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.

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.

Deconvolution of nucleic-acid length distributions: a gel electrophoresis analysis tool and applications.

Next-generation DNA-sequencing (NGS) technologies, which are designed to streamline the acquisition of massive amounts of sequencing data, are nonetheless dependent on various preparative steps to generate DNA fragments of required concentration, purity and average size (molecular weight). Current automated electrophoresis systems for DNA- and RNA-sample quality control, such as Agilent's Bioanalyzer® and TapeStation® products, are costly to acquire and use; they also provide limited information for samples having broad size distributions. Here, we describe a software tool that helps determine the size distribution of DNA fragments in an NGS library, or other DNA sample, based on gel-electrophoretic line profiles. The software, developed as an ImageJ plug-in, allows for straightforward processing of gel images, including lane selection and fitting of univariate functions to intensity distributions. The user selects the option of fitting either discrete profiles in cases where discrete gel bands are visible or continuous profiles, having multiple bands buried under a single broad peak. The method requires only modest imaging capabilities and is a cost-effective, rigorous alternative characterization method to augment existing techniques for library quality control.

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.

DNA cyclization and looping in the wormlike limit: Normal modes and the validity of the harmonic approximation.

For much of the last three decades, Monte Carlo-simulation methods have been the standard approach for accurately calculating the cyclization probability, J, or J factor, for DNA models having sequence-dependent bends or inhomogeneous bending flexibility. Within the last 10 years approaches based on harmonic analysis of semi-flexible polymer models have been introduced, which offer much greater computational efficiency than Monte Carlo techniques. These methods consider the ensemble of molecular conformations in terms of harmonic fluctuations about a well-defined elastic-energy minimum. However, the harmonic approximation is only applicable for small systems, because the accessible conformation space of larger systems is increasingly dominated by anharmonic contributions. In the case of computed values of the J factor, deviations of the harmonic approximation from the exact value of J as a function of DNA length have not been characterized. Using a recent, numerically exact method that accounts for both anharmonic and harmonic contributions to J for wormlike chains of arbitrary size, we report here the apparent error that results from neglecting anharmonic behavior. For wormlike chains having contour lengths less than four times the persistence length, the error in J arising from the harmonic approximation is generally small, amounting to free energies less than the thermal energy, kB T. For larger systems, however, the deviations between harmonic and exact J values increase approximately linearly with size.

Contribution of fluorophore dynamics and solvation to resonant energy transfer in protein-DNA complexes: a molecular-dynamics study.

In Förster resonance energy transfer (FRET) experiments, extracting accurate structural information about macromolecules depends on knowing the positions and orientations of donor and acceptor fluorophores. Several approaches have been employed to reduce uncertainties in quantitative FRET distance measurements. Fluorophore-position distributions can be estimated by surface accessibility (SA) calculations, which compute the region of space explored by the fluorophore within a static macromolecular structure. However, SA models generally do not take fluorophore shape, dye transition-moment orientation, or dye-specific chemical interactions into account. We present a detailed molecular-dynamics (MD) treatment of fluorophore dynamics for an ATTO donor/acceptor dye pair and specifically consider as case studies dye-labeled protein-DNA intermediates in Cre site-specific recombination. We carried out MD simulations in both an aqueous solution and glycerol/water mixtures to assess the effects of experimental solvent systems on dye dynamics. Our results unequivocally show that MD simulations capture solvent effects and dye-dye interactions that can dramatically affect energy transfer efficiency. We also show that results from SA models and MD simulations strongly diverge in cases where donor and acceptor fluorophores are in close proximity. Although atomistic simulations are computationally more expensive than SA models, explicit MD studies are likely to give more realistic results in both homogeneous and mixed solvents. Our study underscores the model-dependent nature of FRET analyses, but also provides a starting point to develop more realistic in silico approaches for obtaining experimental ensemble and single-molecule FRET data.

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.

Measurements of DNA-loop formation via Cre-mediated recombination.

The Cre-recombination system has become an important tool for genetic manipulation of higher organisms and a model for site-specific DNA-recombination mechanisms employed by the λ-Int superfamily of recombinases. We report a novel quantitative approach for characterizing the probability of DNA-loop formation in solution using time-dependent ensemble Förster resonance energy transfer measurements of intra- and inter-molecular Cre-recombination kinetics. Our method uses an innovative technique for incorporating multiple covalent modifications at specific sites in covalently closed DNA. Because the mechanism of Cre recombinase does not conform to a simple kinetic scheme, we employ numerical methods to extract rate constants for fundamental steps that pertain to Cre-mediated loop closure. Cre recombination does not require accessory proteins, DNA supercoiling or particular metal-ion cofactors and is thus a highly flexible system for quantitatively analyzing DNA-loop formation in vitro and in vivo.

The thermodynamics of DNA loop formation, from J to Z.

The formation of DNA loops is a ubiquitous theme in biological processes, including DNA replication, recombination and repair, and gene regulation. These loops are mediated by proteins bound at specific sites along the contour of a single DNA molecule, in some cases many thousands of base pairs apart. Loop formation incurs a thermodynamic cost that is a sensitive function of the length of looped DNA as well as the geometry and elastic properties of the DNA-bound protein. The free energy of DNA looping is logarithmically related to a generalization of the Jacobson-Stockmayer factor for DNA cyclization, termed the J factor. In the present article, we review the thermodynamic origins of this quantity, discuss how it is measured experimentally and connect the macroscopic interpretation of the J factor with a statistical-mechanical description of DNA looping and cyclization.

DNA topology and geometry in Flp and Cre recombination.

The Flp recombinase of yeast and the Cre recombinase of bacteriophage P1 both belong to the lambda-integrase (Int) family of site-specific recombinases. These recombination systems recognize recombination-target sequences that consist of two 13bp inverted repeats flanking a 6 or 8bp spacer sequence. Recombination reactions involve particular geometric and topological relationships between DNA target sites at synapsis, which we investigate using nicked-circular DNA molecules. Examination of the tertiary structure of synaptic complexes formed on nicked plasmid DNAs by atomic-force microscopy, in conjunction with detailed topological analysis using the mathematics of tangles, shows that only a limited number of recombination-site topologies are consistent with the global structures of plasmids bearing directly and inversely repeated sites. The tangle solutions imply that there is significant distortion of the Holliday-junction intermediate relative to the planar structure of the four-way DNA junction present in the Flp and Cre co-crystal structures. Based on simulations of nucleoprotein structures that connect the two-dimensional tangle solutions with three-dimensional models of the complexes, we propose a recombination mechanism in which the synaptic intermediate is characterized by a non-planar, possibly near-tetrahedral, Holliday-junction intermediate. Only modest conformational changes within this structure are needed to form the symmetric, planar DNA junction, which may be characteristic of shorter-lived intermediates along the recombination pathway.

Intricate and Cell Type-Specific Populations of Endogenous Circular DNA (eccDNA) in Caenorhabditis elegans and Homo sapiens.

Investigations aimed at defining the 3D configuration of eukaryotic chromosomes have consistently encountered an endogenous population of chromosome-derived circular genomic DNA, referred to as extrachromosomal circular DNA (eccDNA). While the production, distribution, and activities of eccDNAs remain understudied, eccDNA formation from specific regions of the linear genome has profound consequences on the regulatory and coding capabilities for these regions. Here, we define eccDNA distributions in Caenorhabditis elegans and in three human cell types, utilizing a set of DNA topology-dependent approaches for enrichment and characterization. The use of parallel biophysical, enzymatic, and informatic approaches provides a comprehensive profiling of eccDNA robust to isolation and analysis methodology. Results in human and nematode systems provide quantitative analysis of the eccDNA loci at both unique and repetitive regions. Our studies converge on and support a consistent picture, in which endogenous genomic DNA circles are present in normal physiological states, and in which the circles come from both coding and noncoding genomic regions. Prominent among the coding regions generating DNA circles are several genes known to produce a diversity of protein isoforms, with mucin proteins and titin as specific examples.

Analysis of chemical and enzymatic cleavage frequencies in supercoiled DNA.

Chemical and enzymatic probing methods are powerful techniques for examining details of sequence-dependent structure in DNA and RNA. Reagents that cleave nucleic acid molecules in a structure-specific, but relatively sequence-non-specific manner, such as hydroxyl radical or DNase I, have been used widely to probe helical geometry in nucleic acid structures, nucleic acid-drug complexes, and in nucleoprotein assemblies. Application of cleavage-based techniques to structures present in superhelical DNA has been hindered by the fact that the cleavage pattern attributable to supercoiling-dependent structures is heavily mixed with non-specific cleavage signals that are inevitable products of multiple cleavage events. We present a rigorous mathematical procedure for extracting the cleavage pattern specific to supercoiled DNA and use this method to investigate the hydroxyl radical cleavage pattern in a cruciform DNA structure formed by a 60 bp inverted repeat sequence embedded in a negatively supercoiled plasmid. Our results support the presence of a stem-loop structure in the expected location and suggest that the helical geometry of the cruciform stem differs from that of the normal duplex form.

Functional 20S proteasomes in mature human red blood cells.

The purpose of the present study was to investigate whether functional 20S and/or 26S proteasomes are present within mature human red blood cells (RBCs; depleted of reticulocytes and leukocytes). Double-immunofluorescence confocal microscopy showed the presence of immunoreactive 20S and 19S proteasomal subunit proteins and their partial co-localization within mature RBCs. Proteasomes isolated from mature RBCs displayed 20S activity in vitro; atomic-force and transmission electron microscopy of isolated proteasomes revealed abundant 20S core particles and very few 26S particles. A two-dimensional differential in-gel electrophoresis (2D-DIGE) approach was used to determine if proteasome-dependent protein degradation occurs within mature RBCs. Twenty-eight proteins were identified with altered protein content in response to lactacystin. Seven cytosolic proteins showed an increase and 16 showed a decrease; five membrane proteins showed a decrease. We conclude that the proteins showing increased abundance are either primary or secondary targets of the 20S proteasome and that putatively degraded proteins are secondary targets. Therefore, functional 20S proteasomes exist within mature RBCs. Our study did not detect 26S proteasome activity using the 2D-DIGE approach.

Gel mobilities of linking-number topoisomers and their dependence on DNA helical repeat and elasticity.

Agarose-gel electrophoresis has been used for more than thirty years to characterize the linking-number (Lk) distribution of closed-circular DNA molecules. Although the physical basis of this technique remains poorly understood, the gel-electrophoretic behavior of covalently closed DNAs has been used to determine the local unwinding of DNA by proteins and small-molecule ligands, characterize supercoiling-dependent conformational transitions in duplex DNA, and to measure helical-repeat changes due to shifts in temperature and ionic strength. Those results have been analyzed by assuming that the absolute mobility of a particular topoisomer is mainly a function of the integral number of superhelical turns, and thus a slowly varying function of plasmid molecular weight. In examining the mobilities of Lk topoisomers for a series of plasmids that differ incrementally in size over more than one helical turn, we found that the size-dependent agarose-gel mobility of individual topoisomers with identical values of Lk (but different values of the excess linking number, DeltaLk) vary dramatically over a duplex turn. Our results suggest that a simple semi-empirical relationship holds between the electrophoretic mobility of linking-number topoisomers and their average writhe in solution.

Analysis of DNA topoisomers, knots, and catenanes by agarose gel electrophoresis.

Agarose gel electrophoresis is by far the most widely used method for characterizing the topological state of DNA molecules. Although this technique has been used for more than 30 years, the physical mechanism underlying the resolution of topological states remains poorly understood. However, electrophoretic methods remain the most robust and precise techniques for determining the local unwinding of DNA induced by the binding of proteins and small-molecule ligands, analyzing conformational transitions in duplex DNA, measuring changes in helical repeat that accompany shifts in environmental conditions, and characterizing knotting and linking in duplex DNA.

Statistical-mechanical theory of DNA looping.

The lack of a rigorous analytical theory for DNA looping has caused many DNA-loop-mediated phenomena to be interpreted using theories describing the related process of DNA cyclization. However, distinctions in the mechanics of DNA looping versus cyclization can have profound quantitative effects on the thermodynamics of loop closure. We have extended a statistical mechanical theory recently developed for DNA cyclization to model DNA looping, taking into account protein flexibility. Notwithstanding the underlying theoretical similarity, we find that the topological constraint of loop closure leads to the coexistence of multiple classes of loops mediated by the same protein structure. These loop topologies are characterized by dramatic differences in twist and writhe; because of the strong coupling of twist and writhe within a loop, DNA looping can exhibit a complex overall helical dependence in terms of amplitude, phase, and deviations from uniform helical periodicity. Moreover, the DNA-length dependence of optimal looping efficiency depends on protein elasticity, protein geometry, and the presence of intrinsic DNA bends. We derive a rigorous theory of loop formation that connects global mechanical and geometric properties of both DNA and protein and demonstrates the importance of protein flexibility in loop-mediated protein-DNA interactions.

Analysis of in-vivo LacR-mediated gene repression based on the mechanics of DNA looping.

Interactions of E. coli lac repressor (LacR) with a pair of operator sites on the same DNA molecule can lead to the formation of looped nucleoprotein complexes both in vitro and in vivo. As a major paradigm for loop-mediated gene regulation, parameters such as operator affinity and spacing, repressor concentration, and DNA bending induced by specific or non-specific DNA-binding proteins (e.g., HU), have been examined extensively. However, a complete and rigorous model that integrates all of these aspects in a systematic and quantitative treatment of experimental data has not been available. Applying our recent statistical-mechanical theory for DNA looping, we calculated repression as a function of operator spacing (58-156 bp) from first principles and obtained excellent agreement with independent sets of in-vivo data. The results suggest that a linear extended, as opposed to a closed v-shaped, LacR conformation is the dominant form of the tetramer in vivo. Moreover, loop-mediated repression in wild-type E. coli strains is facilitated by decreased DNA rigidity and high levels of flexibility in the LacR tetramer. In contrast, repression data for strains lacking HU gave a near-normal value of the DNA persistence length. These findings underscore the importance of both protein conformation and elasticity in the formation of small DNA loops widely observed in vivo, and demonstrate the utility of quantitatively analyzing gene regulation based on the mechanics of nucleoprotein complexes.

Fractionation of SWNT/nucleic acid complexes by agarose gel electrophoresis.

We show that aqueous dispersions of single-walled carbon nanotubes (SWNTs), prepared with the aid of nucleic acids (NAs) such as RNA or DNA, can be separated into fractions using agarose gel electrophoresis. In a DC electric field, SWNT/NA complexes migrate in the gel in the direction of positive potential to form well-defined bands. Raman spectroscopy as a function of band position shows that nanotubes having different spectroscopic properties possess different electrophoretic mobilities. The migration patterns for SWNT/RNA and SWNT/DNA complexes differ. Parallel elution of the SWNT/NA complexes from the gel during electrophoresis and subsequent characterization by AFM reveals differences in nanotube diameter, length and curvature. The results suggest that fractionation of nanotubes can be achieved by this procedure. We discuss factors affecting the mobility of the nanotube complexes and propose analytical applications of this technique.