Size-independent comparison of protein three-dimensional structures

Protein structures are routinely compared by their root-mean-square deviation (RMSD) in atomic coordinates after optimal rigid body superposition. What is not so clear is the significance of different RMSD values, particularly above the customary arbitrary cutoff for obvious similarity of 2–3 Å. Our earlier work argued for an intrinsic cutoff for protein similarity that varied with the number of residues in the polypeptide chains being compared. Here we introduce a new measure, ρ, of structural similarity based on RMSD that is independent of the sizes of the molecules involved, or of any other special properties of molecules. When ρ is less than 0.4–0.5, protein structures are visually recognized to be obviously similar, but the mathematically pleasing intrinsic cutoff of ρ>1.0 corresponds to overall similarity in folding motif at a level not usually recognized until smoothing of the polypeptide chain path makes it striking. When the structures are scaled to unit radius of gyration and equal principle moments of inertia, the comparisons are even more universal, since they are no longer obscured by differences in overall size and ellipticity. With increasing chain length, the distribution of ρ for pairs of random structures is skewed to higher values, but the value for the best 1% of the comparisons rises only slowly with the number of residues. This level is close to an intrinsic cutoff between similar and dissimilar comparisons, namely the maximal scaled ρ possible for the two structures to be more similar to each other than one is to the other's mirror image. The intrinsic cutoff is independent of the number of residues or points being compared. For proteins having fewer than 100 residues, the 1% ρ falls below the intrinsic cutoff, so that for very small proteins, geometrically significant similarity can often occur by chance. We believe these ideas will be helpful in judging success in NMR structure determination and protein folding modeling. © 1995 Wiley-Liss, Inc.     

SimRoot: Modelling and visualization of root systems

SimRoot, a geometric simulation model of plant root systems, is described. This model employs a data structure titled the Extensible Tree, which is well suited to the type of data required to model root systems. As implemented on Silicon Graphics workstations, the data structure and visualization code provides for continuous viewing of the simulated root system during growth. SimRoot differs from existing models in the explicit treatment of spatial heterogeneity of physiological processes in the root system, and by inclusion of a kinematic treatment of root axes. Examples are provided of the utility of the model in estimating the fractal geometry of simulated root systems in 1, 2, and 3 dimensional space. We envision continued development of the model to incorporate competition from neighboring root systems, linkage with crop simulation models to simulate root-shoot interactions, explicit treatment of soil heterogeneity, and plasticity of root responses to soil factors such as presence of mycorrhizal associations.     

Human procarboxypeptidase B: three-dimensional structure and implications for thrombin-activatable fibrinolysis inhibitor (TAFI)

Besides their classical role in alimentary protein degradation, zinc-dependant carboxypeptidases also participate in more selective regulatory processes like prohormone and neuropeptide processing or fibrinolysis inhibition in blood plasma. Human pancreatic procarboxypeptidase B (PCPB) is the prototype for those human exopeptidases that cleave off basic C-terminal residues and are secreted as inactive zymogens. One such protein is thrombin-activatable fibrinolysis inhibitor (TAFI), also known as plasma PCPB, which circulates in human plasma as a zymogen bound to plasminogen. The structure of human pancreatic PCPB displays a 95-residue pro-segment consisting of a globular region with an open-sandwich antiparallel-alpha antiparallel-beta topology and a C-terminal alpha-helix, which connects to the enzyme moiety. The latter is a 309-amino acid residue catalytic domain with alpha/beta hydrolase topology and a preformed active site, which is shielded by the globular domain of the pro-segment. The fold of the proenzyme is similar to previously reported procarboxypeptidase structures, also in that the most variable region is the connecting segment that links both globular moieties. However, the empty active site of human procarboxypeptidase B has two alternate conformations in one of the zinc-binding residues, which account for subtle differences in some of the key residues for substrate binding. The reported crystal structure, refined with data to 1.6A resolution, permits in the absence of an experimental structure, accurate homology modelling of TAFI, which may help to explain its properties.     

木本植物的构型及其在植物生态学研究的进展

一般认为 ,木本植物的植株结构由枝系和根系两个亚系统构成[5,3 8] 。其地上部分的枝或茎的顶端分生组织和侧生分生组织通过不断重复的、持续的活动产生新的分枝 ,构成了复杂的枝系结构和多样的形态特征。传统的植物学研究中曾以树木的形态特征作为植物形态学、分类学和植被类型划分的依据。由于植物种群生态学中构件理论的提出[6,4 1] ,人们已经意识到植物体的各构件单元之间的关系和等级结构 ,认为木本植物地上部分存在着两种尺度的整合 ,即各构件单元在枝条水平上的整合以及各枝条构成的冠幅复合体[1,2 1] 。植物体不同的枝系特征以及枝…     

Root architecture in cultivated and wild lettuce (Lactuca spp.)

Root architecture is described for intact root systems of cultivated (Lactuca sativa L.) and wild (L. serriola L.) lettuce, grown for 5 to 6 weeks in greenhouse pot and cylinder experiments in coarse-textured soil. L. sativa cv. Salinas and a sclinas line of L. serriola attained the same biomass at 4 to 6 weeks after planting. Root biomass allocation was also similar, but root architecture differed. In the top zone along the tap root (0 to 5 cm), Salinas tended to produce more laterals, a greater total root length, and more external links (segments that originate at a branch point and end in a meristem) than wild lettuce. In the 5 to 55cm zone of the tap root, these measures were greater in the wild species. These patterns of root structure were generally corroborated by a second cylinder study with a different pair of L. sativa and L. serriola. Regressions of root structural traits were made against total root dry weight as a means to compare root architecture independently of the size of the root system. Regressions demonstrated that production of root segments differed between the two species; for example the slope for the regression of summed external link length in the top 0 to 5 cm with total root dry weight was significantly higher for Salinas, indicating that the rate of construction in the top 0 to 5cm was greater for cultivated than for wild lettuce. Yet, from 5 cm depth to the tap root tip, the rate of construction of external link length was greater in L. serriola. For many of these types of regression, r² and mean slope ± SE suggested that more variation occurred in cultivated than wild lettuce, yet genetic heterogeneity was probably low within the studied taxa. Inadvertent selection may have occurred in the breeding of cultivated lettuce varieties for increased root growth in the surface zone where water and fertilizer are applied, and for greater plasticity in construction of root segments, which might maximize the efficiency of exploitation of soil moisture and nutrients.     

Automated measurement of root length with a three-dimensional high-resolution scanner and image analysis

For measuring the length of root samples, the use of a three-dimensional (3D) scanner is proposed to address the problem of a too low resolution. The scanner's high resolution (up to 354 pixels per cm) enables in the resulting grey-value image very thin roots (diameter 100 m) to be segmented from the background by a simple thresholding operation. After skeletonizing, total length of the roots is calculated by multiplying the number of skeleton pixels by a correction factor. A comparison with the modified Newman Line-Intersect Method showed a correlation of r=0.98. Besides its superior resolution, an advantage of this type of scanner is its focusing depth, which allows root samples to be recorded on the scanbed similarly to a camera-oriented system.     

A comparative view at comprehensive information resources on three-dimensional structures of biological macro-molecules.

The rapidly increasing amount of information on three-dimensional (3D) structures of biological macro-molecules has still an insufficient impact on genome analysis, functional genomics and proteomics as well as on many other fields in biomedicine including disease-related research. There are, however, attempts to make structural data more easily accessible to the bench biologist. As members of the world-wide Protein Data Bank (wwPDB), the RCSB Protein Data Bank (PDB), the Protein Data Bank Japan and the Macromolecular Structure Database are the primary information resources for 3D structures of proteins, nucleic acids, carbohydrates and complexes thereof. In addition, a number of secondary resources have been set up that also provide information on all currently known structures in a relatively comprehensive manner and not focusing on specific features only. They include PDBsum, the OCA browser-database for protein structure/function, the Molecular Modeling Database and the Jena Library of Biological Macromolecules--JenaLib. Both the primary and secondary resources often merge the information in the PDB files with data from other resources and offer additional analysis tools thereby adding value to the original PDB data. Here, we briefly describe these resources from a user's point of view and from a comparative perspective. It is our aim to guide researchers outside the structure biology field in getting the most out of the 3D structure resources.     

Patterns of variability in the diameter of lateral roots in the banana root system

The relative importance of root system structure, plant carbon status and soil environment in the determination of lateral root diameter remains unclear, and was investigated in this study. Banana (Musa acuminata) plants were grown at various moderate levels of soil compaction in two distinct experiments, in a field experiment (FE) and in a glasshouse experiment (GE). Radiant flux density was 5 times lower in GE. The distribution of root diameter was measured for several root branching orders. Root diameters ranged between 0.09 and 0.52 mm for secondary roots and between 0.06 and 0.27 mm for tertiary roots. A relationship was found between the diameter of the parent bearing root and the median diameter of its laterals, which appears to be valid for a wide range of species. Mean lateral root diameter increased with distance to the base of the root and decreased with branching density [number of lateral roots per unit length of bearing root (cm(-1))]. Typical symptoms of low light availability were observed in GE. In this case, lateral root diameter variability was reduced. Although primary root growth was affected by soil compaction, no effects on lateral root diameter were observed.     

Fractal geometry of bean root systems: correlations between spatial and fractal dimension

An obstacle to the study of root architecture is the difficulty of measuring and quantifying the three-dimensional configuration of roots in soil. The objective of this work was to determine if fractal geometry might be useful in estimating the three-dimensional complexity of root architecture from more accessible measurements. A set of results called projection theorems predict that the fractal dimension (FD) of a projection of a root system should be identical to the FD of roots in three-dimensional space (three-dimensional FD). To test this prediction we employed SimRoot, an explicit geometric simulation model of root growth derived from empirical measurements of common bean (Phaseolus vulgaris L.). We computed the three-dimensional FD, FD of horizontal plane intercepts (planar FD), FD of vertical line intercepts (linear FD), and FD of orthogonal projections onto planes (projected FD). Three-dimensional FD was found to differ from corresponding projected FD, suggesting that the analysis of roots grown in a narrow space or excavated and flattened prior to analysis is problematic. A log-linear relationship was found between FD of roots and spatial dimension. This log-linear relationship suggests that the three-dimensional FD of root systems may be accurately estimated from excavations and tracing of root intersections on exposed planes.     

节杆菌K1108乙内酰脲酶三维结构的模建和分析

利用同源模建技术,以节杆菌DSM3745乙内酰脲酶的晶体结构为模板,模建了节杆菌K1108乙内酰脲酶的三维结构。模建的节杆菌K1108乙内酰脲酶结构由一个中心的(α/β)g捅状结构域和富含β-折叠的结构域两个区域组成,富含β-折叠的结构域在中心(α/β)g捅状结构域的侧面,由分子的N端和C端组成。根据K1108乙内酰脲酶和其它酶在结构和活性部位的保守性,确定了K1108乙内酰脲酶的底物结合部位,并对酶的活性中心的特征进行了分析,对L-Hyd的底物选择性进行了解释。     

Interactive visual exploration of overlapping similar structures for three-dimensional microscope images

Background

Recent advances in microscopy enable the acquisition of large numbers of tomographic images from living tissues. Three-dimensional microscope images are often displayed with volume rendering by adjusting the transfer functions. However, because the emissions from fluorescent materials and the optical properties based on point spread functions affect the imaging results, the intensity value can differ locally, even in the same structure. Further, images obtained from brain tissues contain a variety of neural structures such as dendrites and axons with complex crossings and overlapping linear structures. In these cases, the transfer functions previously used fail to optimize image generation, making it difficult to explore the connectivity of these tissues.

Results

This paper proposes an interactive visual exploration method by which the transfer functions are modified locally and interactively based on multidimensional features in the images. A direct editing interface is also provided to specify both the target region and structures with characteristic features, where all manual operations can be performed on the rendered image. This method is demonstrated using two-photon microscope images acquired from living mice, and is shown to be an effective method for interactive visual exploration of overlapping similar structures.

Conclusions

An interactive visualization method was introduced for local improvement of visualization by volume rendering in two-photon microscope images containing regions in which linear nerve structures crisscross in a complex manner. The proposed method is characterized by the localized multidimensional transfer function and interface where the parameters can be determined by the user to suit their particular visualization requirements.     

Characterisation of structural tree root architecture using 3D digitising and AMAPmod software

A low-magnetic-field digitising device combined with AMAPmod, a software designed to analyse plant architecture, provided a very efficient method for measuring and studying the geometry and topology of the structural roots of trees. The digitising device measures co-ordinates in a 3D space. AMAPmod was used to assess several characteristics of the root architecture including spatial position, root lengths and volumes, branching order and branching pattern, and to reconstruct 3D images from the data to check for measurement errors. Structural root systems of three 20 to 28-year-old Quercus petraea and thirty 5-year-old Pinus pinaster were uprooted by using rapid mechanised techniques. Only roots with a diamter larger than 2 mm were measured. A fast and precise spatial localisation in combination with the topological characterisation of all root segments was carried out. Oak showed a stronger more oblique and vertical rooting, more branches, more forks and narrower branching angles than pine. Oak had only few small roots in the north west direction whereas half of pine root volume was located in the 10 cm upper soil volume. The contribution of this new method in the characterisation of structural root systems is discussed and other possible applications of this method in root studies are proposed. Since this method is precise and fairly rapid, it may be used for agronomic testing (i.e. comparing treatments) involving several dozen root systems. Almost all parameters needed for tree root system simulations can be estimated from such data. This revised version was published online in June 2006 with corrections to the Cover Date.     

Evolution of protein 3D structures as diffusion in multidimensional conformational space

A theory of protein spatial-structure evolution in terms of random walks in multidimensional conformational space is proposed. It is shown that the spatial divergence in pairs of homologous proteins depends only on their sequence similarity and is independent of the protein size. X-ray data are reasonably well described in terms of the theory developed. Correspondence to: A.M. Gutin     

Relationship between sequence conservation and three-dimensional structure in a large family of esterases, lipases, and related proteins.

Based on the recently determined X-ray structures of Torpedo californica acetylcholinesterase and Geotrichum candidum lipase and on their three-dimensional superposition, an improved alignment of a collection of 32 related amino acid sequences of other esterases, lipases, and related proteins was obtained. On the basis of this alignment, 24 residues are found to be invariant in 29 sequences of hydrolytic enzymes, and an additional 49 are well conserved. The conservation in the three remaining sequences is somewhat lower. The conserved residues include the active site, disulfide bridges, salt bridges, and residues in the core of the proteins. Most invariant residues are located at the edges of secondary structural elements. A clear structural basis for the preservation of many of these residues can be determined from comparison of the two X-ray structures.     

Fractal geometry and root system structures of heterogeneous plant communities

Above-ground plant growth is widely known in terms of structural diversity. Likewise, the below-ground growth presents a mosaic of heterogeneous structures of differing complexity. In this study, root system structures of heterogeneous plant communities were recorded as integral systems by using the trench profile method. Fractal dimensions of the root images were calculated from image files by the box-counting method. This method allows the structural complexity of such associations to be compared between plant communities, with regard to their potentials for soil resource acquisition and utilization. Distinct and partly significant differences are found (fractal dimension between 1.46±0.09 and 1.71±0.05) in the below-ground structural complexity of plant communities, belonging to different biotope types. The size of the heterogeneous plant community to be examined has an crucial influence on the fractal dimension of the root system structures. The structural heterogeneity becomes particularly evident (fractal dimensions between 1.32 and 1.77) when analysing many small units of a complex root system association. In larger plant communities, a broad variety of below-ground structures is recorded in its entirety, integrating the specific features of single sub-structures. In that way, extreme fractal dimensions are lost and the diversity decreases. Therefore, the analysis of larger units of root system associations provides a general knowledge of the complexity of root system structures for heterogeneous plant communities.     

3DNA: a versatile, integrated software system for the analysis, rebuilding and visualization of three-dimensional nucleic-acid structures

We present a set of protocols showing how to use the 3DNA suite of programs to analyze, rebuild and visualize three-dimensional nucleic-acid structures. The software determines a wide range of conformational parameters, including the identities and rigid-body parameters of interacting bases and base-pair steps, the nucleotides comprising helical fragments, the area of overlap of stacked bases and so on. The reconstruction of three-dimensional structure takes advantage of rigorously defined rigid-body parameters, producing rectangular block representations of the nucleic-acid bases and base pairs and all-atom models with approximate sugar-phosphate backbones. The visualization components create vector-based drawings and scenes that can be rendered as raster-graphics images, allowing for easy generation of publication-quality figures. The utility programs use geometric variables to control the view and scale of an object, for comparison of related structures. The commands run in seconds even for large structures. The software and related information are available at http://3dna.rutgers.edu/.