A simple mathematical model that describes the growth of the area and the number of total and viable cells in yeast colonies


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Abstract

We propose a model, based on the Gompertz equation, to describe the growth of yeasts colonies on agar medium. This model presents several advantages: (i) one equation describes the colony growth, which previously needed two separate ones (linear increase of radius and of the squared radius); (ii) a similar equation can be applied to total and viable cells, colony area or colony radius, because the number of total cells in mature colonies is proportional to their area; and (iii) its parameters estimate the cell yield, the cell concentration that triggers growth limitation and the effect of this limitation on the specific growth rate. To elaborate the model, area, total and viable cells of 600 colonies of Saccharomyces cerevisiae, Debaryomyces fabryi, Zygosaccharomyces rouxii and Rhodotorula glutinis have been measured. With low inocula, viable cells showed an initial short exponential phase when colonies were not visible. This phase was shortened with higher inocula. In visible or mature colonies, cell growth displayed Gompertz-type kinetics. It was concluded that the cells growth in colonies is similar to liquid cultures only during the first hours, the rest of the time they grow, with near-zero specific growth rates, at least for 3 weeks.Significance and Impact of the Study:Mathematical models used to predict microbial growth are based on liquid cultures data. Models describing growth on solid surfaces, highlighting the differences with liquids cultures, are scarce. In this work, we have demonstrated that a single Gompertz equation describes accurately the increase of the yeast colonies, up to the point where they reach their maximum size. The model can be used to quantify the differences in growth kinetics between solid and liquid media. Moreover, as all its parameters have biological meaning, it could be used to build secondary models predicting yeast growth on solid surfaces under several environmental conditions.

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