Exact expressions for the mobility and electrophoretic mobility of a weakly charged sphere in a simple electrolyte

We present (asymptotically) exact expressions for the mobility and electrophoretic mobility of a weakly charged spherical particle in an $1:1$ electrolyte solution. This is done by analytically solving the electro and hydrodynamic equations governing the electric potential and fluid flow with respect to an electric field and a nonelectric force. The resulting formulae are cumbersome, but fully explicit and trivial for computation. In the case of a very small particle compared to the Debye screening length ($R \ll r_D$) our results reproduce proper limits of the classical Debye and Onsager theories, while in the case of a very large particle ($R \gg r_D$) we recover, both, the non-monotonous charge dependence discovered by Levich (1958) as well as the scaling estimate given by Long, Viovy, and Ajdari (1996), while adding the previously unknown coefficients and corrections. The main applicability condition of our solution is charge smallness in the sense that screening remains linear.Comment: 6 pages, 1 figur

Double-digest RADseq loci using standard Illumina indexes improve deep and shallow phylogenetic resolution of Lophodermium, a widespread fungal endophyte of pine needles.

The phylogenetic and population genetic structure of symbiotic microorganisms may correlate with important ecological traits that can be difficult to directly measure, such as host preferences or dispersal rates. This study develops and tests a low-cost double-digest restriction site-associated DNA sequencing (ddRADseq) protocol to reveal among- and within-species genetic structure for Lophodermium, a genus of fungal endophytes whose evolutionary analyses have been limited by the scarcity of informative markers. The protocol avoids expensive barcoded adapters and incorporates universal indexes for multiplexing. We tested for reproducibility and functionality by comparing shared loci from sample replicates and assessed the effects of numbers of ambiguous sites and clustering thresholds on coverage depths, number of shared loci among samples, and phylogenetic reconstruction. Errors between technical replicates were minimal. Relaxing the quality-filtering criteria increased the mean coverage depth per locus and the number of loci recovered within a sample, but had little effect on the number of shared loci across samples. Increasing clustering threshold decreased the mean coverage depth per cluster and increased the number of loci recovered within a sample but also decreased the number of shared loci across samples, especially among distantly related species. The combination of low similarity clustering (70%) and relaxed quality-filtering (allowing up to 30 ambiguous sites per read) performed the best in phylogenetic analyses at both recent and deep genetic divergences. Hence, this method generated sufficient number of shared homologous loci to investigate the evolutionary relationships among divergent fungal lineages with small haploid genomes. The greater genetic resolution also revealed new structure within species that correlated with ecological traits, providing valuable insights into their cryptic life histories

Many-body effects in tracer particle diffusion with applications for single-protein dynamics on DNA

30% of the DNA in E. coli bacteria is covered by proteins. Such high degree of crowding affect the dynamics of generic biological processes (e.g. gene regulation, DNA repair, protein diffusion etc.) in ways that are not yet fully understood. In this paper, we theoretically address the diffusion constant of a tracer particle in a one dimensional system surrounded by impenetrable crowder particles. While the tracer particle always stays on the lattice, crowder particles may unbind to a surrounding bulk and rebind at another or the same location. In this scenario we determine how the long time diffusion constant ${\cal D}$ (after many unbinding events) depends on (i) the unbinding rate of crowder particles $k_{\rm off}$, and (ii) crowder particle line density $\rho$, from simulations (Gillespie algorithm) and analytical calculations. For small $k_{\rm off}$, we find ${\cal D}\sim k_{\rm off}/\rho^2$ when crowder particles are immobile on the line, and ${\cal D}\sim \sqrt{D k_{\rm off}}/\rho$ when they are diffusing; $D$ is the free particle diffusion constant. For large $k_{\rm off}$, we find agreement with mean-field results which do not depend on $k_{\rm off}$. From literature values of $k_{\rm off}$ and $D$, we show that the small $k_{\rm off}$-limit is relevant for in vivo protein diffusion on a crowded DNA. Our results applies to single-molecule tracking experiments.Comment: 10 pages, 8 figure

Zero-Crossing Statistics for Non-Markovian Time Series

In applications spaning from image analysis and speech recognition, to energy dissipation in turbulence and time-to failure of fatigued materials, researchers and engineers want to calculate how often a stochastic observable crosses a specific level, such as zero. At first glance this problem looks simple, but it is in fact theoretically very challenging. And therefore, few exact results exist. One exception is the celebrated Rice formula that gives the mean number of zero-crossings in a fixed time interval of a zero-mean Gaussian stationary processes. In this study we use the so-called Independent Interval Approximation to go beyond Rice's result and derive analytic expressions for all higher-order zero-crossing cumulants and moments. Our results agrees well with simulations for the non-Markovian autoregressive model

Vector triplets at the LHC

Several popular extensions of the Standard Model predict extra vector fields that transform as triplets under the gauge group SU(2)_L. These multiplets contain Z' and W' bosons, with masses and couplings related by gauge invariance. We review some model-independent results about these new vector bosons, with emphasis on di-lepton and lepton-plus-missing-energy signals at the LHC.Comment: LaTex 5 pages. Talk by M. Perez-Victoria at LHCP 2013, Barcelona, Spain, May 13-18, 2013. New reference adde