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. 2017 Dec 21;11(Suppl 7):133.
doi: 10.1186/s12918-017-0509-y.

Construction and analysis of gene-gene dynamics influence networks based on a Boolean model

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Construction and analysis of gene-gene dynamics influence networks based on a Boolean model

Maulida Mazaya et al. BMC Syst Biol. .

Abstract

Background: Identification of novel gene-gene relations is a crucial issue to understand system-level biological phenomena. To this end, many methods based on a correlation analysis of gene expressions or structural analysis of molecular interaction networks have been proposed. They have a limitation in identifying more complicated gene-gene dynamical relations, though.

Results: To overcome this limitation, we proposed a measure to quantify a gene-gene dynamical influence (GDI) using a Boolean network model and constructed a GDI network to indicate existence of a dynamical influence for every ordered pair of genes. It represents how much a state trajectory of a target gene is changed by a knockout mutation subject to a source gene in a gene-gene molecular interaction (GMI) network. Through a topological comparison between GDI and GMI networks, we observed that the former network is denser than the latter network, which implies that there exist many gene pairs of dynamically influencing but molecularly non-interacting relations. In addition, a larger number of hub genes were generated in the GDI network. On the other hand, there was a correlation between these networks such that the degree value of a node was positively correlated to each other. We further investigated the relationships of the GDI value with structural properties and found that there are negative and positive correlations with the length of a shortest path and the number of paths, respectively. In addition, a GDI network could predict a set of genes whose steady-state expression is affected in E. coli gene-knockout experiments. More interestingly, we found that the drug-targets with side-effects have a larger number of outgoing links than the other genes in the GDI network, which implies that they are more likely to influence the dynamics of other genes. Finally, we found biological evidences showing that the gene pairs which are not molecularly interacting but dynamically influential can be considered for novel gene-gene relationships.

Conclusion: Taken together, construction and analysis of the GDI network can be a useful approach to identify novel gene-gene relationships in terms of the dynamical influence.

Keywords: Boolean dynamics; Gene-gene dynamics influence (GDI); Gene-gene molecular interaction (GMI) networks; Knockout mutation; Structural characteristics.

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Figures

Fig. 1
Fig. 1
An illustrative example of computing the gene-gene dynamics influence value. a An example GMI network. Given a network G(V, A) with a set of update rules F, let v 3 a node subjected to the knockout mutation for t ≤ T. The knockout mutation changes F into F where the state value of v 3 is frozen to 0 for t ≤ T. b Identification of wild-type and mutant attractors. Let [0000] ∈ S be an initial state considered in this example. By examining two state trajectories along with F and F , respectively, we obtain two corresponding attractors, 〈G, F, v(0)〉 and 〈G, F , v(0)〉 of which the least common multiple of the lengths is four. c Computation of a distance between wild-type and mutant attractors. Since the greatest common divisor of the lengths of two attractors is two, we examine two different alignments of the state sequences of v 1 in those attractors. The number of different bits between [0101] and [0001] is 1 in case 1 (m = 0), whereas that between [1010] and [0001] is 3 in case 2 (m = 1). Accordingly, the minimum bitwise difference is 1, and hence d(v(0),v3,v1)=14. We can compute μ(v 3, v 1) by averaging out d(v(0), v 3, v 1) over the set of initial states. d The resultant GDI network. The left matrix shows the dynamics influence value for every ordered pair of genes, and the right graph shows the resultant GDI network with nine positive dynamics influence relations
Fig. 2
Fig. 2
Visualization of the GMI and the corresponding GDI networks in the case of AMRN. a The GMI network with |V| = 10 and |A| = 20. Arrow-headed and bar-headed lines indicate activating (positive) and inhibitory (negative) interactions, respectively. b The corresponding GDI network with |V| = 10 and |A | = 38. The gene pairs belonging to MIDI and MNDI groups are represented by black and red colored links, respectively. There was no gene pair belonging to MIDN group
Fig. 3
Fig. 3
Degree distributions of the GMI and the corresponding GDI networks in HSN. a-c Results of degree, in-degree, and out-degree distributions, respectively. The mutation duration time (T) was set to 20 in generating the GDI network. Y-axis represents a log-scaled frequency and blank triangle points (Δ) mean zero value of a frequency. We observed that the proportions of a same bin in GMI and GDI networks are significantly different from each other for most ranges (All P-values were less than 0.003 in (a) except for degree range ‘0–4’, less than 0.0001 in (b) except for in-degree range ‘0–4’, and were less than 0.002 in (c) except for out-degree range ‘0–4’. d Correlation coefficients between degree/in-degree/out-degree values of a node in the GMI and the GDI networks. The mutation duration time was varied from 2 to 20. Each of degree, in-degree, and out-degree of a node in the GDI network showed a significant positive relationship with that in the GMI network (All p-values <0.0001)
Fig. 4
Fig. 4
Relationship of the GDI value to the length of a shortest path in the GDI networks. a-c Results of AMRN, ABAN, and HSN, respectively. Y-axis values mean the correlation coefficients between μ(v i, v j) and l(v i, v j) for all ordered pairs of genes. The mutation duration time was varied from 1 to 10 in (a) and (b), and from 2 to 20 in (c)
Fig. 5
Fig. 5
Relationship of the GDI value to the number of paths in the GDI networks. a-c Results of AMRN, ABAN, and HSN, respectively. Y-axis values mean the correlation coefficients between μ(v i, v j) and n(v i, v j) for all ordered pairs of genes. The mutation duration time was varied from 1 to 10 in (a) and (b), and from 2 to 20 in (c)
Fig. 6
Fig. 6
Out-degree and in-degree comparisons between non-drug targets and drug-targets in GDI network derived from HSN. a Result of out-degree. The average out-degree of the drug-targets with side-effects was larger than those of non-drug targets and drug-targets without side-effects in every mutation duration time except for T = 2 (All P-values <0.0001). b Result of in-degree. Non-drug target, drug-target without side-effect, and drug-target with side-effect are represented by blue, red, and green color, respectively. The average in-degree of the drug-targets with side-effects was smaller than those of non-drug targets and drug-targets without side-effects in every mutation duration time (All P-values <0.0001). The mutation duration time was varied from 2 to 20

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