Network Motifs Research Articles

Fundamental patterns of signal propagation in complex networks.

Various disasters stem from minor perturbations, such as the spread of infectious diseases and cascading failure in power grids. Analyzing perturbations is crucial for both theoretical and application fields. Previous researchers have proposed basic propagation patterns for perturbation and explored the impact of basic network motifs on the collective response to these perturbations. However, the current framework is limited in its ability to decouple interactions and, therefore, cannot analyze more complex structures. In this article, we establish an effective, robust, and powerful propagation framework under a general dynamic model. This framework reveals classical and dense network motifs that exert critical acceleration on signal propagation, often reducing orders of magnitude compared with conclusions generated by previous work. Moreover, our framework provides a new approach to understand the fundamental principles of complex systems and the negative feedback mechanism, which is of great significance for researching system controlling and network resilience.

Microstimulation reveals anesthetic state-dependent effective connectivity of neurons in cerebral cortex.

Complex neuronal interactions underlie cortical information processing that can be compromised in altered states of consciousness. Here intracortical microstimulation was applied to investigate anesthetic state-dependent effective connectivity of neurons in rat visual cortex in vivo. Extracellular activity was recorded at 32 sites in layers 5/6 while stimulating with charge-balanced discrete pulses at each electrode in random order. The same stimulation pattern was applied at three levels of anesthesia with desflurane and in wakefulness. Spikes were sorted and classified by their waveform features as putative excitatory and inhibitory neurons. Network motifs were identified in graphs of effective connectivity constructed from monosynaptic cross-correlograms. Microstimulation caused early (<10 ms) increase followed by prolonged (11-100 ms) decrease in spiking of all neurons throughout the electrode array. The early response of excitatory but not inhibitory neurons decayed rapidly with distance from the stimulation site over 1 mm. Effective connectivity of neurons with significant stimulus response was dense in wakefulness and sparse under anesthesia. The number of network motifs, especially those of higher order, increased rapidly as the anesthesia was withdrawn indicating a substantial increase in network connectivity as the animals woke up. The results illuminate the impact of anesthesia on functional integrity of local cortical circuits affecting the state of consciousness.

Multiple Clusters Discovery Utilizing Network Motifs for Community Improvement: Insights from Tourism and Goods' Transactions

Multiple Clusters Discovery Utilizing Network Motifs for Community Improvement: Insights from Tourism and Goods' Transactions

MoNetExplorer: A Visual Analytics System for Analyzing Dynamic Networks With Temporal Network Motifs.

Partitioning a dynamic network into subsets (i.e., snapshots) based on disjoint time intervals is a widely used technique for understanding how structural patterns of the network evolve. However, selecting an appropriate time window (i.e., slicing a dynamic network into snapshots) is challenging and time-consuming, often involving a trial-and-error approach to investigating underlying structural patterns. To address this challenge, we present MoNetExplorer, a novel interactive visual analytics system that leverages temporal network motifs to provide recommendations for window sizes and support users in visually comparing different slicing results. MoNetExplorer provides a comprehensive analysis based on window size, including (1) a temporal overview to identify the structural information, (2) temporal network motif composition, and (3) node-link-diagram-based details to enable users to identify and understand structural patterns at various temporal resolutions. To demonstrate the effectiveness of our system, we conducted a case study with network researchers using two real-world dynamic network datasets. Our case studies show that the system effectively supports users to gain valuable insights into the temporal and structural aspects of dynamic networks.

Modeling the Flowering Activation Motif during Vernalization in Legumes: A Case Study of M. trancatula.

In many plant species, flowering is promoted by the cold treatment or vernalization. The mechanism of vernalization-induced flowering has been extensively studied in Arabidopsis but remains largely unknown in legumes. The orthologs of the FLC gene, a major regulator of vernalization response in Arabidopsis, are absent or non-functional in the vernalization-sensitive legume species. Nevertheless, the legume integrator genes FT and SOC1 are involved in the transition of the vernalization signal to meristem identity genes, including PIM (AP1 ortholog). However, the regulatory contribution of these genes to PIM activation in legumes remains elusive. Here, we presented the theoretical and data-driven analyses of a feed-forward regulatory motif that includes a vernalization-responsive FT gene and several SOC1 genes, which independently activate PIM and thereby mediate floral transition. Our theoretical model showed that the multiple regulatory branches in this regulatory motif facilitated the elimination of no-sense signals and amplified useful signals from the upstream regulator. We further developed and analyzed four data-driven models of PIM activation in Medicago trancatula in vernalized and non-vernalized conditions in wild-type and fta1-1 mutants. The model with FTa1 providing both direct activation and indirect activation via three intermediate activators, SOC1a, SOC1b, and SOC1c, resulted in the most relevant PIM dynamics. In this model, the difference between regulatory inputs of SOC1 genes was nonessential. As a result, in the M. trancatula model, the cumulative action of SOC1a, SOC1b, and SOC1c was favored. Overall, in this study, we first presented the in silico analysis of vernalization-induced flowering in legumes. The considered vernalization network motif can be supplemented with additional regulatory branches as new experimental data become available.

Deciphering the intricate hierarchical gene regulatory network: unraveling multi-level regulation and modifications driving secondary cell wall formation.

Wood quality is predominantly determined by the amount and the composition of secondary cell walls (SCWs). Consequently, unraveling the molecular regulatory mechanisms governing SCW formation is of paramount importance for genetic engineering aimed at enhancing wood properties. Although SCW formation is known to be governed by a hierarchical gene regulatory network (HGRN), our understanding of how a HGRN operates and regulates the formation of heterogeneous SCWs for plant development and adaption to ever-changing environment remains limited. In this review, we examined the HGRNs governing SCW formation and highlighted the significant key differences between herbaceous Arabidopsis and woody plant poplar. We clarified many confusions in existing literatures regarding the HGRNs and their orthologous gene names and functions. Additionally, we revealed many network motifs including feed-forward loops, feed-back loops, and negative and positive autoregulation in the HGRNs. We also conducted a thorough review of post-transcriptional and post-translational aspects, protein-protein interactions, and epigenetic modifications of the HGRNs. Furthermore, we summarized how the HGRNs respond to environmental factors and cues, influencing SCW biosynthesis through regulatory cascades, including many regulatory chains, wiring regulations, and network motifs. Finally, we highlighted the future research directions for gaining a further understanding of molecular regulatory mechanisms underlying SCW formation.

Imaginary network motifs: Structural patterns of false positives and negatives in social networks

We examine the structural patterns in the cognitive representation of social networks by systematically classifying false positives and negatives. Although existing literature on Cognitive Social Structures (CSS) has begun exploring false positives and negatives by comparing actual and perceived networks, it has not differentiated simultaneous occurrences of true and false positives and negatives on network motifs, such as reciprocity and triadic closure. Here, we propose a theoretical framework to categorize three classes of errors we call imaginary network motifs as combinations of accurately and erroneously perceived ties: (a) partially false, (b) completely false, and (c) mixed false. Using four published CSS data sets, we empirically test which imaginary network motifs are significantly more or less present in different types of perceived networks than the corresponding actual networks. Our results confirm that people not only fill in the blanks as suggested in the prior research but also conceive other imaginary structures. The findings advance our understanding of perception gaps between actual and perceived networks and have implications for designing more accurate network modeling and sampling.

Network-motif delay differential analysis of brain activity during seizures.

Delay Differential Analysis (DDA) is a nonlinear method for analyzing time series based on principles from nonlinear dynamical systems. DDA is extended here to incorporate network aspects to improve the dynamical characterization of complex systems. To demonstrate its effectiveness, DDA with network capabilities was first applied to the well-known Rössler system under different parameter regimes and noise conditions. Network-motif DDA, based on cortical regions, was then applied to invasive intracranial electroencephalographic data from drug-resistant epilepsy patients undergoing presurgical monitoring. The directional network motifs between brain areas that emerge from this analysis change dramatically before, during, and after seizures. Neural systems provide a rich source of complex data, arising from varying internal states generated by network interactions.

Analysis and Forecasting of States of Industrial Networks with Adaptive Topology Based on Network Motifs

Analysis and Forecasting of States of Industrial Networks with Adaptive Topology Based on Network Motifs

ScANANSE gene regulatory network and motif analysis of single-cell clusters

The recent development of single-cell techniques is essential to unravel complex biological systems. By measuring the transcriptome and the accessible genome on a single-cell level, cellular heterogeneity in a biological environment can be deciphered. Transcription factors act as key regulators activating and repressing downstream target genes, and together they constitute gene regulatory networks that govern cell morphology and identity. Dissecting these gene regulatory networks is crucial for understanding molecular mechanisms and disease, especially within highly complex biological systems. The gene regulatory network analysis software ANANSE and the motif enrichment software GimmeMotifs were both developed to analyse bulk datasets. We developed scANANSE, a software pipeline for gene regulatory network analysis and motif enrichment using single-cell RNA and ATAC datasets. The scANANSE pipeline can be run from either R or Python. First, it exports data from standard single-cell objects. Next, it automatically runs multiple comparisons of cell cluster data. Finally, it imports the results back to the single-cell object, where the result can be further visualised, integrated, and interpreted. Here, we demonstrate our scANANSE pipeline on a publicly available PBMC multi-omics dataset. It identifies well-known cell type-specific hematopoietic factors. Importantly, we also demonstrated that scANANSE combined with GimmeMotifs is able to predict transcription factors with both activating and repressing roles in gene regulation.

Tunable Dynamics in a Multistrain Transcriptional Pulse Generator.

One challenge in synthetic biology is the tuning of regulatory components within gene circuits to elicit a specific behavior. This challenge becomes more difficult in synthetic microbial consortia since each strain's circuit must function at the intracellular level and their combination must operate at the population level. Here we demonstrate that circuit dynamics can be tuned in synthetic consortia through the manipulation of strain fractions within the community. To do this, we construct a microbial consortium comprised of three strains of engineered Escherichia coli that, when cocultured, use homoserine lactone-mediated intercellular signaling to create a multistrain incoherent type-1 feedforward loop (I1-FFL). Like naturally occurring I1-FFL motifs in gene networks, this engineered microbial consortium acts as a pulse generator of gene expression. We demonstrate that the amplitude of the pulse can be easily tuned by adjusting the relative population fractions of the strains. We also develop a mathematical model for the temporal dynamics of the microbial consortium. This model allows us to identify population fractions that produced desired pulse characteristics, predictions that were confirmed for all but extreme fractions. Our work demonstrates that intercellular gene circuits can be effectively tuned simply by adjusting the starting fractions of each strain in the consortium.

A gene regulatory network critical for axillary bud dormancy directly controlled by Arabidopsis BRANCHED1.

The Arabidopsis thaliana transcription factor BRANCHED1 (BRC1) plays a pivotal role in the control of shoot branching as it integrates environmental and endogenous signals that influence axillary bud growth. Despite its remarkable activity as a growth inhibitor, the mechanisms by which BRC1 promotes bud dormancy are largely unknown. We determined the genome-wide BRC1 binding sites in vivo and combined these with transcriptomic data and gene co-expression analyses to identify bona fide BRC1 direct targets. Next, we integrated multi-omics data to infer the BRC1 gene regulatory network (GRN) and used graph theory techniques to find network motifs that control the GRN dynamics. We generated an open online tool to interrogate this network. A group of BRC1 target genes encoding transcription factors (BTFs) orchestrate this intricate transcriptional network enriched in abscisic acid-related components. Promoter::β-GLUCURONIDASE transgenic lines confirmed that BTFs are expressed in axillary buds. Transient co-expression assays and studies in planta using mutant lines validated the role of BTFs in modulating the GRN and promoting bud dormancy. This knowledge provides access to the developmental mechanisms that regulate shoot branching and helps identify candidate genes to use as tools to adapt plant architecture and crop production to ever-changing environmental conditions.

MOSER: Scalable Network Motif Discovery Using Serial Test

Given a graph G , a motif (e.g., 3-node clique) is a fundamental building block for G. Recently, motif-based graph analysis has attracted much attention due to its efficacy in tasks such as clustering, ranking, and link prediction. These tasks require Network Motif Discovery (NMD) at the early stage to identify the motifs of G. However, existing NMD solutions have two drawbacks: (1) Lack of theoretical guarantees on the quality of the samples generated using the existing methods, and (2) inefficient algorithms, which are not scalable for large graphs. These limitations hinder the exploration of motifs for analyzing large graphs. To address the above issues, we propose a novel solution named MOSER ( MO tif Discovery using SER ial Test). This novel NMD framework leverages a significance testing method known as the serial test, which differs from the existing solutions. We further propose two fast incremental subgraph counting algorithms, allowing MOSER to scale to larger graphs than ever possible before. Extensive experimental results show that using MOSER can improve the state-of-the-art up to 5 orders of magnitude in efficiency and that the motifs found by MOSER facilitate downstream tasks such as link prediction.

Emergence of cortical network motifs for short-term memory during learning

Learning of adaptive behaviors requires the refinement of coordinated activity across multiple brain regions. However, how neural communications develop during learning remains poorly understood. Here, using two-photon calcium imaging, we simultaneously recorded the activity of layer 2/3 excitatory neurons in eight regions of the mouse dorsal cortex during learning of a delayed-response task. Across learning, while global functional connectivity became sparser, there emerged a subnetwork comprising of neurons in the anterior lateral motor cortex (ALM) and posterior parietal cortex (PPC). Neurons in this subnetwork shared a similar choice code during action preparation and formed recurrent functional connectivity across learning. Suppression of PPC activity disrupted choice selectivity in ALM and impaired task performance. Recurrent neural networks reconstructed from ALM activity revealed that PPC-ALM interactions rendered choice-related attractor dynamics more stable. Thus, learning constructs cortical network motifs by recruiting specific inter-areal communication channels to promote efficient and robust sensorimotor transformation.

A double-negative feedback loop between NtrBC and a small RNA rewires nitrogen metabolism in legume symbionts.

Root nodule endosymbioses between diazotrophic rhizobia and legumes provide the largest input of combined N to the biosphere, thus representing an alternative to harmful chemical fertilizers for sustainable crop production. Rhizobia have evolved intricate strategies to coordinate N assimilation for their own benefit with N2 fixation to sustain plant growth. The rhizobial N status is transduced by the NtrBC two-component system, the seemingly ubiquitous form of N signal transduction in Proteobacteria. Here, we show that the regulatory sRNA NfeR1 (nodule formation efficiency RNA) of the alfalfa symbiont Sinorhizobium meliloti is transcribed from a complex promoter repressed by NtrC in a N-dependent manner and feedback silences ntrBC by complementary base-pairing. These findings unveil a more prominent role of NtrC as a transcriptional repressor than hitherto anticipated and a novel RNA-based mechanism for NtrBC regulation. The NtrBC-NfeR1 double-negative feedback loop accurately rewires symbiotic S. meliloti N metabolism and is likely conserved in α-rhizobia.

Motifs in earthquake networks: Romania, Italy, United States of America, and Japan

We present a detailed description of seismic activity in Romania, Italy, and Japan, as well as the California seismic zone in the United States of America, based on the statistical analysis of the underlying earthquake networks used to model the aforementioned zones. Our results on network connectivity and simple network motifs allow for a complex description of seismic zones, while at the same time reinforcing the current understanding of seismicity as a critical phenomenon. The reported distributions on node connectivity, three-, and four-node motifs are consistent with power-law, i.e., scale-free, distributions over large intervals and are robust across earthquake networks obtained from different discretizations of the seismic zones of interest. In our analysis of the distributions of node connectivity and simple motifs, we distinguish between the global distribution and the power-law part of it with the help of maximum likelihood estimation (MLE) method and complementary cumulative distribution functions (CCDF). The main message is that the distributions reported for the aforementioned seismic zones have large power-law components, extending over some orders of magnitude, independent of discretization. All the results were obtained using publicly available databases and open-source software, as well as a new toolbox available on GitHub, specifically designed to automatically analyze earthquake databases.

On the efficacy of higher-order spectral clustering under weighted stochastic block models

Higher-order structures of networks, namely, small subgraphs of networks (also called network motifs), are widely known to be crucial and essential to the organization of networks. Several works have studied the community detection problem–a fundamental problem in network analysis at the level of motifs. In particular, the higher-order spectral clustering has been developed, where the notion of motif adjacency matrix is introduced as the algorithm's input. However, how the higher-order spectral clustering works and when it performs better than its edge-based counterpart remain largely unknown. To elucidate these problems, the higher-order spectral clustering is investigated from a statistical perspective. The clustering performance of the higher-order spectral clustering is theoretically studied under a weighted stochastic block model, and the resulting bounds are compared with the corresponding results of the edge-based spectral clustering. The upper bounds and simulations show that when the network is dense and the edge weights have a weak signal, higher-order spectral clustering can lead to a performance gain in clustering. Real data experiments also corroborate the merits of higher-order spectral clustering.

Graph-Theoretical Analysis of Biological Networks: A Survey

Biological networks such as protein interaction networks, gene regulation networks, and metabolic pathways are examples of complex networks that are large graphs with small-world and scale-free properties. An analysis of these networks has a profound effect on our understanding the origins of life, health, and the disease states of organisms, and it allows for the diagnosis of diseases to aid in the search for remedial processes. In this review, we describe the main analysis methods of biological networks using graph theory, by first defining the main parameters, such as clustering coefficient, modularity, and centrality. We then survey fundamental graph clustering methods and algorithms, followed by the network motif search algorithms, with the aim of finding repeating subgraphs in a biological network graph. A frequently appearing subgraph usually conveys a basic function that is carried out by that small network, and discovering such a function provides an insight into the overall function of the organism. Lastly, we review network alignment algorithms that find similarities between two or more graphs representing biological networks. A conserved subgraph between the biological networks of organisms may mean a common ancestor, and finding such a relationship may help researchers to derive ancestral relationships and to predict the future evolution of organisms to enable the design of new drugs. We provide a review of the research studies in all of these methods, and conclude using the current challenging areas of biological network analysis, and by using graph theory and parallel processing for high performance analysis.

Statistically validated coeherence and intensity in temporal networks of information flows

We propose a method for characterizing the local structure of weighted multivariate time series networks. We draw intensity and coherence of network motifs, i.e. statistically recurrent subgraphs, to characterize the system behavior via higher-order structures derived upon effective transfer entropy networks. The latter consists of a model-free methodology enabling to correct for small sample biases affecting Shannon transfer entropy, other than conducting inference on the estimated directional time series information flows. We demonstrate the usefulness of our proposed method with an application to a set of global commodity prices. Our main result shows that, despite simple triadic structures are the most intense, coherent and statistically recurrent over time, their intensity suddenly decreases after the Global Financial Crisis, in favor of most complex triadic structures, while all types of subgraphs tend to become more coherent thereafter.

A biologically inspired architecture with switching units can learn to generalize across backgrounds

Humans and other animals navigate different environments effortlessly, their brains rapidly and accurately generalizing across contexts. Despite recent progress in deep learning, this flexibility remains a challenge for many artificial systems. Here, we show how a bio-inspired network motif can explicitly address this issue. We do this using a dataset of MNIST digits of varying transparency, set on one of two backgrounds of different statistics that define two contexts: a pixel-wise noise or a more naturalistic background from the CIFAR-10 dataset. After learning digit classification when both contexts are shown sequentially, we find that both shallow and deep networks have sharply decreased performance when returning to the first background — an instance of the catastrophic forgetting phenomenon known from continual learning. To overcome this, we propose the bottleneck-switching network or switching network for short. This is a bio-inspired architecture analogous to a well-studied network motif in the visual cortex, with additional “switching” units that are activated in the presence of a new background, assuming a priori a contextual signal to turn these units on or off. Intriguingly, only a few of these switching units are sufficient to enable the network to learn the new context without catastrophic forgetting through inhibition of redundant background features. Further, the bottleneck-switching network can generalize to novel contexts similar to contexts it has learned. Importantly, we find that — again as in the underlying biological network motif, recurrently connecting the switching units to network layers is advantageous for context generalization.