Proximity of intracellular regulatory networks to monotone systems

Minimal frustration underlies the usefulness of incomplete regulatory network models in biology

Regulatory networks as large and complex as those implicated in cell-fate choice are expected to exhibit intricate, very high-dimensional dynamics. Cell-fate choice, however, is a macroscopically simple process. Additionally, regulatory network models are almost always incomplete and/or inexact, and do not incorporate all the regulators and interactions that may be involved in cell-fate regulation. In spite of these issues, regulatory network models have proven to be incredibly effective tools for understanding cell-fate choice across contexts and for making useful predictions. Here, we show that minimal frustration-a feature of biological networks across contexts but not of random networks-can compel simple, low-dimensional steady-state behavior even in large and complex networks. Moreover, the steady-state behavior of minimally frustrated networks can be recapitulated by simpler networks such as those lacking many of the nodes and edges and those that treat multiple regulators as one. The present study provides a theoretical explanation for the success of network models in biology and for the challenges in network inference.

The structure balance of gene-gene networks beyond pairwise interactions

Despite its high and direct impact on nearly all biological processes, the underlying structure of gene-gene interaction networks is investigated so far according to pair connections. To address this, we explore the gene interaction networks of the yeast Saccharomyces cerevisiae beyond pairwise interaction using the structural balance theory (SBT). Specifically, we ask whether essential and nonessential gene interaction networks are structurally balanced. We study triadic interactions in the weighted signed undirected gene networks and observe that balanced and unbalanced triads are over and underrepresented in both networks, thus beautifully in line with the strong notion of balance. Moreover, we note that the energy distribution of triads is significantly different in both essential and nonessential networks compared to the shuffled networks. Yet, this difference is greater in the essential network regarding the frequency as well as the energy of triads. Additionally, results demonstrate that triads in the essential gene network are more interconnected through sharing common links, while in the nonessential network they tend to be isolated. Last but not least, we investigate the contribution of all-length signed walks and its impact on the degree of balance. Our findings reveal that interestingly when considering longer cycles, not only, both essential and nonessential gene networks are more balanced compared to their corresponding shuffled networks, but also, the nonessential gene network is more balanced compared to the essential network.

Using high-throughput multi-omics data to investigate structural balance in elementary gene regulatory network motifs

MOTIVATION

The simultaneous availability of ATAC-seq and RNA-seq experiments allows to obtain a more in-depth knowledge on the regulatory mechanisms occurring in gene regulatory networks. In this article, we highlight and analyze two novel aspects that leverage on the possibility of pairing RNA-seq and ATAC-seq data. Namely we investigate the causality of the relationships between transcription factors, chromatin and target genes and the internal consistency between the two omics, here measured in terms of structural balance in the sample correlations along elementary length-3 cycles.

RESULTS

We propose a framework that uses the a priori knowledge on the data to infer elementary causal regulatory motifs (namely chains and forks) in the network. It is based on the notions of conditional independence and partial correlation, and can be applied to both longitudinal and non-longitudinal data. Our analysis highlights a strong connection between the causal regulatory motifs that are selected by the data and the structural balance of the underlying sample correlation graphs: strikingly, >97% of the selected regulatory motifs belong to a balanced subgraph. This result shows that internal consistency, as measured by structural balance, is close to a necessary condition for 3-node regulatory motifs to satisfy causality rules.

AVAILABILITY AND IMPLEMENTATION

The analysis was carried out in MATLAB and the code can be found at https://github.com/albertozenere/Multi-omics-elementary-regulatory-motifs.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

An evolutionary game approach for determination of the structural conflicts in signed networks

Social or biochemical networks can often divide into two opposite alliances in response to structural conflicts between positive (friendly, activating) and negative (hostile, inhibiting) interactions. Yet, the underlying dynamics on how the opposite alliances are spontaneously formed to minimize the structural conflicts is still unclear. Here, we demonstrate that evolutionary game dynamics provides a felicitous possible tool to characterize the evolution and formation of alliances in signed networks. Indeed, an evolutionary game dynamics on signed networks is proposed such that each node can adaptively adjust its choice of alliances to maximize its own fitness, which yet leads to a minimization of the structural conflicts in the entire network. Numerical experiments show that the evolutionary game approach is universally efficient in quality and speed to find optimal solutions for all undirected or directed, unweighted or weighted signed networks. Moreover, the evolutionary game approach is inherently distributed. These characteristics thus suggest the evolutionary game dynamic approach as a feasible and effective tool for determining the structural conflicts in large-scale on-line signed networks.

Novel factors in the pathogenesis of psoriasis and potential drug candidates are found with systems biology approach

Psoriasis is a multifactorial inflammatory skin disease characterized by increased proliferation of keratinocytes, activation of immune cells and susceptibility to metabolic syndrome. Systems biology approach makes it possible to reveal novel important factors in the pathogenesis of the disease. Protein-protein, protein-DNA, merged (containing both protein-protein and protein-DNA interactions) and chemical-protein interaction networks were constructed consisting of differentially expressed genes (DEG) between lesional and non-lesional skin samples of psoriatic patients and/or the encoded proteins. DEGs were determined by microarray meta-analysis using MetaOMICS package. We used STRING for protein-protein, CisRED for protein-DNA and STITCH for chemical-protein interaction network construction. General network-, cluster- and motif-analysis were carried out in each network. Many DEG-coded proteins (CCNA2, FYN, PIK3R1, CTGF, F3) and transcription factors (AR, TFDP1, MEF2A, MECOM) were identified as central nodes, suggesting their potential role in psoriasis pathogenesis. CCNA2, TFDP1 and MECOM might play role in the hyperproliferation of keratinocytes, whereas FYN may be involved in the disturbed immunity in psoriasis. AR can be an important link between inflammation and insulin resistance, while MEF2A has role in insulin signaling. A controller sub-network was constructed from interlinked positive feedback loops that with the capability to maintain psoriatic lesional phenotype. Analysis of chemical-protein interaction networks detected 34 drugs with previously confirmed disease-modifying effects, 23 drugs with some experimental evidences, and 21 drugs with case reports suggesting their positive or negative effects. In addition, 99 unpublished drug candidates were also found, that might serve future treatments for psoriasis.

Early phase of plasticity-related gene regulation and SRF dependent transcription in the hippocampus

Hippocampal organotypic cultures are a highly reliable in vitro model for studying neuroplasticity: in this paper, we analyze the early phase of the transcriptional response induced by a 20 µM gabazine treatment (GabT), a GABA-Ar antagonist, by using Affymetrix oligonucleotide microarray, RT-PCR based time-course and chromatin-immuno-precipitation. The transcriptome profiling revealed that the pool of genes up-regulated by GabT, besides being strongly related to the regulation of growth and synaptic transmission, is also endowed with neuro-protective and pro-survival properties. By using RT-PCR, we quantified a time-course of the transient expression for 33 of the highest up-regulated genes, with an average sampling rate of 10 minutes and covering the time interval [10∶90] minutes. The cluster analysis of the time-course disclosed the existence of three different dynamical patterns, one of which proved, in a statistical analysis based on results from previous works, to be significantly related with SRF-dependent regulation (p-value<0.05). The chromatin immunoprecipitation (chip) assay confirmed the rich presence of working CArG boxes in the genes belonging to the latter dynamical pattern and therefore validated the statistical analysis. Furthermore, an in silico analysis of the promoters revealed the presence of additional conserved CArG boxes upstream of the genes Nr4a1 and Rgs2. The chip assay confirmed a significant SRF signal in the Nr4a1 CArG box but not in the Rgs2 CArG box.

Dynamics of opinion forming in structurally balanced social networks

A structurally balanced social network is a social community that splits into two antagonistic factions (typical example being a two-party political system). The process of opinion forming on such a community is most often highly predictable, with polarized opinions reflecting the bipartition of the network. The aim of this paper is to suggest a class of dynamical systems, called monotone systems, as natural models for the dynamics of opinion forming on structurally balanced social networks. The high predictability of the outcome of a decision process is explained in terms of the order-preserving character of the solutions of this class of dynamical systems. If we represent a social network as a signed graph in which individuals are the nodes and the signs of the edges represent friendly or hostile relationships, then the property of structural balance corresponds to the social community being splittable into two antagonistic factions, each containing only friends.

Trafficking motifs as the basis for two-compartment signaling systems to form multiple stable states

Transport of molecules in cells is a central part of cell biology. Frequently such trafficking is not just for material transport, but also for information propagation, and serves to couple signaling circuits across cellular compartments. Here, I show that trafficking transforms simple local signaling pathways into self-organizing systems that span compartments and confer distinct states and identities to these compartments. I find that three motifs encapsulate the responses of most single-compartment signaling pathways in the context of trafficking. These motifs combine with different trafficking reactions to generate a diverse set of cellular functions. For example, trafficked bistable switches can oscillate or become quad- or tristable, depending on trafficking mechanisms and rates. Furthermore, the analysis shows how compartments participating in traffic can settle to distinct molecular compositions characteristic of distinct organelle identities. This general framework shows how the interplay between molecular movement and local reactions can generate many system functions, and give distinct identities to different parts of the cell.

Elementary signaling modes predict the essentiality of signal transduction network components

Background

Understanding how signals propagate through signaling pathways and networks is a central goal in systems biology. Quantitative dynamic models help to achieve this understanding, but are difficult to construct and validate because of the scarcity of known mechanistic details and kinetic parameters. Structural and qualitative analysis is emerging as a feasible and useful alternative for interpreting signal transduction.

Results

In this work, we present an integrative computational method for evaluating the essentiality of components in signaling networks. This approach expands an existing signaling network to a richer representation that incorporates the positive or negative nature of interactions and the synergistic behaviors among multiple components. Our method simulates both knockout and constitutive activation of components as node disruptions, and takes into account the possible cascading effects of a node's disruption. We introduce the concept of elementary signaling mode (ESM), as the minimal set of nodes that can perform signal transduction independently. Our method ranks the importance of signaling components by the effects of their perturbation on the ESMs of the network. Validation on several signaling networks describing the immune response of mammals to bacteria, guard cell abscisic acid signaling in plants, and T cell receptor signaling shows that this method can effectively uncover the essentiality of components mediating a signal transduction process and results in strong agreement with the results of Boolean (logical) dynamic models and experimental observations.

Conclusions

This integrative method is an efficient procedure for exploratory analysis of large signaling and regulatory networks where dynamic modeling or experimental tests are impractical. Its results serve as testable predictions, provide insights into signal transduction and regulatory mechanisms and can guide targeted computational or experimental follow-up studies. The source codes for the algorithms developed in this study can be found at http://www.phys.psu.edu/~ralbert/ESM.

Monotonicity, frustration, and ordered response: an analysis of the energy landscape of perturbed large-scale biological networks

BACKGROUND

For large-scale biological networks represented as signed graphs, the index of frustration measures how far a network is from a monotone system, i.e., how incoherently the system responds to perturbations.

RESULTS

In this paper we find that the frustration is systematically lower in transcriptional networks (modeled at functional level) than in signaling and metabolic networks (modeled at stoichiometric level). A possible interpretation of this result is in terms of energetic cost of an interaction: an erroneous or contradictory transcriptional action costs much more than a signaling/metabolic error, and therefore must be avoided as much as possible. Averaging over all possible perturbations, however, we also find that unlike for transcriptional networks, in the signaling/metabolic networks the probability of finding the system in its least frustrated configuration tends to be high also in correspondence of a moderate energetic regime, meaning that, in spite of the higher frustration, these networks can achieve a globally ordered response to perturbations even for moderate values of the strength of the interactions. Furthermore, an analysis of the energy landscape shows that signaling and metabolic networks lack energetic barriers around their global optima, a property also favouring global order.

CONCLUSION

In conclusion, transcriptional and signaling/metabolic networks appear to have systematic differences in both the index of frustration and the transition to global order. These differences are interpretable in terms of the different functions of the various classes of networks.

Inferring the Sign of Kinase-Substrate Interactions by Combining Quantitative Phosphoproteomics with a Literature-Based Mammalian Kinome Network

Protein phosphorylation is a reversible post-translational modification commonly used by cell signaling networks to transmit information about the extracellular environment into intracellular organelles for the regulation of the activity and sorting of proteins within the cell. For this study we reconstructed a literature-based mammalian kinase-substrate network from several online resources. The interactions within this directed graph network connect kinases to their substrates, through specific phosphosites including kinasekinase regulatory interactions. However, the "signs" of links, activation or inhibition of the substrate upon phosphorylation, within this network are mostly unknown. Here we show how we can infer the "signs" indirectly using data from quantitative phosphoproteomics experiments applied to mammalian cells combined with the literature-based kinase-substrate network. Our inference method was able to predict the sign for 321 links and 153 phosphosites on 120 kinases, resulting in signed and directed subnetwork of mammalian kinase-kinase interactions. Such an approach can rapidly advance the reconstruction of cell signaling pathways and networks regulating mammalian cells.

Insights into the organization of biochemical regulatory networks using graph theory analyses

Graph theory has been a valuable mathematical modeling tool to gain insights into the topological organization of biochemical networks. There are two types of insights that may be obtained by graph theory analyses. The first provides an overview of the global organization of biochemical networks; the second uses prior knowledge to place results from multivariate experiments, such as microarray data sets, in the context of known pathways and networks to infer regulation. Using graph analyses, biochemical networks are found to be scale-free and small-world, indicating that these networks contain hubs, which are proteins that interact with many other molecules. These hubs may interact with many different types of proteins at the same time and location or at different times and locations, resulting in diverse biological responses. Groups of components in networks are organized in recurring patterns termed network motifs such as feedback and feed-forward loops. Graph analysis revealed that negative feedback loops are less common and are present mostly in proximity to the membrane, whereas positive feedback loops are highly nested in an architecture that promotes dynamical stability. Cell signaling networks have multiple pathways from some input receptors and few from others. Such topology is reminiscent of a classification system. Signaling networks display a bow-tie structure indicative of funneling information from extracellular signals and then dispatching information from a few specific central intracellular signaling nexuses. These insights show that graph theory is a valuable tool for gaining an understanding of global regulatory features of biochemical networks.