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Flat-State Connectivity of Linkages under Dihedral Motions [chapter]

Greg Aloupis, Erik D. Demaine, Vida Dujmović, Jeff Erickson, Stefan Langerman, Henk Meijer, Joseph O'Rourke, Mark Overmars, Michael Soss, Ileana Streinu, Godfried T. Toussaint
2002 Lecture Notes in Computer Science  
doi:10.1007/3-540-36136-7_33 fatcat:acdhqptatrh5lph2w5qpzwioqy

DESIGN OF A NEW DIHEDRAL-ANGLE-CONTROLLED MOLECULAR SCISSORS: A DFT INVESTIGATION

2015 Журнал структурной химии  
unit through ethylene linkage to give the blade moieties two middle-states in addition to open-close motion.  ...  units as the handle parts, which were connected with each other through the ethylene linkage.  ... 
doi:10.15372/jsc20150708 fatcat:csv66h7kdvbaxodouw64657ph4

Geometric Restrictions on Producible Polygonal Protein Chains [chapter]

Erik D. Demaine, Stefan Langerman, Joseph O'Rourke
2003 Lecture Notes in Computer Science  
One consequence is an algorithm that reconfigures between any two flat states of a nonacute chain in O(n) "moves," improving the O(n 2 )-move algorithm in [ADD + 02].  ...  A random configuration of a chain embeds into R 3 by in addition drawing the dihedral angles from any regular distribution.  ...  A chain that can reconfigure in R 3 via dihedral motions between any two of its flat states is called flat-state connected.  ... 
doi:10.1007/978-3-540-24587-2_41 fatcat:qttr6pjssnh6pgbei36klvupjy

Geometric Restrictions on Producible Polygonal Protein Chains

Erik D. ~Demaine, Stefan Langerman, Joseph O'Rourke
2005 Algorithmica  
One consequence is an algorithm that reconfigures between any two flat states of a nonacute chain in O(n) "moves," improving the O(n 2 )-move algorithm in [ADD + 02].  ...  A random configuration of a chain embeds into R 3 by in addition drawing the dihedral angles from any regular distribution.  ...  A chain that can reconfigure in R 3 via dihedral motions between any two of its flat states is called flat-state connected.  ... 
doi:10.1007/s00453-005-1205-7 fatcat:2h62vz5kh5a4dnf5ndmgt2oo6q

Thickness-utilizing deployable hard stops for origami-based design applications

David W. Andrews, Spencer P. Magleby, Larry L. Howell
2020 Mechanical Sciences  
A ThUDS, like a lamina-emergent mechanism, emerges from a flat state and can reside within a sheet.  ...  specific fold states.  ...  The authors acknowledge the support of Bethany Parkinson, Brooklyn Clark, and Lais Oliveira in the fabrication of prototypes, and the National Science Foundation, through NSF (grant no. 1663345), and the  ... 
doi:10.5194/ms-11-395-2020 fatcat:5inpzmug7vdajg6mrcyv7ybgym

Enhanced Conformational Sampling Using Replica Exchange with Concurrent Solute Scaling and Hamiltonian Biasing Realized in One Dimension

Mingjun Yang, Jing Huang, Alexander D. MacKerell
2015 Journal of Chemical Theory and Computation  
However, increased computational cost due to the multidimensionality of exchanges becomes challenging for use on complex systems under explicit solvent conditions.  ...  to be of general utility for the conformational sampling in a wide range of macromolecular systems.  ...  For these linkage motions, all three methods give reasonably good sampling around the statistically important low-free energy states on a simulation time of 100 ns.  ... 
doi:10.1021/acs.jctc.5b00243 pmid:26082676 pmcid:PMC4463548 fatcat:saipvuawhzhehpid7hdpqfz3cu

Three-dimensional structural dynamics of DNA origami Bennett linkages using individual-particle electron tomography

Dongsheng Lei, Alexander E. Marras, Jianfang Liu, Chao-Min Huang, Lifeng Zhou, Carlos E. Castro, Hai-Jun Su, Gang Ren
2018 Nature Communications  
Similarly, the larger dihedral angle was defined as angle θ, and the smaller dihedral angle was defined as angle φ. Both sets of angles determined the overall conformation of Bennett linkages.  ...  In the theoretical model, the conformation of Bennett linkages was characterized by the geometrical constraint from joints that connect adjacent arms of the linkage (Fig. 4a) .  ...  To view a copy of this license, visit http://creativecommons.org/ licenses/by/4.0/.  ... 
doi:10.1038/s41467-018-03018-0 pmid:29426880 pmcid:PMC5807444 fatcat:fvtbnih2pncgvknnhyo37xzicu

Kinetic rosette patterns and tessellations

Valentina Beatini
2017 International Journal of Computational Methods & Experimental Measurements  
The paper investigates the possibility to create kinetic rosette patterns and their tessellations by means of modular linkages which rely on the same type and number of symmetry operations as the reference  ...  kind of models.  ...  The connecting joints can be positioned at any intersecting point between the linkages, and comply with the cyclic or dihedral symmetry of the pattern.  ... 
doi:10.2495/cmem-v5-n4-631-641 fatcat:u4t3jtcobvhjlg7e2jpk7vscta

Modelling rigid origami with quaternions and dual quaternions

W. Wu, Z. You
2010 Proceedings of the Royal Society A  
Through examples, it has been shown that the first method can effectively track the entire rigid-folding procedure of an initially flat or a non-flat pattern with a single vertex or multiple vertices,  ...  and thereby provide judgment for its rigid foldability and flat foldability.  ...  shapes that do not have a flat state at any folding stage.  ... 
doi:10.1098/rspa.2009.0625 fatcat:ujvy56ieive4xl24xgkktrrbee

Solution Conformations of a Trimannoside from Nuclear Magnetic Resonance and Molecular Dynamics Simulations

Eric W. Sayers, James H. Prestegard
2000 Biophysical Journal  
The four major conformations arise from a pair of two-state transitions, one each at the ␣(133) and ␣(136) linkages, whereas the minor conformations result from an additional transition of the ␣(136) linkage  ...  glycosidic linkages in N-linked oligosaccharides.  ...  This work was supported by a grant from the National Institutes of Health, GM33225, and a Howard Hughes Medical Institute Predoctoral Fellowship to E.W.S.  ... 
doi:10.1016/s0006-3495(00)76563-5 pmid:11106634 pmcid:PMC1301205 fatcat:y3gfhj3tebdkznsf33tq47bnke

Topological transitions in the configuration space of non-Euclidean origami [article]

M. Berry, M.E. Lee-Trimble, C.D. Santangelo
2019 arXiv   pre-print
In contrast, the configuration space of negative Gaussian curvature vertices remain connected.  ...  The design of such structures requires a deep understanding of the kinematics of origami fold patterns.  ...  This work was done in part at the Aspen Center for Physics under grant NSF PHY-1607611.  ... 
arXiv:1910.01008v1 fatcat:7pulmewy75dp3al5dk2hz6gkqe

Conformational Sampling of Oligosaccharides Using Hamiltonian Replica Exchange with Two-Dimensional Dihedral Biasing Potentials and the Weighted Histogram Analysis Method (WHAM)

Mingjun Yang, Alexander D. MacKerell
2015 Journal of Chemical Theory and Computation  
polysaccharides under explicit solvent conditions.  ...  of mean force (PMF)) can be improved using the weighted histogram analysis method (WHAM) allowing for the inclusion of data from the excited state replicas in the calculated probability distribution.  ...  Acknowledgments Financial support from the NIH (GM070855 and GM051501) and computational support from the University of Maryland Computer-Aided Drug Design Center are acknowledged.  ... 
doi:10.1021/ct500993h pmid:25705140 pmcid:PMC4334390 fatcat:io3mlnubnraivlard7tsmdz4ni

Self-Assembly of Mesoscale Isomers: The Role of Pathways and Degrees of Freedom

Shivendra Pandey, Daniel Johnson, Ryan Kaplan, Joseph Klobusicky, Govind Menon, David H. Gracias, Bing Xu
2014 PLoS ONE  
We compute the set of all possible assembly pathways and analyze the degrees of freedom or rigidity of intermediates.  ...  Consequently, by manipulating the degrees of freedom of a precursor, we were able to experimentally enrich the formation of one isomer over the other.  ...  In more intuitive terms, the number of internal degree of freedom is the number of independent relative motions of a linkage.  ... 
doi:10.1371/journal.pone.0108960 pmid:25299051 pmcid:PMC4191966 fatcat:6kkqisgfjbe4xoktkntbeepvca

A toy-inspired kirigami pattern and its kinematic performance by applying mechanisms and machine theory

Weiwei Lin, Kunjing Chen, Yuan Gao, Aihua Chen, Fufu Yang, Huijuan Feng
2021 Mechanical Sciences  
The inverse problem of origami that determines the distribution of creases based on the desired shape is very complicated.  ...  Origami that can form various shapes by setting simple creases on the paper and folding along these creases has a lot of applications from the fields of art to engineering.  ...  The authors would like to give sincere thanks to Xiezhao Lin for the proposal and the discussion of studying the toy problem and to anonymous reviewers for their comprehensive comments and valuable suggestions  ... 
doi:10.5194/ms-12-933-2021 fatcat:qfbdiiw355h6nkjgirz57m3v7u

Correlation-based feature selection to identify functional dynamics in proteins [article]

Georg Diez, Daniel Nagel, Gerhard Stock
2022 arXiv   pre-print
of the correlated motions in terms of a functional mechanism.  ...  A crucial first step of such an analysis is the identification of suitable and relevant input coordinates (the so-called features), such as backbone dihedral angles and interresidue distances.  ...  Various extensions of the above correlation analysis are currently under consideration.  ... 
arXiv:2204.02770v2 fatcat:eafet7vg6nhu7eduryc6lqcanq
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