Formal Reasoning about Systems Biology using Theorem Proving

Adnan Rashid, 


System biology provides the basis to understand the behavioral properties of complex biological organisms at different levels of abstraction. Traditionally, analysing systems biology based models of various diseases have been carried out by paper-and-pencil based proofs and simulations. However, these methods cannot provide an accurate analysis, which is a serious drawback for the safety-critical domain of human medicine. In order to overcome these limitations, we propose a framework to formally analyze biological networks and pathways. In particular, we formalize the notion of reaction kinetics in higher-order logic and formally verify some of the commonly used reaction based models of biological networks using the HOL Light theorem prover. Furthermore, we have ported our earlier formalization of Zsyntax, i.e., a deductive language for reasoning about biological networks and pathways, from HOL4 to the HOL Light theorem prover to make it compatible with the above-mentioned formalization of reaction kinetics. To illustrate the usefulness of the proposed framework, we present the formal analysis of three case studies, i.e., the pathway leading to TP53 Phosphorylation, the pathway leading to the death of cancer stem cells and the tumor growth based on cancer stem cells, which is used for the prognosis and future drug designs to treat cancer patients.

Proposed Framework

Proof Script


Reaction Kinetics


  1. S. Ahmad, O. Hasan and U. Siddique, On the Formalization of Zsyntax with Applications in Molecular Biology, Scalable Computing: Practice and Experience, 16(1):37-51, 2015

  2. S. Ahmad, O. Hasan, U. Siddique and S. Tahar, Formalization of Z-Syntax to reason about Molecular Pathways in HOL4, Brazilian Symposium on Formal Methods (SBMF-2014), Springer LNCS 8941, pp. 32-47

  3. S. Ahmad, O. Hasan and U. Siddique, Towards Formal Reasoning about Molecular Pathways in HOL, 23rd IEEE International Conference on Enabling Technologies: Infrastructures for Collaborative Enterprises (WETICE), Parma, Italy, pp. 378 - 383.

Adnan Rashid is a PhD student at the School of Electrical Engineering and Computer Science of National University of Sciences and Technology. He is working on his PhD thesis in the System Analysis & Verification (SAVe) Lab of NUST-SEECS, under the supervision of Dr. Osman Hasan.