Green's-function reaction dynamics: a particle-based approach for simulating biochemical networks in time and space

We have developed a new numerical technique, called Green's-function reaction dynamics (GFRD), that makes it possible to simulate biochemical networks at the particle level and in both time and space. In this scheme, a maximum time step is chosen such that only single particles or pairs of particles have to be considered. For these particles, the Smoluchowski equation can be solved analytically using Green's functions. The main idea of GFRD is to exploit the exact solution of the Smoluchoswki equation to set up an event-driven algorithm, which combines in one step the propagation of the particles in space with the reactions between them. The event-driven nature allows GFRD to make large jumps in time and space when the particles are far apart from each other. Here, we apply the technique to a simple model of gene expression. The simulations reveal that spatial fluctuations can be a major source of noise in biochemical networks. The calculations also show that GFRD is highly efficient. Under biologically relevant conditions, GFRD is up to five orders of magnitude faster than conventional particle-based techniques for simulating biochemical networks in time and space. GFRD is not limited to biochemical networks. It can also be applied to a large number of other reaction-diffusion problems.     

High-resolution Mn EXAFS of the oxygen-evolving complex in photosystem II: structural implications for the Mn4Ca cluster

The biological generation of oxygen by the oxygen-evolving complex in photosystem II (PS II) is one of nature's most important reactions. The recent X-ray crystal structures, while limited by resolutions of 3.2-3.5 A, have located the electron density associated with the Mn4Ca cluster within the multiprotein PS II complex. Detailed structures critically depend on input from spectroscopic techniques, such as EXAFS and EPR/ENDOR, as the XRD resolution does not allow for accurate determination of the position of Mn/Ca or the bridging and terminal ligand atoms. The number and distances of Mn-Mn/Ca/ligand interactions determined from EXAFS provide important constraints for the structure of the Mn4Ca cluster. Here, we present data from a high-resolution EXAFS method using a novel multicrystal monochromator that show three short Mn-Mn distances between 2.7 and 2.8 A and, hence, the presence of three di-mu-oxo-bridged units in the Mn4Ca cluster. This result imposes clear limitations on the proposed structures based on spectroscopic and diffraction data and provides input for refining such structures.     

Characterization of a new tailoring domain in polyketide biogenesis: the amine transferase domain of MycA in the mycosubtilin gene cluster

We report the expression and characterization of a truncated form of MycA from the Mycosubtilin gene cluster from Bacillus subtilis. The MycA fragment contains a new amino transferase (AMT) tailoring domain, allowing the first detailed study of a PLP-dependent enzyme operating in cis within the PKS and NRPS biosynthetic paradigm. As the AMT domain acts on covalently bound beta-ketothioesters, and is therefore a single-turnover system, electrospray ionization-Fourier transform mass spectrometry (ESI-FTMS) was used to observe the amine-transfer reaction both for amine donor substrate specificity and to regiospecifically determine enzyme-bound intermediates. We confirm the function of the AMT domain, dissect the mechanistic steps of amine transfer, identify the preferred amine source, and localize the beta-ketothioester substrate during amine transfer.     

Numerical study of the flow in a three-dimensional thermally driven cavity

Solutions for the fully compressible Navier–Stokes equations are presented for the flow and temperature fields in a cubic cavity with large horizontal temperature differences. The ideal-gas approximation for air is assumed and viscosity is computed using Sutherland's law. The three-dimensional case forms an extension of previous studies performed on a two-dimensional square cavity. The influence of imposed boundary conditions in the third dimension is investigated as a numerical experiment. Comparison is made between convergence rates in case of periodic and free-slip boundary conditions. Results with no-slip boundary conditions are presented as well. The effect of the Rayleigh number is studied.     

Conformational analysis of 1,2-difluoroethane, an ab-initio investigation

Contrary to expectation, the gauche conformer of 1,2-difluoroethane is more stable than the trans conformer in the gas phase. In order to understand the underlying causes of the “gauche effect”, a complete geometry relaxation was performed for the gauche and trans conformers of 1,2-difluoroethane with the 4-21G, 4-31G and 4-31G** basis sets. The 4-31G** optimized geometry of the gauche conformer compares well with the experimental values obtained from a number of electron-diffraction studies. A correction for the correlation energy, calculated by means of second-order Møller—Plesset perturbation theory with the 6-31G** basis set, proves to be essential to obtain a correct estimate of the energy difference between the gauche and trans conformers 1,2-difluoroethane.     

Photostabilizing of bisphenol A polycarbonate by using UV-absorbers and self protective block copolymers based on resorcinol polyarylate blocks

Bisphenol A polycarbonate degrades due to sunlight, humidity and oxygen. In this study two possible techniques to stabilize the polymer were compared, i.e. blending of UV-absorbers (UVAs) into the polymer or using block copolymers based on resorcinol polyarylates. Combination of different analysis techniques shows that the protection by UVAs is not as good as by the resorcinol polyarylate block copolymers. The block copolymer rearranges itself through a photo-Fries rearrangement within hours into a UV-absorbing top layer. Two different block compositions were studied, and the copolymer with the highest concentration of resorcinol polyarylate groups shows the best protection.     

Paper coatings with multi-scale roughness evaluated at different sampling sizes

Papers have a complex hierarchical structure and the end-user functionalities such as hydrophobicity are controlled by a finishing layer. The application of an organic nanoparticle coating and drying of the aqueous dispersion results in an unique surface morphology with microscale domains that are internally patterned with nanoparticles. Better understanding of the multi-scale surface roughness patterns is obtained by monitoring the topography with non-contact profilometry (NCP) and atomic force microscopy (AFM) at different sampling areas ranging from 2000 μm × 2000 μm to 0.5 μm × 0.5 μm. The statistical roughness parameters are uniquely related to each other over the different measuring techniques and sampling sizes, as they are purely statistically determined. However, they cannot be directly extrapolated over the different sampling areas as they represent transitions at the nano-, micro-to-nano and microscale level. Therefore, the spatial roughness parameters including the correlation length and the specific frequency bandwidth should be taken into account for each measurement, which both allow for direct correlation of roughness data at different sampling sizes.     

An analysis of generalised heuristics for vehicle routing and personnel rostering problems

The present study investigates the performance of heuristics while solving problems with routing and rostering characteristics. The target problems include scheduling and routing home care, security and maintenance personnel. In analysing the behaviour of the heuristics and determining the requirements for solving the aforementioned problems, the winning hyper-heuristic from the first International Cross-domain Heuristic Search Challenge (CHeSC 2011) is employed. The completely new application of a hyper-heuristic as an analysis tool offers promising perspectives for supporting dedicated heuristic development. The experimental results reveal that different low-level heuristics perform better on different problems and that their performance varies during a search process. The following characteristics affect the performance of the heuristics: the planning horizon, the number of activities and lastly the number of resources. The body of this paper details both these characteristics and also discusses the required features for embedding in an algorithm to solve problems particularly with a vehicle routing component.     

Graph Duality in Surface Dynamics

Journal of Nonlinear Science - We compare one-dimensional representations for the isotopy stable dynamics of homeomorphisms in two dimensions. We consider the skeleton graph representative, which...     

The modal interpretation of quantum mechanics and its generalization to density operators

We generalize the modal interpretation of quantum mechanics so that it may be applied to composite systems represented by arbitrary density operators. We discuss the interpretation these density operators receive and relate this to the discussion about the interpretation of proper and improper mixtures in the standard interpretation.