Voronoi and Voronoi-related tessellations in studies of protein structure and interaction

The three-dimensional structure of a protein can be modeled by a set of polyhedra drawn around its atoms or residues. The tessellation invented by Voronoi in 1908, and other tessellations of space derived from it, provide versatile representations of three-dimensional structures. In recent years, they have been used to investigate a series of issues relating to proteins: atom and residue volumes, packing, folding, interactions and binding.     

Voro3D: 3D Voronoi tessellations applied to protein structures

SUMMARY: Voro3D is an original easy-to-use tool, which provides a brand new point of view on protein structures through the three-dimensional (3D) Voronoi tessellations. To construct the Voronoi cells associated with each amino acid by a number of different tessellation methods, Voro3D uses a protein structure file in the PDB format as an input. After calculation, different structural properties of interest like secondary structures assignment, environment accessibility and exact contact matrices can be derived without any geometrical cut-off. Voro3D provides also a visualization of these tessellations superimposed on the associated protein structure, from which it is possible to model a polygonal protein surface using a model solvent or to quantify, for instance, the contact areas between a protein and a ligand. AVAILABILITY: The software executable file for PC using Windows 98, 2000, NT, XP can be freely downloaded at http://www.lmcp.jussieu.fr/~mornon/voronoi.html CONTACT: franck.dupuis@sanofi-aventis.com; jean-paul-mornon@imcp.jussieu.fr.     

A simple procedure for simulating samples of tissue using Voronoi diagrams

OBJECTIVE: To describe a simple and quick procedure for modeling samples of tissue with Voronoi diagrams. STUDY DESIGN: Instead of calculating the centers of the so-called Dirichlet domains (i.e., the polygonal areas occupied by individual cells), the centroid of such areas is used to generate Voronoi diagrams. The coordinates of the centroids are calculated by simply averaging the coordinates of the points of the cell contours; that is much simpler and faster than any geometric procedure for locating the Dirichlet centers. Using the centroids as centers, circles are allowed to grow until no space on the surface is available. With this procedure it is easy to control the rate of growth of individual cells or groups of cells according to any rule or rules. It is also possible to simulate the effects of removing > or = 1 cells from the sample. CONCLUSION: The procedure was successfully applied to modeling some of the changes that can occur in a real sample of human corneal endothelium. The procedure is simple, completely automated, efficient and flexible and can be easily implemented on a personal computer. It can be used to test growth or communication strategies among cells.     

Ripening‐induced acceleration of volatile aldehyde generation following tissue disruption in tomato fruit

Hexanal and cis-3-hexenal are principal flavor volatiles in ripe tomato fruit, but whether they accumulate during ripening or are formed upon maceration of the tissue has not been clarified. This has been addressed by measuring levels of these aldehydes in green and ripe fruit with discrimination between intrinsic aldehyde content and aldehyde generation following tissue disruption. Volatile sampling of tomato fruit homogenates was accomplished by purge/trapping, followed by thermal desorption on a gas chromatograph equipped with a mass selective detector. Incubation of some samples with alcohol dehydrogenase to convert the aldehydes to their respective alcohols permitted positive identification of the isomeric form of hexenal as cis-3-hexenal. Red and green tomato fruit homogenized in buffer with saturated CaCl₂ contained low (0.1-0.8 µg g^?1 fresh weight) levels of hexanal and cis-3-hexenal; thus there is minimal endogenous volatile content in intact fruit. Volatile levels increased rapidly, up to 10-fold, following homogenization of ripe tomato fruit in the absence of CaCl₂, and more modestly in corresponding green tomato fruit homogenates. Incubation with the appropriate lipoxygenase/hydroperoxide lyase substrate (linoleic acid for hexanal, linolenic acid for cis-3-hexenal) doubled the amount of volatile compound produced. Hexanal generation was suppressed in the presence of linolenic acid, suggesting that the enzyme complex has greater affinity for this substrate. As well, levels of cis-3-hexenal, but not hexanal, tended to decline within 30 min of homogenization, possibly reflecting a specific degradative process. The results collectively indicate that the contribution of six-carbon aldehydes to tomato fruit flavor is attributable to metabolism invoked following tissue disruption rather than within the intact fruit.     

Vorolign--fast structural alignment using Voronoi contacts

Vorolign, a fast and flexible structural alignment method for two or more protein structures is introduced. The method aligns protein structures using double dynamic programming and measures the similarity of two residues based on the evolutionary conservation of their corresponding Voronoi-contacts in the protein structure. This similarity function allows aligning protein structures even in cases where structural flexibilities exist. Multiple structural alignments are generated from a set of pairwise alignments using a consistency-based, progressive multiple alignment strategy. RESULTS: The performance of Vorolign is evaluated for different applications of protein structure comparison, including automatic family detection as well as pairwise and multiple structure alignment. Vorolign accurately detects the correct family, superfamily or fold of a protein with respect to the SCOP classification on a set of difficult target structures. A scan against a database of >4000 proteins takes on average 1 min per target. The performance of Vorolign in calculating pairwise and multiple alignments is found to be comparable with other pairwise and multiple protein structure alignment methods. AVAILABILITY: Vorolign is freely available for academic users as a web server at http://www.bio.ifi.lmu.de/Vorolign     

A clearance method of measuring tissue blood flow using electrochemical generation of hydrogen

Practical approaches are elaborated as to application of the clearance method using electrochemical hydrogen generation to measure volume blood flow velocity in human and animal organs and tissues. Results from this elaboration and analysis of the obtained experimental data are presented. Some specific features of the method are described.     

Ethylene production by wounded tissue of citrus fruit

Segments cut from young immature fruits and albedo discs excisedfrom both immature and mature fruits of Satsuma mandarin ormature fruits of Natsudaidai produced much ethylene during incubationat 26?C in the dark. Ethylene formation was markedly acceleratedby the application of abscisic acid but markedly delayed by3,5-dibromo-4-hydroxybenzoic acid. Both the stimulation andretardation decreased greatly during the course of incubation.Both compounds seem to be associated with the early stages ofethylene formation by wounded citrus fruit tissues. Albedo discs were fed ¹⁴C methionine labeled at one of threedifferent positions. Of the three radioanalogs (carbon-2, carbon-3and methyl carbon), the label at the 3 position was preferentiallyincorporated into ethylene. This agrees with the former observationthat ethylene is derived from carbon-3 and -4 of methionine.Incorporation of label into ethylene from L-[3-¹⁴C] methioninewas strongly inhibited by L-canaline, L-ethionine, 2,4-dinitrophenoland cycloheximide. Ethylene evolution was also strongly inhibitedby 2,4-dinitrophenol, KCN, NaN₃ and cycloheximide, but lesscompletely by L-canaline and L-ethionine. These results supportthe view that ATP and pyridoxal phosphate are utilized in activationof methionine to form ethylene. (Received October 25, 1977; )     

Soluble and wall-bound glycoproteins of apple fruit tissue

Apple fruit tissue contains small amounts of readily soluble glycoproteins, rich in hydroxyproline; polymethylgalacturonide is not covalently bound to the soluble glycoproteins. Barium hydroxide hydrolysis of apple fruit cell walls liberated glycopeptides containing 4 arabinosyl residues per hydroxyprolyl residue, which were attacked very slowly by α-l-arabinofuranosidase. Hydrazinolysis liberated similar glycopeptides, which were difficult to separate from a polysaccharide containing galactose residues. Protease treatment of walls also released glycopeptides containing hydroxyproline, and a small proportion of these were associated with polyuronide. Polygalacturonase pretreatment of walls led to increased release of hydroxyprolyl residues by protease. Susceptibility of the hydroxyproline containing glycoprotein in the cell wall to attack by protease and arabinosidase did not change during fruit ripening. The amount of an unknown hexosamine associated with the wall was less in ripethan in unripe fruit.     

Heat generation in laser irradiated tissue

Many medical applications involving lasers rely upon the generation of heat within the tissue for the desired therapeutic effect. Determination of the absorbed light energy in tissue is difficult in many cases. Although UV wavelengths of the excimer laser and 10.6 microns wavelength of the CO2 laser are absorbed within the first 20 microns of soft tissue, visible and near infrared wavelengths are scattered as well as absorbed. Typically, multiple scattering is a significant factor in the distribution of light in tissue and the resulting heat source term. An improved model is presented for estimating heat generation due to the absorption of a collimated (axisymmetric) laser beam and scattered light at each point r and z in tissue. Heat generated within tissue is a function of the laser power, the shape and size of the incident beam and the optical properties of the tissue at the irradiation wavelength. Key to the calculation of heat source strength is accurate estimation of the light distribution. Methods for experimentally determining the optical parameters of tissue are discussed in the context of the improved model.     

Water relations and growth of tomato fruit pericarp tissue

The water relations of young tomato fruit pericarp tissue were examined and related to tissue expansion. The relationship between bulk turgor pressure and tissue expansion (as change in fresh mass or length of tissue) was determined in slices of pericarp cut from young, growing fruit by incubation in different osmotic concentrations of polyethylene glycol 6000 or mannitol. The bulk turgor of this tissue was low (about 0.2 MPa), even in fruit from plants that were otherwise fully turgid, whether measured psychrometrically or by length change in osmotic solutions. The rate of tissue growth at maximum turgor was less than that at moderate turgor unless calcium was added to the incubation medium. However, added calcium also decreased the rate of growth at lower turgor pressures. Yield turgor was < 0.1 MPa, but it was increased by the addition of calcium ions. Electrolyte leakage from tissue was greatest at maximum turgor pressure but was decreased by the addition of calcium ions or osmoticum. Tissue growth was unaffected by a range of plant growth regulators (IAA, abscisic acid, benzyladenine and GA₃) but was inhibited, particularly at high turgor, by low concentrations of malic or citric acid. The low turgor pressure of pericarp tissue could be due to the presence of apoplastic solutes within the pericarp, and evidence for this is discussed. Thus, fruit tissue may be able to maintain optimal expansion rates only at moderate turgor and low calcium concentration.     

Visualization of fruit scent using photoluminescence

Photoluminescence with visible emission spectrum was observed and visualized at the surface of certain fruits. This photoluminescence is associated with vapors of natural organic volatiles (odorants) emitted from the fruit surface. The photoluminescence spectra of various fruits (apple, pear, kiwi, and strawberry) were measured in vivo using a number of fluorimetric methods. Fruit aging was found to be accompanied by modification of the photoluminescence spectrum shape and a noticeable increase in the photoluminescence intensity. Laser photoluminescence microscopy in vapors of fruit extracts and artificial compounds was used to assess the contribution of various substances to natural odor emission of fruits. The results of the study show that fluorimetry of odors is a promising method for studying fruits and other objects.     

Skin tissue generation by laser cell printing

For the aim of ex vivo engineering of functional tissue substitutes, Laser-assisted BioPrinting (LaBP) is under investigation for the arrangement of living cells in predefined patterns. So far three-dimensional (3D) arrangements of single or two-dimensional (2D) patterning of different cell types have been presented. It has been shown that cells are not harmed by the printing procedure. We now demonstrate for the first time the 3D arrangement of vital cells by LaBP as multicellular grafts analogous to native archetype and the formation of tissue by these cells. For this purpose, fibroblasts and keratinocytes embedded in collagen were printed in 3D as a simple example for skin tissue. To study cell functions and tissue formation process in 3D, different characteristics, such as cell localisation and proliferation were investigated. We further analysed the formation of adhering and gap junctions, which are fundamental for tissue morphogenesis and cohesion. In this study, it was demonstrated that LaBP is an outstanding tool for the generation of multicellular 3D constructs mimicking tissue functions. These findings are promising for the realisation of 3D in vitro models and tissue substitutes for many applications in tissue engineering.     

Vascular tissue engineering: the next generation

It is the ultimate goal of tissue engineering: an autologous tissue engineered vascular graft (TEVG) that is immunologically compatible, nonthrombogenic, and can grow and remodel. Currently, native vessels are the preferred vascular conduit for procedures such as coronary artery bypass (CABG) or peripheral bypass surgery. However, in many cases these are damaged, have already been harvested, or are simply unusable. The use of synthetic conduits is severely limited in smaller diameter vessels due to increased incidence of thrombosis, infection, and graft failure. Current research has therefore energetically pursued the development of a TEVG that can incorporate into a patient's circulatory system, mimic the vasoreactivity and biomechanics of the native vasculature, and maintain long-term patency.     

Virtual screening using molecular simulations

Effective virtual screening relies on our ability to make accurate prediction of protein-ligand binding, which remains a great challenge. In this work, utilizing the molecular-mechanics Poisson-Boltzmann (or Generalized Born) surface area approach, we have evaluated the binding affinity of a set of 156 ligands to seven families of proteins, trypsin β, thrombin α, cyclin-dependent kinase (CDK), cAMP-dependent kinase (PKA), urokinase-type plasminogen activator, β-glucosidase A, and coagulation factor Xa. The effect of protein dielectric constant in the implicit-solvent model on the binding free energy calculation is shown to be important. The statistical correlations between the binding energy calculated from the implicit-solvent approach and experimental free energy are in the range of 0.56-0.79 across all the families. This performance is better than that of typical docking programs especially given that the latter is directly trained using known binding data whereas the molecular mechanics is based on general physical parameters. Estimation of entropic contribution remains the barrier to accurate free energy calculation. We show that the traditional rigid rotor harmonic oscillator approximation is unable to improve the binding free energy prediction. Inclusion of conformational restriction seems to be promising but requires further investigation. On the other hand, our preliminary study suggests that implicit-solvent based alchemical perturbation, which offers explicit sampling of configuration entropy, can be a viable approach to significantly improve the prediction of binding free energy. Overall, the molecular mechanics approach has the potential for medium to high-throughput computational drug discovery.     

Ethephon application induces symptoms of fruit tissue degeneration in watermelon

Vegetable Research Division, NHRI, 475 Imok-dong, Jangan-gu, Suwon, Gyeonggi-do, 440-706, Republic of Korea Flesh tissue degeneration (called blood-black heart; BBH) of watermelon (Citrullus vulgaris S.) is occasionally observed in Korea. Fruits with BBH have lower quality, a dark-red flesh, and reduced firmness of the rind, often producing an unpleasant flavor. Although causal factors are thought to be undesirable soil moisture conditions, e.g., drought or water-logging, temperature extremes, or virus infection, the mechanism for this physiological disorder is not clearly understood. It is possible that ethylene gas (C₂H₄) is involved in degrading the cell walls. To determine such an implication for ethylene in the occurrence of BBH, we foliar-applied various concentrations of ethephon (100, 200, 400, 800, or 1000 mg L^-1) to watermelon plants at 5 or 10 d prior to harvesting, then monitored the development of this disorder in their fruits. At 400 mg L^-1 or higher, quality was diminished and the fruit had softer rind tissues. About 25% of the fruits harvested at that level exhibited BBH versus 100% of the fruits exposed to 800 or 1000 mg L^-1 ethephon. Concomitant with the onset of BBH, those affected fruits produced elevated amounts of ethylene gas during the 4-d measurement period. Therefore, a high incidence of BBH may well be related to this increased ethylene production, which can be triggered by both unfavorable environmental conditions and inappropriate cultural practices.     

Metabolism of polymethylgalacturonate in apple fruit cortical tissue during ripening

Changes in the composition and metabolism of polymethylgalacturonate were followed in ripening apples. After the onset of ethylene production and fruit softening total polygalacturonate decreased and the water soluble fraction increased. No change was detected in the overall degree of esterification but the esterification of the water soluble fraction increased. Incorporation of radioactivity from methionine-[¹⁴C] into Me groups on polygalacturonate continued during ripening but incorporation from inositol-[³H] decreased sharply. Cell separation probably depends upon the removal of low ester polygalacturonate from the middle lamella by exopolygalacturonase; the continued incorporation from methionine-[¹⁴C] is probably due to synthesis of new polymethylgalacturonate.     

Use of starch-gelled medium for tissue culture of some fruit crops

Six cultivars of apple and two of red raspberry consistently produced equal or significantly better shoot proliferation on modified Murashige and Skoog medium gelled with a mixture of corn starch and Gelrite than on the same medium gelled with agar. Two pear cultivars grown on starch-Gelrite medium produced hyperhydric shoots and almost no growth, but the addition of a polysaccharide hydric control (antivitrifying) agent to the medium eliminated hyperhydricity. The resulting shoot proliferation equaled or exceeded that on the agar-gelled medium. The starch-Gelrite mixture is easy to prepare and gelling agent costs are only 10–15% of agar, or less if starch is purchased in bulk. Although the opaque gray-white medium makes it more difficult to detect internal contaminants, external contaminants are easily discerned.The US Government's right to retain a non-exclusive royalty-free license on and to any copyright is acknowledged.