A Bayesian Non-parametric Mixed-Effects Model of Microbial Phenotypes

Abstract

4Substantive changes in gene expression, metabolism, and the proteome are manifested in overall changes in 5 microbial population growth. Quantifying how microbes grow is therefore fundamental to areas such as genet-6 ics, bioengineering, and food safety. Traditional parametric growth curve models capture the population growth 7 behavior through a set of summarizing parameters. However, estimation of these parameters from data is con-8 founded by random effects such as experimental variability, batch effects or differences in experimental material. 9 A systematic statistical method to identify and correct for such confounding effects in population growth data 10 is not currently available. Further, our previous work has demonstrated that parametric models are insufficient 11 to explain and predict microbial response under non-standard growth conditions. Here we develop a hierarchical 12 Bayesian non-parametric model of population growth that identifies the latent growth behavior and response to 13 perturbation, while simultaneously correcting for random effects in the data. This model enables more accurate 14 estimates of the biological effect of interest, while better accounting for the uncertainty due to technical variation. 15 Additionally, modeling hierarchical variation provides estimates of the relative impact of various confounding 16 effects on measured population growth. 17 1 1 Introduction 18Population growth phenotypes inform studies in microbiology, including gene functional discovery, bioengineering 19 process development, and food safety testing 1-3 . For example, recent advances in microbial functional genomics 20 and phenotyping, or "phenomics", have enabled transformative insights into gene functions, proving critical for 21 mapping the genotype to phenotype relationship 4 . Methods such as genome-wide CRISPRi 5 and targeted genome-22 scale deletion libraries 6,7 frequently rely upon accurate quantitation of microbial population growth as an assay to 23 identify novel mutants with significant growth phenotypes. Population growth is an aggregate measure of all cellular 24 processes and captures how microbial cells adapt and survive in their environmental niche 8 . Because microbial 25 population culturing is a necessary precursor to many experimental procedures in microbiology 9 , reproducible results 26 require accurate quantification of the variability in culture state measured through growth 9,10 . 27Typical analyses of microbial population growth involve estimating parametric models under the assumptions of 28 standard growth conditions comprised of three successive growth phases: (1) lag phase, in which the population adapts 29 to a new environment, typically fresh growth medium at culture inoculation; (2) log phase, when the population 30 grows exponentially at a rate dependent on nutrients in the environment; and (3) stationary phase, where measurable 31 population growth terminates thereby reaching the culture carrying capacity 11 . Recent studies have shown that the 32 estimat...