Survey/review study A Mini Review of Node Centrality Metrics in Biological Networks Mengyuan Wang 1,2, Haiying Wang 1, and Huiru Zheng 1,* 1 School of Computing, Ulster University, Belfast, BT15 1ED, United Kingdom 2 Scotland’s Rural College, Edinburgh, EH25 9RG, United Kingdom * Correspondence: h.zheng@ulster.ac.uk     Received: 31 October 2022 Accepted: 21 November 2022 Published: 22 December 2022   Abstract: The diversity of nodes in a complex network causes each node to have varying significance, and the important nodes often have a significant impact on the structure and function of the network. Although the interpretation of the results of biological networks must always depend on the topological study of nodes, there is presently no consensus on how to use these metrics, and most network analyses always result in a basic interpretation of a limited number of metrics. To thoroughly comprehend biological networks, it is necessary to consistently understand the notion of node centrality. Therefore, for 10 typical nodal metrics in biological networks, the study first assesses their current applications, advantages, disadvantages as well as potential applications. Then, a review of previous studies is provided, and suggestions are made correspondingly for the purpose of improving biological topology algorithms. Finally, the following recommendations are made in this study: (1) a comprehensive and accurate assessment of node centrality necessitates the use of multiple metrics, including both the target node and its surroundings, and density of maximum neighbourhood component(DMNC) can be used as a complement to other node centrality metrics; (2) different centrality metrics can be applied to identify nodes with different functions, which in this study are mapped as modular surroundings, bridging roles, and susceptibility; and (3) the following groups of node centrality can often be verified against each other, including degree and maximum neighbourhood component (MNC), eccentricity, closeness and radiality; stress and betweenness.

Metabolites are the final production of biochemical reactions in the rumen micro-ecological system and are very sensitive to changes in rumen microbes. Nuclear magnetic resonance (NMR) spectroscopy could both identify and quantify the metabolic composition of the ruminal fluid, which reflects the interaction between rumen microbes and diet. The main challenge of untargeted metabolomics is the compound annotation. Based on nonlinear and linear associations between microbial gene abundances and integrals derived from NMR spectra, combined with knowledge of enzymatic reaction from the KEGG database, this study developed a knowledge-driven network-based analytical framework for the inference of metabolites. There were 89 potential metabolites inferred from the integral co-occurrence network. The results are supported by dissimilarity network analysis. The coexistence of non-linear and linear associations between microbial gene abundances and spectral integrals was detected. The study successfully found the corresponding integrals for acetate, butyrate and propionate, which are the major volatile fatty acids (VFA) in the rumen. This novel framework could very efficiently infer metabolites to corresponding integrals from NMR spectra.

Accurate quantification of volatile fatty acid (VFA) concentrations in rumen fluid are essential for research on rumen metabolism. The study comprehensively investigated the pros and cons of High-performance liquid chromatography (HPLC) and 1H Nuclear magnetic resonance (1H-NMR) analysis methods for rumen VFAs quantification. We also investigated the performance of several commonly used data pre-treatments for the two sets of data using correlation analysis, principal component analysis (PCA) and partial least squares discriminant analysis (PLS-DA). The molar proportion and reliability analysis demonstrated that the two approaches produce highly consistent VFA concentrations. In the pre-processing of NMR spectra, line broadening and shim correction may reduce estimated concentrations of metabolites. We observed differences in results using multiplet of different protons from one compound and identified “handle signals” that provided the most consistent concentrations. Different data pre-treatment strategies tested with both HPLC and NMR significantly affected the results of downstream data analysis. “Normalized by sum” pre-treatment can eliminate a large number of positive correlations between NMR-based VFA. A “Combine” strategy should be the first choice when calculating the correlation between metabolites or between samples. The PCA and PLS-DA suggest that except for “Normalize by sum”, pre-treatments should be used with caution.

A better understanding of rumen microbial interactions is crucial for the study of rumen metabolism and methane emissions. Metagenomics-based methods can explore the relationship between microbial genes and metabolites to clarify the effect of microbial function on the host phenotype. This study investigated the rumen microbial mechanisms of methane metabolism in cattle by combining metagenomic data and network-based methods. Based on the relative abundance of 1461 rumen microbial genes and the main volatile fatty acids (VFAs), a multilayer heterogeneous network was constructed, and the functional modules associated with metabolite-microbial genes were obtained by heat diffusion. The PLS model by integrating data from VFAs and microbial genes explained 72.98% variation of methane emissions. Compared with single-layer networks, more previously reported biomarkers of methane prediction can be captured by the multilayer network. More biomarkers with the rank of top 20 topological centralities are from the PLS model of diffusion subset. The heat diffusion algorithm is different from the strategy used by the microbial metabolic system to understand methane phenotype. It inferred 24 novel biomarkers that were preferentially affected by changes in specific VFAs. Results showed that the heat diffusion multilayer network approach improved the understanding of the microbial patterns of VFA affecting methane emissions which represented by the functional genes.