Formal Analysis of the Biological Circuits using Higher-order-logic Theorem Proving

Adnan Rashid

Synthetic Biology is an interdisciplinary field that utilizes well-established engineering principles, ranging from electrical, control and computer systems, for analyzing the biological systems, such as biological circuits, enzymes, pathways and controllers. Traditionally, these biological systems, i.e., the genetic circuits are analyzed using paper-and-pencil proofs and computer-based simulations techniques. However, these methods cannot provide accurate results due to their inherent limitations such as human error-proneness, round-off errors and the unverified algorithms present in the core of the tools, providing such analyses. We propose to use higher-order-logic theorem proving as a complementary technique for analyzing these systems and thus overcome the above-mentioned issues. It is based on developing a mathematical model of the underlying system based on an appropriate logic and analyzing it using deductive reasoning. The involvement of the mathematics and the logical reasoning in this technique ensures the accuracy of the analysis. In this paper, we propose a higher-order-logic theorem proving based framework to formally reason about the genetic circuits used in synthetic biology. The main idea is to, first, model the continuous dynamics of the genetic circuits using differential equations. The next step is to obtain the systems’ transfer function from their corresponding block diagram representations. Finally, the transfer function based analysis of these differential equation based models is performed using the Laplace transform. To illustrate the practical utilization of our proposed framework, we formally analyze the genetic circuits of activated and repressed expressions of protein.

Proof Script

Contact Information

Adnan Rashid is a Research Associate in the System Analysis & Verification (SAVe) Lab of NUST-SEECS, under the supervision of Dr. Osman Hasan.