Asymptotic behavior of the Kleinberg model

We study Kleinberg navigation (the search of a target in a d-dimensional lattice, where each site is connected to one other random site at distance r, with probability proportional to r^{-a}) by means of an exact master equation for the process. We show that the asymptotic scaling behavior for the delivery time T to a target at distance L scales as (ln L)^2 when a=d, and otherwise as L^x, with x=(d-a)/(d+1-a) for ad+1. These values of x exceed the rigorous lower-bounds established by Kleinberg. We also address the situation where there is a finite probability for the message to get lost along its way and find short delivery times (conditioned upon arrival) for a wide range of a's

Self-Organization and Complex Networks

In this chapter we discuss how the results developed within the theory of fractals and Self-Organized Criticality (SOC) can be fruitfully exploited as ingredients of adaptive network models. In order to maintain the presentation self-contained, we first review the basic ideas behind fractal theory and SOC. We then briefly review some results in the field of complex networks, and some of the models that have been proposed. Finally, we present a self-organized model recently proposed by Garlaschelli et al. [Nat. Phys. 3, 813 (2007)] that couples the fitness network model defined by Caldarelli et al. [Phys. Rev. Lett. 89, 258702 (2002)] with the evolution model proposed by Bak and Sneppen [Phys. Rev. Lett. 71, 4083 (1993)] as a prototype of SOC. Remarkably, we show that the results obtained for the two models separately change dramatically when they are coupled together. This indicates that self-organized networks may represent an entirely novel class of complex systems, whose properties cannot be straightforwardly understood in terms of what we have learnt so far.Comment: Book chapter in "Adaptive Networks: Theory, Models and Applications", Editors: Thilo Gross and Hiroki Sayama (Springer/NECSI Studies on Complexity Series

Quantifying the taxonomic diversity in real species communities

We analyze several florae (collections of plant species populating specific areas) in different geographic and climatic regions. For every list of species we produce a taxonomic classification tree and we consider its statistical properties. We find that regardless of the geographical location, the climate and the environment all species collections have universal statistical properties that we show to be also robust in time. We then compare observed data sets with simulated communities obtained by randomly sampling a large pool of species from all over the world. We find differences in the behavior of the statistical properties of the corresponding taxonomic trees. Our results suggest that it is possible to distinguish quantitatively real species assemblages from random collections and thus demonstrate the existence of correlations between species

Inhibition of a NEDD8 Cascade Restores Restriction of HIV by APOBEC3G

<div><p>Cellular restriction factors help to defend humans against human immunodeficiency virus (HIV). HIV accessory proteins hijack at least three different Cullin-RING ubiquitin ligases, which must be activated by the small ubiquitin-like protein NEDD8, in order to counteract host cellular restriction factors. We found that conjugation of NEDD8 to Cullin-5 by the NEDD8-conjugating enzyme UBE2F is required for HIV Vif-mediated degradation of the host restriction factor APOBEC3G (A3G). Pharmacological inhibition of the NEDD8 E1 by MLN4924 or knockdown of either UBE2F or its RING-protein binding partner RBX2 bypasses the effect of Vif, restoring the restriction of HIV by A3G. NMR mapping and mutational analyses define specificity determinants of the UBE2F NEDD8 cascade. These studies demonstrate that disrupting host NEDD8 cascades presents a novel antiretroviral therapeutic approach enhancing the ability of the immune system to combat HIV.</p> </div

UBE2F is required for activation of CRL5^Vif-CBFß<i>in vitro</i>.

<p><b>A,</b> Diagram of the ubiquitination protocol used in panel <b>B</b>. <b>B, </b><i>In vitro</i> ubiquitination of A3G by recombinant CRL5^Vif-CBFß with UBE2R1 as ubiquitin conjugating enzyme requires UBE2F. Immunoblots of ubiquitination reactions containing myc-tagged A3G as the substrate show high-molecular weight polyubiquitin chains, require all protein components of the ubiquitin and NEDD8 activating systems and are only observed when UBE2F (lane 9) but not when UBE2M (lane 10) is used as NEDD8 conjugating enzyme. A3A is not susceptible to Vif and was used as a negative control. <b>C,</b> Coomassie-stained SDS-PAGE of NEDD8ylation “pulse” reaction indicates that under conditions used in panel <b>B</b> indicate CUL5 is completely NEDD8ylated by UBE2F; only a minor fraction (<5%) is NEDD8ylated by UBE2M. <b>D, </b>¹⁵N-HSQC spectral overlays of RBX2_RING in the presence and absence of ∼100 µM, unlabeled full-length UBE2M (top) or UBE2F (bottom).</p

A model illustrating how inhibition of CUL5 NEDD8ylation leads to reduced infectivity of HIV.

<p>Two enzymatic steps must take place in order for CRL5^Vif-CBFß to be properly activated by NEDD8 conjugation, and therefore for A3G-degradation to take place, in cells infected with HIV. First, NEDD8 is loaded onto the E2 UBE2F by NAE. The small molecule MLN4924 is able to inhibit this step, blocking degradation of A3G and thereby reducing viral infectivity. Second, UBE2F is recognized by the RBX2 subunit of CRL5^Vif-CBFß, and transfers NEDD8 to CUL5.</p

Pharmacological inhibition of NEDD8 E1 by MLN4924 blocks the ability of Vif to counteract A3G.

<p><b>A,</b> Single-cycle infectivity assay of HIV_NL4-3 produced in HEK293T cells transfected with empty vector control (white bars) or V5-tagged A3G (black bars, 120 ng) , 1 µg of NL4-3 proviral DNA and treated with indicated concentrations of MLN4924. <b>B,</b> Parallel immunoblots indicating MLN4924 restores steady-state levels of A3G in cells and packaging in virions. <b>C,</b> Quantitation of G to A mutations in gDNA sequences from virions produced in cells treated with either DMSO or 500 nM MLN4924.</p