Nutrient-limited growth with non-linear cell diffusion as a mechanism for floral pattern formation in yeast biofilms
| Autor: | Alexander Tam, Benjamin J. Binder, Ee Lin Tek, Jennifer M. Gardner, Joanna F. Sundstrom, Vladimir Jiranek, J. Edward F. Green, Sanjeeva Balasuriya |
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| Přispěvatelé: | Tam, Alexander, Green, J Edward F, Balasuriya, Sanjeeva, Tek, Ee Lin, Gardner, Jennifer M, Sundstrom, Joanna F, Jiranek, Vladimir, Binder, Benjamin J |
| Rok vydání: | 2017 |
| Předmět: |
Life Sciences & Biomedicine - Other Topics
0301 basic medicine Statistics and Probability Singular perturbation Work (thermodynamics) linear stability analysis Saccharomyces cerevisiae Pattern formation travelling wave solution angular pair-correlation function Models Biological General Biochemistry Genetics and Molecular Biology Diffusion 03 medical and health sciences Reaction–diffusion system geometric singular perturbation theory Diffusion (business) Biology Physics General Immunology and Microbiology biology Applied Mathematics fungi General Medicine Nutrients Models Theoretical biology.organism_classification Yeast mat formation experiment Nonlinear system 030104 developmental biology Modeling and Simulation Biofilms reaction–diffusion Mathematical & Computational Biology General Agricultural and Biological Sciences Biological system |
| Zdroj: | Journal of theoretical biology. 448 |
| ISSN: | 1095-8541 |
| Popis: | 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. Refereed/Peer-reviewed |
| Databáze: | OpenAIRE |
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