52,551 research outputs found

    A Chemical Proteomic Probe for Detecting Dehydrogenases: \u3cem\u3eCatechol Rhodanine\u3c/em\u3e

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    The inherent complexity of the proteome often demands that it be studied as manageable subsets, termed subproteomes. A subproteome can be defined in a number of ways, although a pragmatic approach is to define it based on common features in an active site that lead to binding of a common small molecule ligand (ex. a cofactor or a cross-reactive drug lead). The subproteome, so defined, can be purified using that common ligand tethered to a resin, with affinity chromatography. Affinity purification of a subproteome is described in the next chapter. That subproteome can then be analyzed using a common ligand probe, such as a fluorescent common ligand that can be used to stain members of the subproteome in a native gel. Here, we describe such a fluorescent probe, based on a catechol rhodanine acetic acid (CRAA) ligand that binds to dehydrogenases. The CRAA ligand is fluorescent and binds to dehydrogenases at pH \u3e 7, and hence can be used effectively to stain dehydrogenases in native gels to identify what subset of proteins in a mixture are dehydrogenases. Furthermore, if one is designing inhibitors to target one or more of these dehydrogenases, the CRAA staining can be performed in a competitive assay format, with or without inhibitor, to assess the selectivity of the inhibitor for the targeted dehydrogenase. Finally, the CRAA probe is a privileged scaffold for dehydrogenases, and hence can easily be modified to increase affinity for a given dehydrogenase

    S-Lemma with Equality and Its Applications

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    Let f(x)=xTAx+2aTx+cf(x)=x^TAx+2a^Tx+c and h(x)=xTBx+2bTx+dh(x)=x^TBx+2b^Tx+d be two quadratic functions having symmetric matrices AA and BB. The S-lemma with equality asks when the unsolvability of the system f(x)<0,h(x)=0f(x)<0, h(x)=0 implies the existence of a real number μ\mu such that f(x)+μh(x)0, xRnf(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n. The problem is much harder than the inequality version which asserts that, under Slater condition, f(x)<0,h(x)0f(x)<0, h(x)\le0 is unsolvable if and only if f(x)+μh(x)0, xRnf(x) + \mu h(x)\ge0, ~\forall x\in \mathbb{R}^n for some μ0\mu\ge0. In this paper, we show that the S-lemma with equality does not hold only when the matrix AA has exactly one negative eigenvalue and h(x)h(x) is a non-constant linear function (B=0,b0B=0, b\not=0). As an application, we can globally solve inf{f(x)h(x)=0}\inf\{f(x)\vert h(x)=0\} as well as the two-sided generalized trust region subproblem inf{f(x)lh(x)u}\inf\{f(x)\vert l\le h(x)\le u\} without any condition. Moreover, the convexity of the joint numerical range {(f(x),h1(x),,hp(x)): xRn}\{(f(x), h_1(x),\ldots, h_p(x)):~x\in\Bbb R^n\} where ff is a (possibly non-convex) quadratic function and h1(x),,hp(x)h_1(x),\ldots,h_p(x) are affine functions can be characterized using the newly developed S-lemma with equality.Comment: 34 page

    A Direct Elliptic Solver Based on Hierarchically Low-rank Schur Complements

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    A parallel fast direct solver for rank-compressible block tridiagonal linear systems is presented. Algorithmic synergies between Cyclic Reduction and Hierarchical matrix arithmetic operations result in a solver with O(Nlog2N)O(N \log^2 N) arithmetic complexity and O(NlogN)O(N \log N) memory footprint. We provide a baseline for performance and applicability by comparing with well known implementations of the H\mathcal{H}-LU factorization and algebraic multigrid with a parallel implementation that leverages the concurrency features of the method. Numerical experiments reveal that this method is comparable with other fast direct solvers based on Hierarchical Matrices such as H\mathcal{H}-LU and that it can tackle problems where algebraic multigrid fails to converge
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