Quantum double aspects of surface code models

We revisit the Kitaev model for fault tolerant quantum computing on a square lattice with underlying quantum double $D(G)$ symmetry, where $G$ is a finite group. We provide projection operators for its quasiparticles content as irreducible representations of $D(G)$ and combine this with $D(G)$-bimodule properties of open ribbon excitation spaces $L(s_0,s_1)$ to show how open ribbons can be used to teleport information between their endpoints $s_0,s_1$. We give a self-contained account that builds on earlier work but emphasises applications to quantum computing as surface code theory, including gates on $D(S_3)$. We show how the theory reduces to a simpler theory for toric codes in the case of $D( \Bbb Z_n)\cong \Bbb C\Bbb Z_n^2$, including toric ribbon operators and their braiding. In the other direction, we show how our constructions generalise to $D(H)$ models based on a finite-dimensional Hopf algebra $H$, including site actions of $D(H)$ and partial results on ribbon equivariance even when the Hopf algebra is not semisimple.Comment: 54 pages, many figures both pdf and tk

Inositol 1,3,4,5,6-pentakisphosphate 2-kinase is a distant IPK member with a singular inositide binding site for axial 2-OH recognition

Inositol phosphates (InsPs) are signaling molecules with multiple roles in cells. In particular Graphic (InsP6) is involved in mRNA export and editing or chromatin remodeling among other events. InsP6 accumulates as mixed salts (phytate) in storage tissues of plants and plays a key role in their physiology. Human diets that are exclusively grain-based provide an excess of InsP6 that, through chelation of metal ions, may have a detrimental effect on human health. Ins(1,3,4,5,6)P5 2-kinase (InsP5 2-kinase or Ipk1) catalyses the synthesis of InsP6 from InsP5 and ATP, and is the only enzyme that transfers a phosphate group to the axial 2-OH of the myo-inositide. We present the first structure for an InsP5 2-kinase in complex with both substrates and products. This enzyme presents a singular structural region for inositide binding that encompasses almost half of the protein. The key residues in substrate binding are identified, with Asp368 being responsible for recognition of the axial 2-OH. This study sheds light on the unique molecular mechanism for the synthesis of the precursor of inositol pyrophosphates

A four-helix bundle stores copper for methane oxidation

Methane-oxidising bacteria (methanotrophs) require large quantities of copper for the membrane-bound (particulate) methane monooxygenase (pMMO). Certain methanotrophs are also able to switch to using the iron-containing soluble MMO (sMMO) to catalyse methane oxidation, with this switchover regulated by copper. MMOs are Nature’s primary biological mechanism for suppressing atmospheric levels of methane, a potent greenhouse gas. Furthermore, methanotrophs and MMOs have enormous potential in bioremediation and for biotransformations producing bulk and fine chemicals, and in bioenergy, particularly considering increased methane availability from renewable sources and hydraulic fracturing of shale rock. We have discovered and characterised a novel copper storage protein (Csp1) from the methanotroph Methylosinus trichosporium OB3b that is exported from the cytosol, and stores copper for pMMO. Csp1 is a tetramer of 4-helix bundles with each monomer binding up to 13 Cu(I) ions in a previously unseen manner via mainly Cys residues that point into the core of the bundle. Csp1 is the first example of a protein that stores a metal within an established protein-folding motif. This work provides a detailed insight into how methanotrophs accumulate copper for the oxidation of methane. Understanding this process is essential if the wide-ranging biotechnological applications of methanotrophs are to be realised. Cytosolic homologues of Csp1 are present in diverse bacteria thus challenging the dogma that such organisms do not use copper in this location

Structure of Tagatose-1,6-bisphosphate Aldolase. Insight into chiral discrimination, mechanism, and specificity of class II aldolases

Tagatose-1,6-bisphosphate aldolase (TBPA) is a tetrameric class II aldolase that catalyzes the reversible condensation of dihydroxyacetone phosphate with glyceraldehyde 3-phosphate to produce tagatose 1,6-bisphosphate. The high resolution (1.45 Å) crystal structure of the Escherichia coli enzyme, encoded by the agaY gene, complexed with phosphoglycolohydroxamate (PGH) has been determined. Two subunits comprise the asymmetric unit, and a crystallographic 2-fold axis generates the functional tetramer. A complex network of hydrogen bonds position side chains in the active site that is occupied by two cations. An unusual Na(+) binding site is created using a interaction with Tyr(183) in addition to five oxygen ligands. The catalytic Zn(2+) is five-coordinate using three histidine nitrogens and two PGH oxygens. Comparisons of TBPA with the related fructose-1,6-bisphosphate aldolase (FBPA) identifies common features with implications for the mechanism. Because the major product of the condensation catalyzed by the enzymes differs in the chirality at a single position, models of FBPA and TBPA with their cognate bisphosphate products provide insight into chiral discrimination by these aldolases. The TBPA active site is more open on one side than FBPA, and this contributes to a less specific enzyme. The availability of more space and a wider range of aldehyde partners used by TBPA together with the highly specific nature of FBPA suggest that TBPA might be a preferred enzyme to modify for use in biotransformation chemistry

Reconciled climate response estimates from climate models and the energy budget of Earth

Climate risks increase with mean global temperature, so knowledge about the amount of future global warming should better inform risk assessments for policymakers. Expected near-term warming is encapsulated by the transient climate response (TCR), formally defined as the warming following 70 years of 1% per year increases in atmospheric CO2 concentration, by which point atmospheric CO2 has doubled. Studies based on Earth’s historical energy budget have typically estimated lower values of TCR than climate models, suggesting that some models could overestimate future warming. However, energy-budget estimates rely on historical temperature records that are geographically incomplete and blend air temperatures over land and sea ice with water temperatures over open oceans. We show that there is no evidence that climate models overestimate TCR when their output is processed in the same way as the HadCRUT4 observation-based temperature record3, 4. Models suggest that air-temperature warming is 24% greater than observed by HadCRUT4 over 1861–2009 because slower-warming regions are preferentially sampled and water warms less than air5. Correcting for these biases and accounting for wider uncertainties in radiative forcing based on recent evidence, we infer an observation-based best estimate for TCR of 1.66 °C, with a 5–95% range of 1.0–3.3 °C, consistent with the climate models considered in the IPCC 5th Assessment Report

Automatic rebuilding and optimization of crystallographic structures in the Protein Data Bank

Motivation: Macromolecular crystal structures in the Protein Data Bank (PDB) are a key source of structural insight into biological processes. These structures, some >30 years old, were constructed with methods of their era. With PDB_REDO, we aim to automatically optimize these structures to better fit their corresponding experimental data, passing the benefits of new methods in crystallography on to a wide base of non-crystallographer structure users

Surface warming hiatus caused by increased heat uptake across multiple ocean basins

The first decade of the twenty-first century was characterised by a hiatus in global surface warming. Using ocean model hindcasts and reanalyses we show that heat uptake between the 1990s and 2000s increased by 0.7 ± 0.3Wm−2. Approximately 30% of the increase is associated with colder sea surface temperatures in the eastern Pacific. Other basins contribute via reduced heat loss to the atmosphere, in particular the Southern and subtropical Indian Oceans (30%), and the subpolar North Atlantic (40%). A different mechanism is important at longer timescales (1960s-present) over which the Southern Annular Mode trended upwards. In this period, increased ocean heat uptake has largely arisen from reduced heat loss associated with reduced winds over the Agulhas Return Current and southward displacement of Southern Ocean westerlies

Erratum:The 'pause' in global warming in historical context: II. Comparing models to observations (Environmental Research Letters (2018)13 (123007) DOI: 10.1088/1748-9326/aaf372)

We review the evidence for a putative early 21st-century divergence between global mean surface temperature (GMST) and Coupled Model Intercomparison Project Phase 5 (CMIP5) projections. We provide a systematic comparison between temperatures and projections using historical versions of GMST products and historical versions of model projections that existed at the times when claims about a divergence were made. The comparisons are conducted with a variety of statistical techniques that correct for problems in previous work, including using continuous trends and a Monte Carlo approach to simulate internal variability. The results show that there is no robust statistical evidence for a divergence between models and observations. The impression of a divergence early in the 21st century was caused by various biases in model interpretation and in the observations, and was unsupported by robust statistics

A two-domain elevator mechanism for sodium/proton antiport

Sodium/proton (Na+/H+) antiporters, located at the plasma membrane in every cell, are vital for cell homeostasis1. In humans, their dysfunction has been linked to diseases, such as hypertension, heart failure and epilepsy, and they are well-established drug targets2. The best understood model system for Na+/H+ antiport is NhaA from Escherichia coli1, 3, for which both electron microscopy and crystal structures are available4, 5, 6. NhaA is made up of two distinct domains: a core domain and a dimerization domain. In the NhaA crystal structure a cavity is located between the two domains, providing access to the ion-binding site from the inward-facing surface of the protein1, 4. Like many Na+/H+ antiporters, the activity of NhaA is regulated by pH, only becoming active above pH 6.5, at which point a conformational change is thought to occur7. The only reported NhaA crystal structure so far is of the low pH inactivated form4. Here we describe the active-state structure of a Na+/H+ antiporter, NapA from Thermus thermophilus, at 3 Å resolution, solved from crystals grown at pH 7.8. In the NapA structure, the core and dimerization domains are in different positions to those seen in NhaA, and a negatively charged cavity has now opened to the outside. The extracellular cavity allows access to a strictly conserved aspartate residue thought to coordinate ion binding1, 8, 9 directly, a role supported here by molecular dynamics simulations. To alternate access to this ion-binding site, however, requires a surprisingly large rotation of the core domain, some 20° against the dimerization interface. We conclude that despite their fast transport rates of up to 1,500 ions per second3, Na+/H+ antiporters operate by a two-domain rocking bundle model, revealing themes relevant to secondary-active transporters in general

The 'pause' in global warming in historical context : (II). Comparing models to observations

We review the evidence for a putative early 21st-century divergence between global mean surface temperature (GMST) and Coupled Model Intercomparison Project Phase 5 (CMIP5) projections. We provide a systematic comparison between temperatures and projections using historical versions of GMST products and historical versions of model projections that existed at the times when claims about a divergence were made. The comparisons are conducted with a variety of statistical techniques that correct for problems in previous work, including using continuous trends and a Monte Carlo approach to simulate internal variability. The results show that there is no robust statistical evidence for a divergence between models and observations. The impression of a divergence early in the 21st century was caused by various biases in model interpretation and in the observations, and was unsupported by robust statistics