Bow-tie topological features of metabolic networks and the functional significance

Abstract

Exploring the structural topology of genome-based large-scale metabolic network is essential for investigating possible relations between structure and functionality. Visualization would be helpful for obtaining immediate information about structural organization. In this work, metabolic networks of 75 organisms were investigated from a topological point of view. A spread bow-tie model was proposed to give a clear visualization of the bow-tie structure for metabolic networks. The revealed topological pattern helps to design more efficient algorithm specifically for metabolic networks. This coarse-grained graph also visualizes the vulnerable connections in the network, and thus could have important implication for disease studies and drug target identifications. In addition, analysis on the reciprocal links and main cores in the GSC part of bow-tie also reveals that the bow-tie structure of metabolic networks has its own intrinsic and significant features which are significantly different from those of random networks.Keywords: bioinformatics; metabolic network; bow-tie; random network.As the results of various genome projects, the genome sequences of many organisms are available and the organism specific metabolic networks can be faithfully reconstructed from genome information [1][2][3][4][5][6] . Thus the prediction of function from the metabolic networks has become an essential step in the post-genomic era [4,[7][8][9][10][11] . However, before it is possible to investigate the potential relationship between structure and functionality of a metabolic network, it is necessary to study how the metabolic networks are actually constructed.In recent years there has been a strongly increasing passion in investigating the intricate structures of link topologies in metabolic networks [12][13][14][15][16][17][18][19][20][21] . Many researchers have applied methods from graph theory to treat the metabolic networks as a directed graph consisting of nodes denoting metabolites connected by directed arcs representing reactions. An important finding is that metabolic networks, as well as other real-world complex networks, have topologies that differ markedly from those found in simple randomly connected networks [22] , which suggests that their non-random structures could imply significant organizing principles of metabolic networks.From the computational analysis of genome-based metabolic networks of 65 organisms, Ma and Zeng discovered that the global metabolic network is organized in the form of a bow-tie [15] . On the other hand, from the view of material flows and information flows in the metabolic system, Csete and Doyle described metabolism as several nested bow-ties [23] . It was pointed out that bow-tie architectures facilitate robust biologic function, and based on their design, also have

Influence of assortativity and degree-preserving rewiring on the spectra of networks

“…The inequality (13) with (5) shows that the lower bound for the largest eigenvalue λ 1 of the adjacency matrix A is strictly increasing in the linear degree correlation coefficient ρ D (except for regular graphs). Given the degree vector d is constant, inequality (13) shows that the largest eigenvalue λ 1 is obtained in case we succeed to increase the assortativity of the graph by degree-preserving rewiring, which is discussed in Section 5.…”

“…Consequently, degree correlation related investigations have been performed along various axes: (a) models to generate networks with given a e-mail: h.wang@tudelft.nl degree correlation have been developed [2,3]; (b) the effect of degree correlation on topological properties is studied in [4,5], and (c) the influence of degree correlation in dynamic processes on networks such as the epidemic spreading [6] and on percolation phenomena [7] have been targeted. Relations between degree correlation and other topological or dynamic features are examined experimentally [5] or in a specific network model [6,7]. "Local" assortativity is proposed in [8].…”

Assortativity of complementary graphs

“…Consequently, many a e-mail: h.wang@tudelft.nl b e-mail: w.winterbach@tudelft.nl c e-mail: p.f.a.vanmieghem@tudelft.nl investigations have focused on (a) exploring the relation between assortativity and other topological properties as well as spectra of networks [3][4][5] and (b) understanding the effect of assortativity on dynamic network processes such as the epidemic spreading [6] and percolation phenomena [7]. Relations between degree correlation and other topological or dynamic features are mostly studied experimentally [4] or in a specific network model [6,7]. Recently, we have verified spectral bounds for the assortativity [3] and we have studied how the modularity changes under degree-preserving rewiring [8], which alters the assortativity of the graph.…”

Structural and Functional Analysis of Giant Strong Component of Bacillus thuringiensis Metabolic Network

“…Since Ma and Zeng proposed (24) the "bow tie" structure of metabolic networks, it is increasingly recognized as being a conserved property of complex networks, as highlighted by recent studies (6,20,21,37), and the results suggest that this structure property is functional meaningful for metabolism, disease and the design principle of biological robustness.…”

“…It should be noted that most nodes in S, P and IS part are connected by some single link which are not interested herein, while the metabolites and reactions involved in the GSC part is clearly much less than the whole network, and would be used to reduce the complexity of applying other pathway analysis methods such as extreme pathways and elementary modes (33,34). Furthermore, the GSC is the biggest strongly connected components of a metabolic network and determined structure of the entire network at a certain extent (24,37), thus it would be more detailed analysis herein.…”