Dataset Information

Crossing complexity of space-filling curves reveals entanglement of S-phase DNA.

ABSTRACT: Space-filling curves have been used for decades to study the folding principles of globular proteins, compact polymers, and chromatin. Formally, space-filling curves trace a single circuit through a set of points (x,y,z); informally, they correspond to a polymer melt. Although not quite a melt, the folding principles of Human chromatin are likened to the Hilbert curve: a type of space-filling curve. Hilbert-like curves in general make biologically compelling models of chromatin; in particular, they lack knots which facilitates chromatin folding, unfolding, and easy access to genes. Knot complexity has been intensely studied with the aid of Alexander polynomials; however, the approach does not generalize well to cases of more than one chromosome. Crossing complexity is an understudied alternative better suited for quantifying entanglement between chromosomes. Do Hilbert-like configurations limit crossing complexity between chromosomes? How does crossing complexity for Hilbert-like configurations compare to equilibrium configurations? To address these questions, we extend the Mansfield algorithm to enable sampling of Hilbert-like space filling curves on a simple cubic lattice. We use the extended algorithm to generate equilibrium, intermediate, and Hilbert-like configurational ensembles and compute crossing complexity between curves (chromosomes) in each configurational snapshot. Our main results are twofold: (a) Hilbert-like configurations limit entanglement between chromosomes and (b) Hilbert-like configurations do not limit entanglement in a model of S-phase DNA. Our second result is particularly surprising yet easily rationalized with a geometric argument. We explore ergodicity of the extended algorithm and discuss our results in the context of more sophisticated models of chromatin.

SUBMITTER: Kinney N

PROVIDER: S-EPMC7458320 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

ACCESS DATA

Publications

Crossing complexity of space-filling curves reveals entanglement of S-phase DNA.

Kinney Nick N Hickman Molly M Anandakrishnan Ramu R Garner Harold R HR

PloS one 20200831 8

Space-filling curves have been used for decades to study the folding principles of globular proteins, compact polymers, and chromatin. Formally, space-filling curves trace a single circuit through a set of points (x,y,z); informally, they correspond to a polymer melt. Although not quite a melt, the folding principles of Human chromatin are likened to the Hilbert curve: a type of space-filling curve. Hilbert-like curves in general make biologically compelling models of chromatin; in particular, t ...[more]

PMID: 32866178

Similar Datasets

Project description:BackgroundThe exchange of knowledge between statisticians developing new methodology and clinicians, reviewers or authors applying them is fundamental. This is specifically true for clinical trials with time-to-event endpoints. Thereby, one of the most commonly arising questions is that of equal survival distributions in two-armed trial. The log-rank test is still the gold-standard to infer this question. However, in case of non-proportional hazards, its power can become poor and multiple extensions have been developed to overcome this issue. We aim to facilitate the choice of a test for the detection of survival differences in the case of crossing hazards.MethodsWe restricted the review to the most recent two-armed clinical oncology trials with crossing survival curves. Each data set was reconstructed using a state-of-the-art reconstruction algorithm. To ensure reproduction quality, only publications with published number at risk at multiple time points, sufficient printing quality and a non-informative censoring pattern were included. This article depicts the p-values of the log-rank and Peto-Peto test as references and compares them with nine different tests developed for detection of survival differences in the presence of non-proportional or crossing hazards.ResultsWe reviewed 1400 recent phase III clinical oncology trials and selected fifteen studies that met our eligibility criteria for data reconstruction. After including further three individual patient data sets, for nine out of eighteen studies significant differences in survival were found using the investigated tests. An important point that reviewers should pay attention to is that 28% of the studies with published survival curves did not report the number at risk. This makes reconstruction and plausibility checks almost impossible.ConclusionsThe evaluation shows that inference methods constructed to detect differences in survival in presence of non-proportional hazards are beneficial and help to provide guidance in choosing a sensible alternative to the standard log-rank test.

Dataset Information

Crossing complexity of space-filling curves reveals entanglement of S-phase DNA.

Publications

Crossing complexity of space-filling curves reveals entanglement of S-phase DNA.

Similar Datasets

OmicsDI is part of the ELIXIR infrastructure

Tweets