Analysis of the structure of biological networks often uses statistical tests to establish the over-representation of motifs, which are thought to be important building blocks of such networks, related to their biological functions. However, there is disagreement as to the statistical significance of these motifs, and there are potential problems with standard methods for estimating this significance. Exponential random graph models (ERGMs) are a class of statistical model that can overcome some of the shortcomings of commonly used methods for testing the statistical significance of motifs. ERGMs were first introduced into the bioinformatics literature over ten years ago but have had limited application to biological networks, possibly due to the practical difficulty of estimating model parameters. Advances in estimation algorithms now afford analysis of much larger networks in practical time. We illustrate the application of ERGM to both an undirected protein-protein interaction (PPI) network and directed gene regulatory networks. ERGM models indicate over-representation of triangles in the PPI network, and confirm results from previous research as to over-representation of transitive triangles (feed-forward loop) in an E. coli and a yeast regulatory network. We also confirm, using ERGMs, previous research showing that under-representation of the cyclic triangle (feedback loop) can be explained as a consequence of other topological features.
Most biological processes are described as a series of interactions between proteins and other molecules, and interactions are in turn described in terms of atomic structures. To annotate protein functions as sets of interaction states at atomic resolution, and thereby to better understand the relation between protein interactions and biological functions, we conducted exhaustive all-against-all atomic structure comparisons of all known binding sites for ligands including small molecules, proteins and nucleic acids, and identified recurring elementary motifs. By integrating the elementary moti…
Topological features of gene regulatory networks can be successfully reproduced by a model population evolving under selection for short dynamical attractors. The evolved population of networks exhibit motif statistics, summarized by significance profiles, which closely match those of {\it E. coli, S. cerevsiae} and {\it B. subtilis}, in such features as the excess of linear motifs and feed-forward loops, and deficiency of feedback loops. The slow relaxation to stasis is a hallmark of a rugged fitness landscape, with independently evolving populations exploring distinct valleys strongly differ…
Background: Networks in different domains are characterized by similar global characteristics while differing in local structures. To further extend this concept, we investigated network regularities on a fine scale in order to examine the functional impact of recurring motifs in signed oriented biological networks. In this work we generalize to signaling net works some considerations made on feedback and feed forward loops and extend them by adding a close scrutiny of Linear Triplets, which have not yet been investigate in detail. Results: We studied the role of triplets, either open or close…
The biological processes of cellular decision making and differentiation involve a plethora of signalling pathways and gene regulatory circuits. These networks, in their turn, exhibit a multitude of motifs playing crucial parts in regulating network activity. Here, we compare the topological placement of motifs in gene regulatory and signalling networks and find that it suggests different evolutionary strategies in motif distribution for distinct cellular subnetworks.
Studying the topology of so-called real networks, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are built from small functional units called motifs, which can be found by looking for small subgraphs whose numbers of occurrences in the whole network are surprisingly high. In this article, we propose to define motifs through a local overrepresentation in the network and develop a statistic to detect them without relying on simulations. We then illustrate th…
Studying the topology of so-called {\em real networks}, that is networks obtained from sociological or biological data for instance, has become a major field of interest in the last decade. One way to deal with it is to consider that networks are built from small functional units called {\em motifs}, which can be found by looking for small subgraphs whose numbers of occurrences in the whole network of interest are surprisingly high. In this paper, we propose to define motifs through a local over-representation in the network and develop a statistic which allows us to detect them limiting the n…
Topological network motifs represent functional relationships within and between regulatory and protein-protein interaction networks. Enriched motifs often aggregate into self-contained units forming functional modules. Theoretical models for network evolution by duplication-divergence mechanisms and for network topology by hierarchical scale-free networks have suggested a one-to-one relation between network motif enrichment and aggregation, but this relation has never been tested quantitatively in real biological interaction networks. Here we introduce a novel method for assessing the statist…
Previous studies have inferred robust stability of reaction networks by utilizing linear programs or iterative algorithms. Such algorithms become tedious or computationally infeasible for large networks. In addition, they operate like black-boxes without offering intuition for the structures that are necessary to maintain stability. In this work, we provide several graphical criteria for constructing robust stability certificates, checking robust non-degeneracy, {verifying persistence}, and establishing global stability. By characterizing a set of stability-preserving graph modifications that …
Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network. Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with…
The activation/repression of a given gene is typically regulated by multiple transcription factors (TFs) that bind at the gene regulatory region and recruit RNA polymerase (RNAP). The interactions between the promoter region and TFs and between different TFs specify the dynamic responses of the gene under different physiological conditions. By choosing specific regulatory interactions with up to three transcription factors, we designed several functional motifs, each of which is shown to perform a certain function and can be integrated into larger networks. We analyzed three kinds of networks:…
It is well-known that gene activation/deactivation dynamics may be a major source of randomness in genetic networks, also in the case of large concentrations of the transcription factors. In this work, we investigate the effect of realistic extrinsic noises acting on gene deactivation in a common network motif - the positive feedback of a transcription factor on its own synthesis - under a variety of settings, i.e., distinct cellular types, distribution of proteins and properties of the external perturbations. At variance with standard models where the perturbations are Gaussian unbounded, we …
Signal processing in biological systems is delicately executed by specialised networks, which are modular assemblies of network motifs. The motifs are independently functional circuits found in enormous numbers in any living cell. A very common network motif is the feed-forward loop (FFL), which regulates a downstream node by an upstream one in a direct and an indirect way within the network. If the direct and indirect regulations go antagonistic, the motif is known as an incoherent FFL (ICFFL). The current study is aimed at exploring the reason for the variation in the evolutionary selection …
We present a hybrid model of a biological filter, a genetic circuit which removes fast fluctuations in the cell's internal representation of the extra cellular environment. The model takes the classic feed-forward loop (FFL) motif and represents it as a network of continuous protein concentrations and binary, unobserved gene promoter states. We address the problem of statistical inference and parameter learning for this class of models from partial, discrete time observations. We show that the hybrid representation leads to an efficient algorithm for approximate statistical inference in this c…
Genetically encoded regulatory circuits control biological function. A major focus of systems biology is to understand these circuits by establishing the relationship between specific structures and functions. Of special interest are multifunctional circuits that are capable of performing distinct behaviors without changing their topology. A particularly simple example of such a system is the AC-DC circuit. Found in multiple regulatory processes, this circuit consists of three genes connected in a combination of a toggle switch and a repressilator. Using dynamical system theory we analyze the …
We introduce a general framework for biological systems, called MESSI systems, that describe Modifications of type Enzyme-Substrate or Swap with Intermediates, and we prove general results based on the network structure. Many post-translational modification networks are MESSI systems. For example: the motifs in [Feliu and Wiuf (2012a)], sequential distributive and processive multisite phosphorylation networks, most of the examples in [Angeli et al. (2007)], phosphorylation cascades, two component systems as in [Kothamachu et al. (2015)], the bacterial EnvZ/OmpR network in [Shinar and Feinberg …
Many biological networks have to filter out useful information from a vast excess of spurious interactions. We use computational evolution to predict design features of networks processing ligand categorization. The important problem of early immune response is considered as a case-study. Rounds of evolution with different constraints uncover elaborations of the same network motif we name adaptive sorting. Corresponding network substructures can be identified in current models of immune recognition. Our work draws a deep analogy between immune recognition and biochemical adaptation.
Recent progress in experimental techniques has enabled us to quantitatively study stochastic and flexible behavior of biological systems. For example, gene regulatory networks perform stochastic information processing and their functionalities have been extensively studied. In gene regulatory networks, there are specific subgraphs called network motifs that occur at frequencies much higher than those found in randomized networks. Further understanding of the designing principle of such networks is highly desirable. In a different context, information thermodynamics has been developed as a theo…
