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

Real-Time Detection of State Transitions in Stochastic Signals from Biological Systems

Robust analysis of signals from stochastic biomolecular processes is critical for understanding the dynamics of biological systems. Measured signals typically show multiple states with heterogeneities and a wide range of state lifetimes. Here, we present an algorithm for robust detection of state transitions in experimental time traces where the properties of the underlying states are a priori unknown. The method implements a maximum-likelihood approach to fit models in neighboring windows of data points. Multiple windows are combined to achieve a high sensitivity for state transitions with a wide range of lifetimes. The proposed maximum-likelihood multiple-windows change point detection (MM-CPD) algorithm is computationally extremely efficient and enables real-time signal analysis. By analyzing both simulated and experimental data, we demonstrate that the algorithm provides accurate change point detection in time traces with multiple heterogeneous states that are a priori unknown. A high sensitivity for a wide range of state lifetimes is achieved.

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.

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.

Refining particle positions using circular symmetry

Particle and object tracking is gaining attention in industrial applications and is commonly applied in: colloidal, biophysical, ecological, and micro-fluidic research. Reliable tracking information is heavily dependent on the system under study and algorithms that correctly determine particle position between images. However, in a real environmental context with the presence of noise including particular or dissolved matter in water, and low and fluctuating light conditions, many algorithms fail to obtain reliable information. We propose a new algorithm, the Circular Symmetry algorithm (C-Sym), for detecting the position of a circular particle with high accuracy and precision in noisy conditions. The algorithm takes advantage of the spatial symmetry of the particle allowing for subpixel accuracy. We compare the proposed algorithm with four different methods using both synthetic and experimental datasets. The results show that C-Sym is the most accurate and precise algorithm when tracking micro-particles in all tested conditions and it has the potential for use in applications including tracking biota in their environment.

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.

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.

Sequence Affects the Cyclization of DNA Minicircles

Understanding how the sequence of a DNA molecule affects its dynamic properties is a central problem affecting biochemistry and biotechnology. The process of cyclizing short DNA, as a critical step in molecular cloning, lacks a comprehensive picture of the kinetic process containing sequence information. We have elucidated this process by using coarse-grained simulations, enhanced sampling methods, and recent theoretical advances. We are able to identify the types and positions of structural defects during the looping process at a base-pair level. Correlations along a DNA molecule dictate critical sequence positions that can affect the looping rate. Structural defects change the bending elasticity of the DNA molecule from a harmonic to subharmonic potential with respect to bending angles. We explore the subelastic chain as a possible model in loop formation kinetics. A sequence-dependent model is developed to qualitatively predict the relative loop formation time as a function of DNA sequence.

DNA supercoiling: a regulatory signal for the λ repressor

Topoisomerases, polymerases, and the chirality introduced by the binding of histones or nucleoid-associated proteins affect DNA supercoiling in vivo. However, supercoiling is not just a by-product of DNA metabolism. Supercoiling is an indicator of cell health, it modifies the accessibility of chromatin, and coordinates the transcription of genes. This suggests that regulatory, protein-mediated loops in DNA may sense supercoiling of the genome in which they are embedded. The λ repressor (CI) maintains the quiescent (lysogenic) transcriptome of bacteriophage λ in infected Escherichia coli. CI-mediated looping prevents overexpression of the repressor protein to preserve sensitivity to conditions that trigger virulence (lysis). Experiments were performed to assess how well the CI-mediated DNA loop traps superhelicity and determine whether supercoiling enhances CI-mediated DNA looping. CI oligomers partitioned plasmids into topological domains and prevented the passage of supercoiling between them. Furthermore, in single DNA molecules stretched and twisted with magnetic tweezers, levels of superhelical density confined in CI-mediated DNA loops ranged from -15% or +11%. Finally, in DNA under tensions that may occur in vivo, supercoiling lowered the free energy of loop formation and was essential for DNA looping. Supercoiling-enhanced looping can influence the maintenance of lysogeny in the λ repressor system; it can encode sensitivity to the energy level of the cell and creates independent topological domains of distinct superhelical density.

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.

Single molecule analysis of DNA wrapping and looping by a circular 14mer wheel of the bacteriophage 186 CI repressor

The lytic-lysogenic decision in bacteriophage 186 is governed by the 186 CI repressor protein in a unique way. The 186 CI is proposed to form a wheel-like oligomer that can mediate either wrapped or looped nucleoprotein complexes to provide the cooperative and competitive interactions needed for regulation. Although consistent with structural, biochemical and gene expression data, many aspects of this model are based on inference. Here, we use atomic force microscopy (AFM) to reveal the various predicted wrapped and looped species, and new ones, for CI regulation of lytic and lysogenic transcription. Automated AFM analysis showed CI particles of the predicted dimensions on the DNA, with CI multimerization favoured by DNA binding. Measurement of the length of the wrapped DNA segments indicated that CI may move on the DNA, wrapping or releasing DNA on either side of the wheel. Tethered particle motion experiments were consistent with wrapping and looping of DNA by CI in solution, where in contrast to λ repressor, the looped species were exceptionally stable. The CI regulatory system provides an intriguing comparison with that of nucleosomes, which share the ability to wrap and release similar sized segments of DNA.

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.

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.

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.

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.