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.

Orderly cortical representation of vowels based on formant interaction

Psychophysical experiments have shown that the discrimination of human vowels chiefly relies on the frequency relationship of the first two peaks F1 and F2 of the vowel’s spectral envelope. It has not been possible, however, to relate the two-dimensional (F1,F2)-relationship to the known organization of frequency representation in auditory cortex. We demonstrate that certain spectral integration properties of neurons are topographically organized in primary auditory cortex in such a way that a transformed (F1,F2) relationship sufficient for vowel discrimination is realized.

Two-dimensional IR correlation spectroscopy: Sequential events in the unfolding process of the λ Cro-V55C repressor protein

A question often posed in protein folding/unfolding studies is whether the process is fully cooperative or whether it contains sequential elements. To address this question, one needs tools capable of resolving different events. It seems that, at least in certain cases, two-dimensional (2D) IR correlation spectroscopy can provide answers to this question. To illustrate this point, we have turned to the Cro-V55C dimer of the λ Cro repressor, a protein known to undergo thermal unfolding in two discrete steps through a stable equilibrium intermediate. The secondary structure of this intermediate is compatible with that of a partially unfolded protein and involves a reorganization of the N terminus, whereas the antiparallel β-ribbon formed by the C-terminal part of each subunit remains largely intact. To establish whether the unfolding process involves sequential events, we have performed a 2D correlation analysis of IR spectra recorded over the temperature range of 20–95°C. The 2D IR correlation analysis indeed provides evidence for a sequential formation of the stable intermediate, which is created in three (closely related) steps. A first step entails the unfolding of the short N-terminal β-strand, followed by the unfolding of the α-helices in a second step, and the third step comprises the reorganization of the remaining β-sheet and of some unordered segments in the protein. The complete unfolding of the stable intermediate at higher temperatures also undergoes sequential events that ultimately end with the breaking of the H bonds between the two β-strands at the dimer interface.

Third-generation synchrotron x-ray diffraction of 6-μm crystal of raite, ≈Na3Mn3Ti0.25Si8O20(OH)2⋅10H2O, opens up new chemistry and physics of low-temperature minerals

The crystal structure of raite was solved and refined from data collected at Beamline Insertion Device 13 at the European Synchrotron Radiation Facility, using a 3 × 3 × 65 μm single crystal. The refined lattice constants of the monoclinic unit cell are a = 15.1(1) Å; b = 17.6(1) Å; c = 5.290(4) Å; β = 100.5(2)°; space group C2/m. The structure, including all reflections, refined to a final R = 0.07. Raite occurs in hyperalkaline rocks from the Kola peninsula, Russia. The structure consists of alternating layers of a hexagonal chicken-wire pattern of 6-membered SiO4 rings. Tetrahedral apices of a chain of Si six-rings, parallel to the c-axis, alternate in pointing up and down. Two six-ring Si layers are connected by edge-sharing octahedral bands of Na+ and Mn3+ also parallel to c. The band consists of the alternation of finite Mn–Mn and Na–Mn–Na chains. As a consequence of the misfit between octahedral and tetrahedral elements, regions of the Si–O layers are arched and form one-dimensional channels bounded by 12 Si tetrahedra and 2 Na octahedra. The channels along the short c-axis in raite are filled by isolated Na(OH,H2O)6 octahedra. The distorted octahedrally coordinated Ti4+ also resides in the channel and provides the weak linkage of these isolated Na octahedra and the mixed octahedral tetrahedral framework. Raite is structurally related to intersilite, palygorskite, sepiolite, and amphibole.

Three-dimensional structure of human electron transfer flavoprotein to 2.1-Å resolution

Mammalian electron transfer flavoproteins (ETF) are heterodimers containing a single equivalent of flavin adenine dinucleotide (FAD). They function as electron shuttles between primary flavoprotein dehydrogenases involved in mitochondrial fatty acid and amino acid catabolism and the membrane-bound electron transfer flavoprotein ubiquinone oxidoreductase. The structure of human ETF solved to 2.1-Å resolution reveals that the ETF molecule is comprised of three distinct domains: two domains are contributed by the α subunit and the third domain is made up entirely by the β subunit. The N-terminal portion of the α subunit and the majority of the β subunit have identical polypeptide folds, in the absence of any sequence homology. FAD lies in a cleft between the two subunits, with most of the FAD molecule residing in the C-terminal portion of the α subunit. Alignment of all the known sequences for the ETF α subunits together with the putative FixB gene product shows that the residues directly involved in FAD binding are conserved. A hydrogen bond is formed between the N5 of the FAD isoalloxazine ring and the hydroxyl side chain of αT266, suggesting why the pathogenic mutation, αT266M, affects ETF activity in patients with glutaric acidemia type II. Hydrogen bonds between the 4′-hydroxyl of the ribityl chain of FAD and N1 of the isoalloxazine ring, and between αH286 and the C2-carbonyl oxygen of the isoalloxazine ring, may play a role in the stabilization of the anionic semiquinone. With the known structure of medium chain acyl-CoA dehydrogenase, we hypothesize a possible structure for docking the two proteins.

Tight frames of k-plane ridgelets and the problem of representing objects that are smooth away from d-dimensional singularities in Rn

For each pair (n, k) with 1 ≤ k < n, we construct a tight frame (ρλ : λ ∈ Λ) for L2 (Rn), which we call a frame of k-plane ridgelets. The intent is to efficiently represent functions that are smooth away from singularities along k-planes in Rn. We also develop tools to help decide whether k-plane ridgelets provide the desired efficient representation. We first construct a wavelet-like tight frame on the X-ray bundle χn,k—the fiber bundle having the Grassman manifold Gn,k of k-planes in Rn for base space, and for fibers the orthocomplements of those planes. This wavelet-like tight frame is the pushout to χn,k, via the smooth local coordinates of Gn,k, of an orthonormal basis of tensor Meyer wavelets on Euclidean space Rk(n−k) × Rn−k. We then use the X-ray isometry [Solmon, D. C. (1976) J. Math. Anal. Appl. 56, 61–83] to map this tight frame isometrically to a tight frame for L2(Rn)—the k-plane ridgelets. This construction makes analysis of a function f ∈ L2(Rn) by k-plane ridgelets identical to the analysis of the k-plane X-ray transform of f by an appropriate wavelet-like system for χn,k. As wavelets are typically effective at representing point singularities, it may be expected that these new systems will be effective at representing objects whose k-plane X-ray transform has a point singularity. Objects with discontinuities across hyperplanes are of this form, for k = n − 1.

Brain-wave representation of words by superposition of a few sine waves

Data from three previous experiments were analyzed to test the hypothesis that brain waves of spoken or written words can be represented by the superposition of a few sine waves. First, we averaged the data over trials and a set of subjects, and, in one case, over experimental conditions as well. Next we applied a Fourier transform to the averaged data and selected those frequencies with high energy, in no case more than nine in number. The superpositions of these selected sine waves were taken as prototypes. The averaged unfiltered data were the test samples. The prototypes were used to classify the test samples according to a least-squares criterion of fit. The results were seven of seven correct classifications for the first experiment using only three frequencies, six of eight for the second experiment using nine frequencies, and eight of eight for the third experiment using five frequencies.

Visual attention to surfaces in three-dimensional space.

Although attention plays a significant role in vision, its spatial deployment and spread in the third dimension is not well understood. In visual search experiments we show that we cannot easily focus attention across isodepth loci unless they are part of a well-formed surface with locally coplanar elements. Yet we can easily spread our attention selectively across well-formed surfaces that span an extreme range of stereoscopic depths. In cueing experiments, we show that this spread of attention is, in part, obligatory. Attentional selectivity is reduced when targets and distractors are coplanar with or rest on a common receding stereoscopic plane. We conclude that attention cannot be efficiently allocated to arbitrary depths and extents in space but is linked to and spreads automatically across perceived surfaces.