FtsK-dependent XerCD-dif recombination unlinks replication catenanes in a stepwise manner

Spatio-temporal organization of the E. coli chromosome from base to cellular length scales

Escherichia coli has been a vital model organism for studying chromosomal structure, thanks, in part, to its small and circular genome (4.6 million base pairs) and well-characterized biochemical pathways. Over the last several decades, we have made considerable progress in understanding the intricacies of the structure and subsequent function of the E. coli nucleoid. At the smallest scale, DNA, with no physical constraints, takes on a shape reminiscent of a randomly twisted cable, forming mostly random coils but partly affected by its stiffness. This ball-of-spaghetti-like shape forms a structure several times too large to fit into the cell. Once the physiological constraints of the cell are added, the DNA takes on overtwisted (negatively supercoiled) structures, which are shaped by an intricate interplay of many proteins carrying out essential biological processes. At shorter length scales (up to about 1 kb), nucleoid-associated proteins organize and condense the chromosome by inducing loops, bends, and forming bridges. Zooming out further and including cellular processes, topological domains are formed, which are flanked by supercoiling barriers. At the megabase-scale both large, highly self-interacting regions (macrodomains) and strong contacts between distant but co-regulated genes have been observed. At the largest scale, the nucleoid forms a helical ellipsoid. In this review, we will explore the history and recent advances that pave the way for a better understanding of E. coli chromosome organization and structure, discussing the cellular processes that drive changes in DNA shape, and what contributes to compaction and formation of dynamic structures, and in turn how bacterial chromatin affects key processes such as transcription and replication.

Investigating the mechanism of rough phenotype in a naturally attenuated Brucella strain: insights from whole genome sequencing

Objective

Brucellosis, a significant zoonotic disease, not only impacts animal health but also profoundly influences the host immune responses through gut microbiome. Our research focuses on whole genome sequencing and comparative genomic analysis of these Brucella strains to understand the mechanisms of their virulence changes that may deepen our comprehension of the host immune dysregulation.

Methods

The Brucella melitensis strain CMCC55210 and its naturally attenuated variant CMCC55210a were used as models. Biochemical identification tests and in vivo experiments in mice verified the characteristics of the strain. To understand the mechanism of attenuation, we then performed de novo sequencing of these two strains.

Results

We discovered notable genomic differences between the two strains, with a key single nucleotide polymorphism (SNP) mutation in the manB gene potentially altering lipopolysaccharide (LPS) structure and influencing host immunity to the pathogen. This mutation might contribute to the attenuated strain's altered impact on the host's macrophage immune response, overing insights into the mechanisms of immune dysregulation linked to intracellular survival. Furthermore, we explore that manipulating the Type I restriction-modification system in Brucella can significantly impact its genome stability with the DNA damage response, consequently affecting the host's immune system.

Conclusion

This study not only contributes to understanding the complex relationship between pathogens, and the immune system but also opens avenues for innovative therapeutic interventions in inflammatory diseases driven by microbial and immune dysregulation.

Plasticity in the cell division processes of obligate intracellular bacteria

Most bacteria divide through a highly conserved process called binary fission, in which there is symmetric growth of daughter cells and the synthesis of peptidoglycan at the mid-cell to enable cytokinesis. During this process, the parental cell replicates its chromosomal DNA and segregates replicated chromosomes into the daughter cells. The mechanisms that regulate binary fission have been extensively studied in several model organisms, including Eschericia coli, Bacillus subtilis, and Caulobacter crescentus. These analyses have revealed that a multi-protein complex called the divisome forms at the mid-cell to enable peptidoglycan synthesis and septation during division. In addition, rod-shaped bacteria form a multi-protein complex called the elongasome that drives sidewall peptidoglycan synthesis necessary for the maintenance of rod shape and the lengthening of the cell prior to division. In adapting to their intracellular niche, the obligate intracellular bacteria discussed here have eliminated one to several of the divisome gene products essential for binary fission in E. coli. In addition, genes that encode components of the elongasome, which were mostly lost as rod-shaped bacteria evolved into coccoid organisms, have been retained during the reductive evolutionary process that some coccoid obligate intracellular bacteria have undergone. Although the precise molecular mechanisms that regulate the division of obligate intracellular bacteria remain undefined, the studies summarized here indicate that obligate intracellular bacteria exhibit remarkable plasticity in their cell division processes.

A dicentric bacterial chromosome requires XerC/D site-specific recombinases for resolution

Unlike eukaryotes and archaea, which have multiple replication origins on their chromosomes, bacterial chromosomes usually contain a single replication origin.1 Here, we discovered a dicentric bacterial chromosome with two replication origins, which has resulted from the fusion of the circular and linear chromosomes in Agrobacterium tumefaciens. The fused chromosome is well tolerated, stably maintained, and retains similar subcellular organization and genome-wide DNA interactions found for the bipartite chromosomes. Strikingly, the two replication origins and their partitioning systems are both functional and necessary for cell survival. Finally, we discovered that the site-specific recombinases XerC and XerD2 are essential in cells harboring the fused chromosome but not in cells with bipartite chromosomes. Analysis of actively dividing cells suggests a model in which XerC/D are required to recombine the sister fusion chromosomes when the two centromeres on the same chromosome are segregated to opposite cell poles. Thus, faithful segregation of dicentric chromosomes in bacteria can occur because of site-specific recombination between the sister chromatids during chromosome partitioning. Our study provides a natural comparative platform to examine a bacterial chromosome with multiple origins and a possible explanation for the fundamental difference in bacterial genome architecture relative to eukaryotes and archaea.1.

On the Classification of Polyhedral Links

Knots and links are ubiquitous in chemical systems. Their structure can be responsible for a variety of physical and chemical properties, making them very important in materials development. In this article, we analyze the topological structures of interlocking molecules composed of metal-peptide rings using the concept of polyhedral links. To that end, we discuss the topological classification of alternating polyhedral links.

The Local Topological Free Energy of the SARS-CoV-2 Spike Protein

The novel coronavirus SARS-CoV-2 infects human cells using a mechanism that involves binding and structural rearrangement of its Spike protein. Understanding protein rearrangement and identifying specific amino acids where mutations affect protein rearrangement has attracted much attention for drug development. In this manuscript, we use a mathematical method to characterize the local topology/geometry of the SARS-CoV-2 Spike protein backbone. Our results show that local conformational changes in the FP, HR1, and CH domains are associated with global conformational changes in the RBD domain. The SARS-CoV-2 variants analyzed in this manuscript (alpha, beta, gamma, delta Mink, G614, N501) show differences in the local conformations of the FP, HR1, and CH domains as well. Finally, most mutations of concern are either in or in the vicinity of high local topological free energy conformations, suggesting that high local topological free energy conformations could be targets for mutations with significant impact of protein function. Namely, the residues 484, 570, 614, 796, and 969, which are present in variants of concern and are targeted as important in protein function, are predicted as such from our model.

Observation of optical vortex knots and links associated with topological charge

Knots and links, as three-dimensional topologies, have played a fundamental role in many physical fields. Despite knotted vortex loops having been shown to exist in the light field, the three-dimensional configuration of vortex loop is fixed due to their topological robustness, making the fields with different topologies independent of each other. In this work, we established the mapping between the torus knots/links and the integer topological charge of the optical vortex, and demonstrated the change of the intermediate state with fractional charges. Furthermore, we experimentally observed the transformation process of the three-dimensional topological structure by only changing the topological charge. Remarkably, we revealed two different reconnection mechanisms associated with the odd or even index of the torus topology. We hope these results may provide new insight for the study of singular optics and evolution in other physical fields.

Topological and physical links in soft matter systems

Linking, or multicomponent topological entanglement, is ubiquitous in soft matter systems, from mixtures of polymers and DNA filaments packedin vivoto interlocked line defects in liquid crystals and intertwined synthetic molecules. Yet, it is only relatively recently that theoretical and experimental advancements have made it possible to probe such entanglements and elucidate their impact on the physical properties of the systems. Here, we review the state-of-the-art of this rapidly expanding subject and organize it as follows. First, we present the main concepts and notions, from topological linking to physical linking and then consider the salient manifestations of molecular linking, from synthetic to biological ones. We next cover the main physical models addressing mutual entanglements in mixtures of polymers, both linear and circular. Finally, we consider liquid crystals, fluids and other non-filamentous systems where topological or physical entanglements are observed in defect or flux lines. We conclude with a perspective on open challenges.

Topological complex-energy braiding of non-Hermitian bands

Effects connected with the mathematical theory of knots¹ emerge in many areas of science, from physics^2,3 to biology⁴. Recent theoretical work discovered that the braid group characterizes the topology of non-Hermitian periodic systems⁵, where the complex band energies can braid in momentum space. However, such braids of complex-energy bands have not been realized or controlled experimentally. Here, we introduce a tight-binding lattice model that can achieve arbitrary elements in the braid group of two strands 𝔹₂. We experimentally demonstrate such topological complex-energy braiding of non-Hermitian bands in a synthetic dimension^6,7. Our experiments utilize frequency modes in two coupled ring resonators, one of which undergoes simultaneous phase and amplitude modulation. We observe a wide variety of two-band braiding structures that constitute representative instances of links and knots, including the unlink, the unknot, the Hopf link and the trefoil. We also show that the handedness of braids can be changed. Our results provide a direct demonstration of the braid-group characterization of non-Hermitian topology and open a pathway for designing and realizing topologically robust phases in open classical and quantum systems.

Competitive binding of MatP and topoisomerase IV to the MukB hinge domain

Structural Maintenance of Chromosomes (SMC) complexes have ubiquitous roles in compacting DNA linearly, thereby promoting chromosome organization-segregation. Interaction between the Escherichia coli SMC complex, MukBEF, and matS-bound MatP in the chromosome replication termination region, ter, results in depletion of MukBEF from ter, a process essential for efficient daughter chromosome individualization and for preferential association of MukBEF with the replication origin region. Chromosome-associated MukBEF complexes also interact with topoisomerase IV (ParC₂E₂), so that their chromosome distribution mirrors that of MukBEF. We demonstrate that MatP and ParC have an overlapping binding interface on the MukB hinge, leading to their mutually exclusive binding, which occurs with the same dimer to dimer stoichiometry. Furthermore, we show that matS DNA competes with the MukB hinge for MatP binding. Cells expressing MukBEF complexes that are mutated at the ParC/MatP binding interface are impaired in ParC binding and have a mild defect in MukBEF function. These data highlight competitive binding as a means of globally regulating MukBEF-topoisomerase IV activity in space and time.

The local topological free energy of proteins

Protein folding, the process by which proteins attain a 3-dimensional conformation necessary for their function, remains an important unsolved problem in biology. A major gap in our understanding is how local properties of proteins relate to their global properties. In this manuscript, we use the Writhe and Torsion to introduce a new local topological/geometrical free energy that can be associated to 4 consecutive amino acids along the protein backbone. By analyzing a culled protein dataset from the PDB, our results show that high local topological free energy conformations are independent of sequence and may be involved in the rate limiting step in protein folding. By analyzing a set of 2-state single domain proteins, we find that the total local topological free energy of these proteins correlates with the experimentally observed folding rates reported in Plaxco et al. (2000).

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.

XerD unloads bacterial SMC complexes at the replication terminus

Bacillus subtilis structural maintenance of chromosomes (SMC) complexes are topologically loaded at centromeric sites adjacent to the replication origin by the partitioning protein ParB. These ring-shaped ATPases then translocate down the left and right chromosome arms while tethering them together. Here, we show that the site-specific recombinase XerD, which resolves chromosome dimers, is required to unload SMC tethers when they reach the terminus. We identify XerD-specific binding sites in the terminus region and show that they dictate the site of unloading in a manner that depends on XerD but not its catalytic residue, its partner protein XerC, or the recombination site dif. Finally, we provide evidence that ParB and XerD homologs perform similar functions in Staphylococcus aureus. Thus, two broadly conserved factors that act at the origin and terminus have second functions in loading and unloading SMC complexes that travel between them.

Functional Analysis of the Acinetobacter baumannii XerC and XerD Site-Specific Recombinases: Potential Role in Dissemination of Resistance Genes

Modules composed of a resistance gene flanked by Xer site-specific recombination sites, the vast majority of which were found in Acinetobacter baumannii, are thought to behave as elements that facilitate horizontal dissemination. The A. baumannii xerC and xerD genes were cloned, and the recombinant clones used to complement the cognate Escherichia coli mutants. The complemented strains supported the resolution of plasmid dimers, and, as is the case with E. coli and Klebsiella pneumoniae plasmids, the activity was enhanced when the cells were grown in a low osmolarity growth medium. Binding experiments showed that the partially purified A. baumannii XerC and XerD proteins (XerCAb and XerDAb) bound synthetic Xer site-specific recombination sites, some of them with a nucleotide sequence deduced from existing A. baumannii plasmids. Incubation with suicide substrates resulted in the covalent attachment of DNA to a recombinase, probably XerCAb, indicating that the first step in the recombination reaction took place. The results described show that XerCAb and XerDAb are functional proteins and support the hypothesis that they participate in horizontal dissemination of resistant genes among bacteria.

Loop-closure kinetics reveal a stable, right-handed DNA intermediate in Cre recombination

In Cre site-specific recombination, the synaptic intermediate is a recombinase homotetramer containing a pair of loxP DNA target sites. The enzyme system's strand-exchange mechanism proceeds via a Holliday-junction (HJ) intermediate; however, the geometry of DNA segments in the synapse has remained highly controversial. In particular, all crystallographic structures are consistent with an achiral, planar Holliday-junction (HJ) structure, whereas topological assays based on Cre-mediated knotting of plasmid DNAs are consistent with a right-handed chiral junction. We use the kinetics of loop closure involving closely spaced (131-151 bp) loxP sites to investigate the in-aqueo ensemble of conformations for the longest-lived looped DNA intermediate. Fitting the experimental site-spacing dependence of the loop-closure probability, J, to a statistical-mechanical theory of DNA looping provides evidence for substantial out-of-plane HJ distortion, which unequivocally stands in contrast to the square-planar intermediate geometry from Cre-loxP crystal structures and those of other int-superfamily recombinases. J measurements for an HJ-isomerization-deficient Cre mutant suggest that the apparent geometry of the wild-type complex is consistent with temporal averaging of right-handed and achiral structures. Our approach connects the static pictures provided by crystal structures and the natural dynamics of macromolecules in solution, thus advancing a more comprehensive dynamic analysis of large nucleoprotein structures and their mechanisms.

A topological analysis of difference topology experiments of condensin with topoisomerase II

An experimental technique called difference topology combined with the mathematics of tangle analysis has been used to unveil the structure of DNA bound by the Mu transpososome. However, difference topology experiments can be difficult and time consuming. We discuss a modification that greatly simplifies this experimental technique. This simple experiment involves using a topoisomerase to trap DNA crossings bound by a protein complex and then running a gel to determine the crossing number of the knotted product(s). We develop the mathematics needed to analyze the results and apply these results to model the topology of DNA bound by 13S condensin and by the condensin MukB.

Kinetic pathways of topology simplification by Type-II topoisomerases in knotted supercoiled DNA

The topological state of covalently closed, double-stranded DNA is defined by the knot type $K$ and the linking-number difference $\Delta Lk$ relative to unknotted relaxed DNA. DNA topoisomerases are essential enzymes that control the topology of DNA in all cells. In particular, type-II topoisomerases change both $K$ and $\Delta Lk$ by a duplex-strand-passage mechanism and have been shown to simplify the topology of DNA to levels below thermal equilibrium at the expense of ATP hydrolysis. It remains a key question how small enzymes are able to preferentially select strand passages that result in topology simplification in much larger DNA molecules. Using numerical simulations, we consider the non-equilibrium dynamics of transitions between topological states $(K,\Delta Lk)$ in DNA induced by type-II topoisomerases. For a biological process that delivers DNA molecules in a given topological state $(K,\Delta Lk)$ at a constant rate we fully characterize the pathways of topology simplification by type-II topoisomerases in terms of stationary probability distributions and probability currents on the network of topological states $(K,\Delta Lk)$. In particular, we observe that type-II topoisomerase activity is significantly enhanced in DNA molecules that maintain a supercoiled state with constant torsional tension. This is relevant for bacterial cells in which torsional tension is maintained by enzyme-dependent homeostatic mechanisms such as DNA-gyrase activity.

The Rabl configuration limits topological entanglement of chromosomes in budding yeast

The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers.

A Symmetry Motivated Link Table

Proper identification of oriented knots and 2-component links requires a precise link nomenclature. Motivated by questions arising in DNA topology, this study aims to produce a nomenclature unambiguous with respect to link symmetries. For knots, this involves distinguishing a knot type from its mirror image. In the case of 2-component links, there are up to sixteen possible symmetry types for each link type. The study revisits the methods previously used to disambiguate chiral knots and extends them to oriented 2-component links with up to nine crossings. Monte Carlo simulations are used to report on writhe, a geometric indicator of chirality. There are ninety-two prime 2-component links with up to nine crossings. Guided by geometrical data, linking number, and the symmetry groups of 2-component links, canonical link diagrams for all but five link types (9 5 2, 9 34 2, 9 35 2, 9 39 2, and 9 41 2) are proposed. We include complete tables for prime knots with up to ten crossings and prime links with up to nine crossings. We also prove a result on the behavior of the writhe under local lattice moves.

Topological Polymer Chemistry Designing Complex Macromolecular Graph Constructions

The precision design of topologically intriguing macromolecular architectures has continuously been an attractive challenge in polymer science and polymer materials engineering. A class of multicyclic polymer topologies, including three subclasses of spiro, bridged, and fused forms, are particularly unique not only from a topological geometry viewpoint but also from their biochemical relevance to programmed folding structures. In this Account, we describe recent progress in constructing this class of macromolecules, in particular by means of an electrostatic self-assembly and covalent fixation (ESA-CF) protocol, in which ion-paired polymer self-assemblies are employed as key intermediates. All three dicyclic constructions having either 8 (spiro), manacle (bridged), or θ (fused) forms, as well as a tricyclic trefoil (spiro) graph, have been constructed by the ESA-CF process. Moreover, a triply fused-tetracyclic macromolecular K_3,3 graph has been constructed using a uniform-size dendritic polymer precursor having six cyclic ammonium salt end groups carrying two units of a trifunctional carboxylate counteranion. Remarkably, the K_3,3 graph is known in topological geometry as a prototypical nonplanar graph and has been identified as topologically equivalent to some multicyclic polypeptides (cyclotides) produced through the intramolecular S-S bridging with cysteine residues. A series of single cyclic (ring) polymers having one, two, and even three designated functional groups at the prescribed positions along their cyclic backbone segment (kyklo-telechelics) have also been obtained by the ESA-CF protocol. And in conjunction with a tandem alkyne-azide addition (i.e., click) and an olefin metathesis (i.e., clip) reaction, the precision design of complex multicyclic macromolecular architectures has been achieved. Thus, a series of tri-, tetra-, and even hexacyclic polymer topologies of spiro- and bridged-forms and three doubly fused-tricycle (β-, γ-, and δ-graph) forms, as well as a triply fused-tetracyclic and a quadruply fused-pentacyclic form (unfolded tetrahedron-graph, and "shippo"-form, respectively) were effectively constructed. Furthermore, the hybrid multicyclic polymer constructions comprised of three subclasses of spiro, bridged, and fused units have been produced using complementary pairs of single cyclic and dicyclic kyklo-telechelic precursors obtainable by the ESA-CF process. Upon these synthetic developments, we are now entering into an exciting new era of polymer science and polymer materials engineering based on the precision design of polymer topologies, which appears comparable to the "Cambrian explosion period" experienced in the evolution of life systems.

Pathways of DNA unlinking: A story of stepwise simplification

In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.

Molecular Dynamics Simulation of Supercoiled, Knotted, and Catenated DNA Molecules, Including Modeling of Action of DNA Gyrase

A detailed protocol of molecular dynamics simulations of supercoiled DNA molecules that can be in addition knotted or catenated is described. We also describe how to model ongoing action of DNA gyrase that introduces negative supercoing into DNA molecules. The protocols provide detailed instructions about model parameters, equations of used potentials, simulation, and visualization. Implementation of the model into a frequently used molecular dynamics simulation environment, ESPResSo, is shown step by step.

An Overview of Tyrosine Site-specific Recombination: From an Flp Perspective

Tyrosine site-specific recombinases (YRs) are widely distributed among prokaryotes and their viruses, and were thought to be confined to the budding yeast lineage among eukaryotes. However, YR-harboring retrotransposons (the DIRS and PAT families) and DNA transposons (Cryptons) have been identified in a variety of eukaryotes. The YRs utilize a common chemical mechanism, analogous to that of type IB topoisomerases, to bring about a plethora of genetic rearrangements with important physiological consequences in their respective biological contexts. A subset of the tyrosine recombinases has provided model systems for analyzing the chemical mechanisms and conformational features of the recombination reaction using chemical, biochemical, topological, structural, and single molecule-biophysical approaches. YRs with simple reaction requirements have been utilized to bring about programmed DNA rearrangements for addressing fundamental questions in developmental biology. They have also been employed to trace the topological features of DNA within high-order DNA interactions established by protein machines. The directed evolution of altered specificity YRs, combined with their spatially and temporally regulated expression, heralds their emergence as vital tools in genome engineering projects with wide-ranging biotechnological and medical applications.

Knots cascade detected by a monotonically decreasing sequence of values

Due to reconnection or recombination of neighboring strands superfluid vortex knots and DNA plasmid torus knots and links are found to undergo an almost identical cascade process, that tend to reduce topological complexity by stepwise unlinking. Here, by using the HOMFLYPT polynomial recently introduced for fluid knots, we prove that under the assumption that topological complexity decreases by stepwise unlinking this cascade process follows a path detected by a unique, monotonically decreasing sequence of numerical values. This result holds true for any sequence of standardly embedded torus knots T(2, 2n + 1) and torus links T(2, 2n). By this result we demonstrate that the computation of this adapted HOMFLYPT polynomial provides a powerful tool to measure topological complexity of various physical systems.

Xer Site-Specific Recombination: Promoting Vertical and Horizontal Transmission of Genetic Information

Two related tyrosine recombinases, XerC and XerD, are encoded in the genome of most bacteria where they serve to resolve dimers of circular chromosomes by the addition of a crossover at a specific site, dif. From a structural and biochemical point of view they belong to the Cre resolvase family of tyrosine recombinases. Correspondingly, they are exploited for the resolution of multimers of numerous plasmids. In addition, they are exploited by mobile DNA elements to integrate into the genome of their host. Exploitation of Xer is likely to be advantageous to mobile elements because the conservation of the Xer recombinases and of the sequence of their chromosomal target should permit a quite easy extension of their host range. However, it requires means to overcome the cellular mechanisms that normally restrict recombination to dif sites harbored by a chromosome dimer and, in the case of integrative mobile elements, to convert dedicated tyrosine resolvases into integrases.

Resolution of Multimeric Forms of Circular Plasmids and Chromosomes

One of the disadvantages of circular plasmids and chromosomes is their high sensitivity to rearrangements caused by homologous recombination. Odd numbers of crossing-over occurring during or after replication of a circular replicon result in the formation of a dimeric molecule in which the two copies of the replicon are fused. If they are not converted back to monomers, the dimers of replicons may fail to correctly segregate at the time of cell division. Resolution of multimeric forms of circular plasmids and chromosomes is mediated by site-specific recombination, and the enzymes that catalyze this type of reaction fall into two families of proteins: the serine and tyrosine recombinase families. Here we give an overview of the variety of site-specific resolution systems found on circular plasmids and chromosomes.

Assembly, translocation, and activation of XerCD-dif recombination by FtsK translocase analyzed in real-time by FRET and two-color tethered fluorophore motion

The FtsK dsDNA translocase functions in bacterial chromosome unlinking by activating XerCD-dif recombination in the replication terminus region. To analyze FtsK assembly and translocation, and the subsequent activation of XerCD-dif recombination, we extended the tethered fluorophore motion technique, using two spectrally distinct fluorophores to monitor two effective lengths along the same tethered DNA molecule. We observed that FtsK assembled stepwise on DNA into a single hexamer, and began translocation rapidly (∼ 0.25 s). Without extruding DNA loops, single FtsK hexamers approached XerCD-dif and resided there for ∼ 0.5 s irrespective of whether XerCD-dif was synapsed or unsynapsed. FtsK then dissociated, rather than reversing. Infrequently, FtsK activated XerCD-dif recombination when it encountered a preformed synaptic complex, and dissociated before the completion of recombination, consistent with each FtsK-XerCD-dif encounter activating only one round of recombination.

Conservation of writhe helicity under anti-parallel reconnection

Reconnection is a fundamental event in many areas of science, from the interaction of vortices in classical and quantum fluids, and magnetic flux tubes in magnetohydrodynamics and plasma physics, to the recombination in polymer physics and DNA biology. By using fundamental results in topological fluid mechanics, the helicity of a flux tube can be calculated in terms of writhe and twist contributions. Here we show that the writhe is conserved under anti-parallel reconnection. Hence, for a pair of interacting flux tubes of equal flux, if the twist of the reconnected tube is the sum of the original twists of the interacting tubes, then helicity is conserved during reconnection. Thus, any deviation from helicity conservation is entirely due to the intrinsic twist inserted or deleted locally at the reconnection site. This result has important implications for helicity and energy considerations in various physical contexts.

The FtsK family of DNA translocases finds the ends of circles

A global view of bacterial chromosome choreography during the cell cycle is emerging, highlighting as a next challenge the description of the molecular mechanisms and factors involved. Here, we review one such factor, the FtsK family of DNA translocases. FtsK is a powerful and fast translocase that reads chromosome polarity. It couples segregation of the chromosome with cell division and controls the last steps of segregation in time and space. The second model protein of the family SpoIIIE acts in the transfer of the Bacillus subtilis chromosome during sporulation. This review focuses on the molecular mechanisms used by FtsK and SpoIIIE to segregate chromosomes with emphasis on the latest advances and open questions.

Free-energy calculations for semi-flexible macromolecules: applications to DNA knotting and looping

We present a method to obtain numerically accurate values of configurational free energies of semiflexible macromolecular systems, based on the technique of thermodynamic integration combined with normal-mode analysis of a reference system subject to harmonic constraints. Compared with previous free-energy calculations that depend on a reference state, our approach introduces two innovations, namely, the use of internal coordinates to constrain the reference states and the ability to freely select these reference states. As a consequence, it is possible to explore systems that undergo substantially larger fluctuations than those considered in previous calculations, including semiflexible biopolymers having arbitrary ratios of contour length L to persistence length P. To validate the method, high accuracy is demonstrated for free energies of prime DNA knots with L/P = 20 and L/P = 40, corresponding to DNA lengths of 3000 and 6000 base pairs, respectively. We then apply the method to study the free-energy landscape for a model of a synaptic nucleoprotein complex containing a pair of looped domains, revealing a bifurcation in the location of optimal synapse (crossover) sites. This transition is relevant to target-site selection by DNA-binding proteins that occupy multiple DNA sites separated by large linear distances along the genome, a problem that arises naturally in gene regulation, DNA recombination, and the action of type-II topoisomerases.

Do the same traffic rules apply? Directional chromosome segregation by SpoIIIE and FtsK

Over a decade of studies have tackled the question of how FtsK/SpoIIIE translocases establish and maintain directional DNA translocation during chromosome segregation in bacteria. FtsK/SpoIIIE translocases move DNA in a highly processive, directional manner, where directionality is facilitated by sequences on the substrate DNA molecules that are being transported. In recent years, structural, biochemical, single-molecule and high-resolution microscopic studies have provided new insight into the mechanistic details of directional DNA segregation. Out of this body of work, a series of models have emerged and, ultimately, yielded two seemingly opposing models: the loading model and the target search model. We review these recent mechanistic insights into directional DNA movement and discuss the data that may serve to unite these suggested models, as well as propose future directions that may ultimately solve the debate.

Single-molecule imaging of FtsK translocation reveals mechanistic features of protein-protein collisions on DNA

In physiological settings, DNA translocases will encounter DNA-bound proteins, which must be dislodged or bypassed to allow continued translocation. FtsK is a bacterial translocase that promotes chromosome dimer resolution and decatenation by activating XerCD-dif recombination. To better understand how translocases act in crowded environments, we used single-molecule imaging to visualize FtsK in real time as it collided with other proteins. We show that FtsK can push, evict, and even bypass DNA-bound proteins. The primary factor dictating the outcome of collisions was the relative affinity of the proteins for their specific binding sites. Importantly, protein-protein interactions between FtsK and XerD help prevent removal of XerCD from DNA by promoting rapid reversal of FtsK. Finally, we demonstrate that RecBCD always overwhelms FtsK when these two motor proteins collide while traveling along the same DNA molecule, indicating that RecBCD is capable of exerting a much greater force than FtsK when translocating along DNA.