Determining the bistability parameter ranges of artificially induced lac operon using the root locus method

Area of Science:

• Systems Biology
• Molecular Biology
• Biophysics

Background:

• Gene regulatory networks (GRNs) exhibit complex behaviors like bistability, crucial for cellular differentiation and decision-making.
• The lac operon in Escherichia coli (E. coli) is a model system for studying gene regulation and bistability.
• Previous analyses of lac operon bistability lacked complete parametric conditions.

Purpose of the Study:

• To determine the necessary and sufficient parametric conditions for bistability in the E. coli lac operon.
• To apply the root locus method for a comprehensive analysis of GRN parameter spaces.
• To provide a framework for analyzing biological systems with parameter uncertainties.

Main Methods:

• Employed the root locus method applied to the polynomial equilibrium equation of the lac operon model.
• Utilized an ordinary differential equation system compatible with Hill and Michaelis-Menten kinetics.
• Treated model parameters as variables to analyze steady-state behavior under uncertainty.

Main Results:

• Derived a complete set of necessary and sufficient conditions for lac operon bistability.
• Identified specific parameter ranges that guarantee bistability.
• Demonstrated the applicability of the root locus method to diverse mass action kinetics-based models.

Conclusions:

• The root locus method offers a robust approach to analyzing GRN steady-state dynamics and parameter uncertainties.
• The identified bistability conditions can explain in vivo observations in E. coli.
• Findings support the design of synthetic biological hysteretic switches.