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Two-dimensionality of yeast colony expansion accompanied by pattern formation.

Chen L, Noorbakhsh J, Adams RM, Samaniego-Evans J, Agollah G, Nevozhay D, Kuzdzal-Fick J, Mehta P, Balázsi G - PLoS Comput. Biol. (2014)

Bottom Line: Although the biochemical and molecular requirements for such patterns have been examined, the mechanisms underlying their formation are not entirely clear.Here we develop quantitative methods to accurately characterize the size, shape, and surface patterns of yeast colonies for various combinations of agar and sugar concentrations.We combine these measurements with mathematical and physical models and find that FLO11 gene constrains cells to grow near the agar surface, causing the formation of larger and more irregular colonies that undergo hierarchical wrinkling.

View Article: PubMed Central - PubMed

Affiliation: Department of Systems Biology, The University of Texas MD Anderson Cancer Center, Houston, Texas, United States of America.

ABSTRACT
Yeasts can form multicellular patterns as they expand on agar plates, a phenotype that requires a functional copy of the FLO11 gene. Although the biochemical and molecular requirements for such patterns have been examined, the mechanisms underlying their formation are not entirely clear. Here we develop quantitative methods to accurately characterize the size, shape, and surface patterns of yeast colonies for various combinations of agar and sugar concentrations. We combine these measurements with mathematical and physical models and find that FLO11 gene constrains cells to grow near the agar surface, causing the formation of larger and more irregular colonies that undergo hierarchical wrinkling. Head-to-head competition assays on agar plates indicate that two-dimensional constraint on the expansion of FLO11 wild type (FLO11) cells confers a fitness advantage over FLO11 knockout (flo11Δ) cells on the agar surface.

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Mathematical model of colony expansion.(A–C) A snapshot of the colonies at the end of simulation. Although these simulations are started with circular colonies, over time petals appear. The color scale represents cell density (arbitrary units). (D–F) The maximum colony area is higher upon higher initial glucose concentration, in agreement with the experimental results in Fig. 1. The dimensionless “colony area ratio” was the ratio of colony area to the area of simulation box, and glucose concentration corresponded to the initial value of glucose in the simulation, and was chosen as a constant over space. Time is a rescaled variable measured in arbitrary units. (G–I) Simulated colony irregularity (P2A) plotted as a function of time. Similar to experiments (Fig. 1), in our model P2A is initially at a basal level and then increases abruptly to a large value. This increase in P2A corresponds to petal formation and occurs as a result of competition over glucose among cells that make up the colony rim. Interestingly, the maximum value of P2A decreases with increasing glucose levels. This result is likely due to decreased intercellular competition over nutrients in the early stages of expansion and is compatible with experiments in Fig. 1, where colonies exhibit less structure as glucose levels increase.
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pcbi-1003979-g002: Mathematical model of colony expansion.(A–C) A snapshot of the colonies at the end of simulation. Although these simulations are started with circular colonies, over time petals appear. The color scale represents cell density (arbitrary units). (D–F) The maximum colony area is higher upon higher initial glucose concentration, in agreement with the experimental results in Fig. 1. The dimensionless “colony area ratio” was the ratio of colony area to the area of simulation box, and glucose concentration corresponded to the initial value of glucose in the simulation, and was chosen as a constant over space. Time is a rescaled variable measured in arbitrary units. (G–I) Simulated colony irregularity (P2A) plotted as a function of time. Similar to experiments (Fig. 1), in our model P2A is initially at a basal level and then increases abruptly to a large value. This increase in P2A corresponds to petal formation and occurs as a result of competition over glucose among cells that make up the colony rim. Interestingly, the maximum value of P2A decreases with increasing glucose levels. This result is likely due to decreased intercellular competition over nutrients in the early stages of expansion and is compatible with experiments in Fig. 1, where colonies exhibit less structure as glucose levels increase.

Mentions: Considering that FLO11 mediates the adhesion of cells to abiotic surfaces [18], [20], we hypothesized that this causes the cells to stay closer to the agar surface rather than expanding vertically into the third dimension. Therefore, we developed a phenomenological model (see Methods) for FLO11 cells spreading through a diffusive process in two dimensions corresponding to the surface of the agar, similar to earlier studies of colony growth in bacteria [34], [35], [37], [38]. The model's purpose was to identify mechanisms explaining colony size and shape differences, without intending to reproduce exact biological values. Therefore, we applied rescaling to obtain dimensionless variables, such as time and cell density. Cell growth and colony expansion were assumed to be dependent on glucose availability and glucose could diffuse in two dimensions. Using this model, we plotted the time-courses of colony area and irregularity (P2A) for different initial levels of glucose (Fig. 2). The calculated dependence of maximal colony area on environmental parameters (sugar concentration) resembled what was observed experimentally (Fig. 1, S1 Figure). According to the model, the calculated colony area approached its maximum once depleting the available glucose. Furthermore, increasing initial glucose levels in the model lad to larger maximum colony area as in the experiments. Finally, the model also produced a concave curve of colony area versus time at low glucose levels, and a convex curve at high glucose, as in the experiments (Figs. 1, 2 and S2 Supporting Figure). When we modified the model allowing cells to escape into the vertical direction, we obtained smaller colonies (S6 Figure). Overall, the mathematical models supported the hypothesis that FLO11 yeast colonies tend to grow along the agar surface, which limits their degrees of freedom, leading to larger colony sizes and more irregular colony shapes compared to flo11Δ cells that are free to expand vertically.


Two-dimensionality of yeast colony expansion accompanied by pattern formation.

Chen L, Noorbakhsh J, Adams RM, Samaniego-Evans J, Agollah G, Nevozhay D, Kuzdzal-Fick J, Mehta P, Balázsi G - PLoS Comput. Biol. (2014)

Mathematical model of colony expansion.(A–C) A snapshot of the colonies at the end of simulation. Although these simulations are started with circular colonies, over time petals appear. The color scale represents cell density (arbitrary units). (D–F) The maximum colony area is higher upon higher initial glucose concentration, in agreement with the experimental results in Fig. 1. The dimensionless “colony area ratio” was the ratio of colony area to the area of simulation box, and glucose concentration corresponded to the initial value of glucose in the simulation, and was chosen as a constant over space. Time is a rescaled variable measured in arbitrary units. (G–I) Simulated colony irregularity (P2A) plotted as a function of time. Similar to experiments (Fig. 1), in our model P2A is initially at a basal level and then increases abruptly to a large value. This increase in P2A corresponds to petal formation and occurs as a result of competition over glucose among cells that make up the colony rim. Interestingly, the maximum value of P2A decreases with increasing glucose levels. This result is likely due to decreased intercellular competition over nutrients in the early stages of expansion and is compatible with experiments in Fig. 1, where colonies exhibit less structure as glucose levels increase.
© Copyright Policy
Related In: Results  -  Collection

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Show All Figures
getmorefigures.php?uid=PMC4263361&req=5

pcbi-1003979-g002: Mathematical model of colony expansion.(A–C) A snapshot of the colonies at the end of simulation. Although these simulations are started with circular colonies, over time petals appear. The color scale represents cell density (arbitrary units). (D–F) The maximum colony area is higher upon higher initial glucose concentration, in agreement with the experimental results in Fig. 1. The dimensionless “colony area ratio” was the ratio of colony area to the area of simulation box, and glucose concentration corresponded to the initial value of glucose in the simulation, and was chosen as a constant over space. Time is a rescaled variable measured in arbitrary units. (G–I) Simulated colony irregularity (P2A) plotted as a function of time. Similar to experiments (Fig. 1), in our model P2A is initially at a basal level and then increases abruptly to a large value. This increase in P2A corresponds to petal formation and occurs as a result of competition over glucose among cells that make up the colony rim. Interestingly, the maximum value of P2A decreases with increasing glucose levels. This result is likely due to decreased intercellular competition over nutrients in the early stages of expansion and is compatible with experiments in Fig. 1, where colonies exhibit less structure as glucose levels increase.
Mentions: Considering that FLO11 mediates the adhesion of cells to abiotic surfaces [18], [20], we hypothesized that this causes the cells to stay closer to the agar surface rather than expanding vertically into the third dimension. Therefore, we developed a phenomenological model (see Methods) for FLO11 cells spreading through a diffusive process in two dimensions corresponding to the surface of the agar, similar to earlier studies of colony growth in bacteria [34], [35], [37], [38]. The model's purpose was to identify mechanisms explaining colony size and shape differences, without intending to reproduce exact biological values. Therefore, we applied rescaling to obtain dimensionless variables, such as time and cell density. Cell growth and colony expansion were assumed to be dependent on glucose availability and glucose could diffuse in two dimensions. Using this model, we plotted the time-courses of colony area and irregularity (P2A) for different initial levels of glucose (Fig. 2). The calculated dependence of maximal colony area on environmental parameters (sugar concentration) resembled what was observed experimentally (Fig. 1, S1 Figure). According to the model, the calculated colony area approached its maximum once depleting the available glucose. Furthermore, increasing initial glucose levels in the model lad to larger maximum colony area as in the experiments. Finally, the model also produced a concave curve of colony area versus time at low glucose levels, and a convex curve at high glucose, as in the experiments (Figs. 1, 2 and S2 Supporting Figure). When we modified the model allowing cells to escape into the vertical direction, we obtained smaller colonies (S6 Figure). Overall, the mathematical models supported the hypothesis that FLO11 yeast colonies tend to grow along the agar surface, which limits their degrees of freedom, leading to larger colony sizes and more irregular colony shapes compared to flo11Δ cells that are free to expand vertically.

Bottom Line: Although the biochemical and molecular requirements for such patterns have been examined, the mechanisms underlying their formation are not entirely clear.Here we develop quantitative methods to accurately characterize the size, shape, and surface patterns of yeast colonies for various combinations of agar and sugar concentrations.We combine these measurements with mathematical and physical models and find that FLO11 gene constrains cells to grow near the agar surface, causing the formation of larger and more irregular colonies that undergo hierarchical wrinkling.

View Article: PubMed Central - PubMed

Affiliation: Department of Systems Biology, The University of Texas MD Anderson Cancer Center, Houston, Texas, United States of America.

ABSTRACT
Yeasts can form multicellular patterns as they expand on agar plates, a phenotype that requires a functional copy of the FLO11 gene. Although the biochemical and molecular requirements for such patterns have been examined, the mechanisms underlying their formation are not entirely clear. Here we develop quantitative methods to accurately characterize the size, shape, and surface patterns of yeast colonies for various combinations of agar and sugar concentrations. We combine these measurements with mathematical and physical models and find that FLO11 gene constrains cells to grow near the agar surface, causing the formation of larger and more irregular colonies that undergo hierarchical wrinkling. Head-to-head competition assays on agar plates indicate that two-dimensional constraint on the expansion of FLO11 wild type (FLO11) cells confers a fitness advantage over FLO11 knockout (flo11Δ) cells on the agar surface.

Show MeSH