Jürgen Brickmann

An Empirical Potential Energy Function for Phospholipids: Criteria for Parameter Optimization and Applications

Lipid membranes are an essential component of all living cells. A molecular description of the structure and dynamics of such membranes from either experimental or theoretical approaches is still lacking. This is due in part to the two-dimensional fluid character of membranes (Singer and Nicolson, 1972), which makes difficult a detailed analysis by X-ray diffraction, neutron diffraction, or nuclear magnetic resonance. Detailed structural data of lipid molecules based on X-ray crystallography are available only for the nearly anhydrous crystalline state (Pascher et al, 1992; Small, 1986).

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

SummaryA 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.

Fast generation of molecular surfaces from 3D data fields with an enhanced “marching cube” algorithm

An improved version of the “marching cubes” algorithm [W. Lorensen and H. Cline, Comp. Graph. 21, (1987)] for the generation of isosurfaces from 3D data fields is presented and applied to molecular surfaces. The new algorithm avoids inconsistent pattern definitions of the original one, which lead to artificial gaps. The advantage of a logarithmic interpolation procedure, in particular for data fields typically occurring in molecular science, is demonstrated. An example is the generation of molecular surfaces based upon electron density data.

Lingering Time of the Proton in the Wells of the Double‐Minimum Potential of Hydrogen Bonds

The movement of a proton which moves in a one‐dimensional effective double‐minimum potential V(x) and can pass by means of the tunnel effect from one well into the other was investigated. The lingering times of the proton in the potential wells (a) and (b) were calculated for more than 150 potential models as functions of the height Vmax of the potential barrier separating the two wells, the energy difference ΔV, and separation d of the minima. In the determination of the lingering times, it was assumed that the proton at time t = 0 is to be found with certainty in one of the wells and can be represented by means of a statistical operator related to the eigenstates of a one‐well Hamiltonian H(a)orH(b), respectively. The times determined on this basis were compared with those which result with a quasiclassical method from the classical frequency of oscillation of a particle in a well and from the penetration coefficient of the potential barrier. The deviation between the values determined with both methods...

Force field parameters for carbohydrates

A new set of force field parameters for carbohydrates is reported. The parameter set is based on the CHARMM22 force field of Karplus and co‐workers. The parameterization is based on newly performed high‐level ab initio calculations [MP2/6‐311 + G (2d, 2p)/ /6‐31G**] of fragment molecules. A good agreement of the modified force field and ab initio data is achieved, which is demonstrated with a variety of molecules.

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.

Potential energy function for apatites

An empirical potential energy function for fluor- and for hydroxyapatite is formulated and parametrised. The parameter optimisation involves a hierarchy of reference data and techniques comprising of quantum-chemical calculations for Coulomb interactions and intramolecular contributions, as well as experimental data and molecular dynamics simulations for the remaining nonbonded parameters. For fluorapatite both a flexible and a rigid phosphate model are derived, while for hydroxyapatite only the rigid variant is determined. Simulations with the final models reproduce the experimental crystal parameters within less than 1% deviation for a wide range of temperatures between 73 and 1273 K. In the case of flexible fluorapatite the computed and the experimental infrared spectra at 300 K agree excellently.

Molecular dynamics study of ion transport in transmembrane protein channels

Ion transport through biological membranes often takes place via pore-like protein channels. The elementary process of this transport can be described as a motion of the ion in a quasi-periodic multi-well potential. In this study molecular dynamics simulations of ion transport in a model channel were performed in order to test the validity of reaction-rate theory for this process. The channel is modelled as a hexagonal helix of infinite length, and the ligand groups interacting with the ion are represented by dipoles lining the central hole of the channel. The dipoles interact electrostatically with each other and are allowed to oscillate around an equilibrium orientation. The coupled equations of motion for the ion and the dipoles were solved simultaneously with the aid of a numerical integration procedure. From the calculated ion trajectories it is seen that, particularly at low temperatures, the ion oscillates back and forth in the trapping site many times before it leaves the site and jumps over the barrier. The observed oscillation frequency was found to be virtually temperature-independent (nu 0 approximately equal to 2 X 10(12) s-1) so that the strong increase of transport rate with temperature results almost exclusively from the Arrhenius-type exponential dependence of jump probability w on 1/T. At higher temperatures simultaneous jumps over several barriers occasionally occur. Although the exponential form of w(T) was in agreement with the predictions of rate theory, the activation energy Ea as determined from w(T) was different from the barrier height which was calculated from the static potential of the ion in the channel; the actual transport rate was 1 X 10(3) times higher than the rate predicted from the calculated barrier height. This observation was interpreted by the notion that ion transport in the channel is strongly influenced by thermal fluctuations in the conformation of the ligand system which in turn give rise to fluctuations of barrier height.

Pattern recognition strategies for molecular surfaces: III. Binding site prediction with a neural network

An algorithm for the identification of possible binding sites of biomolecules, which are represented as regions of the molecular surface, is introduced. The algorithm is based on the segmentation of the molecular surface into overlapping patches as described in the first article of this series. 1 The properties of these patches (calculated on the basis of physical and chemical properties) are used for the analysis of the molecular surfaces of 7821 proteins and protein complexes. Special attention is drawn to known protein binding sites. A binding site identification algorithm is realized on the basis of the calculated data using a neural network strategy. The neural network is able to classify surface patches as protein–protein, protein–DNA, protein–ligand, or nonbinding sites. To show the capability of the algorithm, results of the surface analysis and the predictions are presented and discussed with representative examples.

MOLCAD — Computer Aided Visualization and Manipulation of Models in Molecular Science

Visualization techniques in the field of molecular science as realized in the modeling package MOLCAD are described. The MOLCAD package was developed in the group of the authors. It provides state of the art interactive techniques for display and manipulation of three dimensional molecular structures, and molecular properties. MOLCAD offers the standard features used in the field of molecular modeling and advanced tools for the visualization of related data. The visualization techniques are described, and some examples for the application are given.