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

机译:一个简单的数学模型,描述了酵母的生长面积以及总细胞数和活细胞数群落

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摘要

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 twoudseparate 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.
机译:我们提出基于Gompertz方程的模型,以描述琼脂培养基上酵母菌落的生长。该模型具有几个优点:(i)一个方程式描述了菌落的生长,以前需要两个不分开的菌落(半径的线性增加和半径的平方); (ii)因为成熟菌落中的总细胞数与其面积成正比,所以可以对总细胞和存活细胞,菌落面积或菌落半径应用类似的方程式; (iii)其参数估计细胞产量,触发生长限制的细胞浓度以及该限制对比生长速率的影响。为了阐述模型,面积,总细胞和活细胞,对600个酿酒酵母,Fabricy Debaryomyces,rouxii Zygosaccharomyces和Rhodotorula glutinis菌落进行了测定。接种量低时,当菌落不可见时,活细胞显示出初始的短指数期。随着接种量的增加,该阶段缩短。在可见或成熟的菌落中,细胞生长表现出Gompertz型动力学。得出的结论是,菌落中的细胞生长仅在最初的几个小时(其余时间)与液体培养相似,并且至少在3周内具有接近零的比生长速率。

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