text:
@misc{supplemental,
  year = {2019},
  note = {See Supplemental Material at https:// www.overleaf.com/project/5bf089c8f9256e52006d9a4d for detailed derivation of $B_{l_0m_0j_0}^{lmj}$, validation of numerical methods, examples of different unwrapping levels, and tables of effective Kuhn lengths.}
}

@article{hnisz2013,
  title = {Super-{{Enhancers}} in the {{Control}} of {{Cell Identity}} and {{Disease}}},
  volume = {155},
  issn = {00928674},
  language = {en},
  number = {4},
  journal = {Cell},
  doi = {10.1016/j.cell.2013.09.053},
  author = {Hnisz, Denes and Abraham, Brian J. and Lee, Tong Ihn and Lau, Ashley and {Saint-Andr\'e}, Violaine and Sigova, Alla A. and Hoke, Heather A. and Young, Richard A.},
  month = nov,
  year = {2013},
  pages = {934-947},
  file = {/home/bbeltr1/Documents/paper-collection/YoungR/Hnisz et al_2013_Super-Enhancers in the Control of Cell Identity and Disease.pdf}
}

@article{williamson2014,
  title = {Spatial Genome Organization: Contrasting Views from Chromosome Conformation Capture and Fluorescence in Situ Hybridization},
  volume = {28},
  issn = {0890-9369, 1549-5477},
  shorttitle = {Spatial Genome Organization},
  language = {en},
  number = {24},
  journal = {Genes \& Development},
  doi = {10.1101/gad.251694.114},
  author = {Williamson, Iain and Berlivet, Soizik and Eskeland, Ragnhild and Boyle, Shelagh and Illingworth, Robert S. and Paquette, Denis and Dostie, Jos\'ee and Bickmore, Wendy A.},
  month = dec,
  year = {2014},
  pages = {2778-2791},
  file = {/home/bbeltr1/Documents/paper-collection/BickmoreW/Williamson et al_2014_Spatial genome organization.pdf}
}

@article{giorgetti2014,
  title = {Predictive {{Polymer Modeling Reveals Coupled Fluctuations}} in {{Chromosome Conformation}} and {{Transcription}}},
  volume = {157},
  issn = {0092-8674, 1097-4172},
  abstract = {A new level of chromosome organization, topologically associating domains (TADs), was recently uncovered by chromosome conformation capture (3C) techniques. To explore TAD structure and function, we developed a polymer model that can extract the full repertoire of chromatin conformations within TADs from population-based 3C data. This model predicts actual physical distances and to what extent chromosomal contacts vary between cells. It also identifies interactions within single TADs that stabilize boundaries between TADs and allows us to identify and genetically validate key structural elements within TADs. Combining the model's predictions with high-resolution DNA FISH and quantitative RNA FISH for TADs within the X-inactivation center (Xic), we dissect the relationship between transcription and spatial proximity to cis-regulatory elements. We demonstrate that contacts between potential regulatory elements occur in the context of fluctuating structures rather than stable loops and propose that such fluctuations may contribute to asymmetric expression in the Xic during X inactivation.},
  language = {English},
  number = {4},
  journal = {Cell},
  doi = {10.1016/j.cell.2014.03.025},
  author = {Giorgetti, Luca and Galupa, Rafael and Nora, Elph\`ege P. and Piolot, Tristan and Lam, France and Dekker, Job and Tiana, Guido and Heard, Edith},
  month = may,
  year = {2014},
  keywords = {pairwise energies,tad modeling,optimized hi-c modeling},
  pages = {950-963},
  file = {/home/bbeltr1/Documents/paper-collection/Heard/Giorgetti et al_2014_Predictive Polymer Modeling Reveals Coupled Fluctuations in Chromosome.pdf;/home/bbeltr1/Documents/paper-collection/HeardE/Giorgetti et al_2014_Predictive Polymer Modeling Reveals Coupled Fluctuations in Chromosome.pdf;/home/bbeltr1/Documents/zotero/storage/A2I6FAIB/S0092-8674(14)00361-4.html},
  pmid = {24813616, 24813616}
}

@article{haber2012,
  title = {Mating-{{Type Genes}} and {{MAT Switching}} in {{Saccharomyces}} Cerevisiae},
  volume = {191},
  copyright = {Copyright \textcopyright{} 2012 by the Genetics Society of America},
  issn = {0016-6731, 1943-2631},
  abstract = {Mating type in Saccharomyces cerevisiae is determined by two nonhomologous alleles, MATa and MAT{$\alpha$}. These sequences encode regulators of the two different haploid mating types and of the diploids formed by their conjugation. Analysis of the MATa1, MAT{$\alpha$}1, and MAT{$\alpha$}2 alleles provided one of the earliest models of cell-type specification by transcriptional activators and repressors. Remarkably, homothallic yeast cells can switch their mating type as often as every generation by a highly choreographed, site-specific homologous recombination event that replaces one MAT allele with different DNA sequences encoding the opposite MAT allele. This replacement process involves the participation of two intact but unexpressed copies of mating-type information at the heterochromatic loci, HML{$\alpha$} and HMRa, which are located at opposite ends of the same chromosome-encoding MAT. The study of MAT switching has yielded important insights into the control of cell lineage, the silencing of gene expression, the formation of heterochromatin, and the regulation of accessibility of the donor sequences. Real-time analysis of MAT switching has provided the most detailed description of the molecular events that occur during the homologous recombinational repair of a programmed double-strand chromosome break.},
  language = {en},
  number = {1},
  journal = {Genetics},
  doi = {10.1534/genetics.111.134577},
  author = {Haber, James E.},
  month = may,
  year = {2012},
  pages = {33-64},
  file = {/home/bbeltr1/Documents/paper-collection/HaberJ/Haber_2012_Mating-Type Genes and MAT Switching in Saccharomyces cerevisiae.pdf;/home/bbeltr1/Documents/zotero/storage/ZUSZ93PZ/33.html},
  pmid = {22555442}
}

@article{bressan2004,
  title = {Mating Type\textendash{}Dependent Constraints on the Mobility of the Left Arm of Yeast Chromosome {{III}}},
  volume = {164},
  issn = {0021-9525},
  abstract = {Mating-type gene (MAT) switching in budding yeast exhibits donor preference. MATa preferentially recombines with HML near the left telomere of chromosome III, whereas MAT{$\alpha$} prefers HMR near the right telomere. Donor preference is controlled by the recombination enhancer (RE) located proximal to HML. To test if HML is constrained in pairing with MAT{$\alpha$}, we examined live-cell mobility of LacI-GFP\textendash{}bound lactose operator (lacO) arrays inserted at different chromosomal sites. Without induction of recombination, lacO sequences adjacent to HML are strongly constrained in both MAT{$\alpha$} and RE-deleted MATa strains, compared with MATa. In contrast, chromosome movement at HMR or near a telomere of chromosome V is mating-type independent. HML is more constrained in MATa {$\Delta$}re and less constrained in MATa RE+ compared with other sites. Although HML and MATa are not prealigned before inducing recombination, the three-dimensional configuration of MAT, HML, and HMR is mating-type dependent. These data suggest there is constitutive tethering of HML, which is relieved in MATa cells through the action of RE.},
  number = {3},
  journal = {J Cell Biol},
  doi = {10.1083/jcb.200311063},
  author = {Bressan, Debra A. and Vazquez, Julio and Haber, James E.},
  month = feb,
  year = {2004},
  pages = {361-371},
  file = {/home/bbeltr1/Documents/paper-collection/HaberJ/Bressan et al_2004_Mating type–dependent constraints on the mobility of the left arm of yeast.pdf},
  pmid = {14745000},
  pmcid = {PMC2172233}
}

@article{wu1996,
  title = {A 700 Bp Cis-{{Acting Region Controls Mating}}-{{Type Dependent Recombination Along}} the {{Entire Left Arm}} of {{Yeast Chromosome III}}},
  volume = {87},
  issn = {0092-8674},
  abstract = {Homothallic switching of the mating-type MAT a gene in Saccharomyces cerevisiae results from replacement by gene conversion of MAT-Ya DNA with Y{$\alpha$} sequences copied from one of two unexpressed donors. MAT a preferentially recombines with HML{$\alpha$}, located near the left end of chromosome III, but can use HMR{$\alpha$}, near the right chromosome end. MAT a donor preference depends on a 700 bp orientation-independent cis-acting recombination enhancer, located 17 kb proximal to HML. Deletion of this element markedly reduces MAT a's use of a donor inserted at any of four different locations along the leftmost 92 kb of chromosome III. This enhancer is sufficient for donor activation, since it stimulates use of the ``wrong'' donor, when it is inserted 7 kb proximal to HMR.},
  number = {2},
  journal = {Cell},
  doi = {10.1016/S0092-8674(00)81345-8},
  author = {Wu, Xiaohua and Haber, James E},
  month = oct,
  year = {1996},
  pages = {277-285},
  file = {/home/bbeltr1/Documents/paper-collection/HaberJ/Wu_Haber_1996_A 700 bp cis-Acting Region Controls Mating-Type Dependent Recombination Along.pdf;/home/bbeltr1/Documents/zotero/storage/JFD6CSXE/S0092867400813458.html}
}

@article{matsuda2011,
  title = {A Homolog of Male Sex-Determining Factor {{SRY}} Cooperates with a Transposon-Derived {{CENP}}-{{B}} Protein to Control Sex-Specific Directed Recombination},
  volume = {108},
  issn = {0027-8424, 1091-6490},
  abstract = {Schizosaccharomyces pombe cells switch mating type by replacing genetic information at the expressed mat1 locus with sequences copied from mat2-P or mat3-M silent donor loci. The choice of donor locus is dictated by cell type, such that mat2 is the preferred donor in M cells and mat3 is the preferred donor in P cells. Donor choice involves a recombination-promoting complex (RPC) containing Swi2 and Swi5. In P cells, the RPC localizes to a specific DNA element located adjacent to mat3, but in M cells it spreads across the silent mating-type region, including mat2-P. This differential distribution of the RPC regulates nonrandom choice of donors. However, cell-type\textendash{}specific differences in RPC localization are not understood. Here we show that the mat1-M\textendash{}encoded factor Mc, which shares structural and functional similarities with the male sex-determining factor SRY, is highly enriched at the swi2 and swi5 loci and promotes elevated levels of RPC components. Loss of Mc reduces Swi2 and Swi5 to levels comparable to those in P cells and disrupts RPC spreading across the mat2/3 region. Mc also localizes to loci expressed preferentially in M cells and to retrotransposon LTRs. We demonstrate that Mc localization at LTRs and at swi2 requires Abp1, a homolog of transposon-derived CENP-B protein and that loss of Abp1 impairs Swi2 protein expression and the donor choice mechanism. These results suggest that Mc modulates levels of recombination factors, which is important for mating-type donor selection and for the biased gene conversion observed during meiosis, where M cells serve as preferential donors of genetic information.},
  language = {en},
  number = {46},
  journal = {PNAS},
  doi = {10.1073/pnas.1109988108},
  author = {Matsuda, Emiko and {Sugioka-Sugiyama}, Rie and Mizuguchi, Takeshi and Mehta, Sameet and Cui, Bowen and Grewal, Shiv I. S.},
  month = nov,
  year = {2011},
  keywords = {development,transposition,directionality,yeast},
  pages = {18754-18759},
  file = {/home/bbeltr1/Documents/paper-collection/GrewalS/Matsuda et al_2011_A homolog of male sex-determining factor SRY cooperates with a.pdf;/home/bbeltr1/Documents/zotero/storage/QJ443HHG/18754.html},
  pmid = {22042869}
}

@article{yu2012,
  title = {Going in the {{Right Direction}}: {{Mating}}-{{Type Switching}} of {{Schizosaccharomyces}} Pombe {{Is Controlled}} by {{Judicious Expression}} of {{Two Different}} Swi2 {{Transcripts}}},
  volume = {190},
  issn = {0016-6731},
  shorttitle = {Going in the {{Right Direction}}},
  abstract = {Schizosaccharomyces pombe, the fission yeast, cells alternate between P- and M-mating type, controlled by the alternate alleles of the mating-type locus (mat1). The mat1 switching occurs by replacing mat1 with a copy derived from a silenced ``donor locus,'' mat2P or mat3M. The mechanism of donor choice ensuring that switching occurs primarily and productively to the opposite type, called directionality, is largely unknown. Here we identified the mat1-Mc gene, a mammalian sex-determination gene (SRY) homolog, as the primary gene that dictates directionality in M cells. A previously unrecognized, shorter swi2 mRNA, a truncated form of the swi2, was identified, and its expression requires the mat1-Mc function. We also found that the abp1 gene (human CENPB homolog) controls directionality through swi2 regulation. In addition, we implicated a cis-acting DNA sequence in mat2 utilization. Overall, we showed that switching directionality is controlled by judicious expression of two swi2 transcripts through a cell-type-regulated dual promoter. In this respect, this regulation mechanism resembles that of the Drosophila sex-determination Slx gene.},
  number = {3},
  journal = {Genetics},
  doi = {10.1534/genetics.111.137109},
  author = {Yu, Chuanhe and Bonaduce, Michael J. and Klar, Amar J. S.},
  month = mar,
  year = {2012},
  pages = {977-987},
  file = {/home/bbeltr1/Documents/paper-collection/KlarA/Yu et al_2012_Going in the Right Direction.pdf},
  pmid = {22209903},
  pmcid = {PMC3296259}
}

@article{ding2006,
  title = {Meiotic Cohesins Modulate Chromosome Compaction during Meiotic Prophase in Fission Yeast},
  volume = {174},
  issn = {0021-9525},
  abstract = {The meiotic cohesin Rec8 is required for the stepwise segregation of chromosomes during the two rounds of meiotic division. By directly measuring chromosome compaction in living cells of the fission yeast Schizosaccharomyces pombe, we found an additional role for the meiotic cohesin in the compaction of chromosomes during meiotic prophase. In the absence of Rec8, chromosomes were decompacted relative to those of wild-type cells. Conversely, loss of the cohesin-associated protein Pds5 resulted in hypercompaction. Although this hypercompaction requires Rec8, binding of Rec8 to chromatin was reduced in the absence of Pds5, indicating that Pds5 promotes chromosome association of Rec8. To explain these observations, we propose that meiotic prophase chromosomes are organized as chromatin loops emanating from a Rec8-containing axis: the absence of Rec8 disrupts the axis, resulting in disorganized chromosomes, whereas reduced Rec8 loading results in a longitudinally compacted axis with fewer attachment points and longer chromatin loops.},
  number = {4},
  journal = {J Cell Biol},
  doi = {10.1083/jcb.200605074},
  author = {Ding, Da-Qiao and Sakurai, Nobuko and Katou, Yuki and Itoh, Takehiko and Shirahige, Katsuhiko and Haraguchi, Tokuko and Hiraoka, Yasushi},
  month = aug,
  year = {2006},
  pages = {499-508},
  file = {/home/bbeltr1/Documents/paper-collection/HiraokaY/Ding et al_2006_Meiotic cohesins modulate chromosome compaction during meiotic prophase in.pdf},
  pmid = {16893973},
  pmcid = {PMC2064256}
}

@article{ekwall1994,
  title = {Mutations in Rik1, Clr2, Clr3 and Clr4 Genes Asymmetrically Derepress the Silent Mating-Type Loci in Fission Yeast.},
  volume = {136},
  copyright = {Copyright \textcopyright{} 1994 by the Genetics Society of America},
  issn = {0016-6731, 1943-2631},
  abstract = {In Schizosaccharomyces pombe the mating-type information is stored at two transcriptionally silent loci (mat2 and mat3). The region between these sites (K region) is inert for meiotic crossing over. The mating-type genes (M or P) are expressed only when present at a third, active locus (mat1). We have earlier shown that the positional regulation of P genes is based on repression at the silent site, caused by elements in the flanking DNA sequences. In this study we have mutagenized a sterile mat1 deleted strain and selected for cells that are able to conjugate. Recessive mutations of this type should define genes encoding trans-acting factors involved in repression of the silent mating-type loci. Before this work mutations in two genes, clr1 and swi6, had been shown to allow both expression of the silent loci and recombination in the K region. The sensitivity of the present selection is demonstrated by the isolation of new mutations that derepress one or both of the silent loci (M-mating or bi-mating). The frequency of M-mating mutants was almost two orders of magnitude higher than that of bi-mating mutants and in all mutants analyzed mat3-M expression was significantly higher than mat2-P expression. The mutations define three new genes, clr2, clr3 and clr4. In addition we show that the rik1 mutant previously known to allow recombination in the K region also depresses the silent loci.},
  language = {en},
  number = {1},
  journal = {Genetics},
  author = {Ekwall, K. and Ruusala, T.},
  month = jan,
  year = {1994},
  pages = {53-64},
  file = {/home/bbeltr1/Documents/paper-collection/RuusalaT/Ekwall_Ruusala_1994_Mutations in rik1, clr2, clr3 and clr4 genes asymmetrically derepress the.pdf;/home/bbeltr1/Documents/zotero/storage/INHQZV8S/53.html},
  pmid = {8138176}
}

@article{lorentz1994,
  title = {Switching Gene Swi6, Involved in Repression of Silent Mating-Type Loci in Fission Yeast, Encodes a Homologue of Chromatin-Associated Proteins from {{Drosophila}} and Mammals},
  volume = {143},
  issn = {0378-1119},
  abstract = {The switching gene swi6 of Schizosaccharomyces pombe is involved in the repression of the silent mating-type loci mat2 and mat3. We have cloned the gene by functional complementation of the switching defect of the swi6-115 mutation. DNA sequence analyses revealed an open reading frame of 984 bp coding for a putative protein of 328 amino acids (aa). The isolation of a swi6 cDNA confirmed this result. Gene replacement showed that swi6 is not essential for viability. The Swi6 protein is very hydrophilic; it contains 41\% charged aa. A region of 48 aa is homologous to a sequence motif found in the chromatin-associated proteins, HP1 and Polycomb (Drosophila melanogaster), M31, M32 and M33 (mouse), and the human HSM1 protein. This motif is called chromo domain (chromatin organization modifier). Our results indicate that Swi6 is a structural component of chromatin. Swi6 may have the function to compact mat2 and mat3 into a heterochromatin-like conformation which represses the transcription of these silent cassettes.},
  number = {1},
  journal = {Gene},
  doi = {10.1016/0378-1119(94)90619-X},
  author = {Lorentz, Axel and Ostermann, Kai and Fleck, Oliver and Schmidt, Henning},
  month = may,
  year = {1994},
  keywords = {Schizosaccharomyces pombe,silencing,chromo domain,heterochromatin},
  pages = {139-143},
  file = {/home/bbeltr1/Documents/paper-collection/SchmidtH/Lorentz et al_1994_Switching gene swi6, involved in repression of silent mating-type loci in.pdf;/home/bbeltr1/Documents/zotero/storage/FDPXK54U/037811199490619X.html}
}

@article{klar1991,
  title = {Swi6, a Gene Required for Mating-Type Switching, Prohibits Meiotic Recombination in the Mat2-Mat3 "Cold Spot" of Fission Yeast.},
  volume = {129},
  copyright = {Copyright \textcopyright{} 1991 by the Genetics Society of America},
  issn = {0016-6731, 1943-2631},
  abstract = {Mitotic interconversion of the mating-type locus (mat1) of the fission yeast Schizosaccharomyces pombe is initiated by a double-strand break at mat1. The mat2 and mat3 loci act as nonrandom donors of genetic information for mat1 switching such that switches occur primarily (or only) to the opposite mat1 allele. Location of the mat1 "hot spot" for transposition should be contrasted with the "cold spot" of meiotic recombination located within the adjoining mat2-mat3 interval. That is, meiotic interchromosomal recombination in mat2, mat3 and the intervening 15-kilobase region does not occur at all. swi2 and swi6 switching-deficient mutants possess the normal level of double-strand break at mat1, yet they fail to switch efficiently. By testing for meiotic recombination in the cold spot, we found the usual lack of recombination in a swi2 mutant but a significant level of recombination in a swi6 mutant. Therefore, the swi6 gene function is required to keep the donor loci inert for interchromosomal recombination. This finding, combined with the additional result that switching primarily occurs intrachromosomally, suggests that the donor loci are made accessible for switching by folding them onto mat1, thus causing the cold spot of recombination.},
  language = {en},
  number = {4},
  journal = {Genetics},
  author = {Klar, A. J. and Bonaduce, M. J.},
  month = dec,
  year = {1991},
  pages = {1033-1042},
  file = {/home/bbeltr1/Documents/paper-collection/BonaduceM/Klar_Bonaduce_1991_swi6, a gene required for mating-type switching, prohibits meiotic.pdf;/home/bbeltr1/Documents/zotero/storage/CHNW4DHA/1033.html},
  pmid = {1783290}
}

@article{audergon2015,
  title = {Restricted Epigenetic Inheritance of {{H3K9}} Methylation},
  volume = {348},
  copyright = {Copyright \textcopyright{} 2015, American Association for the Advancement of Science},
  issn = {0036-8075, 1095-9203},
  abstract = {Inheritance of a covalent histone modification
Genomic DNA is the repository of all genetic information and is packaged into chromatin. Chromatin is also a repository of regulatory information in the form of covalent marks added to the histones that package the DNA. These marks can determine tissue- and organ-specific gene expression patterns, which must be transmitted to daughter cells to maintain their identity. Ragunathan et al. and Audergon et al. show that in fission yeast, a chromatin mark, like genetic information, can be inherited across many cell generations. The mark can be inherited independently of DNA sequence, DNA methylation, or RNA interference. Thus, histone marks constitute true epigenetic information.
Science, this issue 10.1126/science.1258699; see also p. 132
Posttranslational histone modifications are believed to allow the epigenetic transmission of distinct chromatin states, independently of associated DNA sequences. Histone H3 lysine 9 (H3K9) methylation is essential for heterochromatin formation; however, a demonstration of its epigenetic heritability is lacking. Fission yeast has a single H3K9 methyltransferase, Clr4, that directs all H3K9 methylation and heterochromatin. Using releasable tethered Clr4 reveals that an active process rapidly erases H3K9 methylation from tethering sites in wild-type cells. However, inactivation of the putative histone demethylase Epe1 allows H3K9 methylation and silent chromatin maintenance at the tethering site through many mitotic divisions, and transgenerationally through meiosis, after release of tethered Clr4. Thus, H3K9 methylation is a heritable epigenetic mark whose transmission is usually countered by its active removal, which prevents the unauthorized inheritance of heterochromatin.
Covalent histone modifications are inherited epigenetically across many generations.
Covalent histone modifications are inherited epigenetically across many generations.},
  language = {en},
  number = {6230},
  journal = {Science},
  doi = {10.1126/science.1260638},
  author = {Audergon, Pauline N. C. B. and Catania, Sandra and Kagansky, Alexander and Tong, Pin and Shukla, Manu and Pidoux, Alison L. and Allshire, Robin C.},
  month = apr,
  year = {2015},
  pages = {132-135},
  file = {/home/bbeltr1/Documents/paper-collection/AllshireR/Audergon et al_2015_Restricted epigenetic inheritance of H3K9 methylation.pdf;/home/bbeltr1/Documents/zotero/storage/4VGEK3ED/132.html},
  pmid = {25838386}
}

@article{mao2016,
  title = {Impact of {{Conformational}} and {{Chemical Correlations}} on {{Microphase Segregation}} in {{Random Copolymers}}},
  volume = {49},
  issn = {0024-9297, 1520-5835},
  language = {en},
  number = {11},
  journal = {Macromolecules},
  doi = {10.1021/acs.macromol.5b02639},
  author = {Mao, Shifan and MacPherson, Quinn J. and He, Steve S. and Coletta, Elyse and Spakowitz, Andrew J.},
  month = jun,
  year = {2016},
  pages = {4358-4368},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Mao et al_2016_Impact of Conformational and Chemical Correlations on Microphase Segregation in.pdf}
}

@article{lampo2016,
  title = {Physical {{Modeling}} of {{Dynamic Coupling}} between {{Chromosomal Loci}}},
  volume = {110},
  issn = {0006-3495},
  abstract = {The motion of chromosomal DNA is essential to many biological processes, including segregation, transcriptional regulation, recombination, and packaging. Physical understanding of these processes would be dramatically enhanced through predictive, quantitative modeling of chromosome dynamics of multiple loci. Using a polymer dynamics framework, we develop a~prediction for the correlation in the velocities of two loci on a single chromosome or otherwise connected by chromatin. These predictions reveal that the signature of correlated motion between two loci can be identified by varying the lag time between locus position measurements. In general, this theory predicts that as the lag time interval increases, the dual-loci dynamic behavior transitions from being completely uncorrelated to behaving as an effective single locus. This transition corresponds to the timescale of the stress communication between loci through the intervening segment. This relatively simple framework makes quantitative predictions based on a single timescale fit parameter that can be directly compared to the in~vivo motion of fluorescently labeled chromosome loci. Furthermore, this theoretical framework enables the detection of dynamically coupled chromosome regions from the signature of their correlated motion.},
  number = {2},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2015.11.3520},
  author = {Lampo, Thomas J. and Kennard, Andrew S. and Spakowitz, Andrew J.},
  month = jan,
  year = {2016},
  pages = {338-347},
  file = {/home/bbeltr1/Documents/paper-collection/Spakowitz/Lampo et al_2016_Physical Modeling of Dynamic Coupling between Chromosomal Loci.pdf;/home/bbeltr1/Documents/paper-collection/SpakowitzA/Lampo et al_2016_Physical Modeling of Dynamic Coupling between Chromosomal Loci.pdf;/home/bbeltr1/Documents/zotero/storage/KUHUCG76/S0006349515047049.html}
}

@article{mulligan2015a,
  title = {Interplay of {{Protein Binding Interactions}}, {{DNA Mechanics}}, and {{Entropy}} in~{{DNA Looping Kinetics}}},
  volume = {109},
  issn = {0006-3495},
  abstract = {DNA looping plays a key role in many fundamental biological processes, including gene regulation, recombination, and chromosomal organization. The looping of DNA is often mediated by proteins whose structural features and physical interactions can alter the length scale at which the looping occurs. Looping and unlooping processes are controlled by thermodynamic contributions associated with mechanical deformation of the DNA strand and entropy arising from thermal fluctuations of the conformation. To determine how these confounding effects influence DNA looping and unlooping kinetics, we present a theoretical model that incorporates the role of the protein interactions, DNA mechanics, and conformational entropy. We show that for shorter DNA strands the interaction distance affects the transition state, resulting in a complex relationship between the looped and unlooped state lifetimes and the physical properties of the looped DNA. We explore the range of behaviors that arise with varying interaction distance and DNA length. These results demonstrate how DNA deformation and entropy dictate the scaling of the looping and unlooping kinetics versus the J-factor, establishing the connection between kinetic and equilibrium behaviors. Our results show how the twist-and-bend elasticity of the DNA chain modulates the kinetics and how the influence of the interaction distance fades away at intermediate to longer chain lengths, in agreement with previous scaling predictions.},
  number = {3},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2015.06.054},
  author = {Mulligan, Peter J. and Chen, Yi-Ju and Phillips, Rob and Spakowitz, Andrew J.},
  month = aug,
  year = {2015},
  pages = {618-629},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Mulligan et al_2015_Interplay of Protein Binding Interactions, DNA Mechanics, and Entropy in DNA.pdf;/home/bbeltr1/Documents/zotero/storage/2R7NJXDZ/S0006349515006645.html}
}

@article{mulligan2015,
  title = {Thermodynamic Model of Heterochromatin Formation through Epigenetic Regulation},
  volume = {27},
  issn = {0953-8984, 1361-648X},
  number = {6},
  journal = {Journal of Physics: Condensed Matter},
  doi = {10.1088/0953-8984/27/6/064109},
  author = {Mulligan, Peter J and Koslover, Elena F and Spakowitz, Andrew J},
  month = feb,
  year = {2015},
  pages = {064109},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Mulligan et al_2015_Thermodynamic model of heterochromatin formation through epigenetic regulation.pdf}
}

@article{koslover2014,
  title = {Multiscale Dynamics of Semiflexible Polymers from a Universal Coarse-Graining Procedure},
  volume = {90},
  issn = {1539-3755, 1550-2376},
  language = {en},
  number = {1},
  journal = {Physical Review E},
  doi = {10.1103/PhysRevE.90.013304},
  author = {Koslover, Elena F. and Spakowitz, Andrew J.},
  month = jul,
  year = {2014},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Koslover_Spakowitz_2014_Multiscale dynamics of semiflexible polymers from a universal coarse-graining.pdf}
}

@article{spakowitz2006,
  title = {Wormlike Chain Statistics with Twist and Fixed Ends},
  volume = {73},
  issn = {0295-5075, 1286-4854},
  number = {5},
  journal = {Europhysics Letters (EPL)},
  doi = {10.1209/epl/i2005-10447-9},
  author = {Spakowitz, A. J},
  month = mar,
  year = {2006},
  pages = {684-690},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Spakowitz_2006_Wormlike chain statistics with twist and fixed ends.pdf}
}

@article{wilemski1974,
  title = {Diffusion-controlled Intrachain Reactions of Polymers. {{I Theory}}},
  volume = {60},
  issn = {0021-9606, 1089-7690},
  abstract = {A theory of diffusion-controlled intramolecularly catalyzed reactions of polymer chains in dilute solution is formulated. A closure approximation yields a solubleintegral equation for (essentially) the transient rate of the reaction. The time dependent solution consists of a sum of simple exponential terms whose coefficients and decay constants can be readily calculated. The theory is also applied to luminescence quenching and ring-chain interconversion.},
  number = {3},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1681162},
  author = {Wilemski, Gerald and Fixman, Marshall},
  month = feb,
  year = {1974},
  keywords = {Polymers,Solution polymerization,Chain reactions,Chemical reaction theory,Integral equations},
  pages = {866-877},
  file = {/home/bbeltr1/Documents/paper-collection/FixmanM/Wilemski_Fixman_1974_Diffusion‐controlled intrachain reactions of polymers.pdf;/home/bbeltr1/Documents/zotero/storage/PTGHJE7F/1.html}
}

@article{sung2007,
  title = {First {{Passage Time}} between {{Ends}} of a {{Polymer Chain}}},
  volume = {51},
  number = {3},
  journal = {Journal of the Korean Chemical Society},
  author = {Sung, Jae-Young},
  year = {2007},
  pages = {227--231},
  file = {/home/bbeltr1/Documents/paper-collection/SungJ/Sung_2007_First Passage Time between Ends of a Polymer Chain.pdf}
}

@article{likthman2006,
  title = {First-Passage Problem for the {{Rouse}} Polymer Chain: {{An}} Exact Solution},
  volume = {75},
  issn = {0295-5075, 1286-4854},
  shorttitle = {First-Passage Problem for the {{Rouse}} Polymer Chain},
  number = {6},
  journal = {Europhysics Letters (EPL)},
  doi = {10.1209/epl/i2006-10206-6},
  author = {Likthman, A. E and Marques, C. M},
  month = sep,
  year = {2006},
  pages = {971-977},
  file = {/home/bbeltr1/Documents/paper-collection/MarquesC/Likthman_Marques_2006_First-passage problem for the Rouse polymer chain.pdf}
}

@article{guerin2012,
  title = {Non-{{Markovian}} Polymer Reaction Kinetics},
  volume = {4},
  copyright = {\textcopyright{} 2012 Nature Publishing Group},
  issn = {1755-4330},
  abstract = {Describing the kinetics of polymer reactions, such as the formation of loops and hairpins in nucleic acids or polypeptides, is complicated by the structural dynamics of their chains. Although both intramolecular reactions, such as cyclization, and intermolecular reactions have been studied extensively, both experimentally and theoretically, there is to date no exact explicit analytical treatment of transport-limited polymer reaction kinetics, even in the case of the simplest (Rouse) model of monomers connected by linear springs. We introduce a new analytical approach to calculate the mean reaction time of polymer reactions that encompasses the non-Markovian dynamics of monomer motion. This requires that the conformational statistics of the polymer at the very instant of reaction be determined, which provides, as a by-product, new information on the reaction path. We show that the typical reactive conformation of the polymer is more extended than the equilibrium conformation, which leads to reaction times significantly shorter than predicted by the existing classical Markovian theory.
View full text},
  language = {en},
  number = {7},
  journal = {Nat Chem},
  doi = {10.1038/nchem.1378},
  author = {Gu\'erin, T. and B\'enichou, O. and Voituriez, R.},
  month = jul,
  year = {2012},
  keywords = {Reaction kinetics and dynamics,Polymer chemistry,Theoretical chemistry},
  pages = {568-573},
  file = {/home/bbeltr1/Documents/paper-collection/VoituriezR/Guérin et al_2012_Non-Markovian polymer reaction kinetics.pdf;/home/bbeltr1/Documents/zotero/storage/NR9Q7WHN/nchem.1378.html}
}

@article{guerin2016,
  title = {Mean First-Passage Times of Non-{{Markovian}} Random Walkers in Confinement},
  volume = {534},
  copyright = {\textcopyright{} 2016 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  issn = {0028-0836},
  abstract = {The first-passage time, defined as the time a random walker takes to reach a target point in a confining domain, is a key quantity in the theory of stochastic processes. Its importance comes from its crucial role in quantifying the efficiency of processes as varied as diffusion-limited reactions, target search processes or the spread of diseases. Most methods of determining the properties of first-passage time in confined domains have been limited to Markovian (memoryless) processes. However, as soon as the random walker interacts with its environment, memory effects cannot be neglected: that is, the future motion of the random walker does not depend only on its current position, but also on its past trajectory. Examples of non-Markovian dynamics include single-file diffusion in narrow channels, or the motion of a tracer particle either attached to a polymeric chain or diffusing in simple or complex fluids such as nematics, dense soft colloids or viscoelastic solutions. Here we introduce an analytical approach to calculate, in the limit of a large confining volume, the mean first-passage time of a Gaussian non-Markovian random walker to a target. The non-Markovian features of the dynamics are encompassed by determining the statistical properties of the fictitious trajectory that the random walker would follow after the first-passage event takes place, which are shown to govern the first-passage time kinetics. This analysis is applicable to a broad range of stochastic processes, which may be correlated at long times. Our theoretical predictions are confirmed by numerical simulations for several examples of non-Markovian processes, including the case of fractional Brownian motion in one and higher dimensions. These results reveal, on the basis of Gaussian processes, the importance of memory effects in first-passage statistics of non-Markovian random walkers in confinement.},
  language = {en},
  number = {7607},
  journal = {Nature},
  doi = {10.1038/nature18272},
  author = {Gu\'erin, T. and Levernier, N. and B\'enichou, O. and Voituriez, R.},
  month = jun,
  year = {2016},
  keywords = {Chemical physics,Statistical physics},
  pages = {356-359},
  file = {/home/bbeltr1/Documents/paper-collection/VoituriezR/Guérin et al_2016_Mean first-passage times of non-Markovian random walkers in confinement.pdf;/home/bbeltr1/Documents/zotero/storage/C4VHZ9RC/nature18272.html}
}

@book{redner2001,
  address = {Cambridge},
  title = {A {{Guide To First}}-{{Passage Processes}}},
  isbn = {978-0-511-60601-4},
  publisher = {{Cambridge University Press}},
  author = {Redner, Sidney},
  year = {2001},
  file = {/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/Redner/Redner_2001_A Guide To First-Passage Processes.pdf;/home/bbeltr1/Documents/paper-collection/RednerS/Redner_2001_A Guide To First-Passage Processes.pdf}
}

@article{cheng2010,
  title = {Universality in the {{Timescales}} of {{Internal Loop Formation}} in {{Unfolded Proteins}} and {{Single}}-{{Stranded Oligonucleotides}}},
  volume = {99},
  issn = {00063495},
  language = {en},
  number = {12},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2010.11.017},
  author = {Cheng, Ryan R. and Uzawa, Takanori and Plaxco, Kevin W. and Makarov, Dmitrii E.},
  month = dec,
  year = {2010},
  pages = {3959-3968},
  file = {/home/bbeltr1/Documents/paper-collection/MakarovD/Cheng et al_2010_Universality in the Timescales of Internal Loop Formation in Unfolded Proteins.pdf}
}

@article{cao2015,
  title = {Large Deviations of {{Rouse}} Polymer Chain: {{First}} Passage Problem},
  volume = {143},
  issn = {0021-9606, 1089-7690},
  shorttitle = {Large Deviations of {{Rouse}} Polymer Chain},
  abstract = {The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations and measure the mean first-passage time {$\tau$}(z) for the free end to reach a certain distance z away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of {$\tau$}(z) are observed, with transition between them varying as a function of chain length. We use these simulation results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations leads us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more.},
  number = {20},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.4936130},
  author = {Cao, Jing and Zhu, Jian and Wang, Zuowei and Likhtman, Alexei E.},
  month = nov,
  year = {2015},
  keywords = {Polymers,Boltzmann equations,Entropy,Friction,Particle fluctuations},
  pages = {204105},
  file = {/home/bbeltr1/Documents/paper-collection/LikhtmanA/Cao et al_2015_Large deviations of Rouse polymer chain.pdf;/home/bbeltr1/Documents/zotero/storage/EM9JUQTE/1.html}
}

@article{toan2008,
  title = {Kinetics of {{Loop Formation}} in {{Polymer Chains}} {\textsuperscript{\textdagger}}},
  volume = {112},
  issn = {1520-6106, 1520-5207},
  language = {en},
  number = {19},
  journal = {The Journal of Physical Chemistry B},
  doi = {10.1021/jp076510y},
  author = {Toan, Ngo Minh and Morrison, Greg and Hyeon, Changbong and Thirumalai, D.},
  month = may,
  year = {2008},
  pages = {6094-6106},
  file = {/home/bbeltr1/Documents/paper-collection/ThirumalaiD/Toan et al_2008_Kinetics of Loop Formation in Polymer Chains sup†-sup.pdf}
}

@article{peters2002,
  title = {Efficient {{Brownian}} Dynamics Simulation of Particles near Walls. {{I}}. {{Reflecting}} and Absorbing Walls},
  volume = {66},
  issn = {1063-651X, 1095-3787},
  language = {en},
  number = {5},
  journal = {Physical Review E},
  doi = {10.1103/PhysRevE.66.056701},
  author = {Peters, E. A. J. F. and Barenbrug, Th. M. A. O. M.},
  month = nov,
  year = {2002},
  file = {/home/bbeltr1/Documents/paper-collection/BarenbrugT/Peters_Barenbrug_2002_Efficient Brownian dynamics simulation of particles near walls.pdf}
}

@article{pastor1996,
  title = {Diffusion Limited First Contact of the Ends of a Polymer: {{Comparison}} of Theory with Simulation},
  volume = {105},
  issn = {00219606},
  shorttitle = {Diffusion Limited First Contact of the Ends of a Polymer},
  language = {en},
  number = {9},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.472208},
  author = {Pastor, Richard W. and Zwanzig, Robert and Szabo, Attila},
  year = {1996},
  pages = {3878},
  file = {/home/bbeltr1/Documents/paper-collection/SzaboA/Pastor et al_1996_Diffusion limited first contact of the ends of a polymer.pdf}
}

@misc{GleesonFPTClass,
  title = {Gleeson {{FPT Class Notes SDEs AM4062}}},
  file = {/home/bbeltr1/Documents/paper-collection/undefined/Gleeson FPT Class Notes SDEs AM4062.pdf}
}

@article{aponte-rivera2016,
  title = {Simulation of Hydrodynamically Interacting Particles Confined by a Spherical Cavity},
  volume = {1},
  issn = {2469-990X},
  language = {en},
  number = {2},
  journal = {Physical Review Fluids},
  doi = {10.1103/PhysRevFluids.1.023301},
  author = {{Aponte-Rivera}, Christian and Zia, Roseanna N.},
  month = jun,
  year = {2016},
  file = {/home/bbeltr1/Documents/paper-collection/ZiaR/Aponte-Rivera_Zia_2016_Simulation of hydrodynamically interacting particles confined by a spherical.pdf}
}

@article{fixman1966,
  title = {Polymer {{Dynamics}}: {{Boson Representation}} and {{Excluded}}-{{Volume Forces}}},
  volume = {45},
  issn = {0021-9606, 1089-7690},
  shorttitle = {Polymer {{Dynamics}}},
  abstract = {The matrix formalism previously introduced for the discussion of polymer dynamics is rendered more tractable by the introduction of an explicit operator representation satisfying boson commutation rules. Techniques are devised by which singular functions of segment coordinates may be expanded in a fluctuation series (containing ordered products of boson operators) around an equilibrium or nonequilibrium average. The techniques are here applied to equilibrium excluded-volume expansions, and are shown to give good results. The detailed numerical results are presented in the following paper. The Gaussian potential is adopted for polymer chains in a theta solvent, but methods for its improvement are considered.},
  number = {3},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1727682},
  author = {Fixman, Marshall},
  month = aug,
  year = {1966},
  keywords = {Polymers,Solvents},
  pages = {785-792},
  file = {/home/bbeltr1/Documents/paper-collection/Fixman/Fixman_1966_Polymer Dynamics.pdf;/home/bbeltr1/Documents/paper-collection/FixmanM/Fixman_1966_Polymer Dynamics.pdf;/home/bbeltr1/Documents/zotero/storage/2VD582JS/1.html;/home/bbeltr1/Documents/zotero/storage/9ES66DR6/1.html}
}

@article{fixman1966b,
  title = {Polymer {{Dynamics}}: {{Non}}-{{Newtonian Intrinsic Viscosity}}},
  volume = {45},
  issn = {0021-9606, 1089-7690},
  shorttitle = {Polymer {{Dynamics}}},
  abstract = {The operator techniques developed in the preceding paper are here applied to the determination of the intrinsic viscosity as a function of excluded volume and shear rate. The force constants which represent the excluded-volume interaction are determined, at nonvanishing shear rate, by a criterion of self-consistency. Numerical results are given for the intrinsic viscosity and the equilibrium expansion of the mean-square end-to-end distance.},
  number = {3},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1727683},
  author = {Fixman, Marshall},
  month = aug,
  year = {1966},
  keywords = {Polymers,Shear rate dependent viscosity,Viscosity},
  pages = {793-803},
  file = {/home/bbeltr1/Documents/paper-collection/Fixman/Fixman_1966_Polymer Dynamics.pdf;/home/bbeltr1/Documents/zotero/storage/8FT2XQ66/1.html}
}

@phdthesis{zhang2011,
  title = {Brownian Dynamics Simulation of {{DNA}} in Complex Geometries},
  school = {Citeseer},
  author = {Zhang, Yu},
  year = {2011},
  file = {/home/bbeltr1/Documents/paper-collection/ZhangY/Zhang_2011_Brownian dynamics simulation of DNA in complex geometries.pdf}
}

@article{fixman1965,
  title = {Dynamics of {{Polymer Chains}}},
  volume = {42},
  issn = {0021-9606, 1089-7690},
  abstract = {A general formalism is presented to serve as a basis for the calculation of dynamic properties of chain-polymer solutions. The polymer model which is adopted restricts the applicability of the formalism to dilute or moderately concentrated solutions.},
  number = {11},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1695847},
  author = {Fixman, Marshall},
  month = jun,
  year = {1965},
  keywords = {Polymers,Solution polymerization,General formalism},
  pages = {3831-3837},
  file = {/home/bbeltr1/Documents/paper-collection/FixmanM/Fixman_1965_Dynamics of Polymer Chains.pdf;/home/bbeltr1/Documents/zotero/storage/D5EPIQ2S/1.1695847\;jsessionid=Ou7EzhfAB19wLtfcz_xg21UV.html}
}

@article{pyun1965,
  title = {Intrinsic {{Viscosity}} of {{Polymer Chains}}},
  volume = {42},
  issn = {0021-9606, 1089-7690},
  abstract = {The intrinsic viscosity [{$\eta$}] of polymer chains is recalculated by methods similar to those of Kirkwood and Zimm. The theory is based on the preceding paper by Fixman, with the adoption of a smoothed excluded-volume potential and the following first-order approximation to the operator L which determines the segment coordinate distribution function {$\psi$}; for L acting on the nonequilibrium part of {$\psi$}, only the diagonal part of L in the free-draining basis representation is used. This corresponds qualitatively to the Zimm theory in Hearst\'s version. However, the avoidance of preaveraging the Oseen hydrodynamic interaction tensor in the present work leads to larger values for the relaxation times of various normal modes when the hydrodynamic shielding effect is not negligible. The effect is more pronounced for lower modes, amounting to about eight percent increase in the lowest mode excited by the velocity gradient in the nondraining limit. The value of [{$\eta$}] in the same limit is found to be [{$\eta$}]=2.68\texttimes{}1023 L 3/Mw (L: the root-mean-square end-to-end distance, Mw : the molecular weight of the polymer; cgs units) and is about 5\% lower than that obtained by the Zimm treatment. A similar correction to the flow birefringenceextinction angle is also given.},
  number = {11},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1695848},
  author = {Pyun, Chong Wha and Fixman, Marshall},
  month = jun,
  year = {1965},
  keywords = {Hydrodynamics,Polymers,Viscosity,Birefringence,Normal modes},
  pages = {3838-3844},
  file = {/home/bbeltr1/Documents/paper-collection/FixmanM/Pyun_Fixman_1965_Intrinsic Viscosity of Polymer Chains.pdf;/home/bbeltr1/Documents/zotero/storage/CRV78TE9/1.html}
}

@article{pyun1966,
  title = {Perturbation {{Theory}} of the {{Intrinsic Viscosity}} of {{Polymer Chains}}},
  volume = {44},
  issn = {0021-9606, 1089-7690},
  abstract = {Our previous calculation of the intrinsic viscosity [{$\eta$}] of linear flexible polymer chains is improved by the inclusion of interactions between excitations, which interactions arise mainly from fluctuations in the hydrodynamic interaction tensor. In the equation [{$\eta$}]={$\varphi\times$}1023 L 3/M (where L in the root-mean-square end-to-end distance and M in the molecular weight; cgs units), {$\varphi$} was found to equal 2.68 in the previous zeroth order approximation. In first-order perturbation theory {$\varphi$} decreases to 1.81, and in second order {$\varphi$} rises in excess of 2.66. An approximate summation to infinite order of the interaction responsible for the large decrease in first order, and other considerations are adduced in support of the view that the remaining terms of the perturbation series are relatively small.},
  number = {5},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1726988},
  author = {Pyun, Chong Wha and Fixman, Marshall},
  month = mar,
  year = {1966},
  keywords = {Hydrodynamics,Tensor methods,Polymers,Viscosity,Perturbation theory},
  pages = {2107-2115},
  file = {/home/bbeltr1/Documents/paper-collection/FixmanM/Pyun_Fixman_1966_Perturbation Theory of the Intrinsic Viscosity of Polymer Chains.pdf;/home/bbeltr1/Documents/zotero/storage/X34GFDWJ/1.html}
}

@article{surovtsev2016,
  title = {{{DNA}}-Relay Mechanism Is Sufficient to Explain {{ParA}}-Dependent Intracellular Transport and Patterning of Single and Multiple Cargos},
  volume = {113},
  issn = {0027-8424, 1091-6490},
  abstract = {Spatial ordering of macromolecular components inside cells is important for cellular physiology and replication. In bacteria, ParA/B systems are known to generate various intracellular patterns that underlie the transport and partitioning of low-copy-number cargos such as plasmids. ParA/B systems consist of ParA, an ATPase that dimerizes and binds DNA upon ATP binding, and ParB, a protein that binds the cargo and stimulates ParA ATPase activity. Inside cells, ParA is asymmetrically distributed, forming a propagating wave that is followed by the ParB-rich cargo. These correlated dynamics lead to cargo oscillation or equidistant spacing over the nucleoid depending on whether the cargo is in single or multiple copies. Currently, there is no model that explains how these different spatial patterns arise and relate to each other. Here, we test a simple DNA-relay model that has no imposed asymmetry and that only considers the ParA/ParB biochemistry and the known fluctuating and elastic dynamics of chromosomal loci. Stochastic simulations with experimentally derived parameters demonstrate that this model is sufficient to reproduce the signature patterns of ParA/B systems: the propagating ParA gradient correlated with the cargo dynamics, the single-cargo oscillatory motion, and the multicargo equidistant patterning. Stochasticity of ATP hydrolysis breaks the initial symmetry in ParA distribution, resulting in imbalance of elastic force acting on the cargo. Our results may apply beyond ParA/B systems as they reveal how a minimal system of two players, one binding to DNA and the other modulating this binding, can transform directionally random DNA fluctuations into directed motion and intracellular patterning.},
  language = {en},
  number = {46},
  journal = {PNAS},
  doi = {10.1073/pnas.1616118113},
  author = {Surovtsev, Ivan V. and Campos, Manuel and {Jacobs-Wagner}, Christine},
  month = nov,
  year = {2016},
  keywords = {ParA/B system,active transport,intracellular patterning,mathematical model,partitioning},
  pages = {E7268-E7276},
  file = {/home/bbeltr1/Documents/paper-collection/Jacobs-Wagner/Surovtsev et al_2016_DNA-relay mechanism is sufficient to explain ParA-dependent intracellular.pdf;/home/bbeltr1/Documents/paper-collection/Jacobs-WagnerC/Surovtsev et al_2016_DNA-relay mechanism is sufficient to explain ParA-dependent intracellular.pdf;/home/bbeltr1/Documents/zotero/storage/PF2KTSGM/E7268.html},
  pmid = {27799522}
}

@article{wilemski1973,
  title = {General Theory of Diffusion-controlled Reactions},
  volume = {58},
  issn = {0021-9606, 1089-7690},
  abstract = {A formal mathematical description of diffusion-controlled bimolecular reactions is presented. The theory is completely general with respect to the kinds of reaction processes that may be considered. Besides the presentation of the general formalism, the paper also contains several examples illustrating the application of the theory to a simple many-particule system for simple catalytic bimolecular reactions, including fluorescence quenching. The manner in which approximate solutions may be obtained is also outlined.},
  number = {9},
  journal = {The Journal of Chemical Physics},
  doi = {10.1063/1.1679757},
  author = {Wilemski, Gerald and Fixman, Marshall},
  month = may,
  year = {1973},
  keywords = {Fluorescence,Chemical reaction theory,Catalysis,General formalism},
  pages = {4009-4019},
  file = {/home/bbeltr1/Documents/paper-collection/FixmanM/Wilemski_Fixman_1973_General theory of diffusion‐controlled reactions.pdf;/home/bbeltr1/Documents/zotero/storage/D85DJJM5/1.html}
}

@article{alili2005,
  title = {Representations of the {{First Hitting Time Density}} of an {{Ornstein}}-{{Uhlenbeck Process}} {\textsuperscript{1}}},
  volume = {21},
  issn = {1532-6349, 1532-4214},
  language = {en},
  number = {4},
  journal = {Stochastic Models},
  doi = {10.1080/15326340500294702},
  author = {Alili, L. and Patie, P. and Pedersen, J. L.},
  month = oct,
  year = {2005},
  pages = {967-980},
  file = {/home/bbeltr1/Documents/paper-collection/PedersenJ/Alili et al_2005_Representations of the First Hitting Time Density of an Ornstein-Uhlenbeck.pdf}
}

@article{sokolov2003,
  title = {Cyclization of a {{Polymer}}: {{First}}-{{Passage Problem}} for a {{Non}}-{{Markovian Process}}},
  volume = {90},
  issn = {0031-9007, 1079-7114},
  shorttitle = {Cyclization of a {{Polymer}}},
  language = {en},
  number = {8},
  journal = {Physical Review Letters},
  doi = {10.1103/PhysRevLett.90.080601},
  author = {Sokolov, I. M.},
  month = feb,
  year = {2003},
  file = {/home/bbeltr1/Documents/paper-collection/SokolovI/Sokolov_2003_Cyclization of a Polymer.pdf}
}

@article{ietswaart2014,
  title = {Competing {{ParA Structures Space Bacterial Plasmids Equally}} over the {{Nucleoid}}},
  volume = {10},
  issn = {1553-7358},
  abstract = {Author Summary How DNA is stably inherited through cell division is a fundamental question in cell biology. The most common system that mediates plasmid DNA inheritance in bacteria is through a parABC locus, encoding proteins ParA and ParB, and DNA sequence parC. These components can position plasmids at equally spaced positions throughout a cell to ensure plasmids are present in both daughter cells when the cell divides into two. Here we study the mechanism by which ParA structures achieve this precise positioning. We show that ParA can direct relatively immobile plasmids over the bacterial chromosome using self-organizing, competitive ParA structures, whose disassembly is induced by plasmid parC-bound ParB. More generally these findings will help us to understand transport and regular positioning of intracellular cargo.},
  number = {12},
  journal = {PLOS Computational Biology},
  doi = {10.1371/journal.pcbi.1004009},
  author = {Ietswaart, Robert and Szardenings, Florian and Gerdes, Kenn and Howard, Martin},
  month = dec,
  year = {2014},
  keywords = {Cell staining,Polymers,Polymerization,Cell cycle and cell division,Hydrolysis,Plasmid construction,Plasmids,Simulation and modeling},
  pages = {e1004009},
  file = {/home/bbeltr1/Documents/paper-collection/HowardM/Ietswaart et al_2014_Competing ParA Structures Space Bacterial Plasmids Equally over the Nucleoid.pdf;/home/bbeltr1/Documents/zotero/storage/TD626IWM/article.html}
}

@article{gerdes2010,
  title = {Pushing and {{Pulling}} in {{Prokaryotic DNA Segregation}}},
  volume = {141},
  issn = {0092-8674},
  abstract = {In prokaryotes, DNA can be segregated by three different types of cytoskeletal filaments. The best-understood type of partitioning (par) locus encodes an actin homolog called ParM, which forms dynamically unstable filaments that push plasmids apart in a process reminiscent of mitosis. However, the most common type of par locus, which is present on many plasmids and most bacterial chromosomes, encodes a P loop ATPase (ParA) that distributes plasmids equidistant from one another on the bacterial nucleoid. A third type of par locus encodes a tubulin homolog (TubZ) that forms cytoskeletal filaments that move rapidly with treadmill dynamics.},
  number = {6},
  journal = {Cell},
  doi = {10.1016/j.cell.2010.05.033},
  author = {Gerdes, Kenn and Howard, Martin and Szardenings, Florian},
  month = jun,
  year = {2010},
  pages = {927-942},
  file = {/home/bbeltr1/Documents/paper-collection/SzardeningsF/Gerdes et al_2010_Pushing and Pulling in Prokaryotic DNA Segregation.pdf;/home/bbeltr1/Documents/zotero/storage/5AZ6ZXHE/S0092867410005696.html}
}

@article{lim2014a,
  title = {Evidence for a {{DNA}}-Relay Mechanism in {{ParABS}}-Mediated Chromosome Segregation},
  volume = {3},
  copyright = {\textcopyright{} 2014, Lim et al. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.},
  issn = {2050-084X},
  abstract = {In vitro, in vivo and in silico evidence suggests that bacteria exploit intrinsic chromosomal fluctuations to achieve intracellular transport.},
  language = {en},
  journal = {eLife},
  doi = {10.7554/eLife.02758},
  author = {Lim, Hoong Chuin and Surovtsev, Ivan Vladimirovich and Beltran, Bruno Gabriel and Huang, Fang and Bewersdorf, J\"org and {Jacobs-Wagner}, Christine},
  month = may,
  year = {2014},
  keywords = {intracellular transport,<italic>Caulobacter crescentus</italic>,DNA partitioning,Par system,chromosome dynamics},
  pages = {e02758},
  file = {/home/bbeltr1/Documents/paper-collection/Jacobs-WagnerC/Lim et al_2014_Evidence for a DNA-relay mechanism in ParABS-mediated chromosome segregation.pdf;/home/bbeltr1/Documents/zotero/storage/RBA6TZ9G/e02758.html},
  pmid = {24859756}
}

@article{vecchiarelli2010,
  title = {{{ATP}} Control of Dynamic {{P1 ParA}}\textendash{{DNA}} Interactions: A Key Role for the Nucleoid in Plasmid Partition},
  volume = {78},
  issn = {0950-382X},
  shorttitle = {{{ATP}} Control of Dynamic {{P1 ParA}}\textendash{{DNA}} Interactions},
  abstract = {P1 ParA is a member of the Walker-type family of partition ATPases involved in the segregation of plasmids and bacterial chromosomes. ATPases of this class interact with DNA non-specifically in vitro and colocalize with the bacterial nucleoid to generate a variety of reported patterns in vivo. Here, we directly visualize ParA binding to DNA using total internal reflection fluorescence microscopy. This activity depends on, and is highly specific for ATP. DNA-binding activity is not coupled to ATP hydrolysis. Rather, ParA undergoes a slow multi-step conformational transition upon ATP binding, which licenses ParA to bind non-specific DNA. The kinetics provide a time-delay switch to allow slow cycling between the DNA binding and non-binding forms of ParA. We propose that this time delay, combined with stimulation of ParA's ATPase activity by ParB bound to the plasmid DNA, generates an uneven distribution of the nucleoid-associated ParA, and provides the motive force for plasmid segregation prior to cell division.},
  number = {1},
  journal = {Mol Microbiol},
  doi = {10.1111/j.1365-2958.2010.07314.x},
  author = {Vecchiarelli, Anthony G and Han, Yong-Woon and Tan, Xin and Mizuuchi, Michiyo and Ghirlando, Rodolfo and Biert\"umpfel, Christian and Funnell, Barbara E and Mizuuchi, Kiyoshi},
  month = oct,
  year = {2010},
  pages = {78-91},
  file = {/home/bbeltr1/Documents/paper-collection/MizuuchiK/Vecchiarelli et al_2010_ATP control of dynamic P1 ParA–DNA interactions.pdf},
  pmid = {20659294},
  pmcid = {PMC2950902}
}

@article{vecchiarelli2014,
  title = {A Propagating {{ATPase}} Gradient Drives Transport of Surface-Confined Cellular Cargo},
  volume = {111},
  issn = {0027-8424, 1091-6490},
  language = {en},
  number = {13},
  journal = {Proceedings of the National Academy of Sciences},
  doi = {10.1073/pnas.1401025111},
  author = {Vecchiarelli, Anthony G. and Neuman, Keir C. and Mizuuchi, Kiyoshi},
  month = apr,
  year = {2014},
  pages = {4880-4885},
  file = {/home/bbeltr1/Documents/paper-collection/MizuuchiK/Vecchiarelli et al_2014_A propagating ATPase gradient drives transport of surface-confined cellular.pdf}
}

@article{song2015,
  title = {Building Bridges within the Bacterial Chromosome},
  volume = {31},
  issn = {0168-9525},
  abstract = {All organisms must dramatically compact their genomes to accommodate DNA within the cell. Bacteria use a set of DNA-binding proteins with low sequence specificity called nucleoid-associated proteins (NAPs) to assist in chromosome condensation and organization. By bending or bridging DNA, NAPs also facilitate chromosome segregation and regulate gene expression. Over the past decade, emerging single-molecule and chromosome conformation capture techniques have investigated the molecular mechanisms by which NAPs remodel and organize the bacterial chromosome. In this review we describe how such approaches reveal the biochemical mechanisms of three NAPs that are believed to facilitate DNA bridging: histone-like nucleoid structuring protein (H-NS), ParB, and structural maintenance of chromosomes (SMC). These three proteins form qualitatively different DNA bridges, leading to varied effects on transcription and chromosome segregation.},
  number = {3},
  journal = {Trends in Genetics},
  doi = {10.1016/j.tig.2015.01.003},
  author = {Song, Dan and Loparo, Joseph J.},
  month = mar,
  year = {2015},
  keywords = {single molecule,DNA bridging,chromosome organization,nucleoid-associated protein,structural maintenance of chromosomes},
  pages = {164-173},
  file = {/home/bbeltr1/Documents/paper-collection/LoparoJ/Song_Loparo_2015_Building bridges within the bacterial chromosome.pdf;/home/bbeltr1/Documents/zotero/storage/MAAF492R/S0168952515000141.html}
}

@article{hu2015,
  title = {Directed and Persistent Movement Arises from Mechanochemistry of the {{ParA}}/{{ParB}} System},
  issn = {0027-8424, 1091-6490},
  language = {en},
  journal = {Proceedings of the National Academy of Sciences},
  doi = {10.1073/pnas.1505147112},
  author = {Hu, Longhua and Vecchiarelli, Anthony G. and Mizuuchi, Kiyoshi and Neuman, Keir C. and Liu, Jian},
  month = dec,
  year = {2015},
  pages = {201505147},
  file = {/home/bbeltr1/Documents/paper-collection/LiuJ/Hu et al_2015_Directed and persistent movement arises from mechanochemistry of the ParA-ParB.pdf}
}

@article{wang2014,
  series = {Growth and Development: Eukaryotes/ Prokaryotes},
  title = {Spatial Organization of Bacterial Chromosomes},
  volume = {22},
  issn = {1369-5274},
  abstract = {Bacterial chromosomes are organized in stereotypical patterns that are faithfully and robustly regenerated in daughter cells. Two distinct spatial patterns were described almost a decade ago in our most tractable model organisms. In recent years, analysis of chromosome organization in a larger and more diverse set of bacteria and a deeper characterization of chromosome dynamics in the original model systems have provided a broader and more complete picture of both chromosome organization and the activities that generate the observed spatial patterns. Here, we summarize these different patterns highlighting similarities and differences and discuss the protein factors that help establish and maintain them.},
  journal = {Current Opinion in Microbiology},
  doi = {10.1016/j.mib.2014.09.016},
  author = {Wang, Xindan and Rudner, David Z},
  month = dec,
  year = {2014},
  pages = {66-72},
  file = {/home/bbeltr1/Documents/paper-collection/RudnerD/Wang_Rudner_2014_Spatial organization of bacterial chromosomes.pdf;/home/bbeltr1/Documents/zotero/storage/DSZPP7TP/S1369527414001362.html}
}

@article{badrinarayanan2015,
  title = {Rapid Pairing and Resegregation of Distant Homologous Loci Enables Double-Strand Break Repair in Bacteria},
  volume = {210},
  copyright = {\textcopyright{} 2015 Badrinarayanan et al.. This article is distributed under the terms of an Attribution\textendash{}Noncommercial\textendash{}Share Alike\textendash{}No Mirror Sites license for the first six months after the publication date (see http://www.rupress.org/terms). After six months it is available under a Creative Commons License (Attribution\textendash{}Noncommercial\textendash{}Share Alike 3.0 Unported license, as described at http://creativecommons.org/licenses/by-nc-sa/3.0/).},
  issn = {0021-9525, 1540-8140},
  abstract = {Double-strand breaks (DSBs) can lead to the loss of genetic information and cell death. Although DSB repair via homologous recombination has been well characterized, the spatial organization of this process inside cells remains poorly understood, and the mechanisms used for chromosome resegregation after repair are unclear. In this paper, we introduced site-specific DSBs in Caulobacter crescentus and then used time-lapse microscopy to visualize the ensuing chromosome dynamics. Damaged loci rapidly mobilized after a DSB, pairing with their homologous partner to enable repair, before being resegregated to their original cellular locations, independent of DNA replication. Origin-proximal regions were resegregated by the ParABS system with the ParA structure needed for resegregation assembling dynamically in response to the DSB-induced movement of an origin-associated ParB away from one cell pole. Origin-distal regions were resegregated in a ParABS-independent manner and instead likely rely on a physical, spring-like force to segregate repaired loci. Collectively, our results provide a mechanistic basis for the resegregation of chromosomes after a DSB.},
  language = {en},
  number = {3},
  journal = {J Cell Biol},
  doi = {10.1083/jcb.201505019},
  author = {Badrinarayanan, Anjana and Le, Tung B. K. and Laub, Michael T.},
  month = aug,
  year = {2015},
  pages = {385-400},
  file = {/home/bbeltr1/Documents/paper-collection/LaubM/Badrinarayanan et al_2015_Rapid pairing and resegregation of distant homologous loci enables.pdf;/home/bbeltr1/Documents/zotero/storage/XPBNGU4V/385.html},
  pmid = {26240183}
}

@article{sugawara2011,
  title = {Chemophoresis as a Driving Force for Intracellular Organization: {{Theory}} and Application to Plasmid Partitioning},
  volume = {7},
  issn = {1349-2942},
  shorttitle = {Chemophoresis as a Driving Force for Intracellular Organization},
  abstract = {Biological units such as macromolecules, organelles, and cells are directed to a proper location by gradients of chemicals. We consider a macroscopic element with surface binding sites where chemical adsorption reactions can occur and show that a thermodynamic force generated by chemical gradients acts on the element. By assuming local equilibrium and adopting the grand potential used in thermodynamics, we derive a formula for the ``chemophoresis'' force, which depends on chemical potential gradients and the Langmuir isotherm. The conditions under which the formula is applicable are shown to occur in intracellular reactions. Further, the role of the chemophoresis in the partitioning of bacterial chromosomal loci/plasmids during cell division is discussed. By performing numerical simulations, we demonstrate that the chemophoresis force can contribute to the regular positioning of plasmids observed in experiments.},
  journal = {Biophysics (Nagoya-shi)},
  doi = {10.2142/biophysics.7.77},
  author = {Sugawara, Takeshi and Kaneko, Kunihiko},
  month = sep,
  year = {2011},
  pages = {77-88},
  file = {/home/bbeltr1/Documents/paper-collection/KanekoK/Sugawara_Kaneko_2011_Chemophoresis as a driving force for intracellular organization.pdf},
  pmid = {27857595},
  pmcid = {PMC5036777}
}

@article{surovtsev2016a,
  title = {The {{Slow Mobility}} of the {{ParA Partitioning Protein Underlies Its Steady}}-{{State Patterning}} in {{Caulobacter}}},
  volume = {110},
  issn = {0006-3495},
  abstract = {In bacteria, ParABS systems mediate intracellular transport of various cargos, including chromosomal regions in Caulobacter crescentus. Transport of the ParB/parS partition complex requires the DNA-binding activity of ParA, which transiently tethers the partition complex during translocation. In C.~crescentus, the directionality of the transport is set up by a gradient of ParA whose concentration gradually increases from one end of the cell (old pole) to the other (new pole). Importantly, this ParA gradient is already observed before DNA replication and segregation are initiated when the partition complex is anchored at the old pole. How such micron-scale ParA pattern is established and maintained before the initiation of chromosome segregation has not been experimentally established. Although the stimulation of ParA ATPase activity by the localized ParB/parS partition complex is thought to be involved, this activity alone cannot quantitatively describe the ParA pattern observed inside cells. Instead, our experimental and theoretical study shows that the missing key component for achieving the experimentally observed steady-state ParA patterning is the slow mobility of ParA dimers (D {$\sim$}10-3 {$\mu$}m2/s) due to intermittent DNA binding. Our model recapitulates the entire steady-state ParA distribution observed experimentally, including the shape of the gradient as well as ParA accumulation at the location of the partition complex. Stochastic simulations suggest that cell-to-cell variability in ParA pattern is due to the low ParA copy number in C.~crescentus cells. The model also accounts for an apparent exclusion of ParA from regions with small spacing between partition complexes observed in filamentous cells. Collectively, our work demonstrates that in addition to its function in mediating transport, the conserved DNA-binding property of ParA has a critical function before DNA segregation by setting up a ParA pattern required for transport directionality.},
  number = {12},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2016.05.014},
  author = {Surovtsev, Ivan V. and Lim, Hoong Chuin and {Jacobs-Wagner}, Christine},
  month = jun,
  year = {2016},
  pages = {2790-2799},
  file = {/home/bbeltr1/Documents/paper-collection/Jacobs-WagnerC/Surovtsev et al_2016_The Slow Mobility of the ParA Partitioning Protein Underlies Its Steady-State.pdf;/home/bbeltr1/Documents/zotero/storage/DCW4QCFD/S0006349516302958.html}
}

@article{banigan2011,
  title = {Filament {{Depolymerization Can Explain Chromosome Pulling}} during {{Bacterial Mitosis}}},
  volume = {7},
  issn = {1553-7358},
  abstract = {Author Summary Reliable chromosome segregation is crucial to all dividing cells. In some bacteria, segregation has been found to occur in a rather counterintuitive way: the chromosome attaches to a filament bundle and erodes it by causing depolymerization of the filaments. Moreover, unlike eukaryotic cells, bacteria do not use molecular motors and/or macromolecular tethers to position their chromosomes. This raises the general question of how depolymerizing filaments alone can continuously and robustly pull cargo as the filaments themselves are falling apart. In this work, we introduce the first quantitative physical model for depolymerization-driven translocation in a many-filament system. Our simulations of this model suggest a novel underlying mechanism for robust translocation, namely self-diffusiophoresis, motion of an object in a self-generated concentration gradient in a viscous environment. In this case, the cargo generates and sustains a concentration gradient of filaments by inducing them to depolymerize. We demonstrate that our model agrees well with existing experimental observations such as segregation failure, filament-length-dependent translocation velocity, and chromosomal compaction. In addition, we make several predictions\textendash{}including predictions for the specific modes by which the chromosome binds to the filament structure and triggers its disassembly\textendash{}that can be tested experimentally.},
  number = {9},
  journal = {PLOS Computational Biology},
  doi = {10.1371/journal.pcbi.1002145},
  author = {Banigan, Edward J. and Gelbart, Michael A. and Gitai, Zemer and Wingreen, Ned S. and Liu, Andrea J.},
  month = sep,
  year = {2011},
  keywords = {Polymers,Biochemical simulations,Chromosome structure and function,Chromosomes,Depolymerization,Relaxation time,Simulation and modeling,Translocations},
  pages = {e1002145},
  file = {/home/bbeltr1/Documents/paper-collection/LiuA/Banigan et al_2011_Filament Depolymerization Can Explain Chromosome Pulling during Bacterial.pdf;/home/bbeltr1/Documents/zotero/storage/XM3MMUV2/article.html}
}

@article{gall2016,
  title = {Bacterial Partition Complexes Segregate within the Volume of the Nucleoid},
  volume = {7},
  copyright = {\textcopyright{} 2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.},
  issn = {2041-1723},
  abstract = {In most bacteria and archaea, a broadly conserved mitotic-like apparatus assures the inheritance of duplicated genetic material before cell division. Here, the authors use super-resolution microscopies to dissect the activities required for proper DNA segregation through the nucleoid interior.},
  language = {en},
  journal = {Nature Communications},
  doi = {10.1038/ncomms12107},
  author = {Gall, Antoine Le and Cattoni, Diego I. and Guilhas, Baptiste and {Mathieu-Demazi\`ere}, C\'eline and Oudjedi, Laura and Fiche, Jean-Bernard and Rech, J\'er\^ome and Abrahamsson, Sara and Murray, Heath and Bouet, Jean-Yves and Nollmann, Marcelo},
  month = jul,
  year = {2016},
  pages = {12107},
  file = {/home/bbeltr1/Documents/zotero/storage/G8PKXDSS/ncomms12107.html;/home/bbeltr1/Documents/zotero/storage/MC9IFRAT/ncomms12107.html}
}

@incollection{vecchiarelli2015,
  series = {Building a {{Cell}} from Its {{Component Parts}}},
  title = {Chapter 13 - {{Reconstituting ParA}}/{{ParB}}-Mediated Transport of {{DNA}} Cargo},
  volume = {128},
  abstract = {Protein gradients play key roles in subcellular spatial organization. In bacteria, ParA adenosine triphosphatases, or ATPases, form dynamic gradients on the nucleoid surface, which imparts positional information for the segregation, transport, and positioning of chromosomes, plasmids, and large protein assemblies. Despite the apparent simplicity of these minimal and self-organizing systems, the mechanism remains unclear. The small size of bacteria along with the number of physical and biochemical processes involved in subcellular organization makes it difficult to study these systems under controlled conditions in vivo. We developed a cell-free reconstitution technique that allows for the visualization of ParA-mediated cargo transport on a DNA carpet, which acts as a biomimetic of the nucleoid surface. Here, we present methods to express, purify, and visualize the dynamic properties of the SopABC system from F plasmid, considered a paradigm for the study of ParA-type systems. We hope similar cell-free studies will be used to address the biochemical and biophysical underpinnings of this ubiquitous transport scheme in bacteria.},
  booktitle = {Methods in {{Cell Biology}}},
  publisher = {{Academic Press}},
  author = {Vecchiarelli, Anthony G. and Taylor, James A. and Mizuuchi, Kiyoshi},
  editor = {Marshall, Jennifer Ross {and} Wallace F.},
  year = {2015},
  keywords = {intracellular transport,Bacterial chromosome segregation,ParA ATPase,Plasmid partition,Subcellular organization},
  pages = {243-269},
  file = {/home/bbeltr1/Documents/paper-collection/MarshallJ/Vecchiarelli et al_2015_Chapter 13 - Reconstituting ParA-ParB-mediated transport of DNA cargo.pdf;/home/bbeltr1/Documents/zotero/storage/Q8QV7567/S0091679X15000631.html},
  doi = {10.1016/bs.mcb.2015.01.021}
}

@article{jindal2015,
  title = {Operational {{Principles}} for the {{Dynamics}} of the {{In Vitro ParA}}-{{ParB System}}},
  volume = {11},
  issn = {1553-7358},
  abstract = {Author Summary Segregating genetic material is essential for cell survival over multiple generations. The process underlying the required spatio-temporal organization of DNA is mediated by the ParA-ParB-parS system. Recently, experiments have shown that directed motion can be reconstituted in vitro. In these experiments, a magnetic bead was covered with the protein ParB and was able to move ballistically over a surface of DNA that was bound by the protein ParA. How does this active transport spontaneously emerge? In this paper we present a deterministic model for the dynamics of ParA-ParB proteins. We show how spatial noise in surface bound ParA is sufficient for the creation of a gradient in ParA that can drive motion of ParB in vitro. The model explains certain key aspects of the in vitro ParA-ParB system and leads to testable predictions.},
  number = {12},
  journal = {PLOS Computational Biology},
  doi = {10.1371/journal.pcbi.1004651},
  author = {Jindal, Lavisha and Emberly, Eldon},
  month = dec,
  year = {2015},
  keywords = {Acceleration,Chromosomes,Classical mechanics,DNA replication,Depolymerization,Drag,Motion,Translocations},
  pages = {e1004651},
  file = {/home/bbeltr1/Documents/paper-collection/Emberly/Jindal_Emberly_2015_Operational Principles for the Dynamics of the In Vitro ParA-ParB System.PDF;/home/bbeltr1/Documents/paper-collection/Emberly/Jindal_Emberly_2015_Operational Principles for the Dynamics of the In Vitro ParA-ParB System.PDF;/home/bbeltr1/Documents/paper-collection/EmberlyE/Jindal_Emberly_2015_Operational Principles for the Dynamics of the In Vitro ParA-ParB System.pdf;/home/bbeltr1/Documents/paper-collection/EmberlyE/Jindal_Emberly_2015_Operational Principles for the Dynamics of the In Vitro ParA-ParB System.PDF;/home/bbeltr1/Documents/zotero/storage/VT5KSBEC/article.html}
}

@article{ptacin2010,
  title = {A Spindle-like Apparatus Guides Bacterial Chromosome Segregation},
  volume = {12},
  copyright = {\textcopyright{} 2010 Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved.},
  issn = {1465-7392},
  abstract = {Until recently, a dedicated mitotic apparatus that segregates newly replicated chromosomes into daughter cells was believed to be unique to eukaryotic cells. Here we demonstrate that the bacterium Caulobacter crescentus segregates its chromosome using a partitioning (Par) apparatus that has surprising similarities to eukaryotic spindles. We show that the C. crescentus ATPase ParA forms linear polymers in vitro and assembles into a narrow linear structure in vivo. The centromere-binding protein ParB binds to and destabilizes ParA structures in vitro. We propose that this ParB-stimulated ParA depolymerization activity moves the centromere to the opposite cell pole through a burnt bridge Brownian ratchet mechanism. Finally, we identify the pole-specific TipN protein as a new component of the Par system that is required to maintain the directionality of DNA transfer towards the new cell pole. Our results elucidate a bacterial chromosome segregation mechanism that features basic operating principles similar to eukaryotic mitotic machines, including a multivalent protein complex at the centromere that stimulates the dynamic disassembly of polymers to move chromosomes into daughter compartments.},
  language = {en},
  number = {8},
  journal = {Nat Cell Biol},
  doi = {10.1038/ncb2083},
  author = {Ptacin, Jerod L. and Lee, Steven F. and Garner, Ethan C. and Toro, Esteban and Eckart, Michael and Comolli, Luis R. and Moerner, W. E. and Shapiro, Lucy},
  month = aug,
  year = {2010},
  keywords = {Bacteria,cytoskeleton,Chromosome segregation},
  pages = {791-798},
  file = {/home/bbeltr1/Documents/paper-collection/ShapiroL/Ptacin et al_2010_A spindle-like apparatus guides bacterial chromosome segregation.pdf;/home/bbeltr1/Documents/zotero/storage/93BU262X/ncb2083.html}
}

@unpublished{spakowitza,
  title = {Polymer {{Semiflexibility}}},
  author = {Spakowitz, Andrew},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Spakowitz_Polymer Semiflexibility.pdf}
}

@article{krajina2016,
  title = {Large-{{Scale Conformational Transitions}} in {{Supercoiled DNA Revealed}} by {{Coarse}}-{{Grained Simulation}}},
  volume = {111},
  issn = {00063495},
  language = {en},
  number = {7},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2016.07.045},
  author = {Krajina, Brad A. and Spakowitz, Andrew J.},
  month = oct,
  year = {2016},
  pages = {1339-1349},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Krajina_Spakowitz_2016_Large-Scale Conformational Transitions in Supercoiled DNA Revealed by.pdf}
}

@book{burchard1999,
  address = {Berlin},
  series = {Advances in Polymer Science},
  title = {Branched Polymers. 2: [...]},
  isbn = {978-3-540-65005-8},
  shorttitle = {Branched Polymers. 2},
  number = {143},
  publisher = {{Springer}},
  author = {Burchard, Walther and Roovers, Jacques},
  year = {1999},
  file = {/home/bbeltr1/Documents/paper-collection/RooversJ/Burchard_Roovers_1999_Branched polymers.pdf},
  note = {OCLC: 313258405}
}

@misc{spakowitz,
  title = {{{CHEMENG}} 466: {{Notes}}},
  author = {Spakowitz, Andrew},
  file = {/home/bbeltr1/Documents/paper-collection/Spakowitz, Andrew/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/Spakowitz/Spakowitz_CHEMENG 466.pdf;/home/bbeltr1/Documents/paper-collection/SpakowitzA/Spakowitz_CHEMENG 466.pdf}
}

@article{wiggins2006,
  title = {High Flexibility of {{DNA}} on Short Length Scales Probed by Atomic Force Microscopy},
  volume = {1},
  copyright = {\textcopyright{} 2006 Nature Publishing Group},
  issn = {1748-3387},
  abstract = {The mechanics of DNA bending on intermediate length scales (5\textendash{}100 nm) plays a key role in many cellular processes, and is also important in the fabrication of artificial DNA structures, but previous experimental studies of DNA mechanics have focused on longer length scales than these. We use high-resolution atomic force microscopy on individual DNA molecules to obtain a direct measurement of the bending energy function appropriate for scales down to 5 nm. Our measurements imply that the elastic energy of highly bent DNA conformations is lower than predicted by classical elasticity models such as the worm-like chain (WLC) model. For example, we found that on short length scales, spontaneous large-angle bends are many times more prevalent than predicted by the WLC model. We test our data and model with an interlocking set of consistency checks. Our analysis also shows how our model is compatible with previous experiments, which have sometimes been viewed as confirming the WLC.},
  language = {en},
  number = {2},
  journal = {Nat Nano},
  doi = {10.1038/nnano.2006.63},
  author = {Wiggins, Paul A. and {van der Heijden}, Thijn and {Moreno-Herrero}, Fernando and Spakowitz, Andrew and Phillips, Rob and Widom, Jonathan and Dekker, Cees and Nelson, Philip C.},
  month = nov,
  year = {2006},
  pages = {137-141},
  file = {/home/bbeltr1/Documents/paper-collection/NelsonP/Wiggins et al_2006_High flexibility of DNA on short length scales probed by atomic force microscopy.pdf;/home/bbeltr1/Documents/zotero/storage/VBD5T8QA/nnano.2006.63.html}
}

@article{chen2013,
  title = {Free {{Energy}} and {{Extension}} of a {{Wormlike Chain}} in {{Tube Confinement}}},
  volume = {46},
  issn = {0024-9297, 1520-5835},
  language = {en},
  number = {24},
  journal = {Macromolecules},
  doi = {10.1021/ma4020824},
  author = {Chen, Jeff Z. Y.},
  month = dec,
  year = {2013},
  pages = {9837-9844},
  file = {/home/bbeltr1/Documents/paper-collection/ChenJ/Chen_2013_Free Energy and Extension of a Wormlike Chain in Tube Confinement.pdf}
}

@article{chen2016,
  series = {The {{Effects}} of {{Confinement}} on {{Polymeric Thermal Transitions}} and {{Nanostructuring}}},
  title = {Theory of Wormlike Polymer Chains in Confinement},
  volume = {54\textendash{}55},
  issn = {0079-6700},
  abstract = {A semiflexible polymer chain shows characteristic local chain persistency and finite extensibility. Confinement of such a polymer introduces a confinement length scale that competes with the persistence length. This review describes the basic theoretical formalism for a single wormlike chain in an external confinement potential field and for confined wormlike chains that interact with each other through a potential energy depending on both orientational and positional variables. We present a summary of the current understanding in formulating a calculation for the free energy through a single-chain Green's function theory and multi-chain self-consistent field theory, and in specifying appropriate confinement boundary conditions. The wormlike-chain formalism has the capability to capture physical features in a length scale smaller than the persistence length and in a length scale comparable to the total chain length. It also builds the orientational dependence in the foundation of the formalism, that can be used to describe the coupled orientational and positional dependencies of many polymer problems. It has the advantage over a typical Gaussian-chain formalism for description of the physical properties where these features are the main concerns. However, the mathematical treatment of a wormlike-chain model is much more complicated than that of a Gaussian-chain model, due to the coupling between the orientational and positional degrees of freedom. It is this coupling that gives rise to physical features that are unique in semiflexible-chain systems. Example applications of the theoretical framework are also described here, on calculating the free energy and conformational properties of a confined long wormlike chain, on describing the orientational defect structures of confined liquid crystals, and on demonstrating the orientation-induced surface wetting phenomenon.},
  journal = {Progress in Polymer Science},
  doi = {10.1016/j.progpolymsci.2015.09.002},
  author = {Chen, Jeff Z. Y.},
  month = mar,
  year = {2016},
  keywords = {Physics,Polymers,Computation},
  pages = {3-46},
  file = {/home/bbeltr1/Documents/paper-collection/ChenJ/Chen_2016_Theory of wormlike polymer chains in confinement.pdf;/home/bbeltr1/Documents/zotero/storage/XR4GUZDX/S0079670015001033.html}
}

@article{hong2013,
  title = {Caulobacter Chromosome in Vivo Configuration Matches Model Predictions for a Supercoiled Polymer in a Cell-like Confinement},
  volume = {110},
  issn = {0027-8424, 1091-6490},
  language = {en},
  number = {5},
  journal = {Proceedings of the National Academy of Sciences},
  doi = {10.1073/pnas.1220824110},
  author = {Hong, S.-H. and Toro, E. and Mortensen, K. I. and {de la Rosa}, M. A. D. and Doniach, S. and Shapiro, L. and Spakowitz, A.J. and McAdams, H. H.},
  month = jan,
  year = {2013},
  pages = {1674-1679},
  file = {/home/bbeltr1/Documents/paper-collection/McAdams/Hong et al_2013_Caulobacter chromosome in vivo configuration matches model predictions for a.pdf;/home/bbeltr1/Documents/paper-collection/McAdamsH/Hong et al_2013_Caulobacter chromosome in vivo configuration matches model predictions for a.pdf}
}

@article{tree2013,
  title = {Is {{DNA}} a {{Good Model Polymer}}?},
  volume = {46},
  issn = {0024-9297},
  abstract = {The details surrounding the crossover from wormlike-specific to universal polymeric behavior has been the subject of debate and confusion even for the simple case of a dilute, unconfined wormlike chain. We have directly computed the polymer size, form factor, free energy, and Kirkwood diffusivity for unconfined wormlike chains as a function of molecular weight, focusing on persistence lengths and effective widths that represent single-stranded and double-stranded DNA in a high ionic strength buffer. To do so, we use a chain-growth Monte Carlo algorithm, the pruned-enriched Rosenbluth method (PERM), which allows us to estimate equilibrium and near-equilibrium dynamic properties of wormlike chains over an extremely large range of contour lengths. From our calculations, we find that very large DNA chains ({$\approx$}1\,000\,000, base pairs depending on the choice of size metric) are required to reach flexible, swollen nondraining coils. Furthermore, our results indicate that the commonly used model polymer {$\lambda$}-DNA (48\,500, base pairs) does not exhibit ``ideal'' scaling but exists in the middle of the transition to long-chain behavior. We subsequently conclude that typical DNA used in experiments are too short to serve as an accurate model of long-chain, universal polymer behavior.},
  number = {20},
  journal = {Macromolecules},
  doi = {10.1021/ma401507f},
  author = {Tree, Douglas R. and Muralidhar, Abhiram and Doyle, Patrick S. and Dorfman, Kevin D.},
  month = oct,
  year = {2013},
  pages = {8369-8382},
  file = {/home/bbeltr1/Documents/paper-collection/DorfmanK/Tree et al_2013_Is DNA a Good Model Polymer.pdf;/home/bbeltr1/Documents/zotero/storage/V5SG39G9/ma401507f.html}
}

@phdthesis{lampo,
  title = {Physical {{Modeling}} of {{Particle}} and {{Chromosome Dynamics}} in {{Living Cells}}},
  abstract = {The cellular cytoplasm is a complex, viscoelastic medium whose properties result in a
rich, non-trivial spectrum of transport behaviors for the biomolecules diffusing within
it. While much is known of the biochemistry of these biomolecules, their motion and
organization has only just started to be understood due to advances in fluorescence
microscopy in the last few decades. The disruption of this organization can lead to
a wide variety of disease states or even the death of the cell. Thus a fundamental
physical understanding of these effects could guide novel strategies for the treatment
of infection and disease. Our work develops physical models to better predict the
consequences of the intracellular medium on biomolecular motion and interpret the
results from particle tracking data of RNA-protein particles and chromosome loci in
living cells.
One of the key attributes of the cytoplasm is the high degree of macromolecular
crowding that results in nontrivial transport behaviors. Objects in crowded media
generally exhibit slower rates of diffusion relative to being in pure water, and often ex-
hibit viscoelastic behavior for a broad range of timescales. We examine datasets track-
ing RNA-protein particles in the cytoplasm of Escherichia coli and Saccharomyces
cerevisaie, which show viscoelastic, subdiffusive behavior. We find that these particles
exhibit non-Gaussian displacement distributions in apparent violation of the central
ivlimit theorem and classical diffusion equation. We use a relatively simple framework
to show that this non-Gaussian behavior is primarily due to a broad distribution of
diffusion coefficients between particles in different cells. To gain a better physical
understanding, of these nontrivial behaviors, we use Brownian dynamics simulations
to identify the signatures that are a consequence of crowding in a confinement. We
show that crowding alone between particles with hard-core repulsion is sufficient to
cause subdiffusive, viscoelastic behavior over a broad range of timescales.
Inside each cell are long molecules of DNA which are the main carrier of hereditary
information passed on to daughter cells. This DNA when complexed with proteins
is called chromatin, which exhibits a complex heterogeneous structure that enables
a layer of control over what genetic information is accessible at any given time. The
chromatin must be stable enough to maintain specific cell states and ensure control
of gene expression, yet dynamic and malleable enough to undergo large scale reor-
ganization when necessary for processes such as segregation and loop formation. A
basic theory and understanding of the motion of single chromosome locus modeled
as a polymer in a viscoelastic medium has been previously developed. Continuing on
from this framework, we find that the inclusion of a biasing force on a single polymer
segment is able to accurately describe the directed motion of a locus at the start
of chromosome segregation in bacteria. Recently, experimentalists tracked pairs of
chromosome loci in living cells, but there was not yet a comprehensive theory for
interpreting the motion of two tracked loci relative to one another. Toward this goal,
we develop a theory extending the model for a polymer in a viscoelastic medium to
predict the evolution in the velocity correlations between two dynamically coupled
loci and estimate their stress communication timescale.},
  school = {Stanford University},
  author = {Lampo, Thomas},
  file = {/home/bbeltr1/Documents/paper-collection/LampoT/Lampo_Physical Modeling of Particle and Chromosome Dynamics in Living Cells.pdf}
}

@article{purohit2008,
  title = {Plectoneme Formation in Twisted Fluctuating Rods},
  volume = {56},
  number = {5},
  journal = {Journal of the Mechanics and Physics of Solids},
  author = {Purohit, Prashant K.},
  year = {2008},
  pages = {1715--1729},
  file = {/home/bbeltr1/Documents/paper-collection/PurohitP/Purohit_2008_Plectoneme formation in twisted fluctuating rods.pdf}
}

@article{lampo2017,
  title = {Cytoplasmic {{RNA}}-{{Protein Particles Exhibit Non}}-{{Gaussian Subdiffusive Behavior}}},
  volume = {112},
  issn = {00063495},
  language = {en},
  number = {3},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2016.11.3208},
  author = {Lampo, Thomas J. and Stylianidou, Stella and Backlund, Mikael P. and Wiggins, Paul A. and Spakowitz, Andrew J.},
  month = feb,
  year = {2017},
  pages = {532-542},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Lampo et al_2017_Cytoplasmic RNA-Protein Particles Exhibit Non-Gaussian Subdiffusive Behavior.pdf}
}

@article{vologodskii1995,
  title = {Modeling of Long-Range Electrostatic Interactions in {{DNA}}},
  volume = {35},
  number = {3},
  journal = {Biopolymers},
  author = {Vologodskii, Alexander and Cozzarelli, Nicholas},
  year = {1995},
  pages = {289--296},
  file = {/home/bbeltr1/Documents/paper-collection/Cozzarelli/Vologodskii_Cozzarelli_1995_Modeling of long-range electrostatic interactions in DNA.pdf;/home/bbeltr1/Documents/paper-collection/CozzarelliN/Vologodskii_Cozzarelli_1995_Modeling of long-range electrostatic interactions in DNA.pdf;/home/bbeltr1/Documents/zotero/storage/PDEJ5TD6/abstract.html}
}

@incollection{vologodskii2007,
  title = {Monte {{Carlo}} Simulation of {{DNA}} Topological Properties},
  booktitle = {Topology in Molecular Biology},
  publisher = {{Springer}},
  author = {Vologodskii, Alexander},
  year = {2007},
  pages = {23--41},
  file = {/home/bbeltr1/Documents/paper-collection/Vologodskii/Vologodskii_2007_Monte Carlo simulation of DNA topological properties.pdf;/home/bbeltr1/Documents/paper-collection/VologodskiiA/Vologodskii_2007_Monte Carlo simulation of DNA topological properties.pdf}
}

@article{weber2010,
  title = {Subdiffusive Motion of a Polymer Composed of Subdiffusive Monomers},
  volume = {82},
  issn = {1539-3755, 1550-2376},
  language = {en},
  number = {1},
  journal = {Physical Review E},
  doi = {10.1103/PhysRevE.82.011913},
  author = {Weber, Stephanie C. and Theriot, Julie A. and Spakowitz, Andrew J.},
  month = jul,
  year = {2010},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Weber et al_2010_Subdiffusive motion of a polymer composed of subdiffusive monomers.pdf}
}

@article{tree2013a,
  title = {Is {{DNA}} a {{Good Model Polymer}}?},
  volume = {46},
  issn = {0024-9297, 1520-5835},
  language = {en},
  number = {20},
  journal = {Macromolecules},
  doi = {10.1021/ma401507f},
  author = {Tree, Douglas R. and Muralidhar, Abhiram and Doyle, Patrick S. and Dorfman, Kevin D.},
  month = oct,
  year = {2013},
  pages = {8369-8382},
  file = {/home/bbeltr1/Documents/paper-collection/Dorfman/Tree et al_2013_Is DNA a Good Model Polymer.pdf}
}

@article{zirbel2016,
  title = {Off-Lattice Random Walks with Excluded Volume: A New Method of Generation, Proof of Ergodicity and Numerical Results},
  volume = {49},
  issn = {1751-8121},
  shorttitle = {Off-Lattice Random Walks with Excluded Volume},
  abstract = {We describe a new algorithm, the reflection method, to generate off-lattice random walks of specified, though arbitrarily large, thickness in \#\#IMG\#\# [http://ej.iop.org/images/1751-8121/49/13/135203/jpaaa1316ieqn1.gif] \$\textbackslash{}mathbbR\^3\$ and prove that our method is ergodic on the space of thick walks. The data resulting from our implementation of this method is consistent with the scaling of the squared radius of gyration of random walks, with no thickness constraint. Based on this, we use the data to describe the complex relationship between the presence and nature of knotting and size, thickness and shape of the random walk. We extend the current understanding of excluded volume by expanding the range of analysis of how the squared radius of gyration scales with length and thickness. We also examine the profound effect of thickness on knotting in open chains. We will quantify how thickness effects the size of thick open chains, calculating the growth exponent for squared radius of gyration as a function of thickness. We will also show that for radius \#\#IMG\#\# [http://ej.iop.org/images/1751-8121/49/13/135203/jpaaa1316ieqn2.gif] \$r\textbackslash{}leqslant 0.4\$ , increasing thickness by 0.1 decreases the probability of knot formation by 50\% or more.},
  language = {en},
  number = {13},
  journal = {J. Phys. A: Math. Theor.},
  doi = {10.1088/1751-8113/49/13/135203},
  author = {Zirbel, Laura Plunkett (nee and Chapman, Kyle},
  year = {2016},
  pages = {135203},
  file = {/home/bbeltr1/Documents/paper-collection/ChapmanK/Zirbel_Chapman_2016_Off-lattice random walks with excluded volume.pdf}
}

@article{japaridze2017,
  title = {Hyperplectonemes: {{A Higher Order Compact}} and {{Dynamic DNA Self}}-{{Organization}}},
  volume = {17},
  issn = {1530-6984, 1530-6992},
  shorttitle = {Hyperplectonemes},
  language = {en},
  number = {3},
  journal = {Nano Letters},
  doi = {10.1021/acs.nanolett.6b05294},
  author = {Japaridze, Aleksandre and Muskhelishvili, Georgi and Benedetti, Fabrizio and Gavriilidou, Agni F. M. and Zenobi, Renato and De Los Rios, Paolo and Longo, Giovanni and Dietler, Giovanni},
  month = mar,
  year = {2017},
  pages = {1938-1948},
  file = {/home/bbeltr1/Documents/paper-collection/DietlerG/Japaridze et al_2017_Hyperplectonemes.pdf}
}

@phdthesis{japaridze2015,
  title = {From Polymers to Gene Regulation: {{A}} Bottom up Approach to the Bacterial Chromatin},
  shorttitle = {From Polymers to Gene Regulation},
  school = {\'ECOLE POLYTECHNIQUE F\'ED\'ERALE DE LAUSANNE},
  author = {JAPARIDZE, Aleksandre},
  year = {2015},
  file = {/home/bbeltr1/Documents/paper-collection/JAPARIDZEA/JAPARIDZE_2015_From polymers to gene regulation.pdf}
}

@article{pelletier2012,
  title = {Physical Manipulation of the {{Escherichia}} Coli Chromosome Reveals Its Soft Nature},
  volume = {109},
  number = {40},
  journal = {Proceedings of the National Academy of Sciences},
  author = {Pelletier, James and Halvorsen, Ken and Ha, Bae-Yeun and Paparcone, Raffaella and Sandler, Steven J. and Woldringh, Conrad L. and Wong, Wesley P. and Jun, Suckjoon},
  year = {2012},
  pages = {E2649--E2656},
  file = {/home/bbeltr1/Documents/paper-collection/JunS/Pelletier et al_2012_Physical manipulation of the Escherichia coli chromosome reveals its soft nature.pdf}
}

@article{benedetti2015,
  title = {Effects of Physiological Self-Crowding of {{DNA}} on Shape and Biological Properties of {{DNA}} Molecules with Various Levels of Supercoiling},
  volume = {43},
  issn = {0305-1048},
  number = {4},
  journal = {Nucleic Acids Res},
  doi = {10.1093/nar/gkv055},
  author = {Benedetti, Fabrizio and Japaridze, Aleksandre and Dorier, Julien and Racko, Dusan and Kwapich, Robert and Burnier, Yannis and Dietler, Giovanni and Stasiak, Andrzej},
  month = feb,
  year = {2015},
  pages = {2390-2399},
  file = {/home/bbeltr1/Documents/paper-collection/StasiakA/Benedetti et al_2015_Effects of physiological self-crowding of DNA on shape and biological.pdf;/home/bbeltr1/Documents/zotero/storage/B8Z5UQJ5/Effects-of-physiological-self-crowding-of-DNA-on.html}
}

@article{mchale2010,
  title = {Intramolecular {{Fluorescence Correlation Spectroscopy}} in a {{Feedback Tracking Microscope}}},
  volume = {99},
  issn = {0006-3495},
  language = {English},
  number = {1},
  journal = {Biophysical Journal},
  doi = {10.1016/j.bpj.2010.03.045},
  author = {McHale, Kevin and Mabuchi, Hideo},
  month = jul,
  year = {2010},
  pages = {313-322},
  file = {/home/bbeltr1/Documents/paper-collection/MabuchiH/McHale_Mabuchi_2010_Intramolecular Fluorescence Correlation Spectroscopy in a Feedback Tracking.pdf;/home/bbeltr1/Documents/zotero/storage/AKD78CPJ/S0006-3495(10)00410-8.html},
  pmid = {20655860}
}

@article{rybenkov1993,
  title = {Probability of {{DNA}} Knotting and the Effective Diameter of the {{DNA}} Double Helix},
  volume = {90},
  number = {11},
  journal = {Proceedings of the National Academy of Sciences},
  author = {Rybenkov, Valentin V. and Cozzarelli, Nicholas R. and Vologodskii, Alexander V.},
  year = {1993},
  pages = {5307--5311},
  file = {/home/bbeltr1/Documents/paper-collection/VologodskiiA/Rybenkov et al_1993_Probability of DNA knotting and the effective diameter of the DNA double helix.pdf}
}

@article{nepal2013,
  title = {Structure of {{DNA Coils}} in {{Dilute}} and {{Semidilute Solutions}}},
  volume = {110},
  issn = {0031-9007, 1079-7114},
  language = {en},
  number = {5},
  journal = {Physical Review Letters},
  doi = {10.1103/PhysRevLett.110.058102},
  author = {Nepal, Manish and Yaniv, Alon and Shafran, Eyal and Krichevsky, Oleg},
  month = jan,
  year = {2013},
  file = {/home/bbeltr1/Documents/paper-collection/KrichevskyO/Nepal et al_2013_Structure of DNA Coils in Dilute and Semidilute Solutions.pdf}
}

@article{stigter1977,
  title = {Interactions of Highly Charged Colloidal Cylinders with Applications to Double-Stranded {{DNA}}},
  volume = {16},
  issn = {1097-0282},
  abstract = {This paper presents new applications of the McMillan-Mayer solution theory to dispersions of highly charged colloidal cylinders in monovalent salt solutions. The thermodynamic solution properties are given in terms of the virial expansions relating to a Donnan membrane equilibrium. General expressions are derived for the second Donnan pressure virial coefficient B2 and for the first two salt distribution coefficients A1 and A2. The effect of electric interactions is represented as an increased effective diameter dB or dA of the colloidal cylinder. This yields the simple excluded volume expressions B2 = {$\pi$}dBL2/4 and A1 = {$\pi$}dA2L/4 for hard cylinders of length L and diameter dB and dA, respectively. The coefficient A2 is derived from the dependence of B2 on the salt concentration. Computations are made for double-stranded DNA in sodium chloride solutions with the DNA model developed in the preceding paper: a uniformly charged cylinder, with size and charge consistent with transport experiments, and surrounded by a Gouy double layer. In 1\textendash{}0.005M sodium chloride solutions dB is found to vary from 29 \AA{} to about 220 \AA, and dA from 30 \AA{} to about 170 \AA, with little sensitivity to the uncertainties in the kinetic diameter d {$\approx$} 24 \AA{} and the experimental {$\zeta$} potentials of DNA. Corresponding results predicted by the classical Donnan theory are 6\textendash{}167 times too high for B2. Values of A2 are relatively small, in line with the expected rapid convergence of the virial expansion for the salt distribution. This is consistent with a phase transition from random to parallel orientation of the cylinders predicted first by Onsager for hard cylinders on the basis of B2, but not yet observed for DNA in simple salt solutions.},
  language = {en},
  number = {7},
  journal = {Biopolymers},
  doi = {10.1002/bip.1977.360160705},
  author = {Stigter, Dirk},
  month = jul,
  year = {1977},
  pages = {1435-1448},
  file = {/home/bbeltr1/Documents/paper-collection/StigterD/Stigter_1977_Interactions of highly charged colloidal cylinders with applications to.pdf;/home/bbeltr1/Documents/zotero/storage/Z363K2I8/abstract.html}
}

@article{robertson2006,
  title = {Diffusion of Isolated {{DNA}} Molecules: {{Dependence}} on Length and Topology},
  volume = {103},
  issn = {0027-8424, 1091-6490},
  shorttitle = {Diffusion of Isolated {{DNA}} Molecules},
  abstract = {The conformation and dynamics of circular polymers is a subject of considerable theoretical and experimental interest. DNA is an important example because it occurs naturally in different topological states, including linear, relaxed circular, and supercoiled circular forms. A fundamental question is how the diffusion coefficients of isolated polymers scale with molecular length and how they vary for different topologies. Here, diffusion coefficients D for relaxed circular, supercoiled, and linear DNA molecules of length L ranging from {$\approx$}6 to 290 kbp were measured by tracking the Brownian motion of single molecules. A topology-independent scaling law D {$\sim$} L -{$\nu$} was observed with {$\nu$}L = 0.571 {$\pm$} 0.014, {$\nu$}C = 0.589 {$\pm$} 0.018, and {$\nu$}S = 0.571 {$\pm$} 0.057 for linear, relaxed circular, and supercoiled DNA, respectively, in good agreement with the scaling exponent of {$\nu$} {$\cong$} 0.588 predicted by renormalization group theory for polymers with significant excluded volume interactions. Our findings thus provide evidence in support of several theories that predict an effective diameter of DNA much greater than the Debye screening length. In addition, the measured ratio D Circular/D Linear = 1.32 {$\pm$} 0.014 was closer to the value of 1.45 predicted by using renormalization group theory than the value of 1.18 predicted by classical Kirkwood hydrodynamic theory and agreed well with a value of 1.31 predicted when incorporating a recently proposed expression for the radius of gyration of circular polymers into the Zimm model.},
  language = {en},
  number = {19},
  journal = {PNAS},
  doi = {10.1073/pnas.0601903103},
  author = {Robertson, Rae M. and Laib, Stephan and Smith, Douglas E.},
  month = sep,
  year = {2006},
  keywords = {Hydrodynamics,circular,excluded volume,polyelectrolyte,polymer},
  pages = {7310-7314},
  file = {/home/bbeltr1/Documents/paper-collection/SmithD/Robertson et al_2006_Diffusion of isolated DNA molecules.pdf;/home/bbeltr1/Documents/zotero/storage/IIQ79AH9/7310.html},
  pmid = {16648255}
}

@unpublished{lampoa,
  title = {Polymer {{Dynamics}} in a {{Confined}} and {{Crowded Medium}}},
  author = {Lampo, Thomas J. and Spakowitz, A.J.},
  file = {/home/bbeltr1/Documents/paper-collection/SpakowitzA/Lampo_Spakowitz_Polymer Dynamics in a Confined and Crowded Medium.pdf;/home/bbeltr1/Documents/zotero/storage/BWQ7WB4J/LS-crowdeddynamics.tex;/home/bbeltr1/Documents/zotero/storage/NGUUBKGG/references.bib}
}

@article