Measurement of lactose repressor-mediated loop formation and breakdown in single DNA molecules

The effect of nonspecific binding of lambda repressor on DNA looping dynamics

The λ repressor (CI) protein-induced DNA loop maintains stable lysogeny, yet allows efficient switching to lysis. Herein, the kinetics of loop formation and breakdown has been characterized at various concentrations of protein using tethered particle microscopy and a novel, to our knowledge, method of analysis. Our results show that a broad distribution of rate constants and complex kinetics underlie loop formation and breakdown. In addition, comparison of the kinetics of looping in wild-type DNA and DNA with mutated o3 operators showed that these sites may trigger nucleation of nonspecific binding at the closure of the loop. The average activation energy calculated from the rate constant distribution is consistent with a model in which nonspecific binding of CI between the operators shortens their effective separation, thereby lowering the energy barrier for loop formation and broadening the rate constant distribution for looping. Similarly, nonspecific binding affects the kinetics of loop breakdown by increasing the number of loop-securing protein interactions, and broadens the rate constant distribution for this reaction. Therefore, simultaneous increase of the rate constant for loop formation and reduction of that for loop breakdown stabilizes lysogeny. Given these simultaneous changes, the frequency of transitions between the looped and the unlooped state remains nearly constant. Although the loop becomes more stable thermodynamically with increasing CI concentration, it still opens periodically, conferring sensitivity to environmental changes, which may require switching to lytic conditions.

Kinetics and thermodynamics of phenotype: unwinding and rewinding the nucleosome

Chromatin "remodeling" is widely accepted as the mechanism that permits access to DNA by the transcription machinery. To date, however, there has been no experimental measurement of the changes in the kinetics and thermodynamics of the DNA-histone octamer association that are required to remodel chromatin so that transcription may occur. Here, we present the results of optical tweezer measurements that compare the kinetic and thermodynamic properties of nucleosomes composed of unmodified histones with those of nucleosomes that contain a mutant histone H4 (H4-R45H), which has been shown to allow SWI/SNF remodeling factor-independent transcription from the yeast HO promoter in vivo. Our measurements, carried out in a force-clamp mode, determine the force-dependent unwinding and rewinding rates of the nucleosome inner turn. At each force studied, nucleosomes containing H4-R45H unwind more rapidly and rewind more slowly than nucleosomes containing unmodified H4, indicating that the latter are the more stable. Extrapolation to forces at which the winding and unwinding rates are equal determines the absolute free energy of the nucleosome inner turn to be -32k(B)T for nucleosomes containing unmodified H4 and -27k(B)T for nucleosomes containing H4-R45H. Thus, the "loosening" or "remodeling" caused by this point mutation, which is demonstrated to be sufficient to allow transcriptional machinery access to the HO promoter (in the absence of other remodeling factors), is 5k(B)T. The correlation between the free energy of the nucleosome inner turn and the sin (SWI/SNF-independent) transcription suggests that, beyond partial unwinding, complete histone unwinding may play a role in transcriptional activation.

Sequence dependence of transcription factor-mediated DNA looping

DNA is subject to large deformations in a wide range of biological processes. Two key examples illustrate how such deformations influence the readout of the genetic information: the sequestering of eukaryotic genes by nucleosomes and DNA looping in transcriptional regulation in both prokaryotes and eukaryotes. These kinds of regulatory problems are now becoming amenable to systematic quantitative dissection with a powerful dialogue between theory and experiment. Here, we use a single-molecule experiment in conjunction with a statistical mechanical model to test quantitative predictions for the behavior of DNA looping at short length scales and to determine how DNA sequence affects looping at these lengths. We calculate and measure how such looping depends upon four key biological parameters: the strength of the transcription factor binding sites, the concentration of the transcription factor, and the length and sequence of the DNA loop. Our studies lead to the surprising insight that sequences that are thought to be especially favorable for nucleosome formation because of high flexibility lead to no systematically detectable effect of sequence on looping, and begin to provide a picture of the distinctions between the short length scale mechanics of nucleosome formation and looping.

DNA looping by FokI: the impact of twisting and bending rigidity on protein-induced looping dynamics

Protein-induced DNA looping is crucial for many genetic processes such as transcription, gene regulation and DNA replication. Here, we use tethered-particle motion to examine the impact of DNA bending and twisting rigidity on loop capture and release, using the restriction endonuclease FokI as a test system. To cleave DNA efficiently, FokI bridges two copies of an asymmetric sequence, invariably aligning the sites in parallel. On account of the fixed alignment, the topology of the DNA loop is set by the orientation of the sites along the DNA. We show that both the separation of the FokI sites and their orientation, altering, respectively, the twisting and the bending of the DNA needed to juxtapose the sites, have profound effects on the dynamics of the looping interaction. Surprisingly, the presence of a nick within the loop does not affect the observed rigidity of the DNA. In contrast, the introduction of a 4-nt gap fully relaxes all of the torque present in the system but does not necessarily enhance loop stability. FokI therefore employs torque to stabilise its DNA-looping interaction by acting as a ‘torsional’ catch bond.

DNA looping by FokI: the impact of synapse geometry on loop topology at varied site orientations

Most restriction endonucleases, including FokI, interact with two copies of their recognition sequence before cutting DNA. On DNA with two sites they act in cis looping out the intervening DNA. While many restriction enzymes operate symmetrically at palindromic sites, FokI acts asymmetrically at a non-palindromic site. The directionality of its sequence means that two FokI sites can be bridged in either parallel or anti-parallel alignments. Here we show by biochemical and single-molecule biophysical methods that FokI aligns two recognition sites on separate DNA molecules in parallel and that the parallel arrangement holds for sites in the same DNA regardless of whether they are in inverted or repeated orientations. The parallel arrangement dictates the topology of the loop trapped between sites in cis: the loop from inverted sites has a simple 180° bend, while that with repeated sites has a convoluted 360° turn. The ability of FokI to act at asymmetric sites thus enabled us to identify the synapse geometry for sites in trans and in cis, which in turn revealed the relationship between synapse geometry and loop topology.

Single-molecule views of protein movement on single-stranded DNA

The advent of new technologies allowing the study of single biological molecules continues to have a major impact on studies of interacting systems as well as enzyme reactions. These approaches (fluorescence, optical, and magnetic tweezers), in combination with ensemble methods, have been particularly useful for mechanistic studies of protein-nucleic acid interactions and enzymes that function on nucleic acids. We review progress in the use of single-molecule methods to observe and perturb the activities of proteins and enzymes that function on flexible single-stranded DNA. These include single-stranded DNA binding proteins, recombinases (RecA/Rad51), and helicases/translocases that operate as motor proteins and play central roles in genome maintenance. We emphasize methods that have been used to detect and study the movement of these proteins (both ATP-dependent directional and random movement) along the single-stranded DNA and the mechanistic and functional information that can result from detailed analysis of such movement.

Probing DNA topology using tethered particle motion

Transcription factors mediate the formation of nucleoprotein complexes that are critical for efficient regulation of epigenetic switches. In these complexes, DNA is frequently bent or looped by the protein; other times, strong interactions lead the DNA to fully wrap the regulatory protein(s). The equilibrium between the bending, looping, full and partial wrapping of DNA governs the level of transcriptional regulation and is tuned by biophysical parameters. Characterization of the structure, kinetics, and thermodynamics of formation of such nucleoprotein complexes is fundamental to the understanding of the molecular mechanisms that underlie the operation of the genetic switches controlled by them. Here, we describe in detail how to perform tethered particle motion experiments aimed at understanding how protein-DNA interactions influence the formation and breakdown of these regulatory complexes.

Role of chain entropy in an analytic model of protein binding in single-DNA stretching experiments

We show that the simple analytical model proposed by Zhang and Marko [Phys. Rev. E 77, 031916 (2008)] to illustrate Maxwell relations for single-DNA experiments can be improved by including the zero-force entropy of a Gaussian chain. The resulting model is in excellent agreement with the discrete persistent-chain model and is in a form convenient for analyzing experimental data.

Discrete persistent-chain model for protein binding on DNA

We describe and solve a discrete persistent-chain model of protein binding on DNA, involving an extra σ(i) at a site i of the DNA. This variable takes the value 1 or 0, depending on whether or not the site is occupied by a protein. In addition, if the site is occupied by a protein, there is an extra energy cost ɛ. For a small force, we obtain analytic expressions for the force-extension curve and the fraction of bound protein on the DNA. For higher forces, the model can be solved numerically to obtain force-extension curves and the average fraction of bound proteins as a function of applied force. Our model can be used to analyze experimental force-extension curves of protein binding on DNA, and hence deduce the number of bound proteins in the case of nonspecific binding.

Force-free measurements of the conformations of DNA molecules tethered to a wall

Using an optimized combination of tethered particle motion method, total internal reflection, and a gold nanobead, we measured the three-dimensional distribution of the free end of a tethered DNA molecule. The distribution along the axial z direction (perpendicular to the surface) is found to be Rayleigh-like, in agreement with wormlike chain and freely jointed chain simulations. Using these simulations, we show that the presence of the wall increases the correlations between the orientations of neighboring chain segments compared to free DNA. While the measured and the simulated planar (xy) distributions always agree with that of a Gaussian-random-walk (GRW) model, for short DNA lengths (1 μm) studied in our experiment, the corresponding axial (z) distributions deviate from those predicted for a GRW confined to half-space.

A new method for the covalent attachment of DNA to a surface for single-molecule studies

Attachments between DNA and a surface or bead are often necessary for single-molecule studies of DNA and DNA-protein interactions. In single-molecule mechanical studies using optical or magnetic tweezers, such attachments must be able to withstand the applied forces. Here we present a new method for covalently attaching DNA to a glass surface, which uses N-hydroxysuccinimide (NHS) modified PEG that is suitable for high-force single-molecule mechanical studies. A glass surface is coated with silane-PEG-NHS and DNA is covalently linked through a reaction between the NHS group and an amine modified nucleotide that has been incorporated into the DNA. After DNA attachment, non-reacted NHS groups are hydrolyzed leaving a PEG-covered surface which has the added benefit of reducing non-specific surface interactions. This method permits specific binding of the DNA to the surface through a covalent bond. At the DNA end not attached to the surface, we attach a streptavidin-coated polystyrene bead and measure force-versus-extension using an optical trap. We show that our method allows a tethered DNA molecule to be pulled through its overstretching transition (> 60pN) multiple times. We anticipate this simple yet powerful method will be useful for many researchers.

Determination of the number of proteins bound non-specifically to DNA

We have determined the change in the number of proteins bound non-specifically to DNA as a function of applied force using force-extension measurements on tethered DNA. Using magnetic tweezers, single molecules of λ DNA were repeatedly stretched and relaxed in the absence and presence of 170 nM λ repressor protein (CI). CI binds to six specific sites of λ DNA with nanomolar affinity and also binds non-specifically with micromolar affinity. The force versus extension data were analyzed using a recently developed theoretical framework for quantitative determination of protein binding to the DNA. The results indicate that the non-specific binding of CI changes the force-extension relation significantly in comparison to that of naked DNA. The DNA tether used in our experiment would have about 640 bound repressors, if it was completely saturated with bound proteins. We find that as the pulling force on DNA is reduced from 4.81 to 0.13 pN, approximately 138 proteins bind to DNA, which is about 22% of the length of the tethered DNA. Our results show that 0.13 pN is not low enough to cause saturation of DNA by repressor and 4.81 pN is also not high enough to eliminate all the repressors bound to DNA. This demonstrates that the force-extension relation provides an effective approach for estimating the number of proteins bound non-specifically to a DNA molecule.

Probing DNA conformational changes with high temporal resolution by tethered particle motion

The tethered particle motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150 nm). Notably we demonstrate that, for a particle of radius 20 nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20 ms.

Bead size effects on protein-mediated DNA looping in tethered-particle motion experiments

Tethered particle motion (TPM) has become an important tool for single-molecule studies of biomolecules; however, concerns remain that the method may alter the dynamics of the biophysical process under study. We investigate the effect of the attached microsphere on an illustrative biological example: the formation and breakdown of protein-mediated DNA loops in the lac repressor system. By comparing data from a conventional TPM experiment with 800 nm polystyrene beads and dark-field TPM using 50 nm Au nanoparticles, we found that the lifetimes of the looped and unlooped states are only weakly modified, less than two-fold, by the presence of the large bead. This is consistent with our expectation of weak excluded-volume effects and hydrodynamic surface interactions from the cover glass and microsphere.

Single-molecule TPM studies on the conversion of human telomeric DNA

Human telomere contains guanine-rich (G-rich) tandem repeats of single-stranded DNA sequences at its 3' tail. The G-rich sequences can be folded into various secondary structures, termed G-quadruplexes (G4s), by Hoogsteen basepairing in the presence of monovalent cations (such as Na+ and K+). We developed a single-molecule tethered particle motion (TPM) method to investigate the unfolding process of G4s in the human telomeric sequence AGGG(TTAGGG)3 in real time. The TPM method monitors the DNA tether length change caused by formation of the G4, thus allowing the unfolding process and structural conversion to be monitored at the single-molecule level. In the presence of its antisense sequence, the folded G4 structure can be disrupted and converted to the unfolded conformation, with apparent unfolding time constants of 82 s and 3152 s. We also observed that the stability of the G4 is greatly affected by different monovalent cations. The folding equilibrium constant of G4 is strongly dependent on the salt concentration, ranging from 1.75 at 5 mM Na+ to 3.40 at 15 mM Na+. Earlier spectral studies of Na+- and K+-folded states suggested that the spectral conversion between these two different folded structures may go through a structurally unfolded intermediate state. However, our single-molecule TPM experiments did not detect any totally unfolded intermediate within our experimental resolution when sodium-folded G4 DNA molecules were titrated with high-concentration, excess potassium ions. This observation suggests that a totally unfolding pathway is likely not the major pathway for spectral conversion on the timescale of minutes, and that interconversion among folded states can be achieved by the loop rearrangement. This study also demonstrates that TPM experiments can be used to study conformational changes in single-stranded DNA molecules.

Single-molecule approaches to probe the structure, kinetics, and thermodynamics of nucleoprotein complexes that regulate transcription

Single-molecule experimentation has contributed significantly to our understanding of the mechanics of nucleoprotein complexes that regulate epigenetic switches. In this minireview, we will discuss the application of the tethered-particle motion technique, magnetic tweezers, and atomic force microscopy to (i) directly visualize and thermodynamically characterize DNA loops induced by the lac, gal, and lambda repressors and (ii) understand the mechanistic role of DNA-supercoiling and DNA-bending cofactors in both prokaryotic and eukaryotic systems.

Towards building a chromosome segregation machine

All organisms, from bacteria to humans, face the daunting task of replicating, packaging and segregating up to two metres (about 6 x 10(9) base pairs) of DNA when each cell divides. This task is carried out up to a trillion times during the development of a human from a single fertilized cell. The strategy by which DNA is replicated is now well understood. But when it comes to packaging and segregating a genome, the mechanisms are only beginning to be understood and are often as variable as the organisms in which they are studied.

Femtonewton entropic forces can control the formation of protein-mediated DNA loops

We show that minuscule entropic forces, on the order of 100 fN, can prevent the formation of DNA loops-a ubiquitous means of regulating the expression of genes. We observe a tenfold decrease in the rate of LacI-mediated DNA loop formation when a tension of 200 fN is applied to the substrate DNA, biasing the thermal fluctuations that drive loop formation and breakdown events. Conversely, once looped, the DNA-protein complex is insensitive to applied force. Our measurements are in excellent agreement with a simple polymer model of loop formation in DNA, and show that an antiparallel topology is the preferred LacI-DNA loop conformation for a generic loop-forming construct.

Quantitative analysis of DNA-looping kinetics from tethered particle motion experiments

In this chapter we show the application of a maximum-likelihood-based method to the reconstruction of DNA-looping single-molecule time traces from tethered particle motion experiments. The method does not require time filtering of the data and improves the time resolution by an order of magnitude with respect to the threshold-crossing approach. Moreover, it is not based on presumed kinetic models, overcoming the limitations of other approaches proposed previously, and allowing its applications to mechanisms with complex kinetic schemes. Numerical simulations have been used to test the performances of this analysis over a wide range of time scales. We have then applied this method to determine the looping kinetics of a well-known DNA-looping protein, the lambda-repressor.

Tetramer opening in LacI-mediated DNA looping

Lactose repressor protein (LacI) controls transcription of the genes involved in lactose metabolism in bacteria. Essential to optimal LacI-mediated regulation is its ability to bind simultaneously to two operators, forming a loop on the intervening DNA. Recently, several lines of evidence (both theoretical and experimental) have suggested various possible loop structures associated with different DNA binding topologies and LacI tetramer structural conformations (adopted by flexing about the C-terminal tetramerization domain). We address, specifically, the role of protein opening in loop formation by employing the single-molecule tethered particle motion method on LacI protein mutants chemically cross-linked at different positions along the cleft between the two dimers. Measurements on the wild-type and uncross-linked LacI mutants led to the observation of two distinct levels of short tether length, associated with two different DNA looping structures. Restricting conformational flexibility of the protein by chemical cross-linking induces pronounced effects. Crosslinking the dimers at the level of the N-terminal DNA binding head (E36C) completely suppresses looping, whereas cross-linking near the C-terminal tetramerization domain (Q231C) results in changes of looping geometry detected by the measured tether length distributions. These observations lead to the conclusion that tetramer opening plays a definite role in at least a subset of LacI/DNA loop conformations.

Microscopic mechanism for experimentally observed anomalous elasticity of DNA in two dimensions

By exploring a recent model in which DNA bending elasticity, described by the wormlike chain model, is coupled to basepair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic-force microscopy experiments. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by atomic-force microscopy.

Stretching submicron biomolecules with constant-force axial optical tweezers

Optical tweezers have become powerful tools to manipulate biomolecular systems, but are increasingly difficult to use when the size of the molecules is <1 microm. Many important biological structures and processes, however, occur on the submicron length scale. Therefore, we developed and characterized an optical manipulation protocol that makes this length scale accessible by stretching the molecule in the axial direction of the laser beam, thus avoiding limiting artifacts from steric hindrances from the microscope coverslip and other surface effects. The molecule is held under constant mechanical tension by a combination of optical gradient forces and backscattering forces, eliminating the need for electronic feedback. We demonstrate the utility of this method through a measurement of the force-extension relationship of a 1298 bp ds-DNA molecule.

Entropic boundary effects on the elasticity of short DNA molecules

We have measured the entropic elasticity of double-stranded-DNA molecules ranging from 247 to 1298 bp in length using axial force-clamp optical tweezers. We show that entropic end effects and excluded-volume forces from surface attachments become significant for such short molecules. The effective persistence length of the shortest molecules decreases by a factor of 2 compared to the established value for long molecules, and excluded-volume forces extend the molecules to about one third of their nominal contour length. We interpret these results in the framework of an inextensible semiflexible rod model.

Trajectory approach to two-state kinetics of single particles on sculpted energy landscapes

We study the trajectories of a single colloidal particle as it hops between two energy wells which are sculpted using optical traps. Whereas the dynamical behaviors of such systems are often treated by master-equation methods that focus on particles as actors, we analyze them instead using a trajectory-based variational method called maximum caliber (MaxCal). We show that the MaxCal strategy accurately predicts the full dynamics that we observe in the experiments: From the observed averages, it predicts second and third moments and covariances, with no free parameters. The covariances are the dynamical equivalents of Maxwell-like equilibrium reciprocal relations and Onsager-like dynamical relations.

Dissecting protein-induced DNA looping dynamics in real time

Many proteins that interact with DNA perform or enhance their specific functions by binding simultaneously to multiple target sites, thereby inducing a loop in the DNA. The dynamics and energies involved in this loop formation influence the reaction mechanism. Tethered particle motion has proven a powerful technique to study in real time protein-induced DNA looping dynamics while minimally perturbing the DNA-protein interactions. In addition, it permits many single-molecule experiments to be performed in parallel. Using as a model system the tetrameric Type II restriction enzyme SfiI, that binds two copies of its recognition site, we show here that we can determine the DNA-protein association and dissociation steps as well as the actual process of protein-induced loop capture and release on a single DNA molecule. The result of these experiments is a quantitative reaction scheme for DNA looping by SfiI that is rigorously compared to detailed biochemical studies of SfiI looping dynamics. We also present novel methods for data analysis and compare and discuss these with existing methods. The general applicability of the introduced techniques will further enhance tethered particle motion as a tool to follow DNA-protein dynamics in real time.

First-principles calculation of DNA looping in tethered particle experiments

We calculate the probability of DNA loop formation mediated by regulatory proteins such as Lac repressor (LacI), using a mathematical model of DNA elasticity. Our model is adapted to calculating quantities directly observable in tethered particle motion (TPM) experiments, and it accounts for all the entropic forces present in such experiments. Our model has no free parameters; it characterizes DNA elasticity using information obtained in other kinds of experiments. It assumes a harmonic elastic energy function (or wormlike chain type elasticity), but our Monte Carlo calculation scheme is flexible enough to accommodate arbitrary elastic energy functions. We show how to compute both the 'looping J factor' (or equivalently, the looping free energy) for various DNA construct geometries and LacI concentrations, as well as the detailed probability density function of bead excursions. We also show how to extract the same quantities from recent experimental data on TPM, and then compare to our model's predictions. In particular, we present a new method to correct observed data for finite camera shutter time and other experimental effects. Although the currently available experimental data give large uncertainties, our first-principles predictions for the looping free energy change are confirmed to within about 1 k(B)T, for loops of length around 300 basepairs. More significantly, our model successfully reproduces the detailed distributions of bead excursion, including their surprising three-peak structure, without any fit parameters and without invoking any alternative conformation of the LacI tetramer. Indeed, the model qualitatively reproduces the observed dependence of these distributions on tether length (e.g., phasing) and on LacI concentration (titration). However, for short DNA loops (around 95 basepairs) the experiments show more looping than is predicted by the harmonic-elasticity model, echoing other recent experimental results. Because the experiments we study are done in vitro, this anomalously high looping cannot be rationalized as resulting from the presence of DNA-bending proteins or other cellular machinery. We also show that it is unlikely to be the result of a hypothetical 'open' conformation of the LacI tetramer.

Concentration and length dependence of DNA looping in transcriptional regulation

In many cases, transcriptional regulation involves the binding of transcription factors at sites on the DNA that are not immediately adjacent to the promoter of interest. This action at a distance is often mediated by the formation of DNA loops: Binding at two or more sites on the DNA results in the formation of a loop, which can bring the transcription factor into the immediate neighborhood of the relevant promoter. These processes are important in settings ranging from the historic bacterial examples (bacterial metabolism and the lytic-lysogeny decision in bacteriophage), to the modern concept of gene regulation to regulatory processes central to pattern formation during development of multicellular organisms. Though there have been a variety of insights into the combinatorial aspects of transcriptional control, the mechanism of DNA looping as an agent of combinatorial control in both prokaryotes and eukaryotes remains unclear. We use single-molecule techniques to dissect DNA looping in the lac operon. In particular, we measure the propensity for DNA looping by the Lac repressor as a function of the concentration of repressor protein and as a function of the distance between repressor binding sites. As with earlier single-molecule studies, we find (at least) two distinct looped states and demonstrate that the presence of these two states depends both upon the concentration of repressor protein and the distance between the two repressor binding sites. We find that loops form even at interoperator spacings considerably shorter than the DNA persistence length, without the intervention of any other proteins to prebend the DNA. The concentration measurements also permit us to use a simple statistical mechanical model of DNA loop formation to determine the free energy of DNA looping, or equivalently, the for looping.

Direct demonstration and quantification of long-range DNA looping by the lambda bacteriophage repressor

Recently, it was proposed that DNA looping by the λ repressor (CI protein) strengthens repression of lytic genes during lysogeny and simultaneously ensures efficient switching to lysis. To investigate this hypothesis, tethered particle motion experiments were performed and dynamic CI-mediated looping of single DNA molecules containing the λ repressor binding sites separated by 2317 bp (the wild-type distance) was quantitatively analyzed. DNA containing all three intact operators or with mutated o3 operators were compared. Modeling the thermodynamic data established the free energy of CI octamer-mediated loop formation as 1.7 kcal/mol, which decreased to –0.7 kcal/mol when supplemented by a tetramer (octamer+tetramer-mediated loop). These results support the idea that loops secured by an octamer of CI bound at oL1, oL2, oR1 and oR2 operators must be augmented by a tetramer of CI bound at the oL3 and oR3 to be spontaneous and stable. Thus the o3 sites are critical for loops secured by the CI protein that attenuate cI expression.

Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects

We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri et al 2007 Phys. Rev. Lett. 99 088103). Our discrete helical wormlike chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite size effects in an experimental context, where polydA-polydT is clamped by two G-C strands, as well as for free polymers.

Interconvertible lac repressor-DNA loops revealed by single-molecule experiments

At many promoters, transcription is regulated by simultaneous binding of a protein to multiple sites on DNA, but the structures and dynamics of such transcription factor-mediated DNA loops are poorly understood. We directly examined in vitro loop formation mediated by Escherichia coli lactose repressor using single-molecule structural and kinetics methods. Small ( approximately 150 bp) loops form quickly and stably, even with out-of-phase operator spacings. Unexpectedly, repeated spontaneous transitions between two distinct loop structures were observed in individual protein-DNA complexes. The results imply a dynamic equilibrium between a novel loop structure with the repressor in its crystallographic "V" conformation and a second structure with a more extended linear repressor conformation that substantially lessens the DNA bending strain. The ability to switch between different loop structures may help to explain how robust transcription regulation is maintained even though the mechanical work required to form a loop may change substantially with metabolic conditions.

See me, feel me: methods to concurrently visualize and manipulate single DNA molecules and associated proteins

Direct visualization of DNA and proteins allows researchers to investigate DNA–protein interactions with great detail. Much progress has been made in this area as a result of increasingly sensitive single-molecule fluorescence techniques. At the same time, methods that control the conformation of DNA molecules have been improving constantly. The combination of both techniques has appealed to researchers ever since single-molecule measurements have become possible and indeed first implementations of such combined approaches have proven useful in the study of several DNA-binding proteins in real time. Here, we describe the technical state-of-the-art of various integrated manipulation-and-visualization methods. We first discuss methods that allow only little control over the DNA conformation, such as DNA combing. We then describe DNA flow-stretching approaches that allow more control, and end with the full control on position and extension obtained by manipulating DNA with optical tweezers. The advantages and limitations of the various techniques are discussed, as well as several examples of applications to biophysical or biochemical questions. We conclude with an outlook describing potential future technical developments in combining fluorescence microscopy with DNA micromanipulation technology.

End-to-end distribution for a wormlike chain in arbitrary dimensions

We construct an efficient methodology for calculating wormlike chain statistics in arbitrary D dimensions over all chain rigidities, from fully rigid to completely flexible. The structure of our exact analytical solution for the end-to-end distribution function for a wormlike chain in arbitrary D dimensions in Fourier-Laplace space (i.e., Fourier-transformed end position and Laplace-transformed chain length) adopts the form of an infinite continued fraction, which is advantageous for its compact structure and stability for numerical implementation. We then proceed to present a step-by-step methodology for performing the Fourier-Laplace inversion in order to make full use of our results in general applications. Asymptotic methods for evaluating the Laplace inversion (power-law expansion and Rayleigh-Schrödinger perturbation theory) are employed in order to improve the accuracy of the numerical inversions of the end-to-end distribution function in real space. We adapt our results to the evaluation of the single-chain structure factor, rendering simple, closed-form expressions that facilitate comparison with scattering experiments. Using our techniques, the accuracy of the end-to-end distribution function is enhanced up to the limit of the machine precision. We demonstrate the utility of our methodology with realizations of the chain statistics, giving a general methodology that can be applied to a wide range of biophysical problems.

Single-molecule manipulation reveals supercoiling-dependent modulation of lac repressor-mediated DNA looping

Gene expression regulation is a fundamental biological process which deploys specific sets of genomic information depending on physiological or environmental conditions. Several transcription factors (including lac repressor, LacI) are present in the cell at very low copy number and increase their local concentration by binding to multiple sites on DNA and looping the intervening sequence. In this work, we employ single-molecule manipulation to experimentally address the role of DNA supercoiling in the dynamics and stability of LacI-mediated DNA looping. We performed measurements over a range of degrees of supercoiling between -0.026 and +0.026, in the absence of axial stretching forces. A supercoiling-dependent modulation of the lifetimes of both the looped and unlooped states was observed. Our experiments also provide evidence for multiple structural conformations of the LacI-DNA complex, depending on torsional constraints. The supercoiling-dependent modulation demonstrated here adds an important element to the model of the lac operon. In fact, the complex network of proteins acting on the DNA in a living cell constantly modifies its topological and mechanical properties: our observations demonstrate the possibility of establishing a signaling pathway from factors affecting DNA supercoiling to transcription factors responsible for the regulation of specific sets of genes.

The importance of surfaces in single-molecule bioscience

The last ten years have witnessed an explosion of new techniques that can be used to probe the dynamic behavior of individual biological molecules, leading to discoveries that would not have been possible with more traditional biochemical methods. A common feature among these single-molecule approaches is the need for the biological molecules to be anchored to a solid support surface. This must be done under conditions that minimize nonspecific adsorption without compromising the biological integrity of the sample. In this review we highlight why surface attachments are a critical aspect of many single-molecule studies and we discuss current methods for anchoring biomolecules. Finally, we provide a detailed description of a new method developed by our laboratory for anchoring and organizing hundreds of individual DNA molecules on a surface, allowing "high-throughput" studies of protein-DNA interactions at the single-molecule level.

Geometry of mediating protein affects the probability of loop formation in DNA

Recent single molecule experiments have determined the probability of loop formation in DNA as a function of the DNA contour length for different types of looping proteins. The optimal contour length for loop formation as well as the probability density functions have been found to be strongly dependent on the type of looping protein used. We show, using Monte Carlo simulations and analytical calculations, that these observations can be replicated using the wormlike-chain model for double-stranded DNA if we account for the nonzero size of the looping protein. The simulations have been performed in two dimensions so that bending is the only mode of deformation available to the DNA while the geometry of the looping protein enters through a single variable which is representative of its size. We observe two important effects that seem to directly depend on the size of the enzyme: 1), the overall propensity of loop formation at any given value of the DNA contour length increases with the size of the enzyme; and 2), the contour length corresponding to the first peak as well as the first well in the probability density functions increases with the size of the enzyme. Additionally, the eigenmodes of the fluctuating shape of the looped DNA calculated from simulations and theory are in excellent agreement, and reveal that most of the fluctuations in the DNA occur in regions of low curvature.

Single-molecule atomic force spectroscopy reveals that DnaD forms scaffolds and enhances duplex melting

The Bacillus subtilis DnaD is an essential DNA-binding protein implicated in replication and DNA remodeling. Using single-molecule atomic force spectroscopy, we have studied the interaction of DnaD and its domains with DNA. Our data reveal that binding of DnaD to immobilized single molecules of duplex DNA causes a marked reduction in the 'end-to-end' distance of the DNA in a concentration-dependent manner, consistent with previously reported DnaD-induced looping by scaffold formation. Native DnaD enhances partial melting of the DNA strands. The C-terminal domain (Cd) of DnaD binds to DNA and enhances partial duplex melting but does not cause DNA looping. The Cd-mediated melting is not as efficient as that caused by native DnaD. The N-terminal domain (Nd) does not affect significantly the DNA. A mixture of Nd and Cd fails to recreate the DNA looping effect of native DnaD but produces exactly the same effects as Cd on its own, consistent with the previously reported failure of the separated domains to form DNA-interacting scaffolds.

Maxwell relations for single-DNA experiments: Monitoring protein binding and double-helix torque with force-extension measurements

Single-DNA stretching and twisting experiments provide a sensitive means to detect binding of proteins, via detection of their modification of DNA mechanical properties. However, it is often difficult or impossible to determine the numbers of proteins bound in such experiments, especially when the proteins interact nonspecifically (bind stably at any sequence position) with DNA. Here we discuss how analogs of the Maxwell relations of classical thermodynamics may be defined and used to determine changes in numbers of bound proteins, from measurements of extension as a function of bulk protein concentration. We include DNA twisting in our analysis, which allows us to show how changes in torque along single DNA molecules may be determined from measurements of extension as a function of DNA linking number. We focus on relations relevant to common experimental situations (e.g., magnetic and optical tweezers with or without controlled torque or linking number). The relation of our results to Gibbs adsorption is discussed.

Dynamics and consequences of DNA looping by the FokI restriction endonuclease

Genetic events often require proteins to be activated by interacting with two DNA sites, trapping the intervening DNA in a loop. While much is known about looping equilibria, only a few studies have examined DNA-looping dynamics experimentally. The restriction enzymes that cut DNA after interacting with two recognition sites, such as FokI, can be used to exemplify looping reactions. The reaction pathway for FokI on a supercoiled DNA with two sites was dissected by fast kinetics to reveal, in turn: the initial binding of a protein monomer to each site; the protein–protein association to form the dimer, trapping the loop; the subsequent phosphodiester hydrolysis step. The DNA motion that juxtaposes the sites ought on the basis of Brownian dynamics to take ∼2 ms, but loop capture by FokI took 230 ms. Hence, DNA looping by FokI is rate limited by protein association rather than DNA dynamics. The FokI endonuclease also illustrated activation by looping: it cut looped DNA 400 times faster than unlooped DNA.

Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a one-dimensional Ising model, which describes the internal base-pair states, coupled to a discrete wormlike chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of poly(dA)-poly(dT) and, by inserting the experimentally known bending rigidities, leads to physically reasonable values for the bare Ising model parameters. Among the thermodynamical quantities explicitly calculated within this model are the internal, structural, and mechanical features of the DNA molecule, such as bubble correlation length and two distinct chain persistence lengths. The predicted variation of the mean-square radius as a function of temperature leads to a coherent explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs. Simple limiting formulas, useful for analyzing experiments, are given for the fraction of broken base pairs, Ising and chain correlation functions, effective persistence lengths, and chain mean-square radius, all as a function of temperature and DNA length.

Experimental test of connector rotation during DNA packaging into bacteriophage phi29 capsids

The bacteriophage ϕ29 generates large forces to compact its double-stranded DNA genome into a protein capsid by means of a portal motor complex. Several mechanical models for the generation of these high forces by the motor complex predict coupling of DNA translocation to rotation of the head-tail connector dodecamer. Putative connector rotation is investigated here by combining the methods of single-molecule force spectroscopy with polarization-sensitive single-molecule fluorescence. In our experiment, we observe motor function in several packaging complexes in parallel using video microscopy of bead position in a magnetic trap. At the same time, we follow the orientation of single fluorophores attached to the portal motor connector. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question.

The life cycles of many viruses include a self-assembly stage in which a powerful molecular motor packs the DNA genome into the virus's preformed shell (the capsid). Biochemical and biophysical studies have identified essential components of the packaging machinery and measured various characteristics of the packaging process, while crystallography and electron microscopy have provided snapshots of viral structure before and after packaging. In bacteriophage ϕ29 assembly, the DNA passes into the shell through a channel formed by a structure called the connector. Structurally motivated models over the past 30 years have coupled DNA movement to rotation of the connector relative to the capsid. We describe a direct test of the connector rotation hypothesis, combining magnetic single-molecule manipulation techniques and single-molecule fluorescence spectroscopy. In our experiments, we use a single-dye molecule attached specifically to the connector as a reporter for its orientation and simultaneously observe the translocation of a magnetic bead attached to the DNA that is being packaged. From our data, we can exclude connector rotation with greater than 99% probability and therefore answer a long-standing mechanistic question.

dsDNA compaction into bacteriophage capsids is observed in packaging complexes. Unlike in previous models, this compaction is found not to be driven by a rotating motor complex.

Diffusive hidden Markov model characterization of DNA looping dynamics in tethered particle experiments

In many biochemical processes, proteins bound to DNA at distant sites are brought into close proximity by loops in the underlying DNA. For example, the function of some gene-regulatory proteins depends on such 'DNA looping' interactions. We present a new technique for characterizing the kinetics of loop formation in vitro, as observed using the tethered particle method, and apply it to experimental data on looping induced by lambda repressor. Our method uses a modified ('diffusive') hidden Markov analysis that directly incorporates the Brownian motion of the observed tethered bead. We compare looping lifetimes found with our method (which we find are consistent over a range of sampling frequencies) to those obtained via the traditional threshold-crossing analysis (which can vary depending on how the raw data are filtered in the time domain). Our method does not involve any time filtering and can detect sudden changes in looping behavior. For example, we show how our method can identify transitions between long-lived, kinetically distinct states that would otherwise be difficult to discern.

Elasticity of short DNA molecules: theory and experiment for contour lengths of 0.6-7 microm

The wormlike chain (WLC) model currently provides the best description of double-stranded DNA elasticity for micron-sized molecules. This theory requires two intrinsic material parameters-the contour length L and the persistence length p. We measured and then analyzed the elasticity of double-stranded DNA as a function of L (632 nm-7.03 microm) using the classic solution to the WLC model. When the elasticity data were analyzed using this solution, the resulting fitted value for the persistence length p(wlc) depended on L; even for moderately long DNA molecules (L = 1300 nm), this apparent persistence length was 10% smaller than its limiting value for long DNA. Because p is a material parameter, and cannot depend on length, we sought a new solution to the WLC model, which we call the "finite wormlike chain (FWLC)," to account for effects not considered in the classic solution. Specifically we accounted for the finite chain length, the chain-end boundary conditions, and the bead rotational fluctuations inherent in optical trapping assays where beads are used to apply the force. After incorporating these corrections, we used our FWLC solution to generate force-extension curves, and then fit those curves with the classic WLC solution, as done in the standard experimental analysis. These results qualitatively reproduced the apparent dependence of p(wlc) on L seen in experimental data when analyzed with the classic WLC solution. Directly fitting experimental data to the FWLC solution reduces the apparent dependence of p(fwlc) on L by a factor of 3. Thus, the FWLC solution provides a significantly improved theoretical framework in which to analyze single-molecule experiments over a broad range of experimentally accessible DNA lengths, including both short (a few hundred nanometers in contour length) and very long (microns in contour length) molecules.

Tethered particle motion as a diagnostic of DNA tether length

The tethered particle motion (TPM) technique involves an analysis of the Brownian motion of a bead tethered to a slide by a single DNA molecule. We describe an improved experimental protocol with which to form the tethers, an algorithm for analyzing bead motion visualized using differential interference contrast microscopy, and a physical model with which we have successfully simulated such DNA tethers. Both experiment and theory show that the statistics of the bead motion are quite different from those of a free semiflexible polymer. Our experimental data for chain extension versus tether length fit our model over a range of tether lengths from 109 to 3477 base pairs, using a value for the DNA persistence length that is consistent with those obtained under similar solution conditions by other methods. Moreover, we present the first experimental determination of the full probability distribution function of bead displacements and find excellent agreement with our theoretical prediction. Our results show that TPM is a useful tool for monitoring large conformational changes such as DNA looping.

Analysis of kinetics in noisy systems: application to single molecule tethered particle motion

In the tethered particle motion method the length of a DNA molecule is monitored by measuring the range of diffusion of a microsphere tethered to the surface of a microscope coverslip through the DNA molecule itself. Looping of DNA (induced by binding of a specific protein) can be detected with this method and the kinetics of the looping/unlooping processes can be measured at the single molecule level. The microsphere's position variance represents the experimental variable reporting on the polymer length. Therefore, data windowing is required to obtain position variance from raw position data. Due to the characteristic diffusion time of the microsphere, the low-pass filtering required to attain a good signal/noise ratio (S/N) in the discrimination of looped versus unlooped state impacts significantly the measurement's time resolution. Here we present a method for measuring lifetimes based on half-amplitude thresholding and then correcting the kinetic measurements, taking into account low S/N (leading to false events) and limited time resolution (leading to missed events). This method allows an accurate and unbiased estimation of the kinetic parameters under investigation, independently of the choice of the window used for variance calculation, with potential applications to other single molecule measurements with low S/N.

DNA compaction by the nuclear factor-Y

The nuclear factor-Y (NF-Y), a trimeric, CCAAT-binding transcriptional activator with histone-like subunits, was until recently considered a prototypical promoter transcription factor. However, recent in vivo chromatin immunoprecipitation assays associated with microarray methodologies (chromatin immunoprecipitation on chip experiments) have indicated that a large portion of target sites (40%-50%) are located outside of core promoters. We applied the tethered particle motion technique to the major histocompatibility complex class II enhancer-promoter region to characterize i), the progressive compaction of DNA due to increasing concentrations of NF-Y, ii), the role of specific subunits and domains of NF-Y in the process, and iii), the interplay between NF-Y and the regulatory factor-X, which cooperatively binds to the X-box adjacent to the CCAAT box. Our study shows that NF-Y has histone-like activity, since it binds DNA nonspecifically with high affinity to compact it. This activity, which depends on the presence of all trimer subunits and of their glutamine-rich domains, seems to be attenuated by the transcriptional cofactor regulatory factor-X. Most importantly NF-Y-induced DNA compaction may facilitate promoter-enhancer interactions, which are known to be critical for expression regulation.

Biological consequences of tightly bent DNA: the other life of a macromolecular celebrity

The mechanical properties of DNA play a critical role in many biological functions. For example, DNA packing in viruses involves confining the viral genome in a volume (the viral capsid) with dimensions that are comparable to the DNA persistence length. Similarly, eukaryotic DNA is packed in DNA-protein complexes (nucleosomes), in which DNA is tightly bent around protein spools. DNA is also tightly bent by many proteins that regulate transcription, resulting in a variation in gene expression that is amenable to quantitative analysis. In these cases, DNA loops are formed with lengths that are comparable to or smaller than the DNA persistence length. The aim of this review is to describe the physical forces associated with tightly bent DNA in all of these settings and to explore the biological consequences of such bending, as increasingly accessible by single-molecule techniques.

DNA looping kinetics analyzed using diffusive hidden Markov model

Tethered particle experiments use light microscopy to measure the position of a micrometer-sized bead tethered to a microscope slide via an approximately micrometer-length polymer, to infer the behavior of the invisible polymer. Currently, this method is used to measure rate constants of DNA loop formation and breakdown mediated by repressor protein that binds to the DNA. We report a new technique for measuring these rates using a modified hidden Markov analysis that directly incorporates the diffusive motion of the bead, which is an inherent complication of tethered particle motion because it occurs on a timescale between the sampling frequency and the looping time. We compare looping lifetimes found with our method, which are consistent over a range of sampling frequencies, to those obtained via the traditional threshold-crossing analysis, which vary depending on how the raw data are filtered in the time domain. Our method does not involve such filtering, and so can detect short-lived looping events and sudden changes in looping behavior.