Relating coupled map lattices to integro-difference equations: dispersal-driven instabilities in coupled map lattices

Recently there has been a great deal of interest within the ecological community about the interactions of local populations that are coupled only by dispersal. Models have been developed to consider such scenarios but the theory needed to validate model outcomes has been somewhat lacking. In this paper, we present theory which can be used to understand these types of interaction when population exhibit discrete time dynamics. In particular, we consider a spatial extension to discrete-time models, known as coupled map lattices (CMLs) which are discrete in space. We introduce a general form of the CML and link this to integro-difference equations via a special redistribution kernel. General conditions are then derived for dispersal-driven instabilities. We then apply this theory to two discrete-time models; a predator-prey model and a host-pathogen model.     

Resistance of a terrestrial plant community to local microhabitat changes

The number of plant and animal species that exist today is estimated to be around 8.7 million. Approximately 300,000 of these species are flora. This extremely high species diversity has been puzzling scientist since the beginning of ecological research because most of these species compete for limited resources that should lead to the exclusion of all but few superior species. This can be seen in a number of coexistence model today that can only maintain at most four species at a time. We have shown recently that by incorporating minute differences in microhabitat to a lattice competition model, about 13 species can coexist from an initial number of 20. Here, we improve the model further by considering that microhabitat differences are not fixed but can change over time which can affect coexistence. A primary driver to this alteration is climate change, both natural and human induced. To show the resistance of a lattice plant community model, a dynamic microhabitat locality is incorporated by changing the spatial and species‐specific heterogeneity of each lattice site. We show that even if the microhabitat locality of each plant species is dynamic, diversity can still be maintained in a lattice plant ecosystem model. This shows that natural communities of terrestrial plants can be resistant to the stress of microhabitat locality changes to a certain extent.     

The diet transform of lattice patterns,equivalence relations,and similarity measures

The diet algorithm is introduced for the reduction of square-cell lattice patterns to simpler graphs that contain fewer C ₄ cells. By repeated applications of the algorithm, the lattice pattern is converted into a graph representing the skeletal structure of the pattern. Based on the algorithm, equivalence relations and dissimilarity measures are introduced for lattice patterns, providing tools for shape analysis of planar patterns, such as projections of molecular contour surfaces used in molecular design. This algorithm is applied to a series of examples, illustrating the features of the method.     

单形格子和单形重心设计统计模型的优化分析方法

单形格子和单形重心设计是两种非常实用的配方试验设计方法,但其统计模型的优化分析却很困难．本文通过对单形格子和单形重心设计基本原理的分析,根据数学规划理论,构建了专门对这两种试验设计的统计模型进行优化分析的方法,同时给出了应用实例．     

Identification of a molecular switch that selects between two crystals forms of bovine pancreatic trypsin inhibitor.

Two crystals forms of bovine pancreatic trypsin inhibitor are produced between pH 8.39 and 10.13 when crystals are grown at room temperature from solutions of 1.5 M potassium phosphate. Lower pH values favor the form II crystals, whereas higher pH values favor the form III. The transition from one crystal form to the other occurs at pH 9.35. We examined the crystal lattice contacts in both crystal forms and identified an unusual interaction we believe explains these observations. Spanning the crystallographic 2-fold axis in form III crystals, the Lys 41 side-chain amino nitrogens from 2 symmetry-related molecules are only 2.72 A apart, implying they are hydrogen bonded to one another. In form II crystals, the Lys 41 side-chain amino group is protonated and forms a salt bridge with a solvent-derived phosphate group. For the Lys 41 side-chain amino groups to hydrogen bond in form III crystals, at least 1 member of the pair must be deprotonated. The transition that occurs at pH 9.35 marks the pKa for deprotonation. In solution, the pKa for the Lys 41 side chain is around 10.8. The pKa for one of the interacting Lys 41 side chains in form III crystals is therefore shifted downward by about 1.5 pH units. The energy for lowering the pKa value comes from the many additional intermolecular hydrogen bonds that are present in form III crystals: 19 compared to only 8 in form II crystals.     

Protein components of post‐synaptic density lattice,a backbone structure for type I excitatory synapses

It is essential to study the molecular architecture of post‐synaptic density (PSD ) to understand the molecular mechanism underlying the dynamic nature of PSD , one of the bases of synaptic plasticity. A well‐known model for the architecture of PSD of type I excitatory synapses basically comprises of several scaffolding proteins (scaffold protein model). On the contrary, ‘PSD lattice’ observed through electron microscopy has been considered a basic backbone of type I PSD s. However, major constituents of the PSD lattice and the relationship between the PSD lattice and the scaffold protein model, remain unknown. We purified a PSD lattice fraction from the synaptic plasma membrane of rat forebrain. Protein components of the PSD lattice were examined through immuno‐gold negative staining electron microscopy. The results indicated that tubulin, actin, α‐internexin, and Ca²⁺/calmodulin‐dependent kinase II are major constituents of the PSD lattice, whereas scaffold proteins such as PSD ‐95, SAP 102, GKAP , Shank1, and Homer, were rather minor components. A similar structure was also purified from the synaptic plasma membrane of forebrains from 7‐day‐old rats. On the basis of this study, we propose a ‘PSD lattice‐based dynamic nanocolumn’ model for PSD molecular architecture, in which the scaffold protein model and the PSD lattice model are combined and an idea of dynamic nanocolumn PSD subdomain is also included. In the model, cytoskeletal proteins, in particular, tubulin, actin, and α‐internexin, may play major roles in the construction of the PSD backbone and provide linker sites for various PSD scaffold protein complexes/subdomains.

     

Variability of conformations at crystal contacts in BPTI represent true low-energy structures: correspondence among lattice packing and molecular dynamics structures.

The structures of five basic pancreatic trypsin inhibitor (BPTI) molecules are compared to establish the extent and nature of the conformational variability resulting from crystal packing effects. BPTI is an ideal system to evaluate such factors because of the availability of high resolution X-ray models of five different BPTI structures, each in a different crystal packing environment. Differences observed among the structures are found to be distributed throughout the molecule, although the regions that display most variability are associated with the loop structures (residues 14-17 and 24-29). The regions of structure that show the largest rms deviations from the mean of the five packing motifs correlate well with the presence of intermolecular contacts in the crystal lattice. For most of the molecules there is also a correspondence between a larger number of intermolecular contacts and systematically higher B-factors, although it is not apparent whether this is induced by the crystal contact or results from the fact that the contacts are made predominantly through surface loops. The conformational differences seen among the X-ray models constitute more than local shifts at the lattice contact surfaces, and in fact involve in some cases the making and breaking of intramolecular H-bonds. The magnitudes of the differences among packing models are significantly larger than those usually associated with changes induced by mutagenesis; for instance; the structural differences at the site of mutation observed on removing an internal disulfide from the molecule are significantly less than those associated with lattice contact effects. The crystal packing conformations are compared to representative structures of BPTI generated during a 96-psec molecular dynamics (MD) simulation. This comparison shows a high level of correspondence between the protein flexibility indicated by the X-ray and MD analyses, and specifically between those regions that are most variable. This suggests that the regions that show most variability among the crystal packing models are not artifacts of crystallization, but rather represent true low-energy conformers that have been preferentially selected by crystallization factors.     

Recursive Residuals on a Rectangular Lattice

A set of independent N(O, ρ²) recursive residuals is obtained for a model proposed by GLEESON and McGILCHRIST (1980) to describe spatial dependence among observations on a rectangular lattice. These residuals can be used to test model adequacy in a similar fashion to Box-Jenkins techniques for time series models.     

Terahertz vibration modes in Na/K-ATPase

Mechanical vibration in the Terahertz range is believed to be connected with protein functions. In this paper, we present the results of a normal-mode analysis (modal analysis) of a Na/K-ATPase all-atom model, focusing the attention on low-frequency vibration modes. The numerical model helps in the interpretation of experimental results previously obtained by the authors via Raman spectroscopy of Na/K-ATPase samples, where several unassigned peaks were found in the sub-500 cm^?1 range. In particular, vibration modes corresponding to peaks at 27, 190 and 300 cm^?1, found experimentally, are confirmed here numerically, together with some other modes at lower frequencies (wavenumbers) that were not possible to observe in the experimental test. All the aforementioned modes correspond to vibrations involving the protein ends, i.e. portions directly related to the operating mechanism of the sodium-potassium pump.     

Molecular Dynamics Simulation of Nucleation and Growth of a Binary Quasicrystal

Abstract

The quasicrystal structure is considered to be a new type of ordered phase because its Fourier transform has Laue spots with icosahedral symmetry, which is inconsistent with crystal structure. Computer simulation of the formation process of a quasicrystal was performed by the molecular dynamics method. On the basis of the Strandburg type of quasicrystal model, we developed an algorithm of the formation process of binary quasicrystal reflecting the procedure as realistically as possible. The Fourier transform of some of the obtained structures has shown decagonal symmetry although the spots are rather diffused. It has been shown that the potential parameter and experimental condition should be limited to produce a perfect quasicrystal structure.