Modeling Bacterial Population Growth from Stochastic Single-Cell Dynamics

Abstract

bA few bacterial cells may be sufficient to produce a food-borne illness outbreak, provided that they are capable of adapting and proliferating on a food matrix. This is why any quantitative health risk assessment policy must incorporate methods to accurately predict the growth of bacterial populations from a small number of pathogens. In this aim, mathematical models have become a powerful tool. Unfortunately, at low cell concentrations, standard deterministic models fail to predict the fate of the population, essentially because the heterogeneity between individuals becomes relevant. In this work, a stochastic differential equation (SDE) model is proposed to describe variability within single-cell growth and division and to simulate population growth from a given initial number of individuals. We provide evidence of the model ability to explain the observed distributions of times to division, including the lag time produced by the adaptation to the environment, by comparing model predictions with experiments from the literature for Escherichia coli, Listeria innocua, and Salmonella enterica. The model is shown to accurately predict experimental growth population dynamics for both small and large microbial populations. The use of stochastic models for the estimation of parameters to successfully fit experimental data is a particularly challenging problem. For instance, if Monte Carlo methods are employed to model the required distributions of times to division, the parameter estimation problem can become numerically intractable. We overcame this limitation by converting the stochastic description to a partial differential equation (backward Kolmogorov) instead, which relates to the distribution of division times. Contrary to previous stochastic formulations based on random parameters, the present model is capable of explaining the variability observed in populations that result from the growth of a small number of initial cells as well as the lack of it compared to populations initiated by a larger number of individuals, where the random effects become negligible. Often bacterial contamination of foods starts with a small number of bacteria that are capable of adapting and proliferating by repeated divisions on a given food matrix. At low cell concentrations, standard deterministic models fail to predict the variability of the bacterial population. This is so because at low initial cell numbers, heterogeneity between individuals and its influence on the division times become relevant and have a net influence on the population. Consequently, the behavior of individual bacteria cannot be neglected when assessing possible health risks along the food chain, either during storage or during distribution.Recently, attention has been drawn to the need for modeling and simulation methods to observe and describe the variability of singlecell behavior and small populations (1, 2) in order to produce realistic estimations of safety risks along the food chain, for instance, during storage and distribution or during food pro...

Identification of Unknown Carboxydovore Bacteria Dominant in Deciduous Forest Soil via Succession of Bacterial Communities, coxL Genotypes, and Carbon Monoxide Oxidation Activity in Soil Microcosms

“…Although microbial succession was shaped by stochasticity in the colonial growth dynamic of individual cells (42) and alteration of the chemical structure and bioavailability of soil organic carbon due to autoclaving (43), the taxonomic affiliation of coxL genotypes inferred from phylogenetic analysis resulted in similar distributions compared with the observations made using native deciduous soil (21). Actinobacteria, Alphaproteobacteria, and coxL group x were the dominating coxL genotypes, representing 31% Ϯ 3%, 14% Ϯ 3%, and 53% Ϯ 3% of the total sequences, respectively.…”

Microbiologia Preditiva: Aspectos Gerais E Tendências

“…A vantagem em utilizar modelos estocásticos dá-se pelo fato destes permitirem descrever variabilidade e incerteza, aumentando a qualidade da predição (ALONSO et al, 2014;MEJLHOLM et al, 2015). Modelos estocásticos são compostos por equações probabilísticas que trabalham com a variabilidade dos indivíduos (ANDREONI et al, 2014;GOEL & RICHTER-DYN, 2016).…”

Microrisk Lab: an online freeware for predictive microbiology

“…This functionality may practically help users update the knowledge for the simulation when new evidence is observed. Meanwhile, it is also critical to take account of the uncertainty and variability of model parameters, especially in the application of the individual cell behavior modeling and risk assessment (Natau, 2001;Busschaert, Geeraerd, Uyttendaele, & Van Impe, 2011;Cornu et al, 2011;Koutsoumanis & Lianou, 2013;Alonso, Molina, & Theodoropoulos, 2014;Augustin et al, 2014). Thus, it is essential to introduce the stochastic approach in the prediction and simulation study.…”