Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T05:38:31.686Z Has data issue: false hasContentIssue false
  • English
  • Français

Heterogeneity formation within biofilm systems

Published online by Cambridge University Press:  16 July 2018

ANDREAS C. ARISTOTELOUS ,
YURY GRABOVSKY  and
ISAAC KLAPPER
ANDREAS C. ARISTOTELOUS
Affiliation:
Department of Mathematics, West Chester University, West Chester, PA, USA
YURY GRABOVSKY
Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA, USA email: [email protected]
ISAAC KLAPPER
Affiliation:
Department of Mathematics, Temple University, Philadelphia, PA, USA email: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Biofilms, and collections of embedded microbial communities, present structural heterogeneities with functional consequences for important processes, such as transport. The origin of such structures has been unclear. Here, we propose that they can arise as a consequence of diffusive transport limitation. To illustrate, a model allowing internal heterogeneity is developed. Linear analysis is applied to a simplified version of the model suggesting that heterogeneity forms on (or below) the active layer length, a length scale that may not be suitable for homogenization, with non-trivial implications for system scale properties such as reduction in system-wide diffusive transport efficiency. Numerics suggest that the simplified model provides useful insight into behaviour of the full model. We then show examples based on microcolony formation in host domains and argue that internal heterogeneity can be related to community function.

Keywords

Biofilmsheterogeneitydiffusive transport
Type
Papers
Information
European Journal of Applied Mathematics , Volume 29 , Special Issue 6: Biofilms , December 2018 , pp. 1020 - 1034
Copyright
Copyright © Cambridge University Press 2018 

Footnotes

† The authors acknowledge funding provided for this project by NSF Award Nos. 1517100 and 1720226, and NIH Award No. R01GM109452.

References

[1] Anguige, K., King, J. R. & Ward, J. P. (2005) Modelling antibiotic- and quorum sensing treatment of a spatially-structured Pseudomonas aeruginosa population. J. Math. Biol. 51, 557–594.Google Scholar
[2] Aristotelous, A. C., Karakashian, O. A. & Wise, S. M. (2013) A mixed discontinuous Galerkin, convex splitting scheme for a modified Cahn–Hilliard equation and an efficient non-linear multigrid solver. DCDS-B 18, 2211–2238.Google Scholar
[3] Aristotelous, A. C., Karakashian, O. A. & Wise, S. M. (2015) Adaptive, second-order in time, primitive-variable discontinuous Galerkin schemes for a Cahn–Hilliard equation with a mass source. IMA J. Numer. Anal. 35, 1167–1198.Google Scholar
[4] Aristotelous, A. C. & Haider, M. A. (2014) Use of hybrid discrete cellular models for identification of macroscopic nutrient loss in reaction–diffusion models of tissues. Int. J. Numer. Method Biomed. Eng. 30, 767–780.Google Scholar
[5] Aristotelous, A. C., Klapper, I., Grabovsky, Y., Pabst, B., Pitts, B. & Stewart, P. S. (2015) Diffusive transport through a model host-biofilm system. Phys. Rev. E 92, 022703.Google Scholar
[6] Aristotelous, A. C. & Papanicolaou, N. C. (2016) A discontinuous Galerkin method for unsteady two-dimensional convective flows. In: American Institute of Physics (AIP) Conference Proceedings, Varna, Bulgaria, Vol. 1773, 110002.Google Scholar
[7] Arnold, D. N., Brezzi, F., Cockburn, B. & Marini, L. D. (2002) Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal. 39, 1749–1779.Google Scholar
[8] Bernstein, H. C., Beam, J. P., Kozubal, M. A., Carlson, R. P. & Inskeep, W. P. (2013) In situ analysis of oxygen consumption and diffusive transport in high-temperature acidic iron-oxide microbial mats. Environ. Microbiol. 15, 2360–2370.Google Scholar
[9] Bjarnsholt, T., Jensen, P. Ø., Fiandaca, M. J., Pedersen, J., Hansen, C. R., Andersen, C. B., Pressler, T., Givskov, M. & Høiby, N. (2009) Pseudomonas aeruginosa biofilms in the respiratory tract of cystic fibrosis patients. Pediatr. Pulmonol. 44, 547–558.Google Scholar
[10] Bjarnsholt, T., Alhede, M., Alhede, M., Eickhardt-Sørensen, S. R., Moser, C., Kühl, M., Jensen, Ø. P. & Høiby, N. (2013) The in vivo biofilm. Trends Microbiol. 21, 466–474.Google Scholar
[11] Bramble, J. H. (2003) Multigrid Methods, Research Notes in Mathematics Series, Chapman and Hall/CRC, London.Google Scholar
[12] Brenner, S. C. & Sung, L. Y. (2006) Multigrid algorithms for C0 interior penalty methods. SIAM J. Numer. Anal. 44, 199–223.Google Scholar
[13] Cogan, N. C. (2008) Two-fluid model of biofilm disinfection. Bull. Math. Biol. 70, 800–819.Google Scholar
[14] Cogan, N. G., Cortez, R. & Fauci, L. (2005) Modeling physiological resistance in bacterial biofilms. Bull. Math. Biol. 67 831–853.Google Scholar
[15] Cogan, N. G. & Keener, J. P. (2004) The role of the biofilm matrix in structural development. Math. Med. Biol. 21, 147–166.Google Scholar
[16] Coufort, C., Derlon, N., Ochoa-Chaves, J., Line, A. & Paul, E. (2007) Cohesion and detachment in biofilm systems for different electron acceptor and donors. Water Sci. Technol. 55, 421–428.Google Scholar
[17] Di Pietro, D. A. & Ern, A. (2012) Mathematical Aspects of Discontinuous Galerkin Methods, Springer, Berlin.Google Scholar
[18] Dockery, J. D. & Klapper, I. (2002) Finger formation in biofilms. SIAM J. Appl. Math. 62, 853–869.Google Scholar
[19] Eberl, H. J., Parker, D. F. & Van Loosdrecht, M. C. M. (2001) A new deterministic spatio-temporal continuum model for biofilm development. J. Theor. Med. 3, 161–175.Google Scholar
[20] Eberl, H. J. & Sudarsan, R. (2008) Exposure of biofilms to slow flow fields: The convective contribution to growth and disinfection. J. Theor. Biol. 253, 788–807.Google Scholar
[21] Efendiev, M. A., Demaret, L., Lasser, R. & Eberl, H. J. (2008) Analysis and simulation of a meso-scale model of diffusive resistance of bacterial biofilms to penetration of antibiotics. Adv. Math. Sci. Appl. 18, 269–304.Google Scholar
[22] Galy, O., Latour-Lambert, P., Zrelli, K., Ghigo, J.-M., Beloin, C. & Henry, W. (2012) Mapping of bacterial biofilm local mechanics by magnetic microparticle actuation. Biophys. J. 103, 1400–1408.Google Scholar
[23] Hopf, H. W., Hunt, T. K., West, J. M., Blomquist, P., Goodson, W. H. III, Jensen, J. A., Jonsson, K., Paty, P. B., Rabkin, J. M., Upton, R. A., von Smitten, R. & Whitney, J. D. (1997) Wound tissue oxygen tension predicts the risk of wound infection in surgical patients. Arch. Surg. 132, 997–1004.Google Scholar
[24] James, G. A., Zhao, A. G., Usui, M., Underwood, R. A., Nguyen, H., Beyenal, H., Pulcini, E.d., Hunt, A. A., Bernstein, H. C., Fleckman, P., Olerud, J., Williamson, K., Franklin, M. J. & Stewart, P. S. (2016) Microsensor and transcriptomic signatures of oxygen depletion in biofilms associated with chronic wounds. Wound Repair Regen. 24, 373–383.Google Scholar
[25] Klapper, I. (2013) Productivity and equilibrium in simple biofilm models. Bull. Math. Biol. 74, 2917–2934.Google Scholar
[26] Klapper, I. & Dockery, J. (2006) Role of cohesion in the material description of biofilms. Phys. Rev. E 74, 031902.Google Scholar
[27] Klapper, I. & Dockery, J. (2010) Mathematical description of microbial biofilms. SIAM Rev. 52, 221–265.Google Scholar
[28] Klapper, I., Dockery, J. & Smith, H. (2014) Niche partitioning along an environmental gradient. SIAM J. Appl. Math. 74, 1511–1534.Google Scholar
[29] Lehner, B. A. E., Schmieden, D. T. & Meyer, A. S. (2017) A straightforward approach for 3D bacterial printing. ACS Synth. Biol. 6, 1124–1130.Google Scholar
[30] Lewandowski, L. (2000) MIC and biofilm heterogeneity. Proc. Corros., NACE-400, 1–7.Google Scholar
[31] Mitri, S., Clarke, E. & Foster, K. R. (2016) Resource limitation drives spatial organization in microbial groups. ISME J. 10, 1471–1482.Google Scholar
[32] Nadell, C. D., Drescher, K. & Foster, K. R. (2016) Spatial structure, cooperation and competition in biofilms. Nat. Rev. Microbiol. 14, 589–600.Google Scholar
[33] Picioreanu, C., van Loosdrecht, M. C. & Heijnen, J. J. (2000) Effect of diffusive and convective substrate transport on biofilm structure formation: A two-dimensional modeling study. Biotechnol. Bioeng. 69, 504–515.Google Scholar
[34] Rivière, B. (2008) Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, SIAM, Philadelphia.Google Scholar
[35] Schaffner, M., Rühs, P. A., Coulter, F., Kilcher, S. & Studart, A. R. (2017) 3D printing of bacteria into functional complex materials. Sci. Adv. 3, eaao6804, DOI: 10.1126/sciadv.aao6804.Google Scholar
[36] Schobert, M. & Tielen, P. (2010) Contribution of oxygen-limiting conditions to persistent infection of Pseudomonas aeruginosa. Future Microbiol. 5, 603–621.Google Scholar
[37] SønderholmKoren, K. Koren, K., Wangpraseurt, D., Jensen, P. Ø., Kolpen, M., Kragh, K. N., Bjarnsholt, T. & Kühl, (2018) Tools for studying growth patterns and chemical dynamics of aggregated Pseudomonas aeruginosa exposed to different electron acceptors in an alginate bead model. npj Biofilms Microbiomes 4, art. no. 3.Google Scholar
[38] Stewart, P. S. (2002) Mechanisms of antibiotic resistance in bacterial biofilms. Int. J. Med. Microbiol. 292, 107–113.Google Scholar
[39] Stewart, P. S. & Franklin, M. J. (2008) Physiological heterogeneity in biofilms. Nat. Rev. Microbiol. 6, 199–210.Google Scholar
[40] Stewart, P. S. & Raquepas, J. B. (1995) Implications of reaction-diffusion theory for disinfection of microbial biofilms by reactive antimicrobial agents. Chem. Eng. Sci. 50, 3099–3104.Google Scholar
[41] Szomolay, B., Klapper, I. & Dindos, M. (2010) Analysis of adaptive response to dosing protocols for biofilm control. SIAM J. Appl. Math. 70, 3175–3202.Google Scholar
[42] Szomolay, B., Klapper, I., Dockery, J. & Stewart, P. S. (2005) Adaptive responses to antimicrobial agents in biofilms. Environ. Microbiol. 7, 1186–1191.Google Scholar
[43] Vemaganti, K. (2007) Discontinuous Galerkin methods for periodic boundary value problems. Num. Methods Partial Differ. Equat. 23, 587–596.Google Scholar
[44] Zhang, Z., Nadezhina, E. & Wilkinson, K. J. (2011) Quantifying diffusion in a biofilm of Streptococcus mutans. Antimicrob. Agents Chemother. 55, 1075–1081.Google Scholar