Engineered biosynthesis of novel spinosyns bearing altered deoxyhexose substituents

Novel spinosyns have been prepared by biotransformation, using a genetically engineered strain of Saccharopolyspora erythraea, in which the beta-D-forosamine moiety in glycosidic linkage to the hydroxy group at C17 is replaced by alpha-L-mycarose.     

Recursive Three-Term Recurrence Relations for?the?Jacobi Polynomials on a Triangle

Given a suitable weight on ℝ ^d , there exist many (recursive) three-term recurrence relations for the corresponding multivariate orthogonal polynomials. In principle, these can be obtained by calculating pseudoinverses of a sequence of matrices. Here we give an explicit recursive three-term recurrence for the multivariate Jacobi polynomials on a simplex. This formula was obtained by seeking the best possible three-term recurrence. It defines corresponding linear maps, which have the same symmetries as the spaces of Jacobi polynomials on which they are defined. The key idea behind this formula is that some Jacobi polynomials on a simplex can be viewed as univariate Jacobi polynomials, and for these the recurrence reduces to the univariate three-term recurrence.     

Integral error formulæ for the scale of mean value interpolations which includes Kergin and Hakopian interpolation

Summary. In this paper, we provide an integral error formula for a certain scale of mean value interpolations which includes the multivariate polynomial interpolation schemes of Kergin and Hakopian. This formula involves only derivatives of order one higher than the degree of the interpolating polynomial space, and from it we can obtain sharp -estimates. These -estimates are precisely those that numerical analysts want, to guarantee that a scheme based on such an interpolation has the maximum possible order. Received July 11, 1994 / Revised version received February 12, 1996     

L p -Error Bounds for Hermite Interpolation and the Associated Wirtinger Inequalities

The B-spline representation for divided differences is used, for the first time, to provide L _p -bounds for the error in Hermite interpolation, and its derivatives, thereby simplifying and improving the results to be found in the extensive literature on the problem. These bounds are equivalent to certain Wirtinger inequalities. The major result is the inequality where H_Θ f is the Hermite interpolant to f at the multiset of n points Θ, and is the diameter of . This inequality significantly improves upon Beesack's inequality, on which almost all the bounds given over the last 30 years have been based. Date received: June 24, 1994 Date revised: February 4, 1996.     

Frames for vector spaces and affine spaces

A finite frame for a finite dimensional Hilbert space is simply a spanning sequence. We show that the linear functionals given by the dual frame vectors do not depend on the inner product, and thus it is possible to extend the frame expansion (and other elements of frame theory) to any finite spanning sequence for a vector space. The corresponding coordinate functionals generalise the dual basis (the case when the vectors are linearly independent), and are characterised by the fact that the associated Gramian matrix is an orthogonal projection. Existing generalisations of the frame expansion to Banach spaces involve an analogue of the frame bounds and frame operator.The potential applications of our results are considerable. Whenever there is a natural spanning set for a vector space, computations can be done directly with it, in an efficient and stable way. We illustrate this with a diverse range of examples, including multivariate spline spaces, generalised barycentric coordinates, and vector spaces over the rationals, such as the cyclotomic fields.     

Apparatus for Testing Concrete under Multiaxial Compression at Elevated Temperature (mac2T)

This paper describes a new test facility for determining material mechanical properties of structural concrete. The novel facility subjects 100 mm cubic concrete specimens to true multiaxial compression (σ₁ ≠ σ₂ ≠ σ₃) up to 400 MPa at temperatures of up to 300°C. Forces are delivered through three independent loading frames equipped with servo-controlled hydraulic actuators creating uniform displacement boundary conditions via rigid platens. Specimen deformation is calculated from displacements measured to an accuracy of 10⁻⁶ m using a system of six laser interferometers. The combination of stiff loading frames, rigid platens, an accurate and reliable strain measurement system and a fast control system enables investigation of the material response in the post-peak range. The in-house developed control software allows complex multi-stage experiments involving (i) load and temperature cycling, (ii) small stress probes and (iii) arbitrary (pre-defined) loading paths. The program also enables experiments in which the values of the control parameters and the execution of the test sequences depend on the response of the specimen during the test. The capabilities of the facility are illustrated in this paper by experiments determining the effects of different heat-load regimes on the strength and stiffness of the material and tests identifying the tangent stiffness matrix of the material and the associated changes in the acoustic tensor under multiaxial compression.     

Continuous and Discrete Tight Frames of Orthogonal Polynomials for a Radially Symmetric Weight

This paper considers tight frame decompositions of the Hilbert space ℘ _n of orthogonal polynomials of degree n for a radially symmetric weight on ℝ ^d , e.g., the multivariate Gegenbauer and Hermite polynomials. We explicitly construct a single zonal polynomial p∈℘ _n with the property that each f∈℘ _n can be reconstructed as a sum of its projections onto the orbit of p under SO(d) (symmetries of the weight), and hence of its projections onto the zonal polynomials p _ξ obtained from p by moving its pole to ξ∈S:={ξ∈ℝ ^d :|ξ|=1}. Furthermore, discrete versions of these integral decompositions also hold where SO(d) is replaced by a suitable finite subgroup, and S by a suitable finite subset. One consequence of our decomposition is a simple closed form for the reproducing kernel for ℘ _n .      

First principles modeling of tunnel magnetoresistance of Fe/MgO/Fe trilayers

We report ab initio calculations of nonequilibrium quantum transport properties of Fe/MgO/Fe trilayer structures. The zero bias tunnel magnetoresistance is found to be several thousand percent, and it is reduced to about 1000% when the Fe/MgO interface is oxidized. The tunnel magnetoresistance for devices without oxidization reduces monotonically to zero with a voltage scale of about 0.5-1 V, consistent with experimental observations. We present an understanding of the nonequilibrium transport by investigating microscopic details of the scattering states and the Bloch bands of the Fe leads.     

Cloning and analysis of the spinosad biosynthetic gene cluster of Saccharopolyspora spinosa

BACKGROUND: Spinosad is a mixture of novel macrolide secondary metabolites produced by Saccharopolyspora spinosa. It is used in agriculture as a potent insect control agent with exceptional safety to non-target organisms. The cloning of the spinosyn biosynthetic gene cluster provides the starting materials for the molecular genetic manipulation of spinosad yields, and for the production of novel derivatives containing alterations in the polyketide core or in the attached sugars. RESULTS: We cloned the spinosad biosynthetic genes by molecular probing, complementation of blocked mutants, and cosmid walking, and sequenced an 80 kb region. We carried out gene disruptions of some of the genes and analyzed the mutants for product formation and for the bioconversion of intermediates in the spinosyn pathway. The spinosyn gene cluster contains five large open reading frames that encode a multifunctional, multi-subunit type I polyketide synthase (PKS). The PKS cluster is flanked on one side by genes involved in the biosynthesis of the amino sugar forosamine, in O-methylations of rhamnose, in sugar attachment to the polyketide, and in polyketide cross-bridging. Genes involved in the early common steps in the biosynthesis of forosamine and rhamnose, and genes dedicated to rhamnose biosynthesis, were not located in the 80 kb cluster. CONCLUSIONS: Most of the S. spinosa genes involved in spinosyn biosynthesis are found in one 74 kb cluster, though it does not contain all of the genes required for the essential deoxysugars. Characterization of the clustered genes suggests that the spinosyns are synthesized largely by mechanisms similar to those used to assemble complex macrolides in other actinomycetes. However, there are several unusual genes in the spinosyn cluster that could encode enzymes that generate the most striking structural feature of these compounds, a tetracyclic polyketide aglycone nucleus.