Modelling the Dynamics of Biological Systems with the Geometric Hidden Markov Model

Many biological processes can be described geometrically in a simple way: stem cell differentiation can be represented as a branching tree and cell division can be depicted as a cycle. In this paper we introduce the geometric hidden Markov model (GHMM), a dynamical model whose goal is to capture the low-dimensional characteristics of biological processes from multivariate time series data. The framework integrates a graph-theoretical algorithm for dimensionality reduction with a latent variable model for sequential data. We analyzed time series data generated by an in silico model of a biomolecular circuit, the represillator. The trained model has a simple structure: the latent Markov chain corresponds to a two-dimensional lattice. We show that the short-term and long-term predictions of the GHMM reflect the oscillatory behaviour of the genetic circuit. Analysis of the inferred model with a community detection methods leads to a coarse-grained representation of the process.