Controlling Grain Boundaries by Magnetic Fields.

The ability to use external magnetic fields to influence the microstructure in polycrystalline materials has potential applications in microstructural engineering. To explore this potential and to understand the complex interactions between electromagnetic fields and solid-state matter transport we consider a phase-field-crystal model. Together with efficient and scalable numerical algorithms this allows the examination of the role that external magnetic fields play on the evolution of defect structures and grain boundaries, on diffusive timescales. Examples for planar and circular grain boundaries explain the essential atomistic processes and large scale simulations in 2D are used to obtain statistical data on grain growth under the influence of external fields.

A phase-field-crystal approach to critical nuclei.

We investigate a phase-field-crystal model for homogeneous nucleation. Instead of obtaining the time evolution of a density field towards equilibrium, we use a string method to identify saddle points in phase space. The saddle points allow us to obtain the nucleation barrier and the critical nucleus. The advantage of using the phase-field-crystal model for this task is that it can be used to resolve atomistic effects. The results obtained indicate different properties of the critical nucleus as compared with those for bulk crystals and provide a detailed description of the nucleation process.

Solid-liquid interfacial energies and equilibrium shapes of nanocrystals.

We extract the anisotropy of the solid-liquid interfacial energy of small crystals using phase field crystal simulations. The results indicate a strong dependence of the interfacial energy on the parameters in the phase field crystal model determining the position in the solid-liquid coexistence region in the phase diagram. Furthermore a size dependence of the anisotropy is shown if the crystal shape is reduced to the size of a nucleus.

Algorithmic approach to quantifying the hydrophobic force contribution in protein folding.

Though the electrostatic, ionic, van der Waals, Lennard-Jones, hydrogen bonding, and other forces play an important role in the energy function minimized at a protein's native state, it is widely believed that the hydrophobic force is the dominant term in protein folding. Here we attempt to quantify the extent to which the hydrophobic force determines the positions of the backbone alpha-carbon atoms in PDB data, by applying Monte-Carlo and genetic algorithms to determine the predicted conformation with minimum energy, where only the hydrophobic force is considered (i.e. Dill's HP-model, and refinements using Woese's polar requirement). This is done by computing the root mean square deviation between the normalized distance matrix D = (di,j) (di,j is normalized Euclidean distance between residues ri and rj) for PDB data with that obtained from the output of our algorithms. Our program was run on the database of ancient conserved regions drawn from GenBank 101 generously supplied by W. Gilbert's lab, as well as medium-sized proteins (E. Coli RecA, 2reb, Erythrocruorin, 1eca, and Actinidin 2act). The root mean square deviation (RMSD) between distance matrices derived from the PDB data and from our program output is quite small, and by comparison with RMSD between PDB data and random coils, allows a quantification of the hydrophobic force contribution. A preliminary version of this paper appeared at GCB'99 (http:¿bibiserv.techfak.uni-bielefeld.de/gcb9 9/).

Application of constraint programming techniques for structure prediction of lattice proteins with extended alphabets.

MOTIVATION: Predicting the ground state of biopolymers is a notoriously hard problem in biocomputing. Model systems, such as lattice proteins, are simple tools and valuable to test and improve new methods. Best known are models with sequences composed from a binary (hydrophobic and polar) alphabet. The major drawback is the degeneracy, i.e. the number of different ground state conformations. RESULTS: We show how recently developed constraint programming techniques can be used to solve the structure prediction problem efficiently for a higher order alphabet. To our knowledge it is the first report of an exact and computationally feasible solution to model proteins of length up to 36 and without resorting to maximally compact states. We further show that degeneracy is reduced by more than one order of magnitude and that ground state conformations are not necessarily compact. Therefore, more realistic protein simulations become feasible with our model.

Using constraint programming for lattice protein folding.

We present a global search technique for finding the global minimal conformation of a sequence in Dill's HP-lattice model. The HP-lattice model is a simplified model of proteins, that has become a major tool for investigating general properties of protein folding. The search technique uses constraint programming for efficiently pruning the search tree. We state the problem of structure prediction in the HP-lattice model and describe our implementation using the Oz-system.