Quantum Mechanical/Molecular Mechanical Study on the Enantioselectivity of the Enzymatic Baeyer–Villiger Reaction of 4-Hydroxycyclohexanone

We report a combined quantum mechanical/molecular mechanical (QM/MM) study of the effect of mutations of the Phe434 residue in the active site of cyclohexanone monooxygenase (CHMO) on its enantioselectivity toward 4-hydroxycyclohexanone. In terms of our previously established model of the enzymatic Baeyer–Villiger reaction, enantioselectivity is governed by the preference toward the equatorial ((S)-selectivity) or axial ((R)-selectivity) conformation of the substituent at the C4 carbon atom of the cyclohexanone ring in the Criegee intermediate and the subsequent rate-limiting transition state for migration (TS2). We assess the enantiopreference by locating all relevant TS2 structures at the QM/MM level. In the wild-type enzyme we find that the axial conformation is energetically slightly more stable, thus leading to a small excess of (R)-product. In the Phe434Ser mutant, there is a hydrogen bond between the serine side chain and the equatorial substrate hydroxyl group that is retained during the whole reaction, and hence there is pronounced reverse (S)-enantioselectivity. Another mutant, Phe434Ile, is shown to preserve and enhance the (R)-selectivity. All these findings are in accordance with experiment. The QM/MM calculations allow us to explain the effect of point mutations on CHMO enantioselectivity for the first time at the molecular level by an analysis of the specific interactions between substrate and active-site environment in the TS2 structures that satisfy the basic stereoelectronic requirement of anti-periplanarity for the migrating σ-bond

A New Type of Stereoselectivity in Baeyer–Villiger Reactions: Access to E- and Z-Olefins

A new concept for accessing configurationally defined trisubstituted olefins has been developed. Starting from a common ketone precursor of the type 4-ethylidenecyclohexanone, Baeyer–Villiger monooxygenases are employed as catalysts in diastereoselective Baeyer–Villiger reactions leading to the corresponding E- or Z-configurated lactones. Wild-type cyclohexanone monooxygenase (CHMO) as catalyst delivers the E-isomers and a directed evolution mutant the opposite Z-isomers. Subsequent transition metal-catalyzed chemical transformations of a key product containing a vinyl bromide moiety provide a variety of different trisubstituted E- or Z-olefins. A model based on QM/MM sheds light on the origin of this unusual type of diastereoselectivity. In contrast to this biocatalytic approach, traditional Baeyer–Villiger reagents such as m-CPBA fail to show any selectivity, 1:1 mixtures of E- and Z-olefins being formed

Synthesis of a PID-controller of a trim robust control system of an autonomous underwater vehicle

Autonomous underwater vehicles are often used for performing scientific, emergency or other types of missions under harsh conditions and environments, which can have non-stable, variable parameters. So, the problem of developing autonomous underwater vehicle motion control systems, capable of operating properly in random environments, is highly relevant. The paper is dedicated to the synthesis of a PID-controller of a trim robust control system, capable of keeping an underwater vehicle stable during a translation at different angles of attack. In order to synthesize the PID-controller, two problems were solved: a new method of synthesizing a robust controller was developed and a mathematical model of an underwater vehicle motion process was derived. The newly developed mathematical model structure is simpler than others due to acceptance of some of the system parameters as interval ones. The synthesis method is based on a system poles allocation approach and allows providing the necessary transient process quality in a considered system

Charge migration engineered by localisation: electron-nuclear dynamics in polyenes and glycine

We demonstrate that charge migration can be ‘engineered’ in arbitrary molecular systems if a single localised orbital – that diabatically follows nuclear displacements – is ionised. Specifically, we describe the use of natural bonding orbitals in Complete Active Space Configuration Interaction (CASCI) calculations to form cationic states with localised charge, providing consistently well-defined initial conditions across a zero point energy vibrational ensemble of molecular geometries. In Ehrenfest dynamics simulations following localised ionisation of -electrons in model polyenes (hexatriene and decapentaene) and -electrons in glycine, oscillatory charge migration can be observed for several femtoseconds before dephasing. Including nuclear motion leads to slower dephasing compared to fixed-geometry electron-only dynamics results. For future work, we discuss the possibility of designing laser pulses that would lead to charge migration that is experimentally observable, based on the proposed diabatic orbital approach

Ultrafast Photoinduced Dynamics of 1,3-Cyclohexadiene Using XMS-CASPT2 Surface Hopping

A full-dimensional simulation of the photodissociation of 1,3-cyclohexadiene in the manifold of three electronic states was performed via nonadiabatic surface hopping dynamics using extended multistate complete active space second-order perturbation (XMS-CASPT2) electronic structure theory with fully analytic nonadiabatic couplings. With the 47 ± 8% product quantum yield calculated from the 136 trajectories, generally 400 fs-long, and an estimated excited lifetime of 89 ± 9 fs, our calculations provide a detailed description of the nonadiabatic deactivation mechanism, showing the existence of an extended conical intersection seam along the reaction coordinate. The nature of the preferred reaction pathways on the ground state is discussed and extensive comparison to the previously published full dimensional dynamics calculations is provided

Electron and nuclear dynamics following ionisation of modified bismethylene-adamantane

We have simulated the coupled electron and nuclear dynamics using the Ehrenfest method upon valence ionisation of modified bismethylene-adamantane (BMA) molecules where there is an electron transfer between the two π bonds. We have shown that the nuclear motion significantly affects the electron dynamics after a few fs when the electronic states involved are close in energy. We have also demonstrated how the non-stationary electronic wave packet determines the nuclear motion, more precisely the asymmetric stretching of the two π bonds, illustrating “charge-directed reactivity”. Taking into account the nuclear wave packet width results in the dephasing of electron dynamics with a half-life of 8 fs; this eventually leads to the equal delocalisation of the hole density over the two methylene groups and thus symmetric bond lengths

РОЗКРИТТЯ ІНФОРМАЦІЇ ПРО НАСЛІДКИ НАДЗВИЧАЙНИХ СИТУАЦІЙ У СИСТЕМІ БУХГАЛТЕРСЬКОГО ОБЛІКУ

Nowadays accounting statements is one of the most dynamic accounting method elements. First and foremost it is related to the correspondence of its subject-matter to the demands of different users willing to know economic conditions in reality changing rapidly. Thus, applying methods of economic analysis on the basis of accounting data it is possible to calculate a range of figures giving an opportunity to estimate both financial condition and economic potential of the enterprise in the future and the past. That is why to calculate such figures in the copes of accounting there should be information about emergency consequences cases affecting the production processes, product cost and further the enterprise’s financial results. This condition will allow estimate their influence on the financial figures and economic potential of the enterprise. The directions of financial statement’s expanding in content and form are articulated. Financial statement is improved in order to reflect information about emergency consequences through expanding factors in already existing chapters (as a part of other costs) and formation of the new chapter V «External and internal risks environmental impact» containing information about separation of emergency consequences from activity costs. Fragments of notes to the annual financial statement are developed giving an opportunity to estimate the impact of emergency consequences on noncurrent and current assets and the production process. Building specific information for internal use about emergency consequences is performed on the basis of justified directions of internal reporting formation and development of ways and mechanisms of their factors formation. It allowed to increase quality of information space of business activity management in emergency conditions. The use of suggestions in practice contributed to increasing the information space quality in users’ decision-making and developing a complex of measures to prevent and address the emergency consequences. In its turn analytical measures calculated on the basis of their facts will take into account a number of factors allowing to fully estimate the financial condition and economic potential.На сьогодні бухгалтерська звітність є одним з найбільш динамічних елементів методу обліку. Перш за все, це пов’язано з відповідністю його предметa вимогам різних користувачів, які бажають дізнатися, що економічні умови в реальності швидко змінюються. Тому, застосовуючи методи економічного аналізу на основі даних бухгалтерського обліку, можна розрахувати діапазон цифр, що дають можливість оцінити як фінансовий стан, так і економічний потенціал підприємства в майбутньому і минулому. Тому для обчислення таких цифр у справах бухгалтерського обліку повинна бути інформація про надзвичайні наслідки, що впливають на виробничі процеси, вартість продукції і фінансові результати підприємства. Ця умова дозволить оцінити їхній вплив на фінансові показники та економічний потенціал підприємства. Сформульовано напрями розширення фінансової звітності за змістом і формою. Фінансова звітність удосконалюється з метою відображення інформації про надзвичайні наслідки за рахунок розширення факторів у наявних главах (як частина інших витрат) і формування нової глави V «Зовнішні та внутрішні ризики впливу на навколишнє середовище», що містить інформацію про відокремлення надзвичайних наслідків від витрати на діяльність. Фрагменти приміток до річної фінансової звітності розроблено, що дає можливість оцінити вплив надзвичайних наслідків на необоротні та оборотні активи і виробничий процес. Побудова конкретної інформації для внутрішнього використання про надзвичайні наслідки здійснюється на основі обґрунтованих напрямів формування внутрішньої звітності та розроблення шляхів і механізмів формування їхніх факторів. Це дозволило підвищити якість інформаційного простору управління діловою діяльністю в надзвичайних умовах. Використання пропозицій на практиці сприяло підвищенню якості інформаційного простору при ухваленні рішень користувачами і розробленні комплексу заходів щодо запобігання надзвичайним наслідкам та їх ліквідації . У свою чергу, аналітичні заходи, розраховані на основі їхніх фактів, ураховуватимуть низку факторів, що дозволяють повністю оцінити фінансовий стан та економічний потенціал

Fast Primal-Dual Gradient Method for Strongly Convex Minimization Problems with Linear Constraints

In this paper we consider a class of optimization problems with a strongly convex objective function and the feasible set given by an intersection of a simple convex set with a set given by a number of linear equality and inequality constraints. A number of optimization problems in applications can be stated in this form, examples being the entropy-linear programming, the ridge regression, the elastic net, the regularized optimal transport, etc. We extend the Fast Gradient Method applied to the dual problem in order to make it primal-dual so that it allows not only to solve the dual problem, but also to construct nearly optimal and nearly feasible solution of the primal problem. We also prove a theorem about the convergence rate for the proposed algorithm in terms of the objective function and the linear constraints infeasibility.Comment: Submitted for DOOR 201

Counting and computing regions of DD-decomposition: algebro-geometric approach

New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families of polynomial and matrices is given. For the case of two parametric family more sharp estimate is proven. Theoretic results are supported by various numerical simulations that show higher precision of presented methods with respect to traditional ones. The presented methods are inherently global and could be applied for studying $D$-decomposition for the space of parameters as a whole instead of some prescribed regions. For symbolic computations the Maple v.14 software and its package RegularChains are used.Comment: 16 pages, 8 figure