Our modeling work: structure, results, and what they mean for the project.
Understanding the growth dynamics of microbial populations is fundamental to evaluating the interactions between engineered and natural strains during co-culture. In this study, we established a set of ordinary differential equation (ODE) models to quantitatively describe the growth of each species under different conditions, including single-culture and co-culture systems. The models account for both intrinsic growth behavior and external factors such as nutrient limitation, competition, and antimicrobial inhibition.
For single-culture experiments, the model captures the characteristic sigmoidal growth pattern of bacteria, reflecting the transition from the exponential phase to the stationary phase as nutrients become limited. For co-culture systems, additional interaction terms are introduced to describe how one species affects the growth of another through competition for shared resources or through the secretion of inhibitory substances. In particular, engineered E. Coli strains that produce antimicrobial compounds, such as nisin, are modeled to investigate their suppressive effect on Streptococcus mutans in mixed cultures.
This modeling framework enables the estimation of key biological parameters such as maximum growth rate, carrying capacity, death rate, and inhibition strength. By fitting the model to experimental culture data, we can extract quantitative growth rates and interaction coefficients that characterize both natural and engineered microbial dynamics. These fitted parameters will provide a solid foundation for further comparison of growth efficiency, inhibitory potential, and ecological stability within the co-culture system.
The theoretical analysis of our model provides valuable insights into the underlying dynamics of the microbial system, even before incorporating experimental data. Through equilibrium and nondimensionalization analysis, we identified the key parameters that govern population stability and interspecies interactions. The dimensionless formulation simplifies the system by reducing parameter redundancy and highlights the relative importance of growth, inhibition, and competition terms. This reduction not only facilitates numerical simulation but also clarifies which biological processes most strongly influence system behavior.
The equilibrium analysis revealed multiple potential steady states corresponding to different ecological outcomes, such as coexistence, competitive exclusion, and dominance of the engineered strain. By examining the local stability of these equilibria, we can predict the parameter ranges under which the engineered microorganism successfully suppresses Streptococcus mutans growth. These findings offer theoretical support for designing and optimizing co-culture experiments, as they indicate how factors such as growth-rate ratios and inhibition strength determine the overall system outcome.
Although no experimental fitting has yet been conducted, the model establishes a solid foundation for future data integration. Once culture data are collected, the parameters obtained from fitting will enable quantitative validation of the theoretical predictions and further refinement of the model's assumptions.
This kind of mathematical model analysis serves as a guide for our results and leads us to improve our iGEM project. In this way, the current mathematical framework bridges conceptual understanding and experimental design, serving as a predictive tool for assessing microbial interaction strategies in engineered systems.