Relative, local and global dimension in complex networks

Computational and in vitro analyses of the antibacterial effect of the ethanolic extract of Pluchea indica L. leaves

The most common gram-negative, Escherichia coli, and gram-positive bacteria, Bacillus spp., have evolved different mechanisms that have caused the emergence of multi-drug resistance. As a result, drugs that block the bacterial growth cycle are needed. Here, in silico and in vitro studies were performed to assess compounds in the Pluchea indica leaf extract, a medicinal plant, that can inhibit bacterial proteins. Briefly, P. indica leaves were extracted using ethanol. The crude extract was then subjected to gas chromatography-mass spectrometry for metabolite screening. Molecular docking simulations with rhomboid protease (Rpro) (Protein data bank ID number: 3ZMI from E. coli and filamenting temperature-sensitive mutant Z (FtsZ) protein data bank ID number: 2VAM from Bacillus subtilis were performed. Moreover, the well diffusion method was used to confirm the antibacterial activity of P. indica leaf extract. A total of 10 compounds were identified in the P. indica extract and used for computational analysis. Based on drug-likeness prediction, P. indica compounds may be drug-like molecules. Binding affinity tests indicated that 10,10-Dimethyl-2,6-dimethylenebicyclo(7.2.0)undecan-5.β.-ol and 11,11-Dimethyl-4,8-dimethylenebicyclo(7.2.0)undecan-3-ol had the most negative values. Accordingly, these compounds may be potential ligands that bind to bacterial proteins. The root mean square fluctuation values was <2 Å, indicating stable fluctuation binding for the ligand-protein complex. According to in vitro antibacterial assays, a high concentration (50%) of the P. indica extract markedly inhibited E. coli and B. subtilis, with inhibitory zone diameters of 31.86±1.63 and 21.09±0.09 mm, respectively. Overall, the compounds in the P. indica leaf extract were identified as functional inhibitors of E. coli and B. subtilis proteins via in silico analysis. This may facilitate development of antibacterial agents.

Unraveling the mesoscale organization induced by network-driven processes

Complex systems are characterized by emergent patterns created by the nontrivial interplay between dynamical processes and the networks of interactions on which these processes unfold. Topological or dynamical descriptors alone are not enough to fully embrace this interplay in all its complexity, and many times one has to resort to dynamics-specific approaches that limit a comprehension of general principles. To address this challenge, we employ a metric-that we name Jacobian distance-which captures the spatiotemporal spreading of perturbations, enabling us to uncover the latent geometry inherent in network-driven processes. We compute the Jacobian distance for a broad set of nonlinear dynamical models on synthetic and real-world networks of high interest for applications from biological to ecological and social contexts. We show, analytically and computationally, that the process-driven latent geometry of a complex network is sensitive to both the specific features of the dynamics and the topological properties of the network. This translates into potential mismatches between the functional and the topological mesoscale organization, which we explain by means of the spectrum of the Jacobian matrix. Finally, we demonstrate that the Jacobian distance offers a clear advantage with respect to traditional methods when studying human brain networks. In particular, we show that it outperforms classical network communication models in explaining functional communities from structural data, therefore highlighting its potential in linking structure and function in the brain.

Network Spreading from Network Dimension

Continuous-state network spreading models provide critical numerical and analytic insights into transmission processes in epidemiology, rumor propagation, knowledge dissemination, and many other areas. Most of these models reflect only local features such as adjacency, degree, and transitivity, so can exhibit substantial error in the presence of global correlations typical of empirical networks. Here, we propose mitigating this limitation via a network property ideally suited to capturing spreading. This is the network correlation dimension, which characterizes how the number of nodes within range of a source typically scales with distance. Applying the approach to susceptible-infected-recovered processes leads to a spreading model which, for a wide range of networks and epidemic parameters, can provide more accurate predictions of the early stages of a spreading process than important established models of substantially higher complexity. In addition, the proposed model leads to a basic reproduction number that provides information about the final state not available from popular established models.

Correlation dimension in empirical networks

Network correlation dimension governs the distribution of network distance in terms of a power-law model and profoundly impacts both structural properties and dynamical processes. We develop new maximum likelihood methods which allow us robustly and objectively to identify network correlation dimension and a bounded interval of distances over which the model faithfully represents structure. We also compare the traditional practice of estimating correlation dimension by modeling as a power law the fraction of nodes within a distance to a proposed alternative of modeling as a power law the fraction of nodes at a distance. In addition, we illustrate a likelihood ratio technique for comparing the correlation dimension and small-world descriptions of network structure. Improvements from our innovations are demonstrated on a diverse selection of synthetic and empirical networks. We show that the network correlation dimension model accurately captures empirical network structure over neighborhoods of substantial size and span and outperforms the alternative small-world network scaling model. Our improved methods tend to lead to higher estimates of network correlation dimension, implying that prior studies could have produced or utilized systematic underestimates of dimension.