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Heterogeneity formation within biofilm systems

  • ANDREAS C. ARISTOTELOUS (a1), YURY GRABOVSKY (a2) and ISAAC KLAPPER (a2)

Abstract

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.

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Copyright

Footnotes

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

Footnotes

References

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[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, 557594.
[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, 22112238.
[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, 11671198.
[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, 767780.
[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.
[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.
[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, 17491779.
[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, 23602370.
[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, 547558.
[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, 466474.
[11] Bramble, J. H. (2003) Multigrid Methods, Research Notes in Mathematics Series, Chapman and Hall/CRC, London.
[12] Brenner, S. C. & Sung, L. Y. (2006) Multigrid algorithms for C0 interior penalty methods. SIAM J. Numer. Anal. 44, 199223.
[13] Cogan, N. C. (2008) Two-fluid model of biofilm disinfection. Bull. Math. Biol. 70, 800819.
[14] Cogan, N. G., Cortez, R. & Fauci, L. (2005) Modeling physiological resistance in bacterial biofilms. Bull. Math. Biol. 67 831853.
[15] Cogan, N. G. & Keener, J. P. (2004) The role of the biofilm matrix in structural development. Math. Med. Biol. 21, 147166.
[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, 421428.
[17] Di Pietro, D. A. & Ern, A. (2012) Mathematical Aspects of Discontinuous Galerkin Methods, Springer, Berlin.
[18] Dockery, J. D. & Klapper, I. (2002) Finger formation in biofilms. SIAM J. Appl. Math. 62, 853869.
[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, 161175.
[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, 788807.
[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, 269304.
[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, 14001408.
[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, 9971004.
[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, 373383.
[25] Klapper, I. (2013) Productivity and equilibrium in simple biofilm models. Bull. Math. Biol. 74, 29172934.
[26] Klapper, I. & Dockery, J. (2006) Role of cohesion in the material description of biofilms. Phys. Rev. E 74, 031902.
[27] Klapper, I. & Dockery, J. (2010) Mathematical description of microbial biofilms. SIAM Rev. 52, 221265.
[28] Klapper, I., Dockery, J. & Smith, H. (2014) Niche partitioning along an environmental gradient. SIAM J. Appl. Math. 74, 15111534.
[29] Lehner, B. A. E., Schmieden, D. T. & Meyer, A. S. (2017) A straightforward approach for 3D bacterial printing. ACS Synth. Biol. 6, 11241130.
[30] Lewandowski, L. (2000) MIC and biofilm heterogeneity. Proc. Corros., NACE-400, 1–7.
[31] Mitri, S., Clarke, E. & Foster, K. R. (2016) Resource limitation drives spatial organization in microbial groups. ISME J. 10, 14711482.
[32] Nadell, C. D., Drescher, K. & Foster, K. R. (2016) Spatial structure, cooperation and competition in biofilms. Nat. Rev. Microbiol. 14, 589600.
[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, 504515.
[34] Rivière, B. (2008) Discontinuous Galerkin Methods for Solving Elliptic and Parabolic Equations, SIAM, Philadelphia.
[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.
[36] Schobert, M. & Tielen, P. (2010) Contribution of oxygen-limiting conditions to persistent infection of Pseudomonas aeruginosa. Future Microbiol. 5, 603621.
[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.
[38] Stewart, P. S. (2002) Mechanisms of antibiotic resistance in bacterial biofilms. Int. J. Med. Microbiol. 292, 107113.
[39] Stewart, P. S. & Franklin, M. J. (2008) Physiological heterogeneity in biofilms. Nat. Rev. Microbiol. 6, 199210.
[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, 30993104.
[41] Szomolay, B., Klapper, I. & Dindos, M. (2010) Analysis of adaptive response to dosing protocols for biofilm control. SIAM J. Appl. Math. 70, 31753202.
[42] Szomolay, B., Klapper, I., Dockery, J. & Stewart, P. S. (2005) Adaptive responses to antimicrobial agents in biofilms. Environ. Microbiol. 7, 11861191.
[43] Vemaganti, K. (2007) Discontinuous Galerkin methods for periodic boundary value problems. Num. Methods Partial Differ. Equat. 23, 587596.
[44] Zhang, Z., Nadezhina, E. & Wilkinson, K. J. (2011) Quantifying diffusion in a biofilm of Streptococcus mutans. Antimicrob. Agents Chemother. 55, 10751081.

Keywords

Heterogeneity formation within biofilm systems

  • ANDREAS C. ARISTOTELOUS (a1), YURY GRABOVSKY (a2) and ISAAC KLAPPER (a2)

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