Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN
- Stochastic dynamical systems like gene regulatory networks (GRNs) often exhibit behavior characterized by metastable sets (representing cellular phenotypes), in which trajectories remain for long times, whereas switches between these sets in the phase space are rare events. One way to capture these rare events is to infer the system’s long-term behavior from the spectral characteristics (eigenvalues and eigenvectors) of its Koopman operator. For GRNs, the Koopman operator is based on the chemical master equation (CME), which provides a precise mathematical modeling framework for stochastic GRNs. Since the CME is typically analytically intractable, methods based on discretizing the CME operator have been developed. However, determining the number and location of metastable sets in the phase space as well as the transition rates between them remains computationally challenging, especially for large GRNs with many genes and interactions. A promising alternative method, called ISOKANN (invariant subspaces of Koopman operators with artificial neural networks) has been developed in the context of molecular dynamics. ISOKANN uses a combination of the power iteration and neural networks to learn the basis functions of an invariant subspace of the Koopman operator. In this paper, we extend the application of ISOKANN to the CME operator and apply it to two small GRNs: a genetic toggle switch model and a model for macrophage polarization. Our work opens a new field of application for the ISOKANN algorithm and demonstrates the potential of this algorithm for studying large GRNs.
| Author: | Maryam YousefianORCiD, Luca DonatiORCiD, Alexander SikorskiORCiD, Marcus Weber, Susanna RöblitzORCiD |
|---|---|
| Document Type: | In Proceedings |
| Parent Title (English): | Computational Methods in Systems Biology. CMSB 2025 |
| Volume: | 15959 |
| First Page: | 126 |
| Last Page: | 149 |
| Series: | Lecture Notes in Computer Science |
| Year of first publication: | 2026 |
| DOI: | https://doi.org/10.1007/978-3-032-01436-8_8 |

