Temperature modulation and quadrature detection for selective titration of two-state exchanging reactants

Biological samples exhibit huge molecular diversity over large concentration ranges. Titrating a given compound in such mixtures is often difficult, and innovative strategies emphasizing selectivity are thus demanded. To overcome limitations inherent to thermodynamics, we here present a generic technique where discrimination relies on the dynamics of interaction between the target of interest and a probe introduced in excess. Considering an ensemble of two-state exchanging reactants submitted to temperature modulation, we first demonstrate that the amplitude of the out-of-phase concentration oscillations is maximum for every compound involved in a reaction whose equilibrium constant is equal to unity and whose relaxation time is equal to the inverse of the excitation angular frequency. Taking advantage of this feature, we next devise a highly specific detection protocol and validate it using a microfabricated resistive heater and an epifluorescence microscope, as well as labeled oligonucleotides to model species displaying various dynamic properties. As expected, quantification of a sought for strand is obtained even if interfering reagents are present in similar amounts. Moreover, our approach does not require any separation and is compatible with imaging. It could then benefit some of the numerous binding assays performed every day in life sciences.

Fourier analysis to measure diffusion coefficients and resolve mixtures on a continuous electrophoresis chip

We report a method to measure diffusion coefficients of fluorescent solutes in the 10(2)-10(6) Da molecular mass range in a glass-PDMS chip. Upon applying a permanent electric field, the solute is introduced through a narrow channel into a wide analysis chamber where it migrates along the injection axis and diffuses in two dimensions. The diffusion coefficient is extracted after 1D Fourier transform of the resulting stationary concentration pattern. Analysis is straightforward, requiring no numerical integration or velocity field simulation. The diffusion coefficients measured for fluorescein, rhodamine green-labeled oligonucleotides, and YOYO-1-stained dsDNA fragments agree with the literature values and with our own fluorescence correlation spectroscopy measurements. As shown for 151 and 1257 base pair dsDNA mixtures, the present method allows us to rely on diffusion to quantitatively characterize the nature and the composition of binary mixtures. In particular, we implement a DNA hybridization assay to illustrate the efficiency of the proposed protocol for library screening.

Statistical determination of the step size of molecular motors

Molecular motors are enzymatic proteins that couple the consumption of chemical energy to mechanical displacement. In order to elucidate the translocation mechanisms of these enzymes, it is of fundamental importance to measure the physical step size. The step size can, in certain instances, be directly measured with single-molecule techniques; however, in the majority of cases individual steps are masked by noise. The step size can nevertheless be obtained from noisy single-molecule records through statistical methods. This analysis is analogous to determining the charge of the electron from current shot noise. We review methods for obtaining the step size based on analysing, in both the time and frequency domains, the variance in position from noisy single-molecule records of motor displacement. Additionally, we demonstrate how similar methods may be applied to measure the step size in bulk kinetic experiments.

Tracking topoisomerase activity at the single-molecule level

The recent development of new techniques to manipulate single DNA molecules has opened new opportunities for the study of the enzymes that control DNA topology: the type I and II topoisomerases. These single-molecule assays provide a unique way to study the uncoiling of single supercoiled DNA molecules and the unlinking of two intertwined DNAs. They allow for a detailed characterization of the activity of topoisomerases, including the processivity, the chiral discrimination, and the dependence of their enzymatic rate on ATP concentration, degree of supercoiling, and the tension in the molecule. These results shed new light on the mechanism of these enzymes and their function in vivo.

Topoisomerase IV bends and overtwists DNA upon binding

Escherichia coli topoisomerase IV (Topo IV) is an essential ATP-dependent enzyme that unlinks sister chromosomes during replication and efficiently removes positive but not negative supercoils. In this article, we investigate the binding properties of Topo IV onto DNA in the absence of ATP using a single molecule micromanipulation setup. We find that the enzyme binds cooperatively (Hill coefficient alpha approximately 4) with supercoiled DNA, suggesting that the Topo IV subunits assemble upon binding onto DNA. It interacts preferentially with (+) rather than (-) supercoiled DNA (Kd+=0.15 nM, Kd-=0.23 nM) and more than two orders-of-magnitude more weakly with relaxed DNA (Kd0 approximately 36 nM). Like gyrase but unlike the eukaryotic Topo II, Topo IV bends DNA with a radius 0= 6.4 nm and locally changes its twist and/or its writhe by 0.16 turn per bound complex. We estimate its free energy of binding and study the dynamics of interaction of Topo IV with DNA at the binding threshold. We find that the protein/DNA complex alternates between two states: a weakly bound state where it stays with probability p = 0.89 and a strongly bound state (with probability p = 0.11). The methodology introduced here to characterize the Topo IV/DNA complex is very general and could be used to study other DNA/protein complexes.

Braiding DNA: experiments, simulations, and models

DNA encounters topological problems in vivo because of its extended double-helical structure. As a consequence, the semiconservative mechanism of DNA replication leads to the formation of DNA braids or catenanes, which have to be removed for the completion of cell division. To get a better understanding of these structures, we have studied the elastic behavior of two braided nicked DNA molecules using a magnetic trap apparatus. The experimental data let us identify and characterize three regimes of braiding: a slightly twisted regime before the formation of the first crossing, followed by genuine braids which, at large braiding number, buckle to form plectonemes. Two different approaches support and quantify this characterization of the data. First, Monte Carlo (MC) simulations of braided DNAs yield a full description of the molecules' behavior and their buckling transition. Second, modeling the braids as a twisted swing provides a good approximation of the elastic response of the molecules as they are intertwined. Comparisons of the experiments and the MC simulations with this analytical model allow for a measurement of the diameter of the braids and its dependence upon entropic and electrostatic repulsive interactions. The MC simulations allow for an estimate of the effective torsional constant of the braids (at a stretching force F = 2 pN): C(b) approximately 48 nm (as compared with C approximately 100 nm for a single unnicked DNA). Finally, at low salt concentrations and for sufficiently large number of braids, the diameter of the braided molecules is observed to collapse to that of double-stranded DNA. We suggest that this collapse is due to the partial melting and fraying of the two nicked molecules and the subsequent right- or left-handed intertwining of the stretched single strands.

Single-molecule study of RuvAB-mediated Holliday-junction migration

Branch migration of Holliday junctions is an important step of genetic recombination and DNA repair. In Escherichia coli, this process is driven by the RuvAB complex acting as a molecular motor. Using magnetic tweezers, we studied the RuvAB-directed migration of individual Holliday junctions formed between two approximately 6-kb DNA molecules of identical sequence, and we measured the migration rate at 37 degrees C and 1 mM ATP. We directly demonstrate that RuvAB is a highly processive DNA motor protein that is able to drive continuous and unidirectional branch migration of Holliday junctions at a well defined average speed over several kilobases through homologous sequences. We observed directional inversions of the migration at the DNA molecule boundaries leading to forth-and-back migration of the branch point and allowing us to measure the migration rate in the presence of negative or positive loads. The average migration rate at zero load was found to be approximately 43 bp/sec. Furthermore, the load dependence of the migration rate is small, within the force range of -3.4 pN (hindering force) to +3.4 pN (assisting force).

Single-molecule study of DNA unlinking by eukaryotic and prokaryotic type-II topoisomerases

Type-II topoisomerases are responsible for untangling DNA during replication by removing supercoiled and interlinked DNA structures. Using a single-molecule micromanipulation setup, we follow the real-time decatenation of two mechanically braided DNA molecules by Drosophila melanogaster topoisomerase (Topo) II and Escherichia coli Topo IV. Although Topo II relaxes left-handed (L) and right-handed (R-) braids similarly at a rate of approximately 2.9 s-1, Topo IV has a marked preference for L-braids, which it relaxes completely and processively at a rate of approximately 2.4 s-1. However, Topo IV can unlink R-braids at about half that rate when they supercoil to form L-plectonemes. These results imply that the preferred substrate for unlinking by Topo IV has the symmetry of an L-crossing and shed new light on the decatenation of daughter strands during DNA replication, which are usually assumed to be linked in an R-braid.

Thermophilic topoisomerase I on a single DNA molecule

Control of DNA topology is critical in thermophilic organisms in which heightened ambient temperatures threaten the stability of the double helix. An important role in this control is played by topoisomerase I, a member of the type IA family of topoisomerases. We investigated the binding and activity of this topoisomerase from the hyperthermophilic bacterium Thermotoga maritima on duplex DNA using single molecule techniques, presenting it with various substrates such as (+) plectonemes, (-) plectonemes, and denaturation bubbles. We found the topoisomerase inactive on both types of plectonemes, but active on denaturation bubbles produced at increased stretching forces in underwound DNA. The relaxation rate depended sensitively on the applied force and the protein concentration. These observations could be understood in terms of a preference of the topoisomerase for single-stranded DNA over double-stranded DNA and allowed for a better understanding of activity of the topoisomerase in bulk experiments on circular plasmids. Binding experiments on a single duplex molecule using a mutant unable to perform cleavage confirmed this interpretation and suggested that T.maritima topoisomerase I behaves like an SSB by lowering the denaturation threshold of underwound DNA. Finally, experiments with a unique single-stranded DNA showed that both ends of the cleaved DNA are tightly maintained by the enzyme, supporting an enzyme-bridged mechanism for this topoisomerase.

Stretching single stranded DNA, a model polyelectrolyte

The elastic properties of single stranded (ss)DNA, studied by pulling on an isolated molecule, are shown to agree with a recent model of ssDNA that takes into account base pairings and screened electrostatic repulsion of the phosphodiester backbone. By an appropriate physicochemical treatment, the pairing interactions were suppressed and ssDNA used as an experimental model for a generic polyelectrolyte. The elastic behavior of such an altered ssDNA deviates strongly from the behavior of an ideal polymer. This deviation is shown to result from the elasticity of the chain and its electrostatic self-avoiding interactions.

The mechanism of type IA topoisomerases

The topology of cellular DNA is carefully controlled by enzymes called topoisomerases. By using single-molecule techniques, we monitored the activity of two type IA topoisomerases in real time under conditions in which single relaxation events were detected. The strict one-at-a-time removal of supercoils we observed establishes that these enzymes use an enzyme-bridged strand-passage mechanism that is well suited to their physiological roles and demonstrates a mechanistic unity with type II topoisomerases.

Twisting and stretching single DNA molecules

The elastic properties of DNA are essential for its biological function. They control its bending and twisting as well as the induction of structural modifications in the molecule. These can affect its interaction with the cell machinery. The response of a single DNA molecule to a mechanical stress can be precisely determined in single-molecule experiments which give access to an accurate measurement of the elastic parameters of DNA.

Stress-induced structural transitions in DNA and proteins

The ability to manipulate, stretch and twist biomolecules opens the way to an understanding of their structural transitions. We review some of the recently discovered stress-induced structural transitions in DNA as well as the application of single molecule manipulation techniques to DNA unzipping and to the study of protein folding/unfolding transitions.

Preferential relaxation of positively supercoiled DNA by E. coli topoisomerase IV in single-molecule and ensemble measurements

We show that positively supercoiled [(+) SC] DNA is the preferred substrate for Escherichia coli topoisomerase IV (topo IV). We measured topo IV relaxation of (-) and (+) supercoils in real time on single, tethered DNA molecules to complement ensemble experiments. We find that the preference for (+) SC DNA is complete at low enzyme concentration. Otherwise, topo IV relaxed (+) supercoils at a 20-fold faster rate than (-) supercoils, due primarily to about a 10-fold increase in processivity with (+) SC DNA. The preferential cleavage of (+) SC DNA in a competition experiment showed that substrate discrimination can take place prior to strand passage in the presence or absence of ATP. We propose that topo IV discriminates between (-) and (+) supercoiled DNA by recognition of the geometry of (+) SC DNA. Our results explain how topo IV can rapidly remove (+) supercoils to support DNA replication without relaxing the essential (-) supercoils of the chromosome. They also show that the rate of supercoil relaxation by topo IV is several orders of magnitude faster than hitherto appreciated, so that a single enzyme may suffice at each replication fork.

Replication by a single DNA polymerase of a stretched single-stranded DNA

A new approach to the study of DNA/protein interactions has been opened through the recent advances in the manipulation of single DNA molecules. These allow the behavior of individual molecular motors to be studied under load and compared with bulk measurements. One example of such a motor is the DNA polymerase, which replicates DNA. We measured the replication rate by a single enzyme of a stretched single strand of DNA. The marked difference between the elasticity of single- and double-stranded DNA allows for the monitoring of replication in real time. We have found that the rate of replication depends strongly on the stretching force applied to the template. In particular, by varying the load we determined that the biochemical steps limiting replication are coupled to movement. The replication rate increases at low forces, decreases at forces greater than 4 pN, and ceases when the single-stranded DNA substrate is under a load greater than approximately 20 pN. The decay of the replication rate follows an Arrhenius law and indicates that multiple bases on the template strand are involved in the rate-limiting step of each cycle. This observation is consistent with the induced-fit mechanism for error detection during replication.

Visualization of the space-time impulse response of the subcritical wake of a cylinder

The well-known Benard-von Karman cylinder wake is one of the most challenging phenomena of fluid mechanics. As the Reynolds number of the flow around a cylinder passes through a critical value, alternating vortex shedding appears via a Hopf bifurcation. Theoretical studies of the wake have described the appearance of this self-sustained oscillation as the result of a convective to absolute transition resulting in the formation of a global mode. We illustrate here the convective global regime of the subcritical wake by analyzing visualizations of its impulse response.

Single-molecule analysis of DNA uncoiling by a type II topoisomerase

Type II DNA topoisomerases are ubiquitous ATP-dependent enzymes capable of transporting a DNA through a transient double-strand break in a second DNA segment. This enables them to untangle DNA and relax the interwound supercoils (plectonemes) that arise in twisted DNA. In vivo, they are responsible for untangling replicated chromosomes and their absence at mitosis or meiosis ultimately causes cell death. Here we describe a micromanipulation experiment in which we follow in real time a single Drosophila melanogaster topoisomerase II acting on a linear DNA molecule which is mechanically stretched and supercoiled. By monitoring the DNA's extension in the presence of ATP, we directly observe the relaxation of two supercoils during a single catalytic turnover. By controlling the force pulling on the molecule, we determine the variation of the reaction rate with the applied stress. Finally, in the absence of ATP, we observe the damping of a DNA crossover by a single topoisomerase on at least two different timescales (configurations). These results show that single molecule experiments are a powerful new tool for the study of topoisomerases.

Micro-mechanical measurement of the torsional modulus of DNA

The torsional modulus C of DNA is determined from the difference between the work of stretching a single overwound molecule and the work done in stretching one underwound by the same number of turns. The value obtained C/kBT = 86 +/- 10 nm is within the range (75 +/- 25 nm) estimated by more indirect methods.

Estimating the persistence length of a worm-like chain molecule from force-extension measurements

We describe a simple computation of the worm-like chain model and obtain the corresponding force-versus-extension curve. We propose an improvement to the Marko and Siggia interpolation formula of Bustamante et al (Science 1994, 265:1599-1600) that is useful for fitting experimental data. We apply it to the experimental elasticity curve of single DNA molecules. Finally, we present a tool to study the agreement between the worm-like chain model and experiments.

Stretched and overwound DNA forms a Pauling-like structure with exposed bases

We investigate structural transitions within a single stretched and supercoiled DNA molecule. With negative supercoiling, for a stretching force >0.3 pN, we observe the coexistence of B-DNA and denatured DNA from sigma approximately -0.015 down to sigma = -1. Surprisingly, for positively supercoiled DNA (sigma > +0.037) stretched by 3 pN, we observe a similar coexistence of B-DNA and a new, highly twisted structure. Experimental data and molecular modeling suggest that this structure has approximately 2.62 bases per turn and an extension 75% larger than B-DNA. This structure has tightly interwound phosphate backbones and exposed bases in common with Pauling's early DNA structure [Pauling, L. & Corey, R. B. (1953), Proc. Natl. Acad. Sci. USA 39, 84-97] and an unusual structure proposed for the Pf1 bacteriophage [Liu, D. J. & Day, L. A. (1994) Science 265, 671-674].

Homologous pairing in stretched supercoiled DNA

By using elastic measurements on single DNA molecules, we show that stretching a negatively supercoiled DNA activates homologous pairing in physiological conditions. These experiments indicate that a stretched unwound DNA locally denatures to alleviate the force-driven increase in torsional stress. This is detected by hybridization with 1 kb of homologous single-stranded DNA probes. The stretching force involved (approximately 2 pN) is small compared with those typically developed by molecular motors, suggesting that this process may be relevant to DNA processing in vivo. We used this technique to monitor the progressive denaturation of DNA as it is unwound and found that distinct, stable denaturation bubbles formed, beginning in A+T-rich regions.

Behavior of supercoiled DNA

We study DNA supercoiling in a quantitative fashion by micromanipulating single linear DNA molecules with a magnetic field gradient. By anchoring one end of the DNA to multiple sites on a magnetic bead and the other end to multiple sites on a glass surface, we were able to exert torsional control on the DNA. A rotating magnetic field was used to induce rotation of the magnetic bead, and reversibly over- and underwind the molecule. The magnetic field was also used to increase or decrease the stretching force exerted by the magnetic bead on the DNA. The molecule's degree of supercoiling could therefore be quantitatively controlled and monitored, and tethered-particle motion analysis allowed us to measure the stretching force acting on the DNA. Experimental results indicate that this is a very powerful technique for measuring forces at the picoscale. We studied the effect of stretching forces ranging from 0.01 pN to 100 pN on supercoiled DNA (-0.1 < sigma < 0.2) in a variety of ionic conditions. Other effects, such as stretching-relaxing hysteresis and the braiding of two DNA molecules, are discussed.

pH-dependent specific binding and combing of DNA

Recent developments in the rapid sequencing, mapping, and analysis of DNA rely on the specific binding of DNA to specially treated surfaces. We show here that specific binding of DNA via its unmodified extremities can be achieved on a great variety of surfaces by a judicious choice of the pH. On hydrophobic surfaces the best binding efficiency is reached at a pH of approximately 5.5. At that pH a approximately 40-kbp DNA is 10 times more likely to bind by an extremity than by a midsegment. A model is proposed to account for the differential adsorption of the molecule extremities and midsection as a function of pH. The pH-dependent specific binding can be used to align anchored DNA molecules by a receding meniscus, a process called molecular combing. The resulting properties of the combed molecules will be discussed.

The elasticity of a single supercoiled DNA molecule

Single linear DNA molecules were bound at multiple sites at one extremity to a treated glass cover slip and at the other to a magnetic bead. The DNA was therefore torsionally constrained. A magnetic field was used to rotate the beads and thus to coil and pull the DNA. The stretching force was determined by analysis of the Brownian fluctuations of the bead. Here the elastic behavior of individual lambda DNA molecules over- and underwound by up to 500 turns was studied. A sharp transition was discovered from a low to a high extension state at a force of approximately 0.45 piconewtons for underwound molecules and at a force of approximately 3 piconewtons for overwound ones. These transitions, probably reflecting the formation of alternative structures in stretched coiled DNA molecules, might be relevant for DNA transcription and replication.

Alignment and sensitive detection of DNA by a moving interface

In a process called "molecular combining," DNA molecules attached at one end to a solid surface were extended and aligned by a receding air-water interface and left to dry on the surface. Molecular combing was observed to extend the length of the bacteriophage lambda DNA molecule to 21.5 +/- 0.5 micrometers (unextended length, 16.2 micrometers). With the combing process, it was possible to (i) extend a chromosomal Escherichia coli DNA fragment (10(6) base pairs) and (ii) detect a minute quantity of DNA (10(3) molecules). These results open the way for a faster physical mapping of the genome and for the detection of small quantities of target DNA from a population of molecules.