Individual-based and stochastic modeling of cell population dynamics considering substrate dependency

Modeling bacterial population dynamics remains a challenge in systems biology. Deterministic models often fail to capture the variability seen in real-world cultures. Prior research has shown that deterministic approaches may miss the impact of random fluctuations in cell division and gene expression. However, no prior work had resolved how these stochastic effects interact with substrate-dependent growth kinetics. This gap motivated the development of a model that integrates both individual-level randomness and population-level substrate dependencies. Existing models typically treat cell populations as uniform entities, ignoring heterogeneity among individual cells. This limitation restricts their ability to predict responses to fluctuating substrate levels. The need for a more nuanced approach led researchers to explore individual-based modeling techniques. These methods allow for the simulation of each cell's unique behavior within a population.

The aim of this study was to develop a modeling framework that incorporates both individual-level stochasticity and substrate-dependent growth kinetics. Researchers sought to determine how random variations in cell behavior affect population-level outcomes. The specific problem addressed was the lack of models that simultaneously account for intracellular randomness and substrate inhibition effects. By integrating discrete event simulation with cell growth sub-models, the authors aimed to better represent real-world bacterial dynamics. This approach allows for the investigation of how different growth kinetics influence population behavior. The motivation stemmed from the observation that deterministic models often fail to capture observed variability in cultures. The study also aimed to explore how substrate levels interact with stochastic processes. This work provides a new tool for simulating bacterial cultures under varying environmental conditions.

The researchers constructed an individual-based model using discrete event simulation. Each cell in the model was represented as an independent agent with its own growth kinetics. A sub-model describing cell growth was embedded within the simulation framework. This sub-model could be switched between different kinetic expressions, such as Monod or Andrews kinetics. The model tracked cell division and substrate consumption at the individual level. Random fluctuations in gene expression and division events were simulated using probability distributions. The simulation algorithm advanced in discrete time steps, updating cell states and substrate levels accordingly. The model's output included population distributions, cell mass, and substrate concentration over time.

When Monod kinetics were applied, stochastic effects had minimal impact on overall population growth. Substrate consumption and cell mass increase followed predictable trends despite random fluctuations. However, stochasticity still influenced the distribution of cell sizes and division times. Under Andrews kinetics, the model revealed significant effects of stochasticity on population dynamics. At low initial substrate levels, deterministic models predicted population decline due to inhibition. Stochastic simulations showed that some cells could still proliferate under these conditions. The probability of successful growth increased with higher stochastic variation in division events. These findings suggest that randomness can enable survival in environments that would otherwise be inhibitory.

The authors demonstrated that stochasticity can significantly influence bacterial population dynamics. Their model revealed that randomness in cell behavior can counteract substrate inhibition effects. When using Monod kinetics, stochastic effects had limited impact on population growth profiles. However, under Andrews kinetics, stochasticity became a critical factor in determining population outcomes. The model showed that some cells could overcome substrate inhibition through random division events. These findings suggest that deterministic models may underestimate population resilience. The study highlights the importance of incorporating stochasticity in microbial growth models. The authors propose that future work should explore how these effects scale to larger populations and different environmental conditions.