DREISS: Using State-Space Models to Infer the Dynamics of Gene Expression Driven by External and Internal Regulatory Networks

Daifeng Wang, Fei He, Sergei Maslov, Mark Gerstein

Abstract: Author Summary The dynamics of a biological system can be controlled by its own internal mechanisms and external perturbations. To gain intuition on this, we may draw a comparison with a mass hanging from a spring. The mass will move naturally by itself but its dynamics is also affected by one’s pulling it. That is, the dynamics of the mass is governed by the effect of the external perturbations superimposed on the internal mechanism of the spring (i.e. Hooke’s law). Similarly, given a group of genes, their temporal gene expression dynamics can be controlled by both transcription factors inside the group and external regulatory factors. Therefore, it is useful to identify the expression dynamics that are exclusively controlled by internal or external factors and compare them across various systems. While state-space models have been widely used to decouple the internal and external effects in physical systems, such as the mass and spring, typical biological systems do not have enough time samples to infer all the model’s parameters, and applications of state-space models were not very effective in these instances. Hence, we developed a general-purpose computational method by integrating state-space models and dimensionality reduction to identify temporal gene expression patterns driven by internal and external regulatory networks. We applied our method to the embryonic developmental datasets in the worm and fly (and also in a human cancer context). We successfully identified the temporal expression dynamics of cross-species conserved genes that were driven by conserved and species-specific regulatory networks.