The macroscopic effects of microscopic heterogeneity

Over the past decade, advances in super-resolution microscopy and particle-based modeling have driven an intense interest in investigating spatial heterogeneity at the level of single molecules in cells. Remarkably, it is becoming clear that spatiotemporal correlations between just a few molecules can have profound effects on the signaling behavior of the entire cell. While such correlations are often explicitly imposed by molecular structures such as rafts, clusters, or scaffolds, they also arise intrinsically, due strictly to the small numbers of molecules involved, the finite speed of diffusion, and the effects of macromolecular crowding. In this chapter we review examples of both explicitly imposed and intrinsic correlations, focusing on the mechanisms by which microscopic heterogeneity is amplified to macroscopic effect.Comment: 20 pages, 5 figures. To appear in Advances in Chemical Physic

Plasmonic modes of extreme subwavelength nanocavities

We study the physics of a new type of subwavelength nanocavities. They are based on U-shaped metal-insulator-metal waveguides supporting the excitation of surface plasmon polaritons. The waveguides are simultaneously excited from both sides of the U by incident plane waves. Due to their finite length discrete modes emerge within the nanocavity. We show that the excitation symmetry with respect to the cavity ends permits the observation of even and odd modes. Our investigations include near and far field simulations and predict a strong spectral far field response of the comparable small nanoresonators. The strong near field enhancement observed in the cavity at resonance might be suitable to increase the efficiency of nonlinear optical effects, quantum analogies and might facilitate the development of active optical elements, such as active plasmonic elements

Anomalous fluctuation relations

We study Fluctuation Relations (FRs) for dynamics that are anomalous, in the sense that the diffusive properties strongly deviate from the ones of standard Brownian motion. We first briefly review the concept of transient work FRs for stochastic dynamics modeled by the ordinary Langevin equation. We then introduce three generic types of dynamics generating anomalous diffusion: L\'evy flights, long-time correlated Gaussian stochastic processes and time-fractional kinetics. By combining Langevin and kinetic approaches we calculate the work probability distributions in the simple nonequilibrium situation of a particle subject to a constant force. This allows us to check the transient FR for anomalous dynamics. We find a new form of FRs, which is intimately related to the validity of fluctuation-dissipation relations. Analogous results are obtained for a particle in a harmonic potential dragged by a constant force. We argue that these findings are important for understanding fluctuations in experimentally accessible systems. As an example, we discuss the anomalous dynamics of biological cell migration both in equilibrium and in nonequilibrium under chemical gradients.Comment: book chapter; 25 pages, 10 figures. see http://www.maths.qmul.ac.uk/~klages/smallsys/smallsys_rk.htm

Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems

We introduce a definition of a "localization width" whose logarithm is given by the entropy of the distribution of particle component amplitudes in the Lyapunov vector. Different types of localization widths are observed, for example, a minimum localization width where the components of only two particles are dominant. We can distinguish a delocalization associated with a random distribution of particle contributions, a delocalization associated with a uniform distribution and a delocalization associated with a wave-like structure in the Lyapunov vector. Using the localization width we show that in quasi-one-dimensional systems of many hard disks there are two kinds of dependence of the localization width on the Lyapunov exponent index for the larger exponents: one is exponential, and the other is linear. Differences, due to these kinds of localizations also appear in the shapes of the localized peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the spatial and momentum parts of the Lyapunov vectors. We show that the Krylov relation for the largest Lyapunov exponent $\lambda\sim-\rho\ln\rho$ as a function of the density $\rho$ is satisfied (apart from a factor) in the same density region as the linear dependence of the localization widths is observed. It is also shown that there are asymmetries in the spatial and momentum parts of the Lyapunov vectors, as well as in their $x$ and $y$-components.Comment: 41 pages, 21 figures, Manuscript including the figures of better quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm

High-throughput in vivo vertebrate screening

We demonstrate a high-throughput platform for cellular-resolution in vivo chemical and genetic screens on zebrafish larvae. The system automatically loads zebrafish from reservoirs or multiwell plates, and positions and rotates them for high-speed confocal imaging and laser manipulation of both superficial and deep organs within 19 s without damage. We performed small-scale test screening of retinal axon guidance mutants and neuronal regeneration assays in combination with femtosecond laser microsurgery.National Institutes of Health (U.S.) (Director’s Innovator Award 1-DP2-OD002989–01)David & Lucile Packard Foundation (Award in Science and Engineering)Alfred P. Sloan Foundation (Award)Broad Institute of MIT and Harvard (Sparc Grant)National Science Foundation (U.S.) (Fellowship)Foxconn (Sponsorship

Erythropoietin signaling regulates heme biosynthesis

Heme is required for survival of all cells, and in most eukaryotes, is produced through a series of eight enzymatic reactions. Although heme production is critical for many cellular processes, how it is coupled to cellular differentiation is unknown. Here, using zebrafish, murine, and human models, we show that erythropoietin (EPO) signaling, together with the GATA1 transcriptional target, AKAP10, regulates heme biosynthesis during erythropoiesis at the outer mitochondrial membrane. This integrated pathway culminates with the direct phosphorylation of the crucial heme biosynthetic enzyme, ferrochelatase (FECH) by protein kinase A (PKA). Biochemical, pharmacological, and genetic inhibition of this signaling pathway result in a block in hemoglobin production and concomitant intracellular accumulation of protoporphyrin intermediates. Broadly, our results implicate aberrant PKA signaling in the pathogenesis of hematologic diseases. We propose a unifying model in which the erythroid transcriptional program works in concert with post-translational mechanisms to regulate heme metabolism during normal development

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, the architecture of a promoter, defined as the number, strength and regulatory role of the operators that control the promoter, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect noise in gene expression in a systematic rather than case-by-case fashion. In this article, we make such a systematic investigation, based on a simple microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcription product from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can discriminate between different kinetic models of gene regulation.Comment: 35 pages, 6 figures, Submitte

Mapping Dirac quasiparticles near a single Coulomb impurity on graphene

The response of Dirac fermions to a Coulomb potential is predicted to differ significantly from how non-relativistic electrons behave in traditional atomic and impurity systems. Surprisingly, many key theoretical predictions for this ultra-relativistic regime have not been tested. Graphene, a two-dimensional material in which electrons behave like massless Dirac fermions, provides a unique opportunity to test such predictions. Graphene’s response to a Coulomb potential also offers insight into important material characteristics, including graphene’s intrinsic dielectric constant, which is the primary factor determining the strength of electron–electron interactions in graphene. Here we present a direct measurement of the nanoscale response of Dirac fermions to a single Coulomb potential placed on a gated graphene device. Scanning tunnelling microscopy was used to fabricate tunable charge impurities on graphene, and to image electronic screening around them for a Q = +1|e| charge state. Electron-like and hole-like Dirac fermions were observed to respond differently to a Coulomb potential. Comparing the observed electron–hole asymmetry to theoretical simulations has allowed us to test predictions for how Dirac fermions behave near a Coulomb potential, as well as extract graphene’s intrinsic dielectric constant: ε[subscript g] = 3.0±1.0. This small value of ε[subscript g] indicates that electron–electron interactions can contribute significantly to graphene properties.United States. Office of Naval Research. Multidisciplinary University Research Initiative (Award N00014-09-1-1066)United States. Dept. of Energy. Office of Science (Contract DE-AC02-05CH11231)National Science Foundation (U.S.) (Award DMR-0906539