Noise transmission and delay-induced stochastic oscillations in biochemical network motifs

With the aid of stochastic delayed-feedback differential equations, we derive an analytic expression for the power spectra of reacting molecules included in a generic biological network motif that is incorporated with a feedback mechanism and time delays in gene regulation. We systematically analyse the effects of time delays, the feedback mechanism, and biological stochasticity on the power spectra. It has been clarified that the time delays together with the feedback mechanism can induce stochastic oscillations at the molecular level and invalidate the noise addition rule for a modular description of the noise propagator. Delay-induced stochastic resonance can be expected, which is related to the stability loss of the reaction systems and Hopf bifurcation occurring for solutions of the corresponding deterministic reaction equations. Through the analysis of the power spectrum, a new approach is proposed to estimate the oscillation period.

Multiscale Characteristics and Connection Mechanisms of Attraction Networks:A Trajectory Data Mining Approach Leveraging Geotagged Data

Urban tourism is considered a complex system,and multiscale exploration of the organizational patterns of attraction networks has become a topical issue in urban tourism,so exploring the multiscale characteristics and connection mechanisms of attraction networks is important for understanding the linkages between attractions and even the future destination planning.This paper uses geotagging data to compare the links between attractions in Beijing,China during four different periods:the pre-Olympic period(2004–2007),the Olympic Games and subsequent‘heat period’(2008–2013),the post-Olympic period(2014–2019),and the COVID-19(Corona Virus Disease 2019)pandemic period(2020–2021).The aim is to better understand the evolution and patterns of attraction networks at different scales in Beijing and to provide insights for tourism planning in the destination.The results show that the macro,meso-,and microscales network characteristics of attraction networks have inherent logical relationships that can explain the commonalities and differences in the development process of tourism networks.The macroscale attraction network degree Matthew effect is significant in the four different periods and exhibits a morphological monocentric structure,suggesting that new entrants are more likely to be associated with attractions that already have high value.The mesoscale links attractions according to the common purpose of tourists,and the results of the community segmentation of the attraction networks in the four different periods suggest that the functional polycentric structure describes their clustering effect,and the weak links between clusters result from attractions bound by incomplete information and distance,and the functional polycentric structure with a generally more efficient network of clusters.The pattern structure at the microscale reveals the topological transformation relationship of the regional collaboration pattern,and the attraction network structure in the four different periods has a very similar importance profile structure suggesting that the attraction network has the same construction rules and evolution mechanism,which aids in understanding the attraction network pattern at both macro and micro scales.Important approaches and practical implications for planners and managers are presented.

Oscillatory and anti-oscillatory motifs in genetic regulatory networks

Recently, self-sustained oscillatory genetic regulatory networks （GRNs） have attracted significant attention in the biological field. Given a GRN, it is important to anticipate whether the network could generate oscillation with proper parameters, and what the key ingredients for the oscillation are. In this paper the ranges of some function-related parameters which are favorable to sustained oscillations are considered. In particular, some oscillatory motifs appearing with high-frequency in most of the oscillatory GRNs are observed. Moreover, there are some anti-oscillatory motifs which have a strong oscillation repressing effect. Some conclusions analyzing these motif effects and constructing oscillatory GRNs are provided.

Influence of coupling asymmetry on signal amplification in a three-node motif

The three-node feedforward motif has been revealed to function as a weak signal amplifier. In this motif, two nodes(input nodes) receive a weak input signal and send it unidirectionally to the third node(output node). Here, we change the motif's unidirectional couplings(feedforward) to bidirectional couplings(feedforward and feedback working together).We find that a small asymmetric coupling, in which the feedforward effect is stronger than the feedback effect, may enable the three-node motif to go through two distinct dynamic transitions, giving rise to a double resonant signal response. We present an analytical description of the double resonance, which agrees with the numerical findings.

A Topological Evolution Model Based on the Attraction of the Motif Vertex

As a fundamental problem in the field of the network science,the study of topological evolution model is of great significance for revealing the inherent dynamics and mechanisms of complex network evolution.In order to study the influence of different scales of preferential attachment on topological evolution,a topological evolution model based on the attraction of the motif vertex is proposed.From the perspective of network motif,this model proposes the concept of attraction of the motif vertex based on the degree of the motif,quantifies the influence of local structure on the node preferential attachment,and performs the preferential selection of the new link based on the Local World model.The simulation experiments show that the model has the small world characteristic apparently,and the clustering coefficient varies with the scale of the local world.The degree distribution of the model changes from power-law distribution to exponential distribution with the change of parameters.In some cases,the piecewise power-law distribution is presented.In addition,the proposed model can present a network with different matching patterns as the parameters change.

Prediction of Essential Proteins Using Topological Properties in GO-Pruned PPI Network Based on Machine Learning Methods

The prediction of essential proteins, the minimal set required for a living cell to support cellular life, is an important task to understand the cellular processes of an organism. Fast progress in high-throughput technologies and the production of large amounts of data enable the discovery of essential proteins at the system level by analyzing Protein-Protein Interaction （PPI） networks, and replacing biological or chemical experiments. Furthermore, additional gene-level annotation information, such as Gene Ontology （GO） terms, helps to detect essential proteins with higher accuracy. Various centrality algorithms have been used to determine essential proteins in a PPI network, and, recently motif centrality GO, which is based on network motifs and GO terms, works best in detecting essential proteins in a Baker＇s yeast Saccharomyces cerevisiae PPI network, compared to other centrality algorithms. However, each centrality algorithm contributes to the detection of essential proteins with different properties, which makes the integration of them a logical next step. In this paper, we construct a new feature space, named CENT-ING-GO consisting of various centrality measures and GO terms, and provide a computational approach to predict essential proteins with various machine learning techniques. The experimental results show that CENT-ING-GO feature space improves performance over the INT-GO feature space in previous work by Acencio and Lemke in 2009. We also demonstrate that pruning a PPI with informative GO terms can improve the prediction performance further.

Construction and Analysis of Functional Networks in the Gut Microbiome of Type 2 Diabetes Patients

Although networks of microbial species have been widely used in the analysis of 16S rRNA sequencing data of a microbiome, the construction and analysis of a complete microbial gene network are in general problematic because of the large number of microbial genes in metagenomics studies. To overcome this limitation, we propose to map microbial genes to functional units, including KEGG orthologous groups and the evolutionary genealogy of genes： Non-supervised Orthologous Groups （eggNOG） orthologous groups, to enable the construction and analysis of a microbial functional network. We devised two statistical methods to infer pairwise relationships between microbial functional units based on a deep sequencing dataset of gut microbiome from type 2 diabetes （T2D） patients as well as healthy controls. Networks containing such functional units and their significant interactions were constructed subsequently. We conducted a variety of analyses of global properties, local properties, and functional modules in the resulting functional networks. Our data indicate that besides the observations consistent with the current knowledge, this study provides novel biological insights into the gut microbiome associated with T2D.

Network Motif Detection: Algorithms, Parallel and Cloud Computing,and Related Tools

Network motif is defined as a frequent and unique subgraph pattern in a network, and the search involves counting all the possible instances or listing all patterns, testing isomorphism known as NP-hard and large amounts of repeated processes for statistical evaluation. Although many efficient algorithms have been introduced, exhaustive search methods are still infeasible and feasible approximation methods are yet implausible.Additionally, the fast and continual growth of biological networks makes the problem more challenging. As a consequence, parallel algorithms have been developed and distributed computing has been tested in the cloud computing environment as well. In this paper, we survey current algorithms for network motif detection and existing software tools. Then, we show that some methods have been utilized for parallel network motif search algorithms with static or dynamic load balancing techniques. With the advent of cloud computing services, network motif search has been implemented with MapReduce in Hadoop Distributed File System（HDFS）, and with Storm, but without statistical testing. In this paper, we survey network motif search algorithms in general, including existing parallel methods as well as cloud computing based search, and show the promising potentials for the cloud computing based motif search methods.

Network Analysis Reveals A Signaling RegulatoryLoop in PIK3CA-mutated Breast Cancer Predicting Survival Outcome

Mutated genes are rarely common even in the same pathological type between cancer patients and as such, it has been very challenging to interpret genome sequencing data and difficult to predict clinical outcomes. PIK3 CA is one of a few genes whose mutations are relatively popular in tumors. For example, more than 46.6% of luminal-A breast cancer samples have PIK3 CA mutated, whereas only 35.5% of all breast cancer samples contain PIK3 CA mutations. To understand the function of PIK3 CA mutations in luminal A breast cancer, we applied our recentlyproposed Cancer Hallmark Network Framework to investigate the network motifs in the PIK3CA-mutated luminal A tumors. We found that more than 70% of the PIK3CA-mutated luminal A tumors contain a positive regulatory loop where a master regulator(PDGF-D), a second regulator(FLT1) and an output node(SHC1) work together. Importantly, we found the luminal A breast cancer patients harboring the PIK3 CA mutation and this positive regulatory loop in their tumors have significantly longer survival than those harboring PIK3 CA mutation only in their tumors. These findings suggest that the underlying molecular mechanism of PIK3 CA mutations in luminal A patients can participate in a positive regulatory loop, and furthermore the positive regulatory loop(PDGF-D/FLT1/SHC1) has a predictive power for the survival of the PIK3 CAmutated luminal A patients.

MTMO： an efficient network-centric algorithm for subtree counting and enumeration

Background： The frequency of small subtrees in biological, social, and other types of networks could shed light into the structure, function, and evolution of such networks. However, counting all possible subtrees of a prescribed size can be computationally expensive because of their potentially large number even in small, sparse networks. Moreover, most of the existing algorithms for subtree counting belong to the subtree-centric approaches, which search for a specific single subtree type at a time, potentially taking more time by searching again on the same network. Methods： In this paper, we propose a network-centric algorithm （MTMO） to efficiently count k-size subtrees. Our algorithm is based on the enumeration of all connected sets of k-1 edges, incorporates a labeled rooted tree data structure in the enumeration process to reduce the number of isomorphism tests required, and uses an array-based indexing scheme to simplify the subtree counting method. Results： The experiments on three representative undirected complex networks show that our algorithm is roughly an order of magnitude faster than existing subtree-centric approaches and base network-centric algorithm which does not use rooted tree, allowing for counting larger subtrees in larger networks than previously possible. We also show major differences between unicellular and multicellular organisms. In addition, our algorithm is applied to find network motifs based on pattern growth approach. Conclusions： A network-centric algorithm which allows for a This enables us to count larger motif in larger networks than faster counting of non-induced subtrees is proposed previously.

From Decision to Commitment： The Molecular Memory of Flowering

During the floral transition the shoot apical meristem changes its identity from a vegetative to an inflorescence state. This change in identity can be promoted by external signals, such as inductive photoperiod conditions or vernalization, and is accompanied by changes in expression of key developmental genes. The change in meristem identity is usually not reversible, even if the inductive signal occurs only transiently. This implies that at least some of the key genes must possess an intrinsic memory of the newly acquired expression state that ensures irreversibility of the process. In this review, we discuss different molecular scenarios that may underlie a molecular memory of gene expression.

Statistical Identification of Important Nodes in Biological Systems

Biological systems can be modeled and described by biological networks.Biological networks are typical complex networks with widely real-world applications.Many problems arising in biological systems can be boiled down to the identification of important nodes.For example,biomedical researchers frequently need to identify important genes that potentially leaded to disease phenotypes in animal and explore crucial genes that were responsible for stress responsiveness in plants.To facilitate the identification of important nodes in biological systems,one needs to know network structures or behavioral data of nodes(such as gene expression data).If network topology was known,various centrality measures can be developed to solve the problem;while if only behavioral data of nodes were given,some sophisticated statistical methods can be employed.This paper reviewed some of the recent works on statistical identification of important nodes in biological systems from three aspects,that is,1)in general complex networks based on complex networks theory and epidemic dynamic models;2)in biological networks based on network motifs;and 3)in plants based on RNA-seq data.The identification of important nodes in a complex system can be seen as a mapping from the system to the ranking score vector of nodes,such mapping is not necessarily with explicit form.The three aspects reflected three typical approaches on ranking nodes in biological systems and can be integrated into one general framework.This paper also proposed some challenges and future works on the related topics.The associated investigations have potential real-world applications in the control of biological systems,network medicine and new variety cultivation of crops.