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Universal folding pathways of polyhedron nets.

ABSTRACT: Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects. Understanding this relationship remains a challenge for de novo design of functional structures. Using molecular dynamics simulations, we investigate the refolding of the 24 possible 2D unfoldings ("nets") of the three simplest Platonic shapes and demonstrate that attributes of a net's topology-net compactness and leaves on the cutting graph-correlate with thermodynamic folding propensity. To explain these correlations we exhaustively enumerate the pathways followed by nets during folding and identify a crossover temperature [Formula: see text] below which nets fold via nonnative contacts (bonds must break before the net can fold completely) and above which nets fold via native contacts (newly formed bonds are also present in the folded structure). Folding above [Formula: see text] shows a universal balance between reduction of entropy via the elimination of internal degrees of freedom when bonds are formed and gain in potential energy via local, cooperative edge binding. Exploiting this universality, we devised a numerical method to efficiently compute all high-temperature folding pathways for any net, allowing us to predict, among the combined 86,760 nets for the remaining Platonic solids, those with highest folding propensity. Our results provide a general heuristic for the design of 2D objects to stochastically fold into target 3D geometries and suggest a mechanism by which geometry and folding propensity are related above [Formula: see text], where native bonds dominate folding.

SUBMITTER: Dodd PM

PROVIDER: S-EPMC6055160 | biostudies-literature | 2018 Jul

REPOSITORIES: biostudies-literature

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Universal folding pathways of polyhedron nets.

Dodd Paul M PM Damasceno Pablo F PF Glotzer Sharon C SC

Proceedings of the National Academy of Sciences of the United States of America 20180703 29

Low-dimensional objects such as molecular strands, ladders, and sheets have intrinsic features that affect their propensity to fold into 3D objects. Understanding this relationship remains a challenge for de novo design of functional structures. Using molecular dynamics simulations, we investigate the refolding of the 24 possible 2D unfoldings ("nets") of the three simplest Platonic shapes and demonstrate that attributes of a net's topology-net compactness and leaves on the cutting graph-correla ...[more]

PMID: 29970420

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Project description:BackgroundMass distribution of insecticide-treated nets (ITNs) is a cost-effective way to achieve universal coverage, but maintaining this coverage is more difficult. In addition to commonly used indicators, evaluation of universal coverage should include coverage of effective nets and changes in coverage over time.MethodsLongitudinal and cross-sectional household ITN surveys were carried out from 2010 to 2013 in six locations representing a variety of settings across western Kenya. Five indicators were used to evaluate the current status of universal coverage: 1) ITN ownership--proportion of households that own at least one ITN, 2) access index--ratio of the number of family members over the number of ITNs owned by that household, 3) operational coverage--proportion of the at-risk population potentially covered by ITNs, assuming one ITN for every two people, 4) effective coverage--population coverage of effective ITNs, and 5) usage--proportion of the population that used ITNs the previous night.ResultsITN ownership and operational coverage increased substantially from 2010 to 2013, but this increase was mostly due to the 2011 mass distribution campaign. In 2013, household ITN ownership was on average 84.4% (95% CI [78.4, 90.5]) across the six study areas, and operational coverage was 83.2% (95% CI [72.5, 93.8]). The ITN access rate was 59.1% (95% CI [56.6, 61.7]), and 40.8% (95% CI [38.3, 43.4]) of the people at risk needed more nets to achieve universal coverage. About 88.5% (95% CI [86.1, 90.9]) of the ITNs were below three years old and 16.5% (95% CI [12.1, 20.9]) of the ITNs had hole(s). The estimated effective long-lasting insecticide-treated net (LLIN) coverage was 70.5% (95 CI [58.7, 82.3]). Approximately 18.4% (95% CI [15.5, 21.4]) of the ITNs were shared by more than three persons, and the population ITN usage rate was about 75-87%. The reason for not using ITNs was almost exclusively "net not available".ConclusionCurrent methods of delivering ITNs, i.e., one mass campaign every five years and regular distribution of ITNs from health center can barely maintain the current effective coverage. Inaccessibility and loss of physical integrity of ITNs are major hindrances to achieving and maintaining universal coverage.

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Universal folding pathways of polyhedron nets.

Publications

Universal folding pathways of polyhedron nets.

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