Correlations in the degeneracy of structurally controllable topologies for networks

Uncovering and classifying the role of driven nodes in control of complex networks

The widely used Maximum Matching (MM) method identifies the minimum driver nodes set to control biological and technological systems. Nevertheless, it is assumed in the MM approach that one driver node can send control signal to multiple target nodes, which might not be appropriate in certain complex networks. A recent work introduced a constraint that one driver node can control one target node, and proposed a method to identify the minimum target nodes set under such a constraint. We refer such target nodes to driven nodes. However, the driven nodes may not be uniquely determined. Here, we develop a novel algorithm to classify driven nodes in control categories. Our computational analysis on a large number of biological networks indicates that the number of driven nodes is considerably larger than the number of driver nodes, not only in all examined complete plant metabolic networks but also in several key human pathways, which firstly demonstrate the importance of use of driven nodes in analysis of real-world networks.

Dilations and degeneracy in network controllability

Network controllability asserts a perspective that the structure—the location of edges that connect nodes—of the network contains important information about fundamental characteristics of our ability to change the behavior that evolves on these networks. It can be used, for example, to determine the parts of the system that when influenced by outside controlling signals, can ultimately steer the behavior of the entire network. One of the challenges in utilizing the ideas from network controllability on real systems is that there is typically more than one potential solution (often many) suggested by the topology of the graph that perform equally well. Picking a single candidate from this degenerate solution set over others should be properly motivated, however, to-date our understanding of how these different options are related has been limited. In this work, we operationalize the existing notion of a dilation into a framework that provides clarity on the source of this control degeneracy and further elucidates many of the existing results surrounding degeneracy in the literature.

Neuro-Clinical Signatures of Language Impairments: A Theoretical Framework for Function-to-structure Mapping in Clinics

In the past decades, neuroscientists and clinicians have collected a considerable amount of data and drastically increased our knowledge about the mapping of language in the brain. The emerging picture from the accumulated knowledge is that there are complex and combinatorial relationships between language functions and anatomical brain regions. Understanding the underlying principles of this complex mapping is of paramount importance for the identification of the brain signature of language and Neuro-Clinical signatures that explain language impairments and predict language recovery after stroke. We review recent attempts to addresses this question of language-brain mapping. We introduce the different concepts of mapping (from diffeomorphic one-to-one mapping to many-to-many mapping). We build those different forms of mapping to derive a theoretical framework where the current principles of brain architectures including redundancy, degeneracy, pluri-potentiality and bow-tie network are described.

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

Discrete dynamical modeling shows promise in prioritizing drug combinations for screening efforts by reducing the experimental workload inherent to the vast numbers of possible drug combinations. We have investigated approaches to predict combination responses across different cancer cell lines using logic models generated from one generic prior-knowledge network representing 144 nodes covering major cancer signaling pathways. Cell-line specific models were configured to agree with baseline activity data from each unperturbed cell line. Testing against experimental data demonstrated a high number of true positive and true negative predictions, including also cell-specific responses. We demonstrate the possible enhancement of predictive capability of models by curation of literature knowledge further detailing subtle biologically founded signaling mechanisms in the model topology. In silico model analysis pinpointed a subset of network nodes highly influencing model predictions. Our results indicate that the performance of logic models can be improved by focusing on high-influence node protein activity data for model configuration and that these nodes accommodate high information flow in the regulatory network.

Irrelevance of linear controllability to nonlinear dynamical networks

There has been tremendous development in linear controllability of complex networks. Real-world systems are fundamentally nonlinear. Is linear controllability relevant to nonlinear dynamical networks? We identify a common trait underlying both types of control: the nodal "importance". For nonlinear and linear control, the importance is determined, respectively, by physical/biological considerations and the probability for a node to be in the minimum driver set. We study empirical mutualistic networks and a gene regulatory network, for which the nonlinear nodal importance can be quantified by the ability of individual nodes to restore the system from the aftermath of a tipping-point transition. We find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former large-degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly the irrelevance of linear controllability to these systems. The recent claim of successful application of linear controllability to Caenorhabditis elegans connectome is examined and discussed.