An optimal algorithm for computing angle-constrained spanners

Let S be a set of n points in ℝd. A graph G = (S,E) is called a t-spanner for S, if for any two points p and q in S, the shortest-path distance in G between p and q is at most t|pq|, where |pq| denotes the Euclidean distance between p and q. The graph G is called θ-angle-constrained, if any two distinct edges sharing an endpoint make an angle of at least θ. It is shown that, for any θ with 0 < θ < π/3, a θ-angle-constrained t-spanner can be computed in O(n logn) time, where t depends only on θ

Function of the Diiron Cluster of Escherichia coli Class Ia Ribonucleotide Reductase in Proton-Coupled Electron Transfer

The class Ia ribonucleotide reductase (RNR) from Escherichia coli employs a free-radical mechanism, which involves bidirectional translocation of a radical equivalent or “hole” over a distance of ~35 Å from the stable diferric/tyrosyl-radical (Y[subscript 122]•) cofactor in the β subunit to cysteine 439 (C[subscript 439]) in the active site of the α subunit. This long-range, intersubunit electron transfer occurs by a multistep “hopping” mechanism via formation of transient amino acid radicals along a specific pathway and is thought to be conformationally gated and coupled to local proton transfers. Whereas constituent amino acids of the hopping pathway have been identified, details of the proton-transfer steps and conformational gating within the β sununit have remained obscure; specific proton couples have been proposed, but no direct evidence has been provided. In the key first step, the reduction of Y[subscript 122]• by the first residue in the hopping pathway, a water ligand to Fe[subscript 1] of the diferric cluster was suggested to donate a proton to yield the neutral Y[subscript 122]. Here we show that forward radical translocation is associated with perturbation of the Mössbauer spectrum of the diferric cluster, especially the quadrupole doublet associated with Fe[subscript 1]. Density functional theory (DFT) calculations verify the consistency of the experimentally observed perturbation with that expected for deprotonation of the Fe[subscript 1]-coordinated water ligand. The results thus provide the first evidence that the diiron cluster of this prototypical class Ia RNR functions not only in its well-known role as generator of the enzyme’s essential Y[subscript 122]•, but also directly in catalysis.National Institutes of Health (U.S.) (GM-29595

Structure of the Nucleotide Radical Formed during Reaction of CDP/TTP with the E441Q-α2β2 of E. coli Ribonucleotide Reductase

The Escherichia coli ribonucleotide reductase (RNR) catalyzes the conversion of nucleoside diphosphates to deoxynucleotides and requires a diferric-tyrosyl radical cofactor for catalysis. RNR is composed of a 1:1 complex of two homodimeric subunits: α and β. Incubation of the E441Q-α mutant RNR with substrate CDP and allosteric effector TTP results in loss of the tyrosyl radical and formation of two new radicals on the 200 ms to min time scale. The first radical was previously established by stopped flow UV/vis spectroscopy and pulsed high field EPR spectroscopy to be a disulfide radical anion. The second radical was proposed to be a 4′-radical of a 3′-keto-2′-deoxycytidine 5′-diphosphate. To identify the structure of the nucleotide radical [1′-[superscript 2]H], [2′-[superscript 2]H], [4′-[superscript 2]H], [5′-[superscript 2]H], [U−[superscript 13]C, [superscript 15]N], [U−[superscript 15]N], and [5,6 -[superscript 2]H] CDP and [β-[superscript 2]H] cysteine-α were synthesized and incubated with E441Q-α2β2 and TTP. The nucleotide radical was examined by 9 GHz and 140 GHz pulsed EPR spectroscopy and 35 GHz ENDOR spectroscopy. Substitution of [superscript 2]H at C4′ and C1′ altered the observed hyperfine interactions of the nucleotide radical and established that the observed structure was not that predicted. DFT calculations (B3LYP/IGLO-III/B3LYP/TZVP) were carried out in an effort to recapitulate the spectroscopic observations and lead to a new structure consistent with all of the experimental data. The results indicate, unexpectedly, that the radical is a semidione nucleotide radical of cytidine 5′-diphosphate. The relationship of this radical to the disulfide radical anion is discussed.National Institutes of Health (U.S.) (GM29595)(EB002804)(EB002026

A high‐resolution view of the coordination environment in a paramagnetic metalloprotein from its magnetic properties

Metalloproteins constitute a significant fraction of the proteome of all organisms and their characterization is critical for both basic sciences and biomedical applications. A large portion of metalloproteins bind paramagnetic metal ions, and paramagnetic NMR spectroscopy has been widely used in their structural characterization. However, the signals of nuclei in the immediate vicinity of the metal center are often broadened beyond detection. In this work, we show that it is possible to determine the coordination environment of the paramagnetic metal in the protein at a resolution inaccessible to other techniques. Taking the structure of a diamagnetic analogue as a starting point, a geometry optimization is carried out by fitting the pseudocontact shifts obtained from first principles quantum chemical calculations to the experimental ones