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Use of TSAR as a new tool to analyze the molecular dynamics trajectories of proteins.

There is a lack of tools to analyze simulations of protein molecular dynamics quantitatively. Our aim is to use calmodulin, a prototypical calcium-binding protein, to describe a strategy and some tools for extracting relevant information from dynamics calculations. Our main conclusions are as follows: Autocorrelation vectors may be used to represent a 3D conformation in an n-dimensional space, where n is variable (n < or = 20-30). On such a transformation, classic statistical tools (PCA, clustering, etc.) may be used to differentiate or characterize dynamics trajectories quantitatively. TSAR, an integrated package used for quantitative structure-activity relationships, is well suited (after minor modifications) for such a purpose. Finally, this type of strategy is able to point out the effects of the solvent screening parameters of the Amber software on the dynamics trajectories of calmodulin.

Calmodulin↗

Substrate recognition by ribosome-inactivating protein studied by molecular modeling and molecular electrostatic potentials.

A computer model of dianthin 30, a type 1 ribosome-inactivating protein (RIP), is constructed by homology modeling using two known X-ray structures; a type 1 RIP, pokeweed antiviral protein (PAP), and chain A of a type 2 RIP, ricin. The 3D structure is refined by molecular dynamics and its binding site compared with those of PAP and ricin using molecular electrostatic potential mapping. The differences in the maps obtained clearly show how, despite the similarity of the topology of the binding site, differences in electrostatic potential can account for the experimentally observed differences in substrate recognition and binding. This demonstrates the potential of these techniques for guiding further experimental analyses.

Amino Acid Sequence↗

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.

Algorithms↗

Targeted molecular dynamics: a new approach for searching pathways of conformational transitions.

Molecular dynamics simulations have proven to be a valuable tool to investigate the dynamic behavior of stable macromolecules at finite temperatures. However, considerable conformational transitions take place during a simulation only accidentally or at exceptionally high temperatures far from the range of experimental conditions. Targeted molecular dynamics (TMD) is a method to induce a conformational change to a known target structure at ordinary temperature by applying a time-dependent, purely geometrical constraint. The transition is enforced independently of the height of energy barriers, while the dynamics of the molecule is only minimally influenced by the constraint. Simulations of decaalanine and insulin show the ability of the method to explore the configurational space for pathways accessible at a given temperature. The transitions studied at insulin comprise unfolding of an alpha-helical portion and, in the reverse direction, refolding from an extended conformation. A possible application of TMD is the search for energy barriers and stable intermediates from rather local changes up to protein denaturation.

Computer Graphics↗

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.

Algorithms↗

MOLGEN: personal computer-based modeling system.

MOLGEN is a comprehensive molecular modeling package that runs on personal computers and allows building, drawing, storing, and comparison of molecular structures. The system contains modules for geometry optimization and conformational analysis, and modules for calculation and description of lipophilicity and electrostatic potentials and for their three-dimensional matching based on gnomonic projection. Described here are a systematic conformation search running on PCs and a new approach to 3D similarity analysis of lipophilic potentials. The drug design applicability of the program is further enhanced by database facilities for retrieving and storing any structure data sets. The program features and examples of its applications are presented.

Chemical Phenomena↗

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 advantages 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.

Aprotinin↗

Approximation and visualization of large-scale motion of protein surfaces.

We present a method for the approximation and real-time visualization of large-scale motion of protein surfaces. A molecular surface is represented by an expansion of spherical harmonic functions, and the motion of protein atoms around their equilibrium positions is computed by normal mode analysis. The motion of the surface is approximated by projecting the normal mode vectors of the solvent-accessible atoms to the spherical harmonic representation of the molecular surface. These surface motion vectors are represented by a separate spherical harmonic expansion. Representing the surface geometry and the surface motion vectors by spherical harmonic expansions allows variable-resolution analysis and real-time display of the large-scale surface motion. This technique has been applied to interactive visualization, interactive surface manipulation, and animation.

Computer Graphics↗

Simulating the folding of small proteins by use of the local minimum energy and the free solvation energy yields native-like structures.

Assuming that the protein primary sequence contains all information required to fold a protein into its native tertiary structure, we propose a new computational approach to protein folding by distributing the total energy of the macromolecular system along the torsional axes. We further derive a new semiempirical equation to calculate the total energy of a macromolecular system including its free energy of solvation. The energy of solvation makes an important contribution to the stability of biological structures. The segregation of hydrophilic and hydrophobic domains is essential for the formation of micelles, lipid bilayers, and biological membranes, and it is also important for protein folding. The free energy of solvation consists of two components: one derived from interactions between the atoms of the protein, and the second resulting from interactions between the protein and the solvent. The latter component is expressed as a function of the fractional area of protein atoms accessible to the solvent. The protein-folding procedure described in this article consists of two successive steps: a theoretical transition from an ideal alpha helix to an ideal beta sheet is first imposed on the protein conformation, in order to calculate an initial secondary structure. The most stable secondary structure is built from a combination of the lowest energy structures calculated for each amino acid during this transition. An angular molecular dynamics step is then applied to this secondary structure. In this computational step, the total energy of the system consisting of the sum of the torsional energy, the van der Waals energy, the electrostatic energy, and the solvation energy is minimized. This process yields 3-D structures of minimal total energy that are considered to be the most probable native-like structures for the protein. This method therefore requires no prior hypothesis about either the secondary or the tertiary structure of the protein and restricts the input of data to its sequence. The validity of the results is tested by comparing the crystalline and computed structures of four proteins, i.e., the avian and bovine pancreatic polypeptide (36 residues each), uteroglobin (70 residues), and the calcium-binding protein (75 residues); the C alpha-C alpha maps show significant homologies and the position of secondary structure domains; that of the alpha helices is particularly close.

Animals↗

Visualization of electronic properties of molecules in chemical reactions.

Modern computational methods allow for the tracking of entire chemical reactions, ranging from initial reactants, through transition states, and to the final products. They also permit the computation of a variety of properties that can change as the reaction proceeds from start to finish. Visualization of these reactions is often difficult and usually limited to static displays of specific steps along the reaction paths. This article describes a program, Reaction Viewer, that we have developed to visualize a chemical reaction dynamically. The article also describes the use of this program to see the movement of electrons and other electronic effects, as well as steric ramifications during the reaction.

Computer Graphics↗

Biomolecular visualization using AVS.

Dataflow systems for scientific visualization are becoming increasingly sophisticated in their architecture and functionality. AVS, from Advanced Visual Systems Inc., is a powerful dataflow environment that has been applied to many computation and visualization tasks. An important, yet complex, application area is molecular modeling and biomolecular visualization. Problems in biomolecular visualization tax the capability of dataflow systems because of the diversity of operations that are required and because many operations do not fit neatly into the dataflow paradigm. Here we describe visualization strategies and auxiliary programs developed to enhance the applicability of AVS for molecular modelling. Our visualization strategy is to use general-purpose AVS modules and a small number of chemistry-specific modules. We have developed methods to control AVS using AVS-tool, a programmable interface to the AVS Command Line Interpreter (CLI), and have also developed NAB, a C-like language for writing AVS modules that has extensions for operating on proteins and nucleic acids. This strategy provides a flexible and extensible framework for a wide variety of molecular modeling tasks.

Artificial Intelligence↗

Detection and geometric modeling of molecular surfaces and cavities using digital mathematical morphological operations.

We developed a digital method based on mathematical morphological operations to obtain three types of surfaces: van der Waals surface, solvent-accessible surface, and molecular surface, to extract the cavities on the surface and interior part of the molecule and to extract the ligand portions in contact with the cavities. The molecular surface, the cavities and the portions, and the heme region are visualized using solid modeling. The method enables us to obtain the volumes of the cavities and inhibitor portions and the areas of the surfaces. Solid modeling enables us to obtain cross-sections at arbitrary positions. This will have considerable utility in docking studies.

Computer Graphics↗

FOLD: integrated analysis and display of protein secondary structure.

FOLD, a computer program for the definition and analysis of protein secondary structure, is described. Algorithms implemented in the software are reviewed. These include methods for the identification of simple features such as hydrogen bonds, alpha helices, beta strands, beta bulges, and beta and psi turns. Techniques are also described for the definition and analysis of higher-order structures, such as beta hairpins, beta sheets and their topology, and beta barrels. In addition to considerable textual output the program supports visualization of protein secondary structure in either an atom-based display style or one reproducing the characteristics of a so-called ribbon drawing.

Computer Graphics↗

Models of ion pores in N-type voltage-gated calcium channels.

Two computer models of the outer vestibule of the pore of the N-type voltage-gated Ca2+ channel are predicted. The models are constructed from beta-hairpin peptide segments in the S5-S6 loops of each of the four domains that produce the channel. These hairpins together are modeled to form a short eight-stranded beta barrel. The models contain a ring of glutamates at the base of the barrel, which have been shown by mutagenesis experiments to function as a selectivity filter. These filters are suggested by the models to be of the correct dimensions to allow the permeation of a hydrated calcium ion, where the filter glutamates may substitute for molecules of water from the hydration shell of the ion. The models also suggest that a ring of threonines and an aspartate might be present between the mouth of the pore and the filter, and hence the models may prove useful in suggesting future mutagenesis experiments.

Amino Acid Sequence↗

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.

Computer Communication Networks↗

Visualization and comparison of molecular dynamics simulations of leukotriene C4, leukotriene D4, and leukotriene E4.

Molecular dynamics simulations of leukotriene C4 (LTC4), leukotriene D4 (LTD4), and leukotriene E4 (LTE4) were carried out, and the data were visualized in an animated video format. Three-dimensional ghost images show the positions of the heavy atoms of all three molecules throughout the simulations. The ghost images can be superimposed to give a single three-dimensional image in which the shapes of the most populated conformers of each molecule are apparent and can be compared. Leukotriene D4 was found to occupy mostly T-shaped conformations, while LTC4 occupied mostly cup-shaped conformations, and LTE4 occupied a wide range of conformations spanning the LTD4 and LTC4 types. Digital filtering and graphing of the internal geometries of the molecules as a function of time revealed differences in dynamic behavior. The results are discussed in light of current knowledge about leukotriene receptors.

Computer Graphics↗

A novel representation of protein structure.

Using a nonlinear mapping technique, we demonstrate that proteins folded in two dimensions display the same overall structural features as their three-dimensional counterparts. The two-dimensional representation of protein structure provides a novel way to visualize structural as well as distance information. It may also provide a link for deriving three-dimensional structure from amino acid sequence.

Computer Graphics↗

Neural networks as a tool for compact representation of ab initio molecular potential energy surfaces.

Ab initio quantum chemical calculations of molecular properties such as, e.g., torsional potential energies, require massive computational effort even for moderately sized molecules, if basis sets with a reasonable quality are employed. Using ab initio data on conformational properties of the cofactor (6R,1'R,2'S)-5,6,7,8-tetrahydrobiopterin, we demonstrate that error backpropagation networks can be established that efficiently approximate complicated functional relationships such as torsional potential energy surfaces of a flexible molecule. Our pilot simulations suggest that properly trained neural networks might provide an extremely compact storage medium for quantum chemically obtained information. Moreover, they are outstandingly comfortable tools when it comes to making use of the stored information. One possible application is demonstrated, namely, computation of relaxed torsional energy surfaces.

Biopterins↗