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Timetable (TODW02)

Topological Aspects of DNA Function and Protein Folding

Monday 3rd September 2012 to Friday 7th September 2012

Monday 3rd September 2012
08:30 to 09:00 Registration
09:00 to 09:10 Welcome from John Toland INI 1
09:10 to 09:50 Chromatin Compaction: A Modeling Exploration of Fiber Hetergeoneity and Linker Histone Influence INI 1
09:50 to 10:10 Morning Coffee
10:10 to 10:50 The topological equivalence of the yeast chromosome centromere and the yeast plasmid partitioning locus
Centromeres are the DNA loci responsible for the faithful partitioning of eukaryotic chromosomes. The elaborate protein assembly, called the kinetochore complex, organized at the centromere is responsible for attaching sister chromosomes to the mitotic spindle, thus ensuring their equal segregation during cell division. Centromeres in nearly all eukaryotes are ‘regional’ centromeres- long DNA segments with no consensus sequence elements- that are established epigenetically. Members of the budding yeast lineage are a stark exception. Their chromosomes harbor ‘point’ centromeres- very short centromeres with three well defined sequence elements- that are genetically determined. The yeast centromere chromatin engenders a positive supercoil, presumably due to a nucleosome containing a variant of the histone H3. Yeast harbors a selfish plasmid whose stability is comparable to that of the chromosomes of its host. The plasmid achieves this fidelity of segregation with the help of two partitioning proteins and a partitioning locus called STB (for stability). Strikingly, the chromatin at STB is also positively supercoiled. When STB function is inactivated, its topology shifts to standard negative supercoiling. The magnitudes of the CEN and STB induced positive supercoiling are comparable. The topological equivalence of CEN and STB, along with other functional similarities between the two, are consistent with the notion that the non-standard point centromere had its origin in the partitioning locus of an ancestral plasmid.
10:50 to 11:30 How the genome folds
I describe Hi-C, a novel technology for probing the three-dimensional architecture of whole genomes. Developed together with collaborators at the Broad Institute and UMass Medical School, Hi-C couples proximity-dependent DNA ligation and massively parallel sequencing.

Our lab employs Hi-C to construct spatial proximity maps of the human genome. Using Hi-C, it is possible to confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes. Hi-C maps also reveal an additional level of genome organization that is characterized by the spatial segregation of open and closed chromatin to form two genome-wide compartments. At the megabase scale, the conformation of chromatin is consistent with a fractal globule, a knot-free conformation that enables maximally dense packing while preserving the ability to easily fold and unfold any genomic locus. The fractal globule is distinct from the more commonly used globular equilibrium model. Our results demonstrate the power of Hi-C to map the dynamic conformations of whole genomes.
11:30 to 12:10 L Mirny ([Massachusetts Institute of Technology, USA])
The role of topological constraints on condensed polymers and DNA in human cells
Human DNA is two meters long and is folded into a structure that fits in a cell nucleus of just 5 microns in diameter. Recently developed Hi-C technique provides comprehensive information about genome folding. Our analysis of Hi-C data provides and biophysical polymer modeling show that scaling observed in the data is consistent with non-equilibrium and unknotted polymer state – the crumpled (fractal) globule. We demonstrate that the fractal globule emerges as a result of polymer collapse and has a short lifetime, rapidly mixing while remaining largely unknotted. Long-time dynamics of a condensed polymer reveals that spatial and topological equilibration happen at vastly different time scales and that topological constrains have little effect on relatively short and flexible chains.
12:30 to 13:30 Lunch at Wolfson Court INI 1
13:30 to 14:10 Large scale organization of chromatin
In the cell nucleus chromosomes have a complex architecture serving vital functional purposes. One of the current key open problem concerns the principles which orchestrate their 3D structure. We discuss a model of the molecular mechanisms of chromatin self- organization which we compare against available FISH and Hi-C data.
14:10 to 14:50 S Levene ([University of Texas at Dallas, USA])
All Good Things Must Bend: the Energetics of DNA Shape and Flexibility in Biological Assemblies
DNA-loop formation is an essential mechanistic aspect of many biological processes including gene regulation, DNA replication, and recombination. These loops are mediated by proteins bound at specific sites along the contour of a single DNA molecule and are closely coupled to the topological state of DNA domains through supercoiling, knotting, and linking. The complex interplay between DNA topology and the regulation of DNA transactions remains poorly understood and the effects of a chromatin environment on such interactions are essentially unknown. However, new insights can come from novel experimental approaches and computational models of DNA flexibility and folding under geometric and/or topological constraints. Experimental studies of Cre-loxP recombination and lac-repressor-mediated gene regulation will be used to illustrate the problems and general principles of complex nucleoprotein organization. A new method for directly computing the thermodynamic (i.e., free-energy) cost for mesoscopic models of nucleoprotein assemblies will also be discussed.
14:50 to 15:20 Afternoon Tea and Poster Session
15:20 to 15:40 Structure meets function at the mouse X chromosome inactivation center
Characterizing the folding principles of mammalian chromosomes is of capital importance to understand the complexity of gene expression regulation, particularly during the major transcriptional changes occurring in development. This may help elucidating the mechanisms by which regulatory elements contact gene promoters (i.e. by looping out intervening DNA), understand what is the cell-to-cell variability of these interactions and how it does reflect transcriptional variability. We analyzed a 4.5 Mb region of the X chromosome that includes the X-inactivation center by Chromatin Conformation Capture Carbon-Copy (5C), in order to gain insights into how chromatin structure is organized during early mouse embryonic stem cell (ESC) differentiation. We uncovered that chromatin is organized into Topologically Associating Domains (TADs), within which genomic elements preferentially interact. To fully reconstruct the statistical repertoire of chromatin conformations that give rise to these domains, we have used a combination of Monte Carlo simulations of a polymer model, high-resolution DNA FISH and quantitative RNA FISH. We show that in the TAD that contains the Tsix ncRNA (a master regulator of X-chromosome inactivation), enhancer-promoter contacts take place in a subset of cells where the whole domain is compacted, rather than resulting from stable DNA loops. In these cells, the probability of transcribing a gene is higher than in cells where the domain is in an elongated conformation. We thus show a correlation between the spatial proximity of a promoter and an enhancer and their transcriptional activity at the single cell level.
15:40 to 16:00 F Maggioni ([University of Bergamo, Italy])
Modeling chromatin fibre folding for human embryonic stem cells and cancer cells
All diverse cell types in an organism essentially have an identical genome. Generation of tissue specific cells is through an epigenomic process in which progressive alterations in the chromatin state generates lineage committed cells from pluripotent embryonic stem cells. Ultimately, establishment of terminally differentiated cells results in a stable chromatin state. Chromatin modification can be studied by chromatin immunoprecipitation (ChIP) that identifies regions that are over-represented as transcriptionally active sequences. In this talk we describe chromatin-state maps for pluripotent, cancer and lineagecommitted cells using three-dimensional modelling of fibre conformation. The model takes into account of the local structure of chromatin organised into euchromatin (open chromatin), permissive for gene activation, and heterochromatin (closed chromatin), transcriptionally silenced. Open chromatin is assumed to be modelled by a linker DNA while the closed chromatin by means of a solenoid structure in which DNA winds onto six nucleosome spools per turn with two left-handed superhelical turns around an histone octamer. The model represents a single gyre of a solenoid by means of a torus knot that winds around a torus once in the longitudinal direction and twelve in the meridian direction. Closed and open chromatin is then connected by means of piecewise polynomial transformations based on cubic Hermite spline functions. As reprogramming process is associated both with pluripotency and the neoplastic process, our analyses potentially identify cancer-related epigenetic abnormalities. Chromatin fibre conformation are compared in terms of geometric quantities such as curvature and torsion localization, and relative rates, in relation to filament compaction and packing efficiency. This study provides information on relationships between geometry and the transcriptional regulation in stem cells and cancer cells contributing to pluripotency and self-renewal.
16:00 to 16:20 A Rosa ([SISSA, Trieste, Italy])
Three-dimensional conformations of entangled ring polymers in solution
The physical properties of semi-dilute and dense polymer solutions are dominated by the topological, mutual constraints (the so-called "entanglements") between the chains. For linear chains, entanglements effects are captured by the Edwards-DeGennes reptation model [Doi & Edwards, "The Theory of Polymer Dynamics"; DeGennes, J. Chem. Phys. (1971)]. Within this model, single-chain diffusive behavior proceeds as it was effectively constrained to an almost one-dimensional path along its contour length. The model received experimental validation and it is nowadays accepted. Conversely, a consistent physical picture for unlinked, circular (ring) polymers is still lacking. One obvious way of tackling the problem is by resorting to computer simulations (Monte-Carlo or Molecular Dynamics) of coarse-grained polymer models, which however present the major difficulty of waiting over very long equilibration times when dealing with very long chains. Here, we present preliminary results concerning an alternative, possible way of attacking the problem: we construct "by hand" putative, equilibrated states for entangled ring polymers, by using a restricted ensemble of physical parameters which are calibrated on solutions of small ring polymers which equilibrate fast. Then, we use this model to "predict" chain behavior for much larger ring polymers.
16:20 to 17:00 N Kleckner ([Harvard University, USA])
How E.coli organizes and segregates its chromosome
Live cell imaging of the E.coli nucleoid, illuminated with HupA-mCherry, reveals a well-defined helical ellipsoid that is trapped within the cell radially but not longitudinally. Basic elliposidal shape results from longitudinal density bundling while helicity results from interactions between these bundles and the cell periphery. Unexpectedly, the nucleoid exhibits two distinct types of cyclic dynamic changes, both independent of DNA replication: (1) On time scales of seconds-to-minutes, longitudinal density waves flux through the shape over distances comparable to the length of the nucleoid, resulting in dynamic shape changes. (2) At intervals of ~20min, the nucleoid exhibits ~10min pulses of chromosome elongation. These pulses, which are implemented by elongation-biased density waves, are temporally and functionally linked to step-wise separation of sister chromosomes. The presented findings support a two-component model for sister segregation and the existence of nucleoid stress cycles which, we propose, function to release the nucleoid from linkages that constrain both morphogenetic evolution and separation of sisters. These cycles could comprise a primordial cell cycle, and the same principles could pertain broadly across evolutionary space and time.
17:00 to 18:00 Drinks Reception and Poster Session
18:00 to 18:30 Dinner at Wolfson Court
Tuesday 4th September 2012
08:30 to 09:10 A tangled problem: the structure,function and folding of knotted proteins
Since 2000, when they were first identified by Willie Taylor, the number of knotted proteins within the pdb has increased and there are now nearly 300 such structures. The polypeptide chain of these proteins forms a topologically knotted structure. There are now examples of proteins which form simple 31 trefoil knots, 41, 52 Gordian knots and 61 Stevedore knots. Knotted proteins represent a significant challenge to both the experimental and computational protein folding communities. When and how the polypeptide chain knots during the folding of the protein poses an additional complexity to the folding landscape. We have been studying the structure, folding and function of two types of knotted proteins – the 31-trefoil knotted methyltransferases and 52-knotted ubiquitin C-terminal hydrolases. The first part of the talk will focus on our folding studies on knotted trefoil methyltransferases and will include our work on (i) equilibrium unfolding experiments in chemical denaturants, (ii) kinetic analysis of unfolding/folding pathways, (iii) protein engineering on both the small scale (single point mutants) and large scale (creating N- and C-terminal fusions with a stable beta-grasp domain which are the deepest knotted structures known), (iv) circularisation experiments which establish that the polypeptide chain remains knotted even in the chemically denatured state, and (v) recent in vitro translation work which shows that knotting is rate limiting and also shows how GroEL/GroES play a role in the folding of these proteins in vivo. The second part of the talk will focus on our studies of knotted ubiquitin C-terminal hydrolases – UCH-L1 and UCH-L3. This will include equilibrium and kinetic unfolding and folding studies as well as recent work on the effect of point mutants associated with Parkinson’s Disease on the structure, folding and dynamics of UCH-L1. Recent work on the effect of oxidative damage on the structure of UCH-L1 will also be described and evidence that this protein adopts a partially unfolded form (PUF) on modification with the reactive aldehyde and by-product of cellular oxidative stress, HNE, will be presented. The possible cellular effects of this PUF will be discussed.
09:10 to 09:50 Knotted and unknotted proteins: a comparative study (*)
Knotted proteins, because of their ability to fold reversibly in the same topologically entangled conformation, are the object of an increasing number of experimental and theoretical studies. The aim of the present investigation is to assess, on the basis of presently available structural data, the extent to which knotted proteins are isolated instances in sequence or structure space, and to use comparative schemes to understand whether specific protein segments can be associated to the occurrence of a knot in the native state. A significant sequence homology is found among a sizeable group of knotted and unknotted proteins. In this family, knotted members occupy a primary sub-branch of the phylogenetic tree and differ from unknotted ones only by additional loop segments. These "knot-promoting" loops, whose virtual bridging eliminates the knot, are found in various types of knotted proteins. Valuable insight into how knots form, or are encoded, in proteins could be obtained by targeting these regions in future computational or excision experiments. Results of recent related simulations will be presented.

(*) in collaboration with R. Potestio (MPI Mainz) and H. Orland (CEA Saclay); ref: R. Potestio et al. Plos Comp. Biol. 6, e1000864 (2010),
09:50 to 10:10 Morning Coffee
10:10 to 10:50 M Cieplak ([Polish Academy of Sciences, Warsaw])
Topological features in stretching of proteins
10:50 to 11:30 Conservation of complex knotting and slipknotting patterns in proteins
While analyzing all available protein structures for the presence of knots and slipknots we detected a strict conservation of complex knotting patterns within and between several protein families despite their large sequence divergence. Since protein folding pathways leading to knotted native protein structures are slower and less efficient than those leading to unknotted proteins with similar size and sequence, the strict conservation of the knotting pattern indicates an important physiological role of knots and slipknots in these proteins. Although little is known about the functional role of knots, recent studies have demonstrated a protein-stabilizing ability of knots and slipknots. Some of the conserved knotting patterns occur in proteins forming transmembrane channels where the slipknot loop seems to strap together the transmembrane helices forming the channel. This is joint work with Ken Millett, Andrzej Stasiak and Jose Onuchic.
11:30 to 11:50 Amino acid patterns for protein folding
Understanding protein sequence-structure relationship is a key to solving many problems of molecular biology, such as annotation of genome sequences, protein structure prediction, protein-protein interaction, and protein evolution, among others. These problems are convenient to consider on the level of super-secondary structures, which define arrangement of strands and helices in 3D structures. In this presentation, first, the strict rule which describe how structure elements - beta-strands come together into super-secondary structures of sandwich-like proteins will be presented. Then the main sequence regularities (a specific set of residues at particular positions), which dictate the folding of amino acid sequence will be described. Residues at certain positions constitute the characteristic residue pattern of specific super-secondary structures. The pattern can be viewed as an amino acid 'tag' that brands a sequence as having a particular super-secondary structure.


Alexander Kister and Israel Gelfand, (2009) PNAS, 106, 18996-19000 Alexander Kister (2012) in "Protein super-secondary structures" Ed. A. Kister in "Methods in Molecular Biology' series Humana Press (in press)
11:50 to 12:10 P Szymczak ([University of Warsaw, Poland])
How to untie it-translocation of a knotted protein through a pore
Proteins need to be unfolded when translocated through the pores in mitochondrial and other cellular membranes. Knotted proteins, however, might get stuck during this process since the diameter of the pore is smaller than the size of maximally tightened knot. We report the result of computer simulations of knotted protein translocation, which show how the protein can avoid the topological traps and untie its knot during the translocation
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:10 Computer simulations of knotted DNA and proteins
When mature bacteriophages such as P2 or P4 are assembled in infected cells, a long linear DNA molecule is loaded into the phage capsid and arranges itself in a toroidal, nematic phase. Intriguingly, experiments show that the DNA is not only highly knotted, but also exhibits a rather uncommon knot spectrum. Observation that DNA molecules in bacteriophage capsids preferentially form torus knots provide a sensitive gauge to evaluate various models of DNA arrangement in phage heads. We demonstrate with computer simulations of a simple bead-spring model that an increasing chain stiffness not only leads to nematic ordering and a (somewhat counter-intuitive) increase of knottedness, it is also the decisive factor in promoting formation of DNA torus knots in phage capsids. In the second part of my presentation I will review recent and not so recent advances in the understanding and modelling of protein knots.
14:10 to 14:50 Knots confined to tubes in the simple cubic lattice
Here a polymer is modeled as a self-avoiding polygon in the simple cubic lattice. All knots can be confined to a slab, which is an area bounded by two parallel planes. However not all knots can be constructed in a tube, which is an area bounded by two pairs of parallel planes.

In this talk, we discuss knots and links in a tube and estimate the minimum length required for such a polygon to realize a knot type.
14:50 to 15:20 Afternoon Tea and Poster Session
15:20 to 15:40 Simulations of cyclic and linear DNA chains moderately and strongly confined in nanochannels
Structural properties of flexible and semiflexible cyclic and linear chains confined in nanochannels were studied by molecular simulations mimicking single molecule experiments in microfuidic channels used to analyze genomic macromolecules. Experiments (1) with linear and ring macromolecules showed differences in the response to confinement. Simulations of rings (comprising few persistence lengths per chain, as in plasmid rings (2)) and their linear analogs confirmed these trends (3). The radius of gyration Rg of chains satisfactorily represents the stretching of both chain topologies along the channel. Apart from focus on moderate confinement we show that strong confinement applies also for semiflexible rings, though unanticipated for rings in contrast to linear chains where it is known as Odijk regime. Similar response of chain elongation to the confinement Rg(D) is obtained in the case of rings compared to linear chains. However, the relative chain extension in channel is larger for rings, the strong confinement regime extends to larger channel diameters D and under moderate confinement the extension declines less steeply for rings. These findings are explained (3) in terms of a strong self-avoidance of confined rings relative to their linear analogs, stemming from the increased local density in channel due to looping of cycle. The extension of rings is governed by the same analytical function as for linear chain provided half of the contour length for a cyclic chain is considered at full extension. Orientation correlation function and static structure factor for both topologies point out features responsible for recognition of ring architecture.

(1) F. Persson, P. Utko,W. Reisner, N.B. Larsen, A. Kristensen, Nano Lett. 9, 1382-1385, 2009, (2) P. Cifra, Z. Benková, Macrom. Theory & Simul., 20, 65-74, 2011, (3) Z. Benková, P. Cifra, Macomolecules, 45, 2597-2608, 2012
15:40 to 16:00 Diffusion dynamics of circular DNA mini-rings in solution
In gel electrophoresis it was observed in Ref. [1] that underwound DNA mini-rings migrate slower than overwound DNA mini-rings in EDTA solution. Motivated with the novel observation we have evaluated the diffusion constant of a closed ladder-shaped polymer in solution via Brownian dynamics with hydrodynamic interaction. It gives a model of a supercoiled DNA mini-ring consisting of DNA double strands. Here, the topology of the whole molecule such as the linking number (Lk) of the double DNA strands is conserved in time. By introducing the bending rigidity, we have found that the diffusion constant of a ladder-shaped molecule with base flipping becomes smaller and much more dependent on the linking number, Lk [2]. We thus suggest that the numerical observations should explain the different migration sppeds between the underwound and overwound DNA mini-rings. Here we also recall an interesting observation that for knotted DNAs the migration speeds in gel are proportional to th e diffusion constants in a good solvent.

[1] J.M. Fogg, D.J. Catanese, Jr., G.L. Randall, M.C. Swick, and L. Zechiedrich, Proc. Institute Math. App. Vol. 150 (2009), 73-121. [2] N. Kanaeda, T. Deguchi and L. Zechiedrich, Bussei-Kenkyu Vol. 92 (2009) pp. 145-146.
16:00 to 16:20 Influence of topology in coarse-graining of polymer solutions
We employ computer simulations and integral equation theory techniques to perform coarse-graining of self-avoiding ring polymers with different knotedness and to derive effective interaction potentials [1] between the centers of mass (CM) of these macromolecular entities. Different microscopic models for the monomer-monomer interactions and bonding are employed, bringing about an insensitivity of the effective interactions on the microscopic details and a convergence to a universal form for sufficiently long molecules. The pair effective interactions are shown to be accurate up to within the semidilute regime with additional, many-body forces becoming increasingly important as the polymer concentration grows. The dramatic effects of topological constraints in the form of interaction potentials (see figure) are going to be brought forward and critically discussed [2].

We will also show the big impact of topology on the size scaling of a polymer chain in good/poor solvent conditions. This is accomplished calculating the theta temperature for specific topologies and sizes, of a single chain with two complementary methods: scaling law for radius of gyration [3,4] and second virial coefficient calculation [5]. In addition, we investigate the dependence of shape parameters with topology in good/poor solvent conditions.

[1] C. N. Likos, Physics Reports 348(4-5): 267 (2001)

[2] A. Narros, A. J. Moreno, and C. N. Likos, Soft Matter 9(11):2435 (2010)

[3] M. O. Steinhauser, J. Chem. Phys. 122:094901 (2005)

[3] S. S. Jang, Tahir Ça¡gin and W. A. Goddard, J. Chem. Phys. 119:1843 (2005)

[5] V. Krakoviak, J. P. Hansen and A. A. Louis, Phys. Rev. E 67:041801 (2003)
16:20 to 17:00 Locating knots and slipknots in open and closed macromolecules
Once it was imagined that proteins could be knotted, it was necessary to find procedures to identify the presence and precise location of knots and, later, slipknots in both open and closed macromolecules. While some of the initially proposed strategies were largely effective they often depended upon choices that gave rise to problems. In addition to a review of the historical development of these methods, we will review methods developed in collaboration with Akos Dobay, Andrzej Stasiak, Ben Sheldon and, later, with Rawdon in connection with work with Joanna Sułkowska and Jose Onuchic on protein structures. The relationship of this approach with that of other contemporay researcher will be described.
17:00 to 17:40 E Rawdon ([University of St Thomas, Minnesota, USA])
Knotting of open chains, closed chains and proteins
Some proteins are now classified as being knotted. However, proteins have free ends and knotting, mathematically, is only defined for closed curves. Defining knotting in open chains is tricky and ambiguous. We will show one definition of open knotting and search for knotted arcs within knotted open, closed chains, and proteins. This is joint work with Ken Millett, Andrzej Stasiak, and Joanna Sulkowska.
18:00 to 18:30 Dinner at Wolfson Court
Wednesday 5th September 2012
08:30 to 09:10 Superhelically Driven Structural Transitions in Genomic DNA - Theoretical Analyses, Genomic Distributions and Roles in Regulation
DNA is known to be a highly polymorphic molecule, capable of assuming several alternate conformations in addition to the standard Watson-Crick B-form. These include states of strand separation, left handed helices, cruciforms, and three- and four-stranded structures. Although the B-form is its default conformation in vivo, regions within genomic DNA can be driven into alternate structures by the superhelicity imposed on the molecule by enzymatic activities and by transcription. This talk will present theoretical analyzes of several types of transitions, and of competitions among them. The predicted genomic distributions of locations susceptible to different types of superhelical transitions will be shown, and their statistical significances will be assessed. Several situations will be described where transitions to alternate structures serve biological roles in either normal or pathological processes.
09:10 to 09:50 Co-operative roles for DNA supercoiling and nucleoid-associated proteins in the regulation of bacterial transcription
DNA supercoiling and nucleoid-associated proteins (NAPs) contribute to the regulation of transcription of many bacterial genes. The horizontally-acquired Salmonella pathogenicity island (SPI) genes respond positively to DNA relaxation, to the Fis and H-NS nucleoid-associated proteins and to the OmpR global regulatory protein. The ompR gene is autoregulated and responds positively to DNA relaxation. Binding of the Fis and OmpR proteins to DNA in the SPI-1 and SPI-2 islands and at the ompR gene promoter is differentially sensitive to the topological state of the DNA while H-NS binds regardless of the topological state of the DNA. These data illustrate the overlapping and complex nature of NAP and DNA topological contributions to transcription control in bacteria. They also show that these properties are shared by the core and the horizontally-acquired components of the bacterial genome.
09:50 to 10:10 Morning Coffee
10:10 to 10:50 Chromosomes as topological machines-the role of DNA thermodynamics
The chirality of the DNA molecule underpins its ability to partition superhelicity between twist and writhe. We argue that manipulation of superhelical density and of partitioning by topological devices and processive ATP-dependent motors (DNA and RNA polymerases and topoisomerases) is a fundamental property of both bacterial and eukaryotic chromosomes. On this view chromosomes act as machines in which topological transitions operate at several functional levels - local (e.g. transcription initiation sites), regional (constrained superhelical domains) and global (chromosomes) levels.

The partition between twist and writhe is dependent in part on the sequence of DNA. We have shown that in the E. coli chromosome gradients of DNA gyrase binding sites from the origin to the terminus of DNA replication along both replichores correlate with temporal patterns of gene expression during the growth cycle such that genes expressed during exponential growth are preferentially located in the Ori-proximal region. These observations imply that during exponential growth there exist gradients of superhelical density from the origin to the terminus. Intriguingly the chromosomal DNA sequences exhibit, on average, a gradient of DNA stacking energy in the same direction. We argue that this gradient in the physicochemical properties of DNA integrates the functional response to changes in superhelical density and to regulation by abundant nucleoid-associated proteins.

We further show that the genetic and chromatin organisation in yeast chromatin assembled both in vitro and in vivo is highly dependent on, the stacking/melting energies of DNA sequences. The regions of chromosomes that are sites for topological manipulation (such as transcription and replication initiation sites and preferred sites for topoisomerase II) correlate strongly with low stacking energies and high flexibility. Such regions concomitantly exhibit low nucleosome occupancy. We conclude that the most flexible DNA sequences are, counter-intuitively, poor substrates for octamer deposition. In contrast high nucleosome occupancy correlates with DNA sequences of moderately high stacking energies. In such relatively stiff sequences positioned nucleosomes can often be related to a bending anisotropy appropriate for nucleosome formation.
10:50 to 11:30 How DNA topology and DNA length affect the body's defense against nucleic acids of invading organisms in the blood
It has long been known that human blood contains enzymes that digest DNA to protect the body against invasion by foreign organisms. We set out to determine how DNA length and supercoiling affected DNA vector survival in human serum. Closed circular, supercoiled vectors ranging from ~300 to ~4,000 bp were incubated at 37°C in human serum. Aliquots were taken over several days and were analyzed by gel electrophoresis. We found that digestion in human serum strongly correlated with increasing DNA length. To our surprise, we also uncovered a trend by which serum proteins bound and protected DNA. We recently published that the compaction by DNA supercoiling protected small ( This work was supported by NIH RO1AI054830, Human Frontier Science Program, and Seattle's Children's Hospital Research Foundation, part of NGEC, to L.Z. T.J.B. was supported by NIH Grant T32 GM88129.
11:30 to 11:50 Twisted paths in Euclidean groups: Keeping track of total orientation while traversing DNA
This talk introduces a new mathematical structure for modeling global twist in DNA. The relative rigid-body motion between reference frames attached either to a backbone curve, bi-rods, or individual bases in DNA, can be described well using elements of the Euclidean motion group, SE(n). However, the group law for Euclidean motions does not keep track of overall twist. In the planar case, the universal covering group of SE(2) identifies orientation angle as a quantity on the real line rather than on the circle, and hence keeps track of ``global'' rotations (not modulo 360 degrees). However, in the three-dimensional case, no such structure exists since the the orientational part of the universal cover of SE(3) can be identified with the quaternion sphere. In this talk a new mathematical structure for ``adding'' framed curves and extracting global twist is present. Though reminiscent of the group operation in braid theory and in homotopy theory, this structure is distinctly different, as it is geometric in nature, rather than topological. The motivation for this mathematical structure and its applications to DNA conformation will be presented.
11:50 to 12:10 R Cortini (Imperial College London)
Chiral effects in DNA supercoiling
Supercoiling is a topological property of DNA which is known to be crucially important in the genetic regulation of virtually every living cell. Electrostatic interactions play a fundamental role in determining the conformation of DNA molecules. They are generally taken into account assuming that the charge is homogeneously smeared on the surface of DNA molecules. We developed a theory that instead takes into account the helical pattern of charge on the DNA molecular surfaces. We find that the intrinsic chirality of the charge structures gives rise to important and non trivial phenomena. Crucially, it determines an asymmetry in the energetics of DNA-DNA crossovers: right-handed crossings, occurring in positively supercoiled molecules are more stable than left-handed ones, which occur in negatively supercoiled molecules. We explored the consequences of this fact first by developing a theory of spontaneous DNA braid formation, and then applying it to closed loop DNA supercoilin g and single-molecule DNA micromanipulation experiments. The theory can give an account of some yet unexplained observations and biological facts. It gives a plausible explanation for the occurrence of tight supercoiling of DNA loops observed in cryo-EM and AFM images in high ionic strength environment. It can shed light on the preference for positive supercoiling in hyperthermophylic bacteria and archea. Finally, it induces to reinterpret classical experiments that show that divalent metal ions overwind DNA. The biological implications of these important facts could be very important, and are yet to be fully explored.
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:10 Sequence-Dependent Coarse-Grain Descriptions of DNA: models, methods and simulations INI 1
14:10 to 14:50 K Zakrzewska ([BPC, Paris, France])
DNA recognition studied by molecular simulations
In order to fulfill its biological role DNA has to interact with other molecules, ranging from small ligands to protein complexes. In many cases these molecules intercalate, at least partially, into DNA. This intercalation can involve the conjugated rings of a drug, or the hydrophobic side chains of a protein. How different DNA binding molecules find their target sites, and what role intercalation plays in this mechanism, is still not understood. We try to answer these questions by analyzing the energetic and mechanistic aspects of recognition using molecular simulations at the atomic level. Results will be presented for binding a small drug, daunomycin, and for binding a protein, SRY, a mammalian transcription factor. We will show that daunomycin intercalates into DNA by a complex, multistep process, starting with an intermediate, minor groove bound state. In the case of SRY, the mechanism of DNA sequence specificity, via deformation of the double helix, will be discussed. References: A systematic molecular dynamics study of nearest-neighbor effects on base pair and base pair step conformations and fluctuations in B-DNA, R.Lavery et al. Nucl. Acids Res. (2010) 38(1): 299-313 Protein–DNA Recognition Triggered by a DNA Conformational Switch, 
B. Bouvier et al, Angew. Chem. Int. Ed. 2011, 50, 6516 –6518 Multistep Drug Intercalation: Molecular Dynamics and Free Energy Studies of the Binding of Daunomycin to DNA, M. Wilhelm et al, JACS (2012), published on line.
14:50 to 15:20 Afternoon Tea and Poster Session
15:20 to 15:40 J Baxter (University of Sussex)
The yeast Pif1 family helicase RRM3 promotes DNA unwinding during replisome swivelling
During termination of DNA replication, replisomes overcome the topological tension that occurs as forks converge by coupling final unwinding with fork swivelling. Here I show that cells lacking the DNA helicase RRM3 accumulate terminating late replication intermediates (LRI) in plasmids both with and without characterised pause sites. Rrm3 deletion does not alter the level of swivelling that occurs during termination but its depletion extends the lifetime of LRI while it’s over-expression leads to the rapid unwinding of the LRI. Therefore RRM3 promotes DNA unwinding when the replisome swivels during termination. Potentially, this activity is also generally utilised during DNA replication to bypass topological blocks.
15:40 to 16:00 Denaturation transition of stretched DNA in the presence of DNA-binding ligands
Stretching experiments on DNA in the presence of DNA binding ligands have been shown to reveal insight into biological processes of DNA-ligand binding. We generalize the Poland-Scheraga model to consider DNA denaturation in the presence of an external stretching force and DNA-binding ligands which bind to double-stranded DNA by intercalating between two adjacent base pairs. We obtain the phase diagram of DNA denaturation as a function of temperature, stretching force, and the chemical potential of the DNA-binding ligand. Force-extension relations are compared with recent DNA stretching experiments in the presence of DNA intercalating ethidium and ruthenium complexes.
16:00 to 16:20 Twist neutrality and topological aspects of nucleosomal DNA INI 1
16:20 to 17:00 D Swigon ([University of Pittsburgh, USA])
Dynamics of DNA supercoiling and knotting
Recent experiments on electrostatically induced migration of DNA in nanochanels reveal an intricate phenomenon of compaction of migrating DNA that promotes knotting of the molecule. Subsequent relaxation of the molecule proceeds along several distinct kinetic regimes. The structural details of DNA configurations in different stages of the process are yet unknown. We investigate this and other related phenomena of DNA dynamics using a model in which DNA is represented by a charged elastic rod immersed in a viscous incompressible fluid and the governing equations of the system are solved numerically using the generalized immersed boundary method. The equations of motion of the rod include the fluid–structure interaction, rod elasticity and a combination of two interactions that prevent self-contact, namely the electrostatic interaction and hard-core repulsion. Presented will be results on the effects of electrostatics, steric repulsion, and thermal fluctuations on DNA supe rcoiling and knotting dynamics.
17:00 to 17:40 W Olson ([Rutgers University, New Jersey, USA])
Simulated looping propensities of protein-decorated DNA
Although the genetic messages in DNA are stored in a linear sequence of base pairs, the genomes of living species do not function in a linear fashion. Gene expression is regulated by DNA elements that often lie far apart along the genomic sequence but come close together during genetic processing. The intervening residues form loops, which are organized by the binding of various proteins. For example, in E. coli the Lac repressor protein assembly binds two DNA operators, separated by 92 or 401 base pairs, and suppresses the formation of gene products involved in the metabolism of lactose. The system also includes several highly abundant architectural proteins, such as Fis and HU, which, upon binding, bend a double-helical turn of DNA by 45 degrees or more. In order to gain a better understanding of the mechanics of DNA looping, we have investigated the effects of various proteins on the configurational properties of fragments of DNA, treating the DNA with elastic potentials t hat consider the intrinsic structure and deformability of successive base pairs and incorporating the known three-dimensional structural effects of various proteins on DNA double-helical structure. The presentation will highlight some of the new models and computational techniques that we have developed to generate the three-dimensional configurations of protein-mediated DNA loops and illustrate new insights gained from this work about the effects of various proteins on DNA topology and the apparent contributions of non-specific binding proteins to gene expression.
17:40 to 19:00 Poster Session
19:30 to 22:00 Conference Dinner at Christ's College
Thursday 6th September 2012
09:10 to 09:50 A Maxwell (John Innes Centre, Norwich)
DNA topology and the mechanism of type II DNA topoisomerases
The topology of DNA plays vital roles in its biological function, particularly in the control of gene expression; DNA topoisomerases are enzymes that control DNA topology in all cells. They are divided into two types, I and II, depending on whether their reactions proceed via single- or double-strand breaks in DNA. The type II enzymes (such as bacterial DNA gyrase and DNA topoisomerase IV) cleave DNA in both strands and transport another double-stranded segment of DNA through this break. This process can lead to DNA relaxation, decatenation and unknotting, and, in the case of gyrase, DNA supercoiling, in reactions coupled to the hydrolysis of ATP. Although it is clear to see why supercoiling by gyrase (an endergonic reaction) requires ATP, this is less obvious with other type II enzymes that can only carry out relaxation. One potential role for ATP in the non-supercoiling topoisomerases is in the simplification of DNA topology: generating steady-state distributions of topoiso mers that are simpler than those seen at thermodynamic equilibrium. However, the energetic requirements for topology simplification are very small compared with the free energy available from ATP hydrolysis. Instead we propose that this energy is used to disrupt protein-protein interfaces in the enzyme, which are very stable in order to prevent unwanted DNA cleavage and accidental double-strand breaks in the chromosome. We suggest that this proposed role for ATP in disrupting protein interfaces may apply to other biological systems.

In related experiments, we are aiming to understand the ways in which DNA topology controls gene expression by investigating how DNA recognition is influenced by DNA supercoiling, using a combined approach involving molecular dynamics and biochemical/biophysical methods. In this approach we are using small DNA circles of varying superhelicity and examining DNA triplex formation as model system to study the thermodynamics of supercoiling-dependent DNA recognition.
09:50 to 10:10 Morning Coffee
10:10 to 10:50 Mechanistic studies of type IA topoisomerases
Type I topoisomerases are enzymes that change the topology of DNA by breaking one DNA strand and passing another DNA strand through the break before resealing it. They are subdivided into three groups based on sequence, structural, and mechanistic similarities. Biochemical, biophysical, and structural studies have provided atomic level understanding of the mechanism of action of these enzymes but many unanswered questions regarding their mechanism of action remain. E. coli topoisomerases I and III (Topo I and Topo III) relax negatively supercoiled DNA and also catenate/decatenate DNA molecules. Although these enzymes share the same mechanism of activity and have similar structures, they participate in different cellular processes: Topo I helps maintain the topological state of DNA, whereas Topo III helps resolve recombination and replication intermediates. In bulk experiments Topo I is more efficient at DNA relaxation whereas Topo III is more efficient at catenation/decatenation. To understand the differences in activity by these two highly related type IA topoisomerases, single molecule magnetic tweezers studies were conducted on several different DNA substrates. The experiments show differences in the way the two proteins work at the single molecule level, while also recovering observations from the bulk experiments. Surprisingly, the experiments show that Topo III relaxes DNA very efficiently, but with long pauses between relaxation events, whereas Topo I relaxes DNA more steadily and slowly. The results provide insights into the mechanism of both proteins and suggest reasons why Topo I is more efficient than Topo III at relaxing negatively supercoiled DNA.
10:50 to 11:30 C Soteros ([University of Saskatchewan, Canada])
Knot statistics and knot reduction for a lattice polygon model of local strand passage
From DNA experiments, it is known that type II topoisomerases can reduce the fraction of knots in DNA over that found in randomly cyclized DNA; the amount that the fraction of knots is reduced is one measure of "knot reduction". These enzymes act locally in the DNA by transiently breaking one strand of DNA to allow another strand to pass through (strand passage). Szafron and Soteros have used a self-avoiding polygon model on the simple cubic lattice to model this strand passage action. The details of the combinatorial and topological theory behind this model will be reviewed. Also our Monte Carlo results on how knot reduction depends on the local juxtaposition structure at the strand passage site will be reviewed. We have found correlations between knot reduction and the crossing-sign and crossing-angle at the strand passage site. New results on the effect of the strand passage structure and solvent quality on the knot transition probabilities and knot reduction will also be presented.
11:30 to 11:50 Topo IV is the topoisomerase that knots and unknots sister duplexes during DNA replication
DNA topology plays a crucial role in all living cells. In prokaryotes, negative supercoiling is required to initiate replication and either negative or positive supercoiling assists decatenation. The role of DNA knots, however, remains a mystery. Knots are very harmful for cells if not removed efficiently, but DNA molecules become knotted in vivo. If knots are deleterious, why then does DNA become knotted? Here, we used classical genetics, high resolution two-dimensional agarose gel electrophoresis and atomic force microscopy to show that topoisomerase IV (Topo IV), one of the two type-II DNA topoisomerases in bacteria, is responsible for the knotting and unknotting of sister duplexes during DNA replication. We propose that when progression of the replication forks is impaired, sister duplexes become loosely intertwined. Under these conditions, Topo IV inadvertently makes the strand passages that lead to the formation of knots and removes them later on to allow their correct segregation.
11:50 to 12:10 P Sulkowski ([University of Amsterdam / Caltech / University of Warsaw])
Topological recursion and classification of multi-stranded biopolymer configurations
In this talk I will present the formalism of so-called "topological recursion" and demonstrate how it can be applied to provide a complete classification of multi-stranded configurations of biomolecules. The "topological recursion" is a beautiful and rather sophisticated method arising from random matrix theory, which already found many applications and is currently under very active study in random matrix / statistical physics / high energy physics communities. In particular, I will present how to use this formalism to classify and compute all topologically inequivalent configurations of biomolecules, consisting of arbitrary number of strands, connected by arbitrary number of bonds or basepairs. This solution provides a new application of random matrix theory in the context of biophysics. Our solution has also an independent interpretation in pure mathematics, i.e. it provides certain important characteristics of moduli spaces of Riemann surfaces with boundaries.
12:30 to 13:30 Lunch at Wolfson Court
13:30 to 14:10 DNA in confined geometries: topology effects
DNA can be found in confined geometries in different situations: for examples in viruses, in the chromosome or in artificial structures like in microfluidic devices. It is therefore interesting to study the statistical properties of the DNA depending on its length, concentration and topology. We present here data on circular DNA deposited in 2 dimensions with different concentration up to the overlap concentration c* and study also the effect of the length of the circular DNA. We characterize the statistical properties by determining the end-to-end distance as a function of the contour length, the directional correlation function, the area covered by the plasmids, the shape parameters like the sphericity as a function of the concentration.
14:10 to 14:50 A generic non-specific mechanism for the clustering of DNA and chromosome binding proteins
In this talk I will present a generic mechanism which leads to the clustering of DNA-binding proteins, on either prokaryotic DNA or eukaryotic chromatin. The clustering is driven by DNA-mediated interactions, and remarkably, does not require any affinity between the proteins, which we assume interact purely by steric repulsion. On naked DNA, small proteins cluster to form rows, whereas larger, histone-like proteins, form more disordered aggregates. On flexible fibres such as chromatin, the clustering leads to the formation of quasi-spherical foci.

Additionally I will present results from a simulation of an ensemble of Pol II polymerases and of p65 proteins (a well-characterised transcription factor) interacting with chromosomes 5, 8, 14 and 17. These interactions lead to the formation of foci, or factories, where active regions in the DNA come together. The statistics of the contacts compare favourably with 3C data on contacts made by SAMD4 on chromosome 14 and EXT1 on chromosome 8.
14:50 to 17:40 Free Afternoon
18:00 to 18:30 Dinner at Wolfson Court
Friday 7th September 2012
08:30 to 09:10 Topology of Xer site-specific recombination
Xer site-specific recombination at cer and psi converts bacterial plasmid multimers to monomers so that they can be efficiently segregated to both daughter cells at cell division. Recombination is catalysed by the XerCD recombinase acting at 30 bp core sites, and is regulated by the action of accessory proteins on accessory DNA sequences adjacent to the core sites. Recombination normally occurs between sites in direct repeat in a negatively supercoiled circular DNA molecule, and yields two circular products linked together in a right-handed 4-noded catenane with anti-parallel sites. Intramolecular recombination, and recombination between sites in inverted repeat on an unknotted circular substrate do not normally take place. However, recombination between sites in inverted repeat on right-handed torus knots with 5 or more nodes, or between anti-parallel sites on the two rings of a torus catenane with 6 or more nodes is efficient. In each case, recombination adds one additional node to the catenated or knotted substrate. These results are consistent with a model in which the accessory DNA sequences are interwrapped around the accessory proteins so that 3 interdomainal nodes are trapped by synapsis of the core sites by the XerCD recombinase. Recombination between directly repeated sites on an unknotted circular substrate formed the 4-noded catenane product with a linkage change ( ΔLk) of +4. This result is consistent with current models for strand exchange by the XerCD and other tyrosine recombinases, which predict recombination via a Holliday junction intermediate with no net change in total linkage ( ΔLg = Δcat + ΔLk = 0).
09:10 to 09:50 I Grainge (University of Newcastle, Australia)
Simplification of topology during Xer-mediated recombination
The chromosome of the bacterium Escherichia coli is a single circular DNA molecule of about 4.6 Mbp. Various recombinational repair processes that act upon the DNA during or following its replication can lead to a genetic crossover occurring, which in turn leads to a chromosome dimer being formed. This requires resolution back to two un-catenated single chromosomes before the cell can divide. The dimer resolution reaction is catalysed by the two recombinase proteins, XerC and XerD. Catalysis by XerD is in turn controlled by protein-protein interaction with the gamma subdomain of the FtsK DNA translocase. Recent in vitro data has shown that the interaction between XerD and FtsK-gamma is sufficient to stimulate recombination, but that in the absence of the DNA translocation motor of FtsK, then complex toplogical products result. If the motor is added back to these reactions, then simple, unlinked circular products are seen. DNA translocation is required for efficient chromosome dimer resolution in vivo too, mirroring the other experimental results. The focus of current research is into how XerD catalytic activity is stimulated, and how DNA translocation by FtsK leads to products with a simple toplogy.
09:50 to 10:10 Morning Coffee
10:10 to 10:50 Tangle analysis of protein-DNA complexes
Just like local knots can occur in long extension cords, such knots can also appear in DNA. DNA can be be either linear or circular. Some proteins will cut DNA and change the DNA configuration before resealing the DNA. Thus, if the DNA is circular, the DNA can become knotted. Protein-DNA complexes were first mathematically modeled using tangles in Ernst and Sumners seminal paper, "A calculus for rational tangles: applications to DNA recombination" (Math Proc Camb Phil Soc, 1990). A tangle consists of arcs properly embedded in a 3-dimensional ball. In order to model protein-bound DNA, 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 cr ossings 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.
10:50 to 11:30 DNA unknotting and unlinking
DNA replication is the basis for biological inheritance. In bacteria, reproduction starts with replication of the chromosome into two identical daughter molecules, followed by segregation of the newly replicated chromosomes and division of the parent cell into two daughter cells. In circular chromosomes, problems of entanglement during DNA linking complicate the process of chromosome segregation. In Escherichia coli, DNA unlinking is typically mediated by the type II topoisomerase topoIV. In the absence of topo IV, the site-specific recombination system XerCD mediates sister chromosome unlinking. This reaction is activated at the division septum by a powerful translocase FtsK, which coordinates the last stages of chromosome segregation. The mechanism by which the XerCD-FtsK complex simplifies the topology of DNA remains unclear. Techniques from knot theory and low-dimensional topology, aided by computational tools, are used to study the action of such enzymes. Understanding D NA unlinking by Xer recombination will provide a more complete picture of the chromosome segregation process.

This is joint work with Kai Ishihara, David Sherratt, Koya Shimokawa and Christine Soteros.
11:30 to 11:50 R Scharein ([Hypnagogic Software, Canada])
TopoICE and other software tools for investigating topological problems in DNA
Mathematicians and biologists studying knotting and tangling issues in DNA can benefit from powerful interactive software tools. These can be used to explore what is mathematically possibly in certain kinds of reactions that DNA may undergo (crossing changes or recombination, for example). This information may be helpful in refining biological models or even in suggesting new experiments. In this talk, we will examine several software tools starting with the Topological Interactive Construction Engine (TopoICE). TopoICE has been available as part of the KnotPlot package for several years, in two versions: TopoICE-X (crossing changes) and TopoICE-R (recombination). Here we present these in a revamped, extended and more usable form. Also, we introduce TopoICE-S, intended to investigate knot distances via smoothings. This will be accompanied by newly obtained smoothing distance information. This talk will also unveil TopoICE and other DNA topology tools as free standalone applications (independent of KnotPlot) and running on mobile devices.

This is joint work with Isabel Darcy.
11:50 to 12:10 Summary/Closing Remarks INI 1
12:30 to 13:30 Lunch at Wolfson Court
18:00 to 18:30 Dinner at Wolfson Court
University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons