On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

High-Voltage Electron Tomography of Spindle Pole Bodies and Early Mitotic Spindles in the Yeast Saccharomyces cerevisiaeV⃞

The spindle pole body (SPB) is the major microtubule-organizing center of budding yeast and is the functional equivalent of the centrosome in higher eukaryotic cells. We used fast-frozen, freeze-substituted cells in conjunction with high-voltage electron tomography to study the fine structure of the SPB and the events of early spindle formation. Individual structures were imaged at 5–10 nm resolution in three dimensions, significantly better than can be achieved by serial section electron microscopy. The SPB is organized in distinct but coupled layers, two of which show ordered two-dimensional packing. The SPB central plaque is anchored in the nuclear envelope with hook-like structures. The minus ends of nuclear microtubules (MTs) are capped and are tethered to the SPB inner plaque, whereas the majority of MT plus ends show a distinct flaring. Unbudded cells containing a single SPB retain 16 MTs, enough to attach to each of the expected 16 chromosomes. Their median length is ∼150 nm. MTs growing from duplicated but not separated SPBs have a median length of ∼130 nm and interdigitate over the bridge that connects the SPBs. As a bipolar spindle is formed, the median MT length increases to ∼300 nm and then decreases to ∼30 nm in late anaphase. Three-dimensional models confirm that there is no conventional metaphase and that anaphase A occurs. These studies complement and extend what is known about the three-dimensional structure of the yeast mitotic spindle and further our understanding of the organization of the SPB in intact cells.

The Three-dimensional Study of Chromosomes and Upstream Binding Factor-immunolabeled Nucleolar Organizer Regions Demonstrates Their Nonrandom Spatial Arrangement during Mitosis

The volumic rearrangement of both chromosomes and immunolabeled upstream binding factor in entire well-preserved mitotic cells was studied by confocal microscopy. By using high-quality three-dimensional visualization and tomography, it was possible to investigate interactively the volumic organization of chromosome sets and to focus on their internal characteristics. More particularly, this study demonstrates the nonrandom positioning of metaphase chromosomes bearing nucleolar organizer regions as revealed by their positive upstream binding factor immunolabeling. During the complex morphogenesis of the progeny nuclei from anaphase to late telophase, the equal partitioning of the nucleolar organizer regions is demonstrated by quantification, and their typical nonrandom central positioning within the chromosome sets is revealed.

Linking genome and proteome by mass spectrometry: Large-scale identification of yeast proteins from two dimensional gels

The function of many of the uncharacterized open reading frames discovered by genomic sequencing can be determined at the level of expressed gene products, the proteome. However, identifying the cognate gene from minute amounts of protein has been one of the major problems in molecular biology. Using yeast as an example, we demonstrate here that mass spectrometric protein identification is a general solution to this problem given a completely sequenced genome. As a first screen, our strategy uses automated laser desorption ionization mass spectrometry of the peptide mixtures produced by in-gel tryptic digestion of a protein. Up to 90% of proteins are identified by searching sequence data bases by lists of peptide masses obtained with high accuracy. The remaining proteins are identified by partially sequencing several peptides of the unseparated mixture by nanoelectrospray tandem mass spectrometry followed by data base searching with multiple peptide sequence tags. In blind trials, the method led to unambiguous identification in all cases. In the largest individual protein identification project to date, a total of 150 gel spots—many of them at subpicomole amounts—were successfully analyzed, greatly enlarging a yeast two-dimensional gel data base. More than 32 proteins were novel and matched to previously uncharacterized open reading frames in the yeast genome. This study establishes that mass spectrometry provides the required throughput, the certainty of identification, and the general applicability to serve as the method of choice to connect genome and proteome.

Three-dimensional reconstruction of the recombinant type 3 ryanodine receptor and localization of its amino terminus

Recombinant type 3 ryanodine receptor (RyR3) has been purified in quantities sufficient for structural characterization by cryoelectron microscopy and three-dimensional (3D) reconstruction. Two cDNAs were prepared and expressed in HEK293 cells, one encoding the wild-type RyR3 and the other encoding RyR3 containing glutathione S-transferase (GST) fused to its amino terminus (GST-RyR3). RyR3 was purified from detergent-solubilized transfected cells by affinity chromatography using 12.6-kDa FK506-binding protein in the form of a GST fusion as the affinity ligand. Purification of GST-RyR3 was achieved by affinity chromatography by using glutathione-Sepharose. Purified recombinant RyR3 and GST-RyR3 proteins exhibited high-affinity [3H]ryanodine binding that was sensitive to activation by Ca2+ and caffeine and to inhibition by Mg2+. 3D reconstructions of both recombinant RyR3 and GST-RyR3 appeared very similar to that of the native RyR3 purified from bovine diaphragm. Comparison of the 3D reconstructions of RyR3 and GST-RyR3 revealed that the GST domains and, hence, the amino termini of the RyR3 subunits are located in the “clamp” structures that form the corners of the square-shaped cytoplasmic region of homotetrameric RyR3. This study describes the 3D reconstruction of a recombinant ryanodine receptor and it demonstrates the potential of this technology for characterizing functional and structural perturbations introduced by site-directed mutagenesis.

A β-hairpin structure in a 13-mer peptide that binds α-bungarotoxin with high affinity and neutralizes its toxicity

Snake-venom α-bungarotoxin is a member of the α-neurotoxin family that binds with very high affinity to the nicotinic acetylcholine receptor (AChR) at the neuromuscular junction. The structure of the complex between α-bungarotoxin and a 13-mer peptide (WRYYESSLEPYPD) that binds the toxin with high affinity, thus inhibiting its interactions with AChR with an IC50 of 2 nM, has been solved by 1H-NMR spectroscopy. The bound peptide folds into a β-hairpin structure created by two antiparallel β-strands, which combine with the already existing triple-stranded β-sheet of the toxin to form a five-stranded intermolecular, antiparallel β-sheet. Peptide residues Y3P, E5P, and L8P have the highest intermolecular contact area, indicating their importance in the binding of α-bungarotoxin; W1P, R2P, and Y4P also contribute significantly to the binding. A large number of characteristic hydrogen bonds and electrostatic and hydrophobic interactions are observed in the complex. The high-affinity peptide exhibits inhibitory potency that is better than any known peptide derived from AChR, and is equal to that of the whole α-subunit of AChR. The high degree of sequence similarity between the peptide and various types of AChRs implies that the binding mode found within the complex might possibly mimic the receptor binding to the toxin. The design of the high-affinity peptide was based on our previous findings: (i) the detection of a lead peptide (MRYYESSLKSYPD) that binds α-bungarotoxin, using a phage-display peptide library, (ii) the information about the three-dimensional structure of α-bungarotoxin/lead-peptide complex, and (iii) the amino acid sequence analysis of different AChRs.

An approach to three-dimensional structures of biomolecules by using single-molecule diffraction images

We describe an approach to the high-resolution three-dimensional structural determination of macromolecules that utilizes ultrashort, intense x-ray pulses to record diffraction data in combination with direct phase retrieval by the oversampling technique. It is shown that a simulated molecular diffraction pattern at 2.5-Å resolution accumulated from multiple copies of single rubisco biomolecules, each generated by a femtosecond-level x-ray free electron laser pulse, can be successfully phased and transformed into an accurate electron density map comparable to that obtained by more conventional methods. The phase problem is solved by using an iterative algorithm with a random phase set as an initial input. The convergence speed of the algorithm is reasonably fast, typically around a few hundred iterations. This approach and phasing method do not require any ab initio information about the molecule, do not require an extended ordered lattice array, and can tolerate high noise and some missing intensity data at the center of the diffraction pattern. With the prospects of the x-ray free electron lasers, this approach could provide a major new opportunity for the high-resolution three-dimensional structure determination of single biomolecules.

Photoactive yellow protein: A structural prototype for the three-dimensional fold of the PAS domain superfamily

PAS domains are found in diverse proteins throughout all three kingdoms of life, where they apparently function in sensing and signal transduction. Although a wealth of useful sequence and functional information has become recently available, these data have not been integrated into a three-dimensional (3D) framework. The very early evolutionary development and diverse functions of PAS domains have made sequence analysis and modeling of this protein superfamily challenging. Limited sequence similarities between the ∼50-residue PAS repeats and one region of the bacterial blue-light photosensor photoactive yellow protein (PYP), for which ground-state and light-activated crystallographic structures have been determined to high resolution, originally were identified in sequence searches using consensus sequence probes from PAS-containing proteins. Here, we found that by changing a few residues particular to PYP function, the modified PYP sequence probe also could select PAS protein sequences. By mapping a typical ∼150-residue PAS domain sequence onto the entire crystallographic structure of PYP, we show that the PAS sequence similarities and differences are consistent with a shared 3D fold (the PAS/PYP module) with obvious potential for a ligand-binding cavity. Thus, PYP appears to prototypically exhibit all the major structural and functional features characteristic of the PAS domain superfamily: the shared PAS/PYP modular domain fold of ∼125–150 residues, a sensor function often linked to ligand or cofactor (chromophore) binding, and signal transduction capability governed by heterodimeric assembly (to the downstream partner of PYP). This 3D PAS/PYP module provides a structural model to guide experimental testing of hypotheses regarding ligand-binding, dimerization, and signal transduction.

Three-dimensional structure of human protein kinase C interacting protein 1, a member of the HIT family of proteins.

The three-dimensional structure of protein kinase C interacting protein 1 (PKCI-1) has been solved to high resolution by x-ray crystallography using single isomorphous replacement with anomalous scattering. The gene encoding human PKCI-1 was cloned from a cDNA library by using a partial sequence obtained from interactions identified in the yeast two-hybrid system between PKCI-1 and the regulatory domain of protein kinase C-beta. The PKCI-1 protein was expressed in Pichia pastoris as a dimer of two 13.7-kDa polypeptides. PKCI-1 is a member of the HIT family of proteins, shown by sequence identity to be conserved in a broad range of organisms including mycoplasma, plants, and humans. Despite the ubiquity of this protein sequence in nature, no distinct function has been shown for the protein product in vitro or in vivo. The PKCI-1 protomer has an alpha+beta meander fold containing a five-stranded antiparallel sheet and two helices. Two protomers come together to form a 10-stranded antiparallel sheet with extensive contacts between a helix and carboxy terminal amino acids of a protomer with the corresponding amino acids in the other protomer. PKCI-1 has been shown to interact specifically with zinc. The three-dimensional structure has been solved in the presence and absence of zinc and in two crystal forms. The structure of human PKCI-1 provides a model of this family of proteins which suggests a stable fold conserved throughout nature.

Intrasarcomere [Ca2+] gradients in ventricular myocytes revealed by high speed digital imaging microscopy.

Cardiac muscle contraction is triggered by a small and brief Ca2+ entry across the t-tubular membranes, which is believed to be locally amplified by release of Ca2+ from the adjacent junctional sarcoplasmic reticulum (SR). As Ca2+ diffusion is thought to be markedly attenuated in cells, it has been predicted that significant intrasarcomeric [Ca2+] gradients should exist during activation. To directly test for this, we measured [Ca2+] distribution in single cardiac myocytes using fluorescent [Ca2+] indicators and high speed, three-dimensional digital imaging microscopy and image deconvolution techniques. Steep cytosolic [Ca2+] gradients from the t-tubule region to the center of the sarcomere developed during the first 15 ms of systole. The steepness of these [Ca2+] gradients varied with treatments that altered Ca2+ release from internal stores. Electron probe microanalysis revealed a loss of Ca2+ from the junctional SR and an accumulation, principally in the A-band during activation. We propose that the prolonged existence of [Ca2+] gradients within the sarcomere reflects the relatively long period of Ca2+ release from the SR, the localization of Ca2+ binding sites and Ca2+ sinks remote from sites of release, and diffusion limitations within the sarcomere. The large [Ca2+] transient near the t-tubular/ junctional SR membranes is postulated to explain numerous features of excitation-contraction coupling in cardiac muscle.

Role of aromatic residues in stabilization of the [Fe4S4] cluster in high-potential iron proteins (HiPIPs): physical characterization and stability studies of Tyr-19 mutants of Chromatium vinosum HiPIP.

The functional role of residue Tyr-19 of Chromatium vinosum HiPIP has been evaluated by site-directed mutagenesis experiments. The stability of the [Fe4S4] cluster prosthetic center is sensitive to side-chain replacements. Polar residues result in significant instability, while nonpolar residues (especially with aromatic side chains) maintain cluster stability. Two-dimensional NMR data of native and mutant HiPIPs are consistent with a model where Tyr-19 serves to preserve the structural rigidity of the polypeptide backbone, thereby maintaining a hydrophobic barrier for exclusion of water from the cluster cavity. Solvent accessibility results in more facile oxidation of the cluster by atmospheric oxygen, with subsequent rapid hydrolysis of the [Fe4S4]3+ core.

Rapid mass spectrometric peptide sequencing and mass matching for characterization of human melanoma proteins isolated by two-dimensional PAGE.

We report a general mass spectrometric approach for the rapid identification and characterization of proteins isolated by preparative two-dimensional polyacrylamide gel electrophoresis. This method possesses the inherent power to detect and structurally characterize covalent modifications. Absolute sensitivities of matrix-assisted laser desorption ionization and high-energy collision-induced dissociation tandem mass spectrometry are exploited to determine the mass and sequence of subpicomole sample quantities of tryptic peptides. These data permit mass matching and sequence homology searching of computerized peptide mass and protein sequence data bases for known proteins and design of oligonucleotide probes for cloning unknown proteins. We have identified 11 proteins in lysates of human A375 melanoma cells, including: alpha-enolase, cytokeratin, stathmin, protein disulfide isomerase, tropomyosin, Cu/Zn superoxide dismutase, nucleoside diphosphate kinase A, galaptin, and triosephosphate isomerase. We have characterized several posttranslational modifications and chemical modifications that may result from electrophoresis or subsequent sample processing steps. Detection of comigrating and covalently modified proteins illustrates the necessity of peptide sequencing and the advantages of tandem mass spectrometry to reliably and unambiguously establish the identity of each protein. This technology paves the way for studies of cell-type dependent gene expression and studies of large suites of cellular proteins with unprecedented speed and rigor to provide information complementary to the ongoing Human Genome Project.

Three-dimensional scroll waves of cAMP could direct cell movement and gene expression in Dictyostelium slugs.

Complex three-dimensional waves of excitation can explain the observed cell movement pattern in Dictyostelium slugs. Here we show that these three-dimensional waves can be produced by a realistic model for the cAMP relay system [Martiel, J. L. & Goldbeter, A. (1987) Biophys J. 52, 807-828]. The conversion of scroll waves in the prestalk zone of the slug into planar wave fronts in the prespore zone can result from a smaller fraction of relaying cells in the prespore zone. Further, we show that the cAMP concentrations to which cells in a slug are exposed over time display a simple pattern, despite the complex spatial geometry of the waves. This cAMP distribution agrees well with observed patterns of cAMP-regulated cell type-specific gene expression. The core of the spiral, which is a region of low cAMP concentration, might direct expression of stalk-specific genes during culmination.

Three-dimensional inverse modelling of magnetic anomaly sources based on a genetic algorithm.

We present a modelling method to estimate the 3-D geometry and location of homogeneously magnetized sources from magnetic anomaly data. As input information, the procedure needs the parameters defining the magnetization vector (intensity, inclination and declination) and the Earth's magnetic field direction. When these two vectors are expected to be different in direction, we propose to estimate the magnetization direction from the magnetic map. Then, using this information, we apply an inversion approach based on a genetic algorithm which finds the geometry of the sources by seeking the optimum solution from an initial population of models in successive iterations through an evolutionary process. The evolution consists of three genetic operators (selection, crossover and mutation), which act on each generation, and a smoothing operator, which looks for the best fit to the observed data and a solution consisting of plausible compact sources. The method allows the use of non-gridded, non-planar and inaccurate anomaly data and non-regular subsurface partitions. In addition, neither constraints for the depth to the top of the sources nor an initial model are necessary, although previous models can be incorporated into the process. We show the results of a test using two complex synthetic anomalies to demonstrate the efficiency of our inversion method. The application to real data is illustrated with aeromagnetic data of the volcanic island of Gran Canaria (Canary Islands).

Migração de solutos em basalto fraturado: quantificação experimental em laboratório e validação matemática

A avaliação do risco a contaminação e a escolha de técnicas de remediação de poluentes em aquíferos fraturados depende da quantificação dos fenômenos envolvidos no transporte de solutos. A geometria da fratura, usualmente caracterizada pela abertura, é o principal parâmetro que indiretamente controla o transporte nos aquíferos fraturados. A simplificação mais comum desse problema é assumir que as fraturas são um par de placas planas e paralelas, isto é, com uma abertura constante. No entanto, por causa do limitado número de trabalhos experimentais, não está esclarecida a adequabilidade do uso de uma abertura constante para simular o transporte conservativo em fraturas do Aquífero Serra Geral (ASG), Brasil. O objetivo deste trabalho é avaliar a influência da abertura de uma fratura natural do Aquífero Serra Geral sob o transporte conservativo de solutos. Uma amostra natural de basalto fraturado foi usada em um experimento hidráulico e de transporte de um traçador conservativo (escala de laboratório). O campo de abertura foi medido usando a técnica avançada, de alta resolução e tridimensional, chamada microtomografia computadorizada de raios-X. A concentração de traçador medida foi utilizada para validar uma solução analítica unidimensional da Equação de Advecção-dispersão (ADE). O desemprenho do ajuste da ADE às curvas de passagem experimentais foi avaliado para quatro diferentes tipos de aberturas constantes. Os resultados mostraram que o escoamento de água e o transporte de contaminantes pode ocorrer através de fraturas micrométricas, ocasionando, eventualmente, a contaminação do ASG. A abertura de balanço de massa é a única que pode ser chamada propriamente de \"abertura equivalente\". O uso de aberturas constantes na ADE não permitiu representar completamente o formato das curvas de passagem porque o campo de velocidade não é uniforme e intrinsicamente bidimensional. Portanto, na simulação do transporte deve-se incorporar a heterogeneidade da abertura da fratura.