Logic Integer Programming Models for Signaling Networks

TL;DR

This paper introduces logic and integer programming models for biological signaling networks, enabling qualitative and quantitative analysis with standard software, and includes dynamic models for efficient enumeration of solutions.

Contribution

It presents novel static and dynamic modeling approaches using propositional logic and integer programming for signaling networks in biology.

Findings

Logic models can be solved with standard software.

For certain problems, models reduce to polynomial-time satisfiability.

Dynamic models enable enumeration of solutions in poly-logarithmic time.

Abstract

We propose a static and a dynamic approach to model biological signaling networks, and show how each can be used to answer relevant biological questions. For this we use the two different mathematical tools of Propositional Logic and Integer Programming. The power of discrete mathematics for handling qualitative as well as quantitative data has so far not been exploited in Molecular Biology, which is mostly driven by experimental research, relying on first-order or statistical models. The arising logic statements and integer programs are analyzed and can be solved with standard software. For a restricted class of problems the logic models reduce to a polynomial-time solvable satisfiability algorithm. Additionally, a more dynamic model enables enumeration of possible time resolutions in poly-logarithmic time. Computational experiments are included.