Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

A computational model of the anterior intraparietal area

The monkey anterior intraparietal area (AIP) encodes visual information about three-dimensional object shape that is used to shape the hand for grasping. In robotics a similar role has been played by modules that fit point cloud data to the superquadric family of shapes and its various extensions. We developed a model of shape tuning in AIP based on cosine tuning to superquadric parameters. However, the model did not fit the data well, and we also found that it was difficult to accurately reproduce these parameters using neural networks with the appropriate inputs (modelled on the caudal intraparietal area, CIP). The latter difficulty was related to the fact that there are large discontinuities in the superquadric parameters between very similar shapes. To address these limitations we adopted an alternative shape parameterization based on an Isomap nonlinear dimension reduction. The Isomap was built using gradients and curvatures of object surface depth. This alternative parameterization was low-dimensional (like superquadrics), but data-driven (similar to an alternative clustering approach that is also sometimes used in robotics) and lacked large discontinuities. Isomaps with 16 or more dimensions reproduced the AIP data fairly well. Moreover, we found that the Isomap parameters could be approximated from CIP-like input much more accurately than the superquadric parameters. We conclude that Isomaps, or perhaps alternative dimension reductions of CIP signals, provide a promising model of AIP tuning. We have now started to integrate our model with a robot hand, to explore the efficacy of Isomap shape reductions in grasp planning. Future work will consider dynamics of spike responses and integration with related visual and motor area models.

Global instability analysis and control of three-dimensional long open cavity flow

The three-dimensional wall-bounded open cavity may be considered as a simplified geometry found in industrial applications such as leading gear or slotted flats on the airplane. Understanding the three-dimensional complex flow structure that surrounds this particular geometry is therefore of major industrial interest. At the light of the remarkable former investigations in this kind of flows, enough evidences suggest that the lateral walls have a great influence on the flow features and hence on their instability modes. Nevertheless, even though there is a large body of literature on cavity flows, most of them are based on the assumption that the flow is two-dimensional and spanwise-periodic. The flow over realistic open cavity should be considered. This thesis presents an investigation of three-dimensional wall-bounded open cavity with geometric ratio 6:2:1. To this aim, three-dimensional Direct Numerical Simulation (DNS) and global linear instability have been performed. Linear instability analysis reveals that the onset of the first instability in this open cavity is around Recr 1080. The three-dimensional shear layer mode with a complex structure is shown to be the most unstable mode. I t is noteworthy that the flow pattern of this high-frequency shear layer mode is similar to the observed unstable oscillations in supercritical unstable case. DNS of the cavity flow carried out at different Reynolds number from steady state until a nonlinear saturated state is obtained. The comparison of time histories of kinetic energy presents a clearly dominant energetic mode which shifts between low-frequency and highfrequency oscillation. A complete flow patterns from subcritical cases to supercritical case has been put in evidence. The flow structure at the supercritical case Re=1100 resembles typical wake-shedding instability oscillations with a lateral motion existed in the subcritical cases. Also, This flow pattern is similar to the observations in experiments. In order to validate the linear instability analysis results, the topology of the composite flow fields reconstructed by linear superposition of a three-dimensional base flow and its leading three-dimensional global eigenmodes has been studied. The instantaneous wall streamlines of those composited flows display distinguish influence region of each eigenmode. Attention has been focused on the leading high-frequency shear layer mode; the composite flow fields have been fully recognized with respect to the downstream wave shedding. The three-dimensional shear layer mode is shown to give rise to a typical wake-shedding instability with a lateral motions occurring downstream which is in good agreement with the experiment results. Moreover, the spanwise-periodic, open cavity with the same length to depth ratio has been also studied. The most unstable linear mode is different from the real three-dimensional cavity flow, because of the existence of the side walls. Structure sensitivity of the unstable global mode is analyzed in the flow control context. The adjoint-based sensitivity analysis has been employed to localized the receptivity region, where the flow is more sensible to momentum forcing and mass injection. Because of the non-normality of the linearized Navier-Stokes equations, the direct and adjoint field has a large spatial separation. The strongest sensitivity region is locate in the upstream lip of the three-dimensional cavity. This numerical finding is in agreement with experimental observations. Finally, a prototype of passive flow control strategy is applied.

Congruent Docking of Dimeric Kinesin and ncd into Three-dimensional Electron Cryomicroscopy Maps of Microtubule–Motor ADP Complexes

We present a new map showing dimeric kinesin bound to microtubules in the presence of ADP that was obtained by electron cryomicroscopy and image reconstruction. The directly bound monomer (first head) shows a different conformation from one in the more tightly bound empty state. This change in the first head is amplified as a movement of the second (tethered) head, which tilts upward. The atomic coordinates of kinesin·ADP dock into our map so that the tethered head associates with the bound head as in the kinesin dimer structure seen by x-ray crystallography. The new docking orientation avoids problems associated with previous predictions; it puts residues implicated by proteolysis-protection and mutagenesis studies near the microtubule but does not lead to steric interference between the coiled-coil tail and the microtubule surface. The observed conformational changes in the tightly bound states would probably bring some important residues closer to tubulin. As expected from the homology with kinesin, the atomic coordinates of nonclaret disjunctional protein (ncd)·ADP dock in the same orientation into the attached head in a map of microtubules decorated with dimeric ncd·ADP. Our results support the idea that the observed direct interaction between the two heads is important at some stages of the mechanism by which kinesin moves processively along microtubules.

Functional Hierarchy of Simultaneously Expressed Adhesion Receptors: Integrin α2β1 but Not CD44 Mediates MV3 Melanoma Cell Migration and Matrix Reorganization within Three-dimensional Hyaluronan-containing Collagen MatricesV⃞

Haptokinetic cell migration across surfaces is mediated by adhesion receptors including β1 integrins and CD44 providing adhesion to extracellular matrix (ECM) ligands such as collagen and hyaluronan (HA), respectively. Little is known, however, about how such different receptor systems synergize for cell migration through three-dimensionally (3-D) interconnected ECM ligands. In highly motile human MV3 melanoma cells, both β1 integrins and CD44 are abundantly expressed, support migration across collagen and HA, respectively, and are deposited upon migration, whereas only β1 integrins but not CD44 redistribute to focal adhesions. In 3-D collagen lattices in the presence or absence of HA and cross-linking chondroitin sulfate, MV3 cell migration and associated functions such as polarization and matrix reorganization were blocked by anti-β1 and anti-α2 integrin mAbs, whereas mAbs blocking CD44, α3, α5, α6, or αv integrins showed no effect. With use of highly sensitive time-lapse videomicroscopy and computer-assisted cell tracking techniques, promigratory functions of CD44 were excluded. 1) Addition of HA did not increase the migratory cell population or its migration velocity, 2) blocking of the HA-binding Hermes-1 epitope did not affect migration, and 3) impaired migration after blocking or activation of β1 integrins was not restored via CD44. Because α2β1-mediated migration was neither synergized nor replaced by CD44–HA interactions, we conclude that the biophysical properties of 3-D multicomponent ECM impose more restricted molecular functions of adhesion receptors, thereby differing from haptokinetic migration across surfaces.

Nuclear Pore Complex Number and Distribution throughout the Saccharomyces cerevisiae Cell Cycle by Three-Dimensional Reconstruction from Electron Micrographs of Nuclear Envelopes

The number of nuclear pore complexes (NPCs) in individual nuclei of the yeast Saccharomyces cerevisiae was determined by computer-aided reconstruction of entire nuclei from electron micrographs of serially sectioned cells. Nuclei of 32 haploid cells at various points in the cell cycle were modeled and found to contain between 65 and 182 NPCs. Morphological markers, such as cell shape and nuclear shape, were used to determine the cell cycle stage of the cell being examined. NPC number was correlated with cell cycle stage to reveal that the number of NPCs increases steadily, beginning in G1-phase, suggesting that NPC assembly occurs continuously throughout the cell cycle. However, the accumulation of nuclear envelope observed during the cell cycle, indicated by nuclear surface area, is not continuous at the same rate, such that the density of NPCs per unit area of nuclear envelope peaks in apparent S-phase cells. Analysis of the nuclear envelope reconstructions also revealed no preferred NPC-to-NPC distance. However, NPCs were found in large clusters over regions of the nuclear envelope. Interestingly, clusters of NPCs were most pronounced in early mitotic nuclei and were found to be associated with the spindle pole bodies, but the functional significance of this association is unknown.

The photoisomerization of retinal in bacteriorhodopsin: Experimental evidence for a three-state model

The primary events in the all-trans to 13-cis photoisomerization of retinal in bacteriorhodopsin have been investigated with femtosecond time-resolved absorbance spectroscopy. Spectra measured over a broad range extending from 7000 to 22,400 cm−1 reveal features whose dynamics are inconsistent with a model proposed earlier to account for the highly efficient photoisomerization process. Emerging from this work is a new three-state model. Photoexcitation of retinal with visible light accesses a shallow well on the excited state potential energy surface. This well is bounded by a small barrier, arising from an avoided crossing that separates the Franck–Condon region from the nearby reactive region of the photoisomerization coordinate. At ambient temperatures, the reactive region is accessed with a time constant of ≈500 fs, whereupon the retinal rapidly twists and encounters a second avoided crossing region. The protein mediates the passage into the second avoided crossing region and thereby exerts control over the quantum yield for forming 13-cis retinal. The driving force for photoisomerization resides in the retinal, not in the surrounding protein. This view contrasts with an earlier model where photoexcitation was thought to access directly a reactive region of the excited-state potential and thereby drive the retinal to a twisted conformation within 100–200 fs.

Design of three-dimensional domain-swapped dimers and fibrous oligomers

Three-dimensional (3D) domain-swapped proteins are intermolecularly folded analogs of monomeric proteins; both are stabilized by the identical interactions, but the individual domains interact intramolecularly in monomeric proteins, whereas they form intermolecular interactions in 3D domain-swapped structures. The structures and conditions of formation of several domain-swapped dimers and trimers are known, but the formation of higher order 3D domain-swapped oligomers has been less thoroughly studied. Here we contrast the structural consequences of domain swapping from two designed three-helix bundles: one with an up-down-up topology, and the other with an up-down-down topology. The up-down-up topology gives rise to a domain-swapped dimer whose structure has been determined to 1.5 Å resolution by x-ray crystallography. In contrast, the domain-swapped protein with an up-down-down topology forms fibrils as shown by electron microscopy and dynamic light scattering. This demonstrates that design principles can predict the oligomeric state of 3D domain-swapped molecules, which should aid in the design of domain-swapped proteins and biomaterials.

Three-dimensional cryoelectron microscopy of dimeric kinesin and ncd motor domains on microtubules.

Kinesin and ncd motor proteins are homologous in sequence yet move in opposite directions along microtubules. We have previously shown that monomeric kinesin and ncd bind in the same orientation on equivalent sites relative to the ends of tubulin sheets of known polarity. We now report cryoelectron microscope images of 16-protofilament microtubules decorated with both single- and double-headed kinesin and double-headed ncd. Three-dimensional density maps and difference maps show that, in adenosine 5'-[beta,gamma-imido]triphosphate, both dimeric motors bind tightly to microtubules via one head, leaving the other free, though apparently in a fixed position. The attached heads of dimers bind to tubulin in the same way as single kinesin heads. The second heads are connected to the tops of the first but, whereas the second kinesin head is closely associated with the first, pairs of ncd heads are splayed apart. There is also a distinct difference in orientation: the second kinesin head is tilted toward the microtubule plus end, while the second head of ncd points toward the minus end.

Characterizations of diverse residue clusters in protein three-dimensional structures.

We present new methods for identifying and analyzing statistically significant residue clusters that occur in three-dimensional (3D) protein structures. Residue clusters of different kinds occur in many contexts. They often feature the active site (e.g., in substrate binding), the interface between polypeptide units of protein complexes, regions of protein-protein and protein-nucleic acid interactions, or regions of metal ion coordination. The methods are illustrated with 3D clusters centering on four themes. (i) Acidic or histidine-acidic clusters associated with metal ions. (ii) Cysteine clusters including coordination of metals such as zinc or iron-sulfur structures, cysteine knots prominent in growth factors, multiple sets of buried disulfide pairings that putatively nucleate the hydrophobic core, or cysteine clusters of mostly exposed disulfide bridges. (iii) Iron-sulfur proteins and charge clusters. (iv) 3D environments of multiple histidine residues. Study of diverse 3D residue clusters offers a new perspective on protein structure and function. The algorithms can aid in rapid identification of distinctive sites, suggest correlations among protein structures, and serve as a tool in the analysis of new structures.

Clusters of charged residues in protein three-dimensional structures.

Statistically significant charge clusters (basic, acidic, or of mixed charge) in tertiary protein structures are identified by new methods from a large representative collection of protein structures. About 10% of protein structures show at least one charge cluster, mostly of mixed type involving about equally anionic and cationic residues. Positive charge clusters are very rare. Negative (or histidine-acidic) charge clusters often coordinate calcium, or magnesium or zinc ions [e.g., thermolysin (PDB code: 3tln), mannose-binding protein (2msb), aminopeptidase (1amp)]. Mixed-charge clusters are prominent at interchain contacts where they stabilize quaternary protein formation [e.g., glutathione S-transferase (2gst), catalase (8act), and fructose-1,6-bisphosphate aldolase (1fba)]. They are also involved in protein-protein interaction and in substrate binding. For example, the mixed-charge cluster of aspartate carbamoyl-transferase (8atc) envelops the aspartate carbonyl substrate in a flexible manner (alternating tense and relaxed states) where charge associations can vary from weak to strong. Other proteins with charge clusters include the P450 cytochrome family (BM-3, Terp, Cam), several flavocytochromes, neuraminidase, hemagglutinin, the photosynthetic reaction center, and annexin. In each case in Table 2 we discuss the possible role of the charge clusters with respect to protein structure and function.

Suppression of apoptosis by basement membrane requires three-dimensional tissue organization and withdrawal from the cell cycle.

The basement membrane (BM) extracellular matrix induces differentiation and suppresses apoptosis in mammary epithelial cells, whereas cells lacking BM lose their differentiated phenotype and undergo apoptosis. Addition of purified BM components, which are known to induce beta-casein expression, did not prevent apoptosis, indicating that a more complex BM was necessary. A comparison of culture conditions where apoptosis would or would not occur allowed us to relate inhibition of apoptosis to a complete withdrawal from the cell cycle, which was observed only when cells acquired a three-dimensional alveolar structure in response to BM. In the absence of this morphology, both the GI cyclin kinase inhibitor p21/WAF-1 and positive proliferative signals including c-myc and cyclin DI were expressed and the retinoblastoma protein (Rb) continued to be hyperphosphorylated. When we overexpressed either c-myc in quiescent cells or p21 when cells were still cycling, apoptosis was induced. In the absence of three-dimensional alveolar structures, mammary epithelial cells secrete a number of factors including transforming growth factor alpha and tenascin, which when added exogenously to quiescent cells induced expression of c-myc and interleukin-beta1-converting enzyme (ICE) mRNA and led to apoptosis. These experiments demonstrate that a correct tissue architecture is crucial for long-range homeostasis, suppression of apoptosis, and maintenance of differentiated phenotype.

Three-dimensional functional magnetic resonance imaging of human brain on a clinical 1.5-T scanner.

Functional magnetic resonance imaging (fMRI) is a tool for mapping brain function that utilizes neuronal activity-induced changes in blood oxygenation. An efficient three-dimensional fMRI method is presented for imaging brain activity on conventional, widely available, 1.5-T scanners, without additional hardware. This approach uses large magnetic susceptibility weighting based on the echo-shifting principle combined with multiple gradient echoes per excitation. Motor stimulation, induced by self-paced finger tapping, reliably produced significant signal increase in the hand region of the contralateral primary motor cortex in every subject tested.

Definition of a metal-dependent/Li(+)-inhibited phosphomonoesterase protein family based upon a conserved three-dimensional core structure.

Inositol polyphosphate 1-phosphatase, inositol monophosphate phosphatase, and fructose 1,6-bisphosphatase share a sequence motif, Asp-Pro-(Ile or Leu)-Asp-(Gly or Ser)-(Thr or Ser), that has been shown by crystallographic and mutagenesis studies to bind metal ions and participate in catalysis. We compared the six alpha-carbon coordinates of this motif from the crystal structures of these three phosphatases and found that they are superimposable with rms deviations ranging from 0.27 to 0.60 A. Remarkably, when these proteins were aligned by this motif a common core structure emerged, defined by five alpha-helices and 11 beta-strands comprising 155 residues having rms deviations ranging from 1.48 to 2.66 A. We used the superimposed structures to align the sequences within the common core, and a distant relationship was observed suggesting a common ancestor. The common core was used to align the sequences of several other proteins that share significant similarity to inositol monophosphate phosphatase, including proteins encoded by fungal qa-X and qutG, bacterial suhB and cysQ (identical to amtA), and yeast met22 (identical to hal2). Evolutionary comparison of the core sequences indicate that five distinct branches exist within this family. These proteins share metal-dependent/Li(+)-sensitive phosphomonoesterase activity, and each predicted tree branch exhibits unique substrate specificity. Thus, these proteins define an ancient structurally conserved family involved in diverse metabolic pathways including inositol signaling, gluconeogenesis, sulfate assimilation, and possibly quinone metabolism. Furthermore, we suggest that this protein family identifies candidate enzymes to account for both the therapeutic and toxic actions of Li+ as it is used in patients treated for manic depressive disease.

Sample-to-sample fluctuations of the overlap distributions in the three-dimensional Edwards-Anderson spin glass

We study the sample-to-sample fluctuations of the overlap probability densities from large-scale equilibrium simulations of the three-dimensional Edwards-Anderson spin glass below the critical temperature. Ultrametricity, stochastic stability, and overlap equivalence impose constraints on the moments of the overlap probability densities that can be tested against numerical data. We found small deviations from the Ghirlanda Guerra predictions, which get smaller as system size increases. We also focus on the shape of the overlap distribution, comparing the numerical data to a mean-field-like prediction in which finite-size effects are taken into account by substituting delta functions with broad peaks.