@inproceedings{YousefianDonatiSikorskietal.2026, author = {Yousefian, Maryam and Donati, Luca and Sikorski, Alexander and Weber, Marcus and R{\"o}blitz, Susanna}, title = {Exploring Metastable Dynamics of Gene Regulatory Networks with ISOKANN}, volume = {15959}, booktitle = {Computational Methods in Systems Biology. CMSB 2025}, doi = {10.1007/978-3-032-01436-8_8}, pages = {126 -- 149}, year = {2026}, abstract = {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.}, language = {en} } @article{SikorskiNiknejadWeberetal.2024, author = {Sikorski, Alexander and Niknejad, Amir and Weber, Marcus and Donati, Luca}, title = {Tensor-SqRA: Modeling the transition rates of interacting molecular systems in terms of potential energies}, volume = {160}, journal = {Journal of Chemical Physics}, arxiv = {http://arxiv.org/abs/2311.09779}, doi = {10.1063/5.0187792}, pages = {104112}, year = {2024}, abstract = {Estimating the rate of rare conformational changes in molecular systems is one of the goals of molecular dynamics simulations. In the past few decades, a lot of progress has been done in data-based approaches toward this problem. In contrast, model-based methods, such as the Square Root Approximation (SqRA), directly derive these quantities from the potential energy functions. In this article, we demonstrate how the SqRA formalism naturally blends with the tensor structure obtained by coupling multiple systems, resulting in the tensor-based Square Root Approximation (tSqRA). It enables efficient treatment of high-dimensional systems using the SqRA and provides an algebraic expression of the impact of coupling energies between molecular subsystems. Based on the tSqRA, we also develop the projected rate estimation, a hybrid data-model-based algorithm that efficiently estimates the slowest rates for coupled systems. In addition, we investigate the possibility of integrating low-rank approximations within this framework to maximize the potential of the tSqRA.}, language = {en} }