Understanding Ring Puckering in Small Molecules and Cyclic Peptides

<div>The geometry of a molecule plays a significant role in determining its physical and chemical properties. Despite its importance, there are relatively few studies on ring puckering and conformations, often focused on small cycloalkanes, five- and six-membered carbohydrate rings and specific macrocycle families. We lack a general understanding of the puckering preferences of medium-sized rings and macrocycles. To address this, we provide an extensive conformational analysis of a diverse set of rings. We used Cremer-Pople puckering coordinates to study the trends of the ring conformation across a set of 140,000 diverse small molecules, including small rings, macrocycles and cyclic peptides. By standardizing using key atoms, we show that the ring conformations can be classified into relatively few conformational clusters, based on their canonical forms. The number of such canonical clusters increases slowly with ring size. Ring puckering motions, especially pseudo-rotations, are generally restricted, and differ between clusters. More importantly, we propose models to map puckering preferences to torsion space, which allows us to understand the interrelated changes in torsion angles during pseudo-rotation and other puckering motions. Beyond ring puckers, our models also explain the change in substituent orientation upon puckering. In summary, this work provides an improved understanding of general ring puckering preferences, which will in turn accelerate the identification of low energy ring conformations for applications from polymeric materials to drug binding.</div>

Understanding Ring Puckering in Small Molecules and Cyclic Peptides

<div>The geometry of a molecule plays a significant role in determining its physical and chemical properties. Despite its importance, there are relatively few studies on ring puckering and conformations, often focused on small cycloalkanes, five- and six-membered carbohydrate rings and specific macrocycle families. We lack a general understanding of the puckering preferences of medium-sized rings and macrocycles. To address this, we provide an extensive conformational analysis of a diverse set of rings. We used Cremer-Pople puckering coordinates to study the trends of the ring conformation across a set of 140,000 diverse small molecules, including small rings, macrocycles and cyclic peptides. By standardizing using key atoms, we show that the ring conformations can be classified into relatively few conformational clusters, based on their canonical forms. The number of such canonical clusters increases slowly with ring size. Ring puckering motions, especially pseudo-rotations, are generally restricted, and differ between clusters. More importantly, we propose models to map puckering preferences to torsion space, which allows us to understand the interrelated changes in torsion angles during pseudo-rotation and other puckering motions. Beyond ring puckers, our models also explain the change in substituent orientation upon puckering. In summary, this work provides an improved understanding of general ring puckering preferences, which will in turn accelerate the identification of low energy ring conformations for applications from polymeric materials to drug binding.</div>

Projections generated by Moore–Penrose inverses and core inverses

Let [Formula: see text] be a unital ∗-ring. As is well known, idempotents and projections can be constructed by the Moore–Penrose inverse and the core inverse of an element in [Formula: see text]. In this paper, we mainly investigate characterizations and properties of these types of idempotents and projections. Also, several results in [Hartwig and Spindelböck, Matrices for which [Formula: see text] and [Formula: see text] commute, Linear Multilinear Algebra 14 (1984) 241–256] are extended to a general ∗-ring without ∗-cancellable conditions. As applications, the characterization of EP elements is given.

Dendroindication of ecoclimatic condition in forest remediation area within Northern Steppe of Ukraine

We analyzed ring width, latewood width and earlywood width of Pinus sylvestris trees under normal and flood condition in Dnipropetrovsk region, within Northern Steppe of Ukraine. Precipitation from February to August seems to be the most stable climatic factor which influenced Scots pine growth rate and caused the difference between maximum and minimum ring width in normal conditions. Meteorological conditions were mainly associated with general ring values and earlywood width, and were less associated with latewood width values. Assessment of the effect of climatic signals on tree rings’ growth process in living and dead trees and in the normal and flood condition by analyses of correlation and response function was conducted. Average annual temperatures affected the tree growth negatively in normal conditions and tree increment positively in flood conditions. Annual precipitation was correlated positively with ring width, earlywood width series in normal conditions, but negatively with these series in flood conditions.

Strong shift equivalence and algebraic K-theory

For a semiring \mathcal{R} , the relations of shift equivalence over \mathcal{R} ( \textup{SE-}\mathcal{R} ) and strong shift equivalence over \mathcal{R} ( \textup{SSE-}\mathcal{R} ) are natural equivalence relations on square matrices over \mathcal{R} , important for symbolic dynamics. When \mathcal{R} is a ring, we prove that the refinement of \textup{SE-}\mathcal{R} by \textup{SSE-}\mathcal{R} , in the \textup{SE-}\mathcal{R} class of a matrix A, is classified by the quotient NK_{1}(\mathcal{R})/E(A,\mathcal{R}) of the algebraic K-theory group NK_{1}(\mathcal{R}) . Here, E(A,\mathcal{R}) is a certain stabilizer group, which we prove must vanish if A is nilpotent or invertible. For this, we first show for any square matrix A over \mathcal{R} that the refinement of its \textup{SE-}\mathcal{R} class into \textup{SSE-}\mathcal{R} classes corresponds precisely to the refinement of the \mathrm{GL}(\mathcal{R}[t]) equivalence class of I-tA into \mathrm{El}(\mathcal{R}[t]) equivalence classes. We then show this refinement is in bijective correspondence with NK_{1}(\mathcal{R})/E(A,\mathcal{R}) . For a general ring \mathcal{R} and A invertible, the proof that E(A,\mathcal{R}) is trivial rests on a theorem of Neeman and Ranicki on the K-theory of noncommutative localizations. For \mathcal{R} commutative, we show \cup_{A}E(A,\mathcal{R})=NSK_{1}(\mathcal{R}) ; the proof rests on Nenashev’s presentation of K_{1} of an exact category.

Properties of generalized strongly Drazin invertible elements in general rings

In this paper, we define the generalized strong Drazin inverse in a general ring and investigate this class of inverses. Thus, recent results on the strong Drazin invertible and generalized strong Drazin invertible elements are extended to a more general setting. In particular, we show that [Formula: see text] is generalized strong Drazin invertible in a general ring [Formula: see text] if and only if there exists an idempotent [Formula: see text] such that [Formula: see text] and [Formula: see text] is quasinilpotent in [Formula: see text]. We also prove that if [Formula: see text] is generalized Drazin invertible in [Formula: see text] for some [Formula: see text], so are [Formula: see text], [Formula: see text], [Formula: see text]. This partially answer to a question posed by Mosić.

35-Year Follow-Up of a Case of Ring Chromosome 2: Array-CGH Analysis and Literature Review of the Ring Syndrome

Côté et al. [1981] suggested that ring chromosomes with or without deletions share a common pattern of phenotypic anomalies, regardless of which chromosome is involved. The phenotype of this ‘general ring syndrome' consists of growth failure without malformations, few or no minor anomalies, and mild to moderate mental retardation. We reconsidered the ring chromosome 2 case previously published by Côté et al. [1981], and we characterized it by array CGH, polymorphic markers as well as subtelomere MLPA and FISH analysis. A terminal deletion (q37.3qter) of maternal origin of the long arm of the ring chromosome 2 was detected and confirmed by all the above-mentioned methods. Ring chromosome 2 cases are exceedingly rare. Only 18 cases, including the present one, have been published so far, and our patient is the longest reported survivor, with a 35-year follow-up, and the third case characterized by array-CGH analysis.