Shai Carmi

A model of Internet topology using k-shell decomposition

We study a map of the Internet (at the autonomous systems level), by introducing and using the method of k-shell decomposition and the methods of percolation theory and fractal geometry, to find a model for the structure of the Internet. In particular, our analysis uses information on the connectivity of the network shells to separate, in a unique (no parameters) way, the Internet into three subcomponents: (i) a nucleus that is a small (≈100 nodes), very well connected globally distributed subgraph; (ii) a fractal subcomponent that is able to connect the bulk of the Internet without congesting the nucleus, with self-similar properties and critical exponents predicted from percolation theory; and (iii) dendrite-like structures, usually isolated nodes that are connected to the rest of the network through the nucleus only. We show that our method of decomposition is robust and provides insight into the underlying structure of the Internet and its functional consequences. Our approach of decomposing the network is general and also useful when studying other complex networks.

MEDUSA - New Model of Internet Topology Using k-shell Decomposition

We study a map of the Internet (at the autonomous systems level), by introducing and using the method of k-shell decomposition and the methods of percolation theory and fractal geometry, to find a model for the structure of the Internet. In particular, our analysis uses information on the connectivity of the network shells to separate, in a unique (no parameters) way, the Internet into three subcomponents: (i) a nucleus that is a small (≈100 nodes), very well connected globally distributed subgraph; (ii) a fractal subcomponent that is able to connect the bulk of the Internet without congesting the nucleus, with self-similar properties and critical exponents predicted from percolation theory; and (iii) dendrite-like structures, usually isolated nodes that are connected to the rest of the network through the nucleus only. We show that our method of decomposition is robust and provides insight into the underlying structure of the Internet and its functional consequences. Our approach of decomposing the network is general and also useful when studying other complex networks.

Epidemic Threshold for the Susceptible-Infectious-Susceptible Model on Random Networks

We derive an analytical expression for the critical infection rate rc of the susceptible-infectioussusceptible (SIS) disease spreading model on random networks. To obtain rc, we first calculate the probability of reinfection, π, defined as the probability of a node to reinfect the node that had earlier infected it. We then derive rc from π using percolation theory. We show that π is governed by two effects: (i) The requirement from an infecting node to recover prior to its reinfection, which depends on the disease spreading parameters; and (ii) The competition between nodes that simultaneously try to reinfect the same ancestor, which depends on the network topology.

Sequencing an Ashkenazi reference panel supports population-targeted personal genomics and illuminates Jewish and European origins

The Ashkenazi Jewish (AJ) population is a genetic isolate close to European and Middle Eastern groups, with genetic diversity patterns conducive to disease mapping. Here we report high-depth sequencing of 128 complete genomes of AJ controls. Compared with European samples, our AJ panel has 47% more novel variants per genome and is eightfold more effective at filtering benign variants out of AJ clinical genomes. Our panel improves imputation accuracy for AJ SNP arrays by 28%, and covers at least one haplotype in ≈67% of any AJ genome with long, identical-by-descent segments. Reconstruction of recent AJ history from such segments confirms a recent bottleneck of merely ≈350 individuals. Modelling of ancient histories for AJ and European populations using their joint allele frequency spectrum determines AJ to be an even admixture of European and likely Middle Eastern origins. We date the split between the two ancestral populations to ≈12–25 Kyr, suggesting a predominantly Near Eastern source for the repopulation of Europe after the Last Glacial Maximum.

Persistent ER Stress Induces the Spliced Leader RNA Silencing Pathway (SLS), Leading to Programmed Cell Death in Trypanosoma brucei

Trypanosomes are parasites that cycle between the insect host (procyclic form) and mammalian host (bloodstream form). These parasites lack conventional transcription regulation, including factors that induce the unfolded protein response (UPR). However, they possess a stress response mechanism, the spliced leader RNA silencing (SLS) pathway. SLS elicits shut-off of spliced leader RNA (SL RNA) transcription by perturbing the binding of the transcription factor tSNAP42 to its cognate promoter, thus eliminating trans-splicing of all mRNAs. Induction of endoplasmic reticulum (ER) stress in procyclic trypanosomes elicits changes in the transcriptome similar to those induced by conventional UPR found in other eukaryotes. The mechanism of up-regulation under ER stress is dependent on differential stabilization of mRNAs. The transcriptome changes are accompanied by ER dilation and elevation in the ER chaperone, BiP. Prolonged ER stress induces SLS pathway. RNAi silencing of SEC63, a factor that participates in protein translocation across the ER membrane, or SEC61, the translocation channel, also induces SLS. Silencing of these genes or prolonged ER stress led to programmed cell death (PCD), evident by exposure of phosphatidyl serine, DNA laddering, increase in reactive oxygen species (ROS) production, increase in cytoplasmic Ca2+, and decrease in mitochondrial membrane potential, as well as typical morphological changes observed by transmission electron microscopy (TEM). ER stress response is also induced in the bloodstream form and if the stress persists it leads to SLS. We propose that prolonged ER stress induces SLS, which serves as a unique death pathway, replacing the conventional caspase-mediated PCD observed in higher eukaryotes.

A genome-wide map of hyper-edited RNA reveals numerous new sites

Adenosine-to-inosine editing is one of the most frequent post-transcriptional modifications, manifested as A-to-G mismatches when comparing RNA sequences with their source DNA. Recently, a number of RNA-seq data sets have been screened for the presence of A-to-G editing, and hundreds of thousands of editing sites identified. Here we show that existing screens missed the majority of sites by ignoring reads with excessive (‘hyper’) editing that do not easily align to the genome. We show that careful alignment and examination of the unmapped reads in RNA-seq studies reveal numerous new sites, usually many more than originally discovered, and in precisely those regions that are most heavily edited. Specifically, we discover 327,096 new editing sites in the heavily studied Illumina Human BodyMap data and more than double the number of detected sites in several published screens. We also identify thousands of new sites in mouse, rat, opossum and fly. Our results establish that hyper-editing events account for the majority of editing sites.

Identification of Widespread Ultra-Edited Human RNAs

Adenosine-to-inosine modification of RNA molecules (A-to-I RNA editing) is an important mechanism that increases transciptome diversity. It occurs when a genomically encoded adenosine (A) is converted to an inosine (I) by ADAR proteins. Sequencing reactions read inosine as guanosine (G); therefore, current methods to detect A-to-I editing sites align RNA sequences to their corresponding DNA regions and identify A-to-G mismatches. However, such methods perform poorly on RNAs that underwent extensive editing (“ultra”-editing), as the large number of mismatches obscures the genomic origin of these RNAs. Therefore, only a few anecdotal ultra-edited RNAs have been discovered so far. Here we introduce and apply a novel computational method to identify ultra-edited RNAs. We detected 760 ESTs containing 15,646 editing sites (more than 20 sites per EST, on average), of which 13,668 are novel. Ultra-edited RNAs exhibit the known sequence motif of ADARs and tend to localize in sense strand Alu elements. Compared to sites of mild editing, ultra-editing occurs primarily in Alu-rich regions, where potential base pairing with neighboring, inverted Alus creates particularly long double-stranded RNA structures. Ultra-editing sites are underrepresented in old Alu subfamilies, tend to be non-conserved, and avoid exons, suggesting that ultra-editing is usually deleterious. A possible biological function of ultra-editing could be mediated by non-canonical splicing and cleavage of the RNA near the editing sites.

Fractional Feynman-Kac Equation for Non-Brownian Functionals

We derive backward and forward fractional Schrödinger type of equations for the distribution of functionals of the path of a particle undergoing anomalous diffusion. Fractional substantial derivatives introduced by Friedrich and co-workers [PRL 96, 230601 (2006)] provide the correct fractional framework for the problem at hand. In the limit of normal diffusion we recover the Feynman-Kac treatment of Brownian functionals. For applications, we calculate the distribution of occupation times in half space and show how statistics of anomalous functionals is related to weak ergodicity breaking.

Large-scale DNA editing of retrotransposons accelerates mammalian genome evolution

Retrotransposons had an important role in genome evolution, including the formation of new genes and promoters and the rewiring of gene networks. However, it is unclear how such a repertoire of functions emerged from a relatively limited number of source sequences. Here we show that DNA editing, an antiviral mechanism, accelerated the evolution of mammalian genomes by large-scale modification of their retrotransposon sequences. We find numerous pairs of retrotransposons containing long clusters of G-to-A mutations that cannot be attributed to random mutagenesis. These clusters, which we find across different mammalian genomes and retrotransposon families, are the hallmark of APOBEC3 activity, a potent antiretroviral protein family with cytidine deamination function. As DNA editing simultaneously generates a large number of mutations, each affected element begins its evolutionary trajectory from a unique starting point, thereby increasing the probability of developing a novel function. Our findings thus suggest a potential mechanism for retrotransposon domestication.

Trapping in complex networks

We investigate the trapping problem in Erd˝ os-Renyi (ER) and scale-free (SF) networks. We calculate the evolution of the particle density ρ(t) of random walkers in the presence of one or multiple traps with concentration c. We show using theory and simulations that in ER networks, while for short times ρ(t) ∝ exp(−Act), for longer times ρ(t) exhibits a more complex behavior, with explicit dependence on both the number of traps and the size of the network. In SF networks we reveal the significant impact of the traps location: ρ(t) is drastically different when a trap is placed on a random node compared to the case of the trap being on the node with the maximum connectivity. For the latter case we find ρ(t) ∝ exp −At/N γ−2 γ−1 � kfor all γ> 2, where γ is the exponent of the degree distribution P (k) ∝ k �γ .