We study the voter model on heterogeneous graphs. We exploit the nonconservation of the magnetization to characterize how consensus is reached. For a network of N nodes with an arbitrary but uncorrelated degree distribution, the mean time to reach consensus T(N) scales as Nmu(2)1/mu(2), where mu(k) is the kth moment of the degree distribution. For a power-law degree distribution n(k) approximately k(-nu), T(N) thus scales as N for nu > 3, as N/ln(N for nu = 3, as N((2nu-4)/(nu-1)) for 2 < nu < 3, as (lnN)2 for nu = 2, and as omicron(1) for nu < 2. These results agree with simulation data for networks with both uncorrelated and correlated node degrees.

We study simple interacting particle systems on heterogeneous networks, including the voter model and the invasion process. These are both two-state models in which in an update event an individual changes state to agree with a neighbor. For the voter model, an individual "imports" its state from a randomly-chosen neighbor. Here the average time T N to reach consensus for a network of N nodes with an uncorrelated degree distribution scales as , where μ k is the k th moment of the degree distribution. Quick consensus thus arises on networks with broad degree distributions. We also identify the conservation law that characterizes the route by which consensus is reached. Parallel results are derived for the invasion process, in which the state of an agent is "exported" to a random neighbor. We further generalize to biased dynamics in which one state is favored. The probability for a single fitter mutant located at a node of degree k to overspread the population-the fixation probability-is proportional to k for the voter model and to 1/k for the invasion process.

The evolution of two species with different fitness is investigated on degree-heterogeneous graphs. The population evolves either by one individual dying and being replaced by the offspring of a random neighbor (voter model dynamics) or by an individual giving birth to an offspring that takes over a random neighbor node (invasion process dynamics). The fixation probability for one species to take over a population of N individuals depends crucially on the dynamics and on the local environment. Starting with a single fitter mutant at a node of degree k, the fixation probability is proportional to k for voter model dynamics and to 1/k for invasion process dynamics.

We study the mean time for a random walk to traverse between two arbitrary sites of the Erdős-Renyi random graph. We develop an effective medium approximation that predicts that the mean first-passage time between pairs of nodes, as well as all moments of this first-passage time, are insensitive to the fraction p of occupied links. This prediction qualitatively agrees with numerical simulations away from the percolation threshold. Near the percolation threshold, the statistically meaningful quantity is the mean transit rate, namely, the inverse of the first-passage time. This rate varies non-monotonically with p near the percolation transition. Much of this behavior can be understood by simple heuristic arguments.

Classic semiquantitative proteomic methods have shown that all organisms respond to a mild heat shock by an apparent massive accumulation of a small set of proteins, named heat-shock proteins (HSPs) and a concomitant slowing down in the synthesis of the other proteins. Yet unexplained, the increased levels of HSP messenger RNAs (mRNAs) may exceed 100 times the ensuing relative levels of HSP proteins. We used here high-throughput quantitative proteomics and targeted mRNA quantification to estimate in human cell cultures the mass and copy numbers of the most abundant proteins that become significantly accumulated, depleted, or unchanged during and following 4 h at 41 °C, which we define as mild heat shock. This treatment caused a minor across-the-board mass loss in many housekeeping proteins, which was matched by a mass gain in a few HSPs, predominantly cytosolic HSPCs (HSP90s) and HSPA8 (HSC70). As the mRNAs of the heat-depleted proteins were not significantly degraded and less ribosomes were recruited by excess new HSP mRNAs, the mild depletion of the many housekeeping proteins during heat shock was attributed to their slower replenishment. This differential protein expression pattern was reproduced by isothermal treatments with Hsp90 inhibitors. Unexpectedly, heat-treated cells accumulated 55 times more new molecules of HSPA8 (HSC70) than of the acknowledged heat-inducible isoform HSPA1A (HSP70), implying that when expressed as net copy number differences, rather than as mere “fold change” ratios, new biologically relevant information can be extracted from quantitative proteomic data. Raw data are available via ProteomeXchange with identifier PXD001666.Electronic supplementary materialThe online version of this article (doi:10.1007/s12192-015-0583-2) contains supplementary material, which is available to authorized users.

Chaperonins are cage-like complexes in which nonnative polypeptides prone to aggregation are thought to reach their native state optimally. However, they also may use ATP to unfold stably bound misfolded polypeptides and mediate the out-of-cage native refolding of large proteins. Here, we show that even without ATP and GroES, both GroEL and the eukaryotic chaperonin containing t-complex polypeptide 1 (CCT/TRiC) can unfold stable misfolded polypeptide conformers and readily release them from the access ways to the cage. Reconciling earlier disparate experimental observations to ours, we present a comprehensive model whereby following unfolding on the upper cavity, in-cage confinement is not needed for the released intermediates to slowly reach their native state in solution. As oversticky intermediates occasionally stall the catalytic unfoldase sites, GroES mobile loops and ATP are necessary to dissociate the inhibitory species and regenerate the unfolding activity. Thus, chaperonin rings are not obligate confining antiaggregation cages. They are polypeptide unfoldases that can iteratively convert stable off-pathway conformers into functional proteins.

The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, hierarchical, interregional structure with a highly specific laminar architecture. The last decade has seen the emergence of extensive new data sets on anatomy and connectivity at the whole brain scale, providing promising new directions for studies of cortical function that take into account the inseparability of whole-brain and microcircuit architectures. Here, we present a data-driven computational model of the anatomy of non-barrel primary somatosensory cortex of juvenile rat, which integrates whole-brain scale data while providing cellular and subcellular specificity. This multiscale integration was achieved by building the morphologically detailed model of cortical circuitry embedded within a volumetric, digital brain atlas. The model consists of 4.2 million morphologically detailed neurons belonging to 60 different morphological types, placed in the nonbarrel subregions of the Paxinos and Watson atlas. They are connected by 13.2 billion synapses determined by axo-dendritic overlap, comprising local connectivity and long-range connectivity defined by topographic mappings between subregions and laminar axonal projection profiles, both parameterized by whole brain data sets. Additionally, we incorporated core- and matrix-type thalamocortical projection systems, associated with sensory and higher-order extrinsic inputs, respectively. An analysis of the modeled synaptic connectivity revealed a highly nonrandom topology with substantial structural differences but also synergy between local and long-range connectivity. Long-range connections featured a more divergent structure with a comparatively small group of neurons serving as hubs to distribute excitation to far away locations. Taken together with analyses at different spatial granularities, these results support the notion that local and interregional connectivity exist on a spectrum of scales, rather than as separate and distinct networks, as is commonly assumed. Finally, we predicted how the emergence of primary sensory cortical maps is constrained by the anatomy of thalamo-cortical projections. A subvolume of the model comprising 211,712 neurons in the front limb, jaw, and dysgranular zone has been made freely and openly available to the community.

Recent advances in the urban science make broad use of the notion of scaling. We focus here on the important scaling relationship between the gross metropolitan product (GMP) of a city and its population (pop). It has been demonstrated that GMP ∝ Y Ypopβ with β always greater than 1 and close to 1.2. This fundamental finding highlights a universal rule that holds across countries and cultures and might explain the very nature of cities. However, in an increasingly connected world, the hypothesis that the economy of a city solely depends on its population might be questionable. Using data for 248 cities in the European Union between 2005 and 2010, we found a double GMP/pop scaling regime. For West EU cities, β = 1 over the whole the period, while for post-communist cities β > 1 and increases from ∼1.2 to ∼1.4. The evolution of the scaling exponent describes the convergence of post-communist European cities to open and liberal economies. We propose a simple model of economic convergence in which, under stable political conditions, a linear GMP/pop scaling is expected for all cities. The results suggest that the GMP/pop super-linear scaling represents a phase of economic growth rather than a steady, universal urban feature. The results also suggest that relationships between cities are embedded in their political and economic context and cannot be neglected in explanations of cities, urbanization and urban economics.