Stochastic re-calibration: contextual effects on perceived tilt

The human visual system exaggerates the difference between the tilts of adjacent lines or grating patches. In addition to this tilt illusion, we found that oblique flanks reduced acuity for small changes of tilt in the centre of the visual field. However, no flanks--regardless of their tilts--decreased sensitivity to contrast. Thus, the foveal tilt illusion should not be attributed to orientation-selective lateral inhibition. Nor is it similar to conventional crowding, which typically does not impair letter recognition in the fovea. Our observers behaved as though the reference orientation (horizontal) had a small tilt in the direction of the flanks. We suggest that the extent of this re-calibration varies randomly over trials, and we demonstrate that this stochastic re-calibration can explain flank-induced acuity loss in the fovea.     

Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L(2,3) edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell's nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Reprint of "Three-dimensional elemental mapping of phosphorus by quantitative electron spectroscopic tomography (QuEST)" [J. Struct. Biol. 160 (2007) 35-48

We describe the development of quantitative electron spectroscopic tomography (QuEST), which provides 3-D distributions of elements on a nanometer scale. Specifically, it is shown that QuEST can be applied to map the distribution of phosphorus in unstained sections of embedded cells. A series of 2-D elemental maps is derived from images recorded in the energy filtering transmission electron microscope for a range of specimen tilt angles. A quantitative 3-D elemental distribution is then reconstructed from the elemental tilt series. To obtain accurate quantitative elemental distributions it is necessary to correct for plural inelastic scattering at the phosphorus L_2,3 edge, which is achieved by acquiring unfiltered and zero-loss images at each tilt angle. The data are acquired automatically using a cross correlation technique to correct for specimen drift and focus change between successive tilt angles. An algorithm based on the simultaneous iterative reconstruction technique (SIRT) is implemented to obtain quantitative information about the number of phosphorus atoms associated with each voxel in the reconstructed volume. We assess the accuracy of QuEST by determining the phosphorus content of ribosomes in a eukaryotic cell, and then apply it to estimate the density of nucleic acid in chromatin of the cell’s nucleus. From our experimental data, we estimate that the sensitivity for detecting phosphorus is 20 atoms in a 2.7 nm-sized voxel.     

Three-dimensional reconstruction of chromatin fibers

We have obtained tilt series of thin sections of chromatin fibers embedded in araldite-epon and stained with uranyl acetate. The tilt series contain between 12 and 18 micrographs, spanning tilt ranges between 84 and 117 degrees. Reconstructions in three dimensions have been obtained by filtered back-projection from each tilt series. The reconstructions have been low-pass filtered in order to reduce the amount of noise. In the reconstructions it is possible to approximately localize the nucleosomes. In several regions they show a clear zigzag arrangement, but in other regions it is difficult to determine the sequence of the nucleosomes. In any case there is no clear indication of a solenoidal arrangement. We discuss the rules which may give rise to a 3-D arrangement of the nucleosomal zigzag.     

Three-Dimensional Reconstruction of Chromatin Fibers

Abstract

We have obtained tilt series of thin sections of chromatin fibers embedded in araldite-epon and stained with uranyl acetate. The tilt series contain between 12 and 18 micrographs, spanning tilt ranges between 84 and 117 degrees. Reconstructions in three dimensions have been obtained by filtered back-projection from each tilt series. The reconstructions have been low-pass filtered in order to reduce the amount of noise. In the reconstructions it is possible to approximately localize the nucleosomes. In several regions they show a clear zigzag arrangement, but in other regions it is difficult to determine the sequence of the nucleosomes. In any case there is no clear indication of a solenoidal arrangement. We discuss the rules which may give rise to a 3-D arrangement of the nucleosomal zigzag.     

Small scale membrane mechanics

Large scale changes to lipid bilayer shapes are well represented by the Helfrich model. However, there are membrane processes that take place at smaller length scales that this model cannot address. In this work, we present a one-dimensional continuum model that captures the mechanics of the lipid bilayer membrane at the length scale of the lipids themselves. The model is developed using the Cosserat theory of surfaces with lipid orientation, or ‘tilt’, as the fundamental degree of freedom. The Helfrich model can be recovered as a special case when the curvatures are small and the lipid tilt is everywhere zero. We use the tilt model to study local membrane deformations in response to a protein inclusion. Parameter estimates and boundary conditions are obtained from a coarse-grained molecular model using dissipative particle dynamics (DPD) to capture the same phenomenon. The continuum model is able to reproduce the membrane bending, stretch and lipid tilt as seen in the DPD model. The lipid tilt angle relaxes to the bulk tilt angle within 5–6 nm from the protein inclusion. Importantly, for large tilt gradients induced by the proteins, the tilt energy contribution is larger than the bending energy contribution. Thus, the continuum model of tilt accurately captures behaviors at length scales shorter than the membrane thickness.     

Orientation and dynamics of transmembrane peptides: the power of simple models

In this review we discuss recent insights obtained from well-characterized model systems into the factors that determine the orientation and tilt angles of transmembrane peptides in lipid bilayers. We will compare tilt angles of synthetic peptides with those of natural peptides and proteins, and we will discuss how tilt can be modulated by hydrophobic mismatch between the thickness of the bilayer and the length of the membrane spanning part of the peptide or protein. In particular, we will focus on results obtained on tryptophan-flanked model peptides (WALP peptides) as a case study to illustrate possible consequences of hydrophobic mismatch in molecular detail and to highlight the importance of peptide dynamics for the experimental determination of tilt angles. We will conclude with discussing some future prospects and challenges concerning the use of simple peptide/lipid model systems as a tool to understand membrane structure and function.     

Angle determination for side views in single particle electron microscopy

In order to build a first model in single particle electron microscopy the relative angular orientation of each image of a protein complex must be determined. These orientations can be described by three Eulerian angles. Images of complexes that present the same view can be aligned in two-dimensions and averaged in order to increase their signal-to-noise ratio. Based on these averaged images, several standard approaches exist for determining Euler angles for randomly oriented projection images. The common lines and angular reconstitution methods work well for particles with symmetry while the random conical tilting and related orthogonal tilt reconstruction methods work in most cases but require the acquisition of tilt pairs of images. For the situation where views of particles can be identified that are rotations about a single axis parallel to the grid, an alternative algorithm to determine the orientations of class averages without the need to acquire tilt pairs can be applied. This type of view of a complex is usually called a side view. This paper describes the detailed workings and characterization of an algorithm, named rotational analysis, which uses real-space fiducial markers derived from the averages themselves to determine the Euler angles for side views. We demonstrate how this algorithm works in practice by applying it to a data set of images of affinity-purified bovine mitochondrial ATP synthase.     

Molecular theory of lipid-protein interaction and the Lalpha-HII transition.

We present a molecular-level theory for lipid-protein interaction and apply it to the study of lipid-mediated interactions between proteins and the protein-induced transition from the planar bilayer (Lalpha) to the inverse-hexagonal (HII) phase. The proteins are treated as rigid, membrane-spanning, hydrophobic inclusions of different size and shape, e.g., "cylinder-like," "barrel-like," or "vase-like." We assume strong hydrophobic coupling between the protein and its neighbor lipids. This means that, if necessary, the flexible lipid chains surrounding the protein will stretch, compress, and/or tilt to bridge the hydrophobic thickness mismatch between the protein and the unperturbed bilayer. The system free energy is expressed as an integral over local molecular contributions, the latter accounting for interheadgroup repulsion, hydrocarbon-water surface energy, and chain stretching-tilting effects. We show that the molecular interaction constants are intimately related to familiar elastic (continuum) characteristics of the membrane, such as the bending rigidity and spontaneous curvature, as well as to the less familiar tilt modulus. The equilibrium configuration of the membrane is determined by minimizing the free energy functional, subject to boundary conditions dictated by the size, shape, and spatial distribution of inclusions. A similar procedure is used to calculate the free energy and structure of peptide-free and peptide-rich hexagonal phases. Two degrees of freedom are involved in the variational minimization procedure: the local length and local tilt angle of the lipid chains. The inclusion of chain tilt is particularly important for studying noncylindrical (for instance, barrel-like) inclusions and analyzing the structure of the HII lipid phase; e.g., we find that chain tilt relaxation implies strong faceting of the lipid monolayers in the hexagonal phase. Consistent with experiment, we find that only short peptides (large negative mismatch) can induce the Lalpha --> HII transition. At the transition, a peptide-poor Lalpha phase coexists with a peptide-rich HII phase.     

Reconstruction of the probe angular distribution from a series of electron spin resonance spectra of tilted oriented samples.

Model-independent methods for the reconstruction of the nitroxide spin probe angular distribution of labeled oriented biological assemblies from electron spin resonance (ESR) spectra were investigated. We found that accurate probe angular distribution information could be obtained from the simultaneous consideration of a series of ESR spectra originating from a sample at differing tilt angles relative to the Zeeman magnetic field. Using simulated tilt series data sets, we developed a consistent criteria for judging the reliability of the simulated fit to the data as a function of the free spectral parameters and thereby have increased the significance of the model-independent reconstruction of the probe angular distribution derived from the fit. We have also enhanced the angular resolution measurable with the model-independent methodology by increasing the rank of the order parameters that we can reliably deduce from a spectrum. This enhancement allows us to accurately deduce higher resolution features of the spin probe distribution. Finally we investigated the usefulness of fitting the tilt series data in multiple data sets such that tilt series data from many identical sample preparations are fitted simultaneously. This method proved to be useful in rapidly reducing a large amount of data by eliminating any redundant computations in the application of the enhanced model-independent analysis to identical sets of tilt series data. We applied the methodology developed here to ESR spectra from probe labeled muscle fibers to study the orientation of myosin cross-bridges in fibers. This application is described in the accompanying paper.     

Normal Variation of Talar Tilt of the Ankle in Children

Sixty normal children were examined clinically and radiologically, using a special apparatus with a goniometer and a tensometer to standardize stress tests when applying valgus and varus forces to the ankle. It was noted that the clinical movement of inversion is not entirely due to a subtalar movement; indeed a talar tilt appears to be physiological. The range of normal in these patients, age range 6 to 15 years, was 0 to 27° with an average talar tilt of 7°. The talar tilt is not necessarily the same in both ankles of any one individual and it is never noted in eversion. The talar tilt is more marked in younger children in the position of equinus.When interpreting radiographs of recently injured ankles, it is wise to recall that a talar tilt need not be the result of trauma and that it may be physiological and yet unequal on both sides.     

Effects of exercise and passive head-up tilt on fractal and complexity properties of heart rate dynamics

tk;1Passive head-up tilt and exercise result in specific changes in the spectral characteristics of heart rate (HR) variability as a result of reduced vagal and enhanced sympathetic outflow. Recently analytic methods based on nonlinear system theory have been developed to characterize the nonlinear features in HR dynamics. This study was designed to assess the changes in the fractal and complexity measures of HR behavior during the passive head-up tilt and during exercise. Fractal exponent (alpha(1)) and approximate entropy (ApEn), measures of short-term correlation properties and overall complexity of HR, respectively, along with spectral components of HR variability were analyzed during a passive head-up tilt test (n = 10) and a low-intensity steady-state exercise (n = 20) in healthy subjects. We observed that alpha(1) increased during the tilt test (from 0.85 +/- 0.22 to 1.48 +/- 0.20; P < 0.001) and during the exercise (from 1.00 +/- 0.22 to 1.37 +/- 0. 14; P < 0.001). ApEn also increased during the exercise (from 1.04 +/- 0.11 to 1. 11 +/- 0.08; P < 0.05), but it did not change during the tilt test. The normalized high-frequency spectral component decreased and the low-frequency component increased similarly during both the exercise and the tilt test (P < 0.001 for all). Exercise and passive tilt result in an increase of short-term fractal correlation properties of HR dynamics, which is related to changes in the balance between the low- and high-frequency oscillations in controlled situations. Overall complexity of HR dynamics increases during exercise but not during passive tilt.     

Steep head-down tilt has persisting effects on the distribution of pulmonary blood flow.

Head-down tilt has been shown to increase lung water content in animals and alter the distribution of ventilation in humans; however, its effects on the distribution of pulmonary blood flow in humans are unknown. We hypothesized that head-down tilt would increase the heterogeneity of pulmonary blood flow in humans, an effect analogous to the changes seen in the distribution of ventilation, by increasing capillary hydrostatic pressure and fluid efflux in the lung. To test this, we evaluated changes in the distribution of pulmonary blood flow in seven normal subjects before and after 1 h of 30 degrees head-down tilt using the magnetic resonance imaging technique of arterial spin labeling. Data were acquired in triplicate before tilt and at 10-min intervals for 1 h after tilt. Pulmonary blood flow heterogeneity was quantified by the relative dispersion (standard deviation/mean) of signal intensity for all voxels within the right lung. Relative dispersion was significantly increased by 29% after tilt and remained elevated during the 1 h of measurements after tilt (0.84 +/- 0.06 pretilt, 1.09 +/- 0.09 calculated for all time points posttilt, P < 0.05). We speculate that the mechanism most likely responsible for our findings is that increased pulmonary capillary pressures and fluid efflux in the lung resulting from head-down tilt alters regional blood flow distribution.     

On the Combined Analysis of H and N/H Solid-State NMR Data for Determination of Transmembrane Peptide Orientation and Dynamics

The dynamics of membrane-spanning peptides have a strong affect on the solid-state NMR observables. We present a combined analysis of ²H-alanine quadrupolar splittings together with ¹⁵N/¹H dipolar couplings and ¹⁵N chemical shifts, using two models to treat the dynamics, for the systematic evaluation of transmembrane peptides based on the GWALP23 sequence (acetyl-GGALW(LA)₆LWLAGA-amide). The results indicate that derivatives of GWALP23 incorporating diverse guest residues adopt a range of apparent tilt angles that span 5°–35° in lipid bilayer membranes. By comparing individual and combined analyses of specifically ²H- or ¹⁵N-labeled peptides incorporated in magnetically or mechanically aligned lipid bilayers, we examine the influence of data-set size/identity, and of explicitly modeled dynamics, on the deduced average orientations of the peptides. We conclude that peptides with small apparent tilt values (<∼10°) can be fitted by extensive families of solutions, which can be narrowed by incorporating additional ¹⁵N as well as ²H restraints. Conversely, peptides exhibiting larger tilt angles display more narrow distributions of tilt and rotation that can be fitted using smaller sets of experimental constraints or even with ²H or ¹⁵N data alone. Importantly, for peptides that tilt significantly more than 10° from the bilayer-normal, the contribution from rigid body dynamics can be approximated by a principal order parameter.     

On the combined analysis of ²H and ¹⁵N/¹H solid-state NMR data for determination of transmembrane peptide orientation and dynamics

The dynamics of membrane-spanning peptides have a strong affect on the solid-state NMR observables. We present a combined analysis of ²H-alanine quadrupolar splittings together with ¹⁵N/¹H dipolar couplings and ¹⁵N chemical shifts, using two models to treat the dynamics, for the systematic evaluation of transmembrane peptides based on the GWALP23 sequence (acetyl-GGALW(LA)₆LWLAGA-amide). The results indicate that derivatives of GWALP23 incorporating diverse guest residues adopt a range of apparent tilt angles that span 5°–35° in lipid bilayer membranes. By comparing individual and combined analyses of specifically ²H- or ¹⁵N-labeled peptides incorporated in magnetically or mechanically aligned lipid bilayers, we examine the influence of data-set size/identity, and of explicitly modeled dynamics, on the deduced average orientations of the peptides. We conclude that peptides with small apparent tilt values (<∼10°) can be fitted by extensive families of solutions, which can be narrowed by incorporating additional ¹⁵N as well as ²H restraints. Conversely, peptides exhibiting larger tilt angles display more narrow distributions of tilt and rotation that can be fitted using smaller sets of experimental constraints or even with ²H or ¹⁵N data alone. Importantly, for peptides that tilt significantly more than 10° from the bilayer-normal, the contribution from rigid body dynamics can be approximated by a principal order parameter.     

Dramatic in situ conformational dynamics of the transmembrane protein bacteriorhodopsin.

The conformational dynamic capabilities of the in situ bacteriorhodopsin (bR) can be studied by determination of the changes of the bR net helical segmental tilt angle (the angle between the polypeptide segments and the membrane normal) induced by various perturbations of the purple membrane (PM). The analysis of the far-UV oriented circular dichroism (CD) of the PM provides one means of achieving this. Previous CD studies have indicated that the tilt angle can change from approximately 10 degrees to 39 degrees depending on the perturbants used with no changes in the secondary structure of the bR. A recent study has indicated that the bleaching-induced tilt angle can be enhanced from approximately 24 degrees to 39 degrees by cross-linkage and papain-digestion perturbations which by themselves do not alter the tilt angle. To add further credence, this study has been repeated using midinfrared (IR) linear dichroic spectral analysis. In contrast to the CD method, analysis by the IR method depends on the orientation of the amide plane of the helix assumed. Excellent consistency is achieved between the two methods only when it is assumed that the structural characteristics of the alpha-helices of the bR are equally alpha I and alpha II in nature. Furthermore, the analysis of the IR data becomes essentially independent of the three amide transitions utilized. The net tilt angle of segments completely randomized relative to the incident light must be 54.736 in view of helix symmetry. A value of 54.735 degrees +/- 0.001 degree was achieved by the IR method for the ethanol-treated PM film, establishing this kind of film as an ideal random state standard and demonstrating the accuracy potential of the IR method.     

Dual-Axis Tomography: An Approach with Alignment Methods That Preserve Resolution

Tomographic reconstructions of biological specimens are now routinely being generated in our high voltage electron microscope by tilting the specimen around two orthogonal axes. Separate tomograms are computed from each tilt series. The two tomograms are aligned to each other with general 3-D linear transformations that can correct for distortions between the two tomograms, thus preserving the inherent resolution of the reconstruction throughout its volume. The 3-D Fourier transforms of the two tomograms are then selectively combined to achieve a single tomogram. Unlike a single-axis tomogram, a dual-axis tomogram shows good resolution for extended features at any orientation in the plane of the specimen; it also has improved resolution in the depth of the specimen. Calculations indicate that the improvements available from double tilting and from tilting to higher angles are largely additive. Actual and model data were used to assess whether varying the increment between tilted views in proportion to the cosine of the tilt angle would allow a reduction in the number of pictures required to achieve a given resolution of reconstruction. Analysis by Fourier sector correlation indicated that the variable tilt increment improved the reconstruction in some respects but degraded it in others. A varying tilt increment thus does not give an unqualified improvement, at least when using back-projection algorithms for the reconstruction.     

Feature-based attention modulates orientation-selective responses in human visual cortex

How does feature-based attention modulate neural responses? We used adaptation to quantify the effect of feature-based attention on orientation-selective responses in human visual cortex. Observers were adapted to two superimposed oblique gratings while attending to one grating only. We measured the magnitude of attention-induced orientation-selective adaptation both psychophysically, by the behavioral tilt aftereffect, and physiologically, using fMRI response adaptation. We found evidence for orientation-selective attentional modulation of neuronal responses-a lower fMRI response for the attended than the unattended orientation-in multiple visual areas, and a significant correlation between the magnitude of the tilt aftereffect and that of fMRI response adaptation in V1, the earliest site of orientation coding. These results show that feature-based attention can selectively increase the response of neuronal subpopulations that prefer the attended feature, even when the attended and unattended features are coded in the same visual areas and share the same retinotopic location.     

Spontaneous beat-by-beat fluctuations of total peripheral and cerebrovascular resistance in response to tilt

Beat-by-beat estimates of total peripheral resistance (TPR) can be obtained from continuous measurements of cardiac output by using Doppler ultrasound and noninvasive mean arterial blood pressure (MAP). We employed transfer function analysis to study the heart rate (HR) and vascular response to spontaneous changes in blood pressure from the relationships of systolic blood pressure (SBP) to HR (SBP-->HR), MAP to total peripheral resistance (TPR) and cerebrovascular resistance index (CVRi) (MAP-->TPR and MAP-->CVRi), as well as stroke volume (SV) to TPR in nine healthy subjects in supine and 45 degrees head-up tilt positions. The gain of the SBP-->HR transfer function was reduced with tilt in both the low- (0.03-0.15 Hz) and high-frequency (0.15-0.35 Hz) regions. In contrast, MAP-->TPR transfer function gain was not affected by head-up tilt, but it did increase from low- to high-frequency regions. The phase relationships between MAP-->TPR were unaffected by head-up tilt, but, consistent with an autoregulatory system, changes in MAP were followed by directionally similar changes in TPR, just as observed for the MAP-->CVRi. The SV-->TPR had high coherence with a constant phase of 150-160 degrees. Together, these data that showed changes in MAP preceded changes in TPR, as well as a possible link between SV and TPR, are consistent with complex interactions between the vascular component of the arterial and cardiopulmonary baroreflexes and intrinsic properties such as the myogenic response of the resistance arteries.     

The importance of porphyrin distortions for the ferrochelatase reaction

Ferrochelatase is the terminal enzyme in haem biosynthesis, i.e. the enzyme that inserts a ferrous ion into the porphyrin ring. Suggested reaction mechanisms for this enzyme involve a distortion of the porphyrin ring when it is bound to the enzyme. We have examined the energetics of such distortions using various theoretical calculations. With the density functional B3LYP method we calculate how much energy it costs to tilt one of the pyrrole rings out of the porphyrin plane for an isolated porphyrin molecule without or with a divalent metal ion in the centre of the ring. A tilt of 30 degrees costs 65-130 kJ/mol for most metal ions, but only approximately 48 kJ/mol for free-base (neutral) porphine. This indicates that once the metal is inserted, the porphyrin becomes stiffer and flatter, and therefore binds with lower affinity to a site designed to bind a distorted porphyrin. This would facilitate the release of the product from ferrochelatase. This proposal is strengthened by the fact that the only tested metal ion with a lower distortion energy than free-base porphyrin (Cd(2+)) is an inhibitor of ferrochelatase. Moreover, it costs even less energy to tilt a doubly deprotonated porphine(2-) molecule. This suggests that the protein may lower the acid constant of the pyrrole nitrogen atoms by deforming the porphyrin molecule. We have also estimated the structure of the protoporphyrin IX substrate bound to ferrochelatase using combined quantum chemical and molecular mechanics calculations. The result shows that the protein may distort the porphyrin by approximately 20 kJ/mol, leading to a distinctly non-planar structure. All four pyrrole rings are tilted out of the porphyrin mean plane (1-16 degrees ) but most towards the putative binding site of the metal ion. The predicted tilt is considerably smaller than that observed in the crystal structure of a porphyrin inhibitor.