Mathematical Modeling of Bacterial Growth Using Spline Interpolation and Nonlinear Models
Keywords:
bacterial growth, Logistic Model, Gompertz Model, mathematical modelingAbstract
Bacterial growth modeling is important in food biotechnology, agricultural microbiology, and veterinary medicine. Mathematical models allow estimation of biological parameters and optimization of fermentation processes. This study analyzes bacterial growth using optical density (OD600) measurements over time. Mathematical tools such as interpolation and growth parameter estimation were used to describe the dynamics of microbial biomass. Key biological parameters including growth rate, lag time, and doubling time were estimated from the experimental data. Optical density (OD600) measurements were recorded over a 20‑hour growth experiment. Interpolation was used to visualize the growth curve and numerical differentiation was used to estimate growth rate parameters. The estimated parameters are consistent with typical bacterial growth patterns observed in laboratory cultures. The interpolation curve provides a smooth visualization of biomass increase during the exponential phase and the stationary phase. Mathematical modeling provides a useful framework for analyzing microbial growth dynamics. The methods demonstrated here can be applied in biotechnology, food fermentation studies, and microbial ecology research.
References
Krueger, Justin Michael. "Parameter estimation methods for ordinary differential equation models with applications to microbiology." (2017).
Rolfe, Matthew D., et al. "Lag phase is a distinct growth phase that prepares bacteria for exponential growth and involves transient metal accumulation." Journal of bacteriology 194.3 (2012): 686-701.
Yates, George T., and Thomas Smotzer. "On the lag phase and initial decline of microbial growth curves." Journal of theoretical biology 244.3 (2007): 511-517.
Huang, Lihan. "Optimization of a new mathematical model for bacterial growth." Food Control 32.1 (2013): 283-288.
Zwietering, M. H., F. M. Rombouts, and K. van'T. Riet. "Comparison of definitions of the lag phase and the exponential phase in bacterial growth." Journal of Applied Microbiology 72.2 (1992): 139-145.
López, Sophie, et al. "Statistical evaluation of mathematical models for microbial growth." International journal of food microbiology 96.3 (2004): 289-300.
Hifzan, R. M., et al. "Analysis of Growth Curve with Non-Linear Models of Gompertz and Logistics Model in Female Katjang X Boer Goats in Malaysia." Tropical Animal Science Journal 47.2 (2024).
Akın, Elvan, et al. "Parameter identification for gompertz and logistic dynamic equations." PLoS One 15.4 (2020): e0230582.
Gautam, Lokesh, et al. "Estimation of growth curve parameters using non-linear growth curve models in sonadi sheep." International Journal of Livestock Research 8.9 (2018): 104-113.
Skinner, Guy E., John W. Larkin, and E. Jeffery Rhodehamel. "Mathematical modeling of microbial growth: a review." Journal of food safety 14.3 (1994): 175-217.
