Four-node Motifs Research Articles

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.

Morphological and functional polycentric structure assessment of megacity: An integrated approach with spatial distribution and interaction

Polycentric urban structures are important spatial development strategies in megacities; however, they have decentralized morphologies and functional characteristics that profoundly impact urban space development. Therefore, when promoting sustainable development in urban areas in Shenyang, the only megacity in northeast China, it is important to explore the polycentric spatial development of megacities based on multi-source data, geographic information system spatial analysis, and network model methods. This study was conducted to examine the polycentric structures of the morphological and functional dimensions. The results showed that morphological polycentric space can be defined as “centralized dispersion,” with the functional polycentric only comprised “decentralized concentration.” Additionally, agglomeration sub-centers of the morphological dimension were all on the periphery of the city, although the three sub-centers within the city (M6, M7, and M8) were diffusion types. In the functional dimension, sub-centers F7 and F6 exhibited high centrality and power for both agglomeration and diffusion. Finally, four-node motifs were more important than three-node motifs in the morphological polycentric micro-networks, but their frequency was low, whereas that of three-node motifs were more important than four-node motifs in functional polycentric micro-networks, and their occurrence frequency was high.

CHIEF: Clustering With Higher-Order Motifs in Big Networks

Clustering network vertices is an enabler of various applications such as social computing and Internet of Things. However, challenges arise for clustering when networks increase in scale. This paper proposes CHIEF (Clustering with HIgher-ordEr motiFs), a solution which consists of two motif clustering techniques: standard acceleration CHIEF-ST and approximate acceleration CHIEF-AP. Both algorithms firstly find the maximal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-edge-connected subgraphs within the target networks to lower the network scale by optimizing the network structure with maximal <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>-edge-connected subgraphs, and then use heterogeneous four-node motifs clustering in higher-order dense networks. For CHIEF-ST, we illustrate that all target motifs will be kept after this procedure when the minimum node degree of the target motif is equal or greater than <inline-formula><tex-math notation="LaTeX">$k$</tex-math></inline-formula>. For CHIEF-AP, we prove that the eigenvalues of the adjacency matrix and the Laplacian matrix are relatively stable after this step. CHIEF offers an improved efficiency of motif clustering for big networks, and it verifies higher-order motif significance. Experiments on real and synthetic networks demonstrate that the proposed solutions outperform baseline approaches in large network analysis, and higher-order motifs outperform traditional triangle motifs in clustering.

The series of a four-node motif and coherent type-1 feed-forward loop can provide sensitive detection over arbitrary range of input signal, thereby explain Weber’s law in higher-order sensory processes, and compute logarithm

Weber’s law states that the ratio of the smallest perceptual change in an input signal and the background signal is constant. The law is observed across the perception of weight, light intensity, and sound intensity and pitch. To explain Weber’s law observed in steady-state responses, two models of perception have been proposed, namely the logarithmic and the linear model. This paper argues in favour of the linear model, which requires the sensory system to generate linear input–output relationship over several orders of magnitude. To this end, a four-node motif (FNM) is constructed from first principles whose series provides almost linear relationship between input signal and the output over arbitrary range of input signal. Mathematical analysis into the origin of this quasi-linear relationship shows that the series of coherent type-1 feed-forward loop (C1-FFL) is able to provide perfectly linear input–output relationship over arbitrary range of input signal. FNM also reproduces the neuronal data of numerosity detection study on the monkey. The series of FNM also provides a mechanism for sensitive detection over arbitrary range of input signal when the output has an upper limit. Further, the series of FNM provides a general basis for a class of bow-tie architecture where the number of receptors is much lower than the range of input signal and the “decoded output”. Besides (quasi-)linear input–output relationship, another example of this class of bow-tie architecture that the series of FNM is able to produce is absorption spectra of cone opsins of humans. Further, the series of FNM and C1-FFL, both, can compute logarithm over arbitrary range of input signal.

An Efficient Network Motif Discovery Approach for Co-Regulatory Networks

Co-regulatory networks, which consist of transcription factors (TFs), micro ribose nucleic acids (miRNAs), and target genes, have provided new insight into biological processes, revealing complicated and comprehensive regulatory relationships between biomolecules. To uncover the key co-regulatory mechanisms between these biomolecules, the identification of co-regulatory motifs has become beneficial. However, due to high-computational complexity, it is a hard task to identify co-regulatory network motifs with more than four interacting nodes in large-scale co-regulatory networks. To overcome this limitation, we propose an efficient algorithm, named large co-regulatory network motif (LCNM), to detect large co-regulatory network motifs. This algorithm is able to store a set of co-regulatory network motifs within a $G$ -tries structure. Moreover, we propose two ways to generate candidate motifs. For three- or four-interacting-node motifs, LCNM is able to generate all different types of motif through an enumeration method. For larger network motifs, we adopt a sampling method to generate candidate co-regulatory motifs. The experimental results demonstrate that LCNM cannot only improve the computational performance in exhaustive identification of all of the three- or four-node motifs but can also identify co-regulatory network motifs with a maximum of eight nodes. In addition, we implement a parallel version of our LCNM algorithm to further accelerate the motif detection process.

Centrality and Composition of Four-node Motifs in Metabolic Networks

Analysing subgraph patterns and recurring motifs in networks is a useful way to understand their local topology and func- tion. Motifs have been considered useful in analysing design patterns of networks as well. Three-node patterns (triads) in metabolic networks have been studied to some extent producing classification of organisms based on triads, but their network placement was not analysed. We obtain the frequencies of all four-node subgraphs in a wide range of metabolic networks. We construct significance profiles of subgraphs and employ correlation analysis to compare and contrast these profiles, highlight- ing four-node motifs. We then compute specific centrality measures of nodes involved in each subgraph, namely betweenness centrality and closeness centrality. We observe that multiple four-node motifs exist in metabolic networks. The correlation analysis shows that the significance profiles of Eukaryotic networks are highly correlated across organisms, whereas those of the Prokaryotic networks are correlated less so. The centrality indices of nodes that participate in identified network motifs are shown to be quite high. The analysis provides a tool to pinpoint the transition between evolution stages of Prokaryotic and Eukaryotic metabolic networks.

Fast Revelation of the Motif Mode for a Yeast Protein Interaction Network Through Intelligent Agent-Based Distributed Computing

In the yeast protein-protein interaction network, motif mode, a collection of motifs of special combinations of protein nodes annotated by the molecular function terms of the Gene Ontology, has revealed differences in the conservation constraints within the same topology. In this study, by employing an intelligent agent-based distributed computing method, we are able to discover motif modes in a fast and adaptive manner. Moreover, by focusing on the highly evolutionarily conserved motif modes belonging to the same biological function, we find a large downshift in the distance between nodes belonging to the same motif mode compared with the whole, suggesting that nodes with the same motif mode tend to congregate in a network. Several motif modes with a high conservation of the motif constituents were revealed, but from a new perspective, including that with a three-node motif mode engaged in the protein fate and that with three four-node motif modes involved in the genome maintenance, cellular organization, and transcription. The network motif modes discovered from this method can be linked to the wealth of biological data which require further elucidation with regard to biological functions.