Context shapes: Efficient complementary shape matching for protein-protein docking

We describe an efficient method for partial complementary shape matching for use in rigid protein-protein docking. The local shape features of a protein are represented using boolean data structures called Context Shapes. The relative orientations of the receptor and ligand surfaces are searched using precalculated lookup tables. Energetic quantities are derived from shape complementarity and buried surface area computations, using efficient boolean operations. Preliminary results indicate that our context shapes approach outperforms state-of-the-art geometric shape-based rigid-docking algorithms.     

Building hydrodynamic bead-shell models for rigid bioparticles of arbitrary shape.

The calculation of hydrodynamic and other solution properties of rigid macromolecules, using bead-shell model methodologies, requires the specification of the macromolecular shape in a format that can be interfaced with existing programs for hydrodynamic computations. Here, a procedure is presented for such a structural specification that is applicable to arbitrarily shaped particles. A computer program (MAKEPIXB), in which the user inserts the code needed to determine the structure, produces an structural file that is interpreted by another program (HYDROPIX) which is in charge of the computation of properties. As simple and yet illustrative examples we consider two cases: (1) dimeric structures composed of ellipsoidal subunits; and (2) toroidal structures, presenting simple equations that predict the properties of toroids with varying radial ratios.     

Equivalent radii and ratios of radii from solution properties as indicators of macromolecular conformation, shape, and flexibility

The equivalent radius for any solution property is the radius of a spherical particle having the same value of solution property as that of the macromolecule under consideration. Equivalent radii for different properties present a dependence on size and shape that are more similar than the values of the properties themselves. Furthermore, the ratios of equivalent radii of two properties depend on the conformation (shape or flexibility), but not on the absolute sizes. We define equivalent radii and their ratios, and describe their evaluation for some common models of rigid and flexible macromolecules. Using radii and ratios, we have devised procedures to fit macromolecular models to experimental properties, allowing the determination of the model parameters. Using these quantities, we can construct target functions for an equilibrated, unbiased optimization. The procedures, which have been implemented in public-domain computer programs, are illustrated for rigid, globular proteins, and the rodlike tobacco mosaic virus, and for semiflexible, wormlike heparin molecules.     

Phospholipid membrane bending as assessed by the shape sequence of giant oblate phospholipid vesicles

Vesicle shape transformations caused by decreasing the difference between the equilibrium areas of membrane monolayers were studied on phospholipid vesicles with small volume to membrane area ratios. Slow transformations of the vesicle shape were induced by lowering of the concentration of lipid monomers in the solution outside the vesicle. The complete sequence of shapes consisted of a string of pearls, and wormlike, starfish, discocyte and stomatocyte shapes. The transformation from discocyte to stomatocyte vesicle shapes was analyzed theoretically to see whether these observations accord with the area difference elasticity (ADE) model. The membrane shape equation and boundary conditions were derived for axisymmetrical shapes for low volume vesicles, part of whose membranes are in contact. Calculated shapes were arranged into a phase diagram. The theory predicts that the transition between discocyte and stomatocyte shapes is discontinuous for relatively high volumes and continuous for low volumes. The calculated shape sequences matched well with the observed ones. By assuming a linear decrease of the equilibrium area difference with time, the ratio between the nonlocal and local bending constants is in agreement with reported values.     

Phospholipid membrane bending as assessed by the shape sequence of giant oblate phospholipid vesicles

Vesicle shape transformations caused by decreasing the difference between the equilibrium areas of membrane monolayers were studied on phospholipid vesicles with small volume to membrane area ratios. Slow transformations of the vesicle shape were induced by lowering of the concentration of lipid monomers in the solution outside the vesicle. The complete sequence of shapes consisted of a string of pearls, and wormlike, starfish, discocyte and stomatocyte shapes. The transformation from discocyte to stomatocyte vesicle shapes was analyzed theoretically to see whether these observations accord with the area difference elasticity (ADE) model. The membrane shape equation and boundary conditions were derived for axisymmetrical shapes for low volume vesicles, part of whose membranes are in contact. Calculated shapes were arranged into a phase diagram. The theory predicts that the transition between discocyte and stomatocyte shapes is discontinuous for relatively high volumes and continuous for low volumes. The calculated shape sequences matched well with the observed ones. By assuming a linear decrease of the equilibrium area difference with time, the ratio between the nonlocal and local bending constants is in agreement with reported values.     

Measuring egg size using digital photography: testing Hoyt's method using Florida Scrub-Jay eggs

ABSTRACT.   Egg volumes are most often estimated using a mathematical model that incorporates length and width measurements and a species-specific shape variable. Although adequate in many respects, this technique does not account for intraspecific variation in egg shape. We developed a computer-automated technique that uses calibrated digital photographs to render precise measurements of several egg-size parameters including length, width, volume, and surface area. The system extracts egg outlines from photographs, and divides each egg into latitudinal slices that are subsequently regarded as simple geometric shapes (cylinders or cone frustra) with volumes and surface areas that can be summed to generate size parameters for the entire egg. We tested this technique using 491 eggs from Florida Scrub-Jay ( Aphelocoma coerulescens ) nests and compared the resulting egg volumes with volumes calculated using the preeminent method of estimating volume from linear measurements. Our method was highly accurate, and differences between the volumes from our method and the alternative method were strongly associated with variation in egg shape. Advantages of our technique include decreased handling of eggs and increased accuracy. Software resources and additional information regarding the technique are available at http://www.archbold-station.org/abs/data/birddata/Bridge-JFO-eggsize.htm .     

Structural analysis of interphase X-chromatin based on statistical shape theory

The 3D folding structure formed by different genomic regions of a chromosome is still poorly understood. So far, only relatively simple geometric features, like distances and angles between different genomic regions, have been evaluated. This work is concerned with more complex geometric properties, i.e., the complete shape formed by genomic regions. Our work is based on statistical shape theory and we use different approaches to analyze the considered structures, e.g., shape uniformity test, 3D point-based registration, Fisher distribution, and 3D non-rigid image registration for shape normalization. We have applied these approaches to analyze 3D microscopy images of the X-chromosome where four consecutive genomic regions (BACs) have been simultaneously labeled by multicolor FISH. We have acquired two sets of four consecutive genomic regions with an overlap of three regions. From the experimental results, it turned out that for all data sets the complete structure is non-random. In addition, we found that the shapes of active and inactive X-chromosomal genomic regions are statistically independent. Moreover, we reconstructed the average 3D structure of chromatin in a small genomic region (below 4 Mb) based on five BACs resulting from two overlapping four BAC regions. We found that geometric normalization with respect to the nucleus shape based on non-rigid image registration has a significant influence on the location of the genomic regions.     

Exploiting the potential of three dimensional spatial wavelet analysis to explore nesting of temporal oscillations and spatial variance in simultaneous EEG-fMRI data

Synchronization of the activity in neural networks is a fundamental mechanism of brain function, putatively serving the integration of computations on multiple spatial and temporal scales. Time scales are thought to be nested within distinct spatial scales, so that whereas fast oscillations may integrate local networks, slow oscillations might integrate computations across distributed brain areas. We here describe a newly developed approach that provides potential for the further substantiation of this hypothesis in future studies. We demonstrate the feasibility and important caveats of a novel wavelet-based means of relating time series of three-dimensional spatial variance (energy) of fMRI data to time series of temporal variance of EEG. The spatial variance of fMRI data was determined by employing the three-dimensional dual-tree complex wavelet transform. The temporal variance of EEG data was estimated by using traditional continuous complex wavelets. We tested our algorithm on artificial signals with known signal-to-noise ratios and on empirical resting state EEG-fMRI data obtained from four healthy human subjects. By employing the human posterior alpha rhythm as an exemplar, we demonstrated face validity of the approach. We believe that the proposed method can serve as a suitable tool for future research on the spatiotemporal properties of brain dynamics, hence moving beyond analyses based exclusively in one domain or the other.     

Analysis of models of irregular shape by solution X-ray scattering: the case of the 50S ribosomal subunit from E. coli

Structural models of biological macromolecules can be tested by comparing calculated and experimental solution scattering curves. We have developed an approach for computing scattering shape functions at medium resolution from models proposed on the basis of other techniques such as electron microscopy. We present the results obtained with the 50S ribosomal subunit from Escherichia coli; two models are considered, one proposed by Lake (1976), the other one by Tischendorf et al. (1975). Although the two models are similar in many respects, their scattering shape functions are significantly different. The comparison with the experimental scattering curve allows us to check the scale of the models and, after scaling, to quantitate the agreement between the observed and the calculated curves. Finally, it can provide a starting point for the structural interpretation of the X-ray data.     

The shape of supertrees to come: tree shape related properties of fourteen supertree methods

Using a simple example and simulations, we explore the impact of input tree shape upon a broad range of supertree methods. We find that input tree shape can affect how conflict is resolved by several supertree methods and that input tree shape effects may be substantial. Standard and irreversible matrix representation with parsimony (MRP), MinFlip, duplication-only Gene Tree Parsimony (GTP), and an implementation of the average consensus method have a tendency to resolve conflict in favor of relationships in unbalanced trees. Purvis MRP and the average dendrogram method appear to have an opposite tendency. Biases with respect to tree shape are correlated with objective functions that are based upon unusual asymmetric tree-to-tree distance or fit measures. Split, quartet, and triplet fit, most similar supertree, and MinCut methods (provided the latter are interpreted as Adams consensus-like supertrees) are not revealed to have any bias with respect to tree shape by our example, but whether this holds more generally is an open problem. Future development and evaluation of supertree methods should consider explicitly the undesirable biases and other properties that we highlight. In the meantime, use of a single, arbitrarily chosen supertree method is discouraged. Use of multiple methods and/or weighting schemes may allow practical assessment of the extent to which inferences from real data depend upon methodological biases with respect to input tree shape or size.     

System for flow sorting chromosomes on the basis of pulse shape

Sorting on the basis of the complex features resolved by chromosome slit-scan analysis requires rapid and flexible pulse shape acquisition and processing for determining sort decisions before droplet breakoff. Fluorescence scans of chromosome morphology contain centromeric index and banding information suitable for chromosome classification, but these scans are often characterized by variability in length and height and require sophisticated data processing procedures for identification. Setting sort criteria on such complex morphological data requires digitization and subsequent computation by an algorithm tolerant of variations in overall pulse shape. We demonstrate here the capability to sort individual chromosomes based on their morphological features measured by slit-scan flow cytometry. To do this we have constructed a sort controller capable of acquiring an 128 byte chromosome waveform and executing a series of numerical computations resulting in an area-based centromeric index sort decision in less than 2 ms. The system is configured in a NOVIX microprocessor, programmed in FORTH, and interfaced to a slit-scan flow cytometer data acquisition system. An advantage of this configuration is direct control over the machine state during program execution for minimal processing time. Examples of flow sorted chromosomes are shown with their corresponding fluorescence pulse shapes.     

Hierarchical processing of tactile shape in the human brain

It is not known exactly which cortical areas compute somatosensory representations of shape. This was investigated using positron emission tomography and cytoarchitectonic mapping. Volunteers discriminated shapes by passive or active touch, brush velocity, edge length, curvature, and roughness. Discrimination of shape by active touch, as opposed to passive touch, activated the right anterior lobe of cerebellum only. Areas 3b and 1 were activated by all stimuli. Area 2 was activated with preference for surface curvature changes and shape stimuli. The anterior part of the supramarginal gyrus (ASM) and the cortex lining the intraparietal sulcus (IPA) were activated by active and passive shape discrimination, but not by other mechanical stimuli. We suggest, based on these findings, that somatosensory representations of shape are computed by areas 3b, 1, 2, IPA, and ASM in this hierarchical fashion.     

Design of interacting multi-stable nucleic acids for molecular information processing

Despite an exponential increase in computing power over the past decades, present information technology falls far short of expectations in areas such as cognitive systems and micro robotics. Organisms demonstrate that it is possible to implement information processing in a radically different way from what we have available in present technology, and that there are clear advantages from the perspective of power consumption, integration density, and real-time processing of ambiguous data. Accordingly, the question whether the current silicon substrate and associated computing paradigm is the most suitable approach to all types of computation has come to the fore. Macromolecular materials, so successfully employed by nature, possess uniquely promising properties as an alternate substrate for information processing. The two key features of macromolecules are their conformational dynamics and their self-assembly capabilities. The purposeful design of macromolecules capable of exploiting these features has proven to be a challenge, however, for some groups of molecules it is increasingly practicable. We here introduce an algorithm capable of designing groups self-assembling of nucleic acid molecules with multiple conformational states. Evaluation using natural and artificially designed nucleic acid molecules favours this algorithm significantly, as compared to the probabilistic approach. Furthermore, the thermodynamic properties of the generated candidates are within the same approximation as the customised trans-acting switching molecules reported in the laboratory.     

Glomerular permselection: shape and flow

The selective permeability of the glomerular basement membrane to macromolecules is a function of the size and charge of the macromolecule. Evidence suggests that shape may also be a factor. The orientation of macromolecules in solution is dependent on their size, shape, and frictional interactions with moving solvent molecules. The spaces between the glomerular visceral epithelial cells (slit pores) may produce a non-uniform distribution of fluid flow within the basement membrane, and this non-uniformity may increase during disease. This report is of a model that relates the filtration of rigid prolate ellipsoidal (cigar) shaped macromolecules to the size and shape of the filter and to the velocity of solvent flow. The calculations, using published macromolecular and glomerular parameters correspond well to published data. The glomerular visceral epithelial cell, by altering the number, size and distribution of the intercellular spaces, may regulate the passage of ellipsoidal shaped macromolecules, such as albumin and IgG, into and through glomerular structures.     

Vascular patterning and leaf shape

Morphogenesis of leaf shape and formation of the major elements of leaf vasculature are temporally coordinated during leaf development. Current analyses of mutant phenotypes provide strong support for the role of auxin signaling in vascular pattern formation and indicate that leaf shape and vasculature are developmentally coupled. Two other mechanisms that may contribute to the regulation of these processes are a diffusion-reaction system and long-distance signaling of informational macromolecules.     

Protein structure alignment and fast similarity search using local shape signatures

We present a new method for conducting protein structure similarity searches, which improves on the efficiency of some existing techniques. Our method is grounded in the theory of differential geometry on 3D space curve matching. We generate shape signatures for proteins that are invariant, localized, robust, compact, and biologically meaningful. The invariancy of the shape signatures allows us to improve similarity searching efficiency by adopting a hierarchical coarse-to-fine strategy. We index the shape signatures using an efficient hashing-based technique. With the help of this technique we screen out unlikely candidates and perform detailed pairwise alignments only for a small number of candidates that survive the screening process. Contrary to other hashing based techniques, our technique employs domain specific information (not just geometric information) in constructing the hash key, and hence, is more tuned to the domain of biology. Furthermore, the invariancy, localization, and compactness of the shape signatures allow us to utilize a well-known local sequence alignment algorithm for aligning two protein structures. One measure of the efficacy of the proposed technique is that we were able to perform structure alignment queries 36 times faster (on the average) than a well-known method while keeping the quality of the query results at an approximately similar level.