Graph theoretical analysis of the phytosociological structure of plant communities: The theoretical basis

Summary A method employing samples of variable size is assumed and shown to be useful in the detection of unidirectional associations of one species with another, whether caused by direct influence or by coincidence of ecological requirements. The pattern of these associations from a signed digraph (directed graph), the graph theoretical properties of which give insight into the phytosociological structure of the plant community. The properties of transitivity, balance, homogeneity, reachable sets and types of subgraphs are examined.From a thesis submitted to the University of Toronto in partial fulfilment of the requirements for the degree of Master of Science.     

基于图论模型的蛋白质结构类型的研究

提出了基于图论模型的H系数分类蛋白质结构为H结型和NH结型的方法.论述了蛋白质结构中序列不相邻的C_α原子之间的空间距离与序列相邻的C_α原子之间空间距离的关系.用此方法对PDB的66个单链蛋白质结构进行分类,结果显示H结型占18.2%.H结在全α型中出现比例较高,在全β型中出现比例较小,所以H结倾向出现在含有α螺旋的蛋白质结构中.     

Graph decompositions for demographic loop analysis

A new approach to loop analysis is presented in which decompositions of the total elasticity of a population projection matrix over a set of life history pathways are obtained as solutions of a constrained system of linear equations. In loop analysis, life history pathways are represented by loops in the life cycle graph, and the elasticity of the loop is interpreted as a measure of the contribution of the life history pathway to the population growth rate. Associated with the life cycle graph is a vector space -- the cycle space of the graph -- which is spanned by the loops. The elasticities of the transitions in the life cycle graph can be represented by a vector in the cycle space, and a loop decomposition of the life cycle graph is then defined to be any nonnegative linear combination of the loops which sum to the vector of elasticities. In contrast to previously published algorithms for carrying out loop analysis, we show that a given life cycle graph admits of either a unique loop decomposition or an infinite set of loop decompositions which can be characterized as a bounded convex set of nonnegative vectors. Using this approach, loop decompositions which minimize or maximize a linear objective function can be obtained as solutions of a linear programming problem, allowing us to place lower and upper bounds on the contributions of life history pathways to the population growth rate. Another consequence of our approach to loop analysis is that it allows us to identify the exact tradeoffs in contributions to the population growth rate that must exist between life history pathways.     

New metrics for comparing and assessing discrepancies between RNA 3D structures and models

To benchmark progress made in RNA three-dimensional modeling and assess newly developed techniques, reliable and meaningful comparison metrics and associated tools are necessary. Generally, the average root-mean-square deviations (RMSDs) are quoted. However, RMSD can be misleading since errors are spread over the whole molecule and do not account for the specificity of RNA base interactions. Here, we introduce two new metrics that are particularly suitable to RNAs: the deformation index and deformation profile. The deformation index is calibrated by the interaction network fidelity, which considers base–base-stacking and base–base-pairing interactions within the target structure. The deformation profile highlights dissimilarities between structures at the nucleotide scale for both intradomain and interdomain interactions. Our results show that there is little correlation between RMSD and interaction network fidelity. The deformation profile is a tool that allows for rapid assessment of the origins of discrepancies.     

Unrevealed structural requirements for auxin-like molecules by theoretical and experimental evidences

An computational-biostatistical approach, supported by ab initio optimizations of auxin-like molecules, was used to find biologically meaningful relationships between quantum chemical variables and fresh bioassay's data. It is proven that the auxin-like recognition requires different molecular assembling states. We suggest that the carboxyl group is not the determining factor in explaining the biological auxin-like conduct. The biological effects depends essentially on the chemical condition of the ring system. The aim to find active molecules (quantum objects) via statistical grouping-analysis of molecular quantum similarity measures was verified by bioactivity assays. Next, this approach led to the discovery of a non-carboxylated active auxin-like molecule (2,6-dibromo-phenol). This is the first publication on structure activity relationship of auxin-like molecules, which relies on highly standardized bioassays of different auxins screened in parallel as well as analysed by multi-dimensional scaling.     

From knotted to nested RNA structures: a variety of computational methods for pseudoknot removal

Pseudoknots are abundant in RNA structures. Many computational analyses require pseudoknot-free structures, which means that some of the base pairs in the knotted structure must be disregarded to obtain a nested structure. There is a surprising diversity of methods to perform this pseudoknot removal task, but these methods are often poorly described and studies can therefore be difficult to reproduce (in part, because different procedures may be intuitively obvious to different investigators). Here we provide a variety of algorithms for pseudoknot removal, some of which can incorporate sequence or alignment information in the removal process. We demonstrate that different methods lead to different results, which might affect structure-based analyses. This work thus provides a starting point for discussion of the extent to which these different methods recapture the underlying biological reality. We provide access to reference implementations through a web interface (at http://www.ibi.vu.nl/programs/k2nwww), and the source code is available in the PyCogent project.     

A method for finding optimal RNA secondary structures using a new entropy model (vsfold)

We are developing a program to calculate optimal RNA secondary structures. The model uses di-nucleotide pairing energies as with most traditional approaches. However, for long-range entropy interactions, the approach uses an entropy-loss model based on the accumulated sum of the entropy of bonding between each base-pair weighted inversely by the correlation of the RNA sequence (the Kuhn length). Stiff RNA forms very different structures from flexible RNA. The results demonstrate that the long-range folding is largely governed by this entropy and the Kuhn length.     

Experimental and theoretical investigations of magnetic properties for two low-dimensional spin systems based on bis(2-thioxo-1,3-dithiole-4,5-dithiolato)nickelate monoanion building blocks

Two complexes of [Ni(dmit)₂]⁻ (dmit²⁻ = 2-thioxo-1,3-dithiole-4,5-dithiolate) with nonmagnetic Schiff base cations, 1-(4-bromobenzylideneamino)pyridinium (4-BrBz-1-APy⁺; 1) and 1-(3-nitrobenzylideneamino)pyridinium (3-NO₂Bz-1-APy⁺; 2), have been characterized structurally. Their striking structural feature is the deviation of the [Ni(dmit)₂]⁻ anion from the square-planar environment around the Ni atom with 11.42° and 6.57° dihedral angles (between the mean molecular planes of two dmit²⁻ ligands) in 1 and 2, respectively. These twists arise from the molecular packing interactions between the superimposed anion and cation. In 1, the magnetic [Ni(dmit)₂]⁻ anions are arranged into a wave-shaped regular spin chain, whose magnetism was well fitted by one-dimensional (1D) Heisenberg uniform linear antiferromagnetic chain with |J/k_B| = 66 K. In 2, 1D ladder-shape [Ni(dmit)₂]⁻ chains are formed through lateral-to-lateral S?S contacts between the adjacent anions, which are further aligned into a two-dimensional (2D) anion layer via van der Waals forces. Complex 2 shows Curie-Weiss-type paramagnetic behavior with Curie constant C = 0.421 emu K mol⁻¹ and Weiss constant θ = −1.279 K. The broken-symmetry DFT approach was utilized to evaluate the magnetic coupling nature for 1 and 2, the theoretical analyses performed at ubpw91/lanl2dz level and concerned the so-called “weak bonding” regime approaches qualitatively explained the magnetic behaviors of 1 and 2.