Markov state modelling

Markov state modelling is a powerful computational method for dimensionality reduction of metastable, high dimensional stochastic dynamical systems. By metastable systems, we mean systems with a multimodal stationary density. That means, there are regions in the state space (different modes of the stationary density), where the system dynamics remains for a very long time before it rapidly switches to another metastable region (mode). In other words, switches between different metastable regions (modes) are rare events.

Examples of such systems include molecular conformation dynamics, where the metastable regions are different geometrical states of a molecule (e.g. protein foldings), and stochastic gene-regulatory networks (GRNs), where the metastable regions correspond to cellular phenotypes.

Given the description of such systems on the micro-scale (e.g. the molecular force field or the propensity functions of a regulatory network), we are interested in the answers to the following questions related to the long-term behavior of the system:

  1. Is the system metastable and, if yes, where are the metastable regions located?
  2. What are the transition probabilities and transition pathways between different metastable regions?

Markov state modelling has been established for molecular dynamics, but to make this approach applicable for gene-regulatory networks, the algorithms have to be modified and adjusted towards non-reversible discrete dynamical systems.

This research has been funded from 2021-2025 by the Norwegian Research Council (FRIPRO project 324080). Our aim with this project is to develope new numerical algorithms and software tools that allow us to construct Markov State Models with quantified accuracy for high-dimensional stochastic gene-regulatory networks. We will demonstrate the relevance of Markov state modeling for understanding cellular phenotype switching by applying the algorithm to models for macrophage polarization, T-cell and stem cell differentiation.


Spectral clustering of Markov chain transition matrices with complex eigenvalue, arXiv 2022

Macrophage phenotype transitions in a stochastic gene-regulatory network model, bioRxiv 2022.

Bifurcation and sensitivity analysis reveal key drivers of multistability in a model of macrophage polarization. Journal of Theoretical Biology, 2020