Michael Schlenkrich

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).

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.

Triangulation algorithms for the representation of molecular surface properties

SummaryA 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.

THEORETICAL INVESTIGATIONS ON 1,2-ETHANEDIOL : THE PROBLEM OF INTRAMOLECULAR HYDROGEN BONDS

The conformational space of 1,2‐ethanediol is studied on the basis of ab initio and semiempirical calculations. All possible conformers are treated. The relative energies of the conformers are systematically studied using various basis sets up to 6–311 + G(3df, 3pd) in order to perform calculations as accurate as possible within a reasonable amount of computer time. Electron correlation is included using Møller‐Plesset perturbation theory. We propose two methods to evaluate the basis set superposition error associated with the intramolecular hydrogen bond appearing in some of the conformers. The results of semiempirical calculations are compared with these ab initio calculations.

EWALD SUMMATION VERSUS DIRECT SUMMATION OF SHIFTED-FORCE POTENTIALS FOR THE CALCULATION OF ELECTROSTATIC INTERACTIONS IN SOLIDS : A QUANTITATIVE STUDY

The calculated Madelung energies and Madelung forces of the electrostatic interaction for nine crystal structures are reported. The method of direct summation with two different shifted‐force potentials is compared to the Ewald summation. There is a considerable difference in the convergence of the energy and the force for the two shifted‐force potentials regarding the cutoff radius. The convergence depends not only on the potential itself, but also on the crystal structure. One of the shifted‐force potentials used is implemented in the CHARMM force field. The energy calculated with this potential shows a good convergence for small cutoff radii. With the other shifted‐force potential, the force shows a better convergence for small cutoff radii. The number of pair interactions for obtaining the Madelung limit using the Ewald summation and the direct summation of a shifted‐force potential is also reported. For complex structures like zeolites, the number of relevant pair interactions is smaller using the direct summation of a shifted‐force potential. For simple structures such as cesium chloride, the number of significant pair interactions is smaller using the Ewald summation.

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.

Molecular Dynamic Simulation of the Interface Aqueous Ionic Solution / Lipid Membrane

The interface between an ionic solution and a membrane, modelled by an ensemble of COO− groups with translational and rotational degrees of freedom, is studied by molecular dynamics (MD) computer simulations. The charged membrane leads to a layering of the ions and the water molecules. Several water layers can be distinguished with structural properties very different from those found in the bulk phase.

Triangulation of Molecular Surfaces

An algorithm for the generation of a solid molecular surface from a given number of surface points in 3D space is presented. This surface is represented by a triangle mesh. Such a mesh of triangles is not uniquely defined by the position vectors of the surface points, and there is no straight forward algorithm for triangulation. In this paper a hierarchy of algorithms is described which successfully works for the automatic triangulation of molecular surfaces of all sizes. Some examples are given for the application of this solid surface approach in molecular modelling of proteins.