Tissue Specificity of Sex-biased Gene Expression and the Development of Sexual Dimorphism

One prominent form of phenotypic diversity in nature is the dramatic difference between males and females within a single species. A central genetic obstacle which must be overcome is that two distinct phenotypes must be produced from a single, shared genome. One genetic mechanism that is of particular import that would allow sexes to overcome the limitation of a shared genome is sex-specific regulation of gene expression. Although sex-biased gene expression is generally predicted to increase over ontogeny as male and female phenotypes diverge, this pattern should be most pronounced in tissues that contribute to the most extreme aspects of sexual dimorphism. However, few studies have simultaneously examined multiple tissues throughout development to quantify sex-biased gene expression, which is crucial as sexual dimorphism occurs as a complex developmental process and sex-biased gene expression changes over time and differs among various tissues. We used the brown anole (Anolis sagrei), a lizard that exhibits extreme sexual size dimorphism, to examine sex-, age-, and tissue-specificity of gene expression. Using high-throughput RNA-Seq, we analyzed liver, muscle, and brain transcriptomes at one, four, eight, and twelve months of age. We predicted that (1) sex-biased gene expression would increase during ontogeny as phenotypes diverge between the sexes, (2) ontogenetic increases in sex-biased expression would differ among tissues because of different contributions to sexual dimorphism, and (3) growth-regulatory gene networks would be more sex-biased in liver and muscle than the brain as key contributors to extreme size dimorphism. We also predicted that sex-biased expression of upstream components of growth regulatory (e.g., hormones) networks in the liver would be higher compared to the muscle where there would be higher sex-biased expression of downstream components (e.g., hormone receptors and downstream effectors) in muscle. We determined that sex-biased gene expression increased during development, but that the trajectory of sex-biased expression varied between tissues. The liver had the greatest number of sex-biased growth genes, but the muscle had the greatest divergence of growth gene expression. We also found that while sex-biased expression of growth genes increased sharply during development in the liver and muscle, the brain showed no sex-bias in any growth gene at any point. Our results confirm that sex-biased gene expression increases throughout ontogeny, but also demonstrate tissue-specific trajectories. Our results also suggest that different components of growth-regulatory networks are activated in different tissues. More broadly, our work implies that sex-biased gene expression across the whole transcriptome and within specific regulatory pathways produces sexually dimorphic phenotypes. Related datasets are available at the following location. See readme file below for more information. https://drive.google.com/drive/folders/1J7jGlrCjqm1Ld7iTWtPcvtVp366dAsr4?usp=sharin

Clustering and the hyperbolic geometry of complex networks

Clustering is a fundamental property of complex networks and it is the mathematical expression of a ubiquitous phenomenon that arises in various types of self-organized networks such as biological networks, computer networks or social networks. In this paper, we consider what is called the global clustering coefficient of random graphs on the hyperbolic plane. This model of random graphs was proposed recently by Krioukov et al. as a mathematical model of complex networks, under the fundamental assumption that hyperbolic geometry underlies the structure of these networks. We give a rigorous analysis of clustering and characterize the global clustering coefficient in terms of the parameters of the model. We show how the global clustering coefficient can be tuned by these parameters and we give an explicit formula for this function.Comment: 51 pages, 1 figur

Sustaining the Internet with Hyperbolic Mapping

The Internet infrastructure is severely stressed. Rapidly growing overheads associated with the primary function of the Internet---routing information packets between any two computers in the world---cause concerns among Internet experts that the existing Internet routing architecture may not sustain even another decade. Here we present a method to map the Internet to a hyperbolic space. Guided with the constructed map, which we release with this paper, Internet routing exhibits scaling properties close to theoretically best possible, thus resolving serious scaling limitations that the Internet faces today. Besides this immediate practical viability, our network mapping method can provide a different perspective on the community structure in complex networks

Properties of highly clustered networks

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study SIR-type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.Comment: 7 pages, 2 figures, 1 tabl

Evolution of scale-free random graphs: Potts model formulation

We study the bond percolation problem in random graphs of $N$ weighted vertices, where each vertex $i$ has a prescribed weight $P_i$ and an edge can connect vertices $i$ and $j$ with rate $P_iP_j$. The problem is solved by the $q\to 1$ limit of the $q$-state Potts model with inhomogeneous interactions for all pairs of spins. We apply this approach to the static model having $P_i\propto i^{-\mu} (0<\mu<1)$ so that the resulting graph is scale-free with the degree exponent $\lambda=1+1/\mu$. The number of loops as well as the giant cluster size and the mean cluster size are obtained in the thermodynamic limit as a function of the edge density, and their associated critical exponents are also obtained. Finite-size scaling behaviors are derived using the largest cluster size in the critical regime, which is calculated from the cluster size distribution, and checked against numerical simulation results. We find that the process of forming the giant cluster is qualitatively different between the cases of $\lambda >3$ and $2 < \lambda <3$. While for the former, the giant cluster forms abruptly at the percolation transition, for the latter, however, the formation of the giant cluster is gradual and the mean cluster size for finite $N$ shows double peaks.Comment: 34 pages, 9 figures, elsart.cls, final version appeared in NP

Class of correlated random networks with hidden variables

We study a class models of correlated random networks in which vertices are characterized by \textit{hidden variables} controlling the establishment of edges between pairs of vertices. We find analytical expressions for the main topological properties of these models as a function of the distribution of hidden variables and the probability of connecting vertices. The expressions obtained are checked by means of numerical simulations in a particular example. The general model is extended to describe a practical algorithm to generate random networks with an \textit{a priori} specified correlation structure. We also present an extension of the class, to map non-equilibrium growing networks to networks with hidden variables that represent the time at which each vertex was introduced in the system