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.
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
Anguige K, King J, Ward J, Williams P (2004) Mathematical modelling of therapies targeted at bacterial quorum sensing. Math Biosci 192:39–83
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
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
Ben-Jacob E, Cohen I, Levine H (2000) Cooperative self-organization of microorganisms. Adv Phys 49:395–554
Berg HC (1993) Random walks in biology. Princeton University Press, Princeton
Boles BR, Thoendel M, Singh PK (2004) Self-generated diversity produces insurance effects in biofilm communities. Proc Natl Acad Sci USA 101:16630–16635
Branda SS, Vik Å, Friedman L, Kolter R (2005) Biofilms: the matrix revisited. Trends Microbiol 13:20–26
Brenner K, Arnold FH (2011) Self-organization, layered structure, and aggregation enhance persistence of a synthetic biofilm consortium. PLoS One 6:e16791
Budrene E, Berg H (1995) Dynamics of formation of symmetrical patterns by chemotactic bacteria. Nature 376:49
Budrene EO, Berg HC et al (1991) Complex patterns formed by motile cells of Escherichia coli. Nature 349:630–633
Carpentier B, Cerf O (1993) Biofilms and their consequences, with particular reference to hygiene in the food industry. J Appl Bacteriol 75:499–511
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
Characklis WG, Marshall KC (1990) Biofilms. Wiley, London
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
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
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
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
Cogan N (2006) Effects of persister formation on bacterial response to dosing. J Theor Biol 238:694–703
Cogan N (2007) Incorporating toxin hypothesis into a mathematical model of persister formation and dynamics. J Theor Biol 248:340–349
Cogan N (2013) Concepts in disinfection of bacterial populations. Math Biosci 245:111–125
Cogan N, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21:147–166
Cogan N, Keener JP (2005) Channel formation in gels. SIAM J Appl Math 65:1839–1854
Cogan N, Wolgemuth CW (2005) Pattern formation by bacteria-driven flow. Biophys J 88:2525–2529
Cogan N, Guy RD (2010) Multiphase flow models of biogels from crawling cells to bacterial biofilms. HFSP J 4:11–25
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
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
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
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
Davis M, Purcell A, Thomson S et al (1980) Isolation media for the Pierce’s disease bacterium. Phytopathology 70:425–429
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
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
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
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
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
Donlan RM, Costerton JW (2002) Biofilms: survival mechanisms of clinically relevant microorganisms. Clin Microbiol Rev 15:167–193
Donlan RM et al (2002) Biofilms: microbial life on surfaces. Emerg Infect Dis 8:881–890
Dunne WM (2002) Bacterial adhesion: seen any good biofilms lately? Clin Microbiol Rev 15:155–166
Flemming HC, Wingender J (2010) The biofilm matrix. Nat Rev Microbiol 8:623–633
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
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
Hopkins D (1989) Xylella fastidiosa: xylem-limited bacterial pathogen of plants. Annu Rev Phytopathol 27:271–290
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
Hopkins DL, Mollenhauer HH (1973) Rickettsia-like bacterium associated with Pierce’s disease of grapes. Science 179:298–300
Hopkins D, Purcell A (2002) Xylella fastidiosa: cause of Pierce’s disease of grapevine and other emergent diseases. Plant Dis 86:1056–1066
Klapper I (2012) Productivity and equilibrium in simple biofilm models. Bull Math Biol 74:2917–2934
Klapper I, Dockery J (2006) Role of cohesion in the material description of biofilms. Phys Rev E 74:031902
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
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
LeVeque RJ (1996) High-resolution conservative algorithms for advection in incompressible flow. SIAM J Numer Anal 33:627–665
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
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
Murray JD (2002) Mathematical biology: I. An introduction, vol 17. Springer, Berlin
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
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
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
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
Preziosi L, Tosin A (2009) Multiphase modelling of tumour growth and extracellular matrix interaction: mathematical tools and applications. J Math Biol 58:625–656
Purcell A (1974) Spatial patterns of Pierce’s disease in the napa valley. Am J Enol Viticult 25:162–167
Ramage G, Martínez JP, López-Ribot JL (2006) Candida biofilms on implanted biomaterials: a clinically significant problem. FEMS Yeast Res 6:979–986
Rinaudi LV, Giordano W (2010) An integrated view of biofilm formation in rhizobia. FEMS Microbiol Lett 304:1–11
Stoodley P, Sauer K, Davies D, Costerton J (2002) Biofilms as complex differentiated communities. Annu Rev Microbiol 56:187–209
Trottenberg U, Oosterlee CW, Schuller A (2000) Multigrid. Academic Press, London
Welch R, Kaiser D (2001) Cell behavior in traveling wave patterns of myxobacteria. Proc Natl Acad Sci 98:14907–14912
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
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
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
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
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
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
Corresponding author
Rights and permissions
About this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11538-015-0115-3