Single-cell FRET imaging of transferrin receptor trafficking dynamics by Sfp-catalyzed, site-specific protein labeling

Fluorescence imaging of living cells depends on an efficient and specific method for labeling the target cellular protein with fluorophores. Here we show that Sfp phosphopantetheinyl transferase-catalyzed protein labeling is suitable for fluorescence imaging of membrane proteins that spend at least part of their membrane trafficking cycle at the cell surface. In this study, transferrin receptor 1 (TfR1) was fused to peptide carrier protein (PCP), and the TfR1-PCP fusion protein was specifically labeled with fluorophore Alexa 488 by Sfp. The trafficking of transferrin-TfR1-PCP complex during the process of transferrin-mediated iron uptake was imaged by fluorescence resonance energy transfer between the fluorescently labeled transferrin ligand and TfR1 receptor. We thus demonstrated that Sfp-catalyzed small molecule labeling of the PCP tag represents a practical and efficient tool for molecular imaging studies in living cells.     

Work allocation to stations with varying learning slopes and without buffers

In this paper, we address the problem of allocating the work elements, belonging to the products of a lot, to the stations of an assembly line so as to minimize the makespan. The lots that are processed on the assembly line are characterized by a low overall demand for each product. There is no buffer permitted in between the stations, and the line operates under learning. In particular, the stations’ learning slopes are assumed to be different. We present a procedure to determine the optimal assignments of the workload to the stations under learning variability and show that it considerably affects these assignments.     

A graph-theoretic approach for comparing dimensions of components in simply-graded algebras

Any simple group-grading of a finite dimensional complex algebra induces a natural family of digraphs. We prove that in a digraph without parallel edges, the number of pairs of vertices having a common in-neighbor or a common out-neighbor is at least the number of edges. We deduce that for any simple group-grading, the dimension of the trivial component is maximal.     

On minimum power connectivity problems

Given a (directed or undirected) graph with edge costs, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of its nodes. Motivated by applications for wireless networks, we present polynomial and improved approximation algorithms, as well as inapproximability results, for some classic network design problems under the power minimization criteria. Our main result is for the problem of finding a min-power subgraph that contains k internally-disjoint vs-paths from every node v to a given node s: we give a polynomial algorithm for directed graphs and a logarithmic approximation algorithm for undirected graphs. In contrast, we will show that the corresponding edge-connectivity problems are unlikely to admit even a polylogarithmic approximation.     

On the endomorphism ring of a module noetherian with respect to a torsion theory

IfM is a module torsionfree and noetherian with respect to a torsion theory, ifS is the endomorphism ring ofM, and ifL(S) is the ideal ofS consisting of all endomorphisms with large kernels, thenL(S) is nilpotent and a bound on the index of nilpotency ofL(S) is given.     

Crack growth resistance of shape memory alloys by means of a cohesive zone model

Crack growth resistance of shape memory alloys (SMAs) is dominated by the transformation zone in the vicinity of the crack tip. In this study, the transformation toughening behavior of a slowly propagating crack in an SMA under plane strain conditions and mode I deformation is numerically investigated. A small-scale transformation zone is assumed. A cohesive zone model is implemented to simulate crack growth within a finite element scheme. Resistance curves are obtained for a range of parameters that specify the cohesive traction-separation constitutive law. It is found that the choice of the cohesive strength t₀ has a great influence on the toughening behavior of the material. Moreover, the reversibility of the transformation can significantly reduce the toughening of the alloy. The shape of the initial transformation zone, as well as that of a growing crack is determined. The effect of the Young's moduli ratio of the martensite and austenite phases is examined.     

Motivic torsors

The torsorP _δ=Hom^⊗ (H _DR,H _σ) under the motivic Galois groupG _σ=Aut^⊗ H _δ of the Tannakian category generated by one-motives related by absolute Hodge cycles over a field κ with an embedding σ:k↪ℂ is shown to be determined by its projectionP _σ→P _σ/G _σ ⁰ to a Gal( )-torsor, and by its localizationsP _σ⊕_k k _ξ at a dense subset of orderings ϕ of the field κ, provided κ has virtual cohomological dimension (vcd) one. This result is an application of a recent local-global principle for connected linear algebraic groups over a field κ of vcd ≤1.     

On Lipschitz extension from finite subsets

We prove that for every n ∈ ? there exists a metric space (X, d _X), an n-point subset S ? X, a Banach space (Z, \({\left\| \right\|_Z}\)) and a 1-Lipschitz function f: S → Z such that the Lipschitz constant of every function F: X → Z that extends f is at least a constant multiple of \(\sqrt {\log n} \). This improves a bound of Johnson and Lindenstrauss [JL84]. We also obtain the following quantitative counterpart to a classical extension theorem of Minty [Min70]. For every α ∈ (1/2, 1] and n ∈ ? there exists a metric space (X, d _X), an n-point subset S ? X and a function f: S → ?₂ that is α-Hölder with constant 1, yet the α-Hölder constant of any F: X → ?₂ that extends f satisfies \({\left\| F \right\|_{Lip\left( \alpha \right)}} > {\left( {\log n} \right)^{\frac{{2\alpha - 1}}{{4\alpha }}}} + {\left( {\frac{{\log n}}{{\log \log n}}} \right)^{{\alpha ^2} - \frac{1}{2}}}\). We formulate a conjecture whose positive solution would strengthen Ball’s nonlinear Maurey extension theorem [Bal92], serving as a far-reaching nonlinear version of a theorem of König, Retherford and Tomczak-Jaegermann [KRTJ80]. We explain how this conjecture would imply as special cases answers to longstanding open questions of Johnson and Lindenstrauss [JL84] and Kalton [Kal04].