Bulletin of Mathematical Biology

, Volume 80, Issue 11, pp 2917–2956 | Cite as

A Multiscale Agent-Based Model for the Investigation of E. coli K12 Metabolic Response During Biofilm Formation

  • Majid LatifJr.
  • Elebeoba E. MayEmail author
Original Article


Bacterial biofilm formation is an organized collective response to biochemical cues that enables bacterial colonies to persist and withstand environmental insults. We developed a multiscale agent-based model that characterizes the intracellular, extracellular, and cellular scale interactions that modulate Escherichia coli MG1655 biofilm formation. Each bacterium’s intracellular response and cellular state were represented as an outcome of interactions with the environment and neighboring bacteria. In the intracellular model, environment-driven gene expression and metabolism were captured using statistical regression and Michaelis–Menten kinetics, respectively. In the cellular model, growth, death, and type IV pili- and flagella-dependent movement were based on the bacteria’s intracellular state. We implemented the extracellular model as a three-dimensional diffusion model used to describe glucose, oxygen, and autoinducer 2 gradients within the biofilm and bulk fluid. We validated the model by comparing simulation results to empirical quantitative biofilm profiles, gene expression, and metabolic concentrations. Using the model, we characterized and compared the temporal metabolic and gene expression profiles of sessile versus planktonic bacterial populations during biofilm formation and investigated correlations between gene expression and biofilm-associated metabolites and cellular scale phenotypes. Based on our in silico studies, planktonic bacteria had higher metabolite concentrations in the glycolysis and citric acid cycle pathways, with higher gene expression levels in flagella and lipopolysaccharide-associated genes. Conversely, sessile bacteria had higher metabolite concentrations in the autoinducer 2 pathway, with type IV pili, autoinducer 2 export, and cellular respiration genes upregulated in comparison with planktonic bacteria. Having demonstrated results consistent with in vitro static culture biofilm systems, our model enables examination of molecular phenomena within biofilms that are experimentally inaccessible and provides a framework for future exploration of how hypothesized molecular mechanisms impact bulk community behavior.


Escherichia coli K12 Biofilm Agent-based modeling Quorum sensing Systems biology 



The authors would like to thank Drs. Komal Rasaputra and Cheryl Sershen for providing data and technical consultation, respectively.

Supplementary material

11538_2018_494_MOESM1_ESM.pdf (39.3 mb)
Supplementary material 1 (pdf 40254 KB)


  1. Abramson J, Riistama S, Larsson G, Jasaitis A, Svensson-Ek M, Laakkonen L, Puustinen A, Iwata S, Wikström M (2000) The structure of the ubiquinol oxidase from Escherichia coli and its ubiquinone binding site. Nat Struct Mol Biol 7:910–917Google Scholar
  2. Adair CG, Gorman SP, Feron BM, Byers LM, Jones DS, Goldsmith CE, Moore JE, Kerr JR, Curran MD, Hogg G et al (1999) Implications of endotracheal tube biofilm for ventilator-associated pneumonia. Intensive Care Med 25:1072–1076Google Scholar
  3. Adams B, Ebeida M, Eldred M, Jakeman J, Swiler L, Bohnhoff W, Dalbey K (2013) Dakota, a multilevel parallel object-oriented framework for design optimization, parameter estimation, uncertainty quantification, and sensitivity analysis. Technical report Sandia National LaboratoriesGoogle Scholar
  4. Agladze K, Wang X, Romeo T (2005) Spatial periodicity of Escherichia coli K-12 biofilm microstructure initiates during a reversible, polar attachment phase of development and requires the polysaccharide adhesin PGA. J Bacteriol 187:8237–8246Google Scholar
  5. Alpkvist E, Picioreanu C, van Loosdrecht MCM, Heyden A (2006) Three-dimensional biofilm model with individual cells and continuum EPS matrix. Biotechnol Bioeng 94:961–979Google Scholar
  6. Andersen KB, von Meyenburg K (1977) Charges of nicotinamide adenine nucleotides and adenylate energy charge as regulatory parameters of the metabolism in Escherichia coli. J Biol Chem 252:4151–4156Google Scholar
  7. Apri M, de Gee M, Molenaar J (2012) Complexity reduction preserving dynamical behavior of biochemical networks. J Theor Biol 304:16–26zbMATHGoogle Scholar
  8. Baker JS, Dudley LY (1998) Biofouling in membrane systems: a review. Desalination 118:81–89Google Scholar
  9. Barberis M, Klipp E, Vanoni M, Alberghina L (2007) Cell size at S phase initiation: an emergent property of the G1/S network. PLoS Comput Biol 3:e64Google Scholar
  10. Barrett T, Troup DB, Wilhite SE, Ledoux P, Evangelista C, Kim IF, Tomashevsky M, Marshall KA, Phillippy KH, Sherman PM et al (2011) NCBI GEO: archive for functional genomics data sets-10 years on. Nucleic Acids Res 39:D1005–D1010Google Scholar
  11. Barrios AFG, Zuo R, Hashimoto Y, Yang L, Bentley WE, Wood TK (2006) Autoinducer 2 controls biofilm Formation in Escherichia coli through a novel motility quorum-sensing regulator (MqsR, B3022). J Bacteriol 188:305–316Google Scholar
  12. Becker SA, Feist AM, Mo ML, Hannum G, Palsson BØ, Herrgard MJ (2007) Quantitative prediction of cellular metabolism with constraint-based models: the COBRA toolbox. Nat Protoc 2:727–738Google Scholar
  13. Beloin C, Roux A, Ghigo J-M (2008) Escherichia coli biofilms. Curr Top Microbiol Immunol 322:249–289Google Scholar
  14. Bennett BD, Kimball EH, Gao M, Osterhout R, Van Dien SJ, Rabinowitz JD (2009) Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nat Chem Biol 5:593–599Google Scholar
  15. Biggs MB, Papin JA (2013) Novel multiscale modeling tool applied to Pseudomonas aeruginosa biofilm formation. PloS One 8:e78011Google Scholar
  16. Booth SC, Workentine ML, Wen J, Shaykhutdinov R, Vogel HJ, Ceri H, Turner RJ, Weljie AM (2011) Differences in metabolism between the biofilm and planktonic response to metal stress. J Proteome Res 10:3190–3199Google Scholar
  17. Brown MR, Allison DG, Gilbert P (1988) Resistance of bacterial biofilms to antibiotics: a growth-rate related effect? J Antimicrob Chemother 22:777–780Google Scholar
  18. Busch A, Waksman G (2012) Chaperone-usher pathways: diversity and pilus assembly mechanism. Philos Trans R Soc Lond B Biol Sci 367:1112–1122Google Scholar
  19. Busch A, Phan G, Waksman G (2015) Molecular mechanism of bacterial type 1 and P pili assembly. Philos Trans R Soc Lond Math Phys Eng Sci 373:20130153Google Scholar
  20. Chang A, Schomburg I, Placzek S, Jeske L, Ulbrich M, Xiao M, Sensen CW, Schomburg D (2015) BRENDA in 2015: exciting developments in its 25th year of existence. Nucleic Acids Res 43:D439–D446. CrossRefGoogle Scholar
  21. Chopp DL, Kirisits MJ, Moran B, Parsek MR (2002) A mathematical model of quorum sensing in a growing bacterial biofilm. J Ind Microbiol Biotechnol 29:339–346Google Scholar
  22. Chu W, Zere TR, Weber MM, Wood TK, Whiteley M, Hidalgo-Romano B, Valenzuela E, McLean RJ (2012) Indole production promotes Escherichia coli mixed-culture growth with Pseudomonas aeruginosa by inhibiting quorum signaling. Appl Environ Microbiol 78:411–419Google Scholar
  23. Clark DP (1989) The fermentation pathways of Escherichia coli. FEMS Microbiol Rev 5:223–234Google Scholar
  24. Clegg S, Hughes KT (2002) FimZ is a molecular link between sticking and swimming in Salmonella enterica serovar Typhimurium. J Bacteriol 184:1209–1213Google Scholar
  25. Conrad JC (2012) Physics of bacterial near-surface motility using flagella and type IV pili: implications for biofilm formation. Res Microbiol 163:619–629Google Scholar
  26. Conrad JC, Gibiansky ML, Jin F, Gordon VD, Motto DA, Mathewson MA, Stopka WG, Zelasko DC, Shrout JD, Wong GCL (2011) Flagella and pili-mediated near-surface single-cell motility mechanisms in P. aeruginosa. Biophys J 100:1608–1616Google Scholar
  27. Costerton JW, Stewart PS, Greenberg EP (1999) Bacterial biofilms: a common cause of persistent infections. Science 284:1318–1322Google Scholar
  28. Costerton JW, Montanaro L, Arciola CR (2005) Biofilm in implant infections: its production and regulation. Int J Artif Organs 28:1062–1068Google Scholar
  29. Danese PN, Pratt LA, Kolter R (2000) Exopolysaccharide production is required for development of Escherichia coli K-12 biofilm architecture. J Bacteriol 182:3593–3596Google Scholar
  30. Danø S, Madsen MF, Schmidt H, Cedersund G (2006) Reduction of a biochemical model with preservation of its basic dynamic properties. Febs J 273:4862–4877Google Scholar
  31. Davies DG, Parsek MR, Pearson JP, Iglewski BH, Costerton Jt, Greenberg EP (1998) The involvement of cell-to-cell signals in the development of a bacterial biofilm. Science 280:295–298Google Scholar
  32. De Kievit TR, Gillis R, Marx S, Brown C, Iglewski BH (2001) Quorum-sensing genes in Pseudomonas aeruginosa biofilms: their role and expression patterns. Appl Environ Microbiol 67:1865–1873Google Scholar
  33. DeLisa MP, Wu C-F, Wang L, Valdes JJ, Bentley WE (2001) DNA microarray-based identification of genes controlled by autoinducer 2-stimulated quorum sensing in Escherichia coli. J Bacteriol 183:5239–5247Google Scholar
  34. Doke J (2005) Grabit. m, The MathWorks MatLab Central Website, (March 17, 2005)Google Scholar
  35. Domka J, Lee J, Bansal T, Wood TK (2007) Temporal gene-expression in Escherichia coli K-12 biofilms. Environ Microbiol 9:332–346Google Scholar
  36. Donlan RM (2001) Biofilms and device-associated infections. Emerg Infect Dis 7:277Google Scholar
  37. Duddu R, Chopp DL, Moran B (2009) A two-dimensional continuum model of biofilm growth incorporating fluid flow and shear stress based detachment. Biotechnol Bioeng 103:92–104Google Scholar
  38. Esser DS, Leveau JH, Meyer KM (2015) Modeling microbial growth and dynamics. Appl Microbiol Biotechnol 99:8831–8846Google Scholar
  39. Feist AM, Henry CS, Reed JL, Krummenacker M, Joyce AR, Karp PD, Broadbelt LJ, Hatzimanikatis V, Palsson BØ (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information. Mol Syst Biol 3:121Google Scholar
  40. Fischer E, Zamboni N, Sauer U (2004) High-throughput metabolic flux analysis based on gas chromatography-mass spectrometry derived 13 C constraints. Anal Biochem 325:308–316Google Scholar
  41. Fitzgerald DM, Bonocora RP, Wade JT (2014) Comprehensive mapping of the Escherichia coli flagellar regulatory network. PLoS Genet 10:e1004649Google Scholar
  42. Flemming H-C (2002) Biofouling in water systems-cases, causes and countermeasures. Appl Microbiol Biotechnol 59:629–640Google Scholar
  43. Flemming H-C, Wingender J (2010) The biofilm matrix. Nat Rev Microbiol 8:623–633Google Scholar
  44. Fukuoka S, Kamishima H, Sode K, Karube I (1989) Extracellular lipopolysaccharide production by Erwinia carotovora. J Ferment Bioeng 68:320–324Google Scholar
  45. Funahashi A, Morohashi M, Kitano H, Tanimura N (2003) Cell designer: a process diagram editor for gene-regulatory and biochemical networks. Biosilico 1:159–162Google Scholar
  46. Funahashi A, Matsuoka Y, Jouraku A, Morohashi M, Kikuchi N, Kitano H (2008) Cell designer 3.5: a versatile modeling tool for biochemical networks. IEEE Proc 96:1254–1265Google Scholar
  47. Fuqua C, Parsek MR, Greenberg EP (2001) Regulation of gene expression by cell-to-cell communication: acyl-homoserine lactone quorum sensing. Annu Rev Genet 35:439–468Google Scholar
  48. Fux CA, Costerton JW, Stewart PS, Stoodley P (2005) Survival strategies of infectious biofilms. Trends Microbiol 13:34–40Google Scholar
  49. Gally DL, Rucker TJ, Blomfield IC (1994) The leucine-responsive regulatory protein binds to the fim switch to control phase variation of type 1 fimbrial expression in Escherichia coli K-12. J Bacteriol 176:5665–5672Google Scholar
  50. Genevaux P, Bauda P, DuBow MS, Oudega B (1999) Identification of Tn10 insertions in the rfaG, rfaP, and galU genes involved in lipopolysaccharide core biosynthesis that affect Escherichia coli adhesion. Arch Microbiol 172:1–8Google Scholar
  51. Gillis RJ, Iglewski BH (2004) Azithromycin retards Pseudomonas aeruginosa biofilm formation. J Clin Microbiol 42:5842–5845Google Scholar
  52. Gomez JA, Höffner K, Barton PI (2014) DFBAlab: a fast and reliable MATLAB code for dynamic flux balance analysis. BMC Bioinform 15:409Google Scholar
  53. Gorochowski TE, Matyjaszkiewicz A, Todd T, Oak N, Kowalska K, Reid S, Tsaneva-Atanasova KT, Savery NJ, Grierson CS, di Bernardo M (2012) BSim: an agent-based tool for modeling bacterial populations in systems and synthetic biology. PloS One 7:e42790Google Scholar
  54. Guide MU (1998) The mathworks. Inc Natick 5:333Google Scholar
  55. Guyer JE, Wheeler D, Warren JA (2009) FiPy: partial differential equations with python. Comput Sci Eng 11:6Google Scholar
  56. Hall-Stoodley L, Costerton JW, Stoodley P (2004) Bacterial biofilms: from the natural environment to infectious diseases. Nat Rev Microbiol 2:95–108Google Scholar
  57. Hammer BK, Bassler BL (2003) Quorum sensing controls biofilm formation in vibrio cholerae. Mol Microbiol 50:101–104Google Scholar
  58. Hardie KR, Heurlier K (2008) Establishing bacterial communities by’word of mouth’: LuxS and autoinducer 2 in biofilm development. Nat Rev Microbiol 6:635–643Google Scholar
  59. Herzberg M, Kaye IK, Peti W, Wood TK (2006) YdgG (TqsA) controls biofilm formation in Escherichia coli K-12 through autoinducer 2 transport. J Bacteriol 188:587–598Google Scholar
  60. Heydorn A, Nielsen AT, Hentzer M, Sternberg C, Givskov M, Ersbøll M, Molin S (2000) Quantification of biofilm structures by the novel computer program COMSTAT. Microbiology 146:2395–2407Google Scholar
  61. Hooshangi S, Bentley WE (2011) LsrR quorum sensing “switch” is revealed by a bottom-up approach. PLoS Comput Biol 7:e1002172Google Scholar
  62. Ingledew WJ, Poole RK (1984) The respiratory chains of Escherichia coli. Microbiol Rev 48:222Google Scholar
  63. Itoh Y, Rice JD, Goller C, Pannuri A, Taylor J, Meisner J, Beveridge TJ, Preston JF, Romeo T (2008) Roles of pgaABCD genes in synthesis, modification, and export of the Escherichia coli biofilm adhesin poly-\(\beta \)-1, 6-N-acetyl-D-glucosamine. J Bacteriol 190:3670–3680Google Scholar
  64. Izano EA, Amarante MA, Kher WB, Kaplan JB (2008) Differential roles of Poly-N-Acetylglucosamine surface polysaccharide and extracellular DNA in Staphylococcus aureus and Staphylococcus epidermidis biofilms. Appl Environ Microbiol 74:470–476Google Scholar
  65. Jayaraman A, Wood TK (2008) Bacterial quorum sensing: signals, circuits, and implications for biofilms and disease. Annu Rev Biomed Eng 10:145–167Google Scholar
  66. Kadir TA, Mannan AA, Kierzek AM, McFadden J, Shimizu K (2010) Modeling and simulation of the main metabolism in Escherichia coli and its several single-gene knockout mutants with experimental verification. Microb Cell Fact 9:88Google Scholar
  67. Kanehisa M, Goto S (2000) KEGG: kyoto encyclopedia of genes and genomes. Nucleic Acids Res 28:27–30Google Scholar
  68. Kanehisa M, Goto S, Sato Y, Kawashima M, Furumichi M, Tanabe M (2014) Data, information, knowledge and principle: back to metabolism in KEGG. Nucleic Acids Res 42:D199–D205Google Scholar
  69. Keseler IM, Mackie A, Peralta-Gil M, Santos-Zavaleta A, Gama-Castro S, Bonavides-Martínez C, Fulcher C, Huerta AM, Kothari A, Krummenacker M et al (2013) EcoCyc: fusing model organism databases with systems biology. Nucleic Acids Res 41:D605–D612Google Scholar
  70. Klapper I, Dockery J (2010) Mathematical description of microbial biofilms. SIAM Rev 52:221–265MathSciNetzbMATHGoogle Scholar
  71. Klipp E, Liebermeister W, Wierling C, Kowald A, Lehrach H, Herwig R (2013) Systems biology. Wiley, HobokenGoogle Scholar
  72. Kröger A, Geisler V, Lemma E, Theis F, Lenger R (1992) Bacterial fumarate respiration. Arch Microbiol 158:311–314Google Scholar
  73. Lardon LA, Merkey BV, Martins S, Dotsch A, Picioreanu C, Kreft J-U, Smets BF (2011) iDynoMiCS: next-generation individual-based modelling of biofilms. Env Microbiol 13:2416–34Google Scholar
  74. Lee J, Jayaraman A, Wood TK (2007) Indole is an inter-species biofilm signal mediated by SdiA. BMC Microbiol 7:1Google Scholar
  75. Levskaya A, Chevalier AA, Tabor JJ, Simpson ZB, Lavery LA, Levy M, Davidson EA, Scouras A, Ellington AD, Marcotte EM (2005) Synthetic biology: engineering Escherichia coli to see light. Nature 438:441–442Google Scholar
  76. Lobry JR, Flandrois JP, Carret G, Pave A (1992) Monod’s bacterial growth model revisited. Bull Math Biol 54:117–122zbMATHGoogle Scholar
  77. Logan BE (2009) Exoelectrogenic bacteria that power microbial fuel cells. Nat Rev Microbiol 7:375–381Google Scholar
  78. Mahadevan R, Edwards JS, Doyle FJ (2002) Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J 83:1331–1340Google Scholar
  79. Majors PD, McLean JS, Pinchuk GE, Fredrickson JK, Gorby YA, Minard KR, Wind RA (2005) NMR methods for in situ biofilm metabolism studies. J Microbiol Methods 62:337–344Google Scholar
  80. Marino S, Hogue IB, Ray CJ, Kirschner DE (2008) A methodology for performing global uncertainty and sensitivity analysis in systems biology. J Theor Biol 254:178–196MathSciNetGoogle Scholar
  81. May EE, Sershen CL (2016) Oxygen availability and metabolic dynamics during Mycobacterium tuberculosis latency. IEEE Trans Biomed Eng 63:2036–2046Google Scholar
  82. Merritt JH, Kadouri DE, O’Toole GA (2005) Growing and analyzing static biofilms. Curr Protoc Microbiol 22:1B–1Google Scholar
  83. Millard P, Smallbone K, Mendes P (2017) Metabolic regulation is sufficient for global and robust coordination of glucose uptake, catabolism, energy production and growth in Escherichia coli. PLOS Comput Biol 13(2):e1005396Google Scholar
  84. Miller MB, Bassler BL (2001) Quorum sensing in bacteria. Annu Rev Microbiol 55:165–199Google Scholar
  85. Milo R, Jorgensen P, Moran U, Weber G, Springer M (2009) BioNumbershe database of key numbers in molecular and cell biology. Nucleic Acids Res 38:D750753Google Scholar
  86. Monds RD, O’Toole GA (2009) The developmental model of microbial biofilms: ten years of a paradigm up for review. Trends Microbiol 17:73–87Google Scholar
  87. Monon J (2012) The growth of bacterial cultures. Sel Pap Mol Biol Jacques Monod 11:139Google Scholar
  88. Moreira GC, Palmer K, Whiteley M, Sircili MP, Trabulsi LR, Castro AFP, Sperandio V (2006) Bundle-forming pili and EspA Are involved in biofilm formation by enteropathogenic Escherichia coli. J Bacteriol 188:3952–3961Google Scholar
  89. Neidhardt FC, Ingraham JL, Low KB, Magasanik B, Schaechter M, Umbarger HE eds (1987) Escherichia coli and Salmonella typhimurium. Cellular and molecular biology. Volumes I and II. American Society for Microbiology. Washington, DCGoogle Scholar
  90. Nguyen T, Roddick FA, Fan L (2012) Biofouling of water treatment membranes: a review of the underlying causes, monitoring techniques and control measures. Membranes 2:804–840Google Scholar
  91. Nikerel IE, van Winden WA, Verheijen PJT, Heijnen JJ (2009) Model reduction and a priori kinetic parameter identifiability analysis using metabolome time series for metabolic reaction networks with linlog kinetics. Metab Eng 11:20–30Google Scholar
  92. Okuda S, Freinkman E, Kahne D (2012) Cytoplasmic ATP hydrolysis powers transport of lipopolysaccharide across the periplasm in E. coli. Science 338:1214–1217Google Scholar
  93. Olsen I (2015) Biofilm-specific antibiotic tolerance and resistance. Eur J Clin Microbiol Infect Dis 34:877–886Google Scholar
  94. O’Toole G, Kaplan HB, Kolter R (2000) Biofilm formation as microbial development. Annu Rev Microbiol 54:49–79Google Scholar
  95. Pabst B, Pitts B, Lauchnor E, Stewart PS (2016) Gel-Entrapped Staphylococcus aureus bacteria as models of biofilm infection exhibit growth in dense aggregates, oxygen limitation, antibiotic tolerance, and heterogeneous gene expression. Antimicrob Agents Chemother 60:6294–6301Google Scholar
  96. Paju S, Scannapieco FA (2007) Oral biofilms, periodontitis, and pulmonary infections. Oral Dis 13:508–512Google Scholar
  97. Pammi M, Liang R, Hicks J, Mistretta T-A, Versalovic J (2013) Biofilm extracellular DNA enhances mixed species biofilms of Staphylococcus epidermidis and Candida albicans. BMC Microbiol 13:257Google Scholar
  98. Perkins TK, Johnston OC (1963) A review of diffusion and dispersion in porous media. Soc Pet Eng J 3:70–84Google Scholar
  99. Pizarro G, Griffeath D, Noguera DR (2001) Quantitative cellular automaton model for biofilms. J Environ Eng 127:782–789Google Scholar
  100. Poole RK, Ingledew WJ (1987) Pathways of electrons to oxygen. Escherichia coli and Salmonella Typhimurium: cellular and molecular biology. American Society for Microbiology, Washington, DC, 170-200Google Scholar
  101. Pratt LA, Kolter R (1998) Genetic analysis of Escherichia coli biofilm formation: roles of flagella, motility, chemotaxis and type I pili. Mol Microbiol 30:285–293Google Scholar
  102. Pruss BM, Besemann C, Denton A, Wolfe AJ (2006) A complex transcription network controls the early stages of biofilm development by Escherichia coli. J Bacteriol 188:3731Google Scholar
  103. Raetz C, Reynolds CM, Trent MS, Bishop R (2007) Lipid a modification systems in gram-negative bacteria. Annu Rev Biochem 76:295–329Google Scholar
  104. Ray J, Kirschner DE (2009) Synergy between individual TNF-dependent function determines granuloma performance for controlling Mycobacterium tuberculosis infection. J Immunol 182:3706–3717Google Scholar
  105. Reisner A, Haagensen JAJ, Schembri MA, Zechner EL, Molin S (2003) Development and maturation of Escherichia coli K12 biofilms. Mol Microbiol 48:933–946Google Scholar
  106. Römling U, Galperin MY, Gomelsky M (2013) Cyclic di-GMP: the first 25 years of a universal bacterial second messenger. Microbiol Mol Biol Rev 77:1–52Google Scholar
  107. Salim T, Sershen CL, May EE (2016) Investigating the role of TNF-\(\alpha \) and IFN-\(\gamma \) Activation on the dynamics of iNOS gene expression in LPS stimulated macrophages. PloS One 11:e0153289Google Scholar
  108. Sander R (1999) Compilation of Henry’s law constants for inorganic and organic species of potential importance in environmental chemistry. Max-Planck Institute of Chemistry, Air Chemistry Department Mainz, GermanyGoogle Scholar
  109. Sauro HM (2012) Enzyme kinetics for systems biology. Ambrosius Publishing and Future Skill SoftwareGoogle Scholar
  110. Schellenberger J, Que R, Fleming RM, Thiele I, Orth JD, Feist AM, Zielinski DC, Bordbar A, Lewis NE, Rahmanian S et al (2011) Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2. 0. Nat Protoc 6:1290–1307Google Scholar
  111. Schembri MA, Kjærgaard K, Klemm P (2003) Global gene expression in Escherichia coli biofilms. Mol Microbiol 48:253–267Google Scholar
  112. Schmidt H, Madsen MF, Danø S, Cedersund G (2008) Complexity reduction of biochemical rate expressions. Bioinformatics 24:848–854Google Scholar
  113. Schultz MP (2007) Effects of coating roughness and biofouling on ship resistance and powering. Biofouling 23:331–341Google Scholar
  114. Schultz MP, Swain GW (2000) The influence of biofilms on skin friction drag. Biofouling 15:129–139Google Scholar
  115. Schultz MP, Bendick JA, Holm ER, Hertel WM (2011) Economic impact of biofouling on a naval surface ship. Biofouling 27:87–98Google Scholar
  116. Segovia-Juarez JL, Ganguli S, Kirschner DE (2004) Identifying control mechanisms of granuloma formation during M. tuberculosis infection using an agent-based model. J Theor Biol 231:357–376MathSciNetGoogle Scholar
  117. Senior AE (1988) ATP synthesis by oxidative phosphorylation. Physiol Rev 68:177–231Google Scholar
  118. Serra DO, Richter AM, Klauck G, Mika F, Hengge R (2013) Microanatomy at cellular resolution and spatial order of physiological differentiation in a bacterial biofilm. mBio 4:e00103-13Google Scholar
  119. Sershen CL, Plimpton SJ, May EE (2016) Oxygen modulates the effectiveness of granuloma mediated host response to Mycobacterium tuberculosis: a multiscale computational biology approach. Front Cell Infect Microbiol 6:6Google Scholar
  120. Sheppard M (2012) AllFitDist [Fit all valid parametric probability distributions to data]Google Scholar
  121. Singh VK, Ghosh I (2006) Kinetic modeling of tricarboxylic acid cycle and glyoxylate bypass in Mycobacterium tuberculosis, and its application to assessment of drug targets. Theor Biol Med Model 3:27–27Google Scholar
  122. Singh PK, Schaefer AL, Parsek MR, Moninger TO, Welsh MJ, Greenberg EP (2000) Quorum-sensing signals indicate that cystic fibrosis lungs are infected with bacterial biofilms. Nature. 407:762–764Google Scholar
  123. Singh R, Paul D, Jain RK (2006) Biofilms: implications in bioremediation. Trends Microbiol 14:389–397Google Scholar
  124. Socransky SS, Haffajee AD (2002) Dental biofilms: difficult therapeutic targets. Periodontol 2000 28:12–55Google Scholar
  125. Spoering AL, Lewis K (2001) Biofilms and planktonic cells of Pseudomonas aeruginosa have similar resistance to killing by antimicrobials. J Bacteriol 183:6746–6751Google Scholar
  126. Stewart PS (2002) Mechanisms of antibiotic resistance in bacterial biofilms. Int J Med Microbiol 292:107–113Google Scholar
  127. Stewart PS (2003) Diffusion in Biofilms. J Bacteriol 185:1485Google Scholar
  128. Stoodley P, Sauer K, Davies DG, Costerton JW (2002) Biofilms as complex differentiated communities. Annu Rev Microbiol 56:187–209Google Scholar
  129. Sun X, Medvedovic M (2016) Model reduction and parameter estimation of non-linear dynamical biochemical reaction networks. IET Syst Biol 10:10–16Google Scholar
  130. Trautner BW, Darouiche RO (2004) Role of biofilm in catheter-associated urinary tract infection. Am J Infect Control 32:177–183Google Scholar
  131. Unden G, Bongaerts J (1997) Alternative respiratory pathways of Escherichia coli: energetics and transcriptional regulation in response to electron acceptors. Biochim Biophys Acta BBA-Bioenerg 1320:217–234Google Scholar
  132. Van Houdt R, Michiels CW (2005) Role of bacterial cell surface structures in Escherichia coli biofilm formation. Res Microbiol 156:626–633Google Scholar
  133. Vilain S, Pretorius JM, Theron J, Brözel VS (2009) DNA as an adhesin: bacillus cereus requires extracellular DNA to form biofilms. Appl Environ Microbiol 75:2861–2868Google Scholar
  134. Walters MC, Roe F, Bugnicourt A, Franklin MJ, Stewart PS (2003) Contributions of Antibiotic penetration, oxygen limitation, and low metabolic activity to tolerance of Pseudomonas aeruginosa Biofilms to Ciprofloxacin and Tobramycin. Antimicrob Agents Chemother 47:317–323Google Scholar
  135. Wang X, Preston JF, Romeo T (2004) The pgaABCD locus of Escherichia coli promotes the synthesis of a polysaccharide adhesin required for biofilm formation. J Bacteriol 186:2724–2734Google Scholar
  136. Wang X, Dubey AK, Suzuki K, Baker CS, Babitzke P, Romeo T (2005) CsrA post-transcriptionally represses pgaABCD, responsible for synthesis of a biofilm polysaccharide adhesin of Escherichia coli. Mol Microbiol 56:1648–1663Google Scholar
  137. Waters CM, Bassler BL (2005) Quorum sensing: cell-to-cell communication in bacteria. Annu Rev Cell Dev Biol 21:319–346Google Scholar
  138. Watnick P, Kolter R (2000) Biofilm, city of microbes. J Bacteriol 182:2675–2679Google Scholar
  139. Whitchurch CB, Tolker-Nielsen T, Ragas PC, Mattick JS (2002) Extracellular DNA required for bacterial biofilm formation. Science. 295:1487–1487Google Scholar
  140. Wood TK (2009) Insights on Escherichia coli biofilm formation and inhibition from whole-transcriptome profiling. Environ Microbiol 11:1–15Google Scholar
  141. Wood TK, Barrios AFG, Herzberg M, Lee J (2006) Motility influences biofilm architecture in Escherichia coli. Appl Microbiol Biotechnol 72:361–367Google Scholar
  142. Wood TK, Bentley WE (2007) Signaling in Escherichia coli biofilms. In: Kjelleberg S, Givskov M (eds) The Biofilm Mode of Life: Mechanisms and Adaptations. Horizon Bioscience, UkGoogle Scholar
  143. Xavier KB, Bassler BL (2003) LuxS quorum sensing: more than just a numbers game. Curr Opin Microbiol 6:191–197Google Scholar
  144. Xiong Y, Liu Y (2010) Involvement of ATP and autoinducer-2 in aerobic granulation. Biotechnol Bioeng 105:51–58Google Scholar
  145. Yarwood JM, Bartels DJ, Volper EM, Greenberg EP (2004) Quorum sensing in Staphylococcus aureus biofilms. J Bacteriol 186:1838–1850Google Scholar
  146. Zhang B, Powers R (2012) Analysis of bacterial biofilms using NMR-based metabolomics. Future Med Chem 4:1273–1306Google Scholar
  147. Zhu J, Pei D (2008) A LuxP-based fluorescent sensor for bacterial autoinducer II. ACS Chem Biol 3:110–119Google Scholar
  148. Zhu Z, Wang H, Shang Q, Jiang Y, Cao Y, Chai Y (2012) Time course analysis of Candida albicans metabolites during biofilm development. J Proteome Res 12:2375–2385Google Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringUniversity of HoustonHoustonUSA

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