Generating Triangulated Macromolecular Surfaces by Euclidean Distance Transform

Macromolecular surfaces are fundamental representations of their three-dimensional geometric shape. Accurate calculation of protein surfaces is of critical importance in the protein structural and functional studies including ligand-protein docking and virtual screening. In contrast to analytical or parametric representation of macromolecular surfaces, triangulated mesh surfaces have been proved to be easy to describe, visualize and manipulate by computer programs. Here, we develop a new algorithm of EDTSurf for generating three major macromolecular surfaces of van der Waals surface, solvent-accessible surface and molecular surface, using the technique of fast Euclidean Distance Transform (EDT). The triangulated surfaces are constructed directly from volumetric solids by a Vertex-Connected Marching Cube algorithm that forms triangles from grid points. Compared to the analytical result, the relative error of the surface calculations by EDTSurf is <2–4% depending on the grid resolution, which is 1.5–4 times lower than the methods in the literature; and yet, the algorithm is faster and costs less computer memory than the comparative methods. The improvements in both accuracy and speed of the macromolecular surface determination should make EDTSurf a useful tool for the detailed study of protein docking and structure predictions. Both source code and the executable program of EDTSurf are freely available at http://zhang.bioinformatics.ku.edu/EDTSurf.     

Analytically defined surfaces to analyze molecular interaction properties

Molecular surfaces are widely used for characterizing molecules and displaying and quantifying their interaction properties. Here we consider molecular surfaces defined as isocontours of a function (a sum of exponential functions centered on each atom) that approximately represents electron density. The smoothness is advantageous for surface mapping of molecular properties (e.g., electrostatic potential). By varying parameters, these surfaces can be constructed to represent the van der Waals or solvent-accessible surface of a molecular with any accuracy. We describe numerical algorithms to operate on the analytically defined surfaces. Two applications are considered: (1) We define and locate extremal points of molecular properties on the surfaces. The extremal points provide a compact representation of a property on a surface, obviating the necessity to compute values of the property on an array of surface points as is usually done; (2) a molecular surface patch or interface is projected onto a flat surface (by introducing curvilinear coordinates) with approximate conservation of area for analysis purposes. Applications to studies of protein-protein interactions are described.     

Approximation and characterization of molecular surfaces

The representation and characterization of molecular surfaces are important in many areas of molecular modeling. Parametric representations of protein molecular surfaces are a compact way to describe a surface, and are useful for the evaluation of surface properties such as the normal vector, principal curvatures, and principal curvature directions. Simplified representations of molecular surfaces are useful for efficient rendering and for the display of large-scale surface features. Several techniques for representing surfaces by expansions of spherical harmonic functions have been reported, but these techniques require that the radius function is single valued, that is, each ray from an origin inside the surface intersects the surface at one and only one point. A new technique is described that removes this limitation and can be used to compute surface shape properties. © 1993 John Wiley & Sons, Inc.     

Texture mapping parametric molecular surfaces

Texture mapping is an increasingly popular technique in molecular modeling. It is particularly effective in representing high-resolution surface detail using a low-resolution polygonal model. We describe how texture mapping can be used with parametric molecular surfaces represented as expansions of spherical harmonic functions. We define analytically the texture image and its transformation to a parametric surface. Unlike most methods of texture mapping, this transformation defines a one-to-one correspondence between the surface and the texture; texture coordinates are derived from the location of the surface point and not from physical properties at the surface point. This has advantates for the interactive visualization of surface data. We control the interactive response time by lowering the resolution of the polygon mesh while retaining the high-resolution detail of the texture, or we can lower the resolution of the texture image with the same polygonal model. By using a well-defined convention for texture coordinates, we can use the same image for the original surface or its parametric representation, and we can rapidly switch between images that represent different surface properties without recomputing the texture coordinates. Parametric surfaces allow new flexibility for the visualization of molecular surface data.     

Patient-specific computational haemodynamics: generation of structured and conformal hexahedral meshes from triangulated surfaces of vascular bifurcations

Measuring the blood flow is still limited by current imaging technologies and is generally overcome using computational fluid dynamics (CFD) which, because of the complex geometry of blood vessels, has widely relied on tetrahedral meshes. Hexahedral meshes offer more accurate results with lower-density meshes and faster computation as compared to tetrahedral meshes, but their use is limited by the far more complex mesh generation. We present a robust methodology for conformal and structured hexahedral mesh generation - applicable to complex arterial geometries as bifurcating vessels - starting from triangulated surfaces. Cutting planes are used to slice the lumen surface and to construct longitudinal Bezier splines. Afterwards, an isoparametric transformation is used to map a parametrically defined quadrilateral surface mesh into the vessel volume, resulting in stacks of sections which can then be used for sweeping. Being robust and open source based, this methodology may improve the current standard in patient-specific mesh generation and enhance the reliability of CFD to patient-specific haemodynamics.     

A force-indentation relationship for gymnastic mats.

The mechanical properties of a series of gymnastic surfaces are investigated. A Force--Indentation relationship is obtained for each surface. This law can be used to simulate the ground reaction force during under-foot impact with a gymnastic surface. The law is independent of many of the properties of the striking body and when incorporated into a system of differential equations describing the motion of the impacting body, can be used to compute system responses and to investigate the importance of different properties of the various surfaces. Several examples, using both a single, rigid mass and a four link, articulated system are presented, and demonstrate that the relationship can be satisfactorily incorporated into a solution algorithm for a large-displacement dynamical analysis.     

Patient-specific computational haemodynamics: generation of structured and conformal hexahedral meshes from triangulated surfaces of vascular bifurcations

Measuring the blood flow is still limited by current imaging technologies and is generally overcome using computational fluid dynamics (CFD) which, because of the complex geometry of blood vessels, has widely relied on tetrahedral meshes. Hexahedral meshes offer more accurate results with lower-density meshes and faster computation as compared to tetrahedral meshes, but their use is limited by the far more complex mesh generation. We present a robust methodology for conformal and structured hexahedral mesh generation – applicable to complex arterial geometries as bifurcating vessels – starting from triangulated surfaces. Cutting planes are used to slice the lumen surface and to construct longitudinal Bezier splines. Afterwards, an isoparametric transformation is used to map a parametrically defined quadrilateral surface mesh into the vessel volume, resulting in stacks of sections which can then be used for sweeping. Being robust and open source based, this methodology may improve the current standard in patient-specific mesh generation and enhance the reliability of CFD to patient-specific haemodynamics.     

Reduced surface: An efficient way to compute molecular surfaces

Because of their wide use in molecular modeling, methods to compute molecular surfaces have received a lot of interest in recent years. However, most of the proposed algorithms compute the analytical representation of only the solvent-accessible surface. There are a few programs that compute the analytical representation of the solvent-excluded surface, but they often have problems handling singular cases of self-intersecting surfaces and tend to fail on large molecules (more than 10,000 atoms). We describe here a program called MSMS, which is shown to be fast and reliable in computing molecular surfaces. It relies on the use of the reduced surface that is briefly defined here and from which the solvent-accessible and solvent-excluded surfaces are computed. The four algorithms composing MSMS are described and their complexity is analyzed. Special attention is given to the handling of self-intersecting parts of the solvent-excluded surface called singularities. The program has been compared with Connolly's program PQMS [M. L. Connolly (1993) Journal of Molecular Graphics, Vol. 11, pp. 139–141] on a set of 709 molecules taken from the Brookhaven Data Base. MSMS was able to compute topologically correct surfaces for each molecule in the set. Moreover, the actual time spent to compute surfaces is in agreement with the theoretical complexity of the program, which is shown to be O[n log(n)] for n atoms. On a Hewlett-Packard 9000/735 workstation, MSMS takes 0.73 s to produce a triangulated solvent-excluded surface for crambin (1crn, 46 residues, 327 atoms, 4772 triangles), 4.6 s for thermolysin (3tln, 316 residues, 2437 atoms, 26462 triangles), and 104.53 s for glutamine synthetase (2gls, 5676 residues, 43632 atoms, 476665 triangles). © 1996 John Wiley & Sons, Inc.     

Synthesis, patterning and applications of star-shaped poly(ethylene glycol) biofunctionalized surfaces

Poly(ethylene) glycol (PEG) is an excellent material to modify surfaces to resist non-specific protein adsorption. Linear PEG has been extensively studied both theoretically and experimentally and it has been found that resistance of PEG-coated surfaces to protein adsorption depends mainly on the molecular weight of the polymer and the surface grafting density. End-functionalized star-shaped PEGs allow for interpolymer crosslinking to form a dense layer. An excellent example of such a system consists of a 6-arm PEG/PPG (4 : 1) star polymer functionalized with isocyanate using IPDI. The end functionalization may be further biofunctionalized to recognize specific biomolecules such as streptavidin, His-tagged proteins, amino-terminated oligonucleotides and cell receptors. This functionalization may be patterned into specific geometries using stamping techniques or randomly distributed by statistical reaction of the end group with the biofunctional molecule in solution. The surface preparation uses simple spin-, dip- or spray-coating and produces smooth layers with low background fluorescence. These properties, together with the advantageous chemical properties of PEG, render the surfaces ideal for immobilizing proteins on surfaces with detection limits down to the single molecule level. Proteins immobilized on such surfaces are able to maintain their folded, functional form and are able to completely refold if temporarily exposed to denaturing conditions. Immobilized enzyme molecules were able to perform their function with the same activity as the enzyme in solution. Future directions of using surfaces coated with such crosslinked star polymers in highly sensitive and robust biotechnology applications will be discussed.     

Plotting protein surfaces

This paper presents two methods for drawing solvent-accessible surfaces of proteins on a plotter. One method draws a stack of contours and the other draws a triangulated polyhedral surface. Both methods perform hidden-line elimination. These methods should be very useful in laboratories which do not possess vector or raster colour graphics equipment.     

The surface finite element method for pattern formation on evolving biological surfaces

In this article we propose models and a numerical method for pattern formation on evolving curved surfaces. We formulate reaction-diffusion equations on evolving surfaces using the material transport formula, surface gradients and diffusive conservation laws. The evolution of the surface is defined by a material surface velocity. The numerical method is based on the evolving surface finite element method. The key idea is based on the approximation of Γ by a triangulated surface Γ _h consisting of a union of triangles with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γ _h which are linear affine on each simplex of the polygonal surface. To demonstrate the capability, flexibility, versatility and generality of our methodology we present results for uniform isotropic growth as well as anisotropic growth of the evolution surfaces and growth coupled to the solution of the reaction-diffusion system. The surface finite element method provides a robust numerical method for solving partial differential systems on continuously evolving domains and surfaces with numerous applications in developmental biology, tumour growth and cell movement and deformation.     

Pattern recognition based on color-coded quantum mechanical surfaces for molecular alignment

A pattern recognition algorithm for the alignment of drug-like molecules has been implemented. The method is based on the calculation of quantum mechanical derived local properties defined on a molecular surface. This approach has been shown to be very useful in attempting to derive generalized, non-atom based representations of molecular structure. The visualization of these surfaces is described together with details of the methodology developed for their use in molecular overlay and similarity calculations. In addition, this paper also introduces an additional local property, the local curvature (C _L), which can be used together with the quantum mechanical properties to describe the local shape. The method is exemplified using some problems representing common tasks encountered in molecular similarity. Figure Molecular surfaces for Lorazepam (left) and Diazepam (right)     

Molecular recognition: 3D surface structure comparison by gnomonic projection

This paper outlines a method for gnomonic projection of a molecular surface and a novel application of it to the problem of surface comparison. Semiregular arrays of points are generated by icosahedral tessellation. The surface may be the accessible surface or a chemical parameter surface such as the molecular electrostatic potential. Gnomonic projection retains the 3D characteristics of the inspection surface. Comparison of two surfaces can be achieved by statistical assessment of the pattern match. The method opens the gateway to an optimized search for pattern matches on the surfaces of dissimilar molecular structures.     

Hyaluronan conformations on surfaces: effect of surface charge and hydrophobicity

Extended, relaxed, condensed, and interacting forms of the polysaccharide hyaluronan have been observed by atomic force microscopy (AFM). The types of images obtained depend on the properties of the surfaces used. We have investigated several different surface conditions for HA imaging, including unmodified mica, mica chemically modified with two different kinds of amino-terminated silanes (3-aminopropyltriethoxysilane and N-trimethoxysilylpropyl-N,N,N-trimethylammonium chloride), and highly oriented pyrolytic graphite. We found the degree of HA molecular extension or condensation to be variable, and the number of bound chains per unit area was low, for all of the mica-based surfaces. HA was more easily imaged on graphite, a hydrophobic surface. Chains were frequently observed in high degrees of extension, maintained by favorable interaction with the surface after molecular combing. This observation suggests that the HA macromolecule interacts with graphite through hydrophobic patches along its surface. AFM studies of HA behavior on differing surfaces under well-controlled environmental conditions provides useful insight into the variety of conformations and interactions likely to be found under differing physiological conditions.     

Plant–Microbe Interactions: Wetting of Ivy (Hedera helix L.) Leaf Surfaces in Relation to Colonization by Epiphytic Microorganisms

Abstract Leaf wettability, cuticular wax composition, and microbial colonization of upper and lower leaf surfaces of ivy (Hedera helix L.) was investigated for young and old leaves sampled in June and September. Contact angles of aqueous buffered solutions measured on young leaf surfaces ranged between 76° and 86° and were not dependent on the pH value of the applied droplets. Contact angles measured on old leaf surfaces were up to 32°, significantly lower than on young leaf surfaces. Furthermore, contact angles were significantly lower using aqueous solutions of pH 9.0 compared to pH 3.0, indicating the influence of ionizable functional groups on leaf surface wetting properties. Observed changes in leaf wetting properties did not correlate with different levels of alkanoic acids in cuticular waxes. However, microscopic examination of the leaf surfaces indicated the influence of epiphytic microorganisms on wetting properties of old leaves, since their surfaces were always colonized by epiphytic microorganisms (filamentous fungi, yeasts, and bacteria), whereas surfaces of young leaves were basically clean. In order to analyze the effect of epiphytic microorganisms on leaf surface wetting, surfaces of young and clean ivy leaves were artificially colonized with Pseudomonas fluorescens. This resulted in a significant increase and a pH dependence of leaf surface wetting in the same way as it was observed on old ivy leaf surfaces. From these results it can be deduced that the native wetting properties of leaf surfaces can be significantly masked by the presence of epiphytic microorganisms. The ecological implications of altered wetting properties for microorganisms using the leaf/atmosphere interface as habitat are discussed. Received: 20 March 1999; Accepted: 5 July 1999; Online Publication: 18 July 2000     

Streptavidin 2D Crystal Substrates for Visualizing Biomolecular Processes by Atomic Force Microscopy

Flat substrate surfaces are a key to successful imaging of biological macromolecules by atomic force microscopy (AFM). Although usable substrate surfaces have been prepared for still imaging of immobilized molecules, surfaces that are more suitable have recently been required for dynamic imaging to accompany the progress of the scan speed of AFM. In fact, the state-of-the-art high-speed AFM has achieved temporal resolution of 30 ms, a capacity allowing us to trace molecular processes played by biological macromolecules. Here, we characterize three types of streptavidin two-dimensional crystals as substrates, concerning their qualities of surface roughness, uniformity, stability, and resistance to nonspecific protein adsorption. These crystal surfaces are commonly resistant to nonspecific protein adsorption, but exhibit differences in other properties to some extent. These differences must be taken into consideration, but these crystal surfaces are still useful for dynamic AFM imaging, as demonstrated by observation of calcium-induced changes in calmodulin, GroES binding to GroEL, and actin polymerization on the surfaces.     

Discovery of similar regions on protein surfaces.

Discovery of a similar region on two protein surfaces can lead to important inference about the functional role or molecular interaction of this region for one of the proteins if such information is available for the other. We propose a new characterization of protein surfaces based on a spin-image representation of the surfaces that facilitates the simultaneous search of the entire surface of each of two proteins for a matching region. For a surface point, we introduce spin-image profiles that are related to the degree of exposure of the point to identify structurally equivalent surface regions in two proteins. Unlike some related methods, we do not assume that a known fixed region of one of the protein surfaces is to be matched on the other protein surface. Rather, we search for the largest similar regions on each of the two surfaces. In spite of the fact that this approach is entirely geometric and no use is made of physicochemical properties of the protein surfaces or fold information, it is effective in identifying similar regions on both surfaces even when the region corresponds to a binding site on one of the proteins. The discovery of similar regions on two or more proteins also has implications for drug design and pharmacophore identification. We present experimental results from datasets of more than 50 protein surfaces.     

Protein Molecular Surface Mapped at Different Geometrical Resolutions

Many areas of biochemistry and molecular biology, both fundamental and applications-orientated, require an accurate construction, representation and understanding of the protein molecular surface and its interaction with other, usually small, molecules. There are however many situations when the protein molecular surface gets in physical contact with larger objects, either biological, such as membranes, or artificial, such as nanoparticles. The contribution presents a methodology for describing and quantifying the molecular properties of proteins, by geometrical and physico-chemical mapping of the molecular surfaces, with several analytical relationships being proposed for molecular surface properties. The relevance of the molecular surface-derived properties has been demonstrated through the calculation of the statistical strength of the prediction of protein adsorption. It is expected that the extension of this methodology to other phenomena involving proteins near solid surfaces, in particular the protein interaction with nanoparticles, will result in important benefits in the understanding and design of protein-specific solid surfaces.     

A new generation of polymer nanoparticles for drug delivery.

One of the main interests of using polymer nanoparticles as drug carrier systems is to control the delivery of the drugs including their biodistribution. During the last decade, it was clearly demonstrated that surface properties of nanoparticles were the key factor which determined the in vivo fate of such a carrier. Thus, the purpose of this work was to develop a new method which allows the easy fabrication of nanoparticles with versatile surface properties using polysaccharides. This preparation was based on the use of a redox radical polymerization reaction applied for the first time to the emulsion polymerization of alkylcyanoacrylates in aqueous continuous media. The dispersion of nanoparticles was very stable. The nanoparticle surfaces were coated with polysaccharides and their characteristics can be modulated by the type and the molecular weight of the polysaccharides used during the synthesis. Interestingly the biological properties of the polysaccharide immobilized on the nanoparticle surface can be preserved opening very interesting perspectives for such nanoparticles. This method also offers a new strategy for the design of modular biomimetic nanoparticles as drug carrier systems with multiple functions. One of the applications considered in this work was to use these nanoparticles coupled with haemoglobin as an oxygen carrier.