL by the LasI and Rhll synthases. Consequently, there is no need to include LasI and Rhll as variables in the model system. Third, production of LasR, RhlR, RsaL, 30- C12-HSL, and C4-HSL are assumed to follow the Michaelis-Menten equation (Eq. 3- 6), The Michaelis-Menten equation is a standard equation for modelling gene expression (Edelstein-Keshet, 1987) and it has been used for this purpose by several investigators previously (e.g. Dockery and Keener, 2001; Fagerlind et al. 2003; James et al. 2000): dP V C

In the system, P is the concentration of LasR, RhlR, RsaL, 30-C12-HSL or C4-HSL; dP/di is the rate of change of these products. The parameter Vmax is the maximum rate at which P is produced whereas KM is an affinity parameter determining the affinity between a complex and its cognate promoter (Fersht, 1999). The symbol C denotes one of the concentrations of complex Cy or C2.

3.2.3. LasR With regard to LasR (/?;), there is a loss of free LasR due to its association with 30- C12-HSL (A;) and the 30-C12-HSL antagonist {AJA). This proceeds at rates a; and 04, respectively. On the other hand, the rate of change in the concentration of LasR is increased due to the dissociation of the very same complexes. This occurs at rates Ô1 and Ô4, respectively. It is also assumed that LasR (i.e. free LasR (not in complex with an autoinducer)) is degraded proportionally to its own concentration and that this proceeds at the rate bm. LasR has a maximum rate of production that is determined by VRI whereas KRI is a parameter that determines the affinity between the LasR/30-C12-HSL complex (C;) and the lasR promoter. Taken together, an expression for the rate of change of LasR is formulated as:

^ = + - + - + + T,,, (Eq. 3-7) dt where TRI is the rate of basal transcription of LasR. 3.2.4. RhlR

The rate of change for RhlR (R2) follows the same principle as is the case for LasR. The main difference is that RhlR can bind both its cognate autoinducer C4-HSL, as well as

30-C12-HSL and 30-C12-HSL antagonists. This gives:

- T,,. ^at = + + + (Eq. 3-8)

3.2.5. RsaL

The variable C; affects the rate of change for RsaL in the following manner:

where Vs settles the maximum rate at which RsaL is produced whereas Ks depicts the affinity between the LasR/30-C12-HSL complex and the rsaL promoter. RsaL is naturally degraded at rate bs and the basal production occurs at rate Ts.

3.2.6. Intracellular 30-C12-HSL

Intracellular 30-C12-HSL (A;) is used in the formation of the LasR/30-C12-HSL complex (C7) as well as the formation of the RhlR/30-C12-HSL complex (Cj). The formation of these complexes proceeds at rates cc; and «5, respectively, and they dissociate at rates Si and S3, which leads to the formation of additional free 30C12-

HSL. The parameter VAI depicts the maximum rate at which 30-C12-HSL is produced whereas KAI determines the affinity between the LasR/30-C12-HSL complex and the to/promoter (the "30-C12-HSL promoter" in the model). RsaL is thought to work as a competitive inhibitor and therefore the Michaelis-Menten formula of competitive inhibition can be applied. The parameter Ksi determines the affinity between RsaL and the lasi promoter. Diffusion rates of 30-C12-HSL into or out of the cells are set at the rate DI. The basal production of 30-C12-HSL occurs at rate TAI whereas 30-C12-HSL is degraded at rate BAI. Summing up we get the differential equation:

^ = -a,/?,A, + . x + -A)- y (Eq. 3-10)

3.2.7. Extracellular 30-C12-HSL The concentration of extracellular 30-C12-HSL {AIEX) is positively affected due to the diffusion of intracellular 30-C12-HSL out of the cell. In contrast, there is a loss of extracellular 30-C12-HSL due the diffusion of extracellular 30-C12-HSL into the cell and due to the degradation of extracellular 30-C12-HSL as shown in the differential equation below:

dA^LEX dt = -^MIEX (Eq. 3-11) where BAIEX is the degradation rate for extracellular 30-C12-HSL.

3.2.8. Intracellular C4-HSL The production of C4-HSL (Az) follows the same principles as for the production of 30- C12-HSL. The main distinction is that C4-HSL production is induced by the RhlR/C4- HSL complex instead of the LasR/30C12-HSL complex, as was the case for 30-C12- HSL. In the same manner we get the differential equation:

^ = + + T,, + d, [A,,, - A,). (Eq. 3-12) dt + Q 3.2.9. Extracellular C4-HSL The concentration of extracellular C4-HSL (A2ex) follows the same principles as for extracellular 30-C12-HSL, that is:

dAr, = (Eq.3-13)

3.2.10. Extracellular 30-C12-HSL antagonist

The rate of change in the concentration of extracellular 30-C12-HSL antagonist (Aiae) is given by:

dA^lAE dt = - AJ-^A/IAAE» (Eq. 3-14)

Where Aja is the concentration of intracellular 30-C12-HSL antagonist. The parameter ds is the rate at which extracellular 30-C12-HSL antagonist diffuses into the cell but also the rate at which intracellular 30-C12-HSL antagonist diffuses out of the cell. Extracellular 30-C12-HSL antagonist is degraded at rate b^i.

3.2.11. Intracellular 30-C12-HSL antagonist Regarding the intracellular 30-C12-HSL antagonist (A/A), there is an increase in concentration due to the diffusion of extracellular 30-C12-HSL antagonist into the cell. There is also an increase in the concentration of intracellular 30-C12-HSL antagonist due to the dissociation of the LasR/30-C12-HSL antagonist and the RhlR/30-C12-HSL antagonist complexes and also because of antagonist induced degradation of the very same complexes (the antagonist part of the complexes is not assumed degraded in this degradation reaction). The concentration of intracellular 30-C12-HSL antagonist is negatively affected by its association with LasR and RhlR, and the diffusion out of the cell. There is also a loss caused by degradation (bMi)- Taken together, an equation for the rate of change for intracellular 30-C12-HSL antagonist is formulated as:

(Eq. 3-15) In Fagerlind et al (2003), (Chapter 2), it was shown that the QS system in P. aeruginosa works as a biochemical switch between two stable steady states, one with low levels of autoinducers (uninduced QS system) and one with high levels of autoinducers (induced QS system). It was also shown that the system could switch from the stable steady state with low levels of autoinducers to the stable steady state with high levels of autoinducers when a specific threshold concentration of intracellular autoinducer has been reached. To investigate the affect of different 30-C12-HSL antagonists, the model system was initially driven (without the presence of any antagonists) to the high stable steady state. This was achieved by running the model system until it entered the high stable steady state. Biologically speaking, this symbolizes the growth of a colony until the cell density is high enough for induction of the QS system (see also Fagerlind et al 2003), Chapter 2). When the model system reached the high stable steady state (no change in concentration of the different components over time) the antagonist was added, and its ability to drive the model system to the lower stable steady state was assessed. This scenario was executed with a number of different 30-C12-HSL antagonists as defined by their given properties. The difference between various 30-C12-HSL antagonists was characterized by their ability to induce degradation of the R-proteins and also by the affinity of the 30-C12-HSL antagonist for the R-proteins. This affinity is represented by the ratio (rate constant of the binding reaction between LasR and 30-C12-HSL antagonist/rate constant of the dissociation reaction of LasR and the 30-C12-HSL antagonist). All numerical simulation procedures were programmed in Matlab (The Math Works, Natick, MA, USA). A finite difference method was used to integrate the system of coupled non-linear ordinary differential equations. Since the system is stiff, a multistep method of variable order was used (Shampine and Reichelt, 1997; Shampine et al 1999). 3.3. Results The model simulations showed that the las system is the key system for successful inhibition of the QS system in P. aeruginosa (data not shown). This was expected since this system regulates the action of the rhl system in a hierarchical fashion (Figure 3-1). Therefore, focus is laid on the las system in the rest of the present chapter when considering the influence of different 30-C12-HSL antagonists.

3.3.1. Effect of increasing affinity between LasR and the 30-C12-HSL antagonist Figure 3-2 shows the concentration of a 30-C12-HSL antagonist that is required to silence the system (drive the system to the lower stable steady state) as a function of increasing affinity between the 30-C12-HSL antagonist and LasR. When the affinity between the 30-C12-HSL antagonist and LasR increases, the concentration of the 30- C12-HSL antagonist required to silence the system seems to decrease exponentially. Thus, at lower affinity values, an increase in affinity will result in a considerable difference in the concentration of 30-C12-HSL antagonist required to silence the system. When the affinity between the 30-C12-HSL antagonist and LasR is higher, an increase in the affinity will only have a minor effect on the concentration of 30-C12- HSL antagonist required to silence the system. AffWtyGiM-'') Figure 3-2. The concentration of 30-C12-HSL antagonist required to silence the AHL- system (drive the system to the lower stable steady state) is shown as a function of increasing affinity between LasR and the 30-C12-HSL antagonist. The figure also compares three different rates of 30-C12-HSL antagonist induced degradation of LasR (¿tms). The parameter values used in this example are: a2, aj, «5 = 0.16 jiM"^ = varied, d^ S2, S3, S4, S5 = 0.25 s~\ bm, bR2 = 0.15 s"\ bs = 0.2 s~\ bAi , bAi , bAiEx , bA2EX , bMi, bM2, bM4 = 0.12 s'^ bM3 = [0.03, 0.05, 0.1] TRI, TR2, TS = 0.004 [iMs-\ Tai, TA2 = 0.0036 |iMs-^ Vri , V/^s = 0.7 \iMs-\ Vs = 0.9 iiMs'K VAI ,VA2 =1.0 jiMs'^ KRI ,KR2= 1.2 |iM, = 1.0 |iM, Kai = 0.4 [xM, Kai = 0.7 |iM, Ksi = 1 |iM, di, ds = 0.2 s-^ d2 = 0.4 s-\ 3.3.2. Effect of increasing 30-C12-HSL antagonist induced degradation of LasR In Figure 3-3, the concentration of the 30-C12-HSL antagonist required to inhibit the system is shown as a function of an increasing antagonist induced degradation of LasR. As can be seen in this figure, when the 30-C12-HSL antagonist mediated degradation of LasR increases, the concentration of the 30-C12-HSL antagonist required to silence the system appears to decrease exponentially. This behaviour, which is similar to the behaviour in Figure 3-2, suggests that very small differences in the ability to mediate degradation of LasR between different 30-C12-HSL antagonists could have a major impact on their effectiveness as QSB. In Table 3-2, some examples of the stoichiometric 30-C12-HSL antagonist/30-C12-HSL ratios required for successful inhibition of the model system are shown. Most importantly, if antagonist mediated degradation of LasR is excluded from the model system, no successful inhibition of the system can be obtained under these circumstances (Table 3-2). 15000

Affinity = 0.4 Affinity = 0.64 uM-' Affinity = 2 mVT^

s 10000

1o>

8 5000

0.05 0.36 0.45 O.S bM3 (s'^) Figure 3-3. The concentration of 30-C12-HSL antagonist required to silence the system (drive the system to the lower stable steady state) is shown as a function of increasing 30-C12-HSL antagonist induced degradation of LasR. The figure also compares three different affinity values between LasR and the 30-C12-HSL antagonist. Note, the affinity between 30-C12-HSL and LasR is 0.64 jiM"^ The parameter values used in this example are: au «2, «j, «5 = 0.16 uM"^ s"\ = [0.10, 0.16, 0.50] du S2, Ss, S4, S5 = 0.25 s ^ bRi, bR2 = 0.15 s' ,bs = 0.2 Bai , Bai , bAiEx , bA2Ex , bMi, bM2, bM4 = 0.12 s \ bM3 = varied s \ Tri, Tr2, Ts = 0.004 \iMs-\ Tai, Ta2 = 0.0036 |uMs"\ Vri , = 0.7 |liMs-\ = 0.9 iliMS'^ ^47 , = 1.0 |iMs-\ Kri ,KR2=\2 |iM, Ks = 1.0 |uM, Kai = 0.4 |liM, KA2 = 0.7 |iM, Ksi = 1 |iM, di, ds = 0.2 d2 = 0.4 s-\ Table 3-2. The dependency on LasR degradation of the stoichiometric ratio of 30-C12-

Affinity ¿»Af3 = 0 bM3 = 0M bM3 = 0.03 ¿'M3 = 0.05 bM3 = 0,1 bM3 = 0,2 0.4 NIP NIP -36000:1 -2600:1 -340:1 -110:1 0.64 NIP NIP -18400:1 -1400:1 -190:1 -60:1 2 NIP NIP -3200:1 -300:1 -45:1 -16:1 4 NIP NIP -1000:1 ^ : -100:1 -18:1 -7:1 3.4. Discussion The results presented herein support the notion that the use of 30-C12-HSL antagonists constitutes a potential therapeutic approach against P. aeruginosa mediated infections (Passador et al 1993; Pearson et al 1994; Finch et al 1998). A strong feature of the model is that the results will remain qualitatively the same for a wide range of parameter values. In the simulations, several hundred different parameter values were tested and the outputs consistently showed the same behaviour. Therefore, it is the relationship between the different parameters rather than the actual values of the parameters that determine the behaviour of the system. This is important given that most of the parameter values used in the model system have not been experimentally generated. The parameter values used were adopted from Fagerlind et al (2003) (Chapter 2) in order to match steady state concentrations of 30-C12-HSL reported in the literature (e.g. Pearson et al 1994). Considering the recent theoretical research regarding QS systems (Dockery and Keener, 2001; Fagerlind et al 2003; James et al 2000), the results indicate that the optimal way to suppress an induced phenotype is to identify the conditions required to shift the system to the lower of the two stable steady states. The model suggests that specific 30-C12-HSL antagonists can be developed from structure-function analysis of the ability of the QSB to (1) bind to the R-protein and (2) induce degradation of the R-protein. In the following, the specific conditions required for QSB s to effectively switch the system to the low stable state are discussed.

Manefield et al (1999) showed that the stoichiometric furanone/30-C12-HSL ratio is approximately 400:1 (for successful inhibition). It was suggested that this disproportionate ratio reflects the well-documented high affinity of LasR for 30-C12- HSL (Passador et al 1996), i.e. that the affinity between the furanone and LasR would be much lower compared with 30-C12-HSL and LasR. In contrast, results presented here suggest that differences in affinity may not be the sole reason for this disproportionate ratio. Instead, I propose that this behaviour is the sum of the intricate dynamics of the QS system in P. aeruginosa as introduced by Dockery and Keener (2001) and Fagerlind et al (2003) (Chapter 2), i.e. two stable steady states (with high and low concentration of 30-C12-HSL, respectively) separated by one unstable steady state. The only means by which such a system can be transferred from the high stable steady state to the low stable steady state is to disturb the system in such a way that the concentration of 30-C12-HSL decreases below the unstable steady state concentration. To achieve this, the disturbance in the system (introduced by the 30-C12-HSL antagonist) must be rather powerful. In the model system, the affinity between LasR and 30-C12-HSL is set to 0.64 When the affinity between LasR and the 30-C12- HSL antagonist is 0.64 (or less, i.e. lower affinity), the model predicts that a significantly higher concentration of the 30-C12-HSL antagonist (well above the furanone/30C12-HSL ratio of 400:1) is required for inhibition of the system (Figure 3- 2, Table 3-2).

The model system indicates that there are two simple ways to increase the effectiveness of the QSBs. The first is to increase the affinity between the 30C12-HSL antagonist and LasR (Figure 3-2). However, this may not be feasible since it is unlikely that the affinity between the 30-C12-HSL antagonist and LasR is much higher compared to the affinity between 30-C12-HSL and LasR. The second is to increase the rate of 30-C12-HSL antagonist induced degradation of LasR. The modelling results predict that this will dramatically decrease the concentration of antagonist required to silence the system (Figures 3-2, 3-3; Table 3-2). Thus, the model predicts that stability of LasR is the key parameter for driving the system to the low stable steady state. A similar behaviour was also demonstrated by Manefield et al. (2002) who tested the QSB properties of several structurally similar halogenated furanone compounds. Their results showed that, despite the structural similarity between different halogenated furanones, the QSB properties of different halogenated furanones differed greatly in their ability to inhibit the QS response (see also Table 3-3) and correlated with the antagonist's ability to mediate degradation of the receptor protein. Compound no. 1X40^ 2 0.47 4 0.26 8 0.76 30 0.16 Adopted from Manefield et al 2002, with permission from the publisher. ^ Quantity of QSB (|umol) per HSL (nmol) required to reduce QS activity by 40%, low values indicate strong biological activity. Based on the results, it is suggested that the successful 30-C12-HSL antagonist based

inhibition of the QS system in P. aeruginosa, requires that the 30-C12-HSL antagonist

has a very high affinity for LasR (much higher then 30-C12-HSL) and/or the capacity

to induce rapid degradation of LasR. Since Manefield et al. (2002) showed that

furanones induce rapid degradation of LuxR, we hypothesize that LasR would be

affected in a similar fashion in the presence of furanones or other QSBs. It is also

proposed that the effectiveness and specific interference by the synthetic furanone

compound 30 in the las system in P. aeruginosa (Hentzer et al. 2002) reflects a rapid

degradation of LasR. Since it has been shown that 30-C12-HSL has a very high affinity

for LasR (Passador et al. 1996) it is less likely that the reported effectiveness of

furanone compound 30 is based on a high affinity of LasR. Thus, I would conclude that

the ratio of antagonist to AHL required for successful inhibition of the AHL system is governed more by their ability to degrade the R-protein than by their affinity for the receptor. The results presented in this paper suggest that the use of 30-C12-HSL antagonists may constitute a promising therapeutic approach against P. aeruginosa infections. Furthermore, it is proposed that an effective (high affinity and high degradation) 30-C12-HSL antagonist should be effective even at very low concentrations. In addition, based on the results presented in this paper, it is suggested that even very small differences between different 30-C12-HSL antagonists, both in their affinity for the R-protein, as well as their ability to mediate degradation of the receptor protein, could have a major impact on their effectiveness as QSBs. Therefore, the major challenge for further application of QSBs as anti-bacterial therapeuticals will be to identify or develop synthetic antagonists with specific QSB properties. An optimal

30-C12-HSL antagonist would have a high affinity for LasR (and RhlR) and, most importantly, the capacity to induce a rapid degradation of LasR (and RhlR) and may represent a major advance in the battle against P. aeruginosa infections. Indeed, the model system developed in this study describes the QS system in P. aeruginosa and how it is influenced by the addition of a signal antagonist. However, I suggest that other bacteria with the same QS behaviour (two stable steady states separated by an unstable steady state), e.g. V. fischeri James et al. 2000) would be affected in the same way. If this is true, then optimized signal antagonists may be used as an effective anti-bacterial agent for a wide range of bacterial infections. Chapter 4. Modelling the effect of cell death in the formation of microbial biofilms

4.1. Introduction Bacteria, both in natural and pathogenic ecosystems, are found mainly within surface associated cell assemblages, or biofilms (Costerton et al 1995; O'Toole et al 2000). It was previously accepted that biofilms were flat homogenous structures. This assumption was also reflected in the mathematical models developed at that time to describe biofilms which were represented as simple, homogenous films (Atkinson and Davies, 1974; Harris and Hansford, 1976; Williamson and McCarty, 1976). However, it is now appreciated that biofilms form complex, three-dimensional structures that are frequently composed of microcolonies interspersed with open water channels (Lawrence et al. 1991). The current understanding is that biofilms, in response to varying environmental conditions, can adopt different structures which can range from homogenous monolayers, to heterogeneous structures including mushrooms, ripples, and filamentous streamers (de Beer et al 1994; Stewart et al 1994; Costerton et al 1995; Stoodley et al 1999, 2002a). A computational approach that revolutionized biofilm modelling is cellular automata (CA) (Wimpenny and Colasanti, 1997; Picioreanu et al 1998a, 1998b, 1999; Hermanowicz, 1998, 1999, 2001; Noguera et al 1999; Pizarro et al 2001; Chang et al 2003; Hunt et al 2003, 2004; Laspidou and Rittman, 2004; Chambless et al 2006). CA models are discrete models, in which space, time and properties of the system only can have a finite number of possible states. The model space (domain) is composed of elements organized in a regular spatial lattice/grid (2D or 3D) for which the state of the elements is updated synchronously according to local rules. A common feature of CA biofilm models is their inherent ability to generate a wide range of observed biofilm morphologies (for a review describing CA in more detail, see Ermentrout and Edelstein-Keshet, 1993). A related modelling approach is individual-based modelling (IBM) (Kreft et al 1998, 2001; Xavier et al. 2004, 2005, 2007; Alpkvist et al 2006; Picioreanu et al 2007). The major difference between CA biofilm models and IBM biofilm models lays in the biomass distribution. In a CA biofilm model the biomass is located in a grid (squares or cubes of biomass), whereas an IBM biofilm model is gridless, i.e. biomass (usually modelled as particles) can take any position. Another strong feature associated with IBMs, but also widely used in different CA models (sometimes termed as individual based CA), being that the agents/individuals (e.g. bacteria) are treated individually, as independent entities with there own state and behaviour (Kreft et al 1998, 2001; Xavier et al 2004, 2005, 2007; Alpkvist et al 2006; Picioreanu et al 2007. This individual based feature is particularly useful for studying global complex systems in which individual heterogeneity is important, e.g. in biofilms.

To date, a range of processes have been suggested to contribute to the development of biofilms. These include, for example: adhesion (Cramton et al 1999; Froeliger and Fives-Taylor 2001; Gavin et al 2002; Tsuneda et al 2003); detachment (Alison et al 1998; Sawyer and Hermanowicz, 1998; Hentzer et al 2002); mass transport (CharackUs and Marshall, 1990; de Beer et al 1994); hydrodynamics (Stoodley et al 1999, 2002b), EPS production (Nielsen et al 1996; Tsuneda et al 2003), cell motility (O Toole and Kolter, 1998a; Klausen et al 2003), QS (Davies et al 1998; de Kievit et al 2001; Huber et al 2001; Lynch et al 2002; Labbate et al 2004); cell death (Webb et al 2003; Mai-Prochnow et al 2004, 2006; Barraud et al 2006), DNA excretion (Petersen et al 2005; Allesen-Holm et al. 2006) and active dispersal (Barraud et al. 2006; Prochnow et al. 2006; Koh et al. 2007). Several of these processes have also been theoretically investigated in different modelling attempts, e.g. detachment (Hermanowicz et al. 2001, Picioreanu et al. 2001; Hunt et al. 2003, 2004; Chambless et al. 2006; Bohn et al. 2007), mass transport (Horn and Hempel, 1998), hydrodynamics (Eberl et al. 2000, Picioreanu et al. 2000, 2001), EPS production (Horn et al. 2001; Kreft and Wimpenny, 2001, Xavier et al. 2005), cell motility (Picioreanu et al. 2007), QS (Goryachev et al. 2005; Anguige et al. 2006).

One of the least understood processes, and how it effects biofilm development, is cell death. To date, only a few experimental studies addressing this process have been published. Webb, et al. (2003) observed localized killing and lysis within the centres of microcolonies formed by wild-type P. aeruginosa biofilms, and that cell death involved superinfection by a genomic Pfl-like prophage of P. aeruginosa. They also found evidence that the generation of reactive oxygen species (ROS) was essential for prophage activation and subsequent superinfection and lysis. These findings were recently supported by Barraud et al. (2006), who described peroxynitrite (ONOO ) dependent cell death in mature P. aeruginosa biofilms. In addition, a correlation between ONOO' accumulation, cell death and dispersal was observed. Prochnow et al. (2004), observed a similar death pattern in biofilms formed by the marine bacterium Pseudoalteromonas tunicata. An autotoxic protein designated AlpP, was found to induce cell death in this organism through lysine oxidase activity of AlpP, which generates the reactive oxygen species H2O2. More recently, a similar pattern of cell death and dispersal has also been identified in the opportunistic pathogen Serratia marcescens (Koh et al. 2007). It has been reported that nutrient supply can affect biofilm dispersal and hence would be expected to be closely linked to the process of cell

death in the biofilm. For example, Sauer et al. (2004) reported that changes in nutrient

concentration can induce biofilm dispersal. More recently, it has been observed that

nutrient exhaustion induces dispersal of P. aeruginosa biofilms (Rice and Kjelleberg,

unpublished). Furthermore, Purevdorj-Gage et al (2005) demonstrated that dispersal

only occurred when microcolonies reached a minimum diameter of 80 um, and

suggested that this may be related to mass transfer limitations. Hence, there appears to

be a strong relationship between nutrient concentrations, cell death and dispersal in

microbial biofilms of many species of bacteria.

The objective of this study was to model cell death during biofilm development. The

primary interest was in the pattern of cell death during biofilm development, especially

in the spatial location of cell death and the key question addressed was whether or not a

correlation exists between nutrient availability and localized cell death. Three death

rules, all based on nutrient availability, and how they effect biofilm development were

evaluated. Using these rules, death could occur if: a) cells have been in stationary phase

for a specified number of hours, b) the ratio between biomass formation and

endogenous metabolism falls below a specified value, and c) the cells accumulate a

specified amount of damage as caused by, for example, the production of damaging

reactive oxygen or nitrogen species during biofilm growth. In addition, to asses the results

generated by the model system, experimental biofilm formation of P. aeruginosa under different bulk phase nutrient concentrations were also monitored. Based on the theoretical output as well as the experimental results, the accumulation of damage (rule

3) is suggested to be the main cause of cell death during the formation of microbial biofilms. Moreover, the combined theoretical and experimental results also suggest a strong relationship between nutrient concentration and cell death as lower bulk phase nutrient concentrations tend to result in more and/or earlier cell death during biofilm development. 4.2. Model theory

To model cell death during biofilm development, an individual based CA of a bacterial

biofilm developing on a surface in an aqueous environment is presented. The

environment is a two-dimensional space, containing both nutrients and bacteria. The

bacteria consume nutrients from the surrounding milieu, resulting in a decrease in the

concentration of nutrients and an increase in bacterial growth. Once a bacterium has

doubled its mass, it will divide, resulting in growth of the biofilm. In contrast, the

biofilm can also diminish due to bacterial death and detachment. A comprehensive

description of the different parts and processes of the individual based CA is presented

in the next sections.

4.2.1. Simulation domain

The simulated environment is a two-dimensional (2D) spatial domain (lattice/grid), with

250 elements in ;c-direction {Ex) and 150 elements in y-direction {EY), i.e. a total of

37500 elements {EJOT)- Each element is 3 |xm {Ax) and hence the modelling domain is

750 |xm in width Qx) and 450 jim in height (/y). It is further assumed that each element has the shape of a cube (3 |xm in each direction). Thus, each element occupies a total volume of 27 {Ax)^. This space is suitable to harbour one bacterial cell and its extracellular constituents (Characklis, 1989). Each of the elements is occupied by either a bacterium or an equivalent volume of liquid. The domain is bounded on one side by a solid surface (substratum), on which the biofilm is allowed to develop. The opposite side of the domain represents the bulk liquid containing a reservoir of substrate. In the other two directions, parallel to the growth surface, the concept of periodic boundaries has been applied. Thus, the modelling domain represents a cylindrical surface, with the two edges in x-direction connected to each other, in order to avoid edge effects. As a consequence, if a bacterium goes past the boundary on one side of the domain, it is wrapped to the corresponding opposite domain side.

4.2.2. Substrate diffusion and reaction

The substrate (glucose) concentration is treated as a continuous variable, and hence is represented here by a concentration value in each element, Sc(x,y). Glucose molecules are very small in comparison to a bacterium, so we assume that they can co-reside in an element together with a bacterium. The concentration in each element is the result of diffusion as well as interaction with the bacteria. The diffusional time constant is approximately 100 orders of magnitude smaller than that for bacterial cell division

(Picioreanu, et al 2000). Thus, molecular diffusion can be assumed to be at quasi steady-state with respect to the bacterial growth. Suppressing the coordinates {x,y) and let Ds depict the diffusion coefficient of the substrate. The diffusivity in the biofilm is determined by multiplying the diffusion rate in the aqueous phase {Ds,aq) with the relative effective diffusivity Ds,e/Ds,aq (Stewart, 2003). Let the variable X depict biomass density, calculated as bacterial mass per element volume for occupied elements (0 otherwise). Further, rs(Sc, X) denotes the reaction term (defined below) corresponding to the substrate consumption of the bacteria. Eq. 4-1 is the two-dimensional representation of substrate diffusion and reaction. ds ' ^ Sr ^ Sr -rJS„X). (Eq.4-1) —-+—f- dt dx^ dy y

Equation 4-2 is the equation for the substrate consumption by the bacteria.

/ \ / X (Eq. 4-2) V ^xs J The parameter jimax denotes the maximum specific growth rate, Yxs denotes the yield coefficient, m denotes the maintenance coefficient and Ks denotes the half-saturation coefficient. Eq. 4-1 is discritized in time and space to obtain an explicit solution method (see Ermentrout and Edelstein-Keshet, 1993 for more details about this method) that is solved numerically, and by using small time steps (relative to growth), the quasi steady state solution (no change in the substrate concentration profile over time) is calculated (Picioreanu et al 1998a, 1998b, 1999, 2000). During this step the bacterial density (as well as substrate consumption) in each element is fixed. At quasi steady state, the bacteria are allowed to consume substrate, which is calculated by multiplying Eq. 4-2 by the time step Ai and the element volume (Ax)\ Some of the consumed substrate is converted to biomass and this proceeds according to equation 4-3. ^A' = ^xs (Q, X) - mX , (Eq. 4-3) where B^ is biomass amount. The substrate source is generated by maintaining a constant concentration {Sc bulk) in the bulk liquid, located parallel to the substratum at a given distance {Bu) above the surface of the biofilm. The area located between the bulk liquid and the biofilm is usually named the mass transfer boundary layer. Nutrient concentration gradients result from a combination of nutrient uptake by the bacteria and nutrient transport from the bulk liquid through the mass transfer boundary layer and inside the biofilm. The thickness of the boundary layer is correlated to the flow pattern over the biofilm surface. At high bulk water velocity, the thickness of the boundary layer decreases and results in an increased rate of nutrient diffusion into the biofilm (de Bttvetal 1994). 4.2.3. Damage production The model does not differ between damage causing molecules, for instance reactive oxygen, and damage caused by these molecules, e.g. oxidized macromolecules. As stated in equation 4-4 below, damage production is assumed to be a function of the substrate consumption and endogenous metabolism, (Eq.4-4) The parameter a denotes rate of damage production, p denotes damage removal rate (degradation and repair) whereas WA denotes amount of damage. It is further assumed that damage can not diffuse, i.e. once it has been produced it will remain in the bacterium in which it was produced. However, if a bacterium divides, then the damage will be equally distributed in the two daughter cells.

4.2.4. Cellular automata rules Equation 4-3 is composed of one biomass formation part, Y^^r^ X), and one part for endogenous metabolism, mX . This means that if the ratio between biomass formation and endogenous metabolism (/?), r^ , X )/mX, is higher then 1, the cell exhibits net growth. In contrast, if the described ratio is less then 1, the bacterium has entered stationary phase (no net growth). Three different death rules have been evaluated where the first two simulate the effect of oxidative damage indirectly, whereas the last one accounts for the actual damage in the individual bacteria. The simulated rules are as follows: 1) bacteria die if they have been in stationary phase for a specific number of hours {NH). This is recorded with an individual based counter. If R is below 1 during one hour, the counter increases by one. However, a bacterium also has the possibility to recover if R increases above 1 before it has died. Consequently, if R is above 1 during one hour, the counter decreases by one. However, the counter can never get a value less then zero. 2) Bacteria die if R falls below a certain threshold value. This is an attempt to account for bacterial death under circumstances of low (or no) substrate concentration. 3) Bacteria die if they have accumulated too much damage.

For a bacterium to be able to divide it must produce enough biomass to create a new daughter cell. Therefore, each bacterium is given a specific division value (V^) when it is created, which is the cumulative biomass needed for the bacterium to divide. This value is drawn at random from a Gaussian distribution with a variation of 10% (see Table 4-1). Dividing bacteria exhibit discrete growth, occupying a single element of space until division, at which point they divide into two cells. One daughter cell remains in the original location of the mother cell, whereas the other daughter cell is placed in a neighbouring element. There are eight possible neighbour elements, and the daughter cell is placed in the direction that offers the smallest mechanical resistance (Hermanowicz, 1999). At division/spreading, each direction is checked for free spaces at increasing distances from the dividing cell, and the first direction in which such a free space is found is considered the direction of least mechanical resistance. If two or more directions with equal mechanical resistance are found, one of those is chosen at random. When a direction has been chosen, space is made for the new cell. This is achieved by pushing the entire line of cells between the dividing cell and the closest free space by one element in the chosen direction. After spreading, the region representing the mass transfer boundary layer is updated to fit the new biofilm morphology. Table 4-1. Definition of variables and parameters Variable/ Description Values Unit parameter A Damage production rate 0.0001 - 0.8 m^ P Damage removal rate 0-0.2 h-^ fJmax Maximum specific growth rate 0.3125 At Time step 1 h Ax The element size m BLT Thickness of the mass transfer boundary 18*10"^ m layer B Biomass BA Biomass amount gB CN Number of colonizers (initial bacteria) 8 DS Diffusion coefficient of substrate m^h-^ Ds,aq Diffusion coefficient of substrate 2.52*10'^ m^h-^ (glucose) in the aqueous phase DSJDS.aq Relative effective diffusivity of substrate 1/3 1 in the biofilm Ex Number of elements in x-direction 250 EY Number of elements in y-direction 150 ETOT Total number of elements 37500 Fs Biofilm strength 320 1 Hs Shear stress 1-250 1 Ix Length of the modelling domain 750*10-^ m ly Height of the modeUing domain 450*10-^ m Ks Half-saturation coefficient 2.55 gs m'^ m Maintenance coefficient 0.036 gs gx ^ h'^ NH Number of hours in stationary phase at 24 - 108 h which cell death occur PD Probability for microbial detachment 1 rs Reaction rate of the substrate gs m'^ h'^ R Ratio between biomass formation and 1 endogenous metabolism S Substrate Se Substrate concentration gs m'^ Se bulk Substrate concentration in bulk phase 1,2,3,5 gs m"^ VD Division value 2.63*10"^^ gB w Damage WA Damage amount gw X Biomass density gB m'^ Yxs Yield coefficient 0.45 gx gs'^ Ill

In addition to growth and death, parts of the biofilm can detach. Since detachment is a process not considered here in detail, a simple approach developed by Hermanowicz, (2001) was implemented. For bacteria located at the biomass/liquid interface, the probability of detachment should be an increasing function of the hydrodynamic shear stress. Hermanowicz (2001) also stated that the "strength" of the biofilm should be involved. Thus, with increasing biofilm strength, the probabihty of detachment should decrease. Hermanowicz (2001) described this probability (equation 4-5),

Po=— (Eq.4-5) 1 + Fs K^sj Here Fs denotes the biofilm strength whereas Hs denotes the shear stress. In contrast to Hermanowicz (2001) who assumed a fixed shear stress regardless of the location in the modelling domain, it is here assumed that the shear stress increases as the height of the biofilm increases, i.e. bacteria located at the tip of the biofilm are exposed to a higher shear stress compared to bacteria located near the substratum. This is modelled by a linear increase of Hs as the height of the biofilm increases. More specifically, Hs for a specific biofilm element is assumed to have the same value as the current row number (y-coordinate). In addition, if, as a result of detachment and/or death, bacteria became disconnected from the substratum (direct or indirect), they are removed from the modelling domain (washed away). However, this is only true if they have a connection to the bulk liquid, i.e. bacteria located in the interior of the biofilm are not removed even if they have lost the connection with the substratum. 4.2.5. Parameter values As this model is an individual based CA, all bacteria are simulated as independent entities with there own state (set of parameters) and behaviours. As a consequence, each bacterium has its own set of parameter values, which is an independent copy of the list of default parameter values (Table 4-1). New values were obtained by random draws from a Gaussian distribution with a variation of 10%. As a starting value, the default values given in Table 4-1 were used, thereby avoiding unrestricted "evolution" (Kreft et al 1998). Most of the parameter values denoted in Table 4-1 have been experimentally determined by others, and many of them have also been used in other biofilm models (e.g. Kreft et al 1998, 2001; Picioreanu et al 1998a, 1998b, 1999, 2001; Hunt et al 2003, 2004). However, this is not the case for the parameter values used in the bacterial death processes. Therefore, these values had to be assumed. However, a large number of different value combinations have been tested (see Results) and the results presented are robust and hence, the range of values used are considered appropriate.

4.2.6. Model simulation The state of the simulation domain is updated at discrete time steps. The dynamic of this update is described by the rules, which represent the interaction of each element with its neighbouring element in the domain. These rules also model the processes occurring within the biofilm: colonization, substrate diffusion, growth, damage production, division/spreading, death and detachment (Figure 4-1). The formation of a biofilm begins when a small number of bacteria adheres to a surface at random locations. As these bacteria grow and divide, their offspring spread over the surface and eventually form the mature biofilm. Analogously, the biofilm growth simulation begins with a small number {CN) of randomly placed bacteria. Figure 4-1 describes the sequence of steps during a typical simulation, which consist of: 1) Creation of the modelling domain, and establishment of the parameter values; 2) A fixed number of bacteria are allowed to colonize the substratum at random locations; 3) The substrate concentration field is generated by finding the quasi steady state solution to equation 4-1; 4) The bacteria consume substrate, form biomass and produce damage according to equations

4-2, 4-3 and 4-4, respectively; 5) Determination of whether the bacteria have grown enough to be able to divide; 6) Division/spreading according to the procedure stated above; 7) Determine if the bacteria die based on the death rule used; 8) Death and removal of dead bacteria; 9) Identify bacteria that fulfil the detachment requirements as stated above; 10) Detachment (removal) of bacteria according to equation 4-5; 11)

Check if the maximum number of simulation time steps has been reached, and if not, move forward in time and perform steps 3-11 again; 12) Termination of the simulation.

For each of the three described death rules, a large number of simulations with different parameter combinations were performed. Moreover, since the model has a stochastic nature, five replicate simulations for each parameter combination were executed and evaluated. The model was written in the programming langue of C++ and compiled using Dev C++ (available at the Free Software Foundation). The simulations were carried out on a 2.8 GHz Intel Pentium 4 processor with 1 Gigabyte of memory. To visualize the results of the simulations, Matlab version 7.0.1 was used. star! simulation - set hitial cx)nditions

Colonization Diffusion of substrate 4—No Detachment

4- Yes

Growth and damage production

Figure 4-1. Flow-chart of the biofilm cell death model, describing the sequence of processes during a typical simulation. For a more comprehensive description, see the "model simulation" section. 4.3. Results

Simulation results of the three death rules, as well as results generated by the

experimental laboratory approach are presented. As stated previously, a large number of

simulations have been performed, both to test a range of different parameter values but

also to replicate simulations for each combination of parameter values. Since it is not

possible to show all of the simulations a selection of simulation results, reflecting

typical simulation results, have been selected for presentation here.

4.3.1. Death rule 1 - bacteria die if they have been in stationary phase for a

specific number of hours

This death rule assumes that bacteria die if they have been in stationary phase for a

specific number of hours (NH). During the simulations, values between 24 - 108 hours

(increasing in steps of 12 hours) were tested. In addition, two bulk phase substrate

concentrations, 3 g m" and 5 g m" , were also compared. This gives a total of 80

different simulations for this rule. In Figures 4-2 and 4-3, two representative simulations

using this death rule are presented. In both simulations, bacteria are shown in green

whereas the bulk liquid is shown in black. Bacterial death occurred after 72 hours in

stationary phase and the bulk phase substrate concentrations were 3 g m"^ and 5 g m"^,

respectively. In the simulation using a bulk phase substrate concentrations of 3 g m"^

(Figure 4-2), bacterial death was observed after 150 hours of growth, indicated by hollowing at the bases of the microcolonies. After 250 hours of growth, smaller microcolonies were observed, indicating that sloughing of microcolonies had occurred, which was followed by subsequent regrowth of microcolonies to repeat the biofilm developmental cycle. Biofilm after 100 hours of growth Biofilm after 150 hours of growth

Biofilm after 250 hours of growth Biofilm after 300 hours of growth

Figure 4-2. A simulation in which bacteria (green), growing in a bulk phase (black) substrate concentration (Sc bulk) of 3 g m'^ die after 72 hours in stationary phase (NH). The simulation shows a growth cycle consisting of biofilm growth, bacterial death at the bases of the microcolonies (after 150 hours of growth), sloughing of microcolonies (between 150 and 250 hours) and re-growth of the biofilm (after 300 hours). The domain size is 750 |im (width) by 450 |im (height). The same cycle of biofilm development and death was also observed when a bulk phase

substrate concentration of 5 g m'^ was used (Figure 4-3). As a consequence of the higher substrate concentration, larger microcolonies were observed after 100 hours of development. Moreover, a higher substrate concentration also resulted in faster biofilm development, leading to earlier and more extensive cell death, indicated by much larger voids after 150 of growth, and formation of new voids after 300 hours of growth. For example, the formation of cell death was not seen at 300 hours when a lower bulk phase

substrate concentration was used (Figure 4-2). Thus, four conclusions can be drawn from the simulations: 1) the biofilm grows faster at higher bulk phase substrate concentrations; 2) bacterial death occurs primarily at the base of the microcolonies; 3) bacterial death occurs earlier, and to a higher extent, at higher bulk phase substrate concentrations; 4) bacterial growth and death result in sloughing of large sections of biofilm. This further allows re-growth of the biofilm. Hence, a growth, death, sloughing and re-growth cycle is generated. Biofilm after 100 hours of growth Biofilm after 150 hours of growth

Biofilm after 260 hours of growth Biofilm after 300 hours of growth

Figure 4-3. A simulation in which bacteria (green), growing in a bulk phase (black) substrate concentration {Sc bulk) of 5 g m" , die after 72 hours in stationary phase {NH). The simulation shows a growth cycle consisting of biofilm growth, bacterial death at the bases of the microcolonies (after 150 hours of growth), sloughing of microcolonies (between 150 and 250 hours) and re-growth of the biofilm (after 300 hours). The domain size is 750 \im (width) by 450 |Lim (height). 4.3.2. Death rule 2 - bacteria die as a function of the ratio between biomass

formation and endogenous metabolism

As described above, death rule 2 assumes that bacteria die if their ratio between biomass formation and endogenous metabolism {R value) falls below a certain threshold value.

To evaluate the range of potential R values, a number of initial simulations were performed. These simulations showed that R values within the range of 0 - 0.30 give rise to biofilm morphologies that are often observed in the laboratory (Tolker-Nielsen et al 2000; Hentzer et al 2003; Webb et al. 2003). When R values higher than 0.30 were used, a significant portion of the biofilm died (and sloughed) very early during the model simulations, i.e. before development of any actual microcolonies (not shown). It was therefore assumed that R values above 0.30 not were biologically relevant.

Consequently, only R values in the range of 0 - 0.30 (with incremental steps of 0.025) were considered. Similar to death rule 1, two different bulk phase substrate concentrations, 3 g m'^ and 5 g m'^ were also compared, resulting in a total of 130 simulations using this rule.

The results presented in Figures 4-4 and 4-5 demonstrate that bacteria die when the R value (ratio between biomass formation and endogenous metabolism) is equal to or less than 0.15, irrespective whether the bulk phase concentration is "high", 5 g m"^, (Figure

4-4) or "low", 3 g m' , (Figure 4-5). Two conclusions can be derived from this comparison. At higher substrate concentration: 1) bacteria located in the outer regions of the biofilm in general have a higher R value (in relation to bacteria located in the same regions in lower substrate concentration); 2) bacteria located in the interior regions of the biofilm in general have a lower R value (in relation to bacteria located in the same regions in lower substrate concentration). This is supported by the observation that bacterial death occurs at higher bulk phase substrate concentrations (Figure 4-4), but not at lower bulk phase substrate concentrations (Figure 4-5). Hence, biofilms growing in lower bulk phase substrate concentration show less bacterial death compared to biofilms growing in higher bulk phase substrate concentration. In addition, Figures 4-4 and 4-5 also shows the substrate concentration profiles for the four presented time steps.

The outcomes of death rule 2 share some similarities with the outcomes of death rule 1. These include faster growth of the biofilm at higher bulk phase substrate concentration, (which is independent of the death rule), bacterial death at the base of the microcolonies, as well as sloughing of whole microcolonies. In contrast to death rule 1, which only resulted in cell death at the base of the microcolonies, death rule 2, under certain circumstances, resulted in bacterial death in the upper region (centre) of the microcolonies, i.e. the "cap". A representative simulation showing this behaviour is presented in Figure 4-4 (indicated by an arrow). Biofilm after 50 hours of growth Biofilm after 100 hours of growth

Biofilm after 200 hours of growth

Substrate concentration, after 50 hours of growth Substrate concentration, after 100 hours of growth

Substrate concentration, after 200 hours of growth

Figure 4-4. A simulation in which bacteria, growing with a bulk phase substrate concentration {Sc bulk) of 5 g m"^, die if their R value decreases below or equal 0.15. (A- D) R values of the individual bacteria, as indicated by the colorbar, at four different time steps; 50 hours (A), 100 hours (B), 200 hours (C) and 300 hours (D). Dark red bacteria are the ones with an R value above 1 (bacteria exhibiting net growth). Void spaces indicate areas of cell death, and the white arrow indicates an area of cell death within the interior of the microcolony as opposed to cell death occurring at the base of the biofilm. (E-H) Substrate concentration in g m'^, as indicated by the colorbar, at the four presented time steps; 50 hours (E), 100 hours (F), 200 hours (G) and 300 hours (H). The domain size is 750 |Lim (width) by 450 jiim (height). Biofilm atter 100 hours of growth Biofilm after 200 hours of growth

Biofilm after 300 hours of growth

•

Substrate concentration, after 100 hours of growth Substrate concentration, after 200 hours of growth

Substrate concentration, after 300 hours of growth Substrate concentration, after 400 hours of growth

Figure 4-5. A simulation in which bacteria, growing with a bulk phase substrate concentration (Scbidk) of 3 g m' , die if their R value decreases below or equal 0.15. (A- D) R values of the individual bacteria, as indicated by the colorbar, at four different time steps; 100 hours (A), 200 hours (B), 300 hours (C) and 400 hours (D). Dark red bacteria are the ones with an R value above 1 (bacteria exhibiting net growth). Void spaces indicate areas of cell death. (E-H) Substrate concentration in g m'^, as indicated by the colorbar, at the four presented time steps; 100 hours (E), 200 hours (F), 300 hours (G) and 400 hours (H) The domain size is 750 |Lim (width) by 450 |im (height). 4.3.3. Death rule 3 - bacteria "die" as a function of damage accumulation The third death rule tested examined the effect of total damage accumulated within individual cells. However, in the examples presented below, no actual cell death was implemented. Instead, the focus was on the spatial accumulation of damage, and there were two reasons for this choice: 1) to date, the damage amounts lethal to an individual bacterium are unknown; 2) the values of the parameters that control damage production and damage removal in the model (i.e. a and p) have not been experimentally determined. Therefore, several combinations of a and p values were evaluated, all giving rise to quantitative differences in damage observed during the simulations. Consequently, to be able to compare different combinations of values, it was not valuable to assume a damage killing threshold. A total of 210 different simulations (again using bulk phase substrate concentrations of 3 g m'^ and 5 g m'^, respectively) were performed using this death rule, and based on these simulations data, three different conclusions were made: 1) biofilms growing in the presence of low bulk phase substrate concentrations (3 g m'^) accumulated a higher amount of damage compared to biofilms growing in higher bulk phase substrate concentration (5 g m"^) (Figures 4-6 and 4-7); 2) "fast" growing microcolonies accumulated less damage compared to "slow" growing microcolonies (Figures 4-6 and 4-7); 3) as the rate of damage removal increases (higher p), the total amount of damage decreases and the localization of accumulated damage shifts upward in the biofilm (Figures 4-8 and 4-9).

Thus, model simulation using death rule 3, predicts that more damage accumulates in the biofilm when grown in the lower substrate concentration, compared to biofilms grown in the presence the higher substrate concentration. Indeed, at 3 g m'^ (Figure 4- 6), high amounts of damage were apparent after 150 hours of growth and this was highest across the middle of the microcolony. By 250 hours, almost the entire microcolony appeared as red, indicating high damage amounts. At 5 g m" (Figure 4-7) red, or biofilm areas with high damage amounts, did not appear until 200 hours of simulation. Even at 250 hours, only a small region of individual microcolonies showed significant damage amounts. In these cases, areas of high damage appeared to be found only in the smaller microcolonies and only at the tops of those areas. It was also clear that the biofilm biomass increased much faster for the higher substrate concentration (Figure 4-7), which is consistent with the observations for biofilm development described for death rules 1 and 2 above. Thus, it appears that the slower growing microcolonies accumulate more damage than the faster growing ones, and this outcome seems to be consistent for microcolonies growing in different bulk phase substrate concentrations (Figures 4-6 and 4-7) as well as for microcolonies growing in the same bulk phase substrate concentration (Figure 4-7). This latter finding is visualized in Figure 4-7, in which one large (fast growing) microcolony (yellow arrow) has accumulated much less damage if compared with three smaller (slow growing) microcolonies (red arrows), all growing in the same bulk phase substrate concentration (5 g m-^).

The model simulations using death rule 3 also showed that as the rate of damage removal increases (higher P), the total amount of damage decreases and the localization of accumulated damage (area with the highest amount of damage) shifts upward in the biofilm. These results are visualized in Figures 4-8 (a simulation with "low" rate of damage removal) and 4-9 (a simulation with "high" rate of damage removal). Damage amount after 50 hours of growth Damage amount after 150 hours of growth

Damage amount after 200 hours of growth

Figure 4-6. Simulation of biofilm growth in a bulk phase substrate concentration (Scbuik) 3 3 of 3 g m' , The parameter a (damage production rate) is 0.01 m whereas P (damage removal rate) is 0 hThe colorbar indicates damage amount. The domain size is 750 |Lim (width) by 450 |im (height). Damage amount after 50 hours of growth Damage amount after 150 hours of growth

Damage amount after 200 hours of growth

Figure 4-7. Simulation of biofilm growth in a bulk phase substrate concentration (Scbuik) of 5 g m l The parameter a (damage production rate) is 0.01 m^ whereas P (damage removal rate) is 0 h'\ The colorbar indicates damage amount. The domain size is 750 \im (width) by 450 jim (height). The yellow arrow is pointing at a "fast" growing microcolony, whereas the red arrows are pointing at "slow" growing colonies. Damage amount after 50 hours of growth Damage afrwunt after 150 hours of growth

Damage amount after 250 hours of growth

Figure 4-8. Simulation of biofilm growth in a bulk phase substrate concentration (Scbuik) of 3 g m'\ The parameter a (damage production rate) is 0.1 m^ whereas p (damage removal rate) is 0.001 h'\ The colorbar indicates damage amount. The domain size is 750 |im (width) by 450 |im (height). Damage amount after 50 hours of growth Damage amount after 150 hours of growth

Damage amount after 250 hours of growth

Figure 4-9. Simulation of biofilm growth in a bulk phase substrate concentration {Sc bulk) of 3 g m"^. The parameter a (damage production rate) is 0.1 m^ whereas p (damage removal rate) is 0.01 h ^ The colorbar indicates damage amount. The domain size is 750 jim (width) by 450 \im (height). 4.3.4. Influence of substrate concentration on cell death within laboratory experimental biofilms

Using the model biofilm-forming bacterium P. aeruginosa, biofilm development and patterns of cell death during growth at two glucose concentrations, 0.9 g m'^ (5 mM) and 3.6 g m" (20 mM) were examined. The extent of cell death within the biofilm was examined under epifluorescence microscopy within early (3 day-old) and late (7 day- old) stage biofilms. Representative epifluorescence micrographs from biofilms grown under these conditions are shown in Figure 4-10. At both 0.9 g m'^ and 3.6 g m'^ glucose, biofilms exhibited a similar microcolony-based architecture, forming 3- dimensional structures approximately 50 - 100 |Lim in diameter and height after 3 days under the two conditions. Noticeably, at day 3, the biofilms grown with 0.9 g m'^ glucose showed a high proportion of dead cells within the biofilm, while the biofilm grown with 3.6 g m"^ glucose consisted of microcolonies that lacked any significant areas of dead cells on day 3. On day 7, biofilms grown in the presence of the higher substrate concentration contained microcolonies that were noticeably larger than those grown in the presence of 0.9g m" . However, the microcolonies on day 7 for the lower glucose concentration showed a higher intensity if propridium iodide (PI) staining (dead cells) than the 7 day old biofilm grown at 3.6 g m'^ glucose. 5 mM glucose Syto9 PI

3 days

7 days

20 mM glucose

3 days

7 days

Figure 4-10. Epifluorescence micrographs (magnification x400) of cell death in P. aeruginosa biofilms growing at two different glucose concentrations, 0.9 g m'^ (5 mM) and 3.6 g m'^ (20 mM), respectively. The biofilm was stained with the BacLight, Live- Dead fluorescent stain and shows Syto9 stained live cells in green (left panels) and Propidium iodide stained dead cells in red (right panels). 4.4. Discussion

4.4.1. Death rule 1 - bacteria die if they have been in stationary phase for a

specific number of hours

As stated above, four conclusions were drawn based on the simulations using this death

rule: 1) the biofilm grows faster at higher bulk phase substrate concentrations, 2)

bacterial death occurs primarily at the base of the microcolonies, 3) bacterial death

occurs earlier, and to a higher extent, at higher bulk phase substrate concentrations, and

4) bacterial growth and death result in sloughing of large sections of biofilm. The fact

that a biofilm accumulated more total biomass when the concentration of substrate was

higher in the bulk phase would be expected. Indeed, this observation of higher biomass

accumulation at the higher substrate concentration was observed for all death rules as

well as for the laboratory grown biofilms. Also, the observation that bacterial death

occurred at the base of the microcolonies was not surprising since those regions are

located the furthest away from the substrate source, i.e. the bulk phase. However, the

fact that higher bulk phase substrate concentrations resulted in earlier death was not

expected. These latter two observations are probably related to substrate transport and

consumption. As described above, the substrate is transported by diffusion from the

bulk phase, through the mass transfer boundary layer, and into the biofilm. When the

substrate encounters the biofilm, there will be a concentration decrease due to microbial

consumption, and the concentration will continue to decrease as we move towards the interior regions of the biofilm. At a certain depth, the substrate concentration will not be high enough to maintain bacterial growth and the bacteria will enter stationary phase.

Hence, it is the biomass between the nutrient source and a given location inside the biofilm that determines the substrate concentration at this location, i.e. if there is a high amount of biomass, there will be a lower substrate concentration, and if there is less biomass, there will be a higher substrate concentration at the given location. If two different bulk phase substrate concentrations are compared (as in the simulations presented in Figures 4-2 and 4-3) then the higher one will generate faster biofilm growth. Thus, at a given time point more biomass (larger biofilm) has been formed at a higher bulk phase substrate concentration (if we neglect sloughing that can occur at later stages). Therefore, bacteria located in the interior of biofilms grown at higher bulk phase substrate concentrations will enter stationary phase earlier compared to bacteria located in the interior of biofilms grown at lower bulk phase substrate concentrations. Thus, given that death rule 1 stipulates that cell death is a function of time (number of hours) in stationary phase it becomes clear that high substrate concentrations could lead to earlier cell death within the microcolonies under these conditions.

As noted above, bacterial growth and death result in hollowing of the biofilm/microcolonies, sloughing of large biofilm pieces and subsequent recovery of the biofilm, a cycle that is repeated over time. This outcome is similar to that reported for the 3-dimensional detachment model constructed by Hunt et al (2004). In their model bacteria detached if they were located in a nutrient poor environment for a certain number of hours. The major difference between death rule 1 described above and the detachment rule used by Hunt et al (2004) is that the latter is a function of the substrate concentration surrounding each bacterium whereas the former is a function of the actual growth status of each bacterium, however, both models show similar results. 4.4.2. Death rule 2 - bacteria die as a function of the ratio between biomass formation and endogenous metabolism In contrast to death rule 1, which only resulted in cell death at the base of the microcolonies, simulations using death rule 2 occasionally showed cell death in the upper region of the microcolonies (Figure 4-4). All simulations that resulted in this death pattern shared the same underlying dynamics. First a subpopulation of bacteria died at the base of the largest microcolony, as illustrated in Figure 4-4 (B) after 100 hours of growth. The reason for this outcome is likely to be, as described above for death rule 1, that larger microcolonies consume more substrate compared to the smaller ones, resulting in a steep substrate concentration gradient as the microcolony grows larger, resulting in substrate concentrations that are lower at the base of the microcolony, as can be seen in Figure 4-4 (F). Consequently, the R value will decrease to a low value at the base of the microcolony. As the microcolony continues to grow, more bacteria will die at the base, which will result in the creation of a void, as can be seen after 200 hours of growth (Figure 4-4 (C)). Eventually, after additional bacterial death, the connection between the microcolony and the substratum will be lost, and the entire microcolony will slough (Figure 4-4 (D)). This generates a dramatic increase in the substrate concentration at the location of sloughing (Figure 4-4 (H)), resulting in recovery of the bacteria located at the base of the surrounding microcolonies, i.e. their R values will increase. At this point, it is not the base of the neighbouring microcolonies that have access to the lowest nutrient concentration, but rather the interior of the upper part of the largest neighbouring microcolony (Figure 4-4 (H)). This may be explained by the set up of the model where substrate is transported by diffusion, it is the distance from the nutrient source to a given location inside the biofilm that determines the substrate concentration at this location. As a result, the interior in the upper part of the largest neighbouring microcolony has the lowest substrate concentration, if we look at the landscape as a whole. While the biofilm continues to grow, it is the R values of the bacteria in this region that will decrease the most. Consequently, bacteria will start to die, as can be seen in Figure 4-4 (D) after 300 hours of growth, and a new void will be formed. Furthermore, since the bacteria are modelled as individuals (with their own set of parameter values), not all bacteria in the current location have the same R value. This would account for the surviving bacteria inside the void, a feature that also has been observed in the laboratory (Webb et al 2003; Mai-Prochnow et al 2004). Note that this outcome also is dependent on the detachment rule used in the model, i.e. that bacteria trapped inside a void are not removed due to sloughing even if they have lost their connection with the substratum/rest of the biofilm. Sloughing of individual microcolonies has been observed both in natural biofilms (Lawrence et al 1991; Costerton et al 1995) and in the laboratory (Stoodley et al 1999). Other biofilm models have also been able to describe sloughing of whole microcolonies (e.g. Picioreanu et al 2001; Hunt et al 2003, 2004). However, to my knowledge, this is the first biofilm model that has been able to model the creation of voids in the "cap" of the mushroom shaped microcolonies, as a function of localized cell death.

As described previously, the simulation shown in Figure 4-4 used a bulk phase substrate concentration of 5 g m ^ which can be compared with the simulation in Figure 4-5 in which a bulk phase substrate concentration of 3 g m'^ was used. By comparing these two simulations, one can conclude that in biofilms growing at higher bulk phase substrate concentration: 1) bacteria located in the outer regions of the biofilm in general have a higher R value (in relation to bacteria located in the same regions in lower substrate concentration); 2) bacteria located in the interior regions of the biofilm in general have a lower R value (in relation to bacteria located in the same regions in lower substrate concentration). The explanation for this effect is that a relatively "thick" layer of "fast" growing (increase in biomass) cells in the outer regions of the biofilm will be established when there is a higher bulk phase substrate concentration, (these can be seen as red, yellow and green cells in Figure 4-4). In contrast, when the bulk phase substrate concentration is lower, the layer of growing cells will be thinner and the cells that are active will not grow as fast (Figure 4-5). A region with fast growing cells will consume more substrate compared to a region of the same size with slow growing cells. This feature, together with the fact that the layer of growing cells is thicker (more cell division) at higher bulk phase substrate concentrations, results in more intense depletion of substrate towards the interior regions of the biofilm. Thus, if there is a higher bulk phase substrate concentration, the bacteria located at deeper regions will experience lower substrate concentrations (visualized in Figure 4-4 (E-H)) compared to bacteria growing in biofilms at lower bulk phase substrate concentrations (visualized in Figure 4-5 (E-H)).

4.4.3. Death rule 3 - bacteria "die" as a function of damage accumulation Simulations using death 3 rule showed that slow growing microcolonies accumulate more total damage compared to fast growing microcolonies and this outcome is consistent for microcolonies growing in different bulk phase substrate concentrations (Figures 4-6 and 4-7) as well as for microcolonies growing in the same bulk phase substrate concentration (Figure 4-7). This result is due to the dilution of total damage as the bacteria divide, where the damage is evenly distributed between mother and daughter cells. Consequently, bacteria in stationary phase accumulate damage since it is not diluted by cell division. This agrees with suggestions by others, e.g. Nystrom, (2004), who proposed that increased levels of damaged molecules are an inevitable consequence of growth arrest.

To further test the difference between various bulk phase substrate concentrations, simulations with even lower values (1 and 2 g m"^, respectively) were also performed

(data not shown), and the results agreed with the simulation data for 3 and 5 g m"^ substrate (i.e. more damage at lower, 1 g m^, compared to higher, 2 g m'^, concentrations of substrate). Thus, these additional simulations support the conclusions based on the comparison of 3 g m" and 5 g m' substrate, which indicated that lower substrate concentrations increased damage (and death) within the biofilm.

The model simulations using death rule 3 also showed that as the rate of damage removal increases, the total amount of damage decreases and the localization of accumulated damage (area with the highest amount of damage) shifts upward in the biofilm. These results are visualized in Figures 4-8 (a simulation with "low" rate of damage removal) and 4-9 (a simulation with "high" rate of damage removal). As the biofilm grows, bacteria will produce damage, and if there is no removal of damage (e.g.

Figures 4-6 and 4-7), all damage that is produced will accumulate in the producing bacterium unless it is dividing. However, if removal of damage is considered (Figures

4-8 and 4-9), there will be a loss of damage in all bacteria, not only the ones that are actively dividing. Bacteria located in nutrient poor environments (generally at the bases of the microcolonies) do not produce that much damage since they have very low substrate consumption (if any). In addition, if the bacteria have a low biomass (again, generally at the bases of the microcolonies) there will be very little damage production during endogenous metabolism as well. For non dividing bacteria, it is the relationship between damage production and damage removal that determine if there will be an accumulation of damage or not. If the rate of damage production exceeds the rate of damage removal, damage will be accumulated. In contrast, if the rate of damage production is less then the rate of damage removal, the bacteria will eventually be cleared of damage. In the biofilm system, the rate of damage production increases as we move upwards in the biofilm (since the substrate concentration increases). Therefore, if the rate of damage removal increases, the influence will be most noticeable in the lower biofilm regions, i.e. the regions with low rate of damage production. In conclusion, this result would suggest that damage removal is an important parameter for determining the localisation of damage inside a biofilm.

4.4.4. Differences and similarities between the outcomes of the three tested

death rules

When comparing the results generated using the three death rules, both similarities and differences emerged. Both death rules 1 and 2 initially generated cell death at the bases of the microcolonies. However, death rule 2 occasionally (but not always) showed cell death at the upper parts of the microcolonies at later time points, a behaviour never observed using death rule 1. Both death rules (1 and 2) were sensitive to changes in the bulk phase substrate concentration. Higher substrate concentrations generated earlier and more profound cell death. This was especially noticeable with death rule 2, where a higher bulk phase substrate concentration often resulted in cell death, whereas a lower one did not. This extreme difference was never detected when death rule 1 was used.

Using death rule 3, a lower bulk phase substrate concentration resulted in more damage compared to a higher bulk phase substrate concentration. Presumably, this would lead to more cell death at lower bulk phase substrate concentrations. This result is in contrast to those generated using death rules 1 and 2. In short, death rules 1 and 2, both suggest that cell death will be enhanced with increasing substrate concentration. Only death rule 3, differed in this respect, and suggested that lower substrate concentrations will increase cell death within the biofilm.

4.4.5. Comparisons of cell death in the modelling system and within

laboratory experimental biofilms

To asses the results generated by the model system, biofilm formation of P. aeruginosa under different bulk phase nutrient concentrations was also monitored experimentally.

At day 3, the experimental biofilm grown with 0.9 g m"^ (5 mM) glucose showed a high proportion of dead cells within the biofilm (Figure 4-10). This can be compared with the biofilm grown with higher concentration of 3.6 g m"^ (20 mM) glucose that lacked significant areas of dead cells (Figure 4-10). These results, which indicate a strong effect of substrate concentration on death and damage accumulation in the biofilm, are in agreement with the results generated by the biofilm model system when death rule 3 was implemented. Using death rule 3, the higher substrate concentration resulted in lower levels of damage (Figure 4-6) whilst the lower substrate concentration showed higher levels of damage (Figure 4-7). The likely explanation for this outcome is that slow growing cells (in low nutrient concentration) accumulate more damage compared to fast growing cells (in high nutrient concentration) since they can not dilute the damage through cell division at the same rate as fast growing cells. However, as seen in

Figure 4-10, this effect was largely absent in 7 day old laboratory biofilms, when biofilms grown with 3.6 g m'^ glucose exhibited death/damage throughout the biofilm architecture, which was not seen at 3 days. This observation may be explained by the biofilm growth rate. As a biofilm grows, it will eventually reach a point in which cell growth (and division) will slow down (due to a limitation of nutrients, space, etc). When this happens, the cells in the biofilm start to accumulate damage and the rate of cell death in the biofilm will increase. This is in agreement with the observations reported in

Purevdoj-Gage et al. (2005), where it was observed that biofilm dispersal only occurred once microcolonies reached a threshold size (approximately 80 um in diameter). Thus, accumulation of damage and an increased rate of cell death seem to be an inevitable fate for all biofikn cells regardless of nutrient concentration. Thus, it would appear that nutrient availability influences the timing of cell death during biofilm development, but not death per se. Given that the simulations based on death rule 3 most closely approximate experimental observations from in vitro grown biofilms, in comparison to death rules 1 and 2, it is concluded here that death rule 3 most closely approximates the biological cause of cell death in biofilms. Thus, this data suggests that the accumulation of damage is the main cause of cell death during the formation of microbial biofilms. 4.5. Laboratory experimental biofilms

P. aeruginosa strain PAOl (ATCC 15692) was used. Batch cultures of P. aeruginosa were grown at 37°C with shaking in Luria-Bertani (LB) medium. For cultivation of biofilms, M9 medium containing 48 mM Na2HP04, 22 mM KH2PO4, 9 mM NaCl, 19 mM NH4CI, 2 mM MgS04, 100 jiM CaCh, and either 0.9 g m"^ (5 mM) or 3.6 g m"^ (20 mM) glucose was used. Biofilms were grown in continuous-culture flow cells (channel dimensions, 1 by 4 by 40 mm; flow rate, 150 |il min'^) at room temperature as previously described (Moller et al 1998). Channels were inoculated with overnight cultures and incubated without flow for 1 h at room temperature. Bacterial viability was determined by using a ^¿zcLight LIVE/DEAD bacterial viability staining kit

(Invitrogen). Two stock solutions of stain (SYTO 9 and propidium iodide) were each diluted to a concentration of 3 |nl ml"^ in biofilm medium and injected into the flow channels. Live SYT09-stained cells and dead propidium iodide-stained cells were visualized under epifluorescence microscopy (Olympus BX51) using fluorescein isothiocyanate and tetramethyl rhodamine isothiocyanate optical filters, respectively.

Row cell biofilm experiments were performed by J. S. Webb (School of Biological

Sciences, University of Southampton), to test the model results which indicated that different nutrient concentrations would affect cell death during biofilm development. Chapter 5. Summary and general discussion

5.1. Summary of results

The work presented here has addressed four different aims: 1) development of a mathematical model of the QS system in P. aeruginosas 2) investigation of the dynamics of the QS system in P. aeruginosa when disturbed by AHL antagonists; 3) development of an individual based biofilm model; 4) investigation of the factors mediating cell death during biofilm development.

Model analysis (Chapter 2) demonstrated that the QS system in P. aeruginosa has hysteresis dynamics, i.e. the system consists of two stable steady states (reflecting low and high rates of AHL production, respectively) separated by an unstable steady-state.

Furthermore, AHL production switches on at a higher concentration of AHL (reflecting a high population density, or a population density of any magnitude in a diffusion limited environment) than it switches off. It was also shown in Chapter 2 that the regulators RsaL and Vfr have opposite affects on the system. RsaL, which is an inhibitor in the production of LasI (AHL synthase), was demonstrated to increase the concentration of AHL required to switch on the system, whereas Vfr, which was assumed to have a positive affect on LasR (transcriptional activator) production (Albus et al. 1997), was shown to decrease the concentration of AHL required to switch on the system. Vfr is a homologue of the catabolite repressor protein found in E. coli that responds to changes in carbon source, as sensed via cAMP (West et al. 1994). Thus, QS is linked though Vfr to metabolism in P. aeruginosa which may advance or retard QS expression depending on carbon source utilization. Thus, it seems that P. aeruginosa uses different regulators to adjust the cell density required for switching on the QS system, presumably as a response to different environmental influences. For example,

P. aeruginosa has been isolated from soils, freshwater, cleaning disinfectants, and infection sites from multiple organisms, where nutrients, temperatures, and stresses might differ dramatically. Further, it was also demonstrated that AHL antagonists

(QSBs) have the capacity to uninduce an otherwise induced QS system, i.e. drive the system to the low stable steady state (Chapter 3). However, it was demonstrated that this blocking behaviour is extremely dependent on the parameter values used, since even very small differences had a major influence on the outcome. Most notably, it was shown that the ability of the AHL antagonist to mediate degradation of LasR is the core parameter for successful inhibition of the QS system. Finally, accumulation of damage was predicted to be the main cause of cell death during the formation of microbial biofilms (Chapter 4). Moreover, a strong relationship between nutrient availability and cell death was also found, as lower bulk phase nutrient concentrations resulted in more and/or earlier cell death during biofilm development, presumably because of accumulation of higher amounts of damage. Thus, biofilm mediated cell death and QS are both linked to central metabolic processes, which involve a highly complex and dynamic series of regulatory steps for proper control of biofilm development, QS and central metabolism. 5.2. QS dynamics and regulation

It is currently appreciated that AHL based QS is a form of cell-cell communication which is common among Gram-negative proteobacteria bacteria. It has also been shown that QS regulates a diverse rage of functions, many of which are involved in bacterial- host interactions, such as symbiosis and pathogenicity (Miller and Bassler, 2001). In terms of QS, P. aeruginosa is probably the most intensively studied bacterium. As described in Chapter 1, it has been suggested that six to ten percent of the chromosomal genes of P. aeruginosa are regulated by QS (Arevalo-Ferro et al 2003; Schuster et al

2003; Wagner et al 2003) and approximately one third of the QS regulated genes in P. aeruginosa encode different virulence factors (van Delden and Iglewski, 1998;

Rumbaugh et al 2000; Hentzer et al 2003; Juhas et al 2005; Rasmussen et al 2005b;

Schuster et al 2003; Vasil, 2003; Wagner et al 2003; Winzer and Williams, 2001). QS has also been shown to be involved in the development of biofilms, which is proposed to be important for the survival of this organism in the environment and during infection

(Davies et al 1998; Hentzer et al 2003; Passador et al 1996; Winson et al 1995;

Bjamsholt et al 2005; Shih and Huang, 2002; Hentzer et al 2003). Taken together, the accumulated data suggest that there is great potential for interference with QS in P. aeruginosa (and other bacteria) as a novel strategy to control production of virulence factors and the formation of biofilms. There is a strong need for such a control strategy, especially in the medical context, where the increased incidence of drug resistant bacteria is rendering current antibiotic treatments obsolete.

Even though QS research has been intensively studied over the preceding 20 years, much is still unknown about how QS regulation is integrated into the global control of gene expression in the cell. However, if we want to master QS system (e.g. shut it down) it is vital that we gain a better understanding about its dynamics as well as regulation. One research tool that has obtained much attention recently is mathematical modelling. By using mathematical modelling it is possible to study complex systems, such as QS and biofilm formation, and to identify those processes and parameters that are most important for the system being studied. Thus, modelling may help to identify which parameters are essential for the system to function properly and which parameters only play supportive roles, so that the key steps can be targeted to develop strategies to control bacterial virulence and biofilm formation.

The QS model developed in this thesis (Chapter 2) was based on the QS models developed earlier by James et al (2000) and Dockery and Keener (2001). Comparison of the output from these three different (but related) QS models, indicates that they all showed the same QS dynamics, i.e. that QS works by a hysteretic switching between two stable steady-state solutions, reflecting low and high rates of AHL production. In contrast to the models developed by James et al (2000) and Dockery and Keener (2001), the expression of two different regulators (Vfr and RsaL) were also included in the QS model system developed here (Chapter 2). This allowed for the investigation of not only QS dynamics in P. aeruginosa, but also an improved understanding of how the QS system itself is regulated. To my knowledge, this was the first QS model that considered the addition of accessory regulators to study QS mediated gene expression. By expanding our understanding of the integrated control of QS, it will be possible to identify the "weaknesses" (from the bacterial point of view) of the systems and take advantage if them. For instance, based on the results in Chapter 2, if it were possible to overexpress RsaL production and simultaneously reduce or abohsh Vfr production, such a system would require much higher concentrations of AHL for activation compared to

an unmodified system. In this way, it would be possible to keep the QS system inactive

and hence, reduce virulence factor expression and the expression of genes that are required for biofilm formation or maintenance. Thus, both RsaL and Vfr could be targets for QS control. While Vfr is involved in the regulation of genes outside of the

QS regulon, and hence, may not be appropriate as a QS control strategy (Suh et al

2002), RsaL to date has only been shown to affect the QS system and therefore may be a good candidate for QS control. Therefore, studies aimed at understanding how RsaL expression is controlled, may lead to strategies to reduce QS induction.

Mathematical modelling is ideally suited to identify such weaknesses in a system, such as the QS system in P. aeruginosa. As described previously, with mathematical modelling it is possible to test a large number of different parameters (or hypotheses) in a comparatively shorter amount of time than through the use of laboratory experiments.

This is not to say that mathematical modelling can fully replace laboratory experiments.

Model systems are always simplifications of reality, and the outcomes of such models need to be validated experimentally. But the strength of mathematical modelling is to sort and identify important parameters (or processes) that subsequently can be tested and confirmed in the laboratory. This sequence of work, i.e. prior modelling and subsequent wet-lab experiment based on the modelling results, has been successfully used here. For example, the influence of Vfr was tested in the modelling system, and based on its predicted importance as activator of the QS system in P. aeruginosa, experiments aimed to test the predictions were planed and performed. As described previously, the experimental results confirmed the predictions raised by the modelling system, i.e. that over expression of Vfr would decrease the AHL concentration required for induction of the QS system.

Subsequent to the publication of the work presented in Chapter 2 (Fagerlind et al. 2003), several new QS models have been developed and the general trend is to include more complexity into the model systems, e.g. dynamic population growth and spatial variations in AHL concentration. By doing so, it is possible to develop more realistic models that mimic the biological system better and thus (hopefully) generate more reliable and correct results or predictions. As described in Chapter 1, special attention has been placed on QS and the affects of dynamic population growth and spatial variations in both population density and AHL concentration (e.g. Chopp et al 2003; Koerber et al 2002; Ward et al 2001, 2003, 2004). The inclusion of these additional features is of great importance since bacteria are found mainly within biofilms and because QS plays an important role in the control of biofilm formation and development. In real life biofilms there will always be heterogeneity in cell density at different locations in the biofilms, and this will also be reflected in local AHL concentrations. The position of cells within the biofilm to the bulk liquid is also of major importance, since the bulk liquid can be considered a sink for the AHLs. In this way, it would be easy to envisage a concentration gradient, where there are high concentrations of AHLs in the interior of the biofilm and lower concentrations of AHLs along the periphery of the biofilm, at the interface with the bulk fluid. Hence, a biofilm could be comprised of subpopulations of cells that have an induced QS system while others might be in a non-induced state. However, based on the observations that RsaL and Vfr play significant roles in modulating QS expression, the metabolic status of the cells within the biofilm would have to be taken into account and hence, this rather simplistic expectation of an AHL concentration gradient may not be correct. Moreover, despite the increased complexity (and use of different mathematical approaches) considered in more recent QS models, the main dynamics as predicted previously by James et al. (2000), Dockery and Keener (2001) and Fagerlind et al (2003), Chapter 2) that QS displays hystersis dynamics and low versus high production rate of AHL, as a function of AHL concentration, remain unchanged. 5.3. Inhibition of QS

The awareness that P. aeruginosa, and many other bacteria, uses QS to regulate the

production of virulence factors, as well as biofilm formation, makes this system an ideal

target for control strategies, as suggested by several research groups (e.g. Passador et al.

1993; Pearson et al. 1994; Givskov et al. 1996; Finch et al. 1998). Furthermore, since

QS regulates non-essential traits, the inhibition of QS is not assumed to create the same

strong selective pressure seen with antibiotics. This is an essential feature of novel

therapeutic compounds since we currently face a growing problem with antibiotic

resistance. Given the long evolutionary context for interaction of pathogens and hosts, it

is clear that interference with QS is an approach independently evolved by several

(perhaps many) organisms, which includes both plants (e.g. Daniels et al. 2002; Gao et

al. 2003; Mathesius et al. 2003; Sanchez-Contreras et al. 2007; Teplitski et al. 2000) as

well as algae (e.g. de Nys et al. 1993; Givskov et al. 1996; TepHtski et al 2004). In

addition, many recent studies have also demonstrated the inhibitory affect of QS

inhibitors (or QS blockers, QSBs) in several bacterial species, where the QSBs have

been shown to control a range of phenotypes involved in virulence and surface

colonization (e.g. Kjelleberg et al. 1997; Milton et al. 1997; Lindum et al. 1998;

Manefield et al. 1999, 2001; Rasmussen et al. 2000; Hentzer et al. 2002; Ren et al.

2002; Defoirdt et al. 2006; Lonn-Stensrud et al. 2007). However, those studies relied on

the testing of either libraries of compounds or tested compounds that were readily

available. Experimental design and compound selection were typically based on an empirical process and lacked significant theoretical guidance to identify the key parameters that are essential for successful inhibition. For that reason, the QS model developed in Chapter 2 was updated to investigate the affect of different QSBs (Chapter

3). This updated QS model was based on the QS framework described in Chapter 2, it thus, showed the same QS dynamics, including hysteretic switching between two stable steady-state solutions, reflecting low and high rates of AHL production. In the model developed here, it was shown that inhibitors that increased the degradation of LasR had the best activity as inhibitors. Moreover, this effect was the single most important feature of an inhibitor as predicted by the model. A contemporary QS model that also investigated the affect of QSBs was published by Anguige et al. (2004). Their model system was also largely based on the QS model developed by Dockery and Keener, (2001), with the addition of a dynamic population growth function. Their model also showed hysteretic switching similar to the QS model described in Chapter 3. Furthermore, they confirmed the results of the QS blocking model here (Chapter 2), which showed that QSBs have the capacity to uninduce an otherwise induced QS system, i.e. drive the system to the low stable steady state. Both models demonstrated that the qualitative response to QSB treatment is heavily dependent on the parameter values used, i.e. properties of the QSBs. Indeed, both models showed that even very small differences between different QSBs may have a large impact on their effectiveness as inhibitory molecules. This is another good example when mathematical modelling shows its strength. Here we get predictions of which parameters that are most important for successful inhibition of QS (e.g. the ability of the QSB to mediate degradation of LasR as discussed in Chapter 3). Thus it is valuable to test the effects of changes the predicted properties of existing QSBs, as even small improvements can result in much stronger inhibition of QS. In contrast, to similarly identify core parameters using laboratory based experiments would be very difficult and time consuming to achieve. This experimentally driven process is typically based on the identification of a core parameter, and the subsequent generation of a large library of compounds is typically generated using combinatorial chemistries for subsequent testing. Those libraries, typically consisting of hundreds of compounds, would then be experimentally evaluated to identify those compounds with the best activity. This process, using natural QSBs as scaffold (but without searching for specific parameter improvements) was used to identify synthetic QSBs, which displayed stronger inhibitory properties than those of the natural QSB compounds (Manefield et al 2002). However, if modelling results could be used to first identify key parameters, one could improve and speed up this method, and thus identify QSBs with stronger inhibitory properties in a shorter period of time. The model presented here indicated that it is the effect of the QSB on LasR stability. Therefore, strategies could be developed that would target a QSB to LasR, that destabilises LasR or targets it for proteolytic degradation faster and hence have a stronger activity as a QSB. Recently, Anguige and co-workers have continued to refine their QS/QSB modelling by developing surface based population (biofilm) approaches, in which diffusible QSB is added to the surface on growing biofilms (Anguige et al 2005, 2006). Their results indicated that QSB's, act in the same fashion on a biofilm as they do in the presence of planktonic cells and hence, QSB's should be effective inhibitors of QS processes, e.g. expressions of virulence factors in biofilms.

While the QS model developed in Chapter 2 investigated the induction or activation of the QS system, this is only half of the QS regulation process. When returning to low cell density conditions or perhaps under other conditions (such as substrate limited conditions), it becomes important for the cell to switch off the QS system. For example, in Fig. 2-8, there is a clear decrease in AHL concentration in the late stationary phase samples, 24h, indicating that the QS system is being switched off Therefore, a future development for the existing QS model would be to include the production of QS inhibitors and/or AHL degrading enzymes which have been shown to be produced by P. aeruginosa under substrate limited conditions (Huang et al. 2003). The inclusion of such additional control points would help to close the biological regulatory loop so that the system can be complete, capable of being fully induced or repressed depending on the biological needs and in this way improve our understanding of how QS is controlled as well as improve our ability to design QSBs. 5.4. Biofilms

Biofilms are currently considered as the predominant bacterial life-style. Inside the biofilms bacteria are protected from stresses such as UV light, antibiotics, heavy metals and other antimicrobial agents (Allison et al 1993; Anwar et al 1989, 1990; Donlan and Costerton, 2002; Drenkard, 2003; Teizel and Parsek, 2003). Biofilm development is influenced by a number of different processes such as adhesion (Cramton et al 1999;

Froeliger and Fives-Taylor 2001; Gavin et al 2002; Tsuneda et al 2003); detachment

(Alison et al 1998; Sawyer and Hermanowicz, 1998; Hentzer et al 2002); mass transport (Characklis and Marshall, 1990; de Beer et al 1994); hydrodynamics

(Stoodley et al 1999, 2002b), EPS production (Nielsen et al 1996; Tsuneda et al

2003), cell motility (OToole and Kolter, 1998a; Klausen et al 2003), QS (Davies et al

1998; de Kievit et al 2001; Huber et al 2001; Lynch et al 2002; Labbate et al 2004); cell death (Webb et al 2003; Mai-Prochnow et al 2004, 2006; Barraud et al 2006),

DNA excretion (Petersen et al 2005; Allesen-Holm et al 2006) and active dispersal

(Barraud et al 2006; Prochnow et al 2006; Koh et al 2007). It has also been found that bacteria display multiple phenotypes, with distinct physiological characteristics, during biofilm formation (Prigent-Combare et al 1999; Sauer and Camper, 2001; Sauer et al

2002). For example, Sauer et al (2002) recently demonstrated that P. aeruginosa biofilm formation is composed of five different stages: 1) reversible attachment; 2) irreversible attachment; 3) maturation-1; 4) maturation-2; 5) dispersion. All five stages of biofilm development were shown to have distinct protein production patterns, highlighting that biofilm formation is a true developmental process. It was shown that the average difference in detectable protein expression between each of the five stages of development was 35% (approximately 525 proteins). Moreover, when planktonic cells were compared with maturation-2 stage biofilm cells, more than 800 proteins were shown to have a six-fold or greater change in expression level (over 50% of the proteome). 5.5. Cell death during biofilm development The developmental data of Sauer et al. (2002) clearly highlights that biofilm formation is complex and is effected by multiple processes, mathematical modelling is an ideal approach to study the interdependence between these processes and also to identify those processes and parameters that are most important during biofilm formation. Indeed, biofilm modelling has received much attention during the last decade, and currently many research groups are using biofilm modelling as an investigative tool in addition to laboratory experiments. Most of the biofilm models developed to date, and those that focus on biofilm development in particular, are CA models (Wimpenny and Colasanti, 1997; Hermanowicz, 1998, 1999, 2001; Picioreanu et al 1998a, 1998b, 1999; Noguera et al. 1999; Pizarro et al 2001; Chang et al 2003; Hunt et al 2003, 2004; Laspidou and Rittman, 2004; Chambless et al 2006) or IBMs (Kreft et al 1998, 2001; Kreft and Wimpenny, 2001, Xavier et al 2004, 2005, 2007; Alpkvist et al 2006; Picioreanu et al 2007). There are basic processes which are consistently incorporated into biofilm models, such as substrate diffusion, substrate consumption (resulting in bacterial growth), bacterial division/spreading, and bacterial detachment. The biofilm model developed in Chapter 4 used similar mathematical expressions as those used in many of the previous biofilm models. Examples of such parameters are substrate diffusion (used in e.g. Picioreanu et al 1998a, 1998b, 1999, 2000; Kreft et al 2001; Hunt et al 2003, 2004), substrate consumption and microbial growth (used in e.g. Kreft et al 1998; Picioreanu et al 1998a, 1998b, 1999, 2000), bacterial division/spreading (used in e.g. Hermanowicz, 1999; Chang et al 2003) and bacterial detachment (used in e.g. Hermanowicz, 2001). Thus, these mathematical expressions have been used (and evaluated) by others in the past, and may therefore be considered as accepted. However, one process that has been largely overlooked in biofilm modelling is bacterial death. Experimental studies suggest that bacterial death is an important process during biofilm development and most of the studies also indicate that there is a strong relationship between cell death, dispersal and the formation of phenotypic variants in microbial biofilms (Webb, et al 2003; Prochnow et al 2004, 2006; Barraud et al 2006; Koh et al

2007). In this way, the cell death and dispersal phase of biofilm development is important because it returns the sessile bacteria back into the planktonic phase so that the bacteria can colonise new environments. Given the suggested importance of cell death during biofilm development, it becomes important to understand biologically what drives that process. While there is very little published data to date describing the cause and consequences of cell death during biofilm development, some processes have been suggested to be involved in playing important roles in mediating cell death in biofilms. As described in Chapter 4, Webb and co-workers observed that killing and lysis occurred inside P. aeruginosa biofilms by a mechanism that involved a genomically encoded Pfl-like prophage of P. aeruginosa (Webb et al 2003). Moreover, they also found evidence that the generation of reactive oxygen species (ROS) was essential for prophage activation and subsequent superinfection and lysis. More recently, these findings were refined by Barraud et al (2006), who identified the reactive nitrogen species peroxynitrite (ONOO ) as the intracellular signal mediating cell death in mature P. aeruginosa biofilms. Prochnow et al (2004), observed a similar death pattern in biofilms formed by the marine bacterium Pseudoalteromonas tunicata.

An autotoxic protein designated AlpP, was found to induce cell death in this organism through lysine oxidase activity of AlpP which generates the reactive oxygen species

H2O2 as a by-product. Similar patterns of cell death and dispersal have also been identified in the pathogen Serratia marcescens (Koh et al 2007). Such observations on the correlation between reactive oxygen and nitrogen species and cell death in the biofilm have also been made for planktonic cells. For example, Dukan and colleagues found evidence that oxidative damage of proteins increase during stationary-phase in wild-type E. coli (Dukan and Nystrom, 1999; Dukan et al 2000). Ballesteros et al

(2001) demonstrated that this increase in protein oxidation in stationary phase cells was strongly associated with the production of aberrant proteins in the cells. The reason for the elevated concentration of aberrant proteins in stationary-phase bacteria was speculated to be caused by reduced fidelity of the translational machinery, possibly due to reduced presence of charged tRNAs. Aberrant proteins are more susceptible to oxidation and, thus the elevated oxidation of proteins in stationary-phase bacteria may be due to an increased availability of substrates (aberrant proteins) available for oxidative attack. It is not clear why aberrant proteins are more susceptible to oxidation, but it was speculated that misfolding of the corrupted polypeptide exposes oxidation- sensitive targets that are normally hidden during the translation-folding process

(Ballesteros et al 2001). Furthermore, protein oxidation of aberrant protein does not appear to be sensed by the oxidative defence system and does not require increased generation of ROS (Dukan and Nystrom, 1999). It was further speculated that the life expectancy of bacteria is correlated to the level of oxidative damage, and based on the accumulated data it was suggested that bacteria in stationary phase have a higher death rate compared to growing bacteria (Nystrom, 2004).

To evaluate which factors might be involved in the formation of clusters of dead cells within the biofilm, three different death rules were evaluated (Chapter 4), and to my knowledge this the first model that focuses on bacterial death during biofilm development. The three death rules evaluated in Chapter 4 were based on the current data on bacterial death, as described above. Death rules 1 and 2 assumed that bacteria in stationary phase have a higher death rate compared to growing bacteria (as speculated by Nystrom (2004)), which were based on the fact that oxidation of proteins (damage) have been shown to increase during stationary phase (see above) (Dukan and Nytrom,

1999; Dukan et al. 2000). However, for simplicity no specific expressions of oxidized proteins were included in these two death rules, i.e. the effect of damaged proteins were investigated indirectly. In death rule 1, no difference was made between different bacteria in stationary phase, i.e. the death rate was the same for bacteria in nutrient depleted areas as it was for bacteria in more nutrient rich areas (but not rich enough to sustain net growth). Instead the emphasis was on the total time in stationary phase. This was based on the assumption that damage accumulates in time, i.e. for each hour in stationary phase more damage is added to the total pool of damage, and when a certain amount of damage has been formed (number of hours in stationary phase in the model system), bacterial death will occur.

When implementing death rule 2, bacterial death occurred as a function of the ratio between biomass formation and endogenous metabolism, i.e. distinction between different bacteria in stationary phase was considered. It was assumed that bacteria that have to expend resources on endogenous metaboUsm have a higher death rate compared to bacteria that have sufficient resources to expend on growth processes, i.e. bacteria with low ratios between biomass formation and endogenous metabolism have the highest death rates. This death rule was based on the assumption that the concentration of charged tRNAs is a function of available nutrients. Hence, low nutrient concentrations would result in low concentrations of charged tRNAs, and therefore in high concentrations of aberrant proteins available for oxidative attach (Ballesteros et al. 2001). Thus, the concentration of oxidized/damaged proteins would increase, with an increased rate of bacterial death as a consequence.

In death rule 3, the rate of bacterial death was assumed to be a consequence of damaged molecules, which was similar to death rules 1 and 2. However, in contrast to death rules

1 and 2, in which damage caused cell death indirectly, rule 2 incorporated the production of damage as a function of substrate consumption and endogenous metabolism. This feature allowed all bacteria in the biofilm system to undergo cell death if the amount or concentration of damage was raised, i.e. not only bacteria in stationary phase (as in death rules 1 and 2). Moreover, this feature also allowed one to investigate the effect of damage dilution through bacterial division, a feature that previously has been proposed to be vital for bacterial death/survival (e.g. Nytrom,

2004).

As presented in Chapter 4, the three death rules tested produced different results, i.e. death rules 1 and 2 showed more cell death at higher bulk phase substrate concentration whereas death rule 3 showed more cell death (accumulation of higher amounts of damage, which is assumed to result in cell death) at lower bulk phase substrate concentration. These were intriguing since the influence of different bulk phase substrate concentrations, and its affect on cell death during biofilm formation has not been specifically addressed in previous laboratory experiments. Experimental results often vary between experimental set-ups and between research laboratories and such differences in experimental systems have been used to explain the variation in results.

For example, it has been shown that QS control of biofilm formation exhibits media dependence. In Serratia marcescens, QS is required for maturation of the filamentous biofilm when grown in the defined medium with glucose as a sole carbon source (Rice

et al. 2005). However, if the medium is changed to a rich, complex medium such as

Lauria-Broth, a QS deficient mutant can still form a mature filamentous biofilm (Rice et al. 2005). Similar results have also been demonstrated for biofilms of Burkholderia cepacia (Conway et al 2002). However, little attention has been focused on the difference in carbon source concentration and its affects on biofilm development. The model results presented here indicate that different bulk phase nutrient concentrations

(with the same media) affect the level of cell death during biofilm development. Based on those results, experiments were designed to test this possibility and indeed, the experimental results support the model's conclusions. It is perhaps not unsurprising that differences in carbon source can alter biofilm development due to differences in growth rates, central metabolism etc. However, it was unexpected that differences in concentration of the same carbon source could lead to these dramatic differences because there would be no differences in metabolic pathways or growth rates when growing on the same carbon source.

As noted above, QS has been demonstrated to influence both biofilm structure and function (Davies et al 1998; de Kievit et al 2001; Huber et al 2001; Lynch et al 2002;

Shih and Huang, 2002; Hentzer et al 2003; Labbate et al 2004; Bjamsholt et al 2005).

Therefore, it would strengthen the biofilm cell death model if QS was incorporated. For example, it has been suggested that the Rhl QS component, but not Las, represses expression of the nitrite reductase gene nirS to control production of nitric oxide. Thus, loss of Rhl results in the increased production of nitric oxide and therefore, could either enhance dispersal or mediate cell death (Hassett et al 2002). Therefore, as for the QS system itself, by increasing the complexity of the model to include parameters that have been shown, experimentally or theoretically, to have significant impacts on biofilm development will improve our ability to test hypotheses and make better informed predictions about biological processes.

Bacteria are one of the numerically most predominant forms of life on earth and they preferentially exist as sessile communities, also called biofilms. Biofilms contribute to overall resistance to antimicrobials as well as other stresses and hence, strategies that address bacterial resistance and biofilm formation are important for the next generation of therapeutics. One of the most common bacterial pathogens is P. aeruginosa, a bacterium that uses QS to regulate the production of virulence factors as well as biofilm formation. By taking a modelling approach, this project has extended the current understanding of QS dynamics in P. aeruginosa, and also proposed that QSBs that target the stability of LasR constitutes a potential therapeutic approach against P. aeruginosa mediated infections. Finally, based on an individual based CA approach, it was possible to evaluate the potential contributions of different bacterial death rules during biofilm formation. Based on the modelling approach as well as laboratory data, accumulation of damage was suggested to be the main cause of cell death during biofilm formation. Based on the results that emerged during this project, it would be particularly interesting to see if inhibition of QS indeed would prevent or stop QS based infections in humans, maybe as a result of biofilm clearance. References

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