Formal reasoning about synthetic biology using higher-order-logic theorem proving

Area of Science:

• Synthetic biology
• Formal methods
• Computational biology

Background:

• Traditional analysis of biological systems in synthetic biology relies on paper-and-pencil proofs and simulations.
• These conventional methods have inherent limitations, often failing to ensure accurate results.
• There is a need for more rigorous and accurate analytical approaches in synthetic biology.

Purpose of the Study:

• To propose and utilize higher-order-logic (HOL) theorem proving as a complementary approach for analyzing linear biological systems.
• To develop a HOL-based mathematical model for genetic circuits and bio-controllers.
• To ensure accuracy in the analysis of synthetic biology systems through deductive reasoning.

Main Methods:

• Developing mathematical models of genetic circuits and bio-controllers using HOL.
• Employing deductive reasoning within an interactive theorem prover for analysis.
• Modeling continuous dynamics using differential equations and performing transfer function analysis with Laplace transforms within a theorem prover.

Main Results:

• Formal analysis of genetic circuits including activated/repressed expressions and autoactivation of proteins.
• Analysis of phase lag and lead controllers used in biological applications.
• Demonstration of HOL theorem proving's capability to accurately analyze complex biological system dynamics.

Conclusions:

• Higher-order-logic theorem proving offers a robust and accurate method for analyzing synthetic biology systems.
• This approach overcomes limitations of conventional analysis techniques.
• The integration of logic, mathematics, and deductive reasoning ensures reliable results for biological circuit and controller analysis.