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. 2018 Jul 9;19(Suppl 7):194.
doi: 10.1186/s12859-018-2175-5.

A Study on Multi-Omic Oscillations in Escherichia Coli Metabolic Networks

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Free PMC article

A Study on Multi-Omic Oscillations in Escherichia Coli Metabolic Networks

Francesco Bardozzo et al. BMC Bioinformatics. .
Free PMC article

Abstract

Background: Two important challenges in the analysis of molecular biology information are data (multi-omic information) integration and the detection of patterns across large scale molecular networks and sequences. They are are actually coupled beause the integration of omic information may provide better means to detect multi-omic patterns that could reveal multi-scale or emerging properties at the phenotype levels.

Results: Here we address the problem of integrating various types of molecular information (a large collection of gene expression and sequence data, codon usage and protein abundances) to analyse the E.coli metabolic response to treatments at the whole network level. Our algorithm, MORA (Multi-omic relations adjacency) is able to detect patterns which may represent metabolic network motifs at pathway and supra pathway levels which could hint at some functional role. We provide a description and insights on the algorithm by testing it on a large database of responses to antibiotics. Along with the algorithm MORA, a novel model for the analysis of oscillating multi-omics has been proposed. Interestingly, the resulting analysis suggests that some motifs reveal recurring oscillating or position variation patterns on multi-omics metabolic networks. Our framework, implemented in R, provides effective and friendly means to design intervention scenarios on real data. By analysing how multi-omics data build up multi-scale phenotypes, the software allows to compare and test metabolic models, design new pathways or redesign existing metabolic pathways and validate in silico metabolic models using nearby species.

Conclusions: The integration of multi-omic data reveals that E.coli multi-omic metabolic networks contain position dependent and recurring patterns which could provide clues of long range correlations in the bacterial genome.

Keywords: Antibiotic response; E. coli; Multi-omic metabolic networks; Multi-omic motifs; Multi-omics; omic regularities.

Conflict of interest statement

Ethics approval and consent to participate

No human, animal or plant experiments were performed in this study, and ethics committee approval was therefore not required.

Competing interests

The authors declare that they have no competing interests.

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Figures

Fig. 1
Fig. 1
The E.coli multi-omic space is represented in Figure a: different layers represent different omics. Genomic layer (blue rectangles) presents binary discretized omic values, the same for the other layers. Multi-omics in steady state conditions could be perturbed by induced treatmens thus increasing the number of layers for each multi-omic space. Then, the number of perturbed layers depends on the number of experiment considered. Recurring multi-omic patterns motifs related with pathways are represented with multi-omic layers structure (MLS), as shown in Figure b. Figure b part (1) represents the j-th pathway in relation with its associated set of genes (Figure b part (2)); the resultant multi-omic pattern is shown in Figure b part (3). The recurring multi-omic pattern is an array of pathway gene products multi-omic values arranged by the gene order. Multi-omics on the patterns are oscillating, in other words, low values follow high values and vice-versa. This feature is deeply related to the gene positions as shown in Figure c part (1) and (2). Oscillating multi-omics are present in succession along the pattern as shown in a1 and a2 of Figure d part (1). The patterns lose their oscillating features if two adjacent multi-omic values are not oscillating in an half (a1 of Figure d part (2)) or completely (a1 and a2 of Figure d part (3))
Fig. 2
Fig. 2
In this Figure, the whole procedure block diagram is described. Gray blocks represent the extraction of multi-omic values and structures. Then, the global and the local effects (blue blocks) are computed. The local effect depends on the type of Multi-layered structure (network + sequence) (violet block). Once the multi-omic effects are computed and normalized, then these values are discretised in 0/1. After that, the oscillation measures are computed in the respective structures (networks and sequences). The generated multi-omic patterns (from sequences) and motifs (from networks) are given in input to the algorithm MORA for the computation of their reciprocal influences. This procedure is computed in standard conditions and after perturbations obtaining combined and competing patterns/motifs
Fig. 3
Fig. 3
Multi-omic pattern operon compression is shown in Figure a. The elements that belong to the same operon (e2- e3- e4) are merged to the more frequent multi-omic value: in this case the low one (blue-head cylinder). The path extension is shown in Figure b. In this case, the MLS is modified searching an alternative path, on the global metabolic network, that links two nodes associated to two not oscillating pattern adjacent multi-omics (i.e the multi-omics in the positions e2- e3 and e3- e4). The multi-omic path, chosen from among all the alternative paths on the whole metabolic network, is the shortest path with the most oscillating multi-omics. (i.e in the path extension between e3- e4 is chosen the path p3- p5- p4 (violet dotted lines) and not the path p3- p8- p4
Fig. 4
Fig. 4
Figure 4 (a) part (1): Multi-omics are normalized considering the complete multi-omic space. Figure 4 (a) part (2): For each recurring multi-omic pattern, the multi-omics are normalized considering a small sample filtered from the multi-omic space by a specific pathway of N elements. Then, the global effect vector mov2 and the local effect vector mov1 are obtained: both the vectors have the same lenght but different multi-omic normalized values. Figure 4b part (1): The vectors of the global effect (pink) and the local effect (gray) are binary discretized. Figure 4b part (2): In order to consider the global response to treatments, the missing mov1 oscillations are substituted with the mov2 oscillations (if they are present). In this example the 4-th oscillation is FALSE (a1local) on the local vector and is present (a1global=TRUE) on the global vector. Then, the local effect is updated with the information of the multi-omics that come from the global effect. This procedure is done in steady state conditions and after perturbed by treatments multi-omic values
Fig. 5
Fig. 5
Two steps of the MORA algorithm. In the first step (part a), given the average path length (APL), MORA searches the shortest paths between the two adjacent multi-omics ej and ej+1. of length: ψ∈[1, ⌈APL⌉]. The green dotted line indicates paths of length ψ=1 and the magenta dotted lines represents paths of length ψ=1, MORA does not searches a path of length 3 (which would imply ψ=3) because we supposed that the APL = 2. The algorithm then updates the weight vector infl and moves on the next pattern positions where searches for the next adjacent multi-omics (ej+1 and eh=j+2). In the second step (part b) MORA evaluates the shortest paths for ψ=1 and 2. The array of the weights infl is updated, as shown in the step i to i+3, according to the algorithm
Fig. 6
Fig. 6
The anti-dyadic effect magnitudes (y-axis) and the dyadic effect magnitudes (x-axis) of 66 pathways are shown in Figure a. The pink rectangle underlines the area where the pathways present an anti-dyadic effect m01^1, instead the blue rectangle individuates the area where the average dyadic effect is m1100^1. The pathways with path extensions are shown with blue dots while black dots depict the same pathways without deviations. The number on the dots is the KEGG pathway identifier without its suffix path:eco. In Figure b the anti-dyadic effect is shown on the y-axis m01^ and the pattern similarity σobs to an ideal oscillating multi-omic pattern on the x-axis. Black dots describe pathways without extensions, and triangles depict those with extensions. The black and blue curves correspond to the two-dimensional kernel density estimation both for the dots and for the triangles. The plot is clearly separable with a binary classifier, individuating principally two bands (the black and the blue ones). Both the plots show that pathways without extensions have a median reciprocal influence =1±0.27 per node. Instead, pathways with extensions present a median reciprocal influences of =2±0.62 per node. Pathways with extensions present present better MORA reciprocal influences than pathways without extensions. The pathway is presented with a big shape on the plot if the RI is > 1.5 (more adjacent). Opposite, pathways with RI ≤ 1.5 are classified as less adjacent
Fig. 7
Fig. 7
The anti-dyadic effect magnitudes m01^ (y-axis) and the similarity score magnitudes σobs (x-axis) of 66 pathways are shown in Figure. The 66 pathways with extensions subject to the average effect of 69 treatments are shown with the blue triangles. The same pathways in steady state conditions are represented with black dots. The pathway is presented with a big shape on the plot if the RI is > 1.5 (more adjacent). Opposite, pathways with RI ≤ 1.5 are classified as less adjacent
Fig. 8
Fig. 8
An MLS with high reciprocal influences (RI) but with a low number of oscillating multi-omics is shown in (1). On this MLS, due to the effect of the treatments t, an oscillating multi-omic circuit is activated (orange links in the yellow circle) and is deactivated another one. The MLS become combined due to the effect of t because both the pattern and the pathway show oscillating multi-omics at the same time. Opposite, in (2), the effect of treatments activate and deactivate the same oscillating multi-omic circuits, but, due to the changed pattern elements order, only the pathway shows oscillating multi-omics, instead the pattern shows a low number of oscillations. In this case, the structures are defined competitor. The change of only two multi-omic values (p3 and p5) on the overall pathway and on the pattern (e3 and e5) affect the whole recurring multi-omic pattern and its MLS

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