A Compound I Mimic Reveals the Transient Active Species of a Cytochrome P450 Enzyme: Insight into the Stereoselectivity of P450-Catalysed Oxidations

Catching the structure of cytochrome P450 enzymes in flagrante is crucial for the development of P450 biocatalysts, as most structures collected are found trapped in a precatalytic conformation. At the heart of P450 catalysis lies Cpd I, a short-lived, highly reactive intermediate, whose recalcitrant nature has thwarted most attempts at capturing catalytically relevant poses of P450s. We report the crystal structure of P450BM3 mimicking the state in the precise moment preceding epoxidation, which is in perfect agreement with the experimentally observed stereoselectivity. This structure was attained by incorporation of the stable Cpd I mimic oxomolybdenum mesoporphyrin IX into P450BM3 in the presence of styrene. The orientation of styrene to the Mo-oxo species in the crystal structures sheds light onto the dynamics involved in the rotation of styrene to present its vinyl group to Cpd I. This method serves as a powerful tool for predicting and modelling the stereoselectivity of P450 reactions.     

Front Cover: Enhancement of dielectrophoresis-based particle collection from high conducting fluids due to partial electrode insulation

Dielectrophoresis (DEP) is a successful method to recover nanoparticles from different types of fluid. The DEP force acting on these particles is created by an electrode microarray that produces a nonuniform electric field. To apply DEP to a highly conducting biological fluid, a protective hydrogel coating over the metal electrodes is required to create a barrier between the electrode and the fluid. This protects the electrodes, reduces the electrolysis of water, and allows the electric field to penetrate into the fluid sample. We observed that the protective hydrogel layer can separate from the electrode and form a closed domed structure and that collection of 100 nm polystyrene beads increased when this occurred. To better understand this collection increase, we used COMSOL Multiphysics software to model the electric field in the presence of the dome filled with different materials ranging from low-conducting gas to high conducting phosphate-buffered saline fluids. The results suggest that as the electrical conductivity of the material inside the dome is reduced, the whole dome acts as an insulator which increases electric field intensity at the electrode edge. This increased intensity widens the high-intensity electric field factor zone resulting in increased collection. This informs how dome formation results in increased particle collection and provides insight into how the electric field can be intensified to the increase collection of particles. These results have important applications for increasing the recovery of biologically-derived nanoparticles from undiluted physiological fluids that have high conductance, including the collection of cancer-derived extracellular vesicles from plasma for liquid biopsy applications.     

Development of the Vinylogous Pictet–Spengler Cyclization and Total Synthesis of (±)‐Lundurine A

A novel vinylogous Pictet–Spengler cyclization has been developed for the generation of indole‐annulated medium‐sized rings. The method enables the synthesis of tetrahydroazocinoindoles with a fully substituted carbon center, a prevalent structural motif in many biologically active alkaloids. The strategy has been applied to the total synthesis of (±)‐lundurine A.     

Establishing order in planar subdivisions

A planar subdivision is the partition of the plane induced by an embedded planar graph. A representation of such a subdivision isordered if, for each vertexv of the associated graphG, the (say) clockwise sequence of edges in the embedding ofG incident withv appears explicitly.The worst-case complexity of establishing order in a planar subdivision, i.e., converting an unordered representation into an ordered one, is shown to be (n + log (G)), wheren is the size (number of vertices) of the underlying graphG and (G) is (essentially) the number of topologically distinct embeddings ofG in the plane.This work was supported by the National Science and Engineering Research Council of Canada under Grant A3583. A preliminary version of this paper appeared in theProceedings of the Third Annual ACM Symposium on Computational Geometry.     

Well adjusted: Using expediting and cancelation to manage store replenishment inventory for a seasonal good

We consider an inventory problem that can be translated into a two-period newsvendor setting where the day prior to sales, the newsvendor places an initial preliminary order—a semi-binding forecast—with the publisher. At the beginning of the actual day of sales, the newsvendor has a better forecast for the day’s demand: based on knowing the actual content of the paper, he knows whether it will be a high-demand day due to breaking news or a low-demand day due to slow news. He then can revise the preliminary order quantity by expediting additional papers or canceling all or part of the order, but each of these activities has an associated cost.     

Allostatic load as a complex clinical construct: A case‐based computational modeling approach

Allostatic load (AL) is a complex clinical construct, providing a unique window into the cumulative impact of stress. However, due to its inherent complexity, AL presents two major measurement challenges to conventional statistical modeling (the field's dominant methodology): it is comprised of a complex causal network of bioallostatic systems, represented by an even larger set of dynamic biomarkers; and, it is situated within a web of antecedent socioecological systems, linking AL to differences in health outcomes and disparities. To address these challenges, we employed case‐based computational modeling (CBM), which allowed us to make four advances: (1) we developed a multisystem, 7‐factor (20 biomarker) model of AL's network of allostatic systems; (2) used it to create a catalog of nine different clinical AL profiles (causal pathways); (3) linked each clinical profile to a typology of 23 health outcomes; and (4) explored our results (post hoc) as a function of gender, a key socioecological factor. In terms of highlights, (a) the Healthy clinical profile had few health risks; (b) the pro‐inflammatory profile linked to high blood pressure and diabetes; (c) Low Stress Hormones linked to heart disease, TIA/Stroke, diabetes, and circulation problems; and (d) high stress hormones linked to heart disease and high blood pressure. Post hoc analyses also found that males were overrepresented on the High Blood Pressure (61.2%), Metabolic Syndrome (63.2%), High Stress Hormones (66.4%), and High Blood Sugar (57.1%); while females were overrepresented on the Healthy (81.9%), Low Stress Hormones (66.3%), and Low Stress Antagonists (stress buffers) (95.4%) profiles. © 2015 Wiley Periodicals, Inc. Complexity 21: 291–306, 2016     

Bounding reflection length in an affine Coxeter group

In any Coxeter group, the conjugates of elements in the standard minimal generating set are called reflections, and the minimal number of reflections needed to factor a particular element is called its reflection length. In this article we prove that the reflection length function on an affine Coxeter group has a uniform upper bound. More precisely, we prove that the reflection length function on an affine Coxeter group that naturally acts faithfully and cocompactly on ℝ ⁿ is bounded above by 2n, and we also show that this bound is optimal. Conjecturally, spherical and affine Coxeter groups are the only Coxeter groups with a uniform bound on reflection length.     

Restructuring ordered binary trees

We consider the problem of restructuring an ordered binary tree T, preserving the in-order sequence of its nodes, so as to reduce its height to some target value h. Such a restructuring necessarily involves the downward displacement of some of the nodes of T. Our results, focusing both on the maximum displacement over all nodes and on the maximum displacement over leaves only, provide (i) an explicit tradeoff between the worst-case displacement and the height restriction (including a family of trees that exhibit the worst-case displacements) and (ii) efficient algorithms to achieve height-restricted restructuring while minimizing the maximum node displacement.     

Pseudo Approximation Algorithms with Applications to Optimal Motion Planning

We introduce a technique for computing approximate solutions to optimization problems. If $X$ is the set of feasible solutions, the standard goal of approximation algorithms is to compute $x\in X$ that is an $\varepsilon$-approximate solution in the following sense: $$d(x) \leq (1+\varepsilon)\, d(x^*),$$ where $x^* \in X$ is an optimal solution, $d\colon\ X\rightarrow {\Bbb R}_{\geq 0}$ is the optimization function to be minimized, and $\varepsilon>0$ is an input parameter. Our approach is first to devise algorithms that compute pseudo $\varepsilon$-approximate solutions satisfying the bound $$d(x) \leq d(x_R^*) + \varepsilon R,$$ where $R>0$ is a new input parameter. Here $x^*_R$ denotes an optimal solution in the space $X_R$ of $R$-constrained feasible solutions. The parameter $R$ provides a stratification of $X$ in the sense that (1) $X_R \subseteq X_{R}$ for $R < R$ and (2) $X_R = X$ for $R$ sufficiently large. We first describe a highly efficient scheme for converting a pseudo $\varepsilon$-approximation algorithm into a true $\varepsilon$-approximation algorithm. This scheme is useful because pseudo approximation algorithms seem to be easier to construct than $\varepsilon$-approximation algorithms. Another benefit is that our algorithm is automatically precision-sensitive. We apply our technique to two problems in robotics: (A) Euclidean Shortest Path (3ESP), namely the shortest path for a point robot amidst polyhedral obstacles in three dimensions, and (B) $d_1$-optimal motion for a rod moving amidst planar obstacles (1ORM). Previously, no polynomial time $\varepsilon$-approximation algorithm for (B) was known. For (A), our new solution is simpler than previous solutions and has an exponentially smaller complexity in terms of the input precision.     

Optimal Algorithms for Probabilistic Solitude Detection on Anonymous Rings

Probabilistic algorithms are developed for a basic problem in distributed computation, assuming anonymous, asynchronous, unidirectional rings of processors. The problem, known as Solitude Detection, requires that a nonempty subset of the processors, calledcontenders, determine whether or not there is exactly one contender. Monte Carlo algorithms are developed that err with probability bounded by a specified parameter and exhibit either message or processor termination. The algorithms transmit an optimal expected number of bits, to within a constant factor. Their bit complexities display a surprisingly rich dependence on the kind of termination exhibited and on the processors' knowledge of the size of the ring. Two probabilistic tools are isolated and then combined in various ways to achieve all our algorithms.