Three-dimensional image reconstruction of dephosphorylated smooth muscle heavy meromyosin reveals asymmetry in the interaction between myosin heads and placement of subfragment 2

Regulation of the actin-activated ATPase of smooth muscle myosin II is known to involve an interaction between the two heads that is controlled by phosphorylation of the regulatory light chain. However, the three-dimensional structure of this inactivated form has been unknown. We have used a lipid monolayer to obtain two-dimensional crystalline arrays of the unphosphorylated inactive form of smooth muscle heavy meromyosin suitable for structural studies by electron cryomicroscopy of unstained, frozen-hydrated specimens. The three-dimensional structure reveals an asymmetric interaction between the two myosin heads. The ATPase activity of one head is sterically “blocked” because part of its actin-binding interface is positioned onto the converter domain of the second head. ATPase activity of the second head, which can bind actin, appears to be inhibited through stabilization of converter domain movements needed to release phosphate and achieve strong actin binding. When the subfragment 2 domain of heavy meromyosin is oriented as it would be in an actomyosin filament lattice, the position of the heads is very different from that needed to bind actin, suggesting an additional contribution to ATPase inhibition in situ.

Novel phenomena in dilute electron systems in two dimensions

For the past two decades, all two-dimensional systems of electrons were believed to be insulating in the limit of zero temperature. Recent experiments provide evidence for an unexpected transition to a conducting phase at very low electron densities. The nature of this phase is not understood and is currently the focus of intense theoretical and experimental attention.

Faithful representation of similarities among three-dimensional shapes in human vision.

Efficient and reliable classification of visual stimuli requires that their representations reside a low-dimensional and, therefore, computationally manageable feature space. We investigated the ability of the human visual system to derive such representations from the sensory input-a highly nontrivial task, given the million or so dimensions of the visual signal at its entry point to the cortex. In a series of experiments, subjects were presented with sets of parametrically defined shapes; the points in the common high-dimensional parameter space corresponding to the individual shapes formed regular planar (two-dimensional) patterns such as a triangle, a square, etc. We then used multidimensional scaling to arrange the shapes in planar configurations, dictated by their experimentally determined perceived similarities. The resulting configurations closely resembled the original arrangements of the stimuli in the parameter space. This achievement of the human visual system was replicated by a computational model derived from a theory of object representation in the brain, according to which similarities between objects, and not the geometry of each object, need to be faithfully represented.

Phosphorylation by protein kinase C of serine-23 of the alpha-1 subunit of rat Na+,K(+)-ATPase affects its conformational equilibrium.

Phosphorylation of the alpha-1 subunit of rat Na+,K(+)-ATPase by protein kinase C has been shown previously to decrease the activity of the enzyme in vitro. We have now undertaken an investigation of the mechanism by which this inhibition occurs. Analysis of the phosphorylation of recombinant glutathione S-transferase fusion proteins containing putative cytoplasmic domains of the protein, site-directed mutagenesis, and two-dimensional peptide mapping indicated that protein kinase C phosphorylated the alpha-1 subunit of the rat Na+,K(+)-ATPase within the extreme NH2-terminal domain, on serine-23. The phosphorylation of this residue resulted in a shift in the equilibrium toward the E1 form, as measured by eosin fluorescence studies, and this was associated with a decrease in the apparent K+ affinity of the enzyme, as measured by ATPase activity assays. The rate of transition from E2 to E1 was apparently unaffected by phosphorylation by protein kinase C. These results, together with previous studies that examined the effects of tryptic digestion of Na+,K(+)-ATPase, suggest that the NH2-terminal domain of the alpha-1 subunit, including serine-23, is involved in regulating the activity of the enzyme.

Projection structure of frog rhodopsin in two crystal forms.

Rhodopsin is the G protein-coupled receptor that upon light activation triggers the visual transduction cascade. Rod cell outer segment disc membranes were isolated from dark-adapted frog retinas and were extracted with Tween detergents to obtain two-dimensional rhodopsin crystals for electron crystallography. When Tween 80 was used, tubular structures with a p2 lattice (a = 32 A, b = 83 A, gamma = 91 degrees) were formed. The use of a Tween 80/Tween 20 mixture favored the formation of larger p22(1)2(1) lattices (a = 40 A, b = 146 A, gamma = 90 degrees). Micrographs from frozen hydrated frog rhodopsin crystals were processed, and projection structures to 7-A resolution for the p22(1)2(1) form and to 6-A resolution for the p2 form were calculated. The maps of frog rhodopsin in both crystal forms are very similar to the 9-A map obtained previously for bovine rhodopsin and show that the arrangement of the helices is the same. In a tentative topographic model, helices 4, 6, and 7 are nearly perpendicular to the plane of the membrane. In the higher-resolution projection maps of frog rhodopsin, helix 5 looks more tilted than it appeared previously. The quality of the two frog rhodopsin crystals suggests that they would be suitable to obtain a three-dimensional structure in which all helices would be resolved.

Three-dimensional structure of a cysteine-rich repeat from the low-density lipoprotein receptor.

The low-density lipoprotein (LDL) receptor plays a central role in mammalian cholesterol metabolism, clearing lipoproteins which bear apolipoproteins E and B-100 from plasma. Mutations in this molecule are associated with familial hypercholesterolemia, a condition which leads to an elevated plasma cholesterol concentration and accelerated atherosclerosis. The N-terminal segment of the LDL receptor contains a heptad of cysteine-rich repeats that bind the lipoproteins. Similar repeats are present in related receptors, including the very low-density lipoprotein receptor and the LDL receptor-related protein/alpha 2-macroglobulin receptor, and in proteins which are functionally unrelated, such as the C9 component of complement. The first repeat of the human LDL receptor has been expressed in Escherichia coli as a glutathione S-transferase fusion protein, and the cleaved and purified receptor module has been shown to fold to a single, fully oxidized form that is recognized by the monoclonal antibody IgG-C7 in the presence of calcium ions. The three-dimensional structure of this module has been determined by two-dimensional NMR spectroscopy and shown to consist of a beta-hairpin structure, followed by a series of beta turns. Many of the side chains of the acidic residues, including the highly conserved Ser-Asp-Glu triad, are clustered on one face of the module. To our knowledge, this structure has not previously been described in any other protein and may represent a structural paradigm both for the other modules in the LDL receptor and for the homologous domains of several other proteins. Calcium ions had only minor effects on the CD spectrum and no effect on the 1H NMR spectrum of the repeat, suggesting that they induce no significant conformational change.

Reproducibility and accuracy of echocardiographic measurements of left ventricular parameters using real-time three-dimensional echocardiography

OBJECTIVES We sought to determine whether assessment of left ventricular (LV) function with real-time (RT) three-dimensional echocardiography (3DE) could reduce the variation of sequential LV measurements and provide greater accuracy than two-dimensional echocardiography (2DE). BACKGROUND Real-time 3DE has become feasible as a standard clinical tool, but its accuracy for LV assessment has not been validated. METHODS Unselected patients (n = 50; 41 men; age, 64 +/- 8 years) presenting for evaluation of LV function were studied with 2DE and RT-3DE. Test-retest variation was performed by a complete restudy by a separate sonographer within 1 h without alteration of hemodynamics or therapy. Magnetic resonance imaging (MRI) images were obtained during a breath-hold, and measurements were made off-line. RESULTS The test-retest variation showed similar measurements for volumes but wider scatter of LV mass measurements with M-mode and 2DE than 3DE. The average MRI end-diastolic volume was 172 +/- 53 ml; LV volumes were underestimated by 2DE (mean difference, -54 +/- 33; p < 0.01) but only slightly by RT-3DE (-4 +/- 29; p = 0.31). Similarly, end-systolic volume by MRI (91 +/- 53 ml) was underestimated by 2DE (mean difference, -28 +/- 28; p < 0.01) and by RT-3DE (mean difference, -3 +/- 18; p = 0.23). Ejection fraction by MRI was similar by 2DE (p = 0.76) and RT-3DE (p = 0.74). Left ventricular mass (183 +/- 50 g) was overestimated by M-mode (mean difference, 68 +/- 86 g; p < 0.01) and 2DE (16 +/- 57; p = 0.04) but not RT-3DE (0 +/- 38 g; p = 0.94). There was good inter- and intra-observer correlation between RT-3DE by two sonographers for volumes, ejection fraction, and mass. CONCLUSIONS Real-time 3DE is a feasible approach to reduce test-retest variation of LV volume, ejection fraction, and mass measurements in follow-up LV assessment in daily practice. (C) 2004 by the American College of Cardiology Foundation.

Numerical evaluation of three dimensional effects in planar flow birefringence

The influence of three dimensional effects on isochromatic birefringence is evaluated for planar flows by means of numerical simulation. Two fluid models are investigated in channel and abrupt contraction geometries. In practice, the flows are confined by viewing windows, which alter the stresses along the optical path. The observed optical properties differ therefore from their counterpart in an ideal two-dimensional flow. To investigate the influence of these effects, the stress optical rule and the differential propagation Mueller matrix are used. The material parameters are selected so that a retardation of multiple orders is achieved, as is typical for highly birefringent melts. Errors due to three dimensional effects are mainly found on the symmetry plane, and increase significantly with the flow rate. Increasing the geometric aspect ratio improve the accuracy provided that the error on the retardation is less than one order. (C) 2004 Elsevier B.V. All rights reserved.

Three-dimensional simulation of the rolling of a saturated fibro-porous media

This paper describes recent advances made in computational modelling of the sugar cane liquid extraction process. The saturated fibro-porous material is rolled between circumferentially grooved rolls, which enhance frictional grip and provide a low-resistance path for liquid flow during the extraction process. Previously reported two-dimensional (2D) computational models, account for the large deformation of the porous material by solving the fully coupled governing fibre stress and fluid-flow equations using finite element techniques. While the 2D simulations provide much insight into the overarching cause-effect relationships, predictions of mechanical quantities such as roll separating force and particularly torque as a function of roll speed and degree of compression are not satisfactory for industrial use. It is considered that the unsatisfactory response in roll torque prediction may be due to the stress levels that exist between the groove tips and roots which have been largely neglected in the geometrically simplified 2D model. This paper gives results for both two- and three-dimensional finite element models and highlights their strengths and weaknesses in predicting key milling parameters. (c) 2005 Elsevier B.V. All rights reserved.

Leading coordinate analysis of reaction pathways in proton chain transfer: Application to a two-proton transfer model for the green fluorescent protein

The ‘leading coordinate’ approach to computing an approximate reaction pathway, with subsequent determination of the true minimum energy profile, is applied to a two-proton chain transfer model based on the chromophore and its surrounding moieties within the green fluorescent protein (GFP). Using an ab initio quantum chemical method, a number of different relaxed energy profiles are found for several plausible guesses at leading coordinates. The results obtained for different trial leading coordinates are rationalized through the calculation of a two-dimensional relaxed potential energy surface (PES) for the system. Analysis of the 2-D relaxed PES reveals that two of the trial pathways are entirely spurious, while two others contain useful information and can be used to furnish starting points for successful saddle-point searches. Implications for selection of trial leading coordinates in this class of proton chain transfer reactions are discussed, and a simple diagnostic function is proposed for revealing whether or not a relaxed pathway based on a trial leading coordinate is likely to furnish useful information.

Hierarchical GTM: Constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping. bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the parent visualization plot which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 19-dimensional data sets.

Hierarchical GTM: constructing localized non-linear projection manifolds in a principled way

It has been argued that a single two-dimensional visualization plot may not be sufficient to capture all of the interesting aspects of complex data sets, and therefore a hierarchical visualization system is desirable. In this paper we extend an existing locally linear hierarchical visualization system PhiVis ¸iteBishop98a in several directions: bf(1) We allow for em non-linear projection manifolds. The basic building block is the Generative Topographic Mapping (GTM). bf(2) We introduce a general formulation of hierarchical probabilistic models consisting of local probabilistic models organized in a hierarchical tree. General training equations are derived, regardless of the position of the model in the tree. bf(3) Using tools from differential geometry we derive expressions for local directional curvatures of the projection manifold. Like PhiVis, our system is statistically principled and is built interactively in a top-down fashion using the EM algorithm. It enables the user to interactively highlight those data in the ancestor visualization plots which are captured by a child model. We also incorporate into our system a hierarchical, locally selective representation of magnification factors and directional curvatures of the projection manifolds. Such information is important for further refinement of the hierarchical visualization plot, as well as for controlling the amount of regularization imposed on the local models. We demonstrate the principle of the approach on a toy data set and apply our system to two more complex 12- and 18-dimensional data sets.

Data visualisation with missing data: A non-linear approach

Exploratory analysis of data in all sciences seeks to find common patterns to gain insights into the structure and distribution of the data. Typically visualisation methods like principal components analysis are used but these methods are not easily able to deal with missing data nor can they capture non-linear structure in the data. One approach to discovering complex, non-linear structure in the data is through the use of linked plots, or brushing, while ignoring the missing data. In this technical report we discuss a complementary approach based on a non-linear probabilistic model. The generative topographic mapping enables the visualisation of the effects of very many variables on a single plot, which is able to incorporate far more structure than a two dimensional principal components plot could, and deal at the same time with missing data. We show that using the generative topographic mapping provides us with an optimal method to explore the data while being able to replace missing values in a dataset, particularly where a large proportion of the data is missing.

Applications of fractals to image data compression

Digital image processing is exploited in many diverse applications but the size of digital images places excessive demands on current storage and transmission technology. Image data compression is required to permit further use of digital image processing. Conventional image compression techniques based on statistical analysis have reached a saturation level so it is necessary to explore more radical methods. This thesis is concerned with novel methods, based on the use of fractals, for achieving significant compression of image data within reasonable processing time without introducing excessive distortion. Images are modelled as fractal data and this model is exploited directly by compression schemes. The validity of this is demonstrated by showing that the fractal complexity measure of fractal dimension is an excellent predictor of image compressibility. A method of fractal waveform coding is developed which has low computational demands and performs better than conventional waveform coding methods such as PCM and DPCM. Fractal techniques based on the use of space-filling curves are developed as a mechanism for hierarchical application of conventional techniques. Two particular applications are highlighted: the re-ordering of data during image scanning and the mapping of multi-dimensional data to one dimension. It is shown that there are many possible space-filling curves which may be used to scan images and that selection of an optimum curve leads to significantly improved data compression. The multi-dimensional mapping property of space-filling curves is used to speed up substantially the lookup process in vector quantisation. Iterated function systems are compared with vector quantisers and the computational complexity or iterated function system encoding is also reduced by using the efficient matching algcnithms identified for vector quantisers.