A Modularity-Based Method Reveals Mixed Modules from Chemical-Gene Heterogeneous Network

<div><p>For a multicomponent therapy, molecular network is essential to uncover its specific mode of action from a holistic perspective. The molecular system of a Traditional Chinese Medicine (TCM) formula can be represented by a 2-class heterogeneous network (2-HN), which typically includes chemical similarities, chemical-target interactions and gene interactions. An important premise of uncovering the molecular mechanism is to identify mixed modules from complex chemical-gene heterogeneous network of a TCM formula. We thus proposed a novel method (MixMod) based on mixed modularity to detect accurate mixed modules from 2-HNs. At first, we compared MixMod with Clauset-Newman-Moore algorithm (CNM), Markov Cluster algorithm (MCL), Infomap and Louvain on benchmark 2-HNs with known module structure. Results showed that MixMod was superior to other methods when 2-HNs had promiscuous module structure. Then these methods were tested on a real drug-target network, in which 88 disease clusters were regarded as real modules. MixMod could identify the most accurate mixed modules from the drug-target 2-HN (normalized mutual information 0.62 and classification accuracy 0.4524). In the end, MixMod was applied to the 2-HN of Buchang naoxintong capsule (BNC) and detected 49 mixed modules. By using enrichment analysis, we investigated five mixed modules that contained primary constituents of BNC intestinal absorption liquid. As a matter of fact, the findings of <i>in vitro</i> experiments using BNC intestinal absorption liquid were found to highly accord with previous analysis. Therefore, MixMod is an effective method to detect accurate mixed modules from chemical-gene heterogeneous networks and further uncover the molecular mechanism of multicomponent therapies, especially TCM formulae.</p></div

An illustration of a chemical-gene heterogeneous network.

<p>The blue nodes are chemical constituents and the red nodes represent potential gene targets. This network is an instance of 2-class heterogeneous network [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0125585#pone.0125585.ref009" target="_blank">9</a>], which is more than a simple chemical-gene bipartite graph by including additional interactions between chemicals and between genes. Obviously, there are three mixed modules (1, 2, and 3) in this heterogeneous network. Each mixed module is a highly-interconnected unit in which chemicals directly or indirectly regulate the expression of corresponding genes. Additionally, module A and B are also considered as special cases of mixed module. Such modules may influence the final partition of module detection methods, but make little contribution to uncovering particular molecular mechanism.</p

GM evolutionary stabilization strategy.

Environmental protection talents training (EPTT) is recognized as a key prerequisite for maintaining environmental sustainability, and in order to study the influence of each player on EPTT. This paper innovatively constructs a tripartite evolutionary game model of government, university and enterprise. The equilibrium points and evolutionary stabilization strategies of each participant are solved by replicating the dynamic equations, and the behaviors of each subject in EPTT are analyzed so as to clarify the behavioral characteristics and optimal strategies of the government’s participation in EPTT. The results show that enterprises occupy a more important position in influencing government decisions. The government should reduce the financial incentives for enterprises and replace them with greater policy support. Meanwhile, the government should actively promote the cultivation mechanism that integrates universities and enterprises. The results of the study can provide a decision-making basis for the government to promote the sustainable development of EPTT.</div

Results of US implementation evolution simulation analysis.

Results of US implementation evolution simulation analysis.</p

Performance of five methods on real drug-target heterogeneous network.

<p>All modules include mixed modules and modules of single-class nodes.</p><p>Performance of five methods on real drug-target heterogeneous network.</p

GM excitation evolution simulation analysis results.

GM excitation evolution simulation analysis results.</p

Tests of five methods on benchmark 2-HNs with varying <i>μ</i>_A and <i>μ</i>_B.

<p>(<b>a</b>). Normalized Mutual Informations (NMIs) of five methods on benchmarks with <i>p</i> = 0.5 and <i>μ</i>_B = 0.2. (<b>b</b>). NMIs when <i>p</i> = 0.5 and <i>μ</i>_B = 0.8. (<b>c</b>). NMIs when <i>μ</i>_A = 0.2 and <i>p</i> = 0.5. (<b>d</b>). NMIs when <i>μ</i>_A = 0.8 and <i>p</i> = 0.5. (<b>e</b>)(<b>f</b>)(<b>g</b>)(<b>h</b>). CAs of five methods on 2-HNs with different parameters. In these figures, the variation curve of each method is marked by a unique color as shown in (<b>f</b>).</p

Evolutionary simulation analysis results.

Environmental protection talents training (EPTT) is recognized as a key prerequisite for maintaining environmental sustainability, and in order to study the influence of each player on EPTT. This paper innovatively constructs a tripartite evolutionary game model of government, university and enterprise. The equilibrium points and evolutionary stabilization strategies of each participant are solved by replicating the dynamic equations, and the behaviors of each subject in EPTT are analyzed so as to clarify the behavioral characteristics and optimal strategies of the government’s participation in EPTT. The results show that enterprises occupy a more important position in influencing government decisions. The government should reduce the financial incentives for enterprises and replace them with greater policy support. Meanwhile, the government should actively promote the cultivation mechanism that integrates universities and enterprises. The results of the study can provide a decision-making basis for the government to promote the sustainable development of EPTT.</div

Tests of four methods on weighted benchmarks.

<p>(<b>a</b>). Normalized Mutual Informations (NMIs) of four methods on 2-HNs with different <i>μ</i>_A, <i>μ</i>_B and <i>p</i>. The subnetwork <i>G</i>_A of each 2-HN is weighted according to the weighting scheme of LFR benchmark. (<b>b</b>). NMIs of four methods on 2-HNs with weighted subnetwork <i>G</i>_Π. (<b>c</b>). NMIs of four methods on 2-HNs with weighted <i>G</i>_B.</p

Stability judgment of each equilibrium point.

Environmental protection talents training (EPTT) is recognized as a key prerequisite for maintaining environmental sustainability, and in order to study the influence of each player on EPTT. This paper innovatively constructs a tripartite evolutionary game model of government, university and enterprise. The equilibrium points and evolutionary stabilization strategies of each participant are solved by replicating the dynamic equations, and the behaviors of each subject in EPTT are analyzed so as to clarify the behavioral characteristics and optimal strategies of the government’s participation in EPTT. The results show that enterprises occupy a more important position in influencing government decisions. The government should reduce the financial incentives for enterprises and replace them with greater policy support. Meanwhile, the government should actively promote the cultivation mechanism that integrates universities and enterprises. The results of the study can provide a decision-making basis for the government to promote the sustainable development of EPTT.</div