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.

Mapping the Transcriptional and Fitness Landscapes of a Pathogenic E. coli Strain: The Effects of Organic Acid Stress under Aerobic and Anaerobic Conditions.

Several methods are available to probe cellular responses to external stresses at the whole genome level. RNAseq can be used to measure changes in expression of all genes following exposure to stress, but gives no information about the contribution of these genes to an organism's ability to survive the stress. The relative contribution of each non-essential gene in the genome to the fitness of the organism under stress can be obtained using methods that use sequencing to estimate the frequencies of members of a dense transposon library grown under different conditions, for example by transposon-directed insertion sequencing (TraDIS). These two methods thus probe different aspects of the underlying biology of the organism. We were interested to determine the extent to which the data from these two methods converge on related genes and pathways. To do this, we looked at a combination of biologically meaningful stresses. The human gut contains different organic short-chain fatty acids (SCFAs) produced by fermentation of carbon compounds, and Escherichia coli is exposed to these in its passage through the gut. Their effect is likely to depend on both the ambient pH and the level of oxygen present. We, therefore, generated RNAseq and TraDIS data on a uropathogenic E. coli strain grown at either pH 7 or pH 5.5 in the presence or absence of three SCFAs (acetic, propionic and butyric), either aerobically or anaerobically. Our analysis identifies both known and novel pathways as being likely to be important under these conditions. There is no simple correlation between gene expression and fitness, but we found a significant overlap in KEGG pathways that are predicted to be enriched following analysis of the data from the two methods, and the majority of these showed a fitness signature that would be predicted from the gene expression data, assuming expression to be adaptive. Genes which are not in the E. coli core genome were found to be particularly likely to show a positive correlation between level of expression and contribution to fitness.

Synergistic Impacts of Organic Acids and pH on Growth of Pseudomonas aeruginosa: A Comparison of Parametric and Bayesian Non-parametric Methods to Model Growth.

Different weak organic acids have significant potential as topical treatments for wounds infected by opportunistic pathogens that are recalcitrant to standard treatments. These acids have long been used as bacteriostatic compounds in the food industry, and in some cases are already being used in the clinic. The effects of different organic acids vary with pH, concentration, and the specific organic acid used, but no studies to date on any opportunistic pathogens have examined the detailed interactions between these key variables in a controlled and systematic way. We have therefore comprehensively evaluated the effects of several different weak organic acids on growth of the opportunistic pathogen Pseudomonas aeruginosa. We used a semi-automated plate reader to generate growth profiles for two different strains (model laboratory strain PAO1 and clinical isolate PA1054 from a hospital burns unit) in a range of organic acids at different concentrations and pH, with a high level of replication for a total of 162,960 data points. We then compared two different modeling approaches for the interpretation of this time-resolved dataset: parametric logistic regression (with or without a component to include lag phase) vs. non-parametric Gaussian process (GP) regression. Because GP makes no prior assumptions about the nature of the growth, this method proved to be superior in cases where growth did not follow a standard sigmoid functional form, as is common when bacteria grow under stress. Acetic, propionic and butyric acids were all more detrimental to growth than the other acids tested, and although PA1054 grew better than PAO1 under non-stress conditions, this difference largely disappeared as the levels of stress increased. As expected from knowledge of how organic acids behave, their effect was significantly enhanced in combination with low pH, with this interaction being greatest in the case of propionic acid. Our approach lends itself to the characterization of combinatorial interactions between stressors, especially in cases where their impacts on growth render logistic growth models unsuitable.