From a thin film model for passive suspensions towards the description of osmotic biofilm spreading

Sarah Trinschek; Karin John; Uwe Thiele; Sarah Trinschek; Karin John; Uwe Thiele

doi:10.3934/matersci.2016.3.1138

AIMS Materials Science

2016, Volume 3, Issue 3: 1138-1159. doi: 10.3934/matersci.2016.3.1138

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From a thin film model for passive suspensions towards the description of osmotic biofilm spreading

1.
Institut für Theoretische Physik, Westfälische Wilhelms-Universität Münster, Wilhelm-Klemm-Strasse 9, 48149 Münster, Germany
2.
Laboratoire Interdisciplinaire de Physique (LIPhy), CNRS / Université Grenoble-Alpes, 140 Rue de la Physique, 38402 Grenoble, France
3.
Center of Nonlinear Science (CeNoS), Westfälische Wilhelms-Universität Münster, Corrensstr. 2, 48149 Münster, Germany

Received: 23 May 2016 Accepted: 28 July 2016 Published: 09 August 2016

Biofilms are ubiquitous macro-colonies of bacteria that develop at various interfaces (solid- liquid, solid-gas or liquid-gas). The formation of biofilms starts with the attachment of individual bac- teria to an interface, where they proliferate and produce a slimy polymeric matrix - two processes that result in colony growth and spreading. Recent experiments on the growth of biofilms on agar substrates under air have shown that for certain bacterial strains, the production of the extracellular matrix and the resulting osmotic influx of nutrient-rich water from the agar into the biofilm are more crucial for the spreading behaviour of a biofilm than the motility of individual bacteria. We present a model which de- scribes the biofilm evolution and the advancing biofilm edge for this spreading mechanism. The model is based on a gradient dynamics formulation for thin films of biologically passive liquid mixtures and suspensions, supplemented by bioactive processes which play a decisive role in the osmotic spreading of biofilms. It explicitly includes the wetting properties of the biofilm on the agar substrate via a dis- joining pressure and can therefore give insight into the interplay between passive surface forces and bioactive growth processes.

Keywords:

Citation: Sarah Trinschek, Karin John, Uwe Thiele. From a thin film model for passive suspensions towards the description of osmotic biofilm spreading[J]. AIMS Materials Science, 2016, 3(3): 1138-1159. doi: 10.3934/matersci.2016.3.1138

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Abstract

References

[1]	Donlan RM (2012) Biofilms: Microbial life on surfaces. Emerg Infect Dis 8: 881–890.
[2]	Flemming H, Wingender J (2010) The biofilm matrix. Nat Rev Microbiol 8: 623–633. doi: 10.1038/nrmicro2415
[3]	Picioreanu C, Loosdrecht MCM (2003) Use of mathematical modelling to study biofilm development and morphology , In Biofilms in Medicine, Industry and Environmental Biotechnology - Characteristics, Analysis and Control. IWA Publishing. 413–437.
[4]	Wang Q, Zhang T (2010) Review of mathematical models for biofilms. Solid State Comm 150: 1009–1022. doi: 10.1016/j.ssc.2010.01.021
[5]	Horn H, Lackner S (2014) Modeling of biofilm systems: a review In Productive Biofilms, Springer International Publishing, 150: 53–76.
[6]	Picioreanu C,Van Loosdrecht MCM, Heijnen JJ, et al. (1998) Mathematical modeling of biofilm structure with a hybrid differential-discrete cellular automaton approach. Biotechnol Bioeng 58: 101–116. doi: 10.1002/(SICI)1097-0290(19980405)58:1<101::AID-BIT11>3.0.CO;2-M
[7]	Eberl HJ, Parker DF, Van Loosdrecht (2001) A new deterministic spatio-temporal continuum model for biofilm development. J Theor Biol 3: 161–175.
[8]	Wimpenny JWT, Colasanti R (1997) A unifying hypothesis for the structure of microbial biofilms based on cellular automaton models. FEMS Microbiol Ecol 22: 1–16. doi: 10.1111/j.1574-6941.1997.tb00351.x
[9]	Hermanowicz SW (2001) A simple 2d biofilm model yields a variety of morphological features. Math Biosci 169: 1–14. doi: 10.1016/S0025-5564(00)00049-3
[10]	Cogan NG, Keener JP (2004) The role of the biofilm matrix in structural development. Math Med Biol 21 147–166.
[11]	Zhang T, Cogan NG,Wang Q (2008) Phase field models for biofilms. i. theory and one-dimensional simulations. SIAM J Appl Math 69: 641–669.
[12]	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.
[13]	Winstanley HF, Chapwanya M, McGuinness, MJ, et al. (2011) A polymer - solvent model of biofilm growth. Proc R Soc Lond 467: 1449–1467. doi: 10.1098/rspa.2010.0327
[14]	Ward JP, King JR (2012) Thin-film modelling of biofilm growth and quorum sensing. J Eng Math 73: 71–92. doi: 10.1007/s10665-011-9490-4
[15]	Dillon R, Fauci L, Fogelson A, et al. (1996) Modeling biofilm processes using the immersed boundary method. J Comput Phys 129: 57–73. doi: 10.1006/jcph.1996.0233
[16]	Picioreanu C, Van Loosdrecht MCM, Heijnen JJ (2000) Effect of diffusive and convective substrate transport on biofilm structure formation: A two-dimensional modeling study. Biotechnol Bioeng 69: 504–515. doi: 10.1002/1097-0290(20000905)69:5<504::AID-BIT5>3.0.CO;2-S
[17]	Wanner O, Gujer W (2000) A multispecies biofilm model. Biotechnol Bioeng 28: 314–328.
[18]	Picioreanu C, Kreft JU , van Loosdrecht MCM (2004) Particle-based multidimensional multispecies biofilm model. Appl Environ Microbiol 70: 3024–3040. doi: 10.1128/AEM.70.5.3024-3040.2004
[19]	Alpkvist E, Klapper I (2007) A multidimensional multispecies continuum model for heterogeneous biofilm development. B Math Biol 69: 765–789. doi: 10.1007/s11538-006-9168-7
[20]	Dervaux J, Maginiez JC, Libchaber A (2014) On growth and form of Bacillus subtilis biofilms. Interface Focus 4: 20130051. doi: 10.1098/rsfs.2013.0051
[21]	Seminara A, Angelini TE,Wilking JN, et al. (2012) Osmotic spreading of bacillus subtilis biofilms driven by an extracellular matrix. Proc Natl Acad Sci USA 109: 1116–1121. doi: 10.1073/pnas.1109261108
[22]	Dilanji GE, Teplitski M, Hagen SJ (2014) Entropy-driven motility of sinorhizobium meliloti on a semi-solid surface. Proc Biol Sci 281: 20132575. doi: 10.1098/rspb.2013.2575
[23]	De Dier R, Fauvart M, Michiels J, et al. (2015) The role of biosurfactants in bacterial systems. In The Physical Basis of Bacterial Quorum Communication, Springer, 189–204.
[24]	Fauvart M, Phillips P, Bachaspatimayum D, et al. (2012) Surface tension gradient control of bacterial swarming in colonies of pseudomonas aeruginosa. Soft Matter 8: 70–76. doi: 10.1039/C1SM06002C
[25]	Angelini TE, Roper M , Kolter R, et al. (2009) Bacillus subtilis spreads by surfing on waves of surfactant. Proc Natl Acad Sci USA 106: 18109–18113. doi: 10.1073/pnas.0905890106
[26]	Brenner MP (2014) Fluid mechanical responses to nutrient depletion in fungi and biofilms. Phys Fluids 26: 101306. doi: 10.1063/1.4896587
[27]	Leclére V, Marti R, B´echet M, Fickers P, et al. (2006) The lipopeptides mycosubtilin and surfactin enhance spreading of Bacillus subtilis strains by their surface-active properties. Arch Microbiol 186: 475–483. doi: 10.1007/s00203-006-0163-z
[28]	Lachish U (2007) Osmosis and thermodynamics. Am J Phys 75: 997–998. doi: 10.1119/1.2752822
[29]	Zhang W, Seminara A, Suaris M, et al. (2014) Nutrient depletion in bacillus subtilis biofilms triggers matrix production. New J Phys 16: 015028. doi: 10.1088/1367-2630/16/1/015028
[30]	Wang X, Koehler SA, Wilking JN, et al. (2016) Probing phenotypic growth in expanding Bacillus subtilis biofilms. Appl Environ Microbiol 1–9.
[31]	Thiele U, Todorova DV, Lopez H (2013) Gradient dynamics description for films of mixtures and suspensions: Dewetting triggered by coupled film height and concentration fluctuations. Phys Rev Lett 111: 117801. doi: 10.1103/PhysRevLett.111.117801
[32]	Thiele U (2011) Note on thin film equations for solutions and suspensions. Europ Phys J 197: 213–220.
[33]	Xu X, Thiele U, Qian T (2015) A variational approach to thin film hydrodynamics of binary mixtures. J Phys Condens Matter 27: 085005. doi: 10.1088/0953-8984/27/8/085005
[34]	Thiele U, Archer AJ, Plapp M (2012) Thermodynamically consistent description of the hydrodynamics of free surfaces covered by insoluble surfactants of high concentration. Phys Fluids 24:102107. doi: 10.1063/1.4758476
[35]	de Groot SR, Mazur P (1984) Non-equilibrium Thermodynamics, Dover publications, New York.
[36]	Wilking JN, Angelini TE, Seminara A, et al. (2011) Biofilms as complex fluids. MRS Bull 36: 385–391. doi: 10.1557/mrs.2011.71
[37]	Mitlin VS (1993) Dewetting of solid surface: Analogy with spinodal decomposition. J Colloid Interf Sci 156: 491–497. doi: 10.1006/jcis.1993.1142
[38]	Thiele U (2010) Thin film evolution equations from (evaporating) dewetting liquid layers to epitaxial growth. J Phys Condens Matter 22: 084019. doi: 10.1088/0953-8984/22/8/084019
[39]	Oron A, Davis SH, Bankoff SG (1997) Long-scale evolution of thin liquid films. Rev Mod Phys 69: 931–980. doi: 10.1103/RevModPhys.69.931
[40]	Thiele U (2007) Structure formation in thin liquid films. In Kalliadasis S and Thiele U, Thin Films of Soft Matter, Wien: Springer, 25–93.
[41]	Wilczek M, Tewes WBH, Gurevich SV, et al. (2015) Modelling pattern formation in dip-coating experiments. Math Model Nat Phenom 10: 44–60. doi: 10.1051/mmnp/201510402
[42]	De Gennes PG (1985) Wetting: statics and dynamics. Rev Mod Phys 57: 827. doi: 10.1103/RevModPhys.57.827
[43]	Israelachvili JN (1985) Intermolecular and Surface Forces (With Applications to Colloidal and Biological Systems), Academic Press, London.
[44]	Israelachvili JN (2004) Capillarity and wetting phenomena: Drops, bubbles, pearls, waves, Springer, New York.
[45]	Bonn D, Eggers J, Indekeu J, et al. (2009) Wetting and spreading. Rev Mod Phys 81: 739. doi: 10.1103/RevModPhys.81.739
[46]	Náraigh LÓ , Thiffeault JL (2010) Nonlinear dynamics of phase separation in thin films. Nonlinearity 23: 1559–1583. doi: 10.1088/0951-7715/23/7/003
[47]	Hall-Stoodley L, Costerton JW, Stoodley P (2004) Bacterial biofilms: from the natural environment to infectious diseases. Nat Rev Microbiol 2: 95–108. doi: 10.1038/nrmicro821
[48]	Sutherland IW (2001) Biofilm exopolysaccharides: a strong and sticky framework. Microbiology 147: 3–9. doi: 10.1099/00221287-147-1-3
[49]	Lau PCY, Dutcher JR, Beveridge TJ, et al. (2009) Absolute quantitation of bacterial biofilm adhesion and viscoelasticity by microbead force spectroscopy. Biophys J 7: 2935–2948.
[50]	Warner MRE, Craster RV, Matar OK (2003) Surface patterning via evaporation of ultrathin films containing nanoparticles. Colloid Interf Sci 267: 92–110. doi: 10.1016/S0021-9797(03)00640-4
[51]	Frastia L, Archer AJ, Thiele U (2012) Modelling the formation of structured deposits at receding contact lines of evaporating solutions and suspensions. Soft Matter 8: 11363–11386. doi: 10.1039/c2sm26574e
[52]	Pismen LM, Thiele U (2006) Asymptotic theory for a moving droplet driven by a wettability gradient. Phys Fluids 18: 042104. doi: 10.1063/1.2191015
[53]	Todorova D, Thiele U, Pismen LM (2010) Steady evaporating droplets fed by an influx–the isothermal limit. J Eng Math 73: 17–30.
[54]	Doi M (2011) Onsager's variational principle in soft matter. J Phys Condens Matter 23: 284118. doi: 10.1088/0953-8984/23/28/284118
[55]	Rednikov A, Colinet P (2013) Singularity-free description of moving contact lines for volatile liquids. Phys Rev E 87: 010401. doi: 10.1103/PhysRevE.87.010401
[56]	Dietrich L E, Okegbe C, Price-Whelan A, et al. (2013) Bacterial community morphogenesis is intimately linked to the intracellular redox state. J Bacteriol 195: 1371–1380. doi: 10.1128/JB.02273-12
[57]	Blatt M, Bastian P (2006) The iterative solver template library, In: Applied Parallel Computing. State of the Art in Scientific Computing, Springer, 666–675.
[58]	Bastian P, Blatt M, Dedner A, et al. (2008) A generic grid interface for parallel and adaptive scientific computing. part i: abstract framework. Computing 82: 103–119.
[59]	Bastian P, Blatt M, Dedner A, et al. (2008) A generic grid interface for parallel and adaptive scientific computing. part ii: Implementation and tests in dune. Computing 82: 121–138.
[60]	Kuznetsov, YA (2013) Elements of applied bifurcation theory, Springer, New York, chapter 10.
[61]	Dijkstra HA, Wubs FW, Cliffe AK, et al. (2014) Numerical Bifurcation Methods and their Application to Fluid Dynamics: Analysis beyond Simulation. Commun Comput Phys 15: 1–45. doi: 10.4208/cicp.240912.180613a
[62]	Pototsky A, Bestehorn M , Merkt D, et al. (2005) Morphology changes in the evolution of liquid two-layer films. J Chem Phys 122: 224711. doi: 10.1063/1.1927512
[63]	Lin TS, Rogers S, Tseluiko D, et al. (2016) Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder. [submitted]
[64]	Doedel E, Oldeman B, Champneys A, et al. (2007) Continuation and bifurcation software for ordinary differential equations.
[65]	Doedel E, Keller HB, Kernevez JP (1991) Numerical analysis and control of bifurcation problems (i): bifurcation in finite dimensions. Int J Bifurcat Chaos 1: 493–520. doi: 10.1142/S0218127491000397
[66]	Thiele U, Kamps O, Gurevich SV, editors. (2014) Münsteranian Torturials on Nonlinear Science: Continuation. CeNoS, M¨unster Available from: http://www.unimuenster. de/CeNoS/Lehre/Tutorials. see in particular tutorials drop and thifi.
[67]	Thiele U, Velarde MG, Neuffer K, et al. (2001) Sliding drops in the di use interface model coupled to hydrodynamics. Phys Rev E 64: 061601.
[68]	Murray JD (1993) Mathematical Biology, Springer, New York.

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