Quantitative Proteomics and Differential Protein Abundance Analysis after Depletion of Putative mRNA Receptors in the ER Membrane of Human Cells Identifies Novel Aspects of mRNA Targeting to the ER

In human cells, one-third of all polypeptides enter the secretory pathway at the endoplasmic reticulum (ER). The specificity and efficiency of this process are guaranteed by targeting of mRNAs and/or polypeptides to the ER membrane. Cytosolic SRP and its receptor in the ER membrane facilitate the cotranslational targeting of most ribosome-nascent precursor polypeptide chain (RNC) complexes together with the respective mRNAs to the Sec61 complex in the ER membrane. Alternatively, fully synthesized precursor polypeptides are targeted to the ER membrane post-translationally by either the TRC, SND, or PEX19/3 pathway. Furthermore, there is targeting of mRNAs to the ER membrane, which does not involve SRP but involves mRNA- or RNC-binding proteins on the ER surface, such as RRBP1 or KTN1. Traditionally, the targeting reactions were studied in cell-free or cellular assays, which focus on a single precursor polypeptide and allow the conclusion of whether a certain precursor can use a certain pathway. Recently, cellular approaches such as proximity-based ribosome profiling or quantitative proteomics were employed to address the question of which precursors use certain pathways under physiological conditions. Here, we combined siRNA-mediated depletion of putative mRNA receptors in HeLa cells with label-free quantitative proteomics and differential protein abundance analysis to characterize RRBP1- or KTN1-involving precursors and to identify possible genetic interactions between the various targeting pathways. Furthermore, we discuss the possible implications on the so-called TIGER domains and critically discuss the pros and cons of this experimental approach.     

Some remarks on a class of inverse problems related to the parabolic approximation to the Maxwell equations: a controllability approach

We consider a class of inverse source problems for the parabolic approximation to the Maxwell equations.We relate this to an exact controllability problem; the regularisation of the considered source problems is studied with an optimal control method. Copyright © 2014 John Wiley & Sons, Ltd.     

Singular stochastic Allen–Cahn equations with dynamic boundary conditions

We prove a well-posedness result for stochastic Allen–Cahn type equations in a bounded domain coupled with generic boundary conditions. The (nonlinear) flux at the boundary aims at describing the interactions with the hard walls and is motivated by some recent literature in physics. The singular character of the drift part allows for a large class of maximal monotone operators, generalizing the usual double-well potentials. One of the main novelties of the paper is the absence of any growth condition on the drift term of the evolution, neither on the domain nor on the boundary. A well-posedness result for variational solutions of the system is presented using a priori estimates as well as monotonicity and compactness techniques. A vanishing viscosity argument for the dynamic on the boundary is also presented.     

On the Diophantine equation ax + by = ck

In this paper we investigate the solvability and the representation of the solutions of the equation ax² +by² = ckⁿ. We extend and improve many known results. In particular, we completely solve the equation (a ± 1)x² + (3a ? 1) = 4aⁿ, 2 ? n.     

Modulation spaces, Wiener amalgam spaces, and Brownian motions

We study the local-in-time regularity of the Brownian motion with respect to localized variants of modulation spaces and Wiener amalgam spaces . We show that the periodic Brownian motion belongs locally in time to and 61" alt="View the MathML source" title="View the MathML source" src="http://binary-services.sciencedirect.com/content/image/1-s2.0-S0001870811002854-si4.gif"> for (s−1)q<−1, and the condition on the indices is optimal. Moreover, with the Wiener measure μ on T, we show that and form abstract Wiener spaces for the same range of indices, yielding large deviation estimates. We also establish the endpoint regularity of the periodic Brownian motion with respect to a Besov-type space 61" alt="View the MathML source" title="View the MathML source" src="http://binary-services.sciencedirect.com/content/image/1-s2.0-S0001870811002854-si9.gif">. Specifically, we prove that the Brownian motion belongs to 61" alt="View the MathML source" title="View the MathML source" src="http://binary-services.sciencedirect.com/content/image/1-s2.0-S0001870811002854-si10.gif"> for (s−1)p=−1, and it obeys a large deviation estimate. Finally, we revisit the regularity of Brownian motion on usual local Besov spaces , and indicate the endpoint large deviation estimates.     

On some generalized Lebesgue-Nagell equations

By using known results and elementary arguments, we give all solutions of some generalized Lebesgue-Nagell equations

     

Uniform bounds on the 1-norm of the inverse of lower triangular Toeplitz matrices

A uniform bound on the 1-norm is given for the inverse of a lower triangular Toeplitz matrix with non-negative monotonically decreasing entries whose limit is zero. The new bound is sharp under certain specified constraints. This result is then employed to throw light upon a long standing open problem posed by Brunner concerning the convergence of the one-point collocation method for the Abel equation. In addition, the recent conjecture of Gauthier et al. is proved.     

Analytic solutions for infinite horizon stochastic optimal control problems via finite horizon approximation: A practical guide

We show how infinite horizon stochastic optimal control problems can be solved via studying their finite horizon approximations. This often leads to analytical solutions for the infinite horizon problem by studying phase diagrams, even in cases where the complexity of the finite horizon case does not permit analytic solutions. Our approach can be applied to many problems in dynamic economics.     

Trading water along a river

A set of agents is located along a river. Each agent consumes certain amount of water he receives from his part of the river basin and may sell certain amount to his downstream agent if it is mutually beneficial. Water trading is restricted to two neighboring agents and an agent can only pass water to his downstream agent. We ask if this restricted trade to neighboring agents can implement an efficient allocation of water. We show that the efficient allocation of water can be achieved through the process of downstream bilateral trading. Specifically, we show that this one way “downstream” trading process implements the unique efficient allocation as well as a welfare distribution. We also show that the welfare distribution is in the core of the associated game of the problem. Moreover, we show that the coalition of agents upstream any agent obtains more welfare with the bilateral trading than with the downstream incremental distribution proposed by Ambec and Sprumont (2002) and less than with the upstream incremental distribution proposed by [Ambec and Ehlers, 2008a] and [Ambec and Ehlers, 2008b].     

Effects of heat input on the low power Nd:YAG pulse laser conduction weldability of magnesium alloy AZ61

The effects of heat input on the low power Nd:YAG pulse laser conduction weldability of magnesium alloy AZ61 plates were investigated. The results show that for a hot-extruded AZ61 magnesium alloy plate laser conduction welding, the penetration depth and area of welds cross-section increased with an increase of the heat input. The microstructure of a band zone, which is located in the fusion zone (FZ) and close to the fusion boundary, evolved with an increase of the heat input. Moreover, an increase of the heat input increased the tendency of the formation of solidification cracking and liquation cracking. The porosities and average diameters of pores increased with an increase of the heat input but reduced sharply when a relatively large heat input was achieved. In addition, the degree of formation of craters increased linearly with an increase of the heat input.