Fitting multiple bacterial growth data using continued fraction of straight lines.

Abstract

The growth of a population is the net result of growth and decline in the number of individuals over time. A population grows when the increase in number of individuals is more than the decrease and declines in the opposite scenario. In other words, the growth rate of a population is influenced by two opposing factors, a growth promoting factor and a growth restricting factor. In this work, we estimate growth rates by applying a biological growth model that is based on the continued fraction of straight lines with two parameters a and m. The parameters a and m represent nonlinear i.e. growth restricting and linear i.e. growth promoting parts of the model, respectively. To fit this model, we use a publicly available dataset that exhibits the growth of three different strains of bacteria depending on the concentration gradient of the antibiotic Tetracycline. We also propose a method to automatically estimate growth rates for large-scale applications. Finally, a growth coordinate system with a and m as the axes is used to interpret the estimations. ImportanceIn this work, multiple bacterial growth data has been fitted with a model based on continued fraction of linear growth. The importance of this work lies in the fitting of both growth and death phase with a single model. Rather than modeling growth with differential equations, this model uses algebraic expressions. Therefore, the growth rates are obtained directly from these expressions after fitting. Several of these models can be superposed, and more flexible fits can be obtained based on requirements. There are two parameters that play key roles in fitting. Their values can be expressed on planar plots which are useful to compare multiple growth data. Thus, this methodology provides simpler, generic, flexible and more interpretable growth models.