Schedule for: 24w5267 - The Crossroads of Topology, Combinatorics and Biosciences: Deciphering the Entanglement of Multi-Stranded Nucleic Acids

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Meet and Greet at BIRS Lounge (PDC 2nd Floor)

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

A brief introduction to BIRS with important logistical information, technology instruction, and opportunity for participants to ask questions.

The tensegrity triangle is a versatile DNA motif that crystallizes by self-assembly into designer 3D crystals with rhombohedral symmetry. The tile owes its “tensegrity” nature to a chiral stacking of three double helices woven together by a nearly-circular strand that passes from between the helices by way of four-arm DNA junctions. These junctions are canonically right-handed crossovers which yield a right-handed triangular arrangement. It has been hypothesized that these molecular building blocks would herald the ability to design, construct, and harness novel materials with atomic precision, but the control over local and global structures has remained imprecise. To address this, we have carried out a systematic alteration of the components of this tile to determine the effect of local torsion and winding on the tile topology; and we further characterize the effects of local geometry on the global symmetry of the ensuing crystallographic array using x-ray techniques. We find that tensegrity triangles can be altered in a variety of means. A set of symmetric and asymmetric extensions to the extra-junction regions yield interlocked cubic architectures or oblong cavities, depending on the rotational contribution of the extensions. Alteration of the inter-junction triangle regions imposes torsional stress on the closed shape, which can in turn cause helical bending within to yield chiral hexagonal lattices. We further identify two novel crossover topologies and uncover an accompanying “Rule of Thirds” that describes the handedness of junctions as a result of local twisting. Finally, alteration of ribose stereochemistry causes chiral inversion at each level, yielding fully-invertible quaternary structures with rhombohedral, triclinic, trigonal, tetragonal, hexagonal and cubic symmetry. The interplay between topology, symmetry and chirality yields a set of molecular building blocks that will inform the self-assembly across scales. Simon Vecchioni, Jordan Janowski, Brandon Lu, Karol Woloszyn, Lara Perren, Yoel Ohayon, Ruojie Sha Department of Chemistry, New York University, New York, NY; Van-Anh Bich Pham, Masahico Saito, Nataša Jonoska, Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA; Chengde Mao, Department of Chemistry, Purdue University, West Lafayette, IN.

Emergent technologies in self-assembly present fascinating and challenging design problems, giving rise to a new branch of mathematics, DNA mathematics. Often, the self-assembled objects, e.g. lattices, polyhedral skeletons, or wireframe constructs, may be modeled as spatial graphs. Since these graphs represent physical objects in 3-space, low-dimensional topology plays an important role in DNA mathematics. Here, we present a knotting problem in spatial graphs arising from DNA origami, called origami knotting (O.K.). Design strategies often use a single circular (unknotted) scaffolding strand of DNA which traverses all the edges of the target spatial graph, subject to constraints on how it may pass through the vertices. Since spatial graphs can have complex topologies, controlling knotting in the scaffolding strand becomes important. This leads to a new area in knot theory, where we must understand knotting in Euler circuits in graphs as opposed to the historically studied knotting in graph cycles (intrinsic knotting in graphs). We briefly review existing results for O.K. graphs that use A-trails in the case of cellularly embedded graphs. We then define O-trails to introduce a new formalism for general spatial graphs and use this formalism to begin the exploration of O.K. graphs. Joint work with: Wout Moltmaker, Ada Morse

In this talk, we delve into the realm of band surgeries on knots and links. Through the examination of signatures, Jones polynomials, and various other link invariants, we can effectively demonstrate when band surgeries are not possible between a given pair of links. Moreover, band surgeries find significant applications in establishing mathematical models for DNA recombination and the anti-parallel reconnection of vortex knots and links. Specifically, we will explore how these results can be applied to the characterization of the unlinking of DNA links through site-specific recombination and the untying of vortex knots via anti-parallel reconnection.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Monday 18 March 2:00-3:30 PM US Eastern Time Register here: https://ow.ly/ny3750QK26Z

By regulating access to the primary code, supercoiling and looping can be thought of as secondary DNA codes. Toward “cracking” these secondary codes, we discovered that supercoiling and loop length-dependent site-specific base pair disruptions (Fogg et al. (2021) Nat Commun 12:5683) facilitate very sharp bending to allow DNA to adopt novel DNA conformations (Irobalieva, Fogg et al. (2015) Nat Commun 6:8440). Molecular dynamics simulations revealed that one flipped base, with enough negative supercoiling, expands into a series of adjacent flipped bases to form denaturation bubbles (Randall et al. (2009) Nucleic Acids Res 37:5568); these simulations were verified and we further discovered that site-specific base pair disruptions at one site cause site-specific base pair disruptions at distant sites (Fogg et al. (2021) Nat Commun 12:5683), a remarkable “action at a distance” with major biological consequences. In this talk, I will discuss new findings demonstrating that cations should also be considered a secondary code because they dramatically affect the interplay of supercoiling and looping-dependent site-specific base-pair disruptions and DNA shape to regulate DNA activity. Funded by NIH R35 GM141793.

The use of gene regulation in plasmids to produce specific responses in bacteria is well established but struggles with the limitations of available transcription factors. Superhelicity is the geometric property of how twisted the DNA double helix is. Transcription can generate positive and negative superhelicity in regions of the plasmid. This often interferes with gene regulation but negative twist can promote transcription. In this work we induce negative superhelicity to replace transcription factors as a gene regulation mechanism. We implement a three fold modelling system with feedback between the lab, physics and computational models to help develop the use of superhelical control of gene expression.

A biopolymer can be seen as a simple mathematical curve in 3-space, which can attain many different conformations and is not allowed to cross itself. In this talk we will use a rigorous and general approach to analyze the structures of such macromolecules using new methods in knot theory that extend to open curves in 3-space. In particular, we will discuss the Jones polynomial and Vassiliev measures for single or multi-component systems and discuss their properties. These functions, that are sensitive to both the geometry and the topology of a structure, enable the rigorous characterization of biomolecules without any approximation schemes and provide continuous functions of the curve coordinates. In the context of proteins, these enable the characterization of all proteins (even in the absence of knots) and correlate with experimental folding rates. We discuss how these can be useful in studying multi-stranded nucleic acids.

The branching of an RNA molecule is an important structural characteristic yet difficult to predict correctly, especially for longer sequences. Using plane trees as a combinatorial model for RNA folding, we consider the thermodynamic cost, known as the barrier height, of transitioning between branching configurations. Using branching skew as a coarse energy approximation, we characterize various types of paths in the discrete configuration landscape. In particular, we give sufficient conditions for a path to have both minimal length and minimal branching skew. These results offer some biological insights, notably the potential importance of both hairpin stability and domain architecture to higher resolution RNA barrier height analyses.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

R-loops, transient three-stranded nucleic acids, emerge during transcription when newly formed RNA binds with the template DNA, releasing the coding strand of DNA. Not much is known about the formation process and the three-dimensional structure of R-loops. In this study, we represent an R-loop as a term in a formal grammar and utilize this grammatical framework to predict R-loop formation. Our model is trained using experimental data from SMRF-seq. Although R-loop formation is influenced by both DNA sequence and topology, our grammar, which does not include explicit topological details, accurately predicts R-loop formation for plasmids with varying starting topologies.

The formation of R-loops, three-stranded RNA:DNA hybrids, is a natural consequence of DNA transcription. These distinctive non-B DNA structures have been observed in every organism in which they have been assayed, predominantly forming in conserved genomic regions. However, the mechanisms by which R-loops are formed and stabilized remain to be fully characterized. Through a biochemical approach involving in vitro transcription followed by single-molecule R-loop sequencing, we have systematically tested the impact of DNA sequence/topology, non-template strand single-strand DNA breaks, and single-strand DNA binding proteins on R-loop stabilization. Based on the most extensive and highest resolution single-molecule R-loop dataset to date, we reveal the DNA sequence's ability to drive R-loop formation and its linear relationship with negative supercoiling, as well as how single-strand DNA breaks and single-strand DNA binding proteins exert profound influences on the R-loop landscape. This work deepens our understanding of R-loop behavior, biophysics, and their implications for genomic stability, and has allowed new estimations of nucleic acid energetic constants enabling future improvements in biophysical models.

Meet in foyer of TCPL to participate in the BIRS group photo. The photograph will be taken outdoors, so dress appropriately for the weather. Please don't be late, or you might not be in the official group photo!

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

During DNA replication, DNA polymerases often incorporate ribonucleotides—RNA's building blocks—alongside deoxyribonucleotides into newly synthesized DNA strands. It is estimated that several thousand to millions of ribonucleotides are mistakenly incorporated into the genomes of yeast and human cells each cell cycle, respectively. This incorporation leads to the presence of ribonucleoside monophosphates (rNMPs) in DNA, rendering the DNA more fragile. Despite the potential risk to genomic integrity, rNMPs are ubiquitously found across the evolutionary spectrum, from bacteria to mammals. Utilizing the ribose-seq method for mapping rNMPs in DNA via next-generation sequencing, alongside the Ribose-Map computational toolkit, we generated extensive libraries of rNMPs embedded in genomic DNA obtained from various yeast species, a unicellular green alga, human cells, and human cell lines. Our bioinformatics analysis revealed non-random patterns of rNMP incorporation, including specific strand biases and hotspots. Joint work with: Taehwan, Yang, Deepali Kundnani, Penghao Xu, Mo Sun, Alli Gombolay, Gary Newnam

Weaving DNA strands in homologous recombination Afra Sabei1, Claudia Danilowicz2, Mara Prentiss2, Chantal Prévost1 1.Laboratoire de Biochimie Théorique, CNRS and univ Paris Cité, IBPC, 13 rue Pierre et Marie Curie Paris France 2.Department of Physics, Harvard University, Cambridge, Massachusetts, USA The homologous recombination process catalyzes the faithful repair of DNA double strand breaks (DSB). To this aim, recombinase proteins assemble a helical nucleoprotein filament on a DNA single strand (ssDNA) that results from DSB processing. The filament then searches the genome for a sequence homologous to the ssDNA. Recognition requires that double-stranded genomic DNA (dsDNA) be locally incorporated in the filament, where Watson-Crick functional groups of the complementary strand bases are evaluated via base pairing exchange. Because they are in phase with the helical filament, the three strands in the D-loop are stretched by 50% and unwound by 40%, in addition to being intertwined due to pairing exchange [1]. The recombination mechanism unfolds over several steps involving strand exchange, reverse pairing exchange, destabilization of the strand exchange product due to ATP hydrolysis, and multi-position parallel search [2-4]. ATP hydrolysis driven unbinding of RecA from the D-loop can also create a protein free D-loop [5]. I will present our investigations on different stages of the process and I will discuss hypotheses arising from structural modeling, together with pending questions. References 1. M. Prentiss, C. Prévost, C. Danilowicz (2015) Crit Rev Biochem Mol Biol 50, 453 doi: 10.3109/10409238.2015.1092943 2. D. Yang, B. Boyer, C. Prévost, C. Danilowicz, and M. Prentiss (2015) Nucleic Acids Res 43, 10251 doi: 10.1093/nar/gkv883 3. B. Boyer, C. Danilowicz, M. Prentiss, and C. Prévost (2019) Nucleic Acids Res 47, 7798 doi: 10.1093/nar/gkz667 4. C. Danilowicz, L. Hermans, V. Coljee, C. Prévost and M. Prentiss (2017) Nucleic Acids Res 45, 8448 doi: 10.1093/nar/gkx582 5. C. Danilowicz, E. Vietorisz, V. Godoy-Carter, C. Prévost and M. Prentiss (2021) J Mol Biol 433, 167143

R-loops are nucleic acid structures consisting of a DNA:RNA hybrid and a DNA single strand. They form naturally during transcription when the nascent RNA hybridizes to the template DNA, forcing the coding DNA strand to wrap around the RNA:DNA duplex. Although formation of R-loops can have deleterious effects on genome integrity, there is evidence of their role as potential regulators of gene expression and DNA repair. We use a sliding window approach that accounts for properties of the DNA nucleotide sequence, such as C-richness and CG-skew, to identify segments favoring R-loops. We evaluate these properties on two DNA plasmids that are known to form R-loops and compare results with a recent energetics model from the Chédin Lab. This discrete sequence-based approach for R-loops was an initial step toward a more sophisticated framework using formal grammars.

A distance map is a collection of distances between two points along a spatial curve. It has complete information about the configuration of spatial curve upto mirror image. In fact, we can reconstruct the coordinates of spatial curves using the distance map. The linking number is a classical link invariant with numerous known calculation methods. In this talk, we will discuss a direct calculation of the linking number using the distance map.

Four general themes (a) Topology of DNA and RNA within nanostructures (b) DNA/RNA packing - modelling and experiments (c) Topology of RNA-DNA hybrids - modelling and experiments (d) DNA topology: how DNA supercoiling and other forms of entanglement can affect biological processes Main Room: TCPL 201 Link: https://ubc.zoom.us/j/64276665131?pwd=ZUR4OTdvM3RlSFR0SnpVNk5WUFNWUT09 Meeting ID: 642 7666 5131 Password: 245267 Breakout Room 1: TCPL 202 Link: https://ubc.zoom.us/j/63544036533?pwd=U2xQV1RSSXkwSUo2Y0lwWWZVcnJjUT09 Meeting ID: 635 4403 6533 Password: 245267 Breakout Room 2: TCPL 106 Link: https://ubc.zoom.us/j/62266684726?pwd=U0xOQVBPRVMvaFNXU1RmMW1HbVF3Zz09 Meeting ID: 622 6668 4726 Password: 245267

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Chromosome spatial organisation in the nucleus of cells is fundamental to the regulation of our genome as, for example, it defines the contacts between genes and enhancers. I review recent technological and conceptual developments on the understanding of the underlying molecular mechanisms. In particular, by use of models of polymer physics we tested those mechanisms in single molecules against multiplexed microscopy data in human wild-type and Cohesin depleted cells [1-4]. Next, based on our models, we investigated how large genomic mutations (Structural Variants, SVs), typically associated to human diseases, impact gene activity by rewiring the network of regulatory contacts. The model predictions on the origin of SV phenotypes was finally validated against experiments in cells bearing those mutations [5-9] and mapped extensively across patients. Taken together, those developments are deepening our understanding of the regulation of the human genome and are ushering in novel biomedical approaches for genetic diseases such as congenital disorders and cancer. [1] M. Barbieri et al., Nature SMB 24, 515 (2017) [2] S. Bianco et al., Nature Genetics 50, 662 (2018) [3] M. Conte et al., Nature Com. 11, 3289 (2020) [4] M. Conte et al., Nature Com. 13, 4070 (2022) [5] B.K. Kragesteen et al., Nature Genetics 50, 1463 (2018) [6] G.I. Dellino et al., Nature Genetics 51, 1011 (2019) [7] W. Winick-Ng et al., Nature 599, 684 (2021) [8] L. Fiorillo et al., Nature Meth. 18, 482 (2021) [9] R. Beagrie et al. Nature Meth. 20 1037 (2023)

In this talk I discuss the use of mathematical patterns in genomes (called ‘’genomic signatures”) in conjunction with supervised and unsupervised machine learning, for ultrafast, accurate, and scalable genome classification at all taxonomic levels. In addition, I present our recent findings suggesting that adaptations to extreme temperatures and extreme pH imprint a discernible environmental component in the genomic signature of microbial extremophiles. In particular, the unsupervised learning of unlabelled sequences identified several exemplars of hyperthermophilic organisms with large similarities in their genomic signatures, in spite of belonging to vastly different domains in the Tree of Life.

Genomes are not static! They are dynamic and modify their content and architecture in response to intrinsic and extrinsic signals. Genome dynamics have direct phenotypic consequences in terms of cellular development, programmed function, and disease. Although the genome is classically depicted as linear strings, endogenous Extrachromosomal-circular DNA (eccDNA) comprises DNA products of "genome rewiring" in eukaryotic cells. By becoming physically unlinked from their cognate linear chromosomes, these elements become freed from the constraints of linear linkage, copy-number regulation, and equal partitioning to daughter cells. Thus, these circular elements are direct contributors to genomic diversity and cellular heterogeneity; rendering this process of their formation a remarkable vehicle for rapid cellular evolution. Yet, our understanding of genome rewiring via circular-DNA formation remains a fragmentary aspect of the 4D genome. Using a new DNA-topology-centered genomics workflows (in conjunction with new informatics and computational approaches) to investigate eccDNA-mediated genetic diversity, we have identified various pathology-specific regions of rewired chromosomes in normal and cancer backgrounds. In general, this work resurrects and advances the eccDNA field in addition to providing a missing key element for understanding oncogenic heterogeneity, consideration of which may drive novel diagnostics and reevaluation of current therapies.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

After giving a brief introduction to my software KnotPlot, I will talk about how it may aid researchers in entanglement problems, either for performing experiments or for illustrating the results of those experiments. Several examples will be presented. The presentation will be highly interactive and questions are welcomed. Following the talk will be a hands-on session where I will help people get KnotPlot installed, running and plotting knots on their laptops https://knotplot.com https://imapon.org/rob

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

The properties of the double stranded (ds)DNA molecule in free solution are well understood and accurate quantitative models have been developed and analyzed. An accurate description of DNA under spatial confinement, however, remains an open problem. We chose the bacteriophage as a model system to study DNA under confinement because in most organisms, DNA wraps around histones or histone like proteins that obscure its biophysical properties. Bacteriophages package their dsDNA in a protein container called capsid where it is kept with minimal interactions with other DNA binding structural proteins. Although the overall mathematical expression of the energy of confined dsDNA molecules is mostly unknown, three factors are known to significantly contribute to the free energy of the system. In the capsid, the dsDNA molecule is known to be in its liquid crystalline form due to the high local density of dsDNA fibers; under a very high bending stress due to the comparable size of the dsDNA persistence length in free solution and the capsid diameter (i.e. 45 nm); and under strong electrostatic repulsion due the negative charge and high local density of the dsDNA molecule. In this talk, I will present results from three different mathematical approaches to study the problem of dsDNA packing in bacteriophages. The first approach uses the formation of knots inside viral capsids as a probe for dsDNA packing. These results suggest that confinement of dsDNA increases topological complexity and that the dsDNA molecule is chirally organized inside the viral capsid. The second approach aims at identifying the possible sources of the chiral organization of the viral genome and employs brownian dynamics methods to model data from single molecule studies and suggest that the dsDNA packing reaction can account for the chiral organization of the genome. The third approach uses continuum mechanics of liquid crystals and electrostatics to mathematically describe cryoEM observations and quantify the relative importance of the mechanical and electrostatic components of the free energy of the system. The emergent picture of these approaches suggests that the organization of dsDNA under confinement is driven by electrostatics and the cholesteric component of the liquid crystalline state of the dsDNA molecule.

This talk is joint work with Sofia Lambropoulou and Ioannis Diamantis.We model topological and rigid vertex bonded knots and knotoids so that at the outset the bonds are special labeled arcs in trivalent graphs with univalent endpoints (for knotoid and linkoid structure). With this flexibility, bonds can be contracted to local bonds with a 4-valent vertex aspect, or they can be regarded as flexible parts of a larger network. Since the underlying structure is that of a trivalent graph, we can examine the topological embedding of that graph directly and in terms of knotted paths within it. We extend the notion of rigid vertex graph to a constraints on the trivalent vertices so that long topological bonds can be treated both in the topological and rigid vertex graph categories. Invariants are defined in via tangle insertions into the bonds, coupled with knot theoretic evaluations of the corresponding knots, knotoids and linksoids. Partial topological invariants using the Kauffman bracket are obtained as well. Applications to protein folding will be discussed.

Experiments on DNA in nanochannels have sparked interest in the statistical analysis of knots and links under tubular confinement. As one would expect, the types of entanglements that arise may depend on the confinement conditions. In this talk, I will discuss how certain open conjectures related to linking probabilities in the unconfined setting can be resolved when the links are confined in a lattice tube. Additionally, I will demonstrate a method to determine if a link can be embedded in tubes of specific sizes using a coloring game.

Lunch is served daily between 11:30am and 1:30pm in the Vistas Dining Room, the top floor of the Sally Borden Building.

Crystal structures have been formed by DNA, and single stranded DNA in such crystals possess topological properties beyond their space groups. Examples include whether their components form circles or infinite arcs. To investigate topological properties, we propose to use subgroups of space groups that preserve their components, and define topological invariants, such as linking number, parametrized by subgroup actions on building units. To define topological invariants, we use projections of embedded arcs such that end points are projected to the same points, and study their diagrammatic knot invariants.

The unknotting number is a natural measure of the complexity of a knot, but is notoriously difficult to calculate. Like knots, spatial planar graphs admit a well-defined unknotting number. The study of unknotting in both knots and spatial graphs is relevant in modeling problems arising in molecular biology. This motivates the goal of distinguishing, tabulating and characterizing unknotting numbers. Generalizing the theorem of Scharlemann that unknotting number one knots are prime, we prove that if a composite theta-curve has unknotting number one, then it is the connected sum of an unknotting number one knot and a trivial theta-curve. We will discuss some recent results in which we bound the unknotting numbers of spatial trivalent planar graphs by their signature and a certain slice orbifold Euler characteristic. This is joint work with Baker, Buck, O’Donnol and Taylor.

We discuss here an application of the Simultaneous Perturbation Stochastic Approximation (SPSA) method (Spall, 1992) to efficiently optimize two different lattice polygon models of DNA. In particular, we are using SPSA to find model parameters which best fit DNA experimental knotting probabilities obtained by Shaw and Wang in 1993. The resulting knotting probability fits are of similar quality for both models; however, we observe that the model containing a short-range bending potential has a persistence length that is much more agreeable to that of DNA.

The heterogeneity of many biomolecular structures, such as DNA, is driven by its flexibility. For DNA this allows it to interact with itself and cellular binding partners such as proteins, which can result in complex topologies. DNA conformation is essential to its biological function but its nanometre scale and flexibility makes structural determination challenging on molecules with complex topologies. Atomic force microscopy (AFM) has the resolution to image biomolecular structures in native-like states with sub-molecular accuracy, without labelling or averaging, capturing a wide range of molecular conformations. This range of potential conformations makes high throughput AFM characterisation difficult, and a lack of generalised automated analysis tools which accept the raw data, and provide effective structural characterisation means that currently much is done by hand.   Our new open-source analysis pipeline for the AFM image analysis software TopoStats enables single molecule determination of DNA topology from raw AFM images. The resolution achieved at DNA crossings allows us to determine crossing direction at each point and therefore explicitly determine topology. This is achieved by biasing a skeletonisation algorithm towards the higher regions of the DNA to obtain a more accurate trace along the molecular backbone while retaining the simplicity of single pixels. This approach accounts for tip broadening and other artifacts introduced by AFM imaging and can obtain a DNA trace of correct length even on complex supercoiled molecules. Interrogating the skeleton’s crossing points enables quantitative information as to the crossing architecture for each crossing, including crossing angles, branch counts, and an overlying/underlying classification.  This pipeline provides an open source, high-throughput, automated methodology to identify, quantify and characterise the structure of complex, intertwined molecules. By building into the wider AFM analysis toolbox, TopoStats, we hope this software will be of use to the wider community in determining the structure, interactions and topology of supercoiled DNA, and topologically complex DNAs such as catenanes and knots.

We introduce a novel representation of RNA secondary structures using tree polynomials. These polynomials enable accurate, interpretable and efficient data analysis of extensive RNA secondary structures. With tree polynomials, we identify a strong correlation between the nascent RNA secondary structure and R-loop formation. Tree polynomials allow for predicting R-loop formation with higher precision than previous methods. Furthermore, we can also identify the nascent RNA secondary structure associated with R-loop hot spots using tree polynomials. These results suggest a potential mechanism of R-loop formation involving nascent RNA folding.

Main Room: TCPL 201 Link: https://ubc.zoom.us/j/64276665131?pwd=ZUR4OTdvM3RlSFR0SnpVNk5WUFNWUT09 Meeting ID: 642 7666 5131 Password: 245267 Breakout Room 1: TCPL 202 Link: https://ubc.zoom.us/j/63544036533?pwd=U2xQV1RSSXkwSUo2Y0lwWWZVcnJjUT09 Meeting ID: 635 4403 6533 Password: 245267 Breakout Room 2: TCPL 106 Link: https://ubc.zoom.us/j/62266684726?pwd=U0xOQVBPRVMvaFNXU1RmMW1HbVF3Zz09 Meeting ID: 622 6668 4726 Password: 245267

A buffet dinner is served daily between 5:30pm and 7:30pm in Vistas Dining Room, top floor of the Sally Borden Building.

Breakfast is served daily between 7 and 9am in the Vistas Dining Room, the top floor of the Sally Borden Building.

Motivated by knot energies, the goal of this work is to describe the dynamics of a DNA trefoil knot with excess linking number in an ionized fluid. We consider two approaches: a deterministic approach and a stochastic approach. To study the deterministic dynamics, we use the Generalized Immersed Boundary (GIB) Method - a numerical method that accounts for the fluid structure interaction of an immersed DNA molecule in an ionized fluid. Using the GIB method, we find stable equilibrium configurations of DNA trefoil knots with excess linking number, analyze their symmetries, and approximate saddle configurations. We also analyze the elastic energy of the DNA trefoil throughout the deterministic process. To study the stochastic dynamics, we use the Stochastic Generalized Immersed Boundary (SGIB) Method - an extension of the GIB method which takes into account the random thermal fluctuations within the fluid - to numerically explore the knot energy landscape. For each fixed linking number, we consider the set of equilibrium configurations as the state space for a continuous time, discrete space, Markov chain, and find boundaries in the energy landscape using the Procrustes distance. Finally, given a fixed linking number, we obtain the steady state distribution for the Markov process and compare this to energy estimates obtained from the deterministic process.

The RNA Origami Automated Design (ROAD) software marks a significant advancement in the field of RNA nanotechnology, enabling the precise assembly of large-scale RNA nanostructures that fold accurately during transcription. By algorithmically tailoring both short-range and long-range RNA interactions, ROAD optimizes sequences to fold into patterns of helices and programs cross-links between helices with kissing loop interactions. The accuracy of our designs is supported by CryoEM imaging, which has provided high resolution maps that have helped up fine tune our design parameters. Detailed investigation of RNA origami by CryoEM characterization has revealed a new type of kinetic trapping, where RNA base pairs align correctly but adopt an incorrect 3D conformation because of the order of folding events. In this example, a long re-folding process is required to attain the designed lowest-energy structure. This research demonstrates that, in addition to precise structural design, we also need to anticipate folding barriers that may occur due to the improper timing of folding events during the dynamic condensing process.

5-day workshop participants are welcome to use BIRS facilities (TCPL ) until 3 pm on Friday, although participants are still required to checkout of the guest rooms by 11AM.