# A Parametric Approach to Yeast Growth Curve Estimation and Standardization

[Doktorsavhandling]

The purpose of this thesis is to contribute to the understanding of yeast growth. It builds upon a dataset consisting of growth curves of 576 *Saccharomyces cerevisiae* mutants in eight different environments. The data will be a part of a publicly available phenotypic library, PROPHECY, containing growth curves and characteristics of viable *S. cerevisiae *mutants in a wide variety of growth conditions.

We compare the fits of modifications of logistic, Gompertz, and Chapman-Richards models for the growth curves. The comparisons indicate that the modified Chapman-Richards model describes our growth data best. Relevant information about the behavior of the mutants is obtained by estimating physiologically important growth parameters such as lag time (time to adapt to the environmental change), maximum relative growth rate, and efficiency of growth. We introduce an alternative parameterization of the modified Chapman-Richards model that uses these growth parameters and investigate its uniqueness and parameter restrictions. We also show convexity of its logarithmic parameter space.

One of our findings is that the lag time and the growth rate depend strongly on the initial population size. However, in large-scale experiments with hundreds of strains, it is difficult to have the same constant initial population size. To address this problem and to enable easy visualization of the data, we develop a method to standardize growth curves with respect to the initial population size. The idea is to use a modified Chapman-Richards curve to predict what the behavior of a growth curve would have been, had the population had a fixed standard initial size. As a result, the initial population size correlation with lag time and growth rate reduces remarkably. We also introduce two ways to construct a summary curve from several standardized growth curves.

We suggest a set of filtering methods, based on the standardized and summary curves, in order to detect experiments and individual curves that are atypical or spurious. Finally, we compare the variability of wild type normalized mutant growth parameters from the modified Chapman-Richards, standardized, and summary curves. The variances are typically slightly smaller with the standardizing and summarizing methods than with the direct Chapman-Richards approach.

MSC2000 classification: 62P10

**Nyckelord: **bioscreen, Chapman-Richards model, growth curve, growth rate, lag time, optical density (OD), Saccharomyces cerevisiae, standardized curve, stationary phase OD increment, summary curve

Denna post skapades 2005-12-03. Senast ändrad 2013-09-25.

CPL Pubid: 5618