Continuous rate modeling of bacterial stochastic size dynamics

Area of Science:

• Microbiology
• Theoretical Biology
• Biophysics

Background:

• Bacterial division is inherently stochastic, leading to cell size and protein concentration variability.
• Existing models for stochastic cell-size dynamics are limited and often phenomenological.

Purpose of the Study:

• To develop a general theoretical framework for modeling stochastic bacterial cell-size dynamics.
• To investigate the impact of different division strategies, noisy growth, and cell splitting on bacterial population heterogeneity.

Main Methods:

• Utilized the Chapman-Kolmogorov equation to model continuous growth and division as jump processes.
• Incorporated stochasticity in growth rates, division times, septum position, and initial cell size.
• Analyzed synchronized bacterial populations to predict oscillations in size distribution moments and autocorrelation functions.

Main Results:

• Predicted oscillations in the central moments and autocorrelation function of bacterial size distribution with a period of one doubling time.
• Demonstrated that these oscillations persist despite stochasticity in division times and initial size heterogeneity.
• Showed that oscillations are eliminated only by introducing noise in growth rate or septum position.

Conclusions:

• A robust mathematical framework is essential for understanding the detailed mechanisms of stochastic biological processes.
• The developed model provides a powerful tool to evaluate the effects of different variability sources in bacterial division.
• This approach enhances our comprehension of phenotype variability and informs the development of simplified models.