Graph pebbling is a network optimization model for transporting discrete resources that are consumed in transit: the movement of 2 pebbles across an edge consumes one of the pebbles. The pebbling number of a graph is the fewest number of pebbles t so that, from any initial configuration of t pebbles on its vertices, one can place a pebble on any given target vertex via such pebbling steps. It is known that deciding whether a given configuration on a particular graph can reach a specified target is NP-complete, even for diameter 2 graphs, and that deciding whether the pebbling number has a prescribed upper bound is Π[P over 2]-complete. On the other hand, for many families of graphs there are formulas or polynomial algorithms for computing pebbling numbers; for example, complete graphs, products of paths (including cubes), trees, cycles, diameter 2 graphs, and more. Moreover, graphs having minimum pebbling number are called Class 0, and many authors have studied which graphs are Class 0 and what graph properties guarantee it, with no characterization in sight. In this paper we investigate an important family of diameter 3 chordal graphs called split graphs; graphs whose vertex set can be partitioned into a clique and an independent set. We provide a formula for the pebbling number of a split graph, along with an algorithm for calculating it that runs in O(n[superscript β]) time, where β = 2ω/(ω + 1) [= over ∼] 1.41 and ω [= over ∼] 2.376 is the exponent of matrix multiplication. Furthermore we determine that all split graphs with minimum degree at least 3 are Class 0.

The SH3 domain of the c-Src tyrosine kinase (c-Src-SH3) aggregates to form intertwined dimers and amyloid fibrils at mild acid pHs. In this work, we show that a single mutation of residue Gln128 of this SH3 domain has a significant effect on: (i) its thermal stability; and (ii) its propensity to form amyloid fibrils. The Gln128Glu mutant forms amyloid fibrils at neutral pH but not at mild acid pH, while Gln128Lys and Gln128Arg mutants do not form these aggregates under any of the conditions assayed. We have also solved the crystallographic structures of the wild-type (WT) and Gln128Glu, Gln128Lys and Gln128Arg mutants from crystals obtained at different pHs. At pH 5.0, crystals belong to the hexagonal space group P6₅22 and the asymmetric unit is formed by one chain of the protomer of the c-Src-SH3 domain in an open conformation. At pH 7.0, crystals belong to the orthorhombic space group P2₁2₁2₁, with two molecules at the asymmetric unit showing the characteristic fold of the SH3 domain. Analysis of these crystallographic structures shows that the residue at position 128 is connected to Glu106 at the diverging β-turn through a cluster of water molecules. Changes in this hydrogen-bond network lead to the displacement of the c-Src-SH3 distal loop, resulting also in conformational changes of Leu100 that might be related to the binding of proline rich motifs. Our findings show that electrostatic interactions and solvation of residues close to the folding nucleation site of the c-Src-SH3 domain might play an important role during the folding reaction and the amyloid fibril formation.

A structurally and compositionally well-defined and spectrally tunable artificial light-harvesting system has been constructed in which multiple organic dyes attached to a three-arm-DNA nanostructure serve as an antenna conjugated to a photosynthetic reaction center isolated from Rhodobacter sphaeroides 2.4.1. The light energy absorbed by the dye molecules is transferred to the reaction center, where charge separation takes place. The average number of DNA three-arm junctions per reaction center was tuned from 0.75 to 2.35. This DNA-templated multichromophore system serves as a modular light-harvesting antenna that is capable of being optimized for its spectral properties, energy transfer efficiency, and photostability, allowing one to adjust both the size and spectrum of the resulting structures. This may serve as a useful test bed for developing nanostructured photonic systems.

Photosynthesis, a process catalysed by plants, algae and cyanobacteria converts sunlight to energy thus sustaining all higher life on Earth. Two large membrane protein complexes, photosystem I and II (PSI and PSII), act in series to catalyse the light-driven reactions in photosynthesis. PSII catalyses the light-driven water splitting process, which maintains the Earth’s oxygenic atmosphere. In this process, the oxygen-evolving complex (OEC) of PSII cycles through five states, S₀ to S₄, in which four electrons are sequentially extracted from the OEC in four light-driven charge-separation events. Here we describe time resolved experiments on PSII nano/microcrystals from Thermosynechococcus elongatus performed with the recently developed technique of serial femtosecond crystallography. Structures have been determined from PSII in the dark S₁ state and after double laser excitation (putative S₃ state) at 5 and 5.5 Å resolution, respectively. The results provide evidence that PSII undergoes significant conformational changes at the electron acceptor side and at the Mn₄CaO₅ core of the OEC. These include an elongation of the metal cluster, accompanied by changes in the protein environment, which could allow for binding of the second substrate water molecule between the more distant protruding Mn (referred to as the ‘dangler’ Mn) and the Mn₃CaO_x cubane in the S₂ to S₃ transition, as predicted by spectroscopic and computational studies. This work shows the great potential for time-resolved serial femtosecond crystallography for investigation of catalytic processes in biomolecules.

Telomerase is a specialized reverse transcriptase (RT) containing an intrinsic telomerase RNA (TR) component. It synthesizes telomeric DNA repeats, (GGTTAG)n in humans, by reiteratively copying a precisely defined, short template sequence from the integral TR. The specific mechanism of how the telomerase active site uses this short template region accurately and efficiently during processive DNA repeat synthesis has remained elusive. Here we report that the human TR template, in addition to specifying the DNA sequence, is embedded with a single-nucleotide signal to pause DNA synthesis. After the addition of a dT residue to the DNA primer, which is specified by the 49 rA residue in the template, telomerase extends the DNA primer with three additional nucleotides and then pauses DNA synthesis. This sequence-defined pause site coincides precisely with the helix paired region 1 (P1)-defined physical template boundary and precludes the incorporation of nontelomeric nucleotides from residues outside the template region. Furthermore, this sequence-defined pausing mechanism is a key determinant, in addition to the P1-defined template boundary, for generating the characteristic 6-nt ladder banding pattern of telomeric DNA products in vitro. In the absence of the pausing signal, telomerase stalls nucleotide addition at multiple sites along the template, generating DNA products with heterogeneous terminal repeat registers. Our findings demonstrate that this unique self-regulating mechanism of the human TR template is essential for high-fidelity synthesis of DNA repeats.

Sliding clamps are ring-shaped oligomeric proteins that are essential for processive deoxyribonucleic acid replication. Although crystallographic structures of several clamps have been determined, much less is known about clamp structure and dynamics in solution. Here, we characterized the intrinsic solution stability and oligomerization dynamics of the homodimeric Escherichia coli β and the homotrimeric Saccharomyces cerevisiae proliferating cell nuclear antigen (PCNA) clamps using single-molecule approaches. We show that E. coli β is stable in solution as a closed ring at concentrations three orders of magnitude lower than PCNA. The trimeric structure of PCNA results in slow subunit association rates and is largely responsible for the lower solution stability. Despite this large difference, the intrinsic lifetimes of the rings differ by only one order of magnitude. Our results show that the longer lifetime of the E. coli β dimer is due to more prominent electrostatic interactions that stabilize the subunit interfaces.

A new class of highly active solid base catalysts for biodiesel production was developed by creating hierarchically porous aluminosilicate geopolymer with affordable precursors and modifying the material with varying amounts of calcium. For the catalysts containing ≥8 wt% Ca, almost 100% conversion has been achieved in one hour under refluxing conditions with methanol solvent, and the high catalytic activity was preserved for multiple regeneration cycles. Temperature-programed desorption studies of CO2 indicate that the new base catalyst has three different types of base sites on its surface whose strengths are intermediate between MgO and CaO. The detailed powder X-ray diffraction (PXRD) and X-ray photoelectron spectroscopic (XPS) studies show that the calcium ions were incorporated into the aluminosilicate network of the geopolymer structure, resulting in a very strong ionicity of the calcium and thus the strong basicity of the catalysts. Little presence of CaCO3 in the catalysts was indicated from the thermogravimetric analysis (TGA), XPS and Fourier transform infrared spectroscopy (FT-IR) studies, which may contribute to the observed high catalytic activity and regenerability. The results indicate that new geopolymer-based catalysts can be developed for cost-effective biodiesel production.

Most current approaches for quantification of RNA species in their natural spatial contexts in single cells are limited by a small number of parallel analyses. Here we report a strategy to dramatically increase the multiplexing capacity for RNA analysis in single cells in situ. In this method, transcripts are detected by fluorescence in situ hybridization (FISH). After imaging and data storage, the fluorescence signal is efficiently removed by photobleaching. This enables the reinitiation of FISH to detect other RNA species in the same cell. Through reiterative cycles of hybridization, imaging and photobleaching, the identities, positions and copy numbers of a large number of varied RNA species can be quantified in individual cells in situ. Using this approach, we analyzed seven different transcripts in single HeLa cells with five reiterative RNA FISH cycles. This approach has the potential to detect over 100 varied RNA species in single cells in situ, which will have wide applications in studies of systems biology, molecular diagnosis and targeted therapies.

Multilayer structures of TiO₂/Ag/TiO₂ have been deposited onto flexible substrates by room temperature sputtering to develop indium-free transparent composite electrodes. The effect of Ag thicknesses on optical and electrical properties and the mechanism of conduction have been discussed. The critical thickness (t_c) of Ag mid-layer to form a continuous conducting layer is 9.5 nm and the multilayer has been optimized to obtain a sheet resistance of 5.7 Ω/sq and an average optical transmittance of 90% at 590 nm. The Haacke figure of merit (FOM) for t_c has one of the highest FOMs with 61.4 × 10^-3 Ω^-1/sq.

Lithium-beryllium metal hydrides, which are structurally related to their parent compound, BeH₂, offer the highest hydrogen storage capacity by weight among the metal hydrides (15.93 wt. % of hydrogen for LiBeH₃). Challenging synthesis protocols have precluded conclusive determination of their crystallographic structure to date, but here we analyze directly the hydrogen hopping mechanisms in BeH₂ and LiBeH₃ using quasielastic neutron scattering, which is especially sensitive to single-particle dynamics of hydrogen. We find that, unlike its parent compound BeH₂, lithium-beryllium hydride LiBeH₃ exhibits a sharp increase in hydrogen mobility above 265 K, so dramatic that it can be viewed as melting of hydrogen sublattice. We perform comparative analysis of hydrogen jump mechanisms observed in BeH₂ and LiBeH₃ over a broad temperature range. As microscopic diffusivity of hydrogen is directly related to its macroscopic kinetics, a transition in LiBeH₃ so close to ambient temperature may offer a straightforward and effective mechanism to influence hydrogen uptake and release in this very lightweight hydrogen storage compound.