Perturbation Centrality and Turbine: A Novel Centrality Measure Obtained Using a Versatile Network Dynamics Tool

Analysis of network dynamics became a focal point to understand and predict changes of complex systems. Here we introduce Turbine, a generic framework enabling fast simulation of any algorithmically definable dynamics on very large networks. Using a perturbation transmission model inspired by communicating vessels, we define a novel centrality measure: perturbation centrality. Hubs and inter-modular nodes proved to be highly efficient in perturbation propagation. High perturbation centrality nodes of the Met-tRNA synthetase protein structure network were identified as amino acids involved in intra-protein communication by earlier studies. Changes in perturbation centralities of yeast interactome nodes upon various stresses well recapitulated the functional changes of stressed yeast cells. The novelty and usefulness of perturbation centrality was validated in several other model, biological and social networks. The Turbine software and the perturbation centrality measure may provide a large variety of novel options to assess signaling, drug action, environmental and social interventions. The Turbine algorithm is available at: http://www.turbine.linkgroup.huComment: 21 pages, 4 figues, 1 table, 58 references + a Supplement of 52 pages, 10 figures, 9 tables and 39 references; Turbine algorithm is available at: http://www.turbine.linkgroup.h

Correlation between perturbation centrality and other centrality measures.

<p>Perturbation centrality was compared to other centrality measures calculated as described in <b>Supplementary Methods</b> of <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059.s001" target="_blank">Text S1</a></b>. Spearman correlations above r = 0.7 are marked with bold letters, correlations below r = 0.3 are marked with italics. Highest correlations were observed between perturbation centrality <i>versus</i> closeness centrality, community centrality <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059-Kovcs1" target="_blank">[29]</a> and weighted degree. This underlines the observations that besides geodesic distance (closeness centrality), modular position and degree also contribute to good perturbation properties. Note that measured correlations between perturbation and closeness centralities are much weaker than the correlations between the reciprocal of fill time and closeness centrality (mean is 0.895 in <b>Table S1</b> compared to 0.67 here, p = 0.000487, Wilcoxon rank-sum test; correlations with closeness centrality failed the Shapiro normality test with p = 0.0019)</p>a<p>Network descriptions are given in <b>Supplementary Methods</b> and <b>Table S7</b> of <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059.s001" target="_blank">Text S1</a></b>.</p>b<p>Community centrality was calculated using the LinkLand community detection method of the ModuLand family as described by Kovács <i>et al</i>. <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059-Kovcs1" target="_blank">[29]</a>.</p>c<p>PageRank values were calculated using the algorithm of the igraph library <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059-Csardi1" target="_blank">[59]</a>.</p

Difference in perturbation propagation between benchmark graphs with pronounced and fuzzy modules.

<p>Two times 7 randomly selected scale-free, modular benchmark graphs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059-Lancichinetti1" target="_blank">[28]</a> were generated as described in <b>Supplementary Methods</b> and <b>Table S7</b> of <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059.s001" target="_blank">Text S1</a></b> with ratios of inter-modular edges of 0.05 (∼300 of ∼6,000 edges were inter-modular) and 0.4 (∼2400 of ∼6,000 edges were inter-modular), termed as “pronounced modules” and “fuzzy modules”, respectively. Panel A: average fill times and silencing times, separately for the “fuzzy” and the “pronounced” group of networks. Fill times and silencing times were determined as described in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#s4" target="_blank">Methods</a></b>. Continuous perturbation intensity for fill time was 10,000 units, while initial perturbation intensities for silencing times were 10,000 or 1,000,000 units at low intensity or at high intensity perturbations, respectively. The three asterisk signs mark statistically significant differences with α = 0.001. Dark red bars and light blue bars represent pronounced modules and fuzzy modules, respectively. Bar letter codes refer to Panels showing snapshots of perturbations with identical conditions. Panels B through E show image snapshots created by the Turbine viewer after 50 time-steps of the simulation, using a heat-based color map. (The order of colors marking the lowest to highest perturbation is: black → red → orange → yellow → white). Perturbation values were scaled logarithmically. Panels B and C show the effect of low intensity starting perturbations (S = 10,000), while Panels D and E show the effect of high intensity starting perturbations (S = 1,000,000). Panels B and D show benchmark graphs with pronounced modules, while Panels C and E show benchmark graphs with fuzzy modules.</p

Substrate binding-induced perturbation centrality changes mark important residues of <i>E. coli</i> Met-tRNA synthetase.

<p>Protein structure networks of the substrate-free and substrate-bound forms of <i>E. coli</i> Met-tRNA synthetase protein were generated as described in the <b>Supplementary Methods</b> of <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059.s001" target="_blank">Text S1</a></b>. Perturbation centralities and the underlying protein structure network of Met-tRNA synthetase were calculated and visualized by the Turbine program as described in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#s4" target="_blank">Methods</a></b>, and were overlaid on the 3D image of the substrate-bound form of the protein (and its tRNA^Met complex) generated with PyMOL <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059-Schrdinger1" target="_blank">[58]</a> using ray-tracing. The bottoms of the images show the structure of tRNA^Met. The purple molecule in the middle of the protein structure is the substrate Met-AMP marking the active site of the enzyme, the white sphere on the right is the Zn²⁺ ion. Red signs of Panels A, B and C mark amino acids having the highest <i>increase</i> of perturbation, closeness and betweenness centralities (top 20%) of the substrate-bound form compared to the substrate-free form, respectively. Yellow signs mark those contact amino acids, which are directly bound to the tRNA^Met, evidenced by an atomic distance of less than 4.5Å between any atom of the residue and the tRNA^Met, excluding hydrogens. To avoid overcrowding the image, only those contact amino acids are shown, which have a high increase of their centrality. A separate image showing all tRNA^Met-binding amino acids is shown in <b>Figure S9 of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059.s001" target="_blank">Text S1</a></b>. Note that red-labeled amino acids having the largest increase of perturbation centrality upon substrate binding (Panel A) are clustered around the active site and around both tRNA-binding sites, thus successfully discriminate all important parts of the protein. Amino acids showing the highest change in closeness centrality (Panel B) are smeared around the active site (which also occurs to be near the geometric center of the protein). Amino acids showing the highest change in betweenness centrality (Panel C) are scattered all around the protein.</p

Visualization of the difference among the three top 100 sets of proteins having the highest perturbation centrality in the DIP (2005) yeast interactome.

<p>Perturbation centralities were calculated for three stressed variations of the DIP (2005) yeast interactome according to <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#s4" target="_blank">Methods</a></b>. The properties of the network as well as the method of generating its stressed versions are described in the <b>Supplementary Methods</b>. The sizes of the different areas of the diagram are roughly proportional to the number of proteins in the respective combination of the three sets. Numbers also show the number of proteins in different sets. This quantitative Venn diagram was generated using the Google Charts API. (<a href="https://developers.google.com/chart/image/docs/gallery/venn_charts" target="_blank">https://developers.google.com/chart/image/docs/gallery/venn_charts</a>). The red, green and blue circles show the sets of top 100 proteins having the highest perturbation centrality in the heat-shocked, osmotically- stressed and oxidatively- stressed networks, respectively. This figure illustrates the fact mentioned in the Section “Various stress types induce different perturbation dissipating regions of the yeast interactome” that the most important proteins in heat shock are substantially different from the most important proteins in the other two tested stress types (i.e. in osmotic and oxidative stresses).</p

Average perturbation centralities for different node types in benchmark graphs.

<p>Scale-free, modular benchmark graphs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059-Lancichinetti1" target="_blank">[28]</a> were created as described in <b>Supplementary Methods</b> and <b>Table S7</b> of <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#pone.0078059.s001" target="_blank">Text S1</a></b>. Average perturbation centralities were calculated as described in <b><a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0078059#s4" target="_blank">Methods</a></b> using a starting perturbation of 40,000 units, since the benchmark networks contained 4,000 nodes. 4 node types were discriminated: intra-modular non-hubs, inter-modular non-hubs, intra-modular hubs and inter-modular-hubs, where hubs were nodes having a degree in the top 10%, and inter-modular nodes were nodes with more than 40% inter-modular edges. Different letters on top of the bars mark significantly different groups with α = 0.01 (Wilcoxon rank-sum test). Dark red bars show results obtained using 7 randomly selected benchmark graphs with the ratio of inter-modular nodes set to 0.05, termed as pronounced modules, while light blue bars display data for 7 randomly selected benchmark graphs (with the same seed nodes as the ones used for pronounced modules) with ratio of inter-modular nodes set to 0.4, termed fuzzy modules.</p

Investigation of Deteriorated Dissolution of Amorphous Itraconazole: Description of Incompatibility with Magnesium Stearate and Possible Solutions

Disadvantageous crystallization phenomenon of amorphous itraconazole (ITR) occurring in the course of dissolution process was investigated in this work. A perfectly amorphous form (solid dispersion) of the drug was generated by the electroblowing method (with vinylpyrrolidone-vinyl acetate copolymer), and the obtained fibers were formulated into tablets. Incomplete dissolution of the tablets was noticed under the circumstances of the standard dissolution test, after which a precipitated material could be filtered. The filtrate consisted of ITR and stearic acid since no magnesium content was detectable in it. In parallel with dissolution, ITR forms an insoluble associate, stabilized by hydrogen bonding, with stearic acid deriving from magnesium stearate. This is why dissolution curves do not have the plateaus at 100%. Two ways are viable to tackle this issue: change the lubricant (with sodium stearyl fumarate >95% dissolution can be accomplished) or alter the polymer in the solid dispersion to a type being able to form hydrogen bonds with ITR (e.g., hydroxypropyl methylcellulose). This work draws attention to one possible phenomenon that can lead to a deterioration of originally good dissolution of an amorphous solid dispersion