2019
|
Pouokam, M., Cruz, B., Burgess, S., Segal, M., Vazquez, M., Arsuaga, J. The Rabl configuration limits topological entanglement of chromosomes in budding yeast. Journal Article Scientific Reports, 9 (1), pp. 6795, 2019, ISBN: 2045-2322. Abstract | Links | BibTeX @article{Pouokam2019,
title = {The Rabl configuration limits topological entanglement of chromosomes in budding yeast.},
author = {Pouokam, M., Cruz, B., Burgess, S., Segal, M., Vazquez, M., Arsuaga, J.},
url = {https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6494875/},
doi = {10.1038/s41598-019-42967-4},
isbn = {2045-2322},
year = {2019},
date = {2019-07-04},
journal = {Scientific Reports},
volume = {9},
number = {1},
pages = {6795},
abstract = {The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers. |
Walker, S., Arsuaga, J., Calderer, C., Hiltner, L., Vazquez, M. Fine Structure of Viral dsDNA Encapsidation Journal Article ArXiv e-prints(Condensed Matter - Soft Condensed Matter, submitted), 2019. Links | BibTeX @article{2019arXiv190209188W,
title = {Fine Structure of Viral dsDNA Encapsidation},
author = {Walker, S., Arsuaga, J., Calderer, C., Hiltner, L., Vazquez, M.},
url = {https://arxiv.org/abs/1902.09188},
year = {2019},
date = {2019-02-25},
journal = {ArXiv e-prints(Condensed Matter - Soft Condensed Matter, submitted)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Moore, A., Vazquez, M., Lidman T. Distance one lens space fillings and band surgery on the trefoil knot Journal Article ArXiv e-prints( Algebraic & Geometric Topology, accepted.), 2019. Links | BibTeX @article{2017arXiv171007418L,
title = {Distance one lens space fillings and band surgery on the trefoil knot },
author = {Moore, A., Vazquez, M., Lidman T.},
url = {https://arxiv.org/abs/1710.07418},
year = {2019},
date = {2019-01-01},
journal = {ArXiv e-prints( Algebraic & Geometric Topology, accepted.)},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2018
|
Ibrahim, L., Liu, P., Klingbeil, M., Diao, U., Arsuaga, J. Estimating properties of kinetoplast DNA by fragmentation reactions Journal Article Journal of Physics A: Mathematical and Theoretical, 52 (3), 2018. Links | BibTeX @article{Ibrahim2018,
title = {Estimating properties of kinetoplast DNA by fragmentation reactions},
author = {Ibrahim, L., Liu, P., Klingbeil, M., Diao, U., Arsuaga, J.},
url = {https://doi.org/10.1088/1751-8121/aaf15f},
doi = {https://doi.org/10.1088/1751-8121/aaf15f},
year = {2018},
date = {2018-12-18},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {52},
number = {3},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Moore, A., Vazquez, M. Recent advances on the non-coherent band surgery model for site-specific recombination Journal Article Forthcoming arxiv.org, Forthcoming, ("to appear in Contemporary Mathematics issue on the AMS Special Session on Topology of Biopolymers). Links | BibTeX @article{Moore2018,
title = {Recent advances on the non-coherent band surgery model for site-specific recombination},
author = {Moore, A., Vazquez, M.},
url = {https://arxiv.org/abs/1810.08751},
doi = {1810.08751},
year = {2018},
date = {2018-10-20},
journal = {arxiv.org},
note = {"to appear in Contemporary Mathematics issue on the AMS Special Session on Topology of Biopolymers},
keywords = {},
pubstate = {forthcoming},
tppubtype = {article}
}
|
Moore, A., Vazquez, M. A note on band surgery and the signature of a knot (submitted) Journal Article ArXiv e-prints, 2018. Links | BibTeX @article{2018arXiv180602440M,
title = {A note on band surgery and the signature of a knot (submitted)},
author = {Moore, A., Vazquez, M.},
url = {https://arxiv.org/abs/1806.02440},
year = {2018},
date = {2018-01-01},
journal = {ArXiv e-prints},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Witte, S., Flanner, M.,; Vazquez, M. A Symmetry Motivated Link Table Journal Article Symmetry, 10 , pp. 604, 2018. Links | BibTeX @article{article,
title = {A Symmetry Motivated Link Table},
author = {Witte, S., Flanner, M., and Vazquez, M.},
url = {https://www.mdpi.com/2073-8994/10/11/604},
doi = {10.3390/sym10110604},
year = {2018},
date = {2018-01-01},
journal = {Symmetry},
volume = {10},
pages = {604},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2017
|
Ishihara, K., Pouokam, M., Suzuki, A., Scharein, R., Vazquez, M., Arsuaga, J., Shimokawa, K. Bounds for minimum step number of knots confined to tubes in the simple cubic lattice Journal Article Journal of Physics A: Mathematical and Theoretical, 50 (21), pp. 215601, 2017. Links | BibTeX @article{Ishihara2017,
title = {Bounds for minimum step number of knots confined to tubes in the simple cubic lattice},
author = {Ishihara, K., Pouokam, M., Suzuki, A., Scharein, R., Vazquez, M., Arsuaga, J., Shimokawa, K.},
url = {http://stacks.iop.org/1751-8121/50/i=21/a=215601?key=crossref.08a0faf57c62ce256d0f11a389c8a4c3},
doi = {10.1088/1751-8121/aa6a4f},
year = {2017},
date = {2017-05-01},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {50},
number = {21},
pages = {215601},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Stolz, R., Yoshida, M., Brasher, R., Flanner, M., Ishihara, K., Sherratt, D.-J., Shimokawa, K., Vazquez, M. Pathways of DNA unlinking: A story of stepwise simplification Journal Article Scientific Reports, 7 (1), pp. 12420, 2017, ISBN: 2045-2322. Abstract | Links | BibTeX @article{cite-key,
title = {Pathways of DNA unlinking: A story of stepwise simplification},
author = {Stolz, R., Yoshida, M., Brasher, R., Flanner, M., Ishihara, K., Sherratt, D.-J., Shimokawa, K., Vazquez, M.},
url = {https://doi.org/10.1038/s41598-017-12172-2},
doi = {10.1038/s41598-017-12172-2},
isbn = {2045-2322},
year = {2017},
date = {2017-01-01},
journal = {Scientific Reports},
volume = {7},
number = {1},
pages = {12420},
abstract = {In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA. |
Arsuaga, J., Calderer, M, Hiltner, L., Vazquez, M. A Liquid Crystal Model of Viral DNA Encapsidation (submitted) Journal Article ArXiv e-prints, 2017. BibTeX @article{2017arXiv171200629A,
title = {A Liquid Crystal Model of Viral DNA Encapsidation (submitted)},
author = {Arsuaga, J., Calderer, M, Hiltner, L., Vazquez, M.},
year = {2017},
date = {2017-01-01},
journal = {ArXiv e-prints},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2016
|
Sergio, A.-T., Gonzalez, G., Borrman, T., Garcia, J. L., Arsuaga, J. Topological Analysis of Amplicon Structure in Comparative Genomic Hybridization (CGH) Data: An Application to ERBB2/HER2/NEU Amplified Tumors Book Chapter Bac, Alexandra
and Mari, Jean-Luc (Ed.): Computational Topology in Image Context: 6th International Workshop, CTIC 2016, Marseille, France, June 15-17, 2016, Proceedings, pp. 113–129, Springer International Publishing, Cham, 2016, ISBN: 978-3-319-39441-1. Links | BibTeX @inbook{Ardanza-Trevijano2016,
title = {Topological Analysis of Amplicon Structure in Comparative Genomic Hybridization (CGH) Data: An Application to ERBB2/HER2/NEU Amplified Tumors},
author = { Sergio, A.-T., Gonzalez, G., Borrman, T., Garcia, J. L., Arsuaga, J.},
editor = {Bac, Alexandra
and Mari, Jean-Luc},
url = {http://dx.doi.org/10.1007/978-3-319-39441-1_11},
doi = {10.1007/978-3-319-39441-1_11},
isbn = {978-3-319-39441-1},
year = {2016},
date = {2016-01-01},
booktitle = {Computational Topology in Image Context: 6th International Workshop, CTIC 2016, Marseille, France, June 15-17, 2016, Proceedings},
pages = {113--129},
publisher = {Springer International Publishing},
address = {Cham},
keywords = {},
pubstate = {published},
tppubtype = {inbook}
}
|
2015
|
Arsuaga J., Borrman T., Cavalcante R., Gonzalez G.; Park C Identification of Copy Number Aberrations in Breast Cancer Subtypes using Persistence Topology. Journal Article Microarrays, 4 (3), pp. 339-369, 2015. BibTeX @article{Arsuaga-J.:2015ab,
title = {Identification of Copy Number Aberrations in Breast Cancer Subtypes using Persistence Topology.},
author = {Arsuaga J., Borrman T., Cavalcante R., Gonzalez G. and Park C},
year = {2015},
date = {2015-01-01},
journal = {Microarrays},
volume = {4},
number = {3},
pages = {339-369},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Arsuaga J., Heskia I., Hosten S.,; Maskalevich T. Uncovering Proximity of Chromosome Territories using Classical Algebraic Statistics. Journal Article Journal of Algebraic Statistics., 6 (2), pp. 133-149, 2015. BibTeX @article{Arsuaga-J.:2015aa,
title = {Uncovering Proximity of Chromosome Territories using Classical Algebraic Statistics.},
author = {Arsuaga J., Heskia I., Hosten S., and Maskalevich T.},
year = {2015},
date = {2015-01-01},
journal = {Journal of Algebraic Statistics.},
volume = {6},
number = {2},
pages = {133-149},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Diao Y., Hinson K., Sun Y.; Arsuaga J. The effect of volume exclusion on the formation of DNA minicircle networks. Journal Article J. Phys. A Math Theor., 48 (43), pp. 435202, 2015. BibTeX @article{Diao-Y.:2015aa,
title = {The effect of volume exclusion on the formation of DNA minicircle networks.},
author = {Diao Y., Hinson K., Sun Y. and Arsuaga J.},
year = {2015},
date = {2015-01-01},
journal = {J. Phys. A Math Theor.},
volume = {48},
number = {43},
pages = {435202},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Arsuaga, J.; Jayasinghe, R. G.; Scharein, R. G.; Segal, M. R.; Stolz, R. H.; Vazquez, M. Current theoretical models fail to predict the topological complexity of the human genome Journal Article Front Mol Biosci, 2 , pp. 48, 2015. Links | BibTeX @article{pmid26347874,
title = {Current theoretical models fail to predict the topological complexity of the human genome},
author = {Arsuaga, J. and Jayasinghe, R. G. and Scharein, R. G. and Segal, M. R. and Stolz, R. H. and Vazquez, M.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/26347874},
year = {2015},
date = {2015-01-01},
journal = {Front Mol Biosci},
volume = {2},
pages = {48},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Diao, Y. , Rodriguez, V., Klingbeil, M., Arsuaga, J. Orientation of DNA Minicircles Balances Density and Topological Complexity in Kinetoplast DNA Journal Article PLoS ONE, 10 (6), pp. e0130998, 2015, ISBN: 1932-6203. Abstract | Links | BibTeX @article{Diao:2015aa,
title = {Orientation of DNA Minicircles Balances Density and Topological Complexity in Kinetoplast DNA},
author = {Diao, Y. , Rodriguez, V., Klingbeil, M., Arsuaga, J.},
editor = {Solari, Aldo},
url = {http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4482025/},
doi = {10.1371/journal.pone.0130998},
isbn = {1932-6203},
year = {2015},
date = {2015-01-01},
journal = {PLoS ONE},
volume = {10},
number = {6},
pages = {e0130998},
publisher = {Public Library of Science},
address = {San Francisco, CA USA},
abstract = {Kinetoplast DNA (kDNA), a unique mitochondrial structure common to trypanosomatid parasites, contains thousands of DNA minicircles that are densely packed and can be topologically linked into a chain mail-like network. Experimental data indicate that every minicircle in the network is, on average, singly linked to three other minicircles (i.e., has mean valence 3) before replication and to six minicircles in the late stages of replication. The biophysical factors that determine the topology of the network and its changes during the cell cycle remain unknown. Using a mathematical modeling approach, we previously showed that volume confinement alone can drive the formation of the network and that it induces a linear relationship between mean valence and minicircle density. Our modeling also predicted a minicircle valence two orders of magnitude greater than that observed in kDNA. To determine the factors that contribute to this discrepancy we systematically analyzed the relationship between the topological properties of the network (i.e., minicircle density and mean valence) and its biophysical properties such as DNA bending, electrostatic repulsion, and minicircle relative position and orientation. Significantly, our results showed that most of the discrepancy between the theoretical and experimental observations can be accounted for by the orientation of the minicircles with volume exclusion due to electrostatic interactions and DNA bending playing smaller roles. Our results are in agreement with the three dimensional kDNA organization model, initially proposed by Delain and Riou, in which minicircles are oriented almost perpendicular to the horizontal plane of the kDNA disk. We suggest that while minicircle confinement drives the formation of kDNA networks, it is minicircle orientation that regulates the topological complexity of the network.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Kinetoplast DNA (kDNA), a unique mitochondrial structure common to trypanosomatid parasites, contains thousands of DNA minicircles that are densely packed and can be topologically linked into a chain mail-like network. Experimental data indicate that every minicircle in the network is, on average, singly linked to three other minicircles (i.e., has mean valence 3) before replication and to six minicircles in the late stages of replication. The biophysical factors that determine the topology of the network and its changes during the cell cycle remain unknown. Using a mathematical modeling approach, we previously showed that volume confinement alone can drive the formation of the network and that it induces a linear relationship between mean valence and minicircle density. Our modeling also predicted a minicircle valence two orders of magnitude greater than that observed in kDNA. To determine the factors that contribute to this discrepancy we systematically analyzed the relationship between the topological properties of the network (i.e., minicircle density and mean valence) and its biophysical properties such as DNA bending, electrostatic repulsion, and minicircle relative position and orientation. Significantly, our results showed that most of the discrepancy between the theoretical and experimental observations can be accounted for by the orientation of the minicircles with volume exclusion due to electrostatic interactions and DNA bending playing smaller roles. Our results are in agreement with the three dimensional kDNA organization model, initially proposed by Delain and Riou, in which minicircles are oriented almost perpendicular to the horizontal plane of the kDNA disk. We suggest that while minicircle confinement drives the formation of kDNA networks, it is minicircle orientation that regulates the topological complexity of the network. |
2014
|
Segal, M. R.; Xiong, H.; Capurso, D.; Vazquez, M.; Arsuaga, J. Reproducibility of 3Đ chromatin configuration reconstructions Journal Article Biostatistics, 15 (3), pp. 442–456, 2014. Links | BibTeX @article{pmid24519450,
title = {Reproducibility of 3Đ chromatin configuration reconstructions},
author = {Segal, M. R. and Xiong, H. and Capurso, D. and Vazquez, M. and Arsuaga, J.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24519450},
year = {2014},
date = {2014-07-01},
journal = {Biostatistics},
volume = {15},
number = {3},
pages = {442--456},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Arsuaga J., Diao Y, Klingbeil M.; Rodriguez V. Properties of Topological Networks of Flexible Polygonal Chains. Journal Article Mol. Based. Math. Bio., 2 , pp. 98-106, 2014. BibTeX @article{Arsuaga-J.:2014aa,
title = {Properties of Topological Networks of Flexible Polygonal Chains.},
author = {Arsuaga J., Diao Y, Klingbeil M. and Rodriguez V.},
year = {2014},
date = {2014-01-01},
journal = {Mol. Based. Math. Bio.},
volume = {2},
pages = {98-106},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Ishihara, K., Shimokawa, K., Vazquez, M. Site-specific recombination modeled as a band surgery: applications to Xer recombination Incollection Discrete and topological models in molecular biology, pp. 387–401, Springer, Heidelberg, 2014. Links | BibTeX @incollection{MR3220014,
title = {Site-specific recombination modeled as a band surgery: applications to Xer recombination},
author = {Ishihara, K., Shimokawa, K., Vazquez, M.},
url = {http://dx.doi.org/10.1007/978-3-642-40193-0_18},
doi = {10.1007/978-3-642-40193-0_18},
year = {2014},
date = {2014-01-01},
booktitle = {Discrete and topological models in molecular biology},
pages = {387--401},
publisher = {Springer, Heidelberg},
series = {Nat. Comput. Ser.},
keywords = {},
pubstate = {published},
tppubtype = {incollection}
}
|
2013
|
Shimokawa, K.; Ishihara, K.; Grainge, I.; Sherratt, D. J.; Vazquez, M. FtsK-dependent XerCĐ-dif recombination unlinks replication catenanes in a stepwise manner Journal Article Proc. Natl. Acad. Sci. U.S.A., 110 (52), pp. 20906–20911, 2013. Links | BibTeX @article{pmid24218579,
title = {FtsK-dependent XerCĐ-dif recombination unlinks replication catenanes in a stepwise manner},
author = {Shimokawa, K. and Ishihara, K. and Grainge, I. and Sherratt, D. J. and Vazquez, M.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/24218579},
year = {2013},
date = {2013-12-01},
journal = {Proc. Natl. Acad. Sci. U.S.A.},
volume = {110},
number = {52},
pages = {20906--20911},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Darcy, I. K.; Vazquez, M. Đetermining the topology of stable protein-ĐNA complexes Journal Article Biochem. Soc. Trans., 41 (2), pp. 601–605, 2013. Links | BibTeX @article{pmid23514161,
title = {Đetermining the topology of stable protein-ĐNA complexes},
author = {Darcy, I. K. and Vazquez, M.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23514161},
year = {2013},
date = {2013-04-01},
journal = {Biochem. Soc. Trans.},
volume = {41},
number = {2},
pages = {601--605},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Brasher, R.; Scharein, R. G.; Vazquez, M. New biologically motivated knot table Journal Article Biochem. Soc. Trans., 41 (2), pp. 606–611, 2013. Links | BibTeX @article{pmid23514162,
title = {New biologically motivated knot table},
author = {Brasher, R. and Scharein, R. G. and Vazquez, M.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/23514162},
year = {2013},
date = {2013-04-01},
journal = {Biochem. Soc. Trans.},
volume = {41},
number = {2},
pages = {606--611},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Rodriguez V, Diao Y.; Arsuaga J. Percolation phenomena in randomized topological networks. Journal Article J. Phys.: Conf. Ser., 454 , pp. 012070, 2013. BibTeX @article{Rodriguez-V:2013aa,
title = {Percolation phenomena in randomized topological networks.},
author = {Rodriguez V, Diao Y. and Arsuaga J.},
year = {2013},
date = {2013-01-01},
journal = {J. Phys.: Conf. Ser.},
volume = {454},
pages = {012070},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
2012
|
Diao, Y.; Hinson, K.; Kaplan, R.; Vazquez, M.; Arsuaga, J. Ŧhe effects of density on the topological structure of the mitochondrial ĐNA from trypanosomes Journal Article J Math Biol, 64 (6), pp. 1087–1108, 2012. Links | BibTeX @article{pmid21671031,
title = {Ŧhe effects of density on the topological structure of the mitochondrial ĐNA from trypanosomes},
author = {Diao, Y. and Hinson, K. and Kaplan, R. and Vazquez, M. and Arsuaga, J.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/21671031},
year = {2012},
date = {2012-05-01},
journal = {J Math Biol},
volume = {64},
number = {6},
pages = {1087--1108},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Arsuaga J , Baas N, DeWoskin D, Mizuno H,; Pankov A, Park C A topological signature derived from expression profiles for the identification of breast cancer subtypes. Journal Article Applicable Algebra in Engineering, Communication and Computing, 23 (1), pp. 3-15, 2012. BibTeX @article{Arsuaga-J:2012ac,
title = {A topological signature derived from expression profiles for the identification of breast cancer subtypes.},
author = {Arsuaga J , Baas N, DeWoskin D, Mizuno H, and Pankov A, Park C},
year = {2012},
date = {2012-01-01},
journal = {Applicable Algebra in Engineering, Communication and Computing},
volume = {23},
number = {1},
pages = {3-15},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Arsuaga J, Diao Y; Hinson K, The growth of minicircle networks on regular lattices Journal Article J. of Phys. A: Math. Theor., 45 , pp. 035004, 2012. BibTeX @article{Arsuaga-J:2012ab,
title = {The growth of minicircle networks on regular lattices},
author = {Arsuaga J, Diao Y and Hinson K,},
year = {2012},
date = {2012-01-01},
journal = {J. of Phys. A: Math. Theor.},
volume = {45},
pages = {035004},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Arsuaga J, Diao Y; Hinson K The effect of angle restriction on the topological characteristics of minicircle networks. Journal Article J. Stat. Phys., 146 , pp. 434-445, 2012. BibTeX @article{Arsuaga-J:2012aa,
title = {The effect of angle restriction on the topological characteristics of minicircle networks.},
author = {Arsuaga J, Diao Y and Hinson K},
year = {2012},
date = {2012-01-01},
journal = {J. Stat. Phys.},
volume = {146},
pages = {434-445},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
K Ishihara; R Scharein; Y Diao; J Arsuaga; M Vazquez; K Shimokawa Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice Journal Article Journal of Physics A: Mathematical and Theoretical, 45 (6), pp. 065003, 2012. Abstract | Links | BibTeX @article{Ishihara2012,
title = {Bounds for the minimum step number of knots confined to slabs in the simple cubic lattice},
author = {K Ishihara and R Scharein and Y Diao and J Arsuaga and M Vazquez and K Shimokawa},
url = {http://stacks.iop.org/1751-8121/45/i=6/a=065003},
year = {2012},
date = {2012-01-01},
journal = {Journal of Physics A: Mathematical and Theoretical},
volume = {45},
number = {6},
pages = {065003},
abstract = {Volume confinement is a key determinant of the topology and geometry of a polymer. However, the direct relationship between the two is not fully understood. For instance, recent experimental studies have constructed P4 cosmids, i.e. P4 bacteriophages whose genome sequence and length have been artificially engineered and have shown that upon extraction their DNA knot distribution differs from that of wild-type bacteriophage P4. In particular, it was observed that the complexity of the knots decreases sharply with the length of the packed genome. This problem is the motivation of this paper. Here, a polymer is modeled as a self-avoiding polygon on the simple cubic lattice and the confining condition is such that the polygon is bounded between two parallel planes (i.e. bounded within a slab). We estimate the minimum length required for such a polygon to realize a knot type. Our numerical simulations show that in order to realize a prime knot (with up to ten crossings) in a 1-slab (i.e. a slab of height 1), one needs a polygon of length strictly longer than the minimum length needed to realize the same knot when there is no confining condition. In the case of the trefoil knot, we can in fact establish this result analytically by proving that the minimum length required to tie a trefoil in the 1-slab is 26, which is greater than 24, the known minimum length required to tie a trefoil without a confinement condition. Additionally, we find that in the 1-slab not all geometrical realizations of a given knot type are equivalent under BFACF moves. This suggests that in certain confined volumes, knowing the topology of a polymer is not enough to describe all its states.},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
Volume confinement is a key determinant of the topology and geometry of a polymer. However, the direct relationship between the two is not fully understood. For instance, recent experimental studies have constructed P4 cosmids, i.e. P4 bacteriophages whose genome sequence and length have been artificially engineered and have shown that upon extraction their DNA knot distribution differs from that of wild-type bacteriophage P4. In particular, it was observed that the complexity of the knots decreases sharply with the length of the packed genome. This problem is the motivation of this paper. Here, a polymer is modeled as a self-avoiding polygon on the simple cubic lattice and the confining condition is such that the polygon is bounded between two parallel planes (i.e. bounded within a slab). We estimate the minimum length required for such a polygon to realize a knot type. Our numerical simulations show that in order to realize a prime knot (with up to ten crossings) in a 1-slab (i.e. a slab of height 1), one needs a polygon of length strictly longer than the minimum length needed to realize the same knot when there is no confining condition. In the case of the trefoil knot, we can in fact establish this result analytically by proving that the minimum length required to tie a trefoil in the 1-slab is 26, which is greater than 24, the known minimum length required to tie a trefoil without a confinement condition. Additionally, we find that in the 1-slab not all geometrical realizations of a given knot type are equivalent under BFACF moves. This suggests that in certain confined volumes, knowing the topology of a polymer is not enough to describe all its states. |
2011
|
Blackstone, T, Scharein, R., Varela, R., Diao, Y.,; Arsuaga J. Modeling Chromosome Intermingling Using Overlapping Uniform Random Polygons. Journal Article Journal of Mathematical Biology, 62 (3), pp. 371-89, 2011. BibTeX @article{Blackstone:2011aa,
title = {Modeling Chromosome Intermingling Using Overlapping Uniform Random Polygons.},
author = {Blackstone, T, Scharein, R., Varela, R., Diao, Y., and Arsuaga J.},
year = {2011},
date = {2011-01-01},
journal = {Journal of Mathematical Biology},
volume = {62},
number = {3},
pages = {371-89},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
Portillo, J.; Diao, Y.; Scharein, R.; Arsuaga, J.; Vazquez, M. On the mean and variance of the writhe of random polygons Journal Article J Phys A Math Theor, 44 (27), pp. 275004, 2011. Links | BibTeX @article{pmid25685182,
title = {On the mean and variance of the writhe of random polygons},
author = {Portillo, J. and Diao, Y. and Scharein, R. and Arsuaga, J. and Vazquez, M.},
url = {http://www.ncbi.nlm.nih.gov/pubmed/25685182},
year = {2011},
date = {2011-01-01},
journal = {J Phys A Math Theor},
volume = {44},
number = {27},
pages = {275004},
keywords = {},
pubstate = {published},
tppubtype = {article}
}
|
