A Promiscuous De Novo Retro‐Aldolase Catalyzes Asymmetric Michael Additions via Schiff Base Intermediates

Recent advances in computational design have enabled the development of primitive enzymes for a range of mechanistically distinct reactions. Here we show that the rudimentary active sites of these catalysts can give rise to useful chemical promiscuity. Specifically, RA95.5‐8, designed and evolved as a retro‐aldolase, also promotes asymmetric Michael additions of carbanions to unsaturated ketones with high rates and selectivities. The reactions proceed by amine catalysis, as indicated by mutagenesis and X‐ray data. The inherent flexibility and tunability of this catalyst should make it a versatile platform for further optimization and/or mechanistic diversification by directed evolution.     

Automated solvent system screening for the preparative countercurrent chromatography of pharmaceutical discovery compounds

A fully automated countercurrent chromatography system has been constructed to rapidly screen the commonly used heptane/ethyl acetate/methanol/water solvent system series and translate the results to preparative scale separations. The system utilizes “on‐demand” preparation of the heptane/ethyl acetate/methanol/water solvent system upper and lower phases. Elution‐extrusion countercurrent chromatography was combined with non‐dynamic equilibrium injection reducing the screening time for each heptane/ethyl acetate/methanol/water system to 17 min. The result enabled solvent system development to be reduced to under 2 h. The countercurrent chromatography system was interfaced with a mass spectrometer to allow selective detection of target components in crude medicinal chemistry reaction mixtures. Mass‐directed preparative countercurrent chromatography purification was demonstrated for the first time using a synthetic tetrazole epoxide derived from a routine medicinal chemistry support workflow.     

CompassR Yields Highly Organic-Solvent-Tolerant Enzymes through Recombination of Compatible Substitutions

The CompassR (computer-assisted recombination) rule enables, among beneficial substitutions, the identification of those that can be recombined in directed evolution. Herein, a recombination strategy is systematically investigated to minimize experimental efforts and maximize possible improvements. In total, 15 beneficial substitutions from Bacillus subtilis lipase A (BSLA), which improves resistance to the organic cosolvent 1,4-dioxane (DOX), were studied to compare two recombination strategies, the two-gene recombination process (2GenReP) and the in silico guided recombination process (InSiReP), employing CompassR. Remarkably, both strategies yielded a highly DOX-resistant variant, M4 (I12R/Y49R/E65H/N98R/K122E/L124K), with up to 14.6-fold improvement after screening of about 270 clones. M4 has a remarkably enhanced resistance in 60 % (v/v) acetone (6.0-fold), 30 % (v/v) ethanol (2.1-fold), and 60 % (v/v) methanol (2.4-fold) compared with wild-type BSLA. Molecular dynamics simulations revealed that attracting water molecules by charged surface substitutions is the main driver for increasing the DOX resistance of BSLA M4. Both strategies and obtained molecular knowledge can likely be used to improve the properties of other enzymes with a similar α/β-hydrolase fold.     

一类具有资源约束和优先加工顺序约束极小化加权总完工时间调度优化问题研究

本文针对工件间具有链状优先约束和relocation资源约束的极小化加权总完工时间调度优化问题展开研究.针对这一NP难问题,利用relocation约束的性质和贪婪算法的思想,设计了一个多项式近似算法,并证明了当链不可中断,每个链具有相同工件数和工件间具有相同加工时间时,2为该算法的紧界.     

Low rank matrix recovery from rank one measurements

We study the recovery of Hermitian low rank matrices $X\in {\mathbb{C}}^{n\times n}$ from undersampled measurements via nuclear norm minimization. We consider the particular scenario where the measurements are Frobenius inner products with random rank-one matrices of the form $a_j{a}_j^{?}$ for some measurement vectors $a_1,\dots ,a_m$, i.e., the measurements are given by $b_j=\mathrm{tr}(X{a}_j{a}_j^{?})$. The case where the matrix $X=x{x}^{?}$ to be recovered is of rank one reduces to the problem of phaseless estimation (from measurements $b_j=|〈x,a_j〉{|}^2$) via the PhaseLift approach, which has been introduced recently. We derive bounds for the number m of measurements that guarantee successful uniform recovery of Hermitian rank r matrices, either for the vectors $a_j$, $j=1,\dots ,m$, being chosen independently at random according to a standard Gaussian distribution, or $a_j$ being sampled independently from an (approximate) complex projective t-design with $t=4$. In the Gaussian case, we require $m\ge Crn$ measurements, while in the case of 4-designs we need $m\ge \mathit{Cr}n\log ?(n)$. Our results are uniform in the sense that one random choice of the measurement vectors $a_j$ guarantees recovery of all rank r-matrices simultaneously with high probability. Moreover, we prove robustness of recovery under perturbation of the measurements by noise. The result for approximate 4-designs generalizes and improves a recent bound on phase retrieval due to Gross, Krahmer and Kueng. In addition, it has applications in quantum state tomography. Our proofs employ the so-called bowling scheme which is based on recent ideas by Mendelson and Koltchinskii.     

Tensor train completion: Local recovery guarantees via Riemannian optimization

In this work, we estimate the number of randomly selected elements of a tensor that with high probability guarantees local convergence of Riemannian gradient descent for tensor train completion. We derive a new bound for the orthogonal projections onto the tangent spaces based on the harmonic mean of the unfoldings' singular values and introduce a notion of core coherence for tensor trains. We also extend the results to tensor train completion with auxiliary subspace information and obtain the corresponding local convergence guarantees.