An analytical approach to bistable biological circuit discrimination using real algebraic geometry

Area of Science:

• Systems Biology
• Synthetic Biology
• Biophysics

Background:

• Bistable biomolecular circuits are fundamental to biological networks.
• Understanding design differences is crucial for synthetic biology applications.
• Current methods for comparing bistable circuits can be complex.

Purpose of the Study:

• To explore the application of Sturm's theorem for comparing bistable circuits.
• To assess Sturm's theorem as a simulation-free analysis tool.
• To compare Sturm's theorem with existing methods like Routh-Hurwitz.

Main Methods:

• Application of Sturm's theorem from real algebraic geometry.
• Analysis of genetic toggle and positive feedback circuits.
• Comparison with the Routh-Hurwitz stability criterion.

Main Results:

• Sturm's theorem effectively compares functionally equivalent bistable circuits without numerical simulation.
• Specific circuit topologies influence the size of functional parameter space regions.
• A simple modification to a mutual repressor circuit can induce bistability.

Conclusions:

• Sturm's theorem provides a powerful and easy-to-use method for biomolecular circuit analysis.
• Algebraic geometric techniques may be underutilized in this field.
• The approach offers consistent and more powerful parametric conditions than Routh-Hurwitz.