Motifs emerge from function in model gene regulatory networks

Abstract

Gene regulatory networks allow the control of gene expression patterns in living cells. The study of network topology has revealed that certain subgraphs of interactions or "motifs" appear at anomalously high frequencies. We ask here whether this phenomenon may emerge because of the functions carried out by these networks. Given a framework for describing regulatory interactions and dynamics, we consider in the space of all regulatory networks those that have prescribed functional capabilities. Markov Chain Monte Carlo sampling is then used to determine how these functional networks lead to specific motif statistics in the interactions. In the case where the regulatory networks are constrained to exhibit multistability, we find a high frequency of gene pairs that are mutually inhibitory and self-activating. In contrast, networks constrained to have periodic gene expression patterns (mimicking for instance the cell cycle) have a high frequency of bifan-like motifs involving four genes with at least one activating and one inhibitory interaction.essential interactions | genetic switch | transcription factors E volutionary forces have shaped living organisms since the beginning of life. It is thus not surprising that the framework for understanding features in today's organisms is often based on considering the history of these organisms: a remarkable feature found today may be the trace of an evolutionary trajectory. But one can also take a different perspective, one in which design constraints may play a significant role. The expectation is then that the architecture of living organisms depends not just on their origin, but also on their functional capabilities. In the present context, we are concerned with biological networks. Are the constraints associated with network functionality major determinants of network architecture? We address this question in this paper, albeit using a somewhat narrow notion of functionality based on the output patterns produced by networks.Our focus here is on gene regulatory networks (GRN), the set of interactions between genes. These interactions along with the gene expression machinery allow living cells to control their gene expression patterns. In the last decade, genetic interactions have been measured, modified, engineered, etc., and so quite a lot is known about how any given gene can affect another's expression. Furthermore, small gene networks have been designed to implement simple functions in vivo (1, 2), and much larger sets of interactions have been reconstructed in a number of organisms (3-5). From these large networks it has been possible to show that several "motifs"-subgraphs with given interactions-arise far more often than might be expected (6-9). One of the most studied motif is the so called Feed Forward Loop or FFL, a graph based on three genes where the first regulates the second, and both the first and the second regulate the third. Another example is the bifan motif in which two genes control two others. Biological functions have been proposed for these moti...

Neutral forces acting on intragenomic variability shape the Escherichia coli regulatory network topology

“…These results have been adopted in the systems biology community to the point that "feed-forward loops", "single-input module", and "bifan" are synonymous with motif. Subsequent work has linked the ubiquity of these motifs to convergent evolution driven by functional requirements (14,20). However, when using our evolutionary model, which accounts for events at the genomic level, it emerges that FFLs, SIMs, and bifans all occur within frequencies expected by neutral evolution.…”

“…However, it has been shown that when subjecting CRNs to the various neutral evolutionary forces and tracing their trajectory in time, many of these topological patterns may simply arise spontaneously due to the forces of mutation, recombination, gene duplication, and genetic drift (10, 12). These studies call into question arguments that were made in favor of adaptive explanations for the emergence and conservation of CRN properties (8,(13)(14)(15) and identify important parameters that may significantly affect the evolution of CRNs from a neutral perspective. Specifically (12), they highlighted the role that promoter length, binding-site size, and population size may play in forming certain topological patterns known as motifs.…”

Design principles for robust oscillatory behavior

“…Several studies have made contributions towards identifying some design principles for oscillatory behaviour. Network motifs-recurrent patterns of interactions believed to form the building blocks of any complex network (Milo et al 2002;Yeger-Lotem et al 2004;Barabasi and Oltvai 2004;Alon 2007;Kim et al 2010)-have also been highlighted to some extent for oscillators (Ferrell et al 2011;Wagner 2005;Novak and Tyson 2008;Tsai et al 2008;Burda et al 2011;Lomnitz and Savageau 2014;Noman et al 2015;Semenov et al 2015).…”

The Role of Genotype in the Predictability of Dynamical Behavior in Complex Model Gene Regulatory Networks

“…The relationship of transcriptional repressors to oscillating networks has been previously studied [45,46]. Negative feedback loops (analogous to gene expression suppression) have been associated with oscillating behavior in many biological systems [47], including E. coli [48], the Neurospora circadian oscillator [49], the cell cycle [50], the lac operon system [51] the p53-mdm2 system [52] and NF-kappa B translocation [53].…”