Goussarov-Habiro theory for string links and the Milnor-Johnson correspondence

We study the Goussarov-Habiro finite type invariants theory for framed string links in homology balls. Their degree 1 invariants are computed: they are given by Milnor's triple linking numbers, the mod 2 reduction of the Sato-Levine invariant, Arf and Rochlin's μ invariant. These invariants are seen to be naturally related to invariants of homology cylinders through the Milnor-Johnson correspondence: in particular, an analogue of the Birman-Craggs homomorphism for string links is computed. The relation with Vassiliev theory is studied.     

α2A肾上腺素受体的同源模建及与Yohimbine的对接研究

通过对比多个与α2A-肾上腺素受体同属G-蛋白偶联受体的视紫红质蛋白序列,选择以相似性最大的牛视紫红质蛋白为模板,同源模建了α2A-肾上腺素受体的跨膜结构,并在结构中找到了体积为0.090 nm3,已被报导的活性残基包围的活性位点.运用分子力学与动力学方法研究了此结构突变前后与抑制剂Yohimbine的对接情况,得到了与文献报道相吻合的结果.同时对接研究结果发现,在α2A-肾上腺素受体的结合位点周围的一个由色氨酸和两个苯丙氨酸组成的局部疏水区对抑制剂有稳定作用,并且天冬氨酸113作为氢键受体也对稳定抑制剂有重要作用.     

On minimal subgroups of finite groups

In this paper, the minimal subgroups of a finite group G are studied. Using the normalizes of Sylow subgroups of G, we obtain some sufficient conditions for G to be p-milpotent and supersolvable, which ae extensions of the related results of Burnside, Ito, Buckley and Asaad.     

On (k,\varepsilon)-saddle submanifolds of Riemannian manifolds

The paper continues our (in collaboration with A. Borisenko [J. Differential Geom. Appl. 20 p., to appear]) discovery of the new classes of $(k,\varepsilon)The paper continues our (in collaboration with A. Borisenko [J. Differential Geom. Appl. 20 p., to appear]) discovery of the new classes of -saddle, -parabolic, and -convex submanifolds ( ). These are defined in terms of the eigenvalues of the 2nd fundamental forms of each unit normal of the submanifold, extending the notion of k-saddle, k-parabolic, k-convex submanifolds ( ). It follows that the definition of -saddle submanifolds is equivalent to the existence of -asymptotic subspaces in the tangent space. We prove non-embedding theorems of -saddle submanifolds, theorems about 1-connectedness and homology groups of these submanifolds in Riemannian spaces of positive (sectional or qth Ricci) curvature, in particular, spherical and projective spaces. We apply these results to submanifolds with ‘small’ normal curvature, , and for submanifolds with extrinsic curvature (resp., non-positive) and small codimension, and include some illustrative examples. The results of the paper generalize theorems about totally geodesic, minimal and k-saddle submanifolds by Frankel; Borisenko, Rabelo and Tenenblat; Kenmotsu and Xia; Mendon?a and Zhou.      

Homology representations arising from the half cube, II

In a previous work, we defined a family of subcomplexes of the n-dimensional half cube by removing the interiors of all half cube shaped faces of dimension at least k, and we proved that the reduced homology of such a subcomplex is concentrated in degree k−1. This homology module supports a natural action of the Coxeter group W(Dn) of type D. In this paper, we explicitly determine the characters (over C) of these homology representations, which turn out to be multiplicity free. Regarded as representations of the symmetric group Sn by restriction, the homology representations turn out to be direct sums of certain representations induced from parabolic subgroups. The latter representations of Sn agree (over C) with the representations of Sn on the (k−2)-nd homology of the complement of the k-equal real hyperplane arrangement.     

A highly sensitive and specific enzyme immunoassay for detection of β-amanitin in biological fluids

Polyclonal antisera to -amanitin were generated in sheep and used to construct a competitive ELISA for measurement of the toxin in human serum and urine. The assay had a detection limit of about 80 pg mL^–1, a dynamic range of 80–2,000 pg mL^–1, a cross reactivity of 22% with -amanitin, and no cross reactivities with cyclic peptides from algal sources. Assay responses in buffer, serum, and urine were remarkably similar. Coupling of the toxin to carrier proteins was carried out by previously unreported methods. The key step that allowed the construction of the highly sensitive assay was the introduction of a novel heterologous hapten derivative made of -amanitin-cyanuric chloride derivative. The new derivative overcame the problems of bridge binding that was, in this case, particularly serious with the homologous hapten derivative. The study demonstrated that the developed antiserum and ELISA procedure can be used to detect -amanitin and related toxins from Amanita phalloides in human serum and urine samples from suspected poison cases and enable early treatment to be administered.     

对羟基杏仁酸合成酶三维结构模建及其与底物的分子对接研究

以对羟基苯丙酮酸双氧化酶(HPPD)的晶体结构为模板, 利用同源模建方法构建了与其高度同源、底物相同但催化功能存在明显差别的对羟基杏仁酸合成酶(HMS)的三维结构, 并对模建结构的合理性进行了分析. 在模建结果的基础上, 对HPPD和HMS分别与底物羟苯基丙酮酸(HPP)进行分子对接计算, 比较了二者结合模式的异同, 为两种同源酶在催化方面差异性的合理阐释提供了一些有益的信息.     

毒蕈碱型M1受体的同源模建和分子对接

采用同源模建方法对M1受体的三维结构进行了模拟, 将得到的模型分别与M受体完全激动剂乙酰胆碱和M1受体选择性激动剂占诺美林进行分子对接, 形成非特异性激动和特异性激动的受体-配体复合物. 用分子动力学模拟方法分别将未与小分子对接的M1受体、M1受体-乙酰胆碱复合物、M1受体-占诺美林复合物置于磷脂双膜中模拟10 ns. 将模拟后的蛋白质结构与包含活性分子的测试库对接并将结果打分, 以top5%富集因子(EF)作为评价依据, 用占诺美林优化后的M1受体模型的EF为8.0, 用乙酰胆碱优化后M1受体模型的EF为6.5, 非复合物的EF为1.5. 说明M1受体选择性激动剂复合物进行分子动力学模拟后得到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, 为找到新的选择性M1受体激动剂奠定了基础.     

Minimally separating sets, mediatrices, and Brillouin spaces

Brillouin zones and their boundaries were studied in [J.J.P. Veerman et al., Comm. Math. Phys. 212 (3) (2000) 725] because they play an important role in focal decomposition as first defined by Peixoto in [J. Differential Equations 44 (1982) 271] and in physics [N.W. Ashcroft, N.D. Mermin, Solid State Physics, Holt, Rhinehart, and Winston, 1976; L. Brillouin, Wave Propagation in Periodic Structures, Dover, 1953]. In so-called Brillouin spaces, the boundaries of the Brillouin zones have certain regularity properties which imply that they consist of pieces of mediatrices (or equidistant sets).The purpose of this note is two-fold. First, we give some simple conditions on a metric space which are sufficient for it to be a Brillouin space. These conditions show, for example, that all compact, connected Riemannian manifolds with their usual distance functions are Brillouin spaces. Second, we exhibit a restriction on the Z₂-homology of mediatrices in such manifolds in terms of the Z₂-homology of the manifolds themselves, based on the fact that they are Brillouin spaces. (This will used to obtain a classification up to homeomorphism of surface mediatrices in forthcoming paper [J. Bernhard, J.J.P. Veerman, The topology of surface mediatrices, Portland State University].)