Lac repressor hinge flexibility and DNA looping: single molecule kinetics by tethered particle motion

Tethered Particle Motion Technique in Crowded Media: Compaction of DNA by Globular Macromolecules

Tethered Particle Motion (TPM) is a single molecule technique, which consists in tracking the motion of a nanoparticle (NP) immersed in a fluid and tethered to a glass surface by a DNA molecule. The present work addresses the question of the applicability of TPM to fluids which contain crowders at volume fractions ranging from that of the nucleoid of living bacteria (around 30%) up to the jamming threshold (around 66%). In particular, we were interested in determining whether TPM can be used to characterize the compaction of DNA by globular crowders. To this end, extensive Brownian Dynamics simulations were performed with a specifically built coarse-grained model. Analysis of the simulations reveals several effects not observed in dilute media, which impose constraints on the TPM setup. In particular, the Tethered Fluorophore Motion (TFM) technique, which consists in replacing the NP by a much smaller fluorophore, is probably better suited than standard TPM. Moreover, a sample preparation technique which does not involve hydrophilic patches may be required. Finally, the use of a DNA brush may be needed to achieve DNA concentrations close to in vivo ones.

A Multiplexable Plasmonic Hairpin-DNA Sensor Based On Target-specific Tether Dynamics

The need for measurements of multiple biomarkers simultaneously at subnanomolar concentrations asks for the development of new sensors with high sensitivity, specificity, precision, and accuracy. Currently, multiplexed sensing in single molecule sensors increases the complexity of the system in terms of reagents and sample read-out. In this letter, we propose a novel approach to multiplex hairpin-based single-DNA molecule sensors, which overcomes the limitations of the present approaches for multiplexing. By target-dependent ssDNA hairpin design, we can create DNA tethers that have distinct tether dynamics upon target binding. Our numerical model shows that by changing the stem length of the ssDNA hairpin, significantly different dynamic tether behavior will be observed. By exploiting the distance-dependent coupling of AuNPs to gold films, we can probe this dynamic behavior along the z-axis using a simple laser equipped microscope.

Sensing force and charge at the nanoscale with a single-molecule tether

Measuring the electrophoretic mobility of molecules is a powerful experimental approach for investigating biomolecular processes. A frequent challenge in the context of single-particle measurements is throughput, limiting the obtainable statistics. Here, we present a molecular force sensor and charge detector based on parallelised imaging and tracking of tethered double-stranded DNA functionalised with charged nanoparticles interacting with an externally applied electric field. Tracking the position of the tethered particle with simultaneous nanometre precision and microsecond temporal resolution allows us to detect and quantify the electrophoretic force down to the sub-piconewton scale. Furthermore, we demonstrate that this approach is suitable for detecting changes to the particle charge state, as induced by the addition of charged biomolecules or changes to pH. Our approach provides an alternative route to studying structural and charge dynamics at the single molecule level.

Single-molecule insight into stalled replication fork rescue in Escherichia coli

DNA replication forks stall at least once per cell cycle in Escherichia coli. DNA replication must be restarted if the cell is to survive. Restart is a multi-step process requiring the sequential action of several proteins whose actions are dictated by the nature of the impediment to fork progression. When fork progress is impeded, the sequential actions of SSB, RecG and the RuvABC complex are required for rescue. In contrast, when a template discontinuity results in the forked DNA breaking apart, the actions of the RecBCD pathway enzymes are required to resurrect the fork so that replication can resume. In this review, we focus primarily on the significant insight gained from single-molecule studies of individual proteins, protein complexes, and also, partially reconstituted regression and RecBCD pathways. This insight is related to the bulk-phase biochemical data to provide a comprehensive review of each protein or protein complex as it relates to stalled DNA replication fork rescue.

One-dimensional diffusion of TrpR along DNA enhances its affinity for the operator by chemical ratchet mechanism

Several DNA-binding proteins show the affinities for their specific DNA sites that positively depend on the length of DNA harboring the sites, i. e. antenna effect. DNA looping can cause the effect for proteins with two or more DNA binding sites, i. e. the looping mechanism. One-dimensional diffusion also has been suggested to cause the effect for proteins with single DNA sites, the diffusion mechanism, which could violate detailed balance. We addressed which mechanism is possible for E. coli TrpR showing 10⁴-fold antenna effect with a single DNA binding site. When a trpO-harboring DNA fragment was connected to a nonspecific DNA with biotin-avidin connection, the otherwise sevenfold antenna effect disappeared. This result denies the looping mechanism with an unknown second DNA binding site. The 3.5-fold repression by TrpR in vivo disappeared when a tight LexA binding site was introduced at various sites near the trpO, suggesting that the binding of LexA blocks one-dimensional diffusion causing the antenna effect. These results are consistent with the chemical ratchet recently proposed for TrpR-trpO binding to solve the deviation from detailed balance, and evidence that the antenna effect due to one-dimensional diffusion exists in cells.

RNA Polymerase and Transcription Mechanisms: The Forefront of Physicochemical Studies of Chemical Reactions

The study of transcription and its regulation is an interdisciplinary field that is closely connected with genetics, structural biology, and reaction theory. Among these, although less attention has been paid to reaction theory, it is becoming increasingly useful for research on transcription. Rate equations are commonly used to describe reactions involved in transcription, but they tend to be used unaware of the timescales of relevant physical processes. In this review, we discuss the limitation of rate equation for describing three-dimensional diffusion and one-dimensional diffusion along DNA. We then introduce the chemical ratchet mechanism recently proposed for explaining the antenna effect, an enhancement of the binding affinity to a specific site on longer DNA, which deviates from a thermodynamic rule. We show that chemical ratchet cannot be described with a single set of rate equations but alternative sets of rate equations that temporally switch no faster than the binding reaction.

Protamine loops DNA in multiple steps

Protamine proteins dramatically condense DNA in sperm to almost crystalline packing levels. Here, we measure the first step in the in vitro pathway, the folding of DNA into a single loop. Current models for DNA loop formation are one-step, all-or-nothing models with a looped state and an unlooped state. However, when we use a Tethered Particle Motion (TPM) assay to measure the dynamic, real-time looping of DNA by protamine, we observe the presence of multiple folded states that are long-lived (∼100 s) and reversible. In addition, we measure folding on DNA molecules that are too short to form loops. This suggests that protamine is using a multi-step process to loop the DNA rather than a one-step process. To visualize the DNA structures, we used an Atomic Force Microscopy (AFM) assay. We see that some folded DNA molecules are loops with a ∼10-nm radius and some of the folded molecules are partial loops—c-shapes or s-shapes—that have a radius of curvature of ∼10 nm. Further analysis of these structures suggest that protamine is bending the DNA to achieve this curvature rather than increasing the flexibility of the DNA. We therefore conclude that protamine loops DNA in multiple steps, bending it into a loop.

Statistical physics and mesoscopic modeling to interpret tethered particle motion experiments

Tethered particle motion experiments are versatile single-molecule techniques enabling one to address in vitro the molecular properties of DNA and its interactions with various partners involved in genetic regulations. These techniques provide raw data such as the tracked particle amplitude of movement, from which relevant information about DNA conformations or states must be recovered. Solving this inverse problem appeals to specific theoretical tools that have been designed in the two last decades, together with the data pre-processing procedures that ought to be implemented to avoid biases inherent to these experimental techniques. These statistical tools and models are reviewed in this paper.

Protein-mediated loops in supercoiled DNA create large topological domains

Supercoiling can alter the form and base pairing of the double helix and directly impact protein binding. More indirectly, changes in protein binding and the stress of supercoiling also influence the thermodynamic stability of regulatory, protein-mediated loops and shift the equilibria of fundamental DNA/chromatin transactions. For example, supercoiling affects the hierarchical organization and function of chromatin in topologically associating domains (TADs) in both eukaryotes and bacteria. On the other hand, a protein-mediated loop in DNA can constrain supercoiling within a plectonemic structure. To characterize the extent of constrained supercoiling, 400 bp, lac repressor-secured loops were formed in extensively over- or under-wound DNA under gentle tension in a magnetic tweezer. The protein-mediated loops constrained variable amounts of supercoiling that often exceeded the maximum writhe expected for a 400 bp plectoneme. Loops with such high levels of supercoiling appear to be entangled with flanking domains. Thus, loop-mediating proteins operating on supercoiled substrates can establish topological domains that may coordinate gene regulation and other DNA transactions across spans in the genome that are larger than the separation between the binding sites.

Protein-mediated looping of DNA under tension requires supercoiling

Protein-mediated DNA looping is ubiquitous in chromatin organization and gene regulation, but to what extent supercoiling or nucleoid associated proteins promote looping is poorly understood. Using the lac repressor (LacI), a paradigmatic loop-mediating protein, we measured LacI-induced looping as a function of either supercoiling or the concentration of the HU protein, an abundant nucleoid protein in Escherichia coli. Negative supercoiling to physiological levels with magnetic tweezers easily drove the looping probability from 0 to 100% in single DNA molecules under slight tension that likely exists in vivo. In contrast, even saturating (micromolar) concentrations of HU could not raise the looping probability above 30% in similarly stretched DNA or 80% in DNA without tension. Negative supercoiling is required to induce significant looping of DNA under any appreciable tension.

PLANT: A Method for Detecting Changes of Slope in Noisy Trajectories

Time traces obtained from a variety of biophysical experiments contain valuable information on underlying processes occurring at the molecular level. Accurate quantification of these data can help explain the details of the complex dynamics of biological systems. Here, we describe PLANT (Piecewise Linear Approximation of Noisy Trajectories), a segmentation algorithm that allows the reconstruction of time-trace data with constant noise as consecutive straight lines, from which changes of slopes and their respective durations can be extracted. We present a general description of the algorithm and perform extensive simulations to characterize its strengths and limitations, providing a rationale for the performance of the algorithm in the different conditions tested. We further apply the algorithm to experimental data obtained from tracking the centroid position of lymphocytes migrating under the effect of a laminar flow and from single myosin molecules interacting with actin in a dual-trap force-clamp configuration.

Comparison between Effects of Retroactivity and Resource Competition upon Change in Downstream Reporter Genes of Synthetic Genetic Circuits

Reporter genes have contributed to advancements in molecular biology. Binding of an upstream regulatory protein to a downstream reporter promoter allows quantification of the activity of the upstream protein produced from the corresponding gene. In studies of synthetic biology, analyses of reporter gene activities ensure control of the cell with synthetic genetic circuits, as achieved using a combination of in silico and in vivo experiments. However, unexpected effects of downstream reporter genes on upstream regulatory genes may interfere with in vivo observations. This phenomenon is termed as retroactivity. Using in silico and in vivo experiments, we found that a different copy number of regulatory protein-binding sites in a downstream gene altered the upstream dynamics, suggesting retroactivity of reporters in this synthetic genetic oscillator. Furthermore, by separating the two sources of retroactivity (titration of the component and competition for degradation), we showed that, in the dual-feedback oscillator, the level of the fluorescent protein reporter competing for degradation with the circuits' components is important for the stability of the oscillations. Altogether, our results indicate that the selection of reporter promoters using a combination of in silico and in vivo experiments is essential for the advanced design of genetic circuits.

Tethered multifluorophore motion reveals equilibrium transition kinetics of single DNA double helices

Understanding cellular functions and dysfunctions often begins with quantifying the interactions between the binding partners involved in the processes. Learning about the kinetics of the interactions is of particular importance to understand the dynamics of cellular processes. We created a tethered multifluorophore motion assay using DNA origami that enables over 1-hour-long recordings of the statistical binding and unbinding of single pairs of biomolecules directly in equilibrium. The experimental concept is simple and the data interpretation is very direct, which makes the system easy to use for a wide variety of researchers. Due to the modularity and addressability of the DNA origami-based assay, our system may be readily adapted to study various other molecular interactions.

We describe a tethered multifluorophore motion assay based on DNA origami for revealing bimolecular reaction kinetics on the single-molecule level. Molecular binding partners may be placed at user-defined positions and in user-defined stoichiometry; and binding states are read out by tracking the motion of quickly diffusing fluorescent reporter units. Multiple dyes per reporter unit enable singe-particle observation for more than 1 hour. We applied the system to study in equilibrium reversible hybridization and dissociation of complementary DNA single strands as a function of tether length, cation concentration, and sequence. We observed up to hundreds of hybridization and dissociation events per single reactant pair and could produce cumulative statistics with tens of thousands of binding and unbinding events. Because the binding partners per particle do not exchange, we could also detect subtle heterogeneity from molecule to molecule, which enabled separating data reflecting the actual target strand pair binding kinetics from falsifying influences stemming from chemically truncated oligonucleotides. Our data reflected that mainly DNA strand hybridization, but not strand dissociation, is affected by cation concentration, in agreement with previous results from different assays. We studied 8-bp-long DNA duplexes with virtually identical thermodynamic stability, but different sequences, and observed strongly differing hybridization kinetics. Complementary full-atom molecular-dynamics simulations indicated two opposing sequence-dependent phenomena: helical templating in purine-rich single strands and secondary structures. These two effects can increase or decrease, respectively, the fraction of strand collisions leading to successful nucleation events for duplex formation.

Determining the Transcription Rates Yielding Steady-State Production of mRNA in the Lac Genetic Switch of Escherichia coli

To elucidate the regulatory dynamics of the gene expression activation and inactivation, an in silico biochemical model of the lac circuit in Escherichia coli was used to evaluate the transcription rates that yield the steady-state mRNA production in active and inactive states of the lac circuit. This result can be used in synthetic biology applications to understand the limits of the genetic synthesis. Since most genetic networks involve many interconnected components with positive and negative feedback control, intuitive understanding of their dynamics is often difficult to obtain. Although the kinetic model of the lac circuit considered involves only a single positive feedback, the developed computational framework can be used to evaluate supported ranges of other reaction rates in genetic circuits with more complex regulatory networks. More specifically, the inducible lac gene switch in E. coli is regulated by unbinding and binding of the inducer-repressor complexes to or from the DNA operator to switch the gene expression on and off. The dependency of mRNA production at steady state on different transcription rates and the repressor complexes has been studied by computer simulations in the Lattice Microbe software. Provided that the lac circuit is in active state, the transcription rate is independent of the inducer-repressor complexes present in the cell. In inactive state, the transcription rate is dependent on the specific inducer-repressor complex bound to the operator that inactivates the gene expression. We found that the repressor complex with the largest affinity to the operator yields the smallest range of the feasible transcription rates to yield the steady state while the lac circuit is in inactive state. In contrast, the steady state in active state can be obtained for any value of the transcription rate.

Single-Molecule Tethered Particle Motion: Stepwise Analyses of Site-Specific DNA Recombination

Tethered particle motion/microscopy (TPM) is a biophysical tool used to analyze changes in the effective length of a polymer, tethered at one end, under changing conditions. The tether length is measured indirectly by recording the Brownian motion amplitude of a bead attached to the other end. In the biological realm, DNA, whose interactions with proteins are often accompanied by apparent or real changes in length, has almost exclusively been the subject of TPM studies. TPM has been employed to study DNA bending, looping and wrapping, DNA compaction, high-order DNA⁻protein assembly, and protein translocation along DNA. Our TPM analyses have focused on tyrosine and serine site-specific recombinases. Their pre-chemical interactions with DNA cause reversible changes in DNA length, detectable by TPM. The chemical steps of recombination, depending on the substrate and the type of recombinase, may result in a permanent length change. Single molecule TPM time traces provide thermodynamic and kinetic information on each step of the recombination pathway. They reveal how mechanistically related recombinases may differ in their early commitment to recombination, reversibility of individual steps, and in the rate-limiting step of the reaction. They shed light on the pre-chemical roles of catalytic residues, and on the mechanisms by which accessory proteins regulate recombination directionality.

Measurement of Mesoscale Conformational Dynamics of Freely Diffusing Molecules with Tracking FCS

Few techniques are suited to probe the structure and dynamics of molecular complexes at the mesoscale level (∼100-1000 nm). We have developed a single-molecule technique that uses tracking fluorescence correlation spectroscopy (tFCS) to probe the conformation and dynamics of mesoscale molecular assemblies. tFCS measures the distance fluctuations between two fluorescently labeled sites within an untethered, freely diffusing biomolecule. To achieve subdiffraction spatial resolution, we developed a feedback scheme that allows us to maintain the molecule at an optimal position within the laser intensity gradient for fluorescence correlation spectroscopy. We characterized tFCS spatial sensitivity by measuring the Brownian end-to-end dynamics of DNA molecules as short as 1000 bp. We demonstrate that tFCS detects changes in the compaction of reconstituted nucleosome arrays and can assay transient protein-mediated interactions between distant sites in an individual DNA molecule. Our measurements highlight the applicability of tFCS to a wide variety of biochemical processes involving mesoscale conformational dynamics.

Multiplexed, Tethered Particle Microscopy for Studies of DNA-Enzyme Dynamics

DNA is the carrier of genetic information and, as such, is at the center of most essential cellular processes. To regulate its physiological function, specific proteins and motor enzymes constantly change conformational states with well-controlled dynamics. Twenty-five years ago, Schafer, Gelles, Sheetz, and Landick employed the tethered particle motion (TPM) technique for the first time to study transcription by RNA polymerase at the single-molecule level. TPM has since then remained one of the simplest, most affordable, and yet incisive single-molecule techniques available. It is an in vitro technique which allows investigation of DNA-protein interactions that change the effective length of a DNA tether. In this chapter, we will describe a recent strategy to multiplex TPM which substantially increases the throughput of TPM experiments, as well as a simulation to estimate the time resolution of experiments, such as transcriptional elongation assays, in which lengthy time averaging of the signal is impossible due to continual change of the DNA tether length. These improvements allow efficient study of several DNA-protein systems, including transcriptionally active DNA-RNA polymerase I complexes and DNA-gyrase complexes.

Interplay of Protein Binding Interactions, DNA Mechanics, and Entropy in DNA Looping Kinetics

DNA looping plays a key role in many fundamental biological processes, including gene regulation, recombination, and chromosomal organization. The looping of DNA is often mediated by proteins whose structural features and physical interactions can alter the length scale at which the looping occurs. Looping and unlooping processes are controlled by thermodynamic contributions associated with mechanical deformation of the DNA strand and entropy arising from thermal fluctuations of the conformation. To determine how these confounding effects influence DNA looping and unlooping kinetics, we present a theoretical model that incorporates the role of the protein interactions, DNA mechanics, and conformational entropy. We show that for shorter DNA strands the interaction distance affects the transition state, resulting in a complex relationship between the looped and unlooped state lifetimes and the physical properties of the looped DNA. We explore the range of behaviors that arise with varying interaction distance and DNA length. These results demonstrate how DNA deformation and entropy dictate the scaling of the looping and unlooping kinetics versus the J-factor, establishing the connection between kinetic and equilibrium behaviors. Our results show how the twist-and-bend elasticity of the DNA chain modulates the kinetics and how the influence of the interaction distance fades away at intermediate to longer chain lengths, in agreement with previous scaling predictions.

An information-based approach to change-point analysis with applications to biophysics and cell biology

This article describes the application of a change-point algorithm to the analysis of stochastic signals in biological systems whose underlying state dynamics consist of transitions between discrete states. Applications of this analysis include molecular-motor stepping, fluorophore bleaching, electrophysiology, particle and cell tracking, detection of copy number variation by sequencing, tethered-particle motion, etc. We present a unified approach to the analysis of processes whose noise can be modeled by Gaussian, Wiener, or Ornstein-Uhlenbeck processes. To fit the model, we exploit explicit, closed-form algebraic expressions for maximum-likelihood estimators of model parameters and estimated information loss of the generalized noise model, which can be computed extremely efficiently. We implement change-point detection using the frequentist information criterion (which, to our knowledge, is a new information criterion). The frequentist information criterion specifies a single, information-based statistical test that is free from ad hoc parameters and requires no prior probability distribution. We demonstrate this information-based approach in the analysis of simulated and experimental tethered-particle-motion data.

Flexibility and Disorder in Gene Regulation: LacI/GalR and Hox Proteins

To modulate transcription, a variety of input signals must be sensed by genetic regulatory proteins. In these proteins, flexibility and disorder are emerging as common themes. Prokaryotic regulators generally have short, flexible segments, whereas eukaryotic regulators have extended regions that lack predicted secondary structure (intrinsic disorder). Two examples illustrate the impact of flexibility and disorder on gene regulation: the prokaryotic LacI/GalR family, with detailed information from studies on LacI, and the eukaryotic family of Hox proteins, with specific insights from investigations of Ultrabithorax (Ubx). The widespread importance of structural disorder in gene regulatory proteins may derive from the need for flexibility in signal response and, particularly in eukaryotes, in protein partner selection.

Modulation of DNA loop lifetimes by the free energy of loop formation

Storage and retrieval of the genetic information in cells is a dynamic process that requires the DNA to undergo dramatic structural rearrangements. DNA looping is a prominent example of such a structural rearrangement that is essential for transcriptional regulation in both prokaryotes and eukaryotes, and the speed of such regulations affects the fitness of individuals. Here, we examine the in vitro looping dynamics of the classic Lac repressor gene-regulatory motif. We show that both loop association and loop dissociation at the DNA-repressor junctions depend on the elastic deformation of the DNA and protein, and that both looping and unlooping rates approximately scale with the looping J factor, which reflects the system's deformation free energy. We explain this observation by transition state theory and model the DNA-protein complex as an effective worm-like chain with twist. We introduce a finite protein-DNA binding interaction length, in competition with the characteristic DNA deformation length scale, as the physical origin of the previously unidentified loop dissociation dynamics observed here, and discuss the robustness of this behavior to perturbations in several polymer parameters.

Tethered particle motion reveals that LacI·DNA loops coexist with a competitor-resistant but apparently unlooped conformation

The lac repressor protein (LacI) efficiently represses transcription of the lac operon in Escherichia coli by binding to two distant operator sites on the bacterial DNA and causing the intervening DNA to form a loop. We employed single-molecule tethered particle motion to observe LacI-mediated loop formation and breakdown in DNA constructs that incorporate optimized operator binding sites and intrinsic curvature favorable to loop formation. Previous bulk competition assays indirectly measured the loop lifetimes in these optimized DNA constructs as being on the order of days; however, we measured these same lifetimes to be on the order of minutes for both looped and unlooped states. In a range of single-molecule DNA competition experiments, we found that the resistance of the LacI-DNA complex to competitive binding is a function of both the operator strength and the interoperator sequence. To explain these findings, we present what we believe to be a new kinetic model of loop formation and DNA competition. In this proposed new model, we hypothesize a new unlooped state in which the unbound DNA-binding domain of the LacI protein interacts nonspecifically with nonoperator DNA adjacent to the operator site at which the second LacI DNA-binding domain is bound.

Enhanced tethered-particle motion analysis reveals viscous effects

Tethered-particle motion experiments do not require expensive or technically complex hardware, and increasing numbers of researchers are adopting this methodology to investigate the topological effects of agents that act on the tethering polymer or the characteristics of the polymer itself. These investigations depend on accurate measurement and interpretation of changes in the effective length of the tethering polymer (often DNA). However, the bead size, tether length, and buffer affect the confined diffusion of the bead in this experimental system. To evaluate the effects of these factors, improved measurements to calibrate the two-dimensional range of motion (excursion) versus DNA length were carried out. Microspheres of 160 or 240 nm in radius were tethered by DNA molecules ranging from 225 to 3477 basepairs in length in aqueous buffers containing 100 mM potassium glutamate and 8 mM MgCl2 or 10 mM Tris-HCl and 200 mM KCl, with or without 0.5% Tween added to the buffer, and the motion was recorded. Different buffers altered the excursion of beads on identical DNA tethers. Buffer with only 10 mM NaCl and >5 mM magnesium greatly reduced excursion. Glycerol added to increase viscosity slowed confined diffusion of the tethered beads but did not change excursion. The confined-diffusion coefficients for all tethered beads were smaller than those expected for freely diffusing beads and decreased for shorter tethers. Tethered-particle motion is a sensitive framework for diffusion experiments in which small beads on long leashes most closely resemble freely diffusing, untethered beads.

Multiple LacI-mediated loops revealed by Bayesian statistics and tethered particle motion

The bacterial transcription factor LacI loops DNA by binding to two separate locations on the DNA simultaneously. Despite being one of the best-studied model systems for transcriptional regulation, the number and conformations of loop structures accessible to LacI remain unclear, though the importance of multiple coexisting loops has been implicated in interactions between LacI and other cellular regulators of gene expression. To probe this issue, we have developed a new analysis method for tethered particle motion, a versatile and commonly used in vitro single-molecule technique. Our method, vbTPM, performs variational Bayesian inference in hidden Markov models. It learns the number of distinct states (i.e. DNA–protein conformations) directly from tethered particle motion data with better resolution than existing methods, while easily correcting for common experimental artifacts. Studying short (roughly 100 bp) LacI-mediated loops, we provide evidence for three distinct loop structures, more than previously reported in single-molecule studies. Moreover, our results confirm that changes in LacI conformation and DNA-binding topology both contribute to the repertoire of LacI-mediated loops formed in vitro, and provide qualitatively new input for models of looping and transcriptional regulation. We expect vbTPM to be broadly useful for probing complex protein–nucleic acid interactions.

Lac repressor mediated DNA looping: Monte Carlo simulation of constrained DNA molecules complemented with current experimental results

Tethered particle motion (TPM) experiments can be used to detect time-resolved loop formation in a single DNA molecule by measuring changes in the length of a DNA tether. Interpretation of such experiments is greatly aided by computer simulations of DNA looping which allow one to analyze the structure of the looped DNA and estimate DNA-protein binding constants specific for the loop formation process. We here present a new Monte Carlo scheme for accurate simulation of DNA configurations subject to geometric constraints and apply this method to Lac repressor mediated DNA looping, comparing the simulation results with new experimental data obtained by the TPM technique. Our simulations, taking into account the details of attachment of DNA ends and fluctuations of the looped subsegment of the DNA, reveal the origin of the double-peaked distribution of RMS values observed by TPM experiments by showing that the average RMS value for anti-parallel loop types is smaller than that of parallel loop types. The simulations also reveal that the looping probabilities for the anti-parallel loop types are significantly higher than those of the parallel loop types, even for loops of length 600 and 900 base pairs, and that the correct proportion between the heights of the peaks in the distribution can only be attained when loops with flexible Lac repressor conformation are taken into account. Comparison of the in silico and in vitro results yields estimates for the dissociation constants characterizing the binding affinity between O1 and Oid DNA operators and the dimeric arms of the Lac repressor.

Optical Methods to Study Protein-DNA Interactions in Vitro and in Living Cells at the Single-Molecule Level

The maintenance of intact genetic information, as well as the deployment of transcription for specific sets of genes, critically rely on a family of proteins interacting with DNA and recognizing specific sequences or features. The mechanisms by which these proteins search for target DNA are the subject of intense investigations employing a variety of methods in biology. A large interest in these processes stems from the faster-than-diffusion association rates, explained in current models by a combination of 3D and 1D diffusion. Here, we present a review of the single-molecule approaches at the forefront of the study of protein-DNA interaction dynamics and target search in vitro and in vivo. Flow stretch, optical and magnetic manipulation, single fluorophore detection and localization as well as combinations of different methods are described and the results obtained with these techniques are discussed in the framework of the current facilitated diffusion model.

Interplay of protein and DNA structure revealed in simulations of the lac operon

The E. coli Lac repressor is the classic textbook example of a protein that attaches to widely spaced sites along a genome and forces the intervening DNA into a loop. The short loops implicated in the regulation of the lac operon suggest the involvement of factors other than DNA and repressor in gene control. The molecular simulations presented here examine two likely structural contributions to the in-vivo looping of bacterial DNA: the distortions of the double helix introduced upon association of the highly abundant, nonspecific nucleoid protein HU and the large-scale deformations of the repressor detected in low-resolution experiments. The computations take account of the three-dimensional arrangements of nucleotides and amino acids found in crystal structures of DNA with the two proteins, the natural rest state and deformational properties of protein-free DNA, and the constraints on looping imposed by the conformation of the repressor and the orientation of bound DNA. The predicted looping propensities capture the complex, chain-length-dependent variation in repression efficacy extracted from gene expression studies and in vitro experiments and reveal unexpected chain-length-dependent variations in the uptake of HU, the deformation of repressor, and the folding of DNA. Both the opening of repressor and the presence of HU, at levels approximating those found in vivo, enhance the probability of loop formation. HU affects the global organization of the repressor and the opening of repressor influences the levels of HU binding to DNA. The length of the loop determines whether the DNA adopts antiparallel or parallel orientations on the repressor, whether the repressor is opened or closed, and how many HU molecules bind to the loop. The collective behavior of proteins and DNA is greater than the sum of the parts and hints of ways in which multiple proteins may coordinate the packaging and processing of genetic information.

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.

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.

Real-time single-molecule tethered particle motion experiments reveal the kinetics and mechanisms of Cre-mediated site-specific recombination

Tyrosine family recombinases (YRs) are widely utilized in genome engineering systems because they can easily direct DNA rearrangement. Cre recombinases, one of the most commonly used types of YRs, catalyze site-specific recombination between two loxP sites without the need for high-energy cofactors, other accessory proteins or a specific DNA target sequence between the loxP sites. Previous structural, analytical ultracentrifuge and electrophoretic analyses have provided details of the reaction kinetics and mechanisms of Cre recombinase activity; whether there are reaction intermediates or side pathways involved has been left unaddressed. Using tethered particle motion (TPM), the Cre-mediated site-specific recombination process has been delineated, from beginning to end, at the single-molecule level, including the formation of abortive complexes and wayward complexes blocking inactive nucleoprotein complexes from entering the recombination process. Reversibility in the strand-cleavage/-ligation process and the formation of a thermally stable Holliday junction intermediate were observed within the Cre-mediated site-specific recombination process. Rate constants for each elementary step, which explain the overall reaction outcomes under various conditions, were determined. Taking the findings of this study together, they demonstrate the potential of single-molecule methodology as an alternative approach for exploring reaction mechanisms in detail.

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.

DNA modeling reveals an extended lac repressor conformation in classic in vitro binding assays

Protein-mediated DNA looping, such as that induced by the lactose repressor (LacI) of Escherichia coli, is a well-known gene regulation mechanism. Although researchers have given considerable attention to DNA looping by LacI, many unanswered questions about this mechanism, including the role of protein flexibility, remain. Recent single-molecule observations suggest that the two DNA-binding domains of LacI are capable of splaying open about the tetramerization domain into an extended conformation. We hypothesized that if recent experiments were able to reveal the extended conformation, it is possible that such structures occurred in previous studies as well. In this study, we tested our hypothesis by reevaluating two classic in vitro binding assays using a computational rod model of DNA. The experiments and computations evaluate the looping of both linear DNA and supercoiled DNA minicircles over a broad range of DNA interoperator lengths. The computed energetic minima align well with the experimentally observed interoperator length for optimal loop stability. Of equal importance, the model reveals that the most stable loops for linear DNA occur when LacI adopts the extended conformation. In contrast, for DNA minicircles, optimal stability may arise from either the closed or the extended protein conformation depending on the degree of supercoiling and the interoperator length.

Effect of promoter architecture on the cell-to-cell variability in gene expression

According to recent experimental evidence, promoter architecture, defined by the number, strength and regulatory role of the operators that control transcription, plays a major role in determining the level of cell-to-cell variability in gene expression. These quantitative experiments call for a corresponding modeling effort that addresses the question of how changes in promoter architecture affect variability in gene expression in a systematic rather than case-by-case fashion. In this article we make such a systematic investigation, based on a microscopic model of gene regulation that incorporates stochastic effects. In particular, we show how operator strength and operator multiplicity affect this variability. We examine different modes of transcription factor binding to complex promoters (cooperative, independent, simultaneous) and how each of these affects the level of variability in transcriptional output from cell-to-cell. We propose that direct comparison between in vivo single-cell experiments and theoretical predictions for the moments of the probability distribution of mRNA number per cell can be used to test kinetic models of gene regulation. The emphasis of the discussion is on prokaryotic gene regulation, but our analysis can be extended to eukaryotic cells as well.

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.

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.

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.

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.

Single-molecule DNA analysis

The ability to detect single molecules of DNA or RNA has led to an extremely rich area of exploration of the single most important biomolecule in nature. In cases in which the nucleic acid molecules are tethered to a solid support, confined to a channel, or simply allowed to diffuse into a detection volume, novel techniques have been developed to manipulate the DNA and to examine properties such as structural dynamics and protein-DNA interactions. Beyond the analysis of the properties of nucleic acids themselves, single-molecule detection has enabled dramatic improvements in the throughput of DNA sequencing and holds promise for continuing progress. Both optical and nonoptical detection methods that use surfaces, nanopores, and zero-mode waveguides have been attempted, and one optically based instrument is already commercially available. The breadth of literature related to single-molecule DNA analysis is vast; this review focuses on a survey of efforts in molecular dynamics and nucleic acid sequencing.

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.

Illustrating the steady-state condition and the single-molecule kinetic method with the NMDA receptor

The steady-state is a fundamental aspect of biochemical pathways in cells; indeed, the concept of steady-state is a definition of life itself. In a simple enzyme kinetic scheme, the steady-state condition is easy to define analytically but experimentally often difficult to capture because of its evanescent quality; the initial, constant velocity condition that signifies the steady-state of the E(f) and ES system is often short-lived. The recording of electrophysiologic events through a receptor channel is used here to illustrate the steady-state and to introduce the single-molecule approach to the quantification of biologic kinetic schemes. This article first briefly reviews the Michaelis-Menten and Briggs-Haldane formulations for the simple enzyme kinetic scheme. The salient structural features of the NMDA (N-methyl-D-aspartic acid) receptor are introduced as is the single NMDA molecule patch-clamp method; this is a high-resolution method for recording charge (ion) transfer through this and other ionotropic (ion-conducting) receptors. The concept of a time constant is related directly to a rate constant in showing that durations of channel opening and closing directly provide values for the rate constants that link the various conformation states adopted by the receptor when it is at a steady state. These rate constants provide the basis for illustrating the energy relationships between the multiple protein conformation states that the receptor populates during steady-state ion conduction across the cell membrane. The article emphasizes the advantages of collecting the mean behavior of a single molecule over time in comparison to the mean behavior of a large collection of independent molecules at a single time point.

Synthesis and surface modification of birefringent vaterite microspheres

This paper reports on the synthesis of birefringent vaterite microspheres with narrow size distribution using a seeded growth method. In a post-treatment the microspheres were stabilized and functionalized through coating with a combination of organosilica and silica. The coating vastly enhanced the stability of the vaterite microspheres in biological buffers and allowed the attachment of biomolecules such as DNA or proteins. As an example, streptavidin was attached to the surface of the functionalized microspheres. These results pave the way for the use of birefringent vaterite particles for the micromanipulation of single biological molecules such as DNA or specific proteins in an optical trap capable of exerting and measuring torques. The stabilized birefringent microspheres may also find use for biosensor and biological screening applications.

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.

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.

The persistence length of double stranded DNA determined using dark field tethered particle motion

The wormlike chain model describes the micromechanics of semiflexible polymers by introducing the persistence length. We propose a method of measuring the persistence length of DNA in a controllable near-native environment. Using a dark field microscope, the projected positions of a gold nanoparticle undergoing constrained Brownian motion are captured. The nanoparticle is tethered to a substrate using a single double stranded DNA (dsDNA) molecule and immersed in buffer. No force is exerted on the DNA. We carried out Monte Carlo simulations of the experiment, which give insight into the micromechanics of the DNA and can be used to interpret the motion of the nanoparticle. Our simulations and experiments demonstrate that, unlike other similar experiments, the use of nanometer instead of micrometer sized particles causes particle-substrate and particle-DNA interactions to be of negligible effect on the position distribution of the particle. We also show that the persistence length of the tethering DNA can be estimated with a statistical error of 2 nm, by comparing the statistics of the projected position distribution of the nanoparticle to the Monte Carlo simulations. The persistence lengths of 45 single molecules of four different lengths of dsDNA were measured under the same environmental conditions at high salt concentration. The persistence lengths we found had a mean value of 35 nm (standard error of 2.8 nm), which compares well to previously found values using similar salt concentrations. Our method can be used to directly study the effect of the environmental conditions (e.g., buffer and temperature) on the persistence length.

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.