Exact sequences for the homology of the matching complex

Building on work by Bouc and by Shareshian and Wachs, we provide a toolbox of long exact sequences for the reduced simplicial homology of the matching complex Mn, which is the simplicial complex of matchings in the complete graph Kn. Combining these sequences in different ways, we prove several results about the 3-torsion part of the homology of Mn. First, we demonstrate that there is nonvanishing 3-torsion in whenever , where . By results due to Bouc and to Shareshian and Wachs, is a nontrivial elementary 3-group for almost all n and the bottom nonvanishing homology group of Mn for all n≠2. Second, we prove that is a nontrivial 3-group whenever . Third, for each k?0, we show that there is a polynomial fk(r) of degree 3k such that the dimension of , viewed as a vector space over Z₃, is at most fk(r) for all r?k+2.     

CH/pi hydrogen bonds determine the selectivity of the Src homology 2 domain to tyrosine phosphotyrosyl peptides: an ab initio fragment molecular orbital study

The CH/pi hydrogen bond is a weak molecular force occurring between CH groups (soft acids) and pi-systems (soft bases), and has been recognized to be important in the interaction of proteins with their specific ligands. For instance, it is well known that Src homology-2 protein (SH2) recognizes its specific pTyr peptide in two key regions, pTyr-binding region and specificity-determining region, by the use of attractive molecular forces, including the CH/pi hydrogen bond. We hypothesized that the CH/pi hydrogen bond plays a key role in determining the selectivity of SH2 proteins, and studied this issue by the ab initio fragment molecular orbital (FMO) method. The FMO calculations were carried out, at the HF/6-31G* and MP2/6-31G* level, for SH2 domains of Src, Grb2, P85alpha(N), Syk, and SAP, in complex with corresponding pTyr peptides. CH/pi hydrogen bonds have in fact been found to be important in stabilizing the structure of the complexes. We conclude that the CH/pi hydrogen bond plays an indispensable role in the recognition of SH2 domains with their specific pTyr peptides, thus playing a vital role in the signal transduction system.     

Harnack-Thom theorem for higher cycle groups and Picard varieties

We generalize the Harnack-Thom theorem to relate the ranks of the Lawson homology groups with -coefficients of a real quasiprojective variety with the ranks of its reduced real Lawson homology groups. In the case of zero-cycle group, we recover the classical Harnack-Thom theorem and generalize the classical version to include real quasiprojective varieties. We use Weil's construction of Picard varieties to construct reduced real Picard groups, and Milnor's construction of universal bundles to construct some weak models of classifying spaces of some cycle groups. These weak models are used to produce long exact sequences of homotopy groups which are the main tool in computing the homotopy groups of some cycle groups of divisors. We obtain some congruences involving the Picard number of a nonsingular real projective variety and the rank of its reduced real Lawson homology groups of divisors.

     

CCK1受体的同源模拟和分子对接研究

采用同源建模法对CCK1受体的三维结构进行了模拟,并采用分子动力学方法对模型进行修正和优化,再采用与训练集激动剂和拮抗剂分子对接的方法分别得到激动状态和拮抗状态CCK1受体的三维结构模型。得到的模型使用DOCK对接软件对训练集中的分子进行对接,所得结果与其实际活性拟合度较好,说明我们建立的激动和拮抗状态下的CCK1受体的三维结构模型比较合理,可以作为化合物虚拟筛选的模型对新化合物进行虚拟筛选。     

Vanishing of Tate Homology — An Application of Stable Homology for Complexes

It has been proved that the vanishing of Tate homology is a sufficient condition for the derived depth formula to hold in [J. Pure Appl. Algebra, 219, 464–481(2015)]. In this paper, we investigate when Tate homology vanishes by studying the stable homology theory for complexes. Properties such as the balancedness and vanishing of stable homology for complexes are studied. Our results show that the vanishing of this homology can detect finiteness of homological dimensions of complexes and regularness of rings.     

Homology Modeling of Cyt2Ca1 of Bacillus thuringiensis and Its Molecular Docking with Inositol Monophosphate

Cyt2Ca1 is an insecticidal crystal protein produced by Bacillus thuringiensis ET29 during its stationary phase, and this δ‐endotoxin demonstrates remarkable insecticidal activity against not only insects of the order Coleoptera, but also against fleas, and in particular the larvae of the cat flea, Ctenocephalides felis. The first theoretical model of the three‐dimensional structure of Cyt2Ca1 was predicted and compared with Cyt2Aa, which is lethal to insect larvae. The three‐dimensional structure of the Cyt2Ca1 was obtained by homology modeling on the structures of the Cyt2Aa protein. The deduced model resembles previously reported Cyt2Aa toxin. A binding mode of inositol monophosphate as a polar head group of the putative membrane phospholipid ligand to Cyt2Ca1 was presented using molecular docking. The residues of Leu9, Glu21, Tyr23 and Gln110 of the Cyt2Ca1 toxin are responsible for the interactions with inositol monophosphate via eight hydrogen bonds. Those residues could be important for receptor recognition. This binding simulation will be helpful for the design of mutagenesis experiments aimed at the improvement of toxicity, and lead to a deep understanding of the mechanism of action of Cyt toxins.     

Five-torsion in the homology of the matching complex on 14 vertices

J.L. Andersen proved that there is 5-torsion in the bottom nonvanishing homology group of the simplicial complex of graphs of degree at most two on seven vertices. We use this result to demonstrate that there is 5-torsion also in the bottom nonvanishing homology group of the matching complex on 14 vertices. Combining our observation with results due to Bouc and to Shareshian and Wachs, we conclude that the case n=14 is exceptional; for all other n, the torsion subgroup of the bottom nonvanishing homology group has exponent three or is zero. The possibility remains that there is other torsion than 3-torsion in higher-degree homology groups of when n≥13 and n≠14. Research of J. Jonsson was supported by European Graduate Program “Combinatorics, Geometry, and Computation”, DFG-GRK 588/2.