New fuzzy logic strategies for bio-molecular recognition.

The concepts of molecular similarity and molecular complementarity, playing important roles in the broad field of molecular recognition, are chemical problems, in which the eyeball technique used by a human observer is very successful but which are very hard to code into a computer algorithm. Based on the model of molecular surfaces, our new approach defines overlapping surface patches with similar molecular properties. These patches are used to represent local features of the molecule in a way, which is beyond the atomistic resolution but can nevertheless be applied in partial similarity as well as complementarity analyses in a very general sense. It is shown that this molecular description can be used as the first step in a docking algorithm for complexes, where the structures of both molecules are known, as well as for the identification of possible active sites without the knowledge of specific molecules binding to this site.

Localization and quantification of hydrophobicity: the molecular free energy density (MolFESD) concept and its application to sweetness recognition.

A method for the localization, the quantification, and the analysis of hydrophobicity of a molecule or a molecular fragment is presented. It is shown that the free energy of solvation for a molecule or the transfer free energy from one solvent to another can be represented by a surface integral of a scalar quantity, the molecular free energy surface density (MolFESD), over the solvent accessible surface of that molecule. This MolFESD concept is based on a model approach where the solvent molecules are considered to be small in comparison to the solute molecule, and the solvent can be represented by a continuous medium with a given dielectric constant. The transfer energy surface density for a 1-octanol/water system is empirically determined employing a set of atomic increment contributions and distance dependent membership functions measuring the contribution of the increments to the surface value of the MolFESD. The MolFESD concept can be well used for the quantification of the purely hydrophobic contribution to the binding constants of molecule-receptor complexes. This is demonstrated with the sweeteners sucrose and sucralose and various halogen derivatives. Therein the relative sweetness, which is assumed to be proportional to the binding constant, nicely correlates to the surface integral over the positive, hydrophobic part of the MolFESD, indicating that the sweetness receptor can be characterized by a highly flexible hydrophobic pocket instead of a localized binding site.

Molecular modeling information transfer with VRML: from small molecules to large systems in bioscience.

The suitability of the Virtual Reality Modeling Language (VRML) for the communication of scientists via the internet is demonstrated with recent results from computer assisted cancer research: I. Substrate channels in cytochrome P450 enzymes. II. Binding properties of the wild type and mutated p53 tumor suppressor protein. Complex 3D molecular models were used to visualize new insights in the active site access of cytochrome P450 enzymes and in the p53 protein-DNA binding achieved by the use of computational methods. These 3D models of biomolecular systems were transferred into VRML scenarios. Additional implemented features allow users to receive related information interactively. With these examples it is shown that VRML provides an efficient method for scientific information exchange by the use of complex 3D molecular models.

3D molecular graphics on the World Wide Web.

The Virtual Reality Modeling Language (VRML) is a new tool for the information transfer on the World Wide Web (WWW). We present a short description and some applications in the field of molecular graphics of this new, object oriented language. It is shown that the usage of VRML is a very efficient and powerful method for the transport of molecular models over the net.

Virtual reality modeling language in chemistry.

A new concept in the field of molecular modeling using the information transfer mechanism of the World Wide Web (WWW) is presented. The Virtual Reality Modeling Language (VRML) provides an object-oriented method for the description of molecular models. The structure and capabilities of this new language are introduced. It is shown that the transport of molecular models over the WWW using VRML is a very efficient and powerful method for the exchange of molecular information.

Quantification and visualization of molecular surface flexibility.

Two new methods for the quantification and visualization of the flexibility of molecular surfaces are presented. Both methods rely on results of molecular dynamics (MD) simulations. Whereas method I is based on a simple but fast grid-counting algorithm, method II uses a mapping function that allows for a sharp and clear visualization of atomic RMS fluctuations on a molecular surface. To demonstrate the scope of the methods, MD simulations of two proteins, PTI and ubiquitin, were performed. The flexibility data are mapped onto the molecular surfaces of the proteins and visualized using texture mapping technology available on modern workstations.

Segmentation of protein surfaces using fuzzy logic.

An algorithm has been developed that can be used to divide triangulated molecular surfaces into distinct domains on the basis of physical and topographical molecular properties. Domains are defined by a certain degree of homogeneity concerning one of these properties. The method is based on fuzzy logic strategies, thus taking into consideration the smooth changes of the properties considered along complex macromolecular surfaces. Scalar qualities assigned to every node point on a triangulated surface are translated into linguistic variables, which can then be processed using a special fuzzy dissimilarity operator. Possible applications are demonstrated using surface segmentation for properties like electrostatic potential, lipophilicity and shape for the analysis of serine proteinase substrate/inhibitor specificity.

The Darmstadt workshop on molecular modeling: past and future.

The majority of the contributions in this issue of the Journal of Molecular Graphics are papers that were presented at the Seventh Darmstadt Molecular Modeling Workshop, which took place at the Technical University Darmstadt on May 18-19, 1993. The technical organization of this workshop was again in the hands of the physical chemistry staff of the Technical University, Darmstadt, as it has been for the past six years. The scientific program was coordinated by Stefan Kast from the author's research group. The Darmstadt Workshop has been quite an informal and inexpensive event throughout the years. From 1994 onward, it will also be a specific meeting of the recently founded German-speaking branch of the Molecular Graphics Society. The following notes should help to provide an overview of the past activities and present some ideas for the future of this meeting.

Texture mapping: a new tool for molecular graphics.

The real-time texture mapping capabilities of modern graphics workstations are explored with respect to their applications in a variety of relevant scenarios in interactive molecular modeling techniques. The common usage of texture mapping to reduce geometric complexity while enhancing realism is extended, opening new ways to visualize large amounts of molecular data in a comprehensive fashion. Thus, texture mapping may be employed to (1) display and filter multichannel information of structural properties on molecular surfaces, (2) improve the quality and accuracy of highly complex isodensity contours, (3) increase the rendering speed of space-filling atomic representations by two orders of magnitude and (4) apply volume-rendering techniques to large, three-dimensional density distributions in real time. Implementation of these novel techniques requires only moderate modifications or extensions to existing molecular modeling applications.

A new approach to analysis and display of local lipophilicity/hydrophilicity mapped on molecular surfaces.

A new method for display and analysis of lipophilic/hydrophilic properties on molecular surfaces is presented. The present approach is based on the concept of Crippen and coworkers that the overall hydrophobicity of a molecule (measured as the logarithm of the partition coefficient in an octanol/water system) can be obtained as a superposition of single atom contributions. It is also based on the concept of molecular lipophilicity potentials (MLP) first introduced by Audry and coworkers in order to establish a 3D lipophilicity potential profile in the molecular environment. Instead of using a l/r- or an exponential distance law between the atomic coordinates and a point on the molecular surface, a new distance dependency is introduced for the calculation of an MLP-value on the solvent-accessible surface of the molecule. In the present formalism the Crippen values (introduced for atoms in their characteristic structural environment) are 'projected' onto the van der Waals surface of the molecule by a special weighting procedure. This guarantees that only those atomic fragments contribute significantly to the surface values that are in the close neighbourhood of the surface point. This procedure not only works for small molecules but also allows the characterization of the surfaces of biological macromolecules by means of local lipophilicity. Lipophilic and hydrophilic domains can be recognized by visual inspection of computer-generated images or by computational procedures using fuzzy logic strategies. Local hydrophobicities on different molecular surfaces can be quantitatively compared on the basis of the present approach.

A Monte Carlo simulation of hydration of xanthine-derivatives and their stacked forms.

Results on a Monte Carlo simulation of the hydration of monomer and possible stacked dimer forms of a purine alkaloid series in 200- and 400-water molecule clusters are presented. Investigation of different purine stacked dimers in a 200-water molecule cluster reveals that for caffeine there exists one, for theophylline two and for theobromine four dimers are energetically favorable. For caffeine, the same energetically favored stacked dimer form is observed in both the 200- and 400-water molecule cluster. The main factor stabilizing the preferred dimer stacks is the change in the interaction between water molecules of the monomer cluster and those water molecules in the dimer cluster.

Self similarity of protein surfaces.

Scaling properties of the surfaces of 53 proteins are studied on the basis of experimentally determined 3-D structures of these biological macromolecules. It is found that the surfaces show self similarity within a yardstick range of 1.5 A less than epsilon less than 15 A. The self similarity is measured by the fractal dimension D of the surface. Two different algorithms for the determination of the fractal dimension are applied, both based on cubic yardstick particles. One is related to the contact surface (CS), which was first introduced by Connolly (17), while the other corresponds to the solvent accessible surface (SAS) of Richards (9). The fractal dimensions of both are different. While the CS type approach leads to relatively high values of D in the range 2.5 to 2.6 the SAS approach gives fractal dimensions of D approximately 2.

Hausdorff dimension as a quantification of local roughness of protein surfaces.

Based on structural information from the Brookhaven Protein Data Bank, the contact surfaces of the proteins lysozyme, trypsin, and BPTI (bovine pancreatic trypsin inhibitor) with a spherical test particle of the size of a water molecule have been calculated and systematically analyzed. It is our purpose to establish (i) self-similarity as a statistical concept for the characterization of surface roughness and (ii) the Hausdorff dimension as a measure of the local surface complexity. It is found that the proteins statistically show self-similarity within a yardstick range 1.2 A less than R less than 20 A, and that this concept also holds reasonably for parts of the surface which are not too small.

Molecular dynamics studies of the interface between a model membrane and an aqueous solution.

Molecular Dynamics (MD) computer simulation studies are reported for a system consisting of two model membranes in contact with an aqueous solution. The influence of the membrane on the adjacent liquid is of main interest in the present study. It is therefore attempted to make the system sufficiently large to encompass the entire region between bulk liquid and the membranes. The latter are modeled by two-dimensional arrays of COO- groups with rotational and translational degrees of freedom. The water molecules are represented by the well-tested TIP4P model. The intermolecular potentials are parametrized in terms of Coulomb interactions between partial charges on the molecular frames and empirical, mostly Lennard-Jones (12-6), interactions centered at the atomic positions. A strong layering of the liquid accompanied by an increase in average water density is found in the vicinity of the membrane. The structural perturbation reaches approximately 8 A into the liquid. We discuss the static structure in these layers in terms of atom-atom distance distribution functions and study the average orientation of the water molecule dipoles with respect to the membrane. From the distribution of the ions, we find that less than 50% of the surface charge of the membrane is neutralized by Na+ ions in the first layer above the membrane. A simplified model of the adsorption site of the ion on the membrane is developed from the distance distributions. Finally the hydration of the Na+ in the first adsorbed layer is discussed.

Triangulation algorithms for the representation of molecular surface properties.

A triangulation algorithm for a dotted surface (i.e. a surface defined by point coordinates in three dimensions) is given. The individual triangles are generated on the basis of a hierarchy of strategies according to increasing surface complexity. While for small molecules an elementary algorithm is sufficient to triangulate the surface, large molecules-like proteins-generally need all steps of the hierarchy. Although this program has been developed with the aim of triangulating molecular surfaces, it can in principle be applied to any surface defined by 3D point coordinates.

Structure and dynamics of one-dimensional ionic solutions in biological transmembrane channels.

The structure and dynamics of solvated alkali metal cations in transmembrane channels are treated using the molecular dynamics simulation technique. The simulations are based on a modified Fischer-Brickmann model (Fischer, W., and J. Brickmann, 1983, Biophys. Chem., 18:323-337) for gramicidin A-type channels. The trajectories of all particles in the channel as well as two-dimensional pair correlation functions are analyzed. It is found from the analysis of the stationary simulation state that one-dimensional solvation complexes are formed and that the number of water molecules in the channel varies for different alkali metal cations.

Simulation of voltage-driven hydrated cation transport through narrow transmembrane channels.

Molecular dynamics studies for the voltage-driven transport of the alkali metal ions lithium, sodium, and potassium through gramicidin A-type channels filled with water molecules are presented. The number of water molecules in the channel is obtained from a previous study (Skerra, A., and J. Brickmann, 1987, Biophys. J., 51:969-976). It is shown that the selectivity of the intrachannel ion diffusion through our model pore conforms to the experimentally observed selectivity of the gramicidin A channel. It is demonstrated that the number of water molecules in the channel plays a key role for the selectivity.