From Physics to Pharmacology?

A perturbation-based approach to identifying potentially superfluous network constituents

Constructing networks from empirical time-series data is often faced with the as yet unsolved issue of how to avoid potentially superfluous network constituents. Such constituents can result, e.g., from spatial and temporal oversampling of the system's dynamics, and neglecting them can lead to severe misinterpretations of network characteristics ranging from global to local scale. We derive a perturbation-based method to identify potentially superfluous network constituents that makes use of vertex and edge centrality concepts. We investigate the suitability of our approach through analyses of weighted small-world, scale-free, random, and complete networks.

Network structure from a characterization of interactions in complex systems

Many natural and man-made complex dynamical systems can be represented by networks with vertices representing system units and edges the coupling between vertices. If edges of such a structural network are inaccessible, a widely used approach is to identify them with interactions between vertices, thereby setting up a functional network. However, it is an unsolved issue if and to what extent important properties of a functional network on the global and the local scale match those of the corresponding structural network. We address this issue by deriving functional networks from characterizing interactions in paradigmatic oscillator networks with widely-used time-series-analysis techniques for various factors that alter the collective network dynamics. Surprisingly, we find that particularly key constituents of functional networks—as identified with betweenness and eigenvector centrality—coincide with ground truth to a high degree, while global topological and spectral properties—clustering coefficient, average shortest path length, assortativity, and synchronizability—clearly deviate. We obtain similar concurrences for an empirical network. Our findings are of relevance for various scientific fields and call for conceptual and methodological refinements to further our understanding of the relationship between structure and function of complex dynamical systems.

A straightforward edge centrality concept derived from generalizing degree and strength

Vertex degree—the number of edges that are incident to a vertex—is a fundamental concept in network theory. It is the historically first and conceptually simplest centrality concept to rate the importance of a vertex for a network’s structure and dynamics. Unlike many other centrality concepts, for which joint metrics have been proposed for both vertices and edges, by now there is no concept for an edge centrality analogous to vertex degree. Here, we propose such a concept—termed nearest-neighbor edge centrality—and demonstrate its suitability for a non-redundant identification of central edges in paradigmatic network models as well as in real-world networks from various scientific domains.

Centrality-based identification of important edges in complex networks

Centrality is one of the most fundamental metrics in network science. Despite an abundance of methods for measuring centrality of individual vertices, there are by now only a few metrics to measure centrality of individual edges. We modify various, widely used centrality concepts for vertices to those for edges, in order to find which edges in a network are important between other pairs of vertices. Focusing on the importance of edges, we propose an edge-centrality-based network decomposition technique to identify a hierarchy of sets of edges, where each set is associated with a different level of importance. We evaluate the efficiency of our methods using various paradigmatic network models and apply the novel concepts to identify important edges and important sets of edges in a commonly used benchmark model in social network analysis, as well as in evolving epileptic brain networks.

Modeling fructose-load-induced hepatic de-novo lipogenesis by model simplification

Hepatic de-novo lipogenesis is a metabolic process implemented in the pathogenesis of type 2 diabetes. Clinically, the rate of this process can be ascertained by use of labeled acetate and stimulation by fructose administration. A systems pharmacology model of this process is desirable because it facilitates the description, analysis, and prediction of this experiment. Due to the multiple enzymes involved in de-novo lipogenesis, and the limited data, it is desirable to use single functional expressions to encapsulate the flux between multiple enzymes. To accomplish this we developed a novel simplification technique which uses the available information about the properties of the individual enzymes to bound the parameters of a single governing ‘transfer function’. This method should be applicable to any model with linear chains of enzymes that are well stimulated. We validated this approach with computational simulations and analytical justification in a limiting case. Using this technique we generated a simple model of hepatic de-novo lipogenesis in these experimental conditions that matched prior data. This model can be used to assess pharmacological intervention at specific points on this pathway. We have demonstrated this with prospective simulation of acetyl-CoA carboxylase inhibition. This simplification technique suggests how the constituent properties of an enzymatic chain of reactions gives rise to the sensitivity (to substrate) of the pathway as a whole.