Generalised Dirichelt-to-Neumann map in time dependent domains

We study the heat, linear Schrodinger and linear KdV equations in the domain l(t) < x < ∞, 0 < t < T, with prescribed initial and boundary conditions and with l(t) a given differentiable function. For the first two equations, we show that the unknown Neumann or Dirichlet boundary value can be computed as the solution of a linear Volterra integral equation with an explicit weakly singular kernel. This integral equation can be derived from the formal Fourier integral representation of the solution. For the linear KdV equation we show that the two unknown boundary values can be computed as the solution of a system of linear Volterra integral equations with explicit weakly singular kernels. The derivation in this case makes crucial use of analyticity and certain invariance properties in the complex spectral plane. The above Volterra equations are shown to admit a unique solution.

A method for merging flow-dependent forecast error statistics from an ensemble with static statistics for use in high resolution variational data assimilation

The background error covariance matrix, B, is often used in variational data assimilation for numerical weather prediction as a static and hence poor approximation to the fully dynamic forecast error covariance matrix, Pf. In this paper the concept of an Ensemble Reduced Rank Kalman Filter (EnRRKF) is outlined. In the EnRRKF the forecast error statistics in a subspace defined by an ensemble of states forecast by the dynamic model are found. These statistics are merged in a formal way with the static statistics, which apply in the remainder of the space. The combined statistics may then be used in a variational data assimilation setting. It is hoped that the nonlinear error growth of small-scale weather systems will be accurately captured by the EnRRKF, to produce accurate analyses and ultimately improved forecasts of extreme events.

Regime dependent changes in global precipitation

Assessment of changes in precipitation (P) as a function of percentiles of surface temperature (T) and 500 hPa vertical velocity (ω) are presented, considering present-day simulations and observational estimates from the Global Precipitation Climatology Project (GPCP) combined with the European Centre for Medium-range Weather Forecasts Interim reanalysis (ERA Interim). There is a tendency for models to overestimate P in the warm, subsiding regimes compared to GPCP, in some cases by more than 100%, while many models underestimate P in the moderate temperature regimes. Considering climate change projections between 1980–1999 and 2080–2099, responses in P are characterised by dP/dT ≥ 4%/K over the coldest 10–20% of land points and over warm, ascending ocean points while P declines over the warmest, descending regimes (dP/dT ∼ − 4%/K for model ensemble means). The reduced Walker circulation limits this contrasting dP/dT response in the tropical wet and dry regimes only marginally. Around 70% of the global surface area exhibits a consistent sign for dP/dT in at least 6 out of a 7-member model ensemble when considering P composites in terms of dynamic regime.

Making DNA without iron: induction of a manganese-dependent ribonucleotide reductase in response to iron starvation

Ribonucleotide reductases supply cells with their deoxyribonucleotides. Three enzyme types are known, classes I, II and III. Class II enzymes are anaerobic whereas class I enzymes are aerobic, and so class I and II enzymes are often produced by the same organism under opposing oxygen regimes. Escherichia coli contains two types of class I enzyme (Ia and Ib) with the Fe-dependent Ia enzyme (NrdAB) performing the major role aerobically, leaving the purpose of the Ib enzyme (NrdEF) unclear. Several papers have recently focused on the class Ib enzymes showing that they are Mn (rather than Fe) dependent and suggesting that the E. coli NrdEF may function under redox-stress conditions. A paper published in this issue of Molecular Microbiology from James Imlay's group confirms that this unexplained NrdEF Ib enzyme is Mn-dependent, but shows that it does not substitute for NrdAB during redox stress. Instead, a role during iron restriction is demonstrated. Thus, the purpose of NrdEF (and possibly other class Ib enzymes) is to enhance growth under aerobic, low-iron conditions, and to functionally replace the Fe-dependent NrdAB when iron is unavailable. This finding reveals a new mechanism by which bacteria adjust to life under iron deprivation.

Evidence both L-type and non-L-type voltage-dependent calcium channels contribute to cerebral artery vasospasm following loss of NO in the rat

We recently found block of NO synthase in rat middle cerebral artery caused spasm, associated with depolarizing oscillations in membrane potential (Em) similar in form but faster in frequency (circa 1 Hz) to vasomotion. T-type voltage-gated Ca2+ channels contribute to cerebral myogenic tone and vasomotion, so we investigated the significance of T-type and other ion channels for membrane potential oscillations underlying arterial spasm. Smooth muscle cell membrane potential (Em) and tension were measured simultaneously in rat middle cerebral artery. NO synthase blockade caused temporally coupled depolarizing oscillations in cerebrovascular Em with associated vasoconstriction. Both events were accentuated by block of smooth muscle BKCa. Block of T-type channels or inhibition of Na+/K+-ATPase abolished the oscillations in Em and reduced vasoconstriction. Oscillations in Em were either attenuated or accentuated by reducing [Ca2+]o or block of KV, respectively. TRAM-34 attenuated oscillations in both Em and tone, apparently independent of effects against KCa3.1. Thus, rapid depolarizing oscillations in Em and tone observed after endothelial function has been disrupted reflect input from T-type calcium channels in addition to L-type channels, while other depolarizing currents appear to be unimportant. These data suggest that combined block of T and L-type channels may represent an effective approach to reverse cerebral vasospasm.

Coverage-dependent molecular tilt of carbon monoxide chemisorbed on Pt{110}: A combined LEED and DFT structural analysis

The adsorption of carbon monoxide on the Pt{110} surface at coverages of 0.5 ML and 1.0 ML was investigated using quantitative low-energy electron diffraction (LEED IV) and density-functional theory (DFT). At 0.5 ML CO lifts the reconstruction of the clean surface but does not form an ordered overlayer. At the saturation coverage, 1.0 ML, a well-ordered p(2×1) superstructure with glide line symmetry is formed. It was confirmed that the CO molecules adsorb on top of the Pt atoms in the top-most substrate layer with the molecular axes tilted by ±22° with respect to the surface normal in alternating directions away from the close packed rows of Pt atoms. This is accompanied by significant lateral shifts of 0.55 Å away from the atop sites in the same direction as the tilt. The top-most substrate layer relaxes inwards by −4% with respect to the bulk-terminated atom positions, while the consecutive layers only show minor relaxations. Despite the lack of long-range order in the 0.5 ML CO layer it was possible to determine key structural parameters by LEED IV using only the intensities of the integer-order spots. At this coverage CO also adsorbs on atop sites with the molecular axis closer to the surface normal (b10°). The average substrate relaxations in each layer are similar for both coverages and consistent with DFT calculations performed for a variety of ordered structures with coverages of 1.0 ML and 0.5 ML.

Expression-system-dependent modulation of HIV-1 envelope glycoprotein antigenicity and immunogenicity.

Recombinant expression systems differ in the type of glycosylation they impart on expressed antigens such as the human immunodeficiency virus type 1 (HIV-1) envelope glycoproteins, potentially affecting their biological properties. We performed head-to-head antigenic, immunogenic and molecular profiling of two distantly related Env surface (gp120) antigens produced in different systems: (a) mammalian (293 FreeStyle cells; 293F) cells in the presence of kifunensine, which impart only high-mannose glycans; (b) insect cells (Spodoptera frugiperda, Sf9), which confer mainly paucimannosidic glycans; (c) Sf9 cells recombinant for mammalian glycosylation enzymes (Sf9 Mimic), which impart high-mannose, hybrid and complex glycans without sialic acid; and (d) 293F cells, which impart high-mannose, hybrid and complex glycans with sialic acid. Molecular models revealed a significant difference in gp120 glycan coverage between the Sf9-derived and wild-type mammalian-cell-derived material that is predicted to affect ligand binding sites proximal to glycans. Modeling of solvent-exposed surface electrostatic potentials showed that sialic acid imparts a significant negative surface charge that may influence gp120 antigenicity and immunogenicity. Gp120 expressed in systems that do not incorporate sialic acid displayed increased ligand binding to the CD4 binding and CD4-induced sites compared to those expressed in the system that do, and imparted other more subtle differences in antigenicity in a gp120 subtype-specific manner. Non-sialic-acid-containing gp120 was significantly more immunogenic than the sialylated version when administered in two different adjuvants, and induced higher titers of antibodies competing for CD4 binding site ligand-gp120 interaction. These findings suggest that non-sialic-acid-imparting systems yield gp120 immunogens with modified antigenic and immunogenic properties, considerations that should be considered when selecting expression systems for glycosylated antigens to be used for structure-function studies and for vaccine use.

Temperature dependent SANS from ferritin and apoferritin

SANS from deuterated ferritin and apoferritin solutions over the temperature range 5 to 300 K is presented. Above the freezing point the SANS is well described by Percus-Yevick hard sphere packing. On freezing, highly correlated, partially crystallised, clusters of the proteins form and grow with decreasing temperature. The resulting scattering, characterised by a squared Lorentzian structure factor, indicates a spatial extent of 1000 8, for the protein clusters.

Social networks: evolving graphs with memory dependent edges

The plethora, and mass take up, of digital communication tech- nologies has resulted in a wealth of interest in social network data collection and analysis in recent years. Within many such networks the interactions are transient: thus those networks evolve over time. In this paper we introduce a class of models for such networks using evolving graphs with memory dependent edges, which may appear and disappear according to their recent history. We consider time discrete and time continuous variants of the model. We consider the long term asymptotic behaviour as a function of parameters controlling the memory dependence. In particular we show that such networks may continue evolving forever, or else may quench and become static (containing immortal and/or extinct edges). This depends on the ex- istence or otherwise of certain infinite products and series involving age dependent model parameters. To test these ideas we show how model parameters may be calibrated based on limited samples of time dependent data, and we apply these concepts to three real networks: summary data on mobile phone use from a developing region; online social-business network data from China; and disaggregated mobile phone communications data from a reality mining experiment in the US. In each case we show that there is evidence for memory dependent dynamics, such as that embodied within the class of models proposed here.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Constrained principal component analysis reveals functionally connected load-dependent networks involved in multiple stages of working memory

Constrained principal component analysis (CPCA) with a finite impulse response (FIR) basis set was used to reveal functionally connected networks and their temporal progression over a multistage verbal working memory trial in which memory load was varied. Four components were extracted, and all showed statistically significant sensitivity to the memory load manipulation. Additionally, two of the four components sustained this peak activity, both for approximately 3 s (Components 1 and 4). The functional networks that showed sustained activity were characterized by increased activations in the dorsal anterior cingulate cortex, right dorsolateral prefrontal cortex, and left supramarginal gyrus, and decreased activations in the primary auditory cortex and "default network" regions. The functional networks that did not show sustained activity were instead dominated by increased activation in occipital cortex, dorsal anterior cingulate cortex, sensori-motor cortical regions, and superior parietal cortex. The response shapes suggest that although all four components appear to be invoked at encoding, the two sustained-peak components are likely to be additionally involved in the delay period. Our investigation provides a unique view of the contributions made by a network of brain regions over the course of a multiple-stage working memory trial.