Correlations in the degeneracy of structurally controllable topologies for networks

Abstract

Many dynamic systems display complex emergent phenomena. By directly controlling a subset of system components (nodes) via external intervention it is possible to indirectly control every other component in the system. When the system is linear or can be approximated sufficiently well by a linear model, methods exist to identify the number and connectivity of a minimum set of external inputs (constituting a so-called minimal control topology, or MCT). In general, many MCTs exist for a given network; here we characterize a broad ensemble of empirical networks in terms of the fraction of nodes and edges that are always, sometimes, or never a part of an MCT. We study the relationships between the measures, and apply the methodology to the T-LGL leukemia signaling network as a case study. We show that the properties introduced in this report can be used to predict key components of biological networks, with potentially broad applications to network medicine.

Strategies to Enhance Logic Modeling-Based Cell Line-Specific Drug Synergy Prediction

“…For 38 nodes, inversion or fixation did not affect predictions in any of the cell lines. Taken together, our results support the hypothesis that a subset of nodes may be most decisive for the state of the model (Gao et al, 2014;Puniya et al, 2016;Campbell et al, 2017;Pentzien et al, 2018;Rozum and Albert, 2018;Yang et al, 2018).…”

“…Previous studies have indicated that a subset of nodes have the ability to affect the behavior of the overall network (Gao et al, 2014;Puniya et al, 2016;Campbell et al, 2017;Pentzien et al, 2018;Rozum and Albert, 2018;Yang et al, 2018). Translated to our example, this means that calibration of a set of nodes with such characteristics will determine the activity of the remaining nodes.…”

“…We next set out to examine the importance of correct node activity assessment, specifically posing the question of whether the correct assessment of activity for some nodes matter more than others. Inspired by previous publications exploring the identification of high-influence nodes (Gao et al, 2014;Puniya et al, 2016;Campbell et al, 2017;Pentzien et al, 2018;Rozum and Albert, 2018;Yang et al, 2018) as well as by the concept of target control in network biology, assuming that only a subset of nodes control the system (Gao et al, 2014;Yang et al, 2018), we pursued the goal to identify such nodes in our network as well as features that identify them. For each node we iteratively fixed its activity both at its stable state activity value and after activity inversion followed by computation of new synergy predictions.…”

Irrelevance of linear controllability to nonlinear dynamical networks

“…However, for other networks, some nodes are always or never in a driver set, which give a distribution of nodes in the minimum controller set. The distribution with respect to the topology of the network may be informative and characteristic of some empirical contexts [11,60].…”

“…Using the exact controllability theory [9], we calculate the minimal control set. A key feature of linear network control, which was usually not emphasized in most existing literature on linear controllability [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] but was mentioned in a recent paper [60], is that the minimal control set of nodes is not unique. For a reasonably large network (e.g., of size of a few hundred), there can be vastly many such sets that are equivalent to each other in terms of control realization.…”