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A computational exploration of resilience and evolvability of protein-protein interaction networks - PubMed

  • ️Fri Jan 01 2021

A computational exploration of resilience and evolvability of protein-protein interaction networks

Brennan Klein et al. Commun Biol. 2021.

Abstract

Protein-protein interaction (PPI) networks represent complex intra-cellular protein interactions, and the presence or absence of such interactions can lead to biological changes in an organism. Recent network-based approaches have shown that a phenotype's PPI network's resilience to environmental perturbations is related to its placement in the tree of life; though we still do not know how or why certain intra-cellular factors can bring about this resilience. Here, we explore the influence of gene expression and network properties on PPI networks' resilience. We use publicly available data of PPIs for E. coli, S. cerevisiae, and H. sapiens, where we compute changes in network resilience as new nodes (proteins) are added to the networks under three node addition mechanisms-random, degree-based, and gene-expression-based attachments. By calculating the resilience of the resulting networks, we estimate the effectiveness of these node addition mechanisms. We demonstrate that adding nodes with gene-expression-based preferential attachment (as opposed to random or degree-based) preserves and can increase the original resilience of PPI network in all three species, regardless of gene expression distribution or network structure. These findings introduce a general notion of prospective resilience, which highlights the key role of network structures in understanding the evolvability of phenotypic traits.

© 2021. The Author(s).

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Conflict of interest statement

The authors declare no competing interests.

Figures

Fig. 1
Fig. 1. Change in the Shannon diversity and network resilience.

A visual intuition is provided to depict how network structure is associated with a particular resilience value. a Network resilience is calculated by iteratively isolating fractions of nodes in the network, f, eventually leaving N isolated nodes. b Following every iteration, the Shannon diversity of the component size distribution is calculated, in this case starting at f = 0 (one connected component), and increasing until every node is disconnected, f = 1. c Increasing the fraction of nodes that have been isolated creates a curve of increasing entropy values, which is used to compute the network resilience, as in Eq. (2). d An example of the prospective resilience of the network shown in (a). New nodes are iteratively added to the original network, with m links attached randomly or preferentially based on the degree of nodes in the network.

Fig. 2
Fig. 2. Ribosomal networks.

These species have ribosomal interaction networks that span a range of different network structures. Node colors depict detected communities in the networks. Nodes of a given color are more likely to connect to other nodes of that color. Node size is proportional to gene expression. a S. cerevisiae ribosomal network. b E. coli ribsomoal network. c H. sapiens ribosomal network. d–f Gene expression distribution of ribosomal networks for S. cerevisiae, E. coli, and H. sapiens respectively. g–i Gene expression (in transcripts per million, TPM) plotted against node degree for (S. cerevisiae, E. coli, H. sapiens), respectively. To accentuate clusters of nodes that share degree and gene expression attributes, the points in these plots share the same color as their corresponding nodes in (a–c). Node size is not included here to improve clarity.

Fig. 3
Fig. 3. The effect of attachment mechanism on network structure.

A visual depiction of the effect of adding nodes under different attachment mechanisms. In each example, 10 nodes are added, connecting their m = 4 links to nodes in the original network (indicated by the black nodes). Node size corresponds to its likelihood of gaining new links. a Example network, before node addition. b Example of uniform attachment. c Example of (simulated) gene expression preferential attachment. d Example of degree-based preferential attachment. e–g Depicts the change in the original network’s degree distribution after the addition of 10 nodes, under each attachment mechanism (uniform, gene expression, and degree based). The white bars are transparent to show overlap. While these histograms highlight the change in a single network property (degree, k), one can imagine a number of structural changes occurring following the addition of new nodes, depending on the attachment mechanism.

Fig. 4
Fig. 4. Prospective resilience of three ribosomal networks.

As more nodes are added (horizontal axes), the resilience of the resulting network changes (vertical axes). The color of each curve corresponds to the number of new links that each new node enters the network with, and the line style (solid, dashed, or dotted) corresponds to the three different node attachment mechanisms. a Prospective resilience of S. cerevisiae ribosomal network. b Prospective resilience of E. coli ribosomal network. c Prospective resilience of H. sapiens ribosomal network. Ribbons around each curve correspond to their 95% confidence intervals.

Fig. 5
Fig. 5. Prospective modularity of three ribosomal networks.

As a comparison measure, we also examine how the modularity of the network changes following the addition of new nodes. The color scheme and line styles are the same as in Fig. 4. a Prospective modularity of S. cerevisiae ribosomal network. b Prospective modularity of E. coli ribosomal network. c Prospective modularity of H. sapiens ribosomal network. Crucially, we do not find any evidence that the prospective resilience results observed in Fig. 4 are being driven by the change in the networks' community structures, as the plots here show highly divergent patterns, suggesting that there is a more distinct mechanism underlying prospective resilience.

Fig. 6
Fig. 6. Prospective resilience and randomized gene expression.

We examine if specific gene expression is driving the high prospective resilience of the expression-based attachment rule or if merely attaching nodes based on a shuffled gene expression distribution could bring about these results. Each new node joins with m = 5 for S. cerevisiae and E. coli, and m = 6 for H. sapiens. These values were selected so that the slope of the prospective resilience would be closest to 0.0 when the gene expression was not shuffled (0% shuffled). See Table 2 for how the correlation between a node’s degree and its gene expression changes as noise increases. a Prospective resilience of S. cerevisiae ribosomal network. b Prospective resilience of E. coli ribosomal network. c Prospective resilience of H. sapiens ribosomal network. Notably, we find that the prospective resilience of the networks increases simply by increasing the fraction of nodes with shuffled gene expressions.

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