Skip to main content
Log in

A Two-Dimensional Multiphase Model of Biofilm Formation in Microfluidic Chambers

  • Original Article
  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

The bacterial pathogen Xylella fastidiosa is the causal agent of many pathological conditions of economically important agricultural crops. There is no known cure for X. fastidiosa diseases, and management of the problem is based solely in controlling the population of insect vectors, which is somewhat effective. The bacterium causes disease by forming biofilms inside the vascular system of the plant, a process that is poorly understood. In microfluidic chambers, used as artificial xylem vessels, this bacterium has been observed to reproducibly cluster into a distinct, regular pattern of aggregates, spatially separated by channels of non-biofilm components. We develop a multiphase model in two dimensions, which recapitulates this spatial patterning, suggesting that bacterial growth and attachment/detachment processes are strongly influential modulators of these patterns. This indicates plausible strategies, such as the addition of metals and chelators, for mitigating the severity of diseases induced by this bacterial pathogen.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9

Similar content being viewed by others

References

  • Andersen PC, Brodbeck BV, Oden S, Shriner A, Leite B (2007) Influence of xylem fluid chemistry on planktonic growth, biofilm formation and aggregation of Xylella fastidiosa. FEMS Microbiol Lett 274:210–217

    Article  Google Scholar 

  • Anguige K, King J, Ward J, Williams P (2004) Mathematical modelling of therapies targeted at bacterial quorum sensing. Math Biosci 192:39–83

    Article  MathSciNet  MATH  Google Scholar 

  • Anguige K, King J, Ward J (2006) A multi-phase mathematical model of quorum sensing in a maturing Pseudomonas aeruginosa biofilm. Math Biosci 203:240–276

    Article  MathSciNet  MATH  Google Scholar 

  • Bellomo N, de Angelis E, Preziosi L (2003) Multiscale modeling and mathematical problems related to tumor evolution and medical therapy. J Theor Med 5:111–136

    Article  MATH  Google Scholar 

  • Ben-Jacob E, Cohen I, Levine H (2000) Cooperative self-organization of microorganisms. Adv Phys 49:395–554

    Article  Google Scholar 

  • Berg HC (1993) Random walks in biology. Princeton University Press, Princeton

    Google Scholar 

  • Boles BR, Thoendel M, Singh PK (2004) Self-generated diversity produces insurance effects in biofilm communities. Proc Natl Acad Sci USA 101:16630–16635

    Article  Google Scholar 

  • Branda SS, Vik Å, Friedman L, Kolter R (2005) Biofilms: the matrix revisited. Trends Microbiol 13:20–26

    Article  Google Scholar 

  • Brenner K, Arnold FH (2011) Self-organization, layered structure, and aggregation enhance persistence of a synthetic biofilm consortium. PLoS One 6:e16791

    Article  Google Scholar 

  • Budrene E, Berg H (1995) Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature 376:49

    Article  Google Scholar 

  • Budrene EO, Berg HC et al (1991) Complex patterns formed by motile cells of Escherichia coli. Nature 349:630–633

    Article  Google Scholar 

  • Carpentier B, Cerf O (1993) Biofilms and their consequences, with particular reference to hygiene in the food industry. J Appl Bacteriol 75:499–511

    Article  Google Scholar 

  • Cates M, Marenduzzo D, Pagonabarraga I, Tailleur J (2010) Arrested phase separation in reproducing bacteria creates a generic route to pattern formation. Proc Natl Acad Sci 107:11715–11720

    Article  Google Scholar 

  • Characklis WG, Marshall KC (1990) Biofilms. Wiley, London

    Google Scholar 

  • Chatterjee S, Almeida RPP, Lindow S (2008) Living in two worlds: the plant and insect lifestyles of Xylella fastidiosa. Annu Rev Phytopathol 46:243–271

    Article  Google Scholar 

  • Cheng DW, Lin H, Walker MA, Stenger DC, Civerolo EL (2009) Effects of grape xylem sap and cell wall constituents on in vitro growth, biofilm formation and cellular aggregation of Xylella fastidiosa. Eur J Plant Pathol 125:213–222

    Article  Google Scholar 

  • Choat B, Gambetta GA, Wada H, Shackel KA, Matthews MA (2009) The effects of Pierce’s disease on leaf and petiole hydraulic conductance in Vitis vinifera cv. chardonnay. Physiol Plant 136:384–394

    Article  Google Scholar 

  • Cobine PA, Cruz LF, Navarrete F, Duncan D, Tygart M, De La Fuente L (2013) Xylella fastidiosa differentially accumulates mineral elements in biofilm and planktonic cells. PloS ONE 8:e54936

    Article  Google Scholar 

  • Cogan N (2006) Effects of persister formation on bacterial response to dosing. J Theor Biol 238:694–703

    Article  MathSciNet  Google Scholar 

  • Cogan N (2007) Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics. J Theor Biol 248:340–349

    Article  MathSciNet  Google Scholar 

  • Cogan N (2013) Concepts in disinfection of bacterial populations. Math Biosci 245:111–125

    Article  MathSciNet  MATH  Google Scholar 

  • Cogan N, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21:147–166

    Article  MATH  Google Scholar 

  • Cogan N, Keener JP (2005) Channel formation in gels. SIAM J Appl Math 65:1839–1854

    Article  MathSciNet  MATH  Google Scholar 

  • Cogan N, Wolgemuth CW (2005) Pattern formation by bacteria-driven flow. Biophys J 88:2525–2529

    Article  Google Scholar 

  • Cogan N, Guy RD (2010) Multiphase flow models of biogels from crawling cells to bacterial biofilms. HFSP J 4:11–25

    Article  Google Scholar 

  • Cogan N, Donahue M, Whidden M, De La Fuente L (2013a) Pattern formation exhibited by biofilm formation within microfluidic chambers. Biophys J 104:1867–1874

    Article  Google Scholar 

  • Cogan N, Szomolay B, Dindos M (2013b) Effect of periodic disinfection on persisters in a one-dimensional biofilm model. Bull Math Biol 75:94–123

    Article  MathSciNet  MATH  Google Scholar 

  • Costerton JW, Cheng K, Geesey GG, Ladd TI, Nickel JC, Dasgupta M, Marrie TJ (1987) Bacterial biofilms in nature and disease. Annu Rev Microbiol 41:435–464

    Article  Google Scholar 

  • Cruz LF, Cobine PA, De La Fuente L (2012) Calcium increases Xylella fastidiosa surface attachment, biofilm formation, and twitching motility. Appl Environ Microbiol 78:1321–1331

    Article  Google Scholar 

  • Davis M, Purcell A, Thomson S et al (1980) Isolation media for the Pierce’s disease bacterium. Phytopathology 70:425–429

    Article  Google Scholar 

  • 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 67:1865–1873

    Article  Google Scholar 

  • De La Fuente L, Montanes E, Meng Y, Li Y, Burr TJ, Hoch H, Wu M (2007) Assessing adhesion forces of type I and type IV pili of Xylella fastidiosa bacteria by use of a microfluidic flow chamber. Appl Environ Microbiol 73:2690–2696

    Article  Google Scholar 

  • De La Fuente L, Burr TJ, Hoch HC (2008) Autoaggregation of Xylella fastidiosa cells is influenced by type I and type IV pili. Appl Environ Microbiol 74:5579–5582

    Article  Google Scholar 

  • De La Fuente L, Parker JK, Oliver JE, Granger S, Brannen PM, van Santen E, Cobine PA (2013) The bacterial pathogen Xylella fastidiosa affects the leaf ionome of plant hosts during infection. PLoS One 8(5):e62945. doi:10.1371/journal.pone.0062945

    Article  Google Scholar 

  • De Lima J, Miranda V, Hartung J, Brlansky R, Coutinho A, Roberto S, Carlos E (1998) Coffee leaf scorch bacterium: axenic culture, pathogenicity, and comparison with Xylella fastidiosa of citrus. Plant Dis 82:94–97

    Article  Google Scholar 

  • Donlan RM, Costerton JW (2002) Biofilms: survival mechanisms of clinically relevant microorganisms. Clin Microbiol Rev 15:167–193

    Article  Google Scholar 

  • Donlan RM et al (2002) Biofilms: microbial life on surfaces. Emerg Infect Dis 8:881–890

    Article  Google Scholar 

  • Dunne WM (2002) Bacterial adhesion: seen any good biofilms lately? Clin Microbiol Rev 15:155–166

    Article  MathSciNet  Google Scholar 

  • Flemming HC, Wingender J (2010) The biofilm matrix. Nat Rev Microbiol 8:623–633

    Google Scholar 

  • Gambetta G, Fei J, Rost T, Matthews M (2007) Leaf scorch symptoms are not correlated with bacterial populations during Pierce’s disease. J Exp Bot 58:4037–4046

    Article  Google Scholar 

  • Harman MW, Dunham-Ems SM, Caimano MJ, Belperron AA, Bockenstedt LK, Fu HC, Radolf JD, Wolgemuth CW (2012) The heterogeneous motility of the lyme disease spirochete in gelatin mimics dissemination through tissue. Proc Natl Acad Sci 109:3059–3064

    Article  Google Scholar 

  • Hopkins D (1989) Xylella fastidiosa: xylem-limited bacterial pathogen of plants. Annu Rev Phytopathol 27:271–290

    Article  Google Scholar 

  • Hopkins D (2005) Biological control of Pierce’s disease in the vineyard with strains of Xylella fastidiosa benign to grapevine. Plant Dis 89:1348–1352

    Article  Google Scholar 

  • Hopkins DL, Mollenhauer HH (1973) Rickettsia-like bacterium associated with Pierce’s disease of grapes. Science 179:298–300

    Article  Google Scholar 

  • Hopkins D, Purcell A (2002) Xylella fastidiosa: cause of Pierce’s disease of grapevine and other emergent diseases. Plant Dis 86:1056–1066

    Article  Google Scholar 

  • Klapper I (2012) Productivity and equilibrium in simple biofilm models. Bull Math Biol 74:2917–2934

    Article  MathSciNet  MATH  Google Scholar 

  • Klapper I, Dockery J (2006) Role of cohesion in the material description of biofilms. Phys Rev E 74:031902

    Article  MathSciNet  Google Scholar 

  • Kreft JU, Wimpenny JW (2001) Effect of eps on biofilm structure and function as revealed by an individual-based model of biofilm growth. Water Sci Technol 43:135–142

    Google Scholar 

  • Lambert G, Bergman A, Zhang Q, Bortz D, Austin R (2014) Physics of biofilms: the initial stages of biofilm formation and dynamics. New J Phys 16:045005

    Article  Google Scholar 

  • LeVeque RJ (1996) High-resolution conservative algorithms for advection in incompressible flow. SIAM J Numer Anal 33:627–665

    Article  MathSciNet  MATH  Google Scholar 

  • Machado I, Lopes SP, Sousa AM, Pereira MO (2012) Adaptive response of single and binary Pseudomonas aeruginosa and Escherichia coli biofilms to benzalkonium chloride. J Basic Microbiol 52:43–52

    Article  Google Scholar 

  • Meng Y, Li Y, Galvani CD, Hao G, Turner JN, Burr TJ, Hoch H (2005) Upstream migration of Xylella fastidiosa via pilus-driven twitching motility. J Bacteriol 187:5560–5567

    Article  Google Scholar 

  • Murray JD (2002) Mathematical biology: I. An introduction, vol 17. Springer, Berlin

    Google Scholar 

  • Navarrete F, De La Fuente L (2014) Response of Xylella fastidiosa to zinc: decreased culturability, increased exopolysaccharide production, and formation of resilient biofilms under flow conditions. Appl Environ Microbiol 80:1097–1107

    Article  Google Scholar 

  • Newman KL, Almeida RP, Purcell AH, Lindow SE (2003) Use of a green fluorescent strain for analysis of Xylella fastidiosa colonization of Vitis vinifera. Appl environ Microbiol 69:7319–7327

    Article  Google Scholar 

  • Oliver J, Sefick S, Parker J, Arnold T, Cobine P, De La Fuente L (2014) Ionome changes in Xylella fastidiosa-infected nicotiana tabacum correlate with virulence and discriminate between subspecies of bacterial isolates. Mol Plant Microbe Interact 27:1048–1058

    Article  Google Scholar 

  • Oliver J, Cobine P, de la Fuente L (2015) Xylella fastidiosa isolates from both subsp. multiplex and fastidiosa cause disease on southern highbush blueberry (Vaccinium sp.) under greenhouse conditions. Phytopathology 105:855–862

    Article  Google Scholar 

  • Preziosi L, Tosin A (2009) Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications. J Math Biol 58:625–656

    Article  MathSciNet  MATH  Google Scholar 

  • Purcell A (1974) Spatial patterns of Pierce’s disease in the napa valley. Am J Enol Viticult 25:162–167

    Google Scholar 

  • Ramage G, Martínez JP, López-Ribot JL (2006) Candida biofilms on implanted biomaterials: a clinically significant problem. FEMS Yeast Res 6:979–986

    Article  Google Scholar 

  • Rinaudi LV, Giordano W (2010) An integrated view of biofilm formation in rhizobia. FEMS Microbiol Lett 304:1–11

    Article  Google Scholar 

  • Stoodley P, Sauer K, Davies D, Costerton J (2002) Biofilms as complex differentiated communities. Annu Rev Microbiol 56:187–209

    Article  Google Scholar 

  • Trottenberg U, Oosterlee CW, Schuller A (2000) Multigrid. Academic Press, London

    Google Scholar 

  • Welch R, Kaiser D (2001) Cell behavior in traveling wave patterns of myxobacteria. Proc Natl Acad Sci 98:14907–14912

    Article  Google Scholar 

  • Wells JM, Raju BC, Hung HY, Weisburg WG, Mandelco-Paul L, Brenner DJ (1987) Xylella fastidiosa gen. nov., sp. nov: gram-negative, xylem-limited, fastidious plant bacteria related to xanthomonas spp. Int J Syst Bacteriol 37:136–143

    Article  Google Scholar 

  • Wimpenny JW, Colasanti R (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol 22:1–16

    Article  Google Scholar 

  • Wright GB, Guy RD, Fogelson AL (2008) An efficient and robust method for simulating two-phase gel dynamics. SIAM J Sci Comput 30:2535–2565

    Article  MathSciNet  MATH  Google Scholar 

  • Zaini PA, De La Fuente L, Hoch HC, Burr TJ (2009) Grapevine xylem sap enhances biofilm development by Xylella fastidiosa. FEMS Microbiol Lett 295:129–134

    Article  Google Scholar 

  • Zhang T, Cogan N, Wang Q (2008) Phase-field models for biofilms. II. 2-D numerical simulations of biofilm–flow interaction. Commun Comput Phys 4:72–101

    Google Scholar 

Download references

Acknowledgments

This work is supported by NSF Grant No. 1122378. MW is supported by an IRACDA Fellowship at the University of Michigan.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Mark Whidden.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Whidden, M., Cogan, N., Donahue, M. et al. A Two-Dimensional Multiphase Model of Biofilm Formation in Microfluidic Chambers. Bull Math Biol 77, 2161–2179 (2015). https://doi.org/10.1007/s11538-015-0115-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11538-015-0115-3

Keywords

Navigation