Dataset Information

The braid index of DNA double crossover polyhedral links.

ABSTRACT: In this paper, the authors study the mathematical properties of a class of alternating links called polyhedral links which have been used to model DNA polyhedra. The motivation of such studies is to provide guidance and aid in the research of the properties of certain DNA molecules. For example, such studies can provide characterizations of the structural complexity of DNA molecules. In an earlier work, Cheng and Jin studied the mathematical properties of such polyhedral links and were able to determine the braid index of a double crossover polyhedral link with 4 turn. However, the braid index of a double crossover polyhedral link with 4.5 turn remained an unsolved problem to this date, even though the graphs that admit the double crossover polyhedral links with 4.5 turn have been synthesized. In this paper, we provide a complete formulation of the braid index of a double crossover polyhedral link with an arbitrary turn number. Our approach is more general and it allows us to completely determine the braid indices for a much larger class of links. In the case of the double crossover polyhedral links, our formulation of the braid index is a simple formula based on a simpler graph used as a template to build the double crossover polyhedral links.

SUBMITTER: Cheng XS

PROVIDER: S-EPMC7015418 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

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The braid index of DNA double crossover polyhedral links.

Cheng Xiao-Sheng XS Diao Yuanan Y

PloS one 20200212 2

In this paper, the authors study the mathematical properties of a class of alternating links called polyhedral links which have been used to model DNA polyhedra. The motivation of such studies is to provide guidance and aid in the research of the properties of certain DNA molecules. For example, such studies can provide characterizations of the structural complexity of DNA molecules. In an earlier work, Cheng and Jin studied the mathematical properties of such polyhedral links and were able to d ...[more]

PMID: 32049974

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Project description:BackgroundOne of the key mechanisms underlying OSA is reduced pharyngeal muscle tone during sleep. Data suggest that pharmacologic augmentation of central serotonergic/adrenergic tone increases pharyngeal muscle tone.Research questionWe hypothesized that venlafaxine, a serotonin-norepinephrine reuptake inhibitor, would improve OSA severity.Study design and methodsIn this mechanistic, randomized, double-blind, placebo-controlled crossover trial, 20 patients with OSA underwent two overnight polysomnograms ≥ 4 days apart, receiving either 50 mg of immediate-release venlafaxine or placebo before bedtime. Primary outcomes were the apnea-hypopnea index (AHI) and peripheral oxygen saturation (Spo2) nadir, and secondary outcomes included sleep parameters and pathophysiologic traits with a view toward understanding the impact of venlafaxine on mechanisms underlying OSA.ResultsOverall, there was no significant difference between venlafaxine and placebo regarding AHI (mean reduction, -5.6 events/h [95% CI, -12.0 to 0.9]; P = .09) or Spo2 nadir (median increase, +1.0% [-0.5 to 5]; P = .11). Venlafaxine reduced total sleep time, sleep efficiency, and rapid eye movement (REM) sleep, while increasing non-REM stage 1 sleep (Pall < .05). On the basis of exploratory post hoc analyses venlafaxine decreased ("improved") the ventilatory response to arousal (-30%; P = .049) and lowered ("worsened") the predicted arousal threshold (-13%; [P = .02]; ie, more arousable), with no effects on other pathophysiologic traits (Pall ≥ .3). Post hoc analyses further suggested effect modification by arousal threshold (P = .002): AHI improved by 19% in patients with a high arousal threshold (-10.9 events/h [-3.9 to -17.9]) but tended to increase in patients with a low arousal threshold (+7 events/h [-2.0 to 16]). Other predictors of response were elevated AHI and less collapsible upper airway anatomy at baseline (|r| > 0.5, P ≤ .02).InterpretationIn unselected patients, venlafaxine simultaneously worsened and improved various pathophysiologic traits, resulting in a zero net effect. Careful patient selection based on pathophysiologic traits, or combination therapy with drugs countering its alerting effects, may produce a more robust response.Trial registryClinicalTrials.gov; No.: NCT02714400; URL: www.clinicaltrials.gov.

Dataset Information

The braid index of DNA double crossover polyhedral links.

Publications

The braid index of DNA double crossover polyhedral links.

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