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Abstracts and Talk Materials
Mathematics of DNA Structure, Function, and Interactions
September 16 - 21, 2007

Ramzi Alsallaq (Florida State University)

On the Association of Proteins to Circular DNA: Modeling the Facilitated Rate of Association
December 31, 1969

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.

F. Javier Arsuaga (San Francisco State University)

Mathematical Methods to Study the Relative Position of Chromosomes During Interphase in Human Cells
September 20, 2007

During interphase chromosomes are confined to sub-nuclear regions called chromosome territories. The position of these territories has been associated with a number of biological processes such as cell differentiation and transcription. Furthermore the relative position of chromosomes is believed to have a very important role in the formation of chromosome aberrations in cancer and other human diseases.

Ionizing radiation helps approach the problem of the relative position of chromosomes. When ionizing radiation tracks (gamma rays, X-rays, high energy alpha particles, etc) cross the cell nucleus they release enough energy to disrupt the molecular structure of the DNA (directly or indirectly) and induce DNA double stranded-breaks (DSBs). When DSB free ends are rejoined with free ends different from their original partners, chromosome aberrations are introduced. If the two misrejoined free ends are on different chromosomes, the chromosome aberration is called an interchange, and the number of interchanges observed for each chromosome pair can help indicate chromosome positioning in the nucleus.

In this presentation I will show our current mathematical methods to interrogate mFISH or SKY data for chromosome clustering (i.e. for deviations from randomness in the relative positions of chromosomes). Our approach is based on the hypothesis that chromosomes that are in close proximity form radiation induced chromosome aberrations more often than those that are far apart (known as the proximity effect hypothesis). When applying these methods to human lymphocytes we find two sets of chromosomes that are on average closer to each other than what randomness would predict these are: {1,16,17,19,22}and {13,14,15,21,22} (Cornforth et al. 2002, Arsuaga et al. 2004, Vives et al. 2005).

We are currently characterizing features of nuclear organization that different types of radiations can detect. We are also extending our studies to human fibroblasts for which we are developing data mining methods.

F. Javier Arsuaga (San Francisco State University)

Mathematical Methods to Study the Relative Position of Chromosomes During Interphase in Human Cells
December 31, 1969

Same abstract as the 9/20 talk.

Nathan A. Baker (Washington University School of Medicine)

Assessing the Ability of Continuum Solvation Models to Accurately Model Nucleic Acid Electrostatics
September 19, 2007

Continuum electrostatics methods have become increasingly popular due to their ability to provide approximate descriptions of solvation energies and forces without the expensive sampling required by all-atom solvent models. In particular, the Poisson–Boltzmann equation (PBE) provides electrostatic potentials, solvation energies, and forces by modeling the solvent as a featureless dielectric material and the mobile ions as a continuous distribution of charge. Polar solvation forces and energies obtained from the PBE are often supplemented with simple solvent-accessible surface area (SASA) models of nonpolar solvation. However, while polar and nonpolar continuum models have been assessed on their ability to reproduce global properties, such as solvation free energies, their ability to provide accurate representations of local solvation properties such as forces has not previously been adequately studied. We have performed comparisons of continuum and all-atom models of solvation forces for protein and RNA systems in order to assess the performance of continuum models for biomolecular systems of widely varying charge densities. The results of these comparisons show that current implementations of the PBE are capable of generating polar solvation forces that correlate well with explicit solvent forces for protein systems but provide significantly less accurate representations of polar solvation forces for RNA systems. Conversely, SASA-based nonpolar forces are found to have no significant correlation with nonpolar explicit solvent forces for either protein or RNA molecules. Good correlation between explicit and continuum nonpolar forces is only obtained when area, volume, and attractive dispersion forces are included in the continuum model. We discuss the implications of these studies in the context of molecular simulation as well as the impact of this work on basic models for understanding experimental observations of biomolecular binding and folding.

Meredith Betterton (University of Colorado)

Helicase Unwinding of dsDNA: Velocity, Processivity, and Collective Effects
September 19, 2007

Helicases are molecular motors which unwind double-stranded nucleic acids. Many helicases move with directional bias on single strands, and couple directional translocation to strand separation. We describe a theory of the coupling between translocation and unwinding, which uses an interaction potential to represent passive and active helicase mechanisms. Varying the interaction potential to represent passive or active opening alters the predicted unwinding velocity and processivity of a helicase. We describe the model predictions for the dependence on the interaction potential, helicase step size, and average base-pair binding free energy. New theoretical results on unwinding by multiple interacting helicases are compared to experimental data from the Antoine van Oijen lab, which suggest unwinding by multiple helicases can show a higher apparent velocity and processivity.

Erik Boczko (Vanderbilt University)

Molecular Seismology: An Inverse Problem in Nanobiology
September 20, 2007

The material properties of an elastic fiber like DNA will change in space and time as ligands associate with it. This observation affords a new direction in single molecule studies provided that material properties such as the density profile can be measured in space and time. In fact, this is precisely the objective of seismology, where the mathematics of inverse problems have been employed with success. We argue that inverse problems in elastic media can be directly applied to biophysical problems of fiber-ligand association, and demonstrate that robust algorithms exist to perform material reconstruction in the condensed phase.

Gregory S. Chirikjian (Johns Hopkins University)

Conformational Statistics of DNA
September 16, 2007

DNA can be viewed as a semiflexible polymer, and represented at a coarse scale as a continuous helical elastic rod. In this talk, methods from the theory of Lie groups are used to analyze equilibrium conformations of helical rod models of DNA with end constraints. When the ends of a segment of DNA are free to move, the resulting cloud of reference frames visited by the distal end of the segment relative to the proximal end can be characterized as a probability density function on the Euclidean motion group. The relationship between this pdf and the stiffness parameters of the helical rod model is derived using methods of noncommutative harmonic analysis.

Bernard D. Coleman (Rutgers, The State University of New Jersey)

On Problems in DNA Elasticity in Which Electrostatic Forces, the Sequence Dependence of Elastic Properties and the Impenetrability of the DNA Molecule Must all be Taken into Account
September 16, 2007

In this talk on DNA elasticity, that is based on recent research of Yoav Biton and is an extension of earlier research of Biton, Coleman, and Swigon, it will be shown that there are cases in which self-contact occurs even though the intramolecular electrostatic forces of repulsion are strong. The theory to be presented permits one to calculate minimum energy configurations of supercoiled non-homogeneous DNA minicircles and the dependence on linking number and salt concentration of the proximity and relative orientation of sequentially remote sites whose interaction can be a matter of biological importance.

Y.Y. Biton, B.D. Coleman, D. Swigon, On bifurcations of intrinsically curved, electrically charged, rod-like structures that model DNA molecules in solution, J. Elasticity 87, 187-210, 2007.

Vincent Croquette (École Normale Supérieure)

Real-time Observation of Bacteriophage T4 gp41 Helicase Reveals Unwinding Mechanism
September 19, 2007

Joint work with Timothée Lionnet1, Michelle M. Spiering2, Stephen J. Benkovic2, and David Bensimon1

Helicases are enzymes that couple ATP hydrolysis to the unwinding of double-stranded (ds) nucleic acids. The bacteriophage T4 helicase (gp41) is a hexameric helicase that promotes DNA replication within a highly coordinated protein complex termed the replisome. Despite recent progress, the gp41 unwinding mechanism and regulatory interactions within the replisome remain unclear. Here we use a single tethered DNA hairpin as a real-time reporter of gp41-mediated dsDNA unwinding and ssDNA translocation with 3-bp resolution. Whereas gp41 translocates on ssDNA as fast as the /in vivo/ replication fork (~400 bp/s), its unwinding rate extrapolated to zero force is much slower (~30 bp/s). Taken together, our results have two implications: first, gp41 unwinds DNA through a passive mechanism; second, this weak helicase cannot efficiently unwind the T4 genome alone. Future experiments on the full replisome will be useful to understand how fast and processive replication is achieved.

1LPS, ENS, Paris, France.; 2Dept.of Chemistry, Penn State University, USA.

Feng Cui (National Institutes of Health)

Chicken and Yeast Nucleosomal DNA Sequences Differ at the Ends: A Possible Relation to the Linker Histone Binding
December 31, 1969

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 [1] and yeast [2] 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 [3]. 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 [1]. 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.

[1] Satchwell, S. C. et al. J. Mol. Biol. 191, 659-675 (1986). [2] Segal, E. et al. Nature 442, 772-778 (2006). [3] Freidkin, I. and Katcoff, D. J. Nucleic Acids Res. 29, 4043-4051 (2001).

Jeremy Curuksu (Jacobs University)

Free Energy Simulation Studies of Sharp DNA Bending using a Global Restraint of Space-invariant Internucleotides Rotation Axis
December 31, 1969

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.

Luke Czapla (Rutgers, The State University Of New Jersey )

The Effect of the Nucleoid Protein HU on the Structure, Flexibility, and Ring-closure Properties of DNA Deduced from Monte Carlo Simulation
September 20, 2007

Joint work with David Swigon and Wilma K Olson (PI).

A recently developed Monte Carlo technique for calculating the cyclization propensity of DNA chains has been modified to consider the effect of proteins which bind randomly to the double helix. The method is applied to consider the bacterial nucleoid protein HU, known to bind non-specifically to unmodified double-helical DNA. We simulate chains with a fixed average number of bound protein, with proteins placed in random positions. Our results predict that not only will HU greatly enhance DNA cyclization, as measured by the J factor, but that the effect of helical repeat is greatly reduced and the J factor is nearly constant over a wide range of chain lengths. Moreover, HU induces negative supercoiling which condenses the DNA, consistent with the requirement of HU for bacterial nucleoid condensation. The mechanism of sharp bending and significant untwisting of HU-bound DNA is common among proteins known to restore this nucleoid condensation. Mathematical and computational techniques involved in the Monte Carlo simulation of DNA will be discussed.

Isabel K. Darcy (The University of Iowa)

Tangle Analysis of Protein-DNA Complexes
September 17, 2007

Protein-DNA complexes have been modeled using tangles. A tangle consists of arcs properly embedded in a 3-dimensional ball. The protein is modeled by the 3D ball while the segments of DNA bound by the protein can be thought of as arcs embedded within the protein ball. This is a very simple model of protein-DNA binding, but from this simple model, much information can be gained. The main idea is that when modeling protein-DNA reactions, one would like to know how to draw the DNA. For example, are there any crossings trapped by the protein complex? How do the DNA strands exit the complex? Is there significant bending? Tangle analysis cannot determine the exact geometry of the protein-bound DNA, but it can determine the overall entanglement of this DNA, after which other techniques may be used to more precisely determine the geometry. The latest mathematics and software for solving tangle equations will be discussed.

Melanie DeVries (The University of Iowa)

Generating a Tangle Table for DNA Protein Complex Modeling
December 31, 1969

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.

Marcia O. Fenley (Florida State University)

Exploring Salt-mediated Electrostatics in the Association of TATA Binding Proteins to DNA with a Combined Molecular Mechanics/Poisson-Boltzmann Approach
September 20, 2007

Joint work with Johan H. Bredenberg and Cristina Russo (Institute of Molecular Biophysics, Florida State University, Tallahassee).

TATA box binding proteins (TBPs) from hyperthermophilic and halophilic organisms, e.g. Pyrococcus woesei (Pw), function optimally at high temperatures and/or salt concentrations. Such proteins associate to DNA with different mechanisms than their mesophilic homologues. Halophilic TBPs sequester cations while mesophilic (Greek, meso – intermediate) TBPs may both release and sequester ions from the DNA ion atmosphere upon association. Our results from a Molecular Mechanics/Poisson Boltzmann computational study on the binding of mesophilic and halophilic TBPs to DNA, suggests that the widely used oligocationic binding model for describing nucleic acid association to charged ligands may not depict the whole association process when acidic residues such as Asp and Glu are found in the binding interface. Instead, the distribution and the total number of charged residues may be the main underlying contributor in the association process, since the little correlation between the widely used ion-pair rule and the salt dependence of binding is found in these kind of systems. We also compare the linear and non-linear solution to the Poisson-Boltzmann Equation and find that the latter is in better agreement with experimentally observed differences in the salt dependence of DNA-binding to mesophilic and halophilic TPBs.

Laura Finzi (Emory University)

Lysogeny Maintenance: A Matter of Looping
September 20, 2007

After infecting a host bacterium, bacteriophage lambda, may lie latent (lysogeny), or reproduce and lyse the host bacterium. Only 1 infected cell in 10 million lyses spontaneously, but the switch to lysis is extremely efficient if the bacterial host becomes endangered. The phage protein CI is responsible for maintaining lysogeny by regulating the transcription of itself and genes responsible for lysis. CI mediates a DNA loop by cooperatively binding two triplets of DNA sites separated by 2.3 kbp. Using the tethered particle motion technique and magnetic tweezers we are probing parameters that underlie the remarkable stability of the lysogenic (looped) state.

Xia Hua (Massachusetts Institute of Technology)
Mariel Vazquez (San Francisco State University)

Modelling DNA Unknotting by Type II Topoisomerases
December 31, 1969

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 GM052588)

1 Department of Mathematics, MIT 2 Department of Mathematics, UC Berkeley 3 Department of Mathematics, San Francisco State University

Makkuni Jayaram (The University of Texas at Austin)

Difference Topology: Analysis of DNA Architecture in Complex DNA-protein Assemblies
September 21, 2007

Joint work with Rasika M Harshey, Section of Molecular Genetics and Microbiology, University of Texas at Austin, Austin, TX 78712.

Important DNA transactions in biological systems, replication, transcription, recombination etc., often require the assembly of complex protein machines at specific DNA sites. Within these higher order assemblies, the DNA often follows a defined path, generating a fixed number of duplex crossings characteristic of individual systems. In the absence of crystal structure data, it is well nigh impossible to decipher the DNA topology organized by a particular protein machine. A ‘difference topology’ method, based on site-specific recombination, can be employed to derive this information indirectly. The rationale of the analysis is outlined below.

Simple members of the tyrosine family site-specific recombinases, Flp and Cre, mediate DNA exchange by arranging their target sites in an antiparallel fashion and introducing no DNA crossing during recombination. Flp and Cre are therefore useful in sealing off DNA domains by recombination and preserving the DNA crossings between two sites introduced by another recombinase or transposase protein or a multi-protein complex. The crossings can be displayed and counted as knot crossings or catenane crossings by suitable analytical methods. Knots result when Flp or Cre mediates inversion between a pair of head-to-head sites; catenanes are formed when the recombinase mediates deletion between head-to-tail sites. For a matched pair of inversion and deletion substrates, the crossing numbers between the knot and catenane products will differ by one, and the smaller number will represent the DNA crossings present in the ‘unknown synapse’ being analyzed. The extra node is imposed by the requirement that Flp or Cre recombination sites have to be arranged in antiparallel geometry.

In the case of a system with multiple site interactions, these can be broken down into a series of pairwise interactions, and the crossings between each pair analyzed independently. They may then be summed to arrive at the composite interactions among all of the sites.

The difference topology method can also be useful in revealing the topological changes during the maturation of dynamic DNA-protein assemblies. Furthermore, in cases where identical protein monomers associate with several copies of a consensus DNA site, it can help define the interactions between individual protein subunits and their cognate sites that mould the final architecture of a DNA-protein complex.

Jason D. Kahn (University of Maryland)

Design, Analysis, and Modeling of Protein-DNA Loops
September 20, 2007

DNA looping allows protein transcription factors to act at a distance along DNA. Looping is also a test bed for theories on DNA and protein structure and flexibility. However, most natural DNA loops are not stable enough for structural studies. We have designed and constructed bent DNA molecules that form hyperstable DNA loops anchored by the Lac repressor. Biochemical and fluorescence experiments show that different loop constructs can adopt different conformations, but the shapes of the loops remain uncertain, and the landscape of loop thermodynamics as a function of DNA sequence is not well-explored. We present experimental and theoretical approaches aimed at disentangling the roles of protein and DNA flexibility in this important model system.

Alex Kasman (College of Charleston)

DNA Solitons as an Explanation for Codon Bias
December 31, 1969

This talk will begin with a brief historical introduction to solitons, a nonlinear wave phenomenon that has been of great interest to mathematics and physics since the late 1960's. Among the many mysteries in science for which a soliton model has been proposed is the question of how the transcription "bubble" moves along a DNA molecule during protein production. In particular, the work of Englander in 1980 suggested that it was actually an example of nonlinear dynamics induced by the attraction of the base pairs, taking the form of a discrete Sine-Gordon equation. More recently, inhomogeneous versions of this model have been introduced which take into account the effect of the particular DNA sequence on the dynamics.

I will argue that nonlinear dynamics could also provide an explanation for "codon bias" (the apparent preference for certain codons over others encoding the same amino acid in biological systems). Some numerical experiments will be presented to support this hypothesis, but this work is truly preliminary and it is my hope that the audience will be able to provide guidance and suggestions for the continuation of this project.

Soojeong Kim (The University of Iowa)

A Tangle Analysis of a DNA-protein Complex which Binds Four DNA Segments
December 31, 1969

In the late 80's Ernst and Sumners [1] first introduced the mathematical tangle model of DNA-protein complexes. More recently, in 2002, Pathania, Jayaram and Harshey [2] 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 [3]. They described infinitely many solutions to the same tangle equations, but argued that Pathania et al.'s model is the only biologically reasonable one. The Mu transpososome protein complex binds three DNA segments there exist protein complexes which bind more than three DNA segments. In this talk, I would like to extend some of the 3-string tangle analysis in [3] to DNA protein complex containing four DNA segments.

References: [1] C. Ernst, D. W. Sumners, A calculus for rational tangles: applications to DNA recombination, Math. Proc. Camb. Phil. Soc. 108 (1990), 489-515. [2] 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. [3] I. K. Darcy, J. Luecke, and M. Vazquez, A tangle analysis of the Mu transpososome protein complex which binds three DNA segments, Preprint.

Jörg Langowski (Deutsches Krebsforschungszentrum (Cancer Research)(DKFZ))

Nucleosome and Chromatin Structure and Dynamics Studied by Fluorescence Techniques and Computer Modeling
September 19, 2007

The higher order structure of chromatin depends crucially on the local geometry of the DNA on the nucleosome. Fluorescence resonance energy transfer (FRET) is a very convenient method to measure intramolecular distances in such large biomolecules and thereby obtain information on the DNA geometry. Varying label positions, DNA fragment length, histone modifications and buffer conditions gives valuable insight into the structure of mono- and trinucleosomes. FRET experiments under single-molecule conditions on freely diffusing nucleosomes furthermore demonstrate the resolution of structural subpopulations of nucleosomes and their interconversion.

To combine experimental data with higher-order structural models of the chromatin fiber, we developed a number of coarse-grained approaches to simulating the structure and dynamics of chromatin, ranging from single nucleosomes to the 30 nm chromatin fiber. Based on the known crystallographic structure of the nucleosome and on all- atom molecular dynamics, effective force fields are developed which allow dynamic simulations of mononucleosomes over 0.5 µs in a one- bead-per-residue approximation. For larger length and time scales, the DNA is approximated by a segmented polymer chain and the nucleosomes by rigid cylinders which interact through different salt- dependent interaction potentials. This approach allows for the prediction of possible higher-order structures and their mechanical properties. As examples, we show the unrolling of DNA from the histone core, the response of the 30 nm chromatin fiber to mechanical stretching, and possible regimes of stable and unstable packing of chromatin.

Jörg Langowski (Deutsches Krebsforschungszentrum (Cancer Research)(DKFZ))

Nucleosome and Chromatin Structure and Dynamics Studied by Fluorescence Techniques and Computer Modeling
December 31, 1969

Same abstract as the 9/19 talk.

Richard Lavery (Centre National de la Recherche Scientifique (CNRS))

DNA Mechanics: Deformation and Recognition
September 16, 2007

DNA can easily be deformed by external factors including molecular interactions and applied forces. We have used molecular modeling and simulation to investigate the structural and energetic nature of these deformations both in generic terms and, more finely, to understand their sequence dependence and therefore to decode their role in recognition processes.

Stephen D. Levene (University of Texas at Dallas)

Closing the Loop on Protein-DNA Interactions
September 17, 2007

The formation of DNA loops by proteins bound at distant sites along a single molecule is an essential mechanistic aspect of many biological processes including gene regulation, DNA replication, and recombination. The biological importance of DNA loop formation is underscored by an abundance of architectural proteins in cells such as HU, IHF, and HMGs, which facilitate looping by bending the intervening DNA between cognate protein-binding sites. We have developed a rigorous theory for DNA loop formation that connects the global mechanical and geometric properties of both DNA and protein, including previously neglected phenomena such as conformational flexibility of protein domains. Applications to problems in gene regulation and DNA recombination both in vitro and in vivo will be discussed.

David M.J. Lilley (University of Dundee)

Structure and Dynamics of the Four-way DNA Junction
September 16, 2007

Genetic recombination is important in the repair of double strand DNA breaks, the processing of stalled replication forks and in the generation of genetic diversity in evolution. During this process, two homologous DNA molecules undergo strand exchange to form a four-way DNA (Holliday) junction. The junction adopts a folded structure in the presence of divalent metal ions, generated by pairwise coaxial stacking of helical arms.

DNA junctions display rich dynamic properties including stacking conformer exchange transitions and branch migration. These processes cannot be synchronized, and so are difficult to study in bulk. Single-molecule fluorescence methods have allowed us to detect the transitions directly and to gain new insights into the energy landscape of conformer transitions and branch migration.

Electrostatic interactions are very important in the DNA junction. Folding and dynamics are strongly affected by the presence of metal ions. Conversion of a centrally-located phosphate group to an electrically-neutral methyl phosphonate group in a four-way DNA junction can exert a major influence on its conformation, allowing folding to occur in the absence of metal ions. However, the effect can be strongly dependent on stereochemistry. It is likely that the stereochemical environment of the methyl group affects the interaction with metal ions in the centre of the junction.

Four-way junctions are selectively bound by resolving enzymes; these serve as paradigms for the molecular recognition of DNA structure on a larger scale. We have recently solved the crystal structure of T7 endonuclease I bound to a DNA junction. This reveals how the geometry of the branched DNA can be recognized, while at the same time being distorted by the enzyme. The recognition process exploits the dynamic character of the junction to mould it onto the large binding surface of the protein.

D.M.J. Lilley Structures of helical junctions in nucleic acids Quart. Rev. Biophys. 33, 109-159 (2000).

S.A. McKinney, A.-C. Déclais, D.M.J. Lilley and T. Ha Structural dynamics of individual Holliday junctions Nature Struct. Biol. 10, 93-97 (2003).

J. Liu, A.-C. Déclais and D.M.J. Lilley Electrostatic interactions and the folding of the four-way DNA junction: analysis by selective methyl phosphonate substitution J. Molec. Biol. 343, 851–864 (2004).

S. A. McKinney, A. D. Freeman, D. M. J. Lilley and T. Ha Observing spontaneous branch migration of Holliday junctions one step at a time Proc. Natl. Acad. Sci. USA 102, 5715-5720 (2005).

J. Liu, A.-C. Déclais, S. McKinney, T. Ha, D.G. Norman and D.M.J. Lilley Stereospecific effects determine the structure of a four-way DNA junction Chem. & Biol. 12, 217-228 (2005).

J.M. Hadden, A.-C. Déclais, S.B. Carr, D.M.J. Lilley and S.E.V. Phillips The structural basis of Holliday junction resolution. Submitted for publication (2007).

James Maher (Mayo Clinic)

Approaches to Understanding the Origin and Management of DNA Stiffness
September 20, 2007

Duplex DNA, the genetic material in living cells, is an unusually inflexible biopolymer. The persistence length of duplex DNA corresponds to 150 base pairs under physiological conditions. Surprisingly, the physical origin of this DNA stiffness is unknown. In particular, the contribution of the high negative charge density of DNA to its stiffness remains both uncertain and controversial. The intrinsic inflexibility of DNA is managed in living cells by the formation of nucleoprotein complexes in which DNA is often dramatically bent, kinked and looped.

This presentation will review two related areas of interest to our laboratory. The first concerns approaches to measure or predict the effect of charge density on DNA stiffness. We ask to what extent DNA stiffness is due to DNA charge. The second concerns the mechanism of sequence-nonspecific proteins that stabilize highly-bent DNA structures, thereby reducing the apparent persistence length of DNA. Such proteins include the bacterial HU protein and eukaryotic HMGB proteins. We describe the results of ensemble and single-molecule experiments revealing the effect of HMGB proteins on apparent DNA stiffness. We then describe experiments in living E. coli bacterial cells emphasizing the importance of DNA flexibility enhancement by proteins to facilitate gene repression by DNA looping.

John F. Marko (Northwestern University)

Torque in Stretched and Twisted DNA
September 18, 2007

In experiments where DNA is pulled at constant force and twisted, a mixed state of extended twisted DNA and plectonemically supercoiled DNA is easily obtained. I will review the thermodynamics of this "state coexistence" phenomenon. A particularly elegant use of plectoneme-extended DNA coexistence is as a source of constant torque for single-DNA experiments. I will discuss the estimation of torques and free energies in such experiments, and I will provide some useful closed-form formulae, most notably for the torque in DNA as a function of force. I will review experiments where estimation of DNA torques allowed study of rotational friction during DNA relaxation by type IB and IC topoisomerases. I will also discuss experiments where DNA torques were directly measured rather than estimated.

Reference: J.F. Marko, Torque and dynamics of linking number relaxation in stretched supercoiled DNA, Phys. Rev. E 76, Art. 021926 (2007)

Kyle McQuisten (The University of Iowa)

Tangle Models for Recombinase Action
December 31, 1969

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.

Hyeyoung Moon (The University of Iowa)

Polynomial Invariants, Knot Distances and Topoisomerase Action
December 31, 1969

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.

Ariel Prunell (Institut Jacques Monod)

Nucleosome Dynamics Probed by Torsional Manipulation of Single Chromatin Fibers
September 18, 2007

Single chromatin fibers were reconstituted in vitro by salt dialysis from purified histone octamers and 2×18 tandem repeats of the 5S DNA positioning sequence. The fibers were flanked by naked ∼600 bp DNA spacers and ∼500 bp DNA stickers modified with digoxigenin and biotin destined to be linked respectively to the coated bottom of the flow cell and to the paramagnetic bead. This construction is then placed under the rotating magnet of a magnetic tweezers set-up to exert a torque and a pulling force on the fiber.

The fiber stretching (force-vs.-extension) and torsional (extension-vs.-rotation) behaviors were then recorded. Whereas the stretching behavior is similar to that previously observed by other authors using e. g. optical tweezers, the torsional behavior shows a bell-shaped curve with a breath much larger than obtained with naked DNA of the same length.

These curves were fitted with the worm-like rope model widely used for DNA, which represents the molecule (here the chromatin fiber) as an isotropic elastic rod of defined bending, stretching and twisting moduli. Good fittings were obtained with a fiber bending persistence length of 28 nm and a stretching modulus of 8 pN, in agreement with previous studies. In contrast, the twisting persistence length, obtained here for the fist time, was exceptionally low, ∼5 nm against ∼80 nm for DNA.

Such a fiber high torsional resilience was inconsistent with the existence of nucleosomes locked in their canonical negatively-crossed conformation. In contrast, it could be described by a molecular model of the fiber architecture in which nucleosomes are in a thermodynamic equilibrium between the three conformational states initially identified for single nucleosomes on DNA minicircles (reviewed in ref. 1), depending on the crossing statuses of entry-exit DNAs (negative, null or positive). Beyond applied torsions at which all nucleosomes are forced to cross either negatively or positively, the fiber length decreases rapidly and linearly. By analogy to the torsional behavior of DNA (ref. 2), this was attributed to the formation of plectonemes, in which nucleosomes are extruded to the outside (ref. 3).

When fibers were submitted to large positive torsions beyond their maximal compaction, the backward curves obtained upon reversing the torsion depart from the onward curves. A positive shift is observed at positive torsions which progressively disappears at negative torsions. This reversible hysteresis corresponds to the transition of the nucleosomes to a transient altered state which traps one positive turn. Comparison with the response of fibers of tetrasomes obtained through depletion of H2A-H2B dimers using NAP-1, heparin or salt led us to conclude that the transition involves three main steps : 1) a breaking of the docking of the dimers on the (H3-H4)2 tetramer; 2) a switching of the tetramer from its left-handed to the right-handed chiral conformation previously described (reviewed in ref. 4); and 3) a undetermined rearrangement of the dimers insuring that the overall compaction of the resulting “reversomes” (for reverse nucleosomes) is similar to that of the starting nucleosomes (ref. 5)

This dynamics of the nucleosomes at the level of the entry-exit DNAs, which leads to a large reorganization of the three-dimensional fiber architecture, may affect DNA binding of regulating proteins in vivo, as all tracking processes, e. g. replication and transcription, involve the generation of torsional stress. The nucleosome-reversome transition is likely to serve to relieve the almost insurmountable block against transcription by the main RNA polymerase otherwise exerted by H2A-H2B dimers in the absence of intervening factors.


1) Prunell A. & Sivolob A. (2004) . "Paradox lost : Nucleosome structure and dynamics by the DNA minicircle approach" In Chromatin structure and dynamics : state-of-the-art. (Zlatanova, J. & Leuba, S. H., eds), Elsevier Science, Amsterdam. New Comprehensive Biochemistry, 39, 45-73.

2) Strick, T. R., Allemand, J. F., Bensimon, D., Bensimon, A. and Croquette, V. (1996). The elasticity of a single supercoiled DNA molecule. Science 271, 1835-1837.

3) Bancaud A., Conde e Silva N., Barbi M., Wagner G., Allemand J.-F., Mozziconacci J., Lavelle C., Croquette V., Victor J.-M., Prunell A. & Viovy J.-L. (2006). Structural plasticity of single chromatin fibers revealed by torsional manipulation. Nat. Struct. Mol. Biol. 13, 444-450.

4) Sivolob A. & Prunell A. (2004). Nucleosome conformational flexibility and implications for chromatin dynamics. Phil. Trans. Roy. Soc. A. 362, 1519 - 1547.

5) Bancaud A., Wagner G., Conde e Silva N., Lavelle C., Wong H., Mozziconacci J., Barbi M., Sivolob A., Le Cam E., Mouawad L., Viovy J.-L., Victor J.-M. & Prunell A. (2007). Nucleosome chiral transition under positive torsional stress in single chromatin fibers. Mol. Cell 27, 135-147.

Eric J. Rawdon (University of St. Thomas)

Smallest Containers Enclosing Random Equilateral Polygons
September 16, 2007

Joint work with Akos Dobay, John C. Kern, Kenneth C. Millett, Michael Piatek, Patrick Plunkett, and Andrzej Stasiak.

We explore the shape of random polygons by measuring the average dimensions of smallest boxes, spheres, and polyhedra that enclose the polygons. We present computer simulations to examine the differences between these dimensions for polygons with constrained and unconstrained topology. For each measurement, we find that the scaling profiles for polygons of a particular knot type intersect the scaling profile for phantom polygons. The number of edges at which the profiles intersect is known as the equilibrium length with respect to the given knot type and spatial measurement. These equilbrium lengths are then compared to equilibrium lengths with respect to other spatial measurements mentioned here and computed elsewhere.

Chehrzad Shakiban (University of St. Thomas)

Signature Curves in Classifying DNA Supercoils
December 31, 1969

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.

Andrzej Stasiak (University of Lausanne)

Local Selection Rules that can Determine Specific Pathways of DNA Unknotting by Type II DNA Topoisomerases
September 17, 2007

We performed numerical simulations of DNA chains to understand how local geometry of juxtaposed segments in knotted DNA molecules can guide type II DNA topoisomerases to perform very efficient relaxation of DNA knots. We investigated how the various parameters defining the geometry of intersegmental juxtapositions at sites of intersegmental passage reactions mediated by type II DNA topoisomerases can affect the topological consequences of these reactions. We confirmed the hypothesis that by recognizing specific geometry of juxtaposed DNA segments in knotted DNA molecules type II DNA topoisomerases can maintain the steady-state knotting level below the topological equilibrium. In addition, we revealed that a preference for a particular geometry of juxtaposed segments as sites of strand passage reaction enables type II DNA topoisomerases to select the most efficient pathway of relaxation of complex DNA knots. The analysis of the best selection criteria for efficient relaxation of complex knots revealed that local structures in random configurations of a given knot type statistically behave as analogous local structures in ideal geometric configurations of the corresponding knot type.

Irwin Tobias (Rutgers, The State University Of New Jersey )

A New Twist Step-parameter Coupled to the Chirality of the Global Structure of DNA
September 16, 2007

DNA twist step-parameters are in common use in the community of structural biologists. If, for a molecule with a closed axial curve, the writhing number, a measure of the chiral distortion of the axial curve of the molecule from planarity, is added to the sum over all steps of such twists, the result has no particular significance. This is in marked contrast to the properties of the value obtained . the topological invariant, an integer called the linking number - when the same writhe is added to the total twist we obtain by using step twists defined in a way consistent with the twist associated with supercoiling. Also of interest is the difference in the values of these two step-parameters for DNA in various environments. Thus, when the DNA is relaxed, and not interacting with any proteins, we find, and understand why, the two twists for each step are close in value. On the other hand, when the DNA is interacting with a protein, with the histones in chromatin, for example, there are certain steps for which one observes significant differences. By considering various model structures, we find instances in which we are able to relate the magnitude of an observed difference in twists for a particular step to the specific nature and chirality of the structural distortion being imposed by the protein on the DNA in the region of the step.

Andrew Travers (MRC Laboratory of Molecular Biology)

Chromatin Compaction as a Topological Problem
September 20, 2007

In both bacteria and eukaryotes, maintaining DNA compaction is a sine qua non of chromatin function. At the same time accessibility to transcribing, replicating and recombining enzymes must be maintained. I will argue that these twin requirements can be viewed in the context of the overall topology of, for bacteria, the DNA itself, and of, for eukaryotes, the 30 nm chromatin fibre. In particular, the plectonemic form of supercoiled ropes, either DNA or 30 nm fibres, must, in principle, contain distinguishable structures (interwindings, apical loops, branch points, hammerheads) in contrast to a more monotonous toroid.

In exponentially growing Escherichia coli the 2-start helical interwindings of the plectonemic form of plasmid DNA are stabilised by different nucleoid-associated proteins (NAPs). Nucleation of binding of the NAP H-NS at high affinity sites results in gene silencing and plectoneme stabilisation. Plectonemes are also recognised by RNA polymerase and certain recombinases. The binding of RNA polymerase to loop structures formed at some promoters facilitates binding and for the tyrT promoter potentially locates the thermally unstable -10 hexamer adjacent to the interwindings of a negatively supercoiled plectoneme.

In eukaryotes the requirement for DNA compaction is greater than in bacteria. Whereas a simple DNA plectoneme compacts DNA by ~~2.5 fold, compaction factors of up to 10000 are required in the eukaryotic nucleus. The initial mechanism for compacting DNA is the tight wrapping of ~146 bp in a nucleosome core particle, resulting in a compaction of ~9-10-fold. In vivo these particles can be accurately positioned such that the midpoint of the bound DNA is approximately defined. We have derived from accurately mapped in vivo positions in yeast a translational positioning signal that identifies the midpoint of histone octamer-bound DNA. The minimal signature is 75% of reported and also our newly determined mapped positions in yeast. This putative positioning signal occurs on average once every ~60 bp in yeast genomic DNA sequences. From this apparent redundancy we infer that the preferred positioning of nucleosomes in an array requires an 'organiser' to select a nucleosome for nucleating an array. This organiser could be a strong intrinsic DNA positioning signal or a transcription factor. We present evidence that the DNA sequences specifying 5' proximal (-1 position) nucleosomes of several genes can, under more physiological conditions, outcompete in vitro the strong 601 positioning sequence originally selected by salt gradient dialysis in vitro.

The next stage in the compaction of eukaryotic chromatin is the folding of a nucleosome array into a '30 nm' fibre. We have calculated the dependence of the diameter and packing density of chromatin fibres on linker length and conclude that all current measurements are consistent with a model in which at short linker lengths (corresponding to a nucleosome repeat length of ~ 177 bp) the linker histone can supercoil a 2-start crossed-linker fibre into a helical-ribbon form by changing the exit and entry trajectories of DNA. As the linker length increases in increments of 10 bp (< the 10.5 bp helical repeat of DNA) at a certain point the fibre relaxes into a crossed-linker form with a higher packing density. On this model the 30 nm fibre has a variable topology but maintains a constant packing of nucleosomes.


Maurer, S., Fritz., J., Muskhelishvili, G. and Travers, A. RNA polymerase and an activator form discrete subcomplexes in a transcription initiation complex. EMBO J. 25, 3784-3790 (2006).

Travers, A. and Muskhelishvili, G. A common topology for bacterial and eukaryotic transcription initiation? EMBO Rep. 8, 147-151 (2007).

Bouffartigues, E., Buckle, M., Baudaut, C., Travers, A. and Rimsky, S. High affinity sites direct the cooperative binding of H-NS to a regulatory element required for transcriptional silencing. Nat. Struct. Mol. Biol. 14, 441-448 (2007).

Lang, B. et al. High affinity DNA binding sites for H-NS provide a molecular basis for selective silencing within proteobacterial genomes. Submitted for publication (2007). Wu, C., Bassett, A. and Travers, A. A variable topology for the '30 nm' chromatin fibre. Submitted for publication (2007).


MRC-LMB, Cambridge: M. Madan Babu, Mark Churcher, Edwige Hiriart, Benjamin Lang, Chenyi Wu DAMTP, University of Cambridge: Graeme Mitchison ENS, Cachan: Cyril Baudaut, Emeline Bouffartigues, Malcolm Buckle, Sylvie Rimsky Università di Roma "La Sapienza": Eleonora Agricola, Micaela Caserta, Ernesto Di Mauro, Leonora Verdone Università di Camerino: Claudio Gualerzi, Cynthia Pon, Stefano Stella Jacobs University, Bremen: Claudia Burau, Nicolas Blot, Jurgen Fritz, Marcel Geertz, Sebastian Maurer, Ramesh Mavathur, Georgi Muskhelishvili

Lawrence Varela (San Francisco State University)

Developing Computer Software for Detecting Fluorescent Chromosome Labels
December 31, 1969

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.

Mariel Vazquez (San Francisco State University)

The Mathematics of Site-specific Recombination: 1. Difference Topology Experiments and the Mu Tranpososome; 2. DNA Unlinking by XerCD/FtsK
September 21, 2007

DNA topology is the study of geometrical (supercoiling) and topological (knotting) properties of DNA loops and circular DNA molecules. Multiple cellular processes, such as DNA replication and transcription, affect the topology of DNA. Controlling these changes is key to ensuring stability inside the cell. Changes in DNA topology are mediated by enzymes such as topoisomerases and site-specific recombinases. We have successfully used techniques from knot theory and low-dimensional topology, aided by computational tools, to analyze the action of site-specific recombinases. I will introduce the tangle model and report on two recent analyses:

1. Based on the difference topology experimental results of Pathania, Jayaram, and Harshey (Cell, 2002), we solve 3-string tangle equations to understand the topological structure of DNA within the Mu transpososome. Pathania et al. (2002) proposed one 3-string tangle model for the Mu transpososome. We describe other families of solutions to the same tangle equations and we argue that the model given by Pathania et al. (2000) is the only biologically reasonable one.

2. The FtsK-XerCD system has been to successfully unlink complicated DNA catenanes produced by lambda Int and by DNA replication. We use tangles to argue that a stepwise unlinking by multiple recombination steps is the only plausible mechanism of action.

Alexander Vologodskii (New York University)

Breaking DNA Double Helix by Bending Stress
September 17, 2007

DNA double helix should experience local breaks under sufficient bending or/and unwinding torsional stress. Local distortions of DNA under negative torsional stress have been studied in details, but until now very little has been known about distortions by bending stress. We addressed this question in the current study by probing the structure of very small DNA circles. First, we developed an efficient method to obtain covalently closed DNA minicircles. To detect breaks of regular DNA structure in these minicircles we treated them by single strand-specific endonucleases. This method has been widely used to study local conformational changes in supercoiled plasmids for many years. We showed, in agreement with the previous data obtained on plasmid DNA, that sufficient torsional stress introduces DNA breaks in the minicircles. Choosing the experimental conditions where the influence of torsional stressed was minimized, we found that the double helix is broken by bending deformation in the minicircles of 64-65 bp, but not in the 85-86 bp minicircles. Our data suggest that two different single strand-specific endonucleases, used in the study, have different sensitivity to the breaks created by bending and torsional deformations. We speculate, using this observation, that torsional stress creates open regions in the double helix while strong DNA bending initiates formation of kinks, which preserves the base pairing.

Annika Wedemeier (German Cancer Research Center)

Modelling Diffusional Transport in the Interphase Cell Nucleus
December 31, 1969

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.

Guowei Wei (Michigan State University)

Geometric Flows on Biological Surfaces
December 31, 1969

Same abstract as the 9/19 talk.

Guowei Wei (Michigan State University)

Geometric Glows on Biological Surfaces
September 19, 2007

Joint work with Peter Bates and Shan Zhao.

We introduce a novel concept, the minimal molecular surface (MMS), as a new paradigm for the theoretical modeling of biomolecule-solvent interfaces. When a less polar macromolecule is immersed in a polar environment, the surface free energy minimization occurs naturally to stabilizes the system, and leads to an MMS separating the macromolecule from the solvent. For a given set of atomic constraints (as obstacles), the MMS is defined as one whose mean curvature vanishes away from the obstacles. Mean curvature flows are proposed to compute the MMS. Extensive examples are given to validate the proposed algorithm and illustrate the new concept. We show that the MMS provides an indication to DNA-binding specificity. The use of more general geometric flows, including flows driven by both intrinsic geometric forces and external forces, will also be discussed for biological modeling. We show that the proposed MMS is a special case of family of singularity free biomolecular surfaces.

Shimon Weiss (University of California, Los Angeles)

Single Molecule Probing of Dynamic Conformation, Molecular Interactions and Dynamic Localizations In-vitro, in Live Cells and in Organisms
September 19, 2007

We applied single molecule spectroscopy using alternating laser excitation (ALEX) to the study of transcription initiation by e-coli RNA polymerase. We find that the transcription factor sigma70 is not obligatorily released in the transition from initiation to elongation and that the mechanism for abortive initiation is governed by DNA scrunching.

We also applied ALEX spectroscopy to the study the polymer properties of single-stranded DNA and double-stranded DNA, and to protein folding. We find that the collapsed state of protein L is not driven by native contacts, and we show that Acyl-CoA binding protein (ACBP) has a residual structure in the denatured state. Lastly, we demonstrate the use of peptide-coated quantum dots for the study of lipid rafts in live cells' membranes and for molecular imaging in living cells and small organisms.

Jonathan Widom (Northwestern University)

The Genomic Code for Nucleosome Positioning
September 18, 2007

Eukaryotic genomes are packaged into nucleosome particles that occlude the DNA from interacting with most DNA binding proteins. Nucleosomes are remarkable from a physical perspective because in each nucleosome, one persistence length of DNA – a lengthscale of DNA inflexibility – is wrapped in nearly two complete superhelical turns around a protein core. As a consequence of this extreme DNA bending, nucleosomes have higher affinity for particular DNA sequences that are best-able to sharply bend as required by the nucleosome. We discovered that genomes care where their nucleosomes are located on average, and that genomes manifest this care by encoding an additional layer of genetic information, superimposed on top of other kinds of regulatory and coding information that were previously recognized. We have developed a partial ability to read this nucleosome positioning code and predict the in vivo locations of nucleosomes. Our results suggest that genomes utilize the nucleosome positioning code to facilitate specific chromosome functions including to delineate functional versus nonfunctional binding sites for key gene regulatory proteins, and to define the next higher level of chromosome structure itself.

Lynn Zechiedrich (Baylor College of Medicine)

Supercoiled Minicircle DNA to Probe Topoisomerase-DNA Interactions
September 16, 2007

Joint work with Jonathan M. Fogg, Daniel J. Catanese, Jr., Department of Molecular Virology & Microbiology, Baylor College of Medicine, Houston, TX USA.

DNA topoisomerases are essential enzymes that impact nearly every aspect of DNA metabolism by transiently breaking and passing DNA. Studies of topoisomerases, indeed any protein that acts on DNA, have been severely limited by the lack of experimentally tractable supercoiled DNA. We developed a method to produce milligram quantities of DNA minicircles (

Guohui Zheng (Rutgers, The State University Of New Jersey )

A DNA Base-pair Step Parameter Database
December 31, 1969

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 [1], across multiple DNA-containing structures deposited in the Nucleic Acid Database (NDB) [2]. 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

Victor B. Zhurkin (National Cancer Institute)

A Novel 'Kink-and-Slide' Mechanism of DNA Folding in Chromatin. Implications for Nucleosome Positioning and p53-DNA Binding
September 18, 2007

Despite 30 years of effort, it is still unclear how DNA sequence contributes to the known positioning of nucleosomes. Currently, there is a wide gap between the experimental characterization of positioned nucleosomes in solution and the interpretation of the known high-resolution X-ray structures of nucleosomal DNA. This gap in understanding stems, in our opinion, from the traditional use of a simplified elastic-rod model, in which only the DNA bending and twisting deformations are considered, and the effects of the shearing displacements of adjacent base pairs are neglected. In collaboration with Wilma Olson [1], we have demonstrated that these displacements play a much more important structural role than ever imagined.

First, the lateral Slide deformations observed at sites of local anisotropic bending of DNA define its superhelical trajectory in chromatin. (Note that the nucleosomal DNA twisting remains close, on average, to that in solution [2]. In other words, the 'real' DNA wrapping around the histone core is inconsistent with the conventional model of superhelical DNA, which links changes in superhelical pitch to DNA twisting.) Second, the computed cost of deforming DNA on the nucleosome is sequence specific: in optimally positioned sequences the most easily deformed base-pair steps (CA:TG and TA) occur at sites of large positive Slide and negative Roll (where the DNA bends, or kinks, into the minor groove). Here, we incorporate all the degrees of freedom of 'real' DNA, thereby going beyond the limits of the conventional model - the latter ignores the lateral Slide displacements of base pairs, and as a result, fails to account for the preferable positioning of the TA steps. Indeed, only after lateral Slide displacements are considered, are we able to account for the sequence-specific positioning of nucleosomes in vitro.

In addition to DNA folding in nucleosomes, the shearing deformations are implicated in the sequence-specific recognition of DNA by transcription factors, such as the tumor suppressor protein p53. The DNA bending, twisting and sliding observed in solution upon p53 binding [3] are entirely consistent with the 'Kink-and-Slide' conformation described above. Therefore, structural organization of a p53 binding site in chromatin can regulate its affinity to p53 - for example, exposure of the DNA site on nucleosomal surface (in appropriate orientation) would facilitate the p53 binding. We illustrate the functional importance of this concept by comparing the chromatin organization of two classes of p53 response elements: the high affinity p53 sites inducing cell cycle arrest, and the low affinity sites associated with apoptosis.

Our results indicate that there is a complex interplay between the structural codes encrypted in eukaryotic genomes - one code for DNA packaging in chromatin, and the other code for DNA recognition by regulatory proteins. Rather than being mutually exclusive (as was assumed earlier), the two codes appear to be consistent with each other. At least in some cases, such as p53, the DNA wrapping in nucleosomes can facilitate binding of the transcription factor to its cognate sequence, provided that the latter is properly exposed in chromatin.

[1] Tolstorukov M.Y., Colasanti A.V., McCandlish D., Olson W.K. and Zhurkin V.B. A Novel 'Roll-and-Slide' Mechanism of DNA Folding in Chromatin. Implications for Nucleosome Positioning. J. Mol. Biol. 2007, 371(3): 725-38.

[2] Richmond T.J. and Davey C.A. The structure of DNA in the nucleosome core. Nature 423, 145-150, 2003

[3] Nagaich A.K., Zhurkin V.B., Durell S.R., Jernigan R.L., Appella E. and Harrington R.E. p53-induced DNA bending and twisting: p53 tetramer binds on the outer side of a DNA loop and increases DNA twisting. Proc. Natl. Acad. Sci. USA 96: 1875-1880, 1999.

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