Nonproteolytic cleavage of aspartyl proline bonds in the cellulosomal scaffoldin subunit from Clostridium thermocellum

Previous work from our group [Morag (Morgenstern), E., Bayer, E. A., and Lamed, R. (1991), Appl. Biochem. Biotechnol. 30, 129–136] has demonstrated an anomalous electrophoretic mobility pattern for scaffoldin, the 210-kDa cellulosome-integrating subunit of Clostridium thermocellum. Subsequent evidence [Morag, E., Bayer, E. A., and Lamed, R. (1992), Appl. Biochem. Biotechnol. 33, 205–217] indicated that the effect could be attributed to a nonproteolytic fragmentation of the subunit into a defined series of lowermolecular-weight bands. In the present work, a recombinant segment of the scaffoldin subunit was employed to determine the site(s) of bond breakage. An Asp-Pro sequence within the cohesin domain was identified to be the sensitive peptide bond. This sequence appears quite frequently in the large cellulosomal proteins, and the labile bond may be related to an as yet undescribed physiological role in the hydrolysis of cellulose by cellulosomes.     

Equivalence of positive Hausdorff measure and the open set condition for self-conformal sets

A compact set is self-conformal if it is a finite union of its images by conformal contractions. It is well known that if the conformal contractions satisfy the ``open set condition' (OSC), then has positive -dimensional Hausdorff measure, where is the solution of Bowen's pressure equation. We prove that the OSC, the strong OSC, and positivity of the -dimensional Hausdorff measure are equivalent for conformal contractions; this answers a question of R. D. Mauldin. In the self-similar case, when the contractions are linear, this equivalence was proved by Schief (1994), who used a result of Bandt and Graf (1992), but the proofs in these papers do not extend to the nonlinear setting.

     

Thin points for Brownian motion

Let Θ(x,r) denote the occupation measure of the ball of radius r centered at x for Brownian motion {W_t}_0≤t≤1 in . We prove that for any analytic set E in [0,1], we have

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, where dim_P(E) is the packing dimension of E. We deduce that for any a≥1, the Hausdorff dimension of the set of “thin points” x for which

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, is almost surely 2−2/a; this is the correct scaling to obtain a nondegenerate “multifractal spectrum” for the “thin” part of Brownian occupation measure. The methods of this paper differ considerably from those of our work on Brownian thick points, due to the high degree of correlation in the present case. To prove our results, we establish general criteria for determining which deterministic sets are hit by random fractals of ‘limsup type' in the presence of long-range correlations. The hitting criteria then yield lower bounds on Hausdorff dimension. This refines previous work of Khoshnevisan, Xiao and the second author, that required decay of correlations.     

Excited-state intermolecular proton transfer of firefly luciferin III. Proton transfer to a mild base

Steady-state and time-resolved techniques were employed to study the excited-state proton transfer (ESPT) from d-luciferin, the natural substrate of the firefly luciferase, to the mild acetate base in aqueous solutions. We found that in 1 M aqueous solutions of acetate or higher, a proton transfer (PT) process to the acetate takes place within 30 ps in both H(2)O and D(2)O solutions. The time-resolved emission signal is composed of three components. We found that the short-time component decay time is 300 and 600 fs in H(2)O and D(2)O, respectively. This component is attributed either to a PT process via the shortest water bridged complex available, ROH··H(2)O··Ac(-), or to PT taking place within a contact ion pair. The second time component of 2000 and 3000 fs for H(2)O and D(2)O, respectively, is attributed to ROH* acetate complex, whose proton wire is longer by one water molecule. The decay rate of the third, long-time component is proportional to the acetate concentration. We attribute it to the diffusion-assisted reaction as well as to PT process to the solvent.     

Biased tug-of-war, the biased infinity Laplacian, and comparison with exponential cones

We prove that if ${U\subset \mathbb {R}^n}$ is an open domain whose closure ${\overline U}$ is compact in the path metric, and F is a Lipschitz function on ?U, then for each ${\beta \in \mathbb {R}}$ there exists a unique viscosity solution to the β-biased infinity Laplacian equation $$\beta |\nabla u| + \Delta_\infty u=0$$ on U that extends F, where ${\Delta_\infty u= |\nabla u|^{-2} \sum_{i,j} u_{x_i}u_{x_ix_j} u_{x_j}}$ . In the proof, we extend the tug-of-war ideas of Peres, Schramm, Sheffield and Wilson, and define the β-biased ${\epsilon}$ -game as follows. The starting position is ${x_0 \in U}$ . At the kth step the two players toss a suitably biased coin (in our key example, player I wins with odds of ${\exp(\beta\epsilon)}$ to 1), and the winner chooses x _k with ${d(x_k,x_{k-1}) < \epsilon}$ . The game ends when ${x_k \in \partial U}$ , and player II pays the amount F(x _k ) to player I. We prove that the value ${u^{\epsilon}(x_0)}$ of this game exists, and that ${\|u^\epsilon - u\|_\infty \to 0}$ as ${\epsilon \to 0}$ , where u is the unique extension of F to ${\overline{U}}$ that satisfies comparison with β-exponential cones. Comparison with exponential cones is a notion that we introduce here, and generalizing a theorem of Crandall, Evans and Gariepy regarding comparison with linear cones, we show that a continuous function satisfies comparison with β-exponential cones if and only if it is a viscosity solution to the β-biased infinity Laplacian equation.     

Weak values of electron spin in a double quantum dot

We propose a protocol for a controlled experiment to measure a weak value of the electron's spin in a solid state device. The weak value is obtained by a two step procedure--weak measurement followed by a strong one (postselection), where the outcome of the first measurement is kept provided a second postselected outcome occurs. The setup consists of a double quantum dot and a weakly coupled quantum point contact to be used as a detector. Anomalously large values of the spin of a two electron system are predicted, as well as negative values of the total spin. We also show how to incorporate the adverse effect of decoherence into this procedure.     

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.     

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.     

Practical anodes for Li-ion batteries comprising metallurgical silicon particles and multiwall carbon nanotubes

Journal of Solid State Electrochemistry - Silicon is considered to be a very attractive anode material for next-generation lithium-ion batteries due to its high theoretical capacity...