Discovery of a predicted DNA knot substantiates a model for site-specific recombination

Discovery of a trefoil knot in the RydC RNA: Challenging previous notions of RNA topology

Knots are very common in polymers, including DNA and protein molecules. Yet, no genuine knot has been identified in natural RNA molecules to date. Upon re-examining experimentally determined RNA 3D structures, we discovered a trefoil knot 31, the most basic non-trivial knot, in the RydC RNA. This knotted RNA is a member of a small family of short bacterial RNAs, whose secondary structure is characterized by an H-type pseudoknot. Molecular dynamics simulations suggest a folding pathway of the RydC RNA that starts with a native twisted loop. Based on sequence analyses and computational RNA 3D structure predictions, we postulate that this trefoil knot is a conserved feature of all RydC-related RNAs. The first discovery of a knot in a natural RNA molecule introduces a novel perspective on RNA 3D structure formation and on fundamental research on the relationship between function and spatial structure of biopolymers.

DNA-Topology Simplification by Topoisomerases

The topological properties of DNA molecules, supercoiling, knotting, and catenation, are intimately connected with essential biological processes, such as gene expression, replication, recombination, and chromosome segregation. Non-trivial DNA topologies present challenges to the molecular machines that process and maintain genomic information, for example, by creating unwanted DNA entanglements. At the same time, topological distortion can facilitate DNA-sequence recognition through localized duplex unwinding and longer-range loop-mediated interactions between the DNA sequences. Topoisomerases are a special class of essential enzymes that homeostatically manage DNA topology through the passage of DNA strands. The activities of these enzymes are generally investigated using circular DNA as a model system, in which case it is possible to directly assay the formation and relaxation of DNA supercoils and the formation/resolution of knots and catenanes. Some topoisomerases use ATP as an energy cofactor, whereas others act in an ATP-independent manner. The free energy of ATP hydrolysis can be used to drive negative and positive supercoiling or to specifically relax DNA topologies to levels below those that are expected at thermodynamic equilibrium. The latter activity, which is known as topology simplification, is thus far exclusively associated with type-II topoisomerases and it can be understood through insight into the detailed non-equilibrium behavior of type-II enzymes. We use a non-equilibrium topological-network approach, which stands in contrast to the equilibrium models that are conventionally used in the DNA-topology field, to gain insights into the rates that govern individual transitions between topological states. We anticipate that our quantitative approach will stimulate experimental work and the theoretical/computational modeling of topoisomerases and similar enzyme systems.

Chromatin Is Frequently Unknotted at the Megabase Scale

Knots in the human genome would greatly impact diverse cellular processes ranging from transcription to gene regulation. To date, it has not been possible to directly examine the genome in vivo for the presence of knots. Recently, methods for serial fluorescent in situ hybridization have made it possible to measure the three-dimensional position of dozens of consecutive genomic loci in vivo. However, the determination of whether genomic trajectories are knotted remains challenging because small errors in the localization of a single locus can transform an unknotted trajectory into a highly knotted trajectory and vice versa. Here, we use stochastic closure analysis to determine if a genomic trajectory is knotted in the setting of experimental noise. We analyze 4727 deposited genomic trajectories of a 2-Mb-long chromatin interval from human chromosome 21. For 243 of these trajectories, their knottedness could be reliably determined despite the possibility of localization errors. Strikingly, in each of these 243 cases, the trajectory was unknotted. We note a potential source of bias insofar as knotted contours may be more difficult to reliably resolve. Nevertheless, our data are consistent with a model in which, at the scales probed, the human genome is often free of knots.

Quantitative disclosure of DNA knot chirality by high-resolution 2D-gel electrophoresis

The characterization of knots formed in duplex DNA has proved useful to infer biophysical properties and the spatial trajectory of DNA, both in free solution and across its macromolecular interactions. Since knotting, like supercoiling, makes DNA molecules more compact, DNA knot probability and knot complexity can be assessed by the electrophoretic velocity of nicked DNA circles. However, the chirality of the DNA knots has to be determined by visualizing the sign of their DNA crossings by means of electron microscopy. This procedure, which requires purifying the knotted DNA molecules and coating them with protein, is semi-quantitative and it is impracticable in biological samples that contain little amount of knotted DNA forms. Here, we took advantage of an earlier observation that the two chiral forms of a trefoil knot acquire slightly different electrophoretic velocity when the DNA is supercoiled. We introduced a second gel dimension to reveal these chiral forms in DNA mixtures that are largely unknotted. The result is a high-resolution 2D-gel electrophoresis procedure that quantitatively discerns the fractions of positive- and negative-noded trefoil knots formed in vitro and in vivo systems. This development in DNA knot analysis may uncover valuable information toward disclosing the architecture of DNA ensembles.

Snapshots of a molecular swivel in action

Members of the serine family of site-specific recombinases exchange DNA strands via 180° rotation about a central protein-protein interface. Modeling of this process has been hampered by the lack of structures in more than one rotational state for any individual serine recombinase. Here we report crystal structures of the catalytic domains of four constitutively active mutants of the serine recombinase Sin, providing snapshots of rotational states not previously visualized for Sin, including two seen in the same crystal. Normal mode analysis predicted that each tetramer's lowest frequency mode (i.e. most accessible large-scale motion) mimics rotation: two protomers rotate as a pair with respect to the other two. Our analyses also suggest that rotation is not a rigid body movement around a single symmetry axis but instead uses multiple pivot points and entails internal motions within each subunit.

Two convergent pathways of DNA knotting in replicating DNA molecules as revealed by θ-curve analysis

During DNA replication in living cells some DNA knots are inadvertently produced by DNA topoisomerases facilitating progression of replication forks. The types of DNA knots formed are conditioned by the 3D organization of replicating DNA molecules. Therefore, by characterizing formed DNA knots it is possible to infer the 3D arrangement of replicating DNA molecules. This topological inference method is highly developed for knotted DNA circles. However, partially replicated DNA molecules have the form of θ-curves. In this article, we use mathematical formalism of θ-curves to characterize the full possibilities of how knotting can occur during replication of DNA molecules in vivo. To do this, we reanalyze earlier experimental studies of knotted, partially replicated DNA molecules and the previously proposed pathway of their formation. We propose a general model of knotting in replication intermediates, and demonstrate that there is an additional, equally important, parallel knotting pathway that also explains how DNA topoisomerases can produce experimentally observed knotted θ-curves. Interestingly, both pathways require intertwining of freshly replicated sister duplexes (precatenanes).

DNA knots occur in intracellular chromatin

In vivo DNA molecules are narrowly folded within chromatin fibers and self-interacting chromatin domains. Therefore, intra-molecular DNA entanglements (knots) might occur via DNA strand passage activity of topoisomerase II. Here, we assessed the presence of such DNA knots in a variety of yeast circular minichromosomes. We found that small steady state fractions of DNA knots are common in intracellular chromatin. These knots occur irrespective of DNA replication and cell proliferation, though their abundance is reduced during DNA transcription. We found also that in vivo DNA knotting probability does not scale proportionately with chromatin length: it reaches a value of ∼0.025 in domains of ∼20 nucleosomes but tends to level off in longer chromatin fibers. These figures suggest that, while high flexibility of nucleosomal fibers and clustering of nearby nucleosomes facilitate DNA knotting locally, some mechanism minimizes the scaling of DNA knot formation throughout intracellular chromatin. We postulate that regulation of topoisomerase II activity and the fractal architecture of chromatin might be crucial to prevent a potentially massive and harmful self-entanglement of DNA molecules in vivo.

Shining a Spotlight on DNA: Single-Molecule Methods to Visualise DNA

The ability to watch single molecules of DNA has revolutionised how we study biological transactions concerning nucleic acids. Many strategies have been developed to manipulate DNA molecules to investigate mechanical properties, dynamics and protein–DNA interactions. Imaging methods using small molecules and protein-based probes to visualise DNA have propelled our understanding of complex biochemical reactions involving DNA. This review focuses on summarising some of the methodological developments made to visualise individual DNA molecules and discusses how these probes have been used in single-molecule biophysical assays.

Dynamics of supercoiled DNA with complex knots: large-scale rearrangements and persistent multi-strand interlocking

Knots and supercoiling are both introduced in bacterial plasmids by catalytic processes involving DNA strand passages. While the effects on plasmid organization has been extensively studied for knotting and supercoiling taken separately, much less is known about their concurrent action. Here, we use molecular dynamics simulations and oxDNA, an accurate mesoscopic DNA model, to study the kinetic and metric changes introduced by complex (five-crossing) knots and supercoiling in 2 kbp-long DNA rings. We find several unexpected results. First, the conformational ensemble is dominated by two distinct states, differing in branchedness and knot size. Secondly, fluctuations between these states are as fast as the metric relaxation of unknotted rings. In spite of this, certain boundaries of knotted and plectonemically-wound regions can persist over much longer timescales. These pinned regions involve multiple strands that are interlocked by the cooperative action of topological and supercoiling constraints. Their long-lived character may be relevant for the simplifying action of topoisomerases.

Extending topological surgery to natural processes and dynamical systems

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. We observe that it occurs in natural phenomena where a sphere of dimension 0 or 1 is selected, forces are applied and the manifold in which they occur changes type. For example, 1-dimensional surgery happens during chromosomal crossover, DNA recombination and when cosmic magnetic lines reconnect, while 2-dimensional surgery happens in the formation of tornadoes, in the phenomenon of Falaco solitons, in drop coalescence and in the cell mitosis. Inspired by such phenomena, we introduce new theoretical concepts which enhance topological surgery with the observed forces and dynamics. To do this, we first extend the formal definition to a continuous process caused by local forces. Next, for modeling phenomena which do not happen on arcs or surfaces but are 2-dimensional or 3-dimensional, we fill in the interior space by defining the notion of solid topological surgery. We further introduce the notion of embedded surgery in S3 for modeling phenomena which involve more intrinsically the ambient space, such as the appearance of knotting in DNA and phenomena where the causes and effect of the process lies beyond the initial manifold, such as the formation of black holes. Finally, we connect these new theoretical concepts with a dynamical system and we present it as a model for both 2-dimensional 0-surgery and natural phenomena exhibiting a 'hole drilling' behavior. We hope that through this study, topology and dynamics of many natural phenomena, as well as topological surgery itself, will be better understood.

Topological transformations in proteins: effects of heating and proximity of an interface

Using a structure-based coarse-grained model of proteins, we study the mechanism of unfolding of knotted proteins through heating. We find that the dominant mechanisms of unfolding depend on the temperature applied and are generally distinct from those identified for folding at its optimal temperature. In particular, for shallowly knotted proteins, folding usually involves formation of two loops whereas unfolding through high-temperature heating is dominated by untying of single loops. Untying the knots is found to generally precede unfolding unless the protein is deeply knotted and the heating temperature exceeds a threshold value. We then use a phenomenological model of the air-water interface to show that such an interface can untie shallow knots, but it can also make knots in proteins that are natively unknotted.

Single-molecule analysis of ϕC31 integrase-mediated site-specific recombination by tethered particle motion

Serine and tyrosine site-specific recombinases (SRs and YRs, respectively) provide templates for understanding the chemical mechanisms and conformational dynamics of strand cleavage/exchange between DNA partners. Current evidence suggests a rather intriguing mechanism for serine recombination, in which one half of the cleaved synaptic complex undergoes a 180° rotation relative to the other. The 'small' and 'large' SRs contain a compact amino-terminal catalytic domain, but differ conspicuously in their carboxyl-terminal domains. So far, only one serine recombinase has been analyzed using single substrate molecules. We now utilized single-molecule tethered particle motion (TPM) to follow step-by-step recombination catalyzed by a large SR, phage ϕC31 integrase. The integrase promotes unidirectional DNA exchange between attB and attP sites to integrate the phage genome into the host chromosome. The recombination directionality factor (RDF; ϕC31 gp3) activates the excision reaction (attL × attR). From integrase-induced changes in TPM in the presence or absence of gp3, we delineated the individual steps of recombination and their kinetic features. The gp3 protein appears to regulate recombination directionality by selectively promoting or excluding active conformations of the synapse formed by specific att site partners. Our results support a 'gated rotation' of the synaptic complex between DNA cleavage and joining.

Direct observation of DNA knots using a solid-state nanopore

Long DNA molecules can self-entangle into knots. Experimental techniques for observing such DNA knots (primarily gel electrophoresis) are limited to bulk methods and circular molecules below 10 kilobase pairs in length. Here, we show that solid-state nanopores can be used to directly observe individual knots in both linear and circular single DNA molecules of arbitrary length. The DNA knots are observed as short spikes in the nanopore current traces of the traversing DNA molecules and their detection is dependent on a sufficiently high measurement resolution, which can be achieved using high-concentration LiCl buffers. We study the percentage of molecules with knots for DNA molecules of up to 166 kilobase pairs in length and find that the knotting occurrence rises with the length of the DNA molecule, consistent with a constant knotting probability per unit length. Our experimental data compare favourably with previous simulation-based predictions for long polymers. From the translocation time of the knot through the nanopore, we estimate that the majority of the DNA knots are tight, with remarkably small sizes below 100 nm. In the case of linear molecules, we also observe that knots are able to slide out on application of high driving forces (voltage).

Crossover-site sequence and DNA torsional stress control strand interchanges by the Bxb1 site-specific serine recombinase

DNA segment exchange by site-specific serine recombinases (SRs) is thought to proceed by rigid-body rotation of the two halves of the synaptic complex, following the cleavages that create the two pairs of exchangeable ends. It remains unresolved how the amount of rotation occurring between cleavage and religation is controlled. We report single-DNA experiments for Bxb1 integrase, a model SR, where dynamics of individual synapses were observed, using relaxation of supercoiling to report on cleavage and rotation events. Relaxation events often consist of multiple rotations, with the number of rotations per relaxation event and rotation velocity sensitive to DNA sequence at the center of the recombination crossover site, torsional stress and salt concentration. Bulk and single-DNA experiments indicate that the thermodynamic stability of the annealed, but cleaved, crossover sites controls ligation efficiency of recombinant and parental synaptic complexes, regulating the number of rotations during a breakage-religation cycle. The outcome is consistent with a ‘controlled rotation’ model analogous to that observed for type IB topoisomerases, with religation probability varying in accord with DNA base-pairing free energies at the crossover site. Significantly, we find no evidence for a special regulatory mechanism favoring ligation and product release after a single 180° rotation.

Controlled rotation mechanism of DNA strand exchange by the Hin serine recombinase

DNA strand exchange by serine recombinases has been proposed to occur by a large-scale rotation of halves of the recombinase tetramer. Here we provide the first direct physical evidence for the subunit rotation mechanism for the Hin serine invertase. Single-DNA looping assays using an activated mutant (Hin-H107Y) reveal specific synapses between two hix sites. Two-DNA “braiding” experiments, where separate DNA molecules carrying a single hix are interwound, show that Hin-H107Y cleaves both hix sites and mediates multi-step rotational relaxation of the interwinding. The variable numbers of rotations in the DNA braid experiments are in accord with data from bulk experiments that follow DNA topological changes accompanying recombination by the hyperactive enzyme. The relatively slow Hin rotation rates, combined with pauses, indicate considerable rotary friction between synapsed subunit pairs. A rotational pausing mechanism intrinsic to serine recombinases is likely to be crucial for DNA ligation and for preventing deleterious DNA rearrangements.

Serine Resolvases

Serine resolvases are an interesting group of site-specific recombinases that, in their native contexts, resolve large fused replicons into smaller separated ones. Some resolvases are encoded by replicative transposons and resolve the transposition product, in which the donor and recipient molecules are fused, into separate replicons. Other resolvases are encoded by plasmids and function to resolve plasmid dimers into monomers. Both types are therefore involved in the spread and maintenance of antibiotic-resistance genes. Resolvases and the closely related invertases were the first serine recombinases to be studied in detail, and much of our understanding of the unusual strand exchange mechanism of serine recombinases is owed to those early studies. Resolvases and invertases have also served as paradigms for understanding how DNA topology can be harnessed to regulate enzyme activity. Finally, their relatively modular structure, combined with a wealth of structural and biochemical data, has made them good choices for engineering chimeric recombinases with designer specificity. This chapter focuses on the current understanding of serine resolvases, with a focus on the contributions of structural studies.

Molecular knots in biology and chemistry

Knots and entanglements are ubiquitous. Beyond their aesthetic appeal, these fascinating topological entities can be either useful or cumbersome. In recent decades, the importance and prevalence of molecular knots have been increasingly recognised by scientists from different disciplines. In this review, we provide an overview on the various molecular knots found in naturally occurring biological systems (DNA, RNA and proteins), and those created by synthetic chemists. We discuss the current knowledge in these fields, including recent developments in experimental and, in some cases, computational studies which are beginning to shed light into the complex interplay between the structure, formation and properties of these topologically intricate molecules.

The Serine Recombinases

In site-specific recombination, two short DNA sequences (‘sites’) are each cut at specific points in both strands, and the cut ends are rejoined to new partners. The enzymes that mediate recognition of the sites and the subsequent cutting and rejoining steps are called recombinases. Most recombinases fall into one of two families according to similarities of their protein sequences and mechanisms; these families are known as the tyrosine recombinases and the serine recombinases, the names referring to the conserved amino acid residue that attacks the DNA phosphodiester and becomes covalently linked to a DNA strand end during catalysis. This chapter gives an overview of our current understanding of the serine recombinases, their types, biological roles, structures, catalytic mechanisms, mechanisms of regulation, and applications.

A proposed mechanism for IS607-family serine transposases

Background

The transposases encoded by the IS607 family of mobile elements are unusual serine recombinases with an inverted domain order and minimal specificity for target DNA.

Results

Structural genomics groups have determined three crystal structures of the catalytic domains of IS607 family transposases. The dimers formed by these catalytic domains are very different from those seen for other serine recombinases and include interactions that usually only occur upon formation of a synaptic tetramer.

Conclusions

Based on these structures, we propose a model for how IS607-family transposases could form a synaptic tetramer. The model suggests that, unlike other serine recombinases, these enzymes carry out sequence-specific DNA binding and catalysis in trans: the DNA binding and catalytic domains of each subunit are proposed to interact with different DNA duplexes. The model also suggests an explanation for the minimal target DNA specificity.

Determining the topology of stable protein–DNA complexes

Difference topology is an experimental technique that can be used to unveil the topological structure adopted by two or more DNA segments in a stable protein–DNA complex. Difference topology has also been used to detect intermediates in a reaction pathway and to investigate the role of DNA supercoiling. In the present article, we review difference topology as applied to the Mu transpososome. The tools discussed can be applied to any stable nucleoprotein complex.

Gated rotation mechanism of site-specific recombination by ϕC31 integrase

Integrases, such as that of the Streptomyces temperate bacteriophage ϕC31, promote site-specific recombination between DNA sequences in the bacteriophage and bacterial genomes to integrate or excise the phage DNA. ϕC31 integrase belongs to the serine recombinase family, a large group of structurally related enzymes with diverse biological functions. It has been proposed that serine integrases use a "subunit rotation" mechanism to exchange DNA strands after double-strand DNA cleavage at the two recombining att sites, and that many rounds of subunit rotation can occur before the strands are religated. We have analyzed the mechanism of ϕC31 integrase-mediated recombination in a topologically constrained experimental system using hybrid "phes" recombination sites, each of which comprises a ϕC31 att site positioned adjacent to a regulatory sequence recognized by Tn3 resolvase. The topologies of reaction products from circular substrates containing two phes sites support a right-handed subunit rotation mechanism for catalysis of both integrative and excisive recombination. Strand exchange usually terminates after a single round of 180° rotation. However, multiple processive "360° rotation" rounds of strand exchange can be observed, if the recombining sites have nonidentical base pairs at their centers. We propose that a regulatory "gating" mechanism normally blocks multiple rounds of strand exchange and triggers product release after a single round.

The spectrum of filament entanglement complexity and an entanglement phase transition

DNA, hair, shoelaces, vortex lines, rope, proteins, integral curves, thread, magnetic flux tubes, cosmic strings and extension cords; filaments come in all sizes and with diverse qualities. Filaments tangle, with profound results: DNA replication is halted, field energy is stored, polymer materials acquire their remarkable properties, textiles are created and shoes stay on feet. We classify entanglement patterns by the rate with which entanglement complexity grows with the length of the filament. We show which rates are possible and which are expected in arbitrary circumstances. We identify a fundamental phase transition between linear and nonlinear entanglement rates. We also find (perhaps surprising) relationships between total curvature, bending energy and entanglement.

Recombining DNA by protein swivels

Two new reports on serine recombinases, one of a crystal snapshot in an alternate rotational conformer poised for DNA cleavage (Keenholtz et al., 2011), and a second employing single-DNA molecule approaches (Bai et al., 2011), provide strong support for the subunit rotation model for exchanging DNA strands.

A topological framework for the computation of the HOMFLY polynomial and its application to proteins

Polymers can be modeled as open polygonal paths and their closure generates knots. Knotted proteins detection is currently achieved via high-throughput methods based on a common framework insensitive to the handedness of knots. Here we propose a topological framework for the computation of the HOMFLY polynomial, an handedness-sensitive invariant. Our approach couples a multi-component reduction scheme with the polynomial computation. After validation on tabulated knots and links the framework was applied to the entire Protein Data Bank along with a set of selected topological checks that allowed to discard artificially entangled structures. This led to an up-to-date table of knotted proteins that also includes two newly detected right-handed trefoil knots in recently deposited protein structures. The application range of our framework is not limited to proteins and it can be extended to the topological analysis of biological and synthetic polymers and more generally to arbitrary polygonal paths.

Topoisomerases and site-specific recombinases: similarities in structure and mechanism

The processes of DNA topoisomerization and site-specific recombination are fundamentally similar: DNA cleavage by forming a phospho-protein covalent linkage, DNA topological rearrangement, and DNA ligation coupled with protein regeneration. Type IB DNA topoisomerases are structurally and mechanistically homologous to tyrosine recombinases. Both enzymes nick DNA double helices independent of metal ions, form 3'-phosphotyrosine intermediates, and rearrange the free 5' ends relative to the uncut strands by swiveling. In contrast, serine recombinases generate 5'-phospho-serine intermediates. A 180° relative rotation of the two halves of a 100 kDa terameric serine recombinase and DNA complex has been proposed as the mechanism of strand exchange. Here I propose an alternative mechanism. Interestingly, the catalytic domain of serine recombinases has structural similarity to the TOPRIM domain, conserved among all Type IA and Type II topoisomerases and responsible for metal binding and DNA cleavage. TOPRIM topoisomerases also cleave DNA to generate 5'-phosphate and 3'-OH groups. Based on the existing biochemical data and crystal structures of topoisomerase II and serine recombinases bound to pre- and post-cleavage DNA, I suggest a strand passage mechanism for DNA recombination by serine recombinases. This mechanism is reminiscent of DNA topoisomerization and does not require subunit rotation.

Properties of knotted ring polymers. II. Transport properties

We have calculated the hydrodynamic radius R(h) and intrinsic viscosity [eta] of both lattice self-avoiding rings and lattice theta-state rings that are confined to specific knot states by our path-integration technique. We observe that naive scaling arguments based on the equilibrium polymer size fail for both the hydrodynamic radius and the intrinsic viscosity, at least over accessible chain lengths. (However, we do conjecture that scaling laws will nevertheless prevail at sufficiently large N.) This failure is attributed to a "double" cross-over. One cross-over effect is the transition from delocalized to localized knotting: in short chains, the knot is distributed throughout the chain, while in long chains it becomes localized in only a portion of the chain. This transition occurs slowly with increasing N. The other cross-over, superimposed upon the first, is the so-called "draining" effect, in which transport properties maintain dependence on local structure out to very large N. The hydrodynamic mobility of knotted rings of the same length and backbone structure is correlated with the average crossing number X of the knots. The same correlation between mobility and knot complexity X has been observed for the gel-electrophoretic mobility of cyclic DNA molecules.

Macromolecular knot in good and poor solvents: a Monte Carlo simulation

The probability and dimension of the simple macromolecular knots over a wide range of temperatures corresponding from good to poor solvents are investigated by Monte Carlo simulation. Macromolecular knots are modeled as rings of self-avoiding walks on a simple cubic lattice with the nearest neighbor attractions. We found that there is a minimum probability for the unknotted ring at a certain temperature. The size dependence of trivial, trefoil, and figure-eight knots on chain lengths and temperatures is presented. The simulation results for the size dependence on the knot's complication in different solvents are in good qualitative agreement with prediction of the scaling model proposed by Grosberg et al. The critical exponent for long chain is independent of the knot types based on the simulation results, although the mean square radius of gyration is influenced significantly by the knot types for a shorter length macromolecular ring. We calculated the ratio of the topological invariant p of trefoil knot and figure-eight knot and found that the ratio is approaching to 1.3 with the increasing of the chain length.

Biophysics of knotting

Knots appear in a wide variety of biophysical systems, ranging from biopolymers, such as DNA and proteins, to macroscopic objects, such as umbilical cords and catheters. Although significant advancements have been made in the mathematical theory of knots and some progress has been made in the statistical mechanics of knots in idealized chains, the mechanisms and dynamics of knotting in biophysical systems remain far from fully understood. We report on recent progress in the biophysics of knotting-the formation, characterization, and dynamics of knots in various biophysical contexts.

Orchestrating serine resolvases

A remarkable feature of the serine resolvases is their regulation: the wild-type enzymes will catalyse intra- but not inter-molecular recombination, can sense the relative orientation of their sites and can exchange strands directionally, despite the fact that there is no net release of chemical bond energy. The key to this regulation is that they are only active within a large intertwined complex called the 'synaptosome'. Because substrate topology greatly facilitates (or, in other cases, inhibits) formation of the synaptosome, it acts as a 'topological filter'. Within the defined topology of the synaptosome, strand exchange releases supercoiling tension, providing an energy source to bias the reaction direction. The regulatory portion of this complex contains additional copies of the recombinase and sometimes other DNA-bending proteins. We are using a combination of X-ray crystallography, biochemistry and genetics to model the full synaptic complex and to understand how the regulatory portion activates the crossover-site-bound recombinases.

Type III restriction enzymes cleave DNA by long-range interaction between sites in both head-to-head and tail-to-tail inverted repeat

Cleavage of viral DNA by the bacterial Type III Restriction-Modification enzymes requires the ATP-dependent long-range communication between a distant pair of DNA recognition sequences. The classical view is that Type III endonuclease activity is only activated by a pair of asymmetric sites in a specific head-to-head inverted repeat. Based on this assumption and due to the presence of helicase domains in Type III enzymes, various motor-driven DNA translocation models for communication have been suggested. Using both single-molecule and ensemble assays we demonstrate that Type III enzymes can also cleave DNA with sites in tail-to-tail repeat with high efficiency. The ability to distinguish both inverted repeat substrates from direct repeat substrates in a manner independent of DNA topology or accessory proteins can only be reconciled with an alternative sliding mode of communication.

DNA-DNA interactions in bacteriophage capsids are responsible for the observed DNA knotting

Recent experiments showed that the linear double-stranded DNA in bacteriophage capsids is both highly knotted and neatly structured. What is the physical basis of this organization? Here we show evidence from stochastic simulation techniques that suggests that a key element is the tendency of contacting DNA strands to order, as in cholesteric liquid crystals. This interaction favors their preferential juxtaposition at a small twist angle, thus promoting an approximately nematic (and apolar) local order. The ordering effect dramatically impacts the geometry and topology of DNA inside phages. Accounting for this local potential allows us to reproduce the main experimental data on DNA organization in phages, including the cryo-EM observations and detailed features of the spectrum of DNA knots formed inside viral capsids. The DNA knots we observe are strongly delocalized and, intriguingly, this is shown not to interfere with genome ejection out of the phage.

The Hin recombinase assembles a tetrameric protein swivel that exchanges DNA strands

Most site-specific recombinases can be grouped into two structurally and mechanistically different classes. Whereas recombination by tyrosine recombinases proceeds with little movements by the proteins, serine recombinases exchange DNA strands by a mechanism requiring large quaternary rearrangements. Here we use site-directed crosslinking to investigate the conformational changes that accompany the formation of the synaptic complex and the exchange of DNA strands by the Hin serine recombinase. Efficient crosslinking between residues corresponding to the ‘D-helix’ region provides the first experimental evidence for interactions between synapsed subunits within this region and distinguishes between different tetrameric conformers that have been observed in crystal structures of related serine recombinases. Crosslinking profiles between cysteines introduced over the 35 residue E-helix region that constitutes most of the proposed rotating interface both support the long helical structure of the region and provide strong experimental support for a subunit rotation mechanism that mediates DNA exchange.

Observation and analysis of coherent optical waves emitted from large-Fresnel number degenerate cavities

We demonstrate that the coherent optical waves emitted from large-Fresnel-number degenerate cavities persistently display a sort of salient intensity variations. We use the representation of the coherent states to explore the origin of the salient intensity variations and find that these coherent laser waves arise from a quadrature superposition of two degenerate coherent states. With the analytical representation of the superposed coherent states, we verify that these coherent laser waves possess a large angular momentum per photon.

Architecture of a serine recombinase-DNA regulatory complex

An essential feature of many site-specific recombination systems is their ability to regulate the direction and topology of recombination. Resolvases from the serine recombinase family assemble an interwound synaptic complex that harnesses negative supercoiling to drive the forward reaction and promote recombination between properly oriented sites. To better understand the interplay of catalytic and regulatory functions within these synaptic complexes, we have solved the structure of the regulatory site synapse in the Sin resolvase system. It reveals an unexpected synaptic interface between helix-turn-helix DNA-binding domains that is also highlighted in a screen for synapsis mutants. The tetramer defined by this interface provides the foundation for a robust model of the synaptic complex, assembled entirely from available crystal structures, that gives insight into how the catalytic activity of Sin and other serine recombinases may be regulated.

Production of highly knotted DNA by means of cosmid circularization inside phage capsids

BACKGROUND

The formation of DNA knots is common during biological transactions. Yet, functional implications of knotted DNA are not fully understood. Moreover, potential applications of DNA molecules condensed by means of knotting remain to be explored. A convenient method to produce abundant highly knotted DNA would be highly valuable for these studies.

RESULTS

We had previously shown that circularization of the 11.2 kb linear DNA of phage P4 inside its viral capsid generates complex knots by the effect of confinement. We demonstrate here that this mechanism is not restricted to the viral genome. We constructed DNA cosmids as small as 5 kb and introduced them inside P4 capsids. Such cosmids were then recovered as a complex mixture of highly knotted DNA circles. Over 250 mug of knotted cosmid were typically obtained from 1 liter of bacterial culture.

CONCLUSION

With this biological system, DNA molecules of varying length and sequence can be shaped into very complex and heterogeneous knotted forms. These molecules can be produced in preparative amounts suitable for systematic studies and applications.

Predicting knot or catenane type of site-specific recombination products

Site-specific recombination on supercoiled circular DNA yields a variety of knotted or catenated products. Here, we present a topological model of this process and characterize all possible products of the most common substrates: unknots, unlinks, and torus knots and catenanes. This model tightly prescribes the knot or catenane type of previously uncharacterized data. We also discuss how the model helps to distinguish products of distributive recombination and, in some cases, determine the order of processive recombination products.

Mechanisms of site-specific recombination

Integration, excision, and inversion of defined DNA segments commonly occur through site-specific recombination, a process of DNA breakage and reunion that requires no DNA synthesis or high-energy cofactor. Virtually all identified site-specific recombinases fall into one of just two families, the tyrosine recombinases and the serine recombinases, named after the amino acid residue that forms a covalent protein-DNA linkage in the reaction intermediate. Their recombination mechanisms are distinctly different. Tyrosine recombinases break and rejoin single strands in pairs to form a Holliday junction intermediate. By contrast, serine recombinases cut all strands in advance of strand exchange and religation. Many natural systems of site-specific recombination impose sophisticated regulatory mechanisms on the basic recombinational process to favor one particular outcome of recombination over another (for example, excision over inversion or deletion). Details of the site-specific recombination processes have been revealed by recent structural and biochemical studies of members of both families.