Boolean Networks (BNs) are an efficient modeling formalism with applications in various research fields such as mathematics, computer science, and more recently systems biology. One crucial problem in the BN research is to enumerate all fixed points, which has been proven crucial in the analysis and control of biological systems. Indeed, in that field, BNs originated from the pioneering work of R. Thomas on gene regulation and from the start were characterized by their asymptotic behavior: complex attractors and fixed points. The former being notably more difficult to compute exactly, and specific to certain biological systems, the computation of stable states (fixed points) has been the standard way to analyze those BNs for years. However, with the increase in model size and complexity of Boolean update functions, the existing methods for this problem show their limitations. To our knowledge, all the state-of-the-art methods for the fixed point enumeration problem rely on Answer Set Programming (ASP). Motivated by these facts, in this work we propose two new efficient ASP-based methods to solve this problem. We evaluate them on both real-world and pseudo-random models, showing that they vastly outperform four state-of-the-art methods as well as can handle very large and complex models.
The newly proposed encodings not only overcome the inherent bottlenecks of the existing ones but also possess several characteristic advantages in the sense of ASP. Furthermore, these results exhibit the great potential of ASP to tackle complex challenges in biology. Specifically, we plan to generalize the proposed ASP encodings to handle more complex problems in Boolean networks (possibly in multi-valued networks and Petri nets that are also prominent modeling formalisms in systems biology), such as, the enumeration of trap spaces and the enumeration of complex attractors.
Symbiose groups seminars: https://www.cesgo.org/symbiose/seminars/efficient-enumeration-of-fixed-…