<span class=strong>Reception and Poster Session</span>
Monday, September 17, 2007 - 4:45pm - 6:15pm
- Mathematical Methods to Study the Relative Position of Chromosomes During Interphase in Human Cells
F. Javier Arsuaga (San Francisco State University)
Same abstract as the 9/20 talk.
- DNA Solitons as an Explanation for Codon Bias
Alex Kasman (College of Charleston)
This talk will begin with a brief historical introduction
a nonlinear wave phenomenon that has been of great
mathematics and physics since the late 1960's. Among the
mysteries in science for which a soliton model has been
the question of how the transcription bubble moves
along a DNA
molecule during protein production. In particular, the
Englander in 1980 suggested that it was actually an
nonlinear dynamics induced by the attraction of the base
the form of a discrete Sine-Gordon equation. More
inhomogeneous versions of this model have been introduced
into account the effect of the particular DNA sequence on
I will argue that nonlinear dynamics could also provide
for codon bias (the apparent preference for certain
others encoding the same amino acid in biological
numerical experiments will be presented to support this
but this work is truly preliminary and it is my hope that
will be able to provide guidance and suggestions for the
of this project.
- On the Association of Proteins to Circular DNA: Modeling the Facilitated Rate of Association
Ramzi Alsallaq (Florida State University)
The facilitated diffusion-limited rate of association of
proteins to there specific sites on circular
DNA substrates is derived based on surface-potential model. We
assume the protein performs 3D diffusive motion whether be it in the relatively small region where it is exposed to the surface force,
or outside in the bulk. The obtained rate is compared to the
corresponding rate of association to symmetrically linearized DNA template with reflecting ends, and the two rates are found comparable for contour lengths that are longer than 185bp . This suggests considering other mechanisms when the measured rates of association to these different topologies are found different. The accuracy of the analytical models is verified by numerical simulations.
- Polynomial Invariants, Knot Distances and Topoisomerase Action
Hyeyoung Moon (The University of Iowa)
The knot distance between two knots is defined as the minimum number of crossing changes that convert one knot to the other. Knot distances are related to the study of topoisomerase action. Type II topoisomerases are enzymes that break the backbone of DNA and allow passage of another segment of DNA through the break before resealing the break. In other words, these enzymes are involved in changing crossings of DNA knots. Using some mathematical theories, knot distances have been tabulated for rational knots, some non-rational knots and composite of rational knots up to 13 crossings. However, there are still undetermined distances in the knot distance table. Here I would like to apply some polynomial invariants to improve lower bounds of knot distances. In particular, I generalized proposition 3.1 in the paper,' Polynomial values, the linking form and unknotting numbers' by A. Stoimenow.
- Nucleosome and Chromatin Structure and Dynamics Studied by Fluorescence Techniques and Computer Modeling
Jörg Langowski (Deutsches Krebsforschungszentrum (Cancer Research)(DKFZ))
Same abstract as the 9/19 talk.
- Signature Curves in Classifying DNA Supercoils
Chehrzad Shakiban (University of Minnesota, Twin Cities)
Signature curves are unique curves which are assigned to two or three dimensional closed curves and are invariant under rigid motions -- such as rotation. They are most useful in computer vision applications because they allow any object to be represented by its unique signature curve regardless of its position. In this poster you can see how signature curves are calculated continuously and discretely using a numerical method. You can then see how an analog of Latent Semantic Analysis (a statistical method) is to categorize signature curves. Two applications are discussed: One in sorting leaves in the Euclidean plane and the other in sorting Supercoiled DNA molecules as space curves.
- A DNA Base-pair Step Parameter Database
Guohui Zheng (Rutgers, The State University Of New Jersey )
We present our DNA base-pair step parameter database, and its web
interface. The DNA base-pair step parameter database is a relational
database designed to gather double helical DNA base-pair step
parameters, generated using the 3DNA software package , across
multiple DNA-containing structures deposited in the Nucleic Acid
Database (NDB) . Although the NDB provides DNA base-pair step
parameters for all structures that we include in our database, the NDB
is structure specific, meaning that it provides information about
individual structures. Our database is aimed to integrate nucleic acid
information across multiple structures, collect data samples for a
specific parameter or parameter set, and offer a basis for statistical
inference of DNA mechanical properties. The database collects
base-pair step parameters in different categories, such as resolution,
presence or absence of ligands, and protein folding family. It also
contains a subset of non-redundant protein-DNA complex structures,
based on clustering the sequences and folds of the proteins complexed
to DNA and the sequences of the bound DNA, with a resolution of 3.0
Angstrom or better. This non-redundant dataset provides a useful data
pool for statistical inference, reducing bias from redundant
structures. The latest version of the database, updated through June
2007, contains information from a total of 1389 DNA-containing crystal
structures with 23036 base-pair steps.
1. Olson, W. K., Lu, X.-J., 3DNA: a software package for the
analysis, rebuilding and visualization of three-dimensional nucleic
acid structures. Nucleic Acids. Res., 2003. 31(17): 5108-5121.
2. Berman, H. M., Olson, W. K., Beveridge, D. L., Westbrook, J.,
Gelbin, A., Demeny, T., Hsieh, S.-H., Srinivasan, A. R., and
Schneider, B., The Nucleic Acid Database: A Comprehensive Relational
- Generating a Tangle Table for DNA Protein Complex Modeling
Melanie DeVries (The University of Iowa)
A tangle is an object consisting of arcs properly embedded in a 3-dimensional ball. This is a simple model for DNA protein complexes. The protein is thought of as a 3D ball, while the segments of DNA are represented by the arcs. While a tangle is a simple model for a DNA protein complex, it is often not easy to determine what tangle describes a given complex. One method involves checking every tangle up to a given crossing number. Hence a table of tangles has been created. This was done by generating all possible tangles by taking all permutations of a numerical encoding of tangles, a generalization of the Dowker code, and using variations of Reidemeister moves and invariants to remove tangles and differentiate tangles on the list. This table can be used for various purposes such as to improve distance tables and to solve tangle equations.
- Tangle Models for Recombinase Action
Kyle McQuisten (The University of Iowa)
Recombinases are enzymes that bind and manipulate strands of DNA. The action within the enzyme is not observable directly, but can be inferred using equations involving topological objects called tangles. A 2-string tangle is a ball along with two arcs properly embedded within the ball. When modeling a DNA/enzyme complex with a 2-string tangle, the ball represents the enzyme that binds the two DNA segments, and the two arcs represent the DNA segments themselves. When recombinases are applied to circular DNA, different DNA knots can be formed. Equations using the tangle model of Sumners and Ernst can then be used to understand the action of the enzyme. Solutions will be presented for the class of knots called Montesinos knots.
- Modelling DNA Unknotting by Type II Topoisomerases
Xia Hua (Massachusetts Institute of Technology)Mariel Vazquez (San Francisco State University)
Xia Hua1, Nathan Shayefar2, Itamar
Landau2, Reuben Brascher3,
Juliet Portillo3 and Mariel Vazquez3
DNA knots and links affect crucial cellular processes such as
DNA replication, transcription regulation, chromatin
modification and cell division. Type II topoisomerases simplify
DNA knots and links efficiently by performing strand-passage on
DNA strands. Experimental studies have shown that these enzymes
simplify the topology of DNA below thermodynamical equilibrium.
However the key behind their efficiency is yet to be revealed.
Motivated by these experimental observations, we study random
transitions of knotted polygonal chains of fixed length. We use
a modified BFACF algorithm to sample an ensemble of polygons of
a fixed knot type in Z3 according to the Boltzmann
distribution. We perform random strand-passage on the polygons
using a novel algorithm that operates at the
Dowker-Thistlethwaite code level. Topological biases are
introduced at the strand-passage step and one-step transition
probabilities and steady state distributions are obtained.
Finally we explore the effect of the solution’s ionic strength
on the steady state distributions.
This work is funded by an NIH MBRS SCORE grant to MV (S06
1 Department of Mathematics, MIT
2 Department of Mathematics, UC Berkeley
3 Department of Mathematics, San Francisco State University
- A Tangle Analysis of a DNA-protein Complex which Binds Four DNA Segments
Soojeong Kim (The University of Iowa)
In the late 80's Ernst and Sumners  first introduced the
mathematical tangle model of DNA-protein complexes.
More recently, in 2002, Pathania, Jayaram and Harshey 
designed a new
methodology called difference topology in order to derive the
number of DNA crossings trapped in an unknown synapse. Pathania et al
revealed the topological structure within the Mu transpososome
consisted of three DNA segments containing five nodes.
These experimental results were also analyzed in . They
described infinitely many
solutions to the same tangle equations, but argued
that Pathania et al.'s model is the only biologically reasonable
The Mu transpososome protein complex binds three DNA
there exist protein complexes which bind more than three DNA
this talk, I would like to extend some of the 3-string tangle
analysis in  to DNA
protein complex containing four DNA segments.
 C. Ernst, D. W. Sumners, A calculus for rational tangles:
applications to DNA
recombination, Math. Proc. Camb. Phil. Soc. 108 (1990),
 S. Pathania, M. Jayaram, and R. Harshey, Path of DNA within
the Mu transpososome:
Transposase interaction bridging two Mu ends and the enhancer
trap five DNA superdoils,
Cell 109 (2002), 425-436.
 I. K. Darcy, J. Luecke, and M. Vazquez, A tangle analysis
of the Mu transpososome
protein complex which binds three DNA segments, Preprint.
- Chicken and Yeast Nucleosomal DNA Sequences Differ at the Ends: A Possible Relation to the Linker Histone Binding
Feng Cui (National Institutes of Health)
The linker histones (LH) bind at the entry/exit points of nucleosomal DNA and protect additional ~20 bp. It remains unknown, however, what are the DNA sequence features facilitating the LH binding. To address this question, we analyzed the ~20-bp fragments flanking the chicken  and yeast  nucleosome core particles (NCP) by ‘extracting’ them from the corresponding genomes. The two species differ in LH abundance quite substantially: the fraction of the LH-associated nucleosomes varies from ~100% in chicken to 2-3% in yeast . Therefore, we expected that the difference in stoichiometry of the LH binding would be reflected in the DNA sequence organization.
We found that several ‘minor-groove bendable’ dimers (AA:TT and AT, denoted as AT2) are distributed differently in the two sets of sequences. In yeast, the periodic oscillation of these dimers extends beyond the ends of nucleosomal DNA; the ‘internal’ peaks are in phase with the ‘external’ AT2 peaks observed in flanking sequences. For the chicken NCP, the AT2 peaks in the flanking sequences are out of phase with the nucleosomal AA:TT peaks . In our interpretation, this difference reflects different spatial trajectories of DNA at the entry/exit points. In most of the yeast nucleosomes (depleted of LH), the DNA at the ends of NCP fragments follows its ‘natural extension’ trajectory, leaving no space for the linker histones. By contrast, the chicken DNA adopts an additional ‘out-of-phase’ bend at the NCP end (not visible in the NCP Xray structures), thereby making enough space to accommodate the linker histone.
Furthermore, the AT2 elements are distributed asymmetrically between the two ends of chicken NCP sequences, consistent with the asymmetric, off-axis location of LH on the nucleosome. Thus, our findings suggest that the ‘out-of-phase’ AT-rich elements characteristic of the chicken NCP flanking sequences, represent a novel feature associated with LH binding.
 Satchwell, S. C. et al. J. Mol. Biol. 191, 659-675 (1986).
 Segal, E. et al. Nature 442, 772-778 (2006).
 Freidkin, I. and Katcoff, D. J. Nucleic Acids Res. 29, 4043-4051 (2001).
- Developing Computer Software for Detecting Fluorescent Chromosome Labels
Lawrence Varela (San Francisco State University)
Organization of chromosomes in the living cell is believed to be a key
factor in many biological processes such as gene expression, replication
and repair. Furthermore this organization is severely disrupted during the
progression of certain diseases such as cancer.
Fluorescent labels are routinely used in the clinics for diagnosis and are
increasingly used to study chromosome structure and nuclear architecture.
However many of these studies are performed manually thus limiting our
ability to perform high-throughput approaches.
Here we propose a segmentation method for detecting fluorescent labels in
fixed cells. Our image analysis algorithm follows a modified approach of
image binarization, connected-component analysis, and statistical
analysis. In the presence of reasonable noisy data, fuzzy image segments,
our image analyzer detects DNA proximity and arrangement within the cell
nucleus. Our image analysis tool provides an additional means for
scientists to verify chromosome structure and nuclear architecture during
various stages of cell duplication.
- Free Energy Simulation Studies of Sharp DNA Bending using a Global Restraint of Space-invariant Internucleotides Rotation Axis
Jeremy Curuksu (Jacobs University)
The poster present a DNA bending restraining method for use during Umbrella Sampling Molecular Dynamics based on the orientation of local screw axis. Result are reported on free energy simulations of induced bending on short DNA fragments which reproduce the stress-strain curve of bend angle probabilities recently obtained by AFM experiments on the same length scale. Our results suggest a two-states transition (associated to flexible base-pair kink) between bend angle conformers. We also present an Hamiltonian Replica Exchange technique to improve limited sampling due to strongly bent conformations trapped in local energy minima.
- Modelling Diffusional Transport in the Interphase Cell Nucleus
Annika Wedemeier (German Cancer Research Center)
In recent years great progress has been made in the view of the living cell as a regulatory network in time.
However, a quantitative description of the transport of biomolecules in the dense macromolecular network
of chromatin fibers in the interphase cell nucleus is still missing. Furthermore, it is not yet clear to what
extent macromolecular mobility is affected by structural components of the nucleus.
This work contributes to the understanding of this process by developing a theoretical description of network
diffusion in the interphase cell nucleus. To model the situation in the cell nucleus a lattice approach is used
minimizing computational time and effort. Our model leads to a quantitative understanding of transport
behaviour which is directly related to chromatin morphology. Changes of these characteristics are known to
occur upon apoptosis or malignant transformations.
The crowded environment of chromatin fibers in the nucleus is simulated by a simplified version of the bond
fluctuation method originally desrcibed by Carmesin et al (Macromolecules 1988,21, p.2819) in combination
with a Metropolis Monte Carlo procedure. This yields well equilibrated polymer chains satisfying static properties
such as end-to-end distance.
It is investigated how the diffusion coefficient of particles of a given size depends on the 3D geometry of the
network of chromatin fibers and their density in the nucleus. We show that the diffusion cofficient is proportional
to the volume fraction of the freely accessible space. Additionally, we investigate to what extent structural
properties of the fibers, such as persistence length and contour length, influence the diffusion coefficient. We
observe that neither the contour length nor the persistence length of the fibers affects the diffusional transport
of small particles.
Furthermore, we found that the translational diffusion of the mass centers of the chromatin fibers is anomalous.
- Macroscopic Modeling of a Circular Rod with Twist and Bend in a Viscous Fluid
Same abstract as the 9/19 talk.
- Geometric Flows on Biological Surfaces
Guowei Wei (Michigan State University)
Same abstract as the 9/19 talk.