Gene regulatory network inference using out of equilibrium statistical mechanics

Abstract

Spatiotemporal control of gene expression is fundamental to multicellular life. Despite prodigious efforts, the encoding of gene expression regulation in eukaryotes is not understood. Gene expression analyses nourish the hope to reverse engineer effector-target gene networks using inference techniques. Inference from noisy and circumstantial data relies on using robust models with few parameters for the underlying mechanisms. However, a systematic path to gene regulatory network reverse engineering from functional genomics data is still impeded by fundamental problems. Recently, Johannes Berg from the Theoretical Physics Institute of Cologne University has made two remarkable contributions that significantly advance the gene regulatory network inference problem. Berg, who uses gene expression data from yeast, has demonstrated a nonequilibrium regime for mRNA concentration dynamics and was able to map the gene regulatory process upon simple stochastic systems driven out of equilibrium. The impact of his demonstration is twofold, affecting both the understanding of the operational constraints under which transcription occurs and the capacity to extract relevant information from highly time-resolved expression data. Berg has used his observation to predict target genes of selected transcription factors, and thereby, in principle, demonstrated applicability of his out of equilibrium statistical mechanics approach to the gene network inference problem.

Figure 1. Time delays and resulting Inference limits.

(A) Many different effective delay times might be observed in the coupling of cellular processes leading to transcription and mRNA stability regulation. Signal diffusion, transcription activation of a target gene in euchromatin or heterochromatin, mRNA elongation, maturing, export, specific and generic degradation, translation, and feedback all have different, often sequence or molecular species specific time constants. While most of these processes seem to occur on sufficient close time scales in order to permit modeling using minimal models without having to resort to multiscale approaches (Castiglione et al., 2008), documented cases such the one schematized in (B) pose a limit on inference in the absence of any additional information.

Figure 2. Time-scale heterogeneity in chromatin dynamics.

The author is convinced that due to a computer glitch, the “ultimate answer” was only mistakenly indicated as “42” and rather should have read “chromatin” (Adams, 1979). Chromatin structural and functional dynamics are known to happen at very different time and space scales. Chromatin “breathing,” the rapid local oscillations between a primed and an active state (Metivier, 2008) is likely as fast as transcription initiation “green arrows” and hence is probably sufficiently well captured by the noise term in the driven Langevin equation, whereas the establishment of, for instance, gene differentiation programs involves time scales at or in excess of cellular generation times “red arrows” and hence should have a significant contribution to the long-term behavior of the system. This aspect does not yet seem to be treated appropriately in the different modeling approaches, and it can be expected that faithful gene regulatory network inference will profit significantly from including chromatin dynamics in the models.