Predicting microbial growth dynamics in response to nutrient availability

Developing mathematical models to accurately predict microbial growth dynamics remains a key challenge in ecology, evolution, biotechnology, and public health. To reproduce and grow, microbes need to take up essential nutrients from the environment, and mathematical models classically assume that the nutrient uptake rate is a saturating function of the nutrient concentration. In nature, microbes experience different levels of nutrient availability at all environmental scales, yet parameters shaping the nutrient uptake function are commonly estimated for a single initial nutrient concentration. This hampers the models from accurately capturing microbial dynamics when the environmental conditions change. To address this problem, we conduct growth experiments for a range of micro-organisms, including human fungal pathogens, baker’s yeast, and common coliform bacteria, and uncover the following patterns. We observed that the maximal nutrient uptake rate and biomass yield were both decreasing functions of initial nutrient concentration. While a functional form for the relationship between biomass yield and initial nutrient concentration has been previously derived from first metabolic principles, here we also derive the form of the relationship between maximal nutrient uptake rate and initial nutrient concentration. Incorporating these two functions into a model of microbial growth allows for variable growth parameters and enables us to substantially improve predictions for microbial dynamics in a range of initial nutrient concentrations, compared to keeping growth parameters fixed.Author summary: Our ability to predict microbial population dynamics is of key importance for the fields of ecology, evolution, biotechnology, and public health. Yet, current mathematical models used to predict microbial growth have an inherent limitation. They are parameterised using empirical measurements of microbial growth performed at a single initial nutrient concentration. This overlooks the fact that in nature microbes face different levels of nutrient availability at all environmental scales: from glucose fluctuations in the blood of critically ill patients to dissolved organic carbon fluctuations in marine environments. Current literature overwhelmingly suggests that estimating growth parameters at a single initial nutrient concentration hampers the models from accurately capturing microbial dynamics when the environmental conditions change. Here we tackle this problem using an interplay between mathematical modelling and laboratory experiments spanning human fungal pathogens, common coliform bacteria, and baker’s yeast. We propose a modelling approach that incorporates growth parameters as a function of initial nutrient concentration. Importantly, we demonstrate that our approach performs significantly better at predicting microbial growth and the outcomes of between-species competition across different initial nutrient concentrations, compared to the classical models which assume fixed growth parameters.