Hyperbolicity Measures "Democracy" in Real-World Networks

We analyze the hyperbolicity of real-world networks, a geometric quantity that measures if a space is negatively curved. In our interpretation, a network with small hyperbolicity is "aristocratic", because it contains a small set of vertices involved in many shortest paths, so that few elements "connect" the systems, while a network with large hyperbolicity has a more "democratic" structure with a larger number of crucial elements. We prove mathematically the soundness of this interpretation, and we derive its consequences by analyzing a large dataset of real-world networks. We confirm and improve previous results on hyperbolicity, and we analyze them in the light of our interpretation. Moreover, we study (for the first time in our knowledge) the hyperbolicity of the neighborhood of a given vertex. This allows to define an "influence area" for the vertices in the graph. We show that the influence area of the highest degree vertex is small in what we define "local" networks, like most social or peer-to-peer networks. On the other hand, if the network is built in order to reach a "global" goal, as in metabolic networks or autonomous system networks, the influence area is much larger, and it can contain up to half the vertices in the graph. In conclusion, our newly introduced approach allows to distinguish the topology and the structure of various complex networks

Chronic Cognitive Dysfunction after Traumatic Brain Injury Is Improved with a Phosphodiesterase 4B Inhibitor

Learning and memory impairments are common in traumatic brain injury (TBI) survivors. However, there are no effective treatments to improve TBI-induced learning and memory impairments. TBI results in decreased cAMP signaling and reduced cAMP-response-element binding protein (CREB) activation, a critical pathway involved in learning and memory. TBI also acutely upregulates phosphodiesterase 4B2 (PDE4B2), which terminates cAMP signaling by hydrolyzing cAMP. We hypothesized that a subtype-selective PDE4B inhibitor could reverse the learning deficits induced by TBI. To test this hypothesis, adult male Sprague-Dawley rats received sham surgery or moderate parasagittal fluid-percussion brain injury. At 3 months postsurgery, animals were administered a selective PDE4B inhibitor or vehicle before cue and contextual fear conditioning, water maze training and a spatial working memory task. Treatment with the PDE4B inhibitor significantly reversed the TBI-induced deficits in cue and contextual fear conditioning and water maze retention. To further understand the underlying mechanisms of these memory impairments, we examined hippocampal long-term potentiation (LTP). TBI resulted in a significant reduction in basal synaptic transmission and impaired expression of LTP. Treatment with the PDE4B inhibitor significantly reduced the deficits in basal synaptic transmission and rescued LTP expression. The PDE4B inhibitor reduced tumor necrosis factor-α levels and increased phosphorylated CREB levels after TBI, suggesting that this drug inhibited molecular pathways in the brain known to be regulated by PDE4B. These results suggest that a subtype-selective PDE4B inhibitor is a potential therapeutic to reverse chronic learning and memory dysfunction and deficits in hippocampal synaptic plasticity following TBI. SIGNIFICANCE STATEMENT Currently, there are an estimated 3.2–5.3 million individuals living with disabilities from traumatic brain injury (TBI) in the United States, and 8 of 10 of these individuals report cognitive disabilities (Thurman et al., 1999; Lew et al., 2006; Zaloshnja et al., 2008). One of the molecular mechanisms associated with chronic cognitive disabilities is impaired cAMP signaling in the hippocampus. In this study, we report that a selective phosphodiesterase 4B (PDE4B) inhibitor reduces chronic cognitive deficits after TBI and rescues deficits in hippocampal long-term potentiation. These results suggest that PDE4B inhibition has the potential to improve learning and memory ability and overall functioning for people living with TBI