A simulation of FABP in water. The protein carries a large water-filled cavity in the interior. How can we extract this internal water?


top of page

    

    

Essentially, we represent the protein barrel by its C_α skeleton, triangulate it, and determine all water molecules inside the polyhedron.

    

Some details on the algorithm. The triangulation exploits locality and can thus be performed in linear time.

    

Using the above algorithm, we may analyze the entire trajectory and identify the distribution of 3 (apo) and 4 (holo) water molecules which in NMR experiments have been found to be particularly immobile,


top of page

    

or analyze the entire interior water density

    

or even time-resolved interaction potentials with other water, with protein residues, and with the ligand to improve our understanding of the internal water dynamics.

    

Carbopeptoids are homooligomers of sugar-containing peptides, and they serve as rigidified peptide models with potential applications as drugs that block protein-protein interactions and inhibit enzyme catalysis.


top of page

    

MD simulations reproduce experimentally (NOE) derived distance constraints. Cluster analyses of MD trajectories demonstrates, however, that the experimentally postulated helical structure is only one of several dominating structural motifs comprising the entire ensemble, and that the unfolded state is in fact not structureless. Such insight is hard if not impossible to obtain from experiment alone.

    

Cluster analysis combining the ensembles of the tetrapeptide and equally long blocks of the hexapeptide demonstrates the repetition of structural motifs in longer peptide chains, a result, that was postulated in experimental studies. Note the "overlapping" (blue/red) clusters in the graph.

    

MD simulations often apply a distance-cutoff for pair potentials, and the scan of the atom pair matrix is one of the very time-critical parts of such an MD simulation. While linear-scaling grid-cell techniques become efficient for very large system sizes, improved double-loop algorithms are beneficial for intermediate sizes often considered in current-day simulations.


top of page

    

Here we take advantage of the fast processor cache found in modern CPUs and replace the row-wise atom pair scan (unshaded) by a window scan (shaded) which can process a number of pairs that scales quadratically, rather than linearly, with the number of atoms loaded into cache memory. The triangular atom-pair matrix may be reordered to become rectangular, in which case all rhombic windows become quadratic.

    

Fullerenes were discovered in the mid-80's and have attracted a lot of attention as new allotropes of carbon. The prototype buckminsterfullerene, C₆₀, is spherical due to its high symmetry.


top of page

    

Despite earlier claims, however, our semiempirical calculations have shown that larger fullerenes of icosahedral symmetry prefer facetted over spherical shapes. These results were confirmed by more rigorous density functional calculations . The picture above shows the facetted form of C₉₆₀ from two different perspectives and a hypothetical spherical alternative.

    

The development of accurate extrapolation formulas for electron correlation energies is an important field in ab initio thermochemistry. Electron correlation energies are known to converge slowly to the complete basis set limit, and finite basis set calculations will thus carry substantial error. On the other hand, computational restraints usually force one to resort to small basis-set calculations. The graph compares residual errors for our newly developed and theoretically well-motivated extrapolation formula (2nd and 4th panel) to those of the best alternative formulations (1st and 3rd panels). The large improvement is expected to have a significant impact on producing reliable ab initio reference data for the calibration of empirical and semiempirical potentials.


top of page

    

The ATOMIC approach was developed with the needs in mind that are posed by the calibration of modern approximate models of quantum chemistry, such as semiempirical methods. It is a robust and computationally efficient approach to otherwise dauntingly expensive calculations of atomization energies. The graph shows how the use of bond separation reactions (BSRs) helps to reduce errors in each of the components contributing to the CCSD(T)(full) atomization energy at the complete-basis set limit. Each single chart shows RMS errors for a particular component as function of the basis-set cardinal number, without (top) or with (bottom) extrapolation. In practice only small basis-set calculations are feasible for larger systems.


top of page

    

Corrections to atomization energies beyond the CCSD(T) level of theory are estimated from thermoneutral BSRs. This simplification renders the calculation of these corrections a trivial task of summing up bond increments. Such an approach is astonishingly accurate for scalar relativistic corrections and works reasonably well even for CCSDTQ-CCSD(T) corrections.