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Out-of-Equilibrium Dynamics of the Bose-Hubbard Model

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2013
Abstract: 

The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.

Document type: 
Article
File(s): 

Additional Annotation Enhances Potential For Biologically-Relevant Analysis Of The Illumina Infinium HumanMethylation450 Beadchip Array

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2013
Abstract: 

Background

Measurement of genome-wide DNA methylation (DNAm) has become an important avenue for investigating potential physiologically-relevant epigenetic changes. Illumina Infinium (Illumina, San Diego, CA, USA) is a commercially available microarray suite used to measure DNAm at many sites throughout the genome. However, it has been suggested that a subset of array probes may give misleading results due to issues related to probe design. To facilitate biologically significant data interpretation, we set out to enhance probe annotation of the newest Infinium array, the HumanMethylation450 BeadChip (450 k), with >485,000 probes covering 99% of Reference Sequence (RefSeq) genes (National Center for Biotechnology Information (NCBI), Bethesda, MD, USA). Annotation that was added or expanded on includes: 1) documented SNPs in the probe target, 2) probe binding specificity, 3) CpG classification of target sites and 4) gene feature classification of target sites.

Results

Probes with documented SNPs at the target CpG (4.3% of probes) were associated with increased within-tissue variation in DNAm. An example of a probe with a SNP at the target CpG demonstrated how sample genotype can confound the measurement of DNAm. Additionally, 8.6% of probes mapped to multiple locations in silico. Measurements from these non-specific probes likely represent a combination of DNAm from multiple genomic sites. The expanded biological annotation demonstrated that based on DNAm, grouping probes by an alternative high-density and intermediate-density CpG island classification provided a distinctive pattern of DNAm. Finally, variable enrichment for differentially methylated probes was noted across CpG classes and gene feature groups, dependant on the tissues that were compared.

Conclusion

DNAm arrays offer a high-throughput approach for which careful consideration of probe content should be utilized to better understand the biological processes affected. Probes containing SNPs and non-specific probes may affect the assessment of DNAm using the 450 k array. Additionally, probe classification by CpG enrichment classes and to a lesser extent gene feature groups resulted in distinct patterns of DNAm. Thus, we recommend that compromised probes be removed from analyses and that the genomic context of DNAm is considered in studies deciphering the biological meaning of Illumina 450 k array data.

Document type: 
Article
File(s): 

Regulation of DNA Replication within the Immunoglobulin Heavy-Chain Locus During B Cell Commitment

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2012
Abstract: 

The temporal order of replication of mammalian chromosomes appears to be linked to their functional organization, but the process that establishes and modifies this order during cell differentiation remains largely unknown. Here, we studied how the replication of the Igh locus initiates, progresses, and terminates in bone marrow pro-B cells undergoing B cell commitment. We show that many aspects of DNA replication can be quantitatively explained by a mechanism involving the stochastic firing of origins (across the S phase and the Igh locus) and extensive variations in their firing rate (along the locus). The firing rate of origins shows a high degree of coordination across Igh domains that span tens to hundreds of kilobases, a phenomenon not observed in simple eukaryotes. Differences in domain sizes and firing rates determine the temporal order of replication. During B cell commitment, the expression of the B-cell-specific factor Pax5 sharply alters the temporal order of replication by modifying the rate of origin firing within various Igh domains (particularly those containing Pax5 binding sites). We propose that, within the Igh CH-3′RR domain, Pax5 is responsible for both establishing and maintaining high rates of origin firing, mostly by controlling events downstream of the assembly of pre-replication complexes.

Document type: 
Article
File(s): 

Vital Dye Reaction and Granule Localization in Periplasm of Escherichia coli

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2012
Abstract: 

Background

Tetrazolium salts are widely used in biology as indicators of metabolic activity – hence termed vital dyes – but their reduction site is still debated despite decades of intensive research. The prototype, 2,3,5- triphenyl tetrazolium chloride, which was first synthesized a century ago, often generates a single formazan granule at the old pole of Escherichia coli cells after reduction. So far, no explanation for their pole localization has been proposed.

Method/Principal Findings

Here we provide evidence that the granules form in the periplasm of bacterial cells. A source of reducing power is deduced to be thiol groups destined to become disulfides, since deletion of dsbA, coding for thiol-oxidase, enhances the formation of reduced formazan. However, pervasive reduction did not result in a random distribution of formazan aggregates. In filamentous cells, large granules appear at regular intervals of about four normal cell-lengths, consistent with a diffusion-to-capture model. Computer simulations of a minimal biophysical model showed that the pole localization of granules is a spontaneous process, i.e. small granules in a normal size bacterium have lower energy at the poles. This biased their diffusion to the poles. They kept growing there and eventually became fixed.

Conclusions

We observed that formazan granules formed in the periplasm after reduction of tetrazolium, which calls for re-evaluation of previous studies using cell-free systems that liberate inaccessible intracellular reductant and potentially generate artifacts. The localization of formazan granules in E. coli cells can now be understood. In living bacteria, the seeds formed at or migrated to the new pole would become visible only when that new pole already became an old pole, because of the relatively slow growth rate of granules relative to cell division.

Document type: 
Article
File(s): 

Modeling Inhomogeneous DNA Replication Kinetics

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2012
Abstract: 

In eukaryotic organisms, DNA replication is initiated at a series of chromosomal locations called origins, where replication forks are assembled proceeding bidirectionally to replicate the genome. The distribution and firing rate of these origins, in conjunction with the velocity at which forks progress, dictate the program of the replication process. Previous attempts at modeling DNA replication in eukaryotes have focused on cases where the firing rate and the velocity of replication forks are homogeneous, or uniform, across the genome. However, it is now known that there are large variations in origin activity along the genome and variations in fork velocities can also take place. Here, we generalize previous approaches to modeling replication, to allow for arbitrary spatial variation of initiation rates and fork velocities. We derive rate equations for left- and right-moving forks and for replication probability over time that can be solved numerically to obtain the mean-field replication program. This method accurately reproduces the results of DNA replication simulation. We also successfully adapted our approach to the inverse problem of fitting measurements of DNA replication performed on single DNA molecules. Since such measurements are performed on specified portion of the genome, the examined DNA molecules may be replicated by forks that originate either within the studied molecule or outside of it. This problem was solved by using an effective flux of incoming replication forks at the model boundaries to represent the origin activity outside the studied region. Using this approach, we show that reliable inferences can be made about the replication of specific portions of the genome even if the amount of data that can be obtained from single-molecule experiments is generally limited.

Document type: 
Article

Chromosome Driven Spatial Patterning of Proteins in Bacteria

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2010
Abstract: 

The spatial patterning of proteins in bacteria plays an important role in many processes, from cell division to chemotaxis. In the asymmetrically dividing bacteria Caulobacter crescentus, a scaffolding protein, PopZ, localizes to both poles and aids the differential patterning of proteins between mother and daughter cells during division. Polar patterning of misfolded proteins in Escherechia coli has also been shown, and likely plays an important role in cellular ageing. Recent experiments on both of the above systems suggest that the presence of chromosome free regions along with protein multimerization may be a mechanism for driving the polar localization of proteins. We have developed a simple physical model for protein localization using only these two driving mechanisms. Our model reproduces all the observed patterns of PopZ and misfolded protein localization - from diffuse, unipolar, and bipolar patterns and can also account for the observed patterns in a variety of mutants. The model also suggests new experiments to further test the role of the chromosome in driving protein patterning, and whether such a mechanism is responsible for helping to drive the differentiation of the cell poles.

Document type: 
Article
File(s): 

BEAF Regulates Cell-Cycle Genes through the Controlled Deposition of H3K9 Methylation Marks into Its Conserved Dual-Core Binding Sites

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2008-12-23
Abstract: 

Chromatin insulators/boundary elements share the ability to insulate a transgene from its chromosomal context by blocking promiscuous enhancer–promoter interactions and heterochromatin spreading. Several insulating factors target different DNA consensus sequences, defining distinct subfamilies of insulators. Whether each of these families and factors might possess unique cellular functions is of particular interest. Here, we combined chromatin immunoprecipitations and computational approaches to break down the binding signature of the Drosophila boundary element–associated factor (BEAF) subfamily. We identify a dual-core BEAF binding signature at 1,720 sites genome-wide, defined by five to six BEAF binding motifs bracketing 200 bp AT-rich nuclease-resistant spacers. Dual-cores are tightly linked to hundreds of genes highly enriched in cell-cycle and chromosome organization/segregation annotations. siRNA depletion of BEAF from cells leads to cell-cycle and chromosome segregation defects. Quantitative RT-PCR analyses in BEAF-depleted cells show that BEAF controls the expression of dual core–associated genes, including key cell-cycle and chromosome segregation regulators. beaf mutants that impair its insulating function by preventing proper interactions of BEAF complexes with the dual-cores produce similar effects in embryos. Chromatin immunoprecipitations show that BEAF regulates transcriptional activity by restricting the deposition of methylated histone H3K9 marks in dual-cores. Our results reveal a novel role for BEAF chromatin dual-cores in regulating a distinct set of genes involved in chromosome organization/segregation and the cell cycle.

Document type: 
Article
File(s): 

Design and Construction of a One-Dimensional DNA Track for an Artificial Molecular Motor

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2012
Abstract: 

DNA is a versatile heteropolymer that shows great potential as a building block for a diverse array of nanostructures. We present here a solution to the problem of designing and synthesizing a DNA-based nanostructure that will serve as the track along which an artificial molecular motor processes. This one-dimensional DNA track exhibits periodically repeating elements that provide specific binding sites for the molecular motor. Besides these binding elements, additional sequences are necessary to label specific regions within the DNA track and to facilitate track construction. Designing an ideal DNA track sequence presents a particular challenge because of the many variable elements that greatly expand the number of potential sequences from which the ideal sequence must be chosen. In order to find a suitable DNA sequence, we have adapted a genetic algorithm which is well suited for a large but sparse search space. This algorithm readily identifies long DNA sequences that include all the necessary elements to both facilitate DNA track construction and to present appropriate binding sites for the molecular motor. We have successfully experimentally incorporated the sequence identified by the algorithm into a long DNA track meeting the criteria for observation of the molecular motor's activity.

Document type: 
Article

Out-of-Equilibrium Dynamics of the Bose-Hubbard Model

Author: 
Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2013
Abstract: 

The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to  the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions.

Document type: 
Article

Developing 1D Nanostructure Arrays for Future Nanophotonics

Peer reviewed: 
Yes, item is peer reviewed.
Date created: 
2006
Abstract: 

There is intense and growing interest inone-dimensional (1-D) nanostructures from the perspectiveof their synthesis and unique properties,especially with respect to their excellent opticalresponse and an ability to form heterostructures. Thisreview discusses alternative approaches to preparationand organization of such structures, and their potentialproperties. In particular, molecular-scale printing ishighlighted as a method for creating organizedpre-cursor structure for locating nanowires, as well asvapor–liquid–solid (VLS) templated growth using nano-channel alumina (NCA), and deposition of 1-Dstructures with glancing angle deposition (GLAD). Asregards novel optical properties, we discuss as anexample, finite size photonic crystal cavity structuresformed from such nanostructure arrays possessing highQ and small mode volume, and being ideal for developingfuture nanolasers.

Document type: 
Article