Detecting differential growth of microbial populations with Gaussian process regression

Abstract

Microbial growth curves are used to study differential effects of media, genetics, and stress on microbial population growth. Consequently, many modeling frameworks exist to capture microbial population growth measurements. However, current models are designed to quantify growth under conditions for which growth has a specific functional form. Extensions to these models are required to quantify the effects of perturbations, which often exhibit nonstandard growth curves. Rather than assume specific functional forms for experimental perturbations, we developed a general and robust model of microbial population growth curves using Gaussian process (GP) regression. GP regression modeling of high-resolution time-series growth data enables accurate quantification of population growth and allows explicit control of effects from other covariates such as genetic background. This framework substantially outperforms commonly used microbial population growth models, particularly when modeling growth data from environmentally stressed populations. We apply the GP growth model and develop statistical tests to quantify the differential effects of environmental perturbations on microbial growth across a large compendium of genotypes in archaea and yeast. This method accurately identifies known transcriptional regulators and implicates novel regulators of growth under standard and stress conditions in the model archaeal organism Halobacterium salinarum. For yeast, our method correctly identifies known phenotypes for a diversity of genetic backgrounds under cyclohexamide stress and also detects previously unidentified oxidative stress sensitivity across a subset of strains. Together, these results demonstrate that the GP models are interpretable, recapitulating biological knowledge of growth response while providing new insights into the relevant parameters affecting microbial population growth.

Systematic Discovery of Archaeal Transcription Factor Functions in Regulatory Networks through Quantitative Phenotyping Analysis

“…The effects of stress and genetics on growth are then quantified by testing for statistically significant differences in the estimated parameters for different conditions ( 46 ). However, we previously showed that the impact of genetics and stress perturbations on growth are more accurately captured with a nonparametric Gaussian process (GP) model ( 35 ). In contrast to parametric models, GPs have the advantage of learning these relations directly from the data and do not require explicit equations describing the effects of stress and genetics on growth, which are typically unknown in the case of phenotypic discovery.…”

“…A novel nonparametric model was developed using a Gaussian process framework to quantify these phenotypes. We used recently developed statistical tests ( 35 ) and developed new tests to identify significant differential growth between the trajectories of these TF knockouts relative to that of the control strain. The results revealed that a surprising number of TFs are required for optimal growth under multiple stress conditions, indicating a high level of interconnectivity within the GRN.…”

Systems biology analysis of the Clostridioides difficile core-genome contextualizes microenvironmental evolutionary pressures leading to genotypic and phenotypic divergence

“…The significant increase in growth at 10 mM supplementation of trehalose indicates that the substitution may increase affinity of the PTS for trehalose transport, improve efficiency of transport, or increase expression and/or stability of the transporter however the role of the this E258D substitution in trehalose uptake still needs to be explored. Analysis of the growth curves by Gaussian Process modeling 38 allowed us to quantify growth rate, area under the curve, and carrying capacity of the isolates in each condition (Fig. 3C ).…”

A decay effect of the bacterial growth rate associated with genome reduction

“…To describe and/or predict S-shaped growth curves, a number of mathematical models have been proposed, such as the Logistic (Verhulst, 1845; 1847) and Gompertz (Winsor, 1932) models, and revised and expanded repeatedly to better understand the biological process of bacterial growth under varied conditions (Fujikawa and Morozumi, 2005; Kargi, 2009; Koseki and Nonaka, 2012; Alonso et al, 2014; Desmond-Le Quemener and Bouchez, 2014; Hermsen et al, 2015). Although the growth curve of the most representative bacterium, Escherichia coli , has been examined since the 1930s (Winsor, 1932), the indescribable complexity of the growth dynamics of E. coli remain and are still under investigation with other models to understand the current differential growth dynamics (Swain et al, 2016; Tonner et al, 2017).…”