- Physical Review Journals
All JournalsPhysics Magazine

Physical Review E

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Microbial mutualism at a distance: The role of geometry in diffusive exchanges

François J. Peaudecerf1,*, Freddy Bunbury2, Vaibhav Bhardwaj2, Martin A. Bees3, Alison G. Smith2, Raymond E. Goldstein1,†, and Ottavio A. Croze4,‡

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
  • 2Department of Plant Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EA, United Kingdom
  • 3Department of Mathematics, University of York, Heslington, York Y010 5DD, United Kingdom
  • 4Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom

  • *Present address: Institut für Umweltingenieurwissenschaften, ETH Zürich, Stefano-Franscini-Platz 5, 8093 Zürich, Switzerland; peaudecerf@ifu.baug.ethz.ch
  • †R.E.Goldstein@damtp.cam.ac.uk
  • ‡oac24@cam.ac.uk
PDF

Phys. Rev. E 97, 022411 – Published 20 February, 2018

DOI: https://doi.org/10.1103/PhysRevE.97.022411

Abstract

The exchange of diffusive metabolites is known to control the spatial patterns formed by microbial populations, as revealed by recent studies in the laboratory. However, the matrices used, such as agarose pads, lack the structured geometry of many natural microbial habitats, including in the soil or on the surfaces of plants or animals. Here we address the important question of how such geometry may control diffusive exchanges and microbial interaction. We model mathematically mutualistic interactions within a minimal unit of structure: two growing reservoirs linked by a diffusive channel through which metabolites are exchanged. The model is applied to study a synthetic mutualism, experimentally parametrized on a model algal-bacterial co-culture. Analytical and numerical solutions of the model predict conditions for the successful establishment of remote mutualisms, and how this depends, often counterintuitively, on diffusion geometry. We connect our findings to understanding complex behavior in synthetic and naturally occurring microbial communities.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (55)

  1. N. A. Abreu and M. E. Taga, FEMS Microbiol. Rev. 40, 648 (2016).
  2. S. Widder, R. J. Allen, T. Pfeiffer, T. P. Curtis, C. Wiuf, W. T. Sloan, O. X. Cordero, S. P. Brown, B. Momeni, W. Shou, H. Kettle, H. J. Flint, A. F. Haas, B. Laroche, J.-U. Kreft, P. B. Rainey, S. Freilich, S. Schuster, K. Milderstedt, J. R. van der Meer et al., ISME J. 10, 2557 (2016).
  3. M. B. Cooper and A. G. Smith, Curr. Opin. Plant Biol. 26, 147 (2015).
  4. W. R. Harcombe, W. J. Riehl, I. Dukovski, B. R. Granger, A. Betts, A. H. Lang, G. Bonilla, A. Kar, N. Leiby, P. Mehta, C. J. Marx, and D. Segrè, Cell Rep. 7, 1104 (2014).
  5. A. L. McCully, B. LaSarre, and J. B. McKinlay, Environ. Microbiol. 19, 3538 (2017).
  6. B. LaSarre, A. L. McCully, J. T. Lennon, and J. B. McKinlay, ISME J. 11, 337 (2017).
  7. B. Allen, J. Gore, and M. A. Nowak, eLife 2, e01169 (2013).
  8. H. J. Kim, J. Q. Boedicker, J. W. Choi, and R. F. Ismagilov, Proc. Natl. Acad. Sci. USA 105, 18188 (2008).
  9. E. F. Y. Hom and A. W. Murray, Science (NY) 345, 94 (2014).
  10. M. T. Croft, A. D. Lawrence, E. Raux-Deery, M. J. Warren, and A. G. Smith, Nature (London) 438, 90 (2005).
  11. E. Kazamia, H. Czesnick, T. T. V. Nguyen, M. T. Croft, E. Sherwood, S. Sasso, S. J. Hodson, M. J. Warren, and A. G. Smith, Environ. Microbiol. 14, 1466 (2012).
  12. H. Wang, J. Tomasch, M. Jarek, and I. Wagner-Döbler, Front. Microbiol. 5, 311 (2014).
  13. E. Segev, T. P. Wyche, K. H. Kim, J. Petersen, C. Ellebrandt, H. Vlamakis, N. Barteneva, J. N. Paulson, L. Chai, J. Clardy, and R. Kolter, eLife 5, e17473 (2016).
  14. J. D. Murray, Mathematical Biology (Springer, Berlin, 1989), Chap. 3, p. 83.
  15. A. R. Thompson, R. M. Nisbet, and R. J. Schmitt, J. Anim. Ecol. 75, 1239 (2006).
  16. J. N. Holland and D. L. DeAngelis, Ecol. Lett. 12, 1357 (2009).
  17. J. N. Holland and D. L. DeAngelis, Ecology 91, 1286 (2010).
  18. M. A. Grant, E. Kazamia, P. Cicuta, and A. G. Smith, ISME J. 8, 1418 (2014).
  19. R. M. May, Ecology 54, 638 (1973).
  20. T. Okuyama and J. N. Holland, Ecol. Lett. 11, 208 (2008).
  21. B. Momeni, L. Xie, and W. Shou, eLife 6, e25051 (2017).
  22. T. A. Hoek, K. Axelrod, T. Biancalani, E. A. Yurtsev, J. Liu, and J. Gore, PLoS Biol. 14, e1002540 (2016).
  23. I. H. Lee, A. G. Fredrickson, and H. M. Tsuchiya, Biotechnol. Bioeng. 18, 513 (1976).
  24. H. Wang, H. L. Smith, Y. Kuang, and J. J. Elser, SIAM J. Appl. Math. 68, 503 (2007).
  25. B. Momeni, A. J. Waite, and W. Shou, eLife 2, e00960 (2013).
  26. M. J. I. Müller, B. I. Neugeboren, D. R. Nelson, and A. W. Murray, Proc. Natl. Acad. Sci. USA 111, 1037 (2014).
  27. C. D. Nadell, K. Drescher, and K. R. Foster, Nat. Rev. Micro. 14, 589 (2016).
  28. K. Z. Coyte, H. Tabuteau, E. A. Gaffney, K. R. Foster, and W. M. Durham, Proc. Natl. Acad. Sci. USA 114, E161 (2017).
  29. J. Monod, Annu. Rev. Microbiol. 3, 371 (1949).
  30. C. Paul, M. A. Mausz, and G. Pohnert, Metabolomics 9, 349 (2013).
  31. F. J. Pérez-Reche, S. N. Taraskin, W. Otten, M. P. Viana, L. da F. Costa, and C. A. Gilligan, Phys. Rev. Lett. 109, 098102 (2012).
  32. E. Karzbrun, A. M. Tayar, V. Noireaux, and R. H. Bar-Ziv, Science 345, 829 (2014).
  33. B. S. Khatri, A. Free, and R. J. Allen, J. Theor. Biol. 314, 120 (2012).
  34. E. F. Y. Hom, P. Aiyar, D. Schaeme, M. Mittag, and S. Sasso, Trends Plant Sci. 20, 689 (2015).
  35. M. Cavaliere, S. Feng, O. S. Soyer, and J. I. Jiménez, Environ. Microbiol. 19, 2949 (2017).
  36. J. Liu, R. Martinez-Corral, A. Prindle, D.-y. D. Lee, J. Larkin, M. Gabalda-Sagarra, J. Garcia-Ojalvo, and G. M. Süel, Science 356, 638 (2017).
  37. J. Mathiesen, N. Mitarai, K. Sneppen, and A. Trusina, Phys. Rev. Lett. 107, 188101 (2011).
  38. T. J. Battin, K. Besemer, M. M. Bengtsson, A. M. Romani, and A. I. Packmann, Nat. Rev. Microbiol. 14, 251 (2016).
  39. E. Pagaling, F. Strathdee, B. M. Spears, M. E. Cates, R. J. Allen, and A. Free, ISME J. 8, 19 (2014).
  40. E. Kazamia, K. E. Helliwell, S. Purton, and A. G. Smith, Ecol. Lett. 19, 810 (2016).
  41. F. A. d. A. Barbuto, Numerical inversion of Laplace transforms through Zakian's algorithm (Python recipe), (2002), http://code.activestate.com/recipes/127469-numerical-inversion-of-laplace-transforms-through-/.
  42. D. J. Halsted and D. E. Brown, Chem. Eng. J. 3, 312 (1972).
  43. J. Abate and W. Whitt, INFORMS J. Comput. 18, 408 (2006).
  44. V. Yukalov, E. Yukalova, and D. Sornette, Phys. D (Amsterdam, Neth.) 241, 1270 (2012).
  45. B. Amsden, Macromolecules 31, 8382 (1998).
  46. T. Ferenci, Res. Microbiol. 150, 431 (1999).
  47. D. K. Button, Microbiol. Rev. 49, 270 (1985).
  48. H. Senn, U. Lendenmann, M. Snozzi, G. Hamer, and T. Egli, Biochim. Biophys. Acta 1201, 424 (1994).
  49. M. R. Droop, J. Plankton Res. 29, 107 (2007).
  50. D. H. Miller, I. S. Mellman, D. T. A. Lamport, and M. Miller, J. Cell Biol. 63, 420 (1974).
  51. N. R. Boyle and J. A. Morgan, BMC Syst. Biol. 3, 4 (2009).
  52. N. Kamjunke and J. Tittel, J. Phycol. 45, 807 (2009).
  53. J. Gonzalez-Lopez, V. Salmeron, J. Moreno, and A. Ramos-Cormenzana, Soil Biol. Biochem. 15, 711 (1983).
  54. H. Link, B. Anselment, and D. Weuster-Botz, Metabolomics 4, 240 (2008).
  55. E. Raux, A. Lanois, F. Levillayer, M. J. Warren, E. Brody, A. Rambach, and C. Thermes, J. Bacteriol. 178, 753 (1996).

Outline

Information

Phys. Rev. E 97, 022411– Published 20 February, 2018
  • Received 19 December 2017
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation