Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms
Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms
Previous experiments have shown that mature yeast mat biofilms develop a floral morphology, characterised by the formation of petal-like structures. In this work, we investigate the hypothesis that nutrient-limited growth is the mechanism by which these floral patterns form. To do this, we use a combination of experiments and mathematical analysis. In mat formation experiments of the yeast species Saccharomyces cerevisiae, we observe that mats expand radially at a roughly constant speed, and eventually undergo a transition from circular to floral morphology. To determine the extent to which nutrient-limited growth can explain these features, we adopt a previously proposed mathematical model for yeast growth. The model consists of a coupled system of reaction–diffusion equations for the yeast cell density and nutrient concentration, with a non-linear, degenerate diffusion term for cell spread. Using geometric singular perturbation theory and numerics, we show that the model admits travelling wave solutions in one dimension, which enables us to infer the diffusion ratio from experimental data. We then use a linear stability analysis to show that two-dimensional planar travelling wave solutions for feasible experimental parameters are linearly unstable to non-planar perturbations. This provides a potential mechanism by which petals can form, and allows us to predict the characteristic petal width. There is good agreement between these predictions, numerical solutions to the model, and experimental data. We therefore conclude that the non-linear cell diffusion mechanism provides a possible explanation for pattern formation in yeast mat biofilms, without the need to invoke other mechanisms such as flow of extracellular fluid, cell adhesion, or changes to cellular shape or behaviour.
Angular pair-correlation function, Geometric singular perturbation theory, Linear stability analysis, Mat formation experiment, Reaction–diffusion, Saccharomyces cerevisiae, Travelling wave solution
122-141
Tam, Alexander
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Green, J. Edward F.
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Balasuriya, Sanjeeva
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Tek, Ee Lin
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Gardner, Jennifer M.
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Sundstrom, Joanna F.
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Jiranek, Vladimir
8e5a8dfd-f5b2-43e3-928b-11dff324abc7
Binder, Benjamin J.
4b861311-8ad2-417c-903a-1d35e541d14b
7 July 2018
Tam, Alexander
4037506d-a50e-4a08-8a92-d2022a387932
Green, J. Edward F.
79f22dac-8b72-45d9-8e6a-1b9c93ea8afd
Balasuriya, Sanjeeva
42c5f7a4-ba27-4410-a64e-8a2bfdba19a9
Tek, Ee Lin
7692691a-a6a2-4a7b-964e-235f8ea0ec03
Gardner, Jennifer M.
0d95188b-206d-4817-8437-e163351f6e7f
Sundstrom, Joanna F.
6c6b3452-dfb3-4b5c-aa42-c721eed7b9bb
Jiranek, Vladimir
8e5a8dfd-f5b2-43e3-928b-11dff324abc7
Binder, Benjamin J.
4b861311-8ad2-417c-903a-1d35e541d14b
Tam, Alexander, Green, J. Edward F., Balasuriya, Sanjeeva, Tek, Ee Lin, Gardner, Jennifer M., Sundstrom, Joanna F., Jiranek, Vladimir and Binder, Benjamin J.
(2018)
Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms.
Journal of Theoretical Biology, 448, .
(doi:10.1016/j.jtbi.2018.04.004).
Abstract
Previous experiments have shown that mature yeast mat biofilms develop a floral morphology, characterised by the formation of petal-like structures. In this work, we investigate the hypothesis that nutrient-limited growth is the mechanism by which these floral patterns form. To do this, we use a combination of experiments and mathematical analysis. In mat formation experiments of the yeast species Saccharomyces cerevisiae, we observe that mats expand radially at a roughly constant speed, and eventually undergo a transition from circular to floral morphology. To determine the extent to which nutrient-limited growth can explain these features, we adopt a previously proposed mathematical model for yeast growth. The model consists of a coupled system of reaction–diffusion equations for the yeast cell density and nutrient concentration, with a non-linear, degenerate diffusion term for cell spread. Using geometric singular perturbation theory and numerics, we show that the model admits travelling wave solutions in one dimension, which enables us to infer the diffusion ratio from experimental data. We then use a linear stability analysis to show that two-dimensional planar travelling wave solutions for feasible experimental parameters are linearly unstable to non-planar perturbations. This provides a potential mechanism by which petals can form, and allows us to predict the characteristic petal width. There is good agreement between these predictions, numerical solutions to the model, and experimental data. We therefore conclude that the non-linear cell diffusion mechanism provides a possible explanation for pattern formation in yeast mat biofilms, without the need to invoke other mechanisms such as flow of extracellular fluid, cell adhesion, or changes to cellular shape or behaviour.
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Published date: 7 July 2018
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Funding Information:
A. T. would like to acknowledge funding support from the A. F. Pillow Applied Mathematics Trust, and from the Australian Government under the Research Training Program. J. E. F. G. acknowledges funding from an ARC Discovery Early Career Researcher Award (DE130100031). S. B. acknowledges funding from an ARC Future Fellowship (FT130100484). B. J. B. would like to acknowledge funding provided by the Australian government under the Australian Research Council (ARC) Discovery project DP160102644 . E. L. T. was supported by an Adelaide Graduate Research Scholarship (University of Adelaide) and funding from Wine Australia ( GWR Ph1305 ). J. M. G. and J. F. S. were supported by ARC Discovery Project DP130103547 awarded to V. J. This work was supported with supercomputing resources provided by the Phoenix High Performance Computing service at the University of Adelaide. The authors wish to acknowledge several helpful comments from anonymous referees that contributed significant improvements to this research. 9
Publisher Copyright:
© 2018 Elsevier Ltd
Keywords:
Angular pair-correlation function, Geometric singular perturbation theory, Linear stability analysis, Mat formation experiment, Reaction–diffusion, Saccharomyces cerevisiae, Travelling wave solution
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Local EPrints ID: 482657
URI: http://eprints.soton.ac.uk/id/eprint/482657
ISSN: 0022-5193
PURE UUID: 9077ffbc-55b3-409b-b1c2-921045969cd5
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Date deposited: 11 Oct 2023 16:48
Last modified: 18 Mar 2024 04:12
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Author:
Alexander Tam
Author:
J. Edward F. Green
Author:
Sanjeeva Balasuriya
Author:
Ee Lin Tek
Author:
Jennifer M. Gardner
Author:
Joanna F. Sundstrom
Author:
Vladimir Jiranek
Author:
Benjamin J. Binder
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