A Bayesian non-parametric mixed-effects model of microbial growth curves

Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genetics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth behavior through a set of summarizing parameters. However, estimation of these parameters from data is confounded by random effects such as experimental variability, batch effects or differences in experimental material. A systematic statistical method to identify and correct for such confounding effects in population growth data is not currently available. Further, our previous work has demonstrated that parametric models are insufficient to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding effects on measured population growth.Author summary: Quantifying how microbes grow in response to stress is required for effective treatment of microbial infections, food safety, and understanding the effects of environmental change. Current models that quantify microbial growth characteristics such as exponential growth rate are based on assumptions that microbial growth curves will adopt a sigmoid form with characteristic lag, logarithmic, and stationary phases. These models are therefore inaccurate when applied to microbes growing under stress. Substantial variability across experiments that measure microbial growth further compounds the issue. Here we report a new statistical model freed from the assumption of optimum growth. This model also properly corrects for experimental variability, enabling researchers to monitor, quantify, and understand how microbial growth changes in response to gradations of stress. We apply this model to two microbial test systems to accurately quantify how pathogenic bacteria respond to acidic antimicrobial treatments, and how environmentally important microbes withstand stress.