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1. Quantifying the effects of long-range 13C-13C dipolar coupling on measured relaxation rates in RNA

   https://doi.org/10.1007/s10858-021-00368-8  

   Olenginski, Lukasz T.; Dayie, Theodore K. (May 2021, Journal of Biomolecular NMR)

   Abstract Selective stable isotope labeling has transformed structural and dynamics analysis of RNA by NMR spectroscopy. These methods can remove 13 C- 13 C dipolar couplings that complicate 13 C relaxation analyses. While these phenomena are well documented for sites with adjacent 13 C nuclei (e.g. ribose C1′), less is known about so-called isolated sites (e.g. adenosine C2). To investigate and quantify the effects of long-range (> 2 Å) 13 C- 13 C dipolar interactions on RNA dynamics, we simulated adenosine C2 relaxation rates in uniformly [U- 13 C/ 15 N]-ATP or selectively [2- 13 C]-ATP labeled RNAs. Our simulations predict non-negligible 13 C- 13 C dipolar contributions from adenosine C4, C5, and C6 to C2 longitudinal (R 1 ) relaxation rates in [U- 13 C/ 15 N]-ATP labeled RNAs. Moreover, these contributions increase at higher magnetic fields and molecular weights to introduce discrepancies that exceed 50%. This will become increasingly important at GHz fields. Experimental R 1 measurements in the 61 nucleotide human hepatitis B virus encapsidation signal ε RNA labeled with [U- 13 C/ 15 N]-ATP or [2- 13 C]-ATP corroborate these simulations. Thus, in the absence of selectively labeled samples, long-range 13 C- 13 C dipolar contributions must be explicitly taken into account when interpreting adenosine C2 R 1 rates in terms of motional models for large RNAs. 

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2. On the rank of a random binary matrix

   https://doi.org/10.1137/1.9781611975482.58  

   Cooper, Colin; Frieze, Alan; Pegden, Wesley (January 2019, Proceedings of the annual ACM-SIAM Symposium on Discrete Algorithms)

   We study the rank of a random n × m matrix An, m; k with entries from GF(2), and exactly k unit entries in each column, the other entries being zero. The columns are chosen independently and uniformly at random from the set of all (nk) such columns. We obtain an asymptotically correct estimate for the rank as a function of the number of columns m in terms of c, n, k, and where m = cn/k. The matrix An, m; k forms the vertex-edge incidence matrix of a k-uniform random hypergraph H. The rank of An, m; k can be expressed as follows. Let |C2| be the number of vertices of the 2-core of H, and | E (C2)| the number of edges. Let m* be the value of m for which |C2| = |E(C2)|. Then w.h.p. for m < m* the rank of An, m; k is asymptotic to m, and for m ≥ m* the rank is asymptotic to m – |E(C2)| + |C2|. In addition, assign i.i.d. U[0, 1] weights Xi, i ∊ 1, 2, … m to the columns, and define the weight of a set of columns S as X(S) = ∑j∊S Xj. Define a basis as a set of n – 1 (k even) linearly independent columns. We obtain an asymptotically correct estimate for the minimum weight basis. This generalises the well-known result of Frieze [On the value of a random minimum spanning tree problem, Discrete Applied Mathematics, (1985)] that, for k = 2, the expected length of a minimum weight spanning tree tends to ζ(3) ∼ 1.202. 

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3. Climbing the diagonal Clifford hierarchy

   https://doi.org/10.20935/AcadQuant7957  

   Hu, Jingzhen; Liang, Qingzhong; Calderbank, Robert (October 2025, Academia Quantum)

   Magic state distillation and the Shor factoring algorithm make essential use of logical diagonal gates. We introduce a method of synthesizing CSS codes that realize a target logical diagonal gate at some level l in the Clifford hierarchy. The method combines three basic operations: concatenation, removal of Z-stabilizers, and addition of X-stabilizers. It explicitly tracks the logical gate induced by a diagonal physical gate that preserves a CSS code. The first step is concatenation, where the input is a CSS code and a physical diagonal gate at level l inducing a logical diagonal gate at the same level. The output is a new code for which a physical diagonal gate at level l + 1 induces the original logical gate. The next step is judicious removal of Z-stabilizers to increase the level of the induced logical operator. We identify three ways of climbing the logical Clifford hierarchy from level l to level l + 1 , each built on a recursive relation on the Pauli coefficients of the induced logical operators. Removal of Z-stabilizers may reduce distance, and the purpose of the third basic operation, addition of X-stabilizers, is to compensate for such losses. The approach to logical gate synthesis taken in prior work focuses on the code states, resulting in sufficient conditions for a CSS code to be fixed by a transversal Z-rotation. In contrast, we derive necessary and sufficient conditions by analyzing the action of a transversal diagonal gate on the stabilizer group that determines the code. The power of our approach to logical gate synthesis is demonstrated by two proofs of concept: the [ [ 2 l + 1 − 2 , 2 , 2 ] ] triorthogonal code family and the [ [ 2 m , m r , 2 min { r , m − r } ] ] quantum Reed–Muller code family. 

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4. Two-bond ¹³ C– ¹³ C spin-coupling constants in saccharides: dependencies on exocyclic hydroxyl group conformation

   https://doi.org/10.1039/d1cp03320d  

   Lin, Jieye; Meredith, Reagan J.; Oliver, Allen G.; Carmichael, Ian; Serianni, Anthony S. (October 2021, Physical Chemistry Chemical Physics)

   Seven doubly 13 C-labeled isotopomers of methyl β- d -glucopyranoside, methyl β- d -xylopyranoside, methyl β- d -galactopyranoside, methyl β- d -galactopyranosyl-(1→4)-β- d -glucopyranoside and methyl β- d -galactopyranosyl-(1→4)-β- d -xylopyranoside were prepared, crystallized, and studied by single-crystal X-ray crystallography and solid-state 13 C NMR spectroscopy to determine experimentally the dependence of 2 J C1,C3 values in aldopyranosyl rings on the C1–C2–O2–H torsion angle, θ 2 , involving the C2 carbon of the C1–C2–C3 coupling pathway. Using X-ray crystal structures to determine θ 2 in crystalline samples and by selecting compounds that exhibit a relatively wide range of θ 2 values in the crystalline state, 2 J C1,C3 values measured in crystalline samples were plotted against θ 2 and the resulting plot compared to that obtained from density functional theory (DFT) calculations. For θ 2 values ranging from ∼90° to ∼240°, very good agreement was observed between the experimental and theoretical plots, providing strong validation of DFT-calculated spin-coupling dependencies on exocyclic C–O bond conformation involving the central carbon of geminal C–C–C coupling pathways. These findings provide new experimental evidence supporting the use of 2 J CCC values as non-conventional spin-coupling constraints in MA′AT conformational modeling of saccharides in solution, and the use of NMR spin-couplings not involving coupled hydroxyl hydrogens as indirect probes of C–O bond conformation. Solvomorphism was observed in crystalline βGal-(1→4)-βGlcOCH 3 wherein the previously-reported methanol solvate form was found to spontaneously convert to a monohydrate upon air-drying, leading to small but discernible conformational changes in, and a new crystalline form of, this disaccharide. 

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5. Mechanistic insights of cycling stability of ferrocene catholytes in aqueous redox flow batteries

   https://doi.org/10.1039/D1EE03251H  

   Luo, Jian; Hu, Maowei; Wu, Wenda; Yuan, Bing; Liu, T. Leo (March 2022, Energy & Environmental Science)

   Water soluble ferrocene (Fc) derivatives are promising cathode materials for aqueous organic redox flow batteries (AORFBs) towards scalable energy storage. However, their structure–performance relationship and degradation mechanism in aqueous electrolytes remain unclear. Herein, physicochemical and electrochemical properties, battery performance, and degradation mechanisms of three Fc catholytes, (ferrocenylmethyl)trimethylammonium chloride (C1-FcNCl), (2-ferrocenyl-ethyl)trimethylammonium chloride (C2-FcNCl), and (3-ferrocenyl-propyl)trimethylammonium chloride (C3-FcNCl) in pH neutral aqueous electrolytes were systemically investigated. UV-Vis and gas chromatography (GC) studies confirmed the thermal and photolytic C x -Cp − ligand dissociation decomposition pathways of both discharged and charged states of C1-FcNCl and C2-FcNCl catholytes. In contrast, in the case of the C3-FcNCl catholyte, the electron-donating 3-(trimethylammonium)propyl group strengthens the coordination between the C 3 -Cp − ligand and the Fe 3+ or Fe 2+ center and thus mitigates the ligand-dissociation degradation. Consistently, the Fc electrolytes displayed cycling stability in both half-cell and full-cell flow batteries in the order of C1-FcNCl < C2-FcNCl < C3-FcNCl. 

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