Schedule for: 19w5226 - The Topology of Nucleic Acids: Research at the Interface of Low-Dimensional Topology, Polymer Physics and Molecular Biology

Alice Pyne 1*†, Agnes Noy 2†, Kavit Main 1, Lesley Mitchenall 3, Anthony Maxwell 3, Sarah Harris 4*

DNA in the cell is tangled and twisted, adopts complex topologies, is decorated with a myriad of DNA binding proteins and is frequently maintained under superhelical stress (1). To process DNA, biology has evolved DNA packaging machines, such as eukaryotic histones and prokaryotic gyrases, that maintain order in this topological landscape. Unlike the crystalline, linear DNA that led to the discovery of its double helical nature (2), there is now a growing appreciation that the context of DNA in the wider genome is vital to its function (3). Understanding how DNA behaves in its cellular environment is currently as challenge of complexity, which can be enhanced by a better understanding of the fundamental properties of DNA. This includes how DNA responds to supercoiling and stress (4) to interact with other oligonucleotides and proteins.

Here, we use a combination of high-resolution AFM (5) and atomistic MD simulations (6) to provide unparalleled single molecule insight into the structure of DNA under superhelical stress down to the base pair level (Figure 1). We use DNA minicircles, only twice the persistence length of DNA, to probe the structure and function of supercoiled DNA(7). We observe that though the discrete, quantised nature of these minicircles may imply a homogenous population, the innate flexibility of DNA under superhelical stress results in a large heterogenous population. Furthermore, we show that DNA at this length scale is highly dynamic, and able to change its conformation even whilst tethered to a surface. We believe that it is this dynamic conformational heterogeneity which allows for supercoiled DNA to bind with a diverse range of substrates. We demonstrate that two distinct binding modalities, triplex formation and repressor factor binding, which either rigidify or bend DNA, are both able to be accommodated within the large conformational population of DNA minicircles.

Through combining high resolution microscopy and atomistic simulations, we provide a toolkit to understand the structure and dynamics of supercoiled DNA. We observe conformational changes in DNA and associated binding proteins at sub-nanometre spatial resolution and sub second temporal resolution. These results improve our understanding of DNA structure, and how this may influence the interaction of DNA with itself, diagnostic therapeutics, and innate proteins - key in regulating gene expression.

• Arsuaga, Javier: Quantification of the entanglement complexity of the yeast genome reveals a bias towards simplicity
• Eng, Jeremy: Linking Probabilities in a Confined Polymer System
• Frias, Jose: The minimum prism volume for knots and links in the cubic lattice
• Jonoska, Natasa: An Annotation Algorithm for DNA Rearrangements
• Medina, Carolina: Automated Topological Analysis of Microscopy Images of DNA Molecules
• Njagarah, John: The effect of electrostatic interactions in minicircle networks
• Schmirler, Matthew: Fitting a Lattice Polygon Model to Experimental DNA results
• Walker, David: BAMBI: The Bayesian Analysis of Mu Bacteriophage Insertions
• Ziraldo, Rick: Topological Characterization of Single DNA Molecules by Tethered Fluorophore Motion

The problem of compacting genomes while still performing cellular processes is common to all life forms. The current view for E. coli is a compacted genome with well-organized domains where replication initiates and terminates. Some studies have suggested that these and other regions are sequestered or compartmentalized such that there is little to no interaction between them. We have exploited the high efficiency and promiscuity of phage Mu transposition to directly measure the in vivo rates of interactions between genomic loci, and have developed new tools for analyzing the proximity of loci across the genome. We observe widespread contacts between all regions of the E. coli chromosome, revealing a dynamic, effectively un-compartmentalized genome. We detect long-range interactions between several genes in different gene families such as dna and rrna, implicating spatial proximity of many distantly co-regulated genes for the first time in a prokaryote. We also see a higher interaction between the two halves of the chromosome during replication, consistent with the deduced proximity and higher mobility of the chromosomal arms as they segregate during replication. Our work advances a new view of genome organization in E. coli.

Principled approaches from polymer physics are important to make sense of the complexity of experimental data on chromosome 3D architecture and to explain their underlying molecular mechanisms. I discuss first the current picture of the spatial organisation of our DNA across genomic scales at the single cell level, as emerging from technologies such as microscopy, Hi-C, SPRITE or GAM [1]. Next, I discuss how different models of polymer physics can help understanding the origin of the patterns in the data and the underlying folding mechanisms [2,3,4]. Finally, I show that polymer physics can be used to predict the impact of large mutations (Structural Variants) on chromosome structure, in particular on how the network of contacts between genes and regulators is rewired, hence enabling the identification of their pathogenic potential [5,6].

[1] R.A. Beagrie, A. Scialdone, M. Schueler, D.C.A. Kraemer, M. Chotalia, S.Q. Xie, M. Barbieri, I. de Santiago, L.-M. Lavitas, M.R. Branco, J. Fraser, J. Dostie, L. Game, N. Dillon, P.A.W. Edwards, M. Nicodemi*, A. Pombo*, Complex multi-enhancer contacts captured by Genome Architecture Mapping (GAM), a novel ligation-free approach. Nature 543, 519 (2017).

[2] A.M. Chiariello, S. Bianco, C. Annunziatella, A. Esposito, M. Nicodemi, Polymer physics of chromosome large-scale 3D organisation, Scientific Reports 6, 29775 (2016).

[3] M. Barbieri, S.Q. Xie, E. Torlai Triglia, A.M. Chiariello, S. Bianco, I. de Santiago, M.R. Branco, D. Rueda, M. Nicodemi*, A. Pombo*, Active and poised promoter states drive folding of the extended HoxB locus in mouse embryonic stem cells. Nature Struct. Mol. Bio, 24, 515 (2017).

[4] C.A. Brackley, J. Johnson, D. Michieletto, A. N. Morozov, M. Nicodemi*, P. R. Cook*, and D. Marenduzzo*, Nonequilibrium Chromosome Looping via Molecular Slip Links, Phys. Rev. Lett. 108, 158103 (2017)

[5] S. Bianco, D.G. Lupiáñez, A.M. Chiariello, C. Annunziatella, K. Kraft, R. Schöpflin, L. Wittler, G. Andrey, M. Vingron, A. Pombo, S. Mundlos*, M. Nicodemi*, Polymer physics predicts the effects of structural variants on chromatin architecture, Nature Genetics 50, 662 (2018).

[6] B.K. Kragesteen, M. Spielmann, C. Paliou, V. Heinrich, R. Schoepflin, A. Esposito, C. Annunziatella, S. Bianco, A.M. Chiariello, I. Jerković, I. Harabula, P. Guckelberger, M. Pechstein, L. Wittler, W.-L. Chan, M. Franke, D.G. Lupiáñez, K. Kraft, B. Timmermann, M. Vingron, A. Visel, M. Nicodemi*, S. Mundlos* and G. Andrey*, Dynamic 3D Chromatin Architecture Determines Enhancer Specificity and Morphogenetic Identity in Limb Development, Nature Genetics 50, 1463 (2018).

• Arsuaga, Javier: Quantification of the entanglement complexity of the yeast genome reveals a bias towards simplicity
• Eng, Jeremy: Linking Probabilities in a Confined Polymer System
• Frias, Jose: The minimum prism volume for knots and links in the cubic lattice
• Jonoska, Natasa: An Annotation Algorithm for DNA Rearrangements
• Medina, Carolina: Automated Topological Analysis of Microscopy Images of DNA Molecules
• Njagarah, John: The effect of electrostatic interactions in minicircle networks
• Schmirler, Matthew: Fitting a Lattice Polygon Model to Experimental DNA results
• Walker, David: BAMBI: The Bayesian Analysis of Mu Bacteriophage Insertions
• Ziraldo, Rick: Topological Characterization of Single DNA Molecules by Tethered Fluorophore Motion

Difference topology: The DNA path within a high-order DNA-protein assembly can be revealed from the topology of DNA knots and links formed by the action of Flp or Cre site-specific recombinase on target sites placed close to (and flanking) the assembly. This ‘analysis is experimentally simple, and has broad applicability. Choice between alternative reaction mechanisms: Recombination product topologies resulting from a fixed synaptic topology can help distinguish between alternative modes of site arrangement and strand exchange by a given recombinase enzyme. Conserved biological functions revealed by conserved topology of DNA loci in vivo:  DNA topology can reveal evolutionary relationships between two diverged DNA loci that perform analogous but distinct biological functions. The unusual positive chromatin writhe at the centromeres of yeast chromosomes is shared by the partitioning locus of an extrachromosomal circular DNA element present in the yeast nucleus. This finding lends credence to the possible origin of these loci from a common ancestor that once directed the segregation of both the chromosomes and the plasmid during cell division. Chemical chirality in DNA recombination: The active site of the Flp/Cre recombinase contains two conserved positively charged side-chains (Arg-I and Arg-II) responsible for compensating the negative charge on the non-brridging oxygen atoms of the scissile phosphate group. When one of the oxygens is replaced by a neutral group, one of the arginine residues becomes dispensable. The reactivity of DNA substrates containing substitutions at either of the two oxygens with Flp/Cre lacking either of the two arginines reveals the chirality of Arg-oxygen interactions, and defines the stereochemical course of the recombination reaction.

Riccardo Ziraldo^1,†, Andreas Hanke^2,*^,† and Stephen D. Levene^1,3,4*

Departments of ¹Bioengineering, ³Biological Sciences, and ⁴Physics, University of Texas at Dallas, Richardson, TX 75080, USA

² Department of Physics and Astronomy, University of Texas Rio Grande Valley, Brownsville, TX 78520, USA 

In vivo, DNA is subjected to torsional and stretching stress due to different cellular processes like protein binding, transcription and replication, that are capable of distorting DNA structure beyond its helicoidal shape. On one hand, DNA is subjected to a supercoiling stress that coils the fiber around itself and opens the double helix facilitating the formation of melting bubbles. On the other hand, different proteins like the TATA-binding protein and the recombinase enzyme RecA can overstretch DNA up till 40% beyond its contour length. In this workshop I will show which are the effect of these disturbing factors on the molecule of DNA through the use of molecular dynamics simulations at atomic level.

For analysing DNA dynamics due to thermal fluctuation, my team is developing SerraNA, which is a program that calculates the overall elastic constants of DNA from ensembles obtained by molecular simulations [1]. In addition, we also performed simulations on overstretching DNA within the biological regime: up to 40% on extension and within the in vivo range of supercoiling density) exhibit the capacity of the molecule to present melting bubbles independently to torsional stress, even on positively supercoiled DNA [2].

In parallel, torsionally-stressed DNA minicircles are being studied by a combination of high-resolution AFM experiments and atomistic simulations, describing for the first time the structural details of supercoiled DNA at a sub-helical scale [3]. Finally, the DNA-bending IHF protein is embedded on the same type of DNA minicircles for analysing its effect on the global and local shape [4].

1. Noy et al, Phys Rev Lett, (2012), 109, 228101.

2. Shepherd, Noy and Leake et al, In preparation

3. Pyne, Noy, Main, Velasco, Mitchenall, Cugliandolo, Piperakis, Stevenson, Hoogenboom, Bates, Maxwell and Harris, In preparation

4. Watson, Guilbau, Yoshua, Fogg, Zechiedrich, Leake and Noy, In preparation

Recently, polymers of complex chemical connectivity expressed with graphs have been synthesized in experiments [1-3]. It is indeed marvelous that even such polymers expressed with K_3,3 bipartite graph have been produced [2]. We call polymers with nontrivial structures in chemical connectivity topological polymers. We also call polymers with nontrivial topology of spatial graphs as embeddings in three dimensions topological polymers [4].

The Rouse dynamics of a polymer plays an important role in the dynamical aspects of the polymer in dilute solution, and also in melts if the molecular weight is small [5]. In this talk, we formulate the Rouse dynamics of the topological polymer with a given graph. We derive several physical consequences of the model. In particular, we compare the experimental data of Size Exclusion Chromatography (SEC) of some topological polymers with their theoretical estimates of the mean-square radius of gyration obtained by the Gaussian method [6]. We argue physical backgrounds of SEC data and discuss how they are consistent.

After reviewing the method for constructing Gaussian random configurations of a topological polymer, i.e. Gaussian random graph embeddings [6], we derive the normal coordinates and modes for the topological polymer. Here we remark that while the Moore-Penrose generalized inverse matrix has been addressed for general Gaussian molecules about three decades ago [7], it seems that important consequences were found later independently [8]. Moreover, it has not been known until quite recently how to generate Gaussian random configurations of a given topological polymer [6]. In fact, we can calculate any physical quantity at least numerically by taking the ensemble averages over generated configurations. It is quite nontrivial to generate such random walks that satisfy the constraints of all independent loops in the graph.

The results of this talk are obtained in collaboration with Jason Cantarella, Clayton Shonkwiler, and Erica Uehara.

1)    Topological Polymer Chemistry: Progress of cyclic polymers in synthesis, properties and

 functions, Y. Tezuka ed., World Scientific, Singapore, 2013.    

2)    T. Suzuki, T. Yamamoto and Y. Tezuka. J. Am. Chem. Soc., 2014, 136, 10148–10155.

3)    Y. Tezuka. Acc. Chem. Res., 2017, 50, 2661–2672.

4)    E. Uehara and T. Deguchi, J. Chem. Phys. 2016, 145, 164905.

5)    M. Doi and S. F. Edwards, The Theory of Polymer Dynamics, Oxford University Press, Oxford, 1986. 

6)    J. Cantarella, T. Deguchi, C. Shonkwiler and E. Uehara, in preparation.

7)    B. E. Eichinger, Macromolecules, 1980, 13, 1-11.

8)  E. Estrada and N. Hatano, Chem. Phys. Let. 2010, 486, 166–170.