Multiple LacI-mediated loops revealed by Bayesian statistics and 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.

Detecting DNA Loops Using Tethered Particle Motion

The range of motion of a micron-sized bead tethered by a single polymer provides a dynamic readout of the effective length of the polymer. The excursions of the bead may reflect the intrinsic flexibility and/or topology of the polymer as well as changes due to the action activity of ligands that bind the polymer. This is a simple yet powerful experimental approach to investigate such interactions between DNA and proteins as demonstrated by experiments with the lac repressor. This protein forms a stable, tetrameric oligomer with two binding sites and can produce a loop of DNA between recognition sites separated along the length of a DNA molecule.

Single-Molecule Sandwich Aptasensing on Nanoarrays by Tethered Particle Motion Analysis

High-throughput single-molecule techniques are expected to challenge the demand for rapid, simple, and sensitive detection methods in health and environmental fields. Based on a single-DNA-molecule biochip for the parallelization of tethered particle motion analyses by videomicroscopy coupled to image analysis and its smart combination with aptamers, we successfully developed an aptasensor enabling the detection of single target molecules by a sandwich assay. One aptamer is grafted to the nanoparticles tethered to the surface by a long DNA molecule bearing the second aptamer in its middle. The detection and quantification of the target are direct. The recognition of the target by a pair of aptamers leads to a looped configuration of the DNA-particle complex associated with a restricted motion of the particles, which is monitored in real time. An analytical range extending over 3 orders of magnitude of target concentration with a limit of detection in the picomolar range was obtained for thrombin.

Bayesian Inference: The Comprehensive Approach to Analyzing Single-Molecule Experiments

Biophysics experiments performed at single-molecule resolution provide exceptional insight into the structural details and dynamic behavior of biological systems. However, extracting this information from the corresponding experimental data unequivocally requires applying a biophysical model. In this review, we discuss how to use probability theory to apply these models to single-molecule data. Many current single-molecule data analysis methods apply parts of probability theory, sometimes unknowingly, and thus miss out on the full set of benefits provided by this self-consistent framework. The full application of probability theory involves a process called Bayesian inference that fully accounts for the uncertainties inherent to single-molecule experiments. Additionally, using Bayesian inference provides a scientifically rigorous method of incorporating information from multiple experiments into a single analysis and finding the best biophysical model for an experiment without the risk of overfitting the data. These benefits make the Bayesian approach ideal for analyzing any type of single-molecule experiment.

LPS-binding IgG arrests actively motile Salmonella Typhimurium in gastrointestinal mucus

The gastrointestinal (GI) mucosa is coated with a continuously secreted mucus layer that serves as the first line of defense against invading enteric bacteria. We have previously shown that antigen-specific immunoglobulin G (IgG) can immobilize viruses in both human airway and genital mucus secretions through multiple low-affinity bonds between the array of virion-bound IgG and mucins, thereby facilitating their rapid elimination from mucosal surfaces and preventing mucosal transmission. Nevertheless, it remains unclear whether weak IgG-mucin crosslinks could reinforce the mucus barrier against the permeation of bacteria driven by active flagella beating, or in predominantly MUC2 mucus gel. Here, we performed high-resolution multiple particle tracking to capture the real-time motion of hundreds of individual fluorescent Salmonella Typhimurium in fresh, undiluted GI mucus from Rag1^-/- mice, and analyzed the motion using a hidden Markov model framework. In contrast to control IgG, the addition of anti-lipopolysaccharide IgG to GI mucus markedly reduced the progressive motility of Salmonella by lowering the swim speed and retaining individual bacteria in an undirected motion state. Effective crosslinking of Salmonella to mucins was dependent on Fc N-glycans. Our findings implicate IgG-mucin crosslinking as a broadly conserved function that reduces mucous penetration of both bacterial and viral pathogens.

Sequence-dependent dynamics of synthetic and endogenous RSSs in V(D)J recombination

Developing lymphocytes of jawed vertebrates cleave and combine distinct gene segments to assemble antigen-receptor genes. This process called V(D)J recombination that involves the RAG recombinase binding and cutting recombination signal sequences (RSSs) composed of conserved heptamer and nonamer sequences flanking less well-conserved 12- or 23-bp spacers. Little quantitative information is known about the contributions of individual RSS positions over the course of the RAG-RSS interaction. We employ a single-molecule method known as tethered particle motion to track the formation, lifetime and cleavage of individual RAG-12RSS-23RSS paired complexes (PCs) for numerous synthetic and endogenous 12RSSs. We reveal that single-bp changes, including in the 12RSS spacer, can significantly and selectively alter PC formation or the probability of RAG-mediated cleavage in the PC. We find that some rarely used endogenous gene segments can be mapped directly to poor RAG binding on their adjacent 12RSSs. Finally, we find that while abrogating RSS nicking with Ca2+ leads to substantially shorter PC lifetimes, analysis of the complete lifetime distributions of any 12RSS even on this reduced system reveals that the process of exiting the PC involves unidentified molecular details whose involvement in RAG-RSS dynamics are crucial to quantitatively capture kinetics in V(D)J recombination.

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.

Parallelized DNA tethered bead measurements to scrutinize DNA mechanical structure

Tethering beads to DNA offers a panel of single molecule techniques for the refined analysis of the conformational dynamics of DNA and the elucidation of the mechanisms of enzyme activity. Recent developments include the massive parallelization of these techniques achieved by the fabrication of dedicated nanoarrays by soft nanolithography. We focus here on two of these techniques: the Tethered Particle motion and Magnetic Tweezers allowing analysis of the behavior of individual DNA molecules in the absence of force and under the application of a force and/or a torque, respectively. We introduce the experimental protocols for the parallelization and discuss the benefits already gained, and to come, for these single molecule investigations.

Modeling Barrier Properties of Intestinal Mucus Reinforced with IgG and Secretory IgA against Motile Bacteria

The gastrointestinal (GI) tract is lined with a layer of viscoelastic mucus gel, characterized by a dense network of entangled and cross-linked mucins together with an abundance of antibodies (Ab). Secretory IgA (sIgA), the predominant Ab isotype in the GI tract, is a dimeric molecule with 4 antigen-binding domains capable of inducing efficient clumping of bacteria, or agglutination. IgG, another common Ab at mucosal surfaces, can cross-link individual viruses to the mucin mesh through multiple weak bonds between IgG-Fc and mucins, a process termed muco-trapping. Relative contributions by agglutination versus muco-trapping in blocking permeation of motile bacteria through mucus remain poorly understood. Here, we developed a mathematical model that takes into account physiologically relevant spatial dimensions and time scales, binding and unbinding rates between Ab and bacteria as well as between Ab and mucins, the diffusivities of Ab, and run-tumble motion of active bacteria. Our model predicts both sIgA and IgG can accumulate on the surface of individual bacteria at sufficient quantities and rates to enable trapping individual bacteria in mucins before they penetrate the mucus layer. Furthermore, our model predicts that agglutination only modestly improves the ability for antibodies to block bacteria permeation through mucus. These results suggest that while sIgA is the most potent Ab isotype overall at stopping bacterial penetration, IgG may represent a practical alternative for mucosal prophylaxis and therapy. Our work improves the mechanistic understanding of Ab-enhanced barrier properties of mucus and highlights the ability for muco-trapping Ab to protect against motile pathogens at mucosal surfaces.

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.

An automated Bayesian pipeline for rapid analysis of single-molecule binding data

Single-molecule binding assays enable the study of how molecular machines assemble and function. Current algorithms can identify and locate individual molecules, but require tedious manual validation of each spot. Moreover, no solution for high-throughput analysis of single-molecule binding data exists. Here, we describe an automated pipeline to analyze single-molecule data over a wide range of experimental conditions. In addition, our method enables state estimation on multivariate Gaussian signals. We validate our approach using simulated data, and benchmark the pipeline by measuring the binding properties of the well-studied, DNA-guided DNA endonuclease, TtAgo, an Argonaute protein from the Eubacterium Thermus thermophilus. We also use the pipeline to extend our understanding of TtAgo by measuring the protein’s binding kinetics at physiological temperatures and for target DNAs containing multiple, adjacent binding sites.

Analysis of single-molecule binding assays still requires substantial manual user intervention. Here, the authors present a pipeline for rapid, automated analysis of co-localization single-molecule spectroscopy images, with a modular user interface that can be adjusted to a range of experimental conditions.

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.

Variational Algorithms for Analyzing Noisy Multistate Diffusion Trajectories

Single-particle tracking offers a noninvasive high-resolution probe of biomolecular reactions inside living cells. However, efficient data analysis methods that correctly account for various noise sources are needed to realize the full quantitative potential of the method. We report algorithms for hidden Markov-based analysis of single-particle tracking data, which incorporate most sources of experimental noise, including heterogeneous localization errors and missing positions. Compared to previous implementations, the algorithms offer significant speedups, support for a wider range of inference methods, and a simple user interface. This will enable more advanced and exploratory quantitative analysis of single-particle tracking data.

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.

Tethered Particle Motion: An Easy Technique for Probing DNA Topology and Interactions with Transcription Factors

Tethered Particle Motion (TPM) is a versatile in vitro technique for monitoring the conformations a linear macromolecule, such as DNA, can exhibit. The technique involves monitoring the diffusive motion of a particle anchored to a fixed point via the macromolecule of interest, which acts as a tether. In this chapter, we provide an overview of TPM, review the fundamental principles that determine the accuracy with which effective tether lengths can be used to distinguish different tether conformations, present software tools that assist in capturing and analyzing TPM data, and provide a protocol which uses TPM to characterize lac repressor-induced DNA looping. Critical to any TPM assay is the understanding of the timescale over which the diffusive motion of the particle must be observed to accurately distinguish tether conformations. Approximating the tether as a Hookean spring, we show how to estimate the diffusion timescale and discuss how it relates to the confidence with which tether conformations can be distinguished. Applying those estimates to a lac repressor titration assay, we describe how to perform a TPM experiment. We also provide graphically driven software which can be used to speed up data collection and analysis. Lastly, we detail how TPM data from the titration assay can be used to calculate relevant molecular descriptors such as the J factor for DNA looping and lac repressor-operator dissociation constants. While the included protocol is geared toward studying DNA looping, the technique, fundamental principles, and analytical methods are more general and can be adapted to a wide variety of molecular systems.

Proteins mediating DNA loops effectively block transcription

Loops are ubiquitous topological elements formed when proteins simultaneously bind to two noncontiguous DNA sites. While a loop‐mediating protein may regulate initiation at a promoter, the presence of the protein at the other site may be an obstacle for RNA polymerases (RNAP) transcribing a different gene. To test whether a DNA loop alters the extent to which a protein blocks transcription, the lac repressor (LacI) was used. The outcome of in vitro transcription along templates containing two LacI operators separated by 400 bp in the presence of LacI concentrations that produced both looped and unlooped molecules was visualized with scanning force microscopy (SFM). An analysis of transcription elongation complexes, moving for 60 s at an average of 10 nt/s on unlooped DNA templates, revealed that they more often surpassed LacI bound to the lower affinity O2 operator than to the highest affinity Os operator. However, this difference was abrogated in looped DNA molecules where LacI became a strong roadblock independently of the affinity of the operator. Recordings of transcription elongation complexes, using magnetic tweezers, confirmed that they halted for several minutes upon encountering a LacI bound to a single operator. The average pause lifetime is compatible with RNAP waiting for LacI dissociation, however, the LacI open conformation visualized in the SFM images also suggests that LacI could straddle RNAP to let it pass. Independently of the mechanism by which RNAP bypasses the LacI roadblock, the data indicate that an obstacle with looped topology more effectively interferes with transcription.

Decoding Single Molecule Time Traces with Dynamic Disorder

Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm—Variational Bayes-double chain Markov model (VB-DCMM)—to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na⁺ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA.

We have developed a new algorithm to better decode single molecule data with dynamic disorder. Our new algorithm, which represents a substantial improvement over other methodologies, can detect the presence of dynamic disorder in each trajectory and quantify the kinetic characteristics of underlying energy landscape. As a model system, we applied our algorithm to the single molecule FRET time traces of H-DNA. While duplex-triplex transitions of H-DNA are conventionally interpreted in terms of two-state kinetics, slowly varying dynamic patterns corresponding to hidden internal states can also be identified from the individual time traces. Our algorithm reveals that at least 4 distinct internal states are required to correctly interpret the data.

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.

Empirical Bayes methods enable advanced population-level analyses of single-molecule FRET experiments

Many single-molecule experiments aim to characterize biomolecular processes in terms of kinetic models that specify the rates of transition between conformational states of the biomolecule. Estimation of these rates often requires analysis of a population of molecules, in which the conformational trajectory of each molecule is represented by a noisy, time-dependent signal trajectory. Although hidden Markov models (HMMs) may be used to infer the conformational trajectories of individual molecules, estimating a consensus kinetic model from the population of inferred conformational trajectories remains a statistically difficult task, as inferred parameters vary widely within a population. Here, we demonstrate how a recently developed empirical Bayesian method for HMMs can be extended to enable a more automated and statistically principled approach to two widely occurring tasks in the analysis of single-molecule fluorescence resonance energy transfer (smFRET) experiments: 1), the characterization of changes in rates across a series of experiments performed under variable conditions; and 2), the detection of degenerate states that exhibit the same FRET efficiency but differ in their rates of transition. We apply this newly developed methodology to two studies of the bacterial ribosome, each exemplary of one of these two analysis tasks. We conclude with a discussion of model-selection techniques for determination of the appropriate number of conformational states. The code used to perform this analysis and a basic graphical user interface front end are available as open source software.