Multiple-bond kinetics from single-molecule pulling experiments: evidence for multiple NCAM bonds

The kinetic parameters of single bonds between neural cell adhesion molecules were determined from atomic force microscope measurements of the forced dissociation of the homophilic protein-protein bonds. The analytical approach described provides a systematic procedure for obtaining rupture kinetics for single protein bonds from bond breakage frequency distributions obtained from single-molecule pulling experiments. For these studies, we used the neural cell adhesion molecule (NCAM), which was recently shown to form two independent protein bonds. The analysis of the bond rupture data at different loading rates, using the single-bond full microscopic model, indicates that the breakage frequency distribution is most sensitive to the distance to the transition state and least sensitive to the molecular spring constant. The analysis of bond failure data, however, motivates the use of a double-bond microscopic model that requires an additional kinetic parameter. This double-bond microscopic model assumes two independent NCAM-NCAM bonds, and more accurately describes the breakage frequency distribution, particularly at high loading rates. This finding agrees with recent surface-force measurements, which showed that NCAM forms two spatially distinct bonds between opposed proteins.     

Models for recovering the energy landscape of conformational transitions from single-molecule pulling experiments

Single-molecule force spectroscopy is a powerful experimental technique for probing intermolecular forces and conformational transitions of individual molecules. This technique involves measuring the mechanical response of a molecule subjected to a constant or time-varying force. Statistical mechanics has played a pivotal role in interpreting force measurements in terms of the underlying kinetics and energy landscape of the molecular transition being studied. Here, we provide a didactic review of various statistical–mechanical models used for analysing these measurements, emphasising the theoretical ideas and assumptions used in deriving these models.     

Single-molecule pulling experiments: when the stiffness of the pulling device matters

Using Langevin modeling, we investigate the role of the experimental setup on the unbinding forces measured in single-molecule pulling experiments. We demonstrate that the stiffness of the pulling device, K_eff, may influence the unbinding forces through its effect on the barrier heights for both unbinding and rebinding processes. Under realistic conditions the effect of K_eff on the rebinding barrier is shown to play the most important role. This results in a significant increase of the mean unbinding force with the stiffness for a given loading rate. Thus, in contrast to the phenomenological Bell model, we find that the loading rate (the multiplicative value K_effV, V being the pulling velocity) is not the only control parameter that determines the mean unbinding force. If interested in intrinsic properties of a molecular system, we recommend probing the system in the parameter range corresponding to a weak spring and relatively high loading rates where rebinding is negligible.     

Thermodynamic and kinetic aspects of RNA pulling experiments

Recent single-molecule pulling experiments have shown how it is possible to manipulate RNA molecules using laser tweezers. In this article we investigate a minimal model for the experimental setup which includes an RNA molecule connected to two polymers (handles) and a bead trapped in the optical potential and attached to one of the handles. We start by considering the case of small single-domain RNA molecules, which unfold in a cooperative way. The model qualitatively reproduces the experimental results and allows us to investigate the influence of the bead and handles on the unfolding reaction. A main ingredient of the model is to consider the appropriate statistical ensemble and the corresponding thermodynamic potential describing thermal fluctuations in the system. We then investigate several questions relevant to extract thermodynamic information from experimental data. The kinetics of unfolding is also studied by introducing a dynamical model. Finally, we apply the model to the more general problem of a multidomain RNA molecule with Mg(2+) tertiary contacts that unfolds in a sequential way.     

Loop extrusion: theory meets single-molecule experiments

Chromosomes are organized as chromatin loops that promote segregation, enhancer-promoter interactions, and other genomic functions. Loops were hypothesized to form by ‘loop extrusion,’ by which structural maintenance of chromosomes (SMC) complexes, such as condensin and cohesin, bind to chromatin, reel it in, and extrude it as a loop. However, such exotic motor activity had never been observed. Following an explosion of indirect evidence, recent single-molecule experiments directly imaged DNA loop extrusion by condensin and cohesin in vitro. These experiments observe rapid (kb/s) extrusion that requires ATP hydrolysis and stalls under pN forces. Surprisingly, condensin extrudes loops asymmetrically, challenging previous models. Extrusion by cohesin is symmetric but requires the protein Nipbl. We discuss how SMC complexes may perform their functions on chromatin in vivo.     

Temperature softening of a protein in single-molecule experiments

Mechanical flexibility is crucial for the function of proteins. However, such material properties are not easily accessible experimentally. We used single-molecule force spectroscopy to study the stiffness of a single domain of Dictyostelium discoideum filamin (ddFLN4) in a temperature range from 5 degrees C to 37 degrees C. Analyzing the distributions of unfolding forces allowed us to extract transition barrier heights and positions of the underlying energy landscape. We found a marked narrowing of unfolding force distributions with increasing temperature. This narrowing reflects an increase in transition state position from 2.7 A to 7.8 A and thus a reduction of the molecular spring constant of the protein by a factor of 7. We suggest this temperature softening reflects a shift in the nature of the interactions responsible for mechanical stability from hydrogen bonds to hydrophobic interactions. This result has important consequences for all interpretations of protein mechanical studies if experimental results obtained at room temperature are to be transferred to physiological temperatures.     

Evaluation of pyrimidine PNA binding to ssDNA targets from nonequilibrium melting experiments.

Slow kinetics of homopyrimidine PNA binding to single stranded DNA and RNA targets is manifested in significant hysteresis in thermal UV absorption experiments. We have compared temperatures of dissociation (Tdis) and reassociation (Tass) for triplexes formed by DNA and single or bis PNAs with K50 derived from gel mobility experiments. Results indicated there was no correlation between Tdis and K50 while reasonable correlation between Tass and K50 was found. This correlation enabled use of easy thermal UV absorption experiments for evaluation of PNA binding to DNA/RNA targets.     

DNA origami as biocompatible surface to match single-molecule and ensemble experiments

Single-molecule experiments on immobilized molecules allow unique insights into the dynamics of molecular machines and enzymes as well as their interactions. The immobilization, however, can invoke perturbation to the activity of biomolecules causing incongruities between single molecule and ensemble measurements. Here we introduce the recently developed DNA origami as a platform to transfer ensemble assays to the immobilized single molecule level without changing the nano-environment of the biomolecules. The idea is a stepwise transfer of common functional assays first to the surface of a DNA origami, which can be checked at the ensemble level, and then to the microscope glass slide for single-molecule inquiry using the DNA origami as a transfer platform. We studied the structural flexibility of a DNA Holliday junction and the TATA-binding protein (TBP)-induced bending of DNA both on freely diffusing molecules and attached to the origami structure by fluorescence resonance energy transfer. This resulted in highly congruent data sets demonstrating that the DNA origami does not influence the functionality of the biomolecule. Single-molecule data collected from surface-immobilized biomolecule-loaded DNA origami are in very good agreement with data from solution measurements supporting the fact that the DNA origami can be used as biocompatible surface in many fluorescence-based measurements.     

Direct observation of chemo-mechanical coupling in DnaK by single-molecule force experiments

Protein allostery requires a communication channel for functional regulation between distal sites within a protein. In the molecular chaperone Hsp70, a two-domain enzyme, the ATP/ADP status of an N-terminal nucleotide-binding domain regulates the substrate affinity of a C-terminal substrate-binding domain. Recently available three-dimensional structures of Hsp70 in ATP/ADP states have provided deep insights into molecular pathways of allosteric signals. However, direct mechanical probing of long-range allosteric coupling between the ATP hydrolysis step and domain states is missing. Using laser optical tweezers, we examined the mechanical properties of a truncated two-domain DnaK(1–552ye) in apo/ADP/ATP- and peptide-bound states. We find that in the apo and ADP states, DnaK domains are mechanically stable and rigid. However, in the ATP state, substrate-binding domain (SBD)¹ye is mechanically destabilized as the result of interdomain docking followed by the unfolding of the α-helical lid. By observing the folding state of the SBD, we could observe the continuous ATP/ADP cycling of the enzyme in real time with a single molecule. The SBD lid closure is strictly coupled to the chemical steps of the ATP hydrolysis cycle even in the presence of peptide substrate.     

Identifying molecular dynamics in single-molecule FRET experiments with burst variance analysis

Histograms of single-molecule Förster resonance energy transfer (FRET) efficiency are often used to study the structures of biomolecules and relate these structures to function. Methods like probability distribution analysis analyze FRET histograms to detect heterogeneities in molecular structure, but they cannot determine whether this heterogeneity arises from dynamic processes or from the coexistence of several static structures. To this end, we introduce burst variance analysis (BVA), a method that detects dynamics by comparing the standard deviation of FRET from individual molecules over time to that expected from theory. Both simulations and experiments on DNA hairpins show that BVA can distinguish between static and dynamic sources of heterogeneity in single-molecule FRET histograms and can test models of dynamics against the observed standard deviation information. Using BVA, we analyzed the fingers-closing transition in the Klenow fragment of Escherichia coli DNA polymerase I and identified substantial dynamics in polymerase complexes formed prior to nucleotide incorporation; these dynamics may be important for the fidelity of DNA synthesis. We expect BVA to be broadly applicable to single-molecule FRET studies of molecular structure and to complement approaches such as probability distribution analysis and fluorescence correlation spectroscopy in studying molecular dynamics.     

Direct measurement of single-molecule visco-elasticity in atomic force microscope force-extension experiments

Measuring the visco-elastic properties of biological macromolecules constitutes an important step towards the understanding of dynamic biological processes, such as cell adhesion, muscle function, or plant cell wall stability. Force spectroscopy techniques based on the atomic force microscope (AFM) are increasingly used to study the complex visco-elastic response of (bio-)molecules on a single-molecule level. These experiments either require that the AFM cantilever is actively oscillated or that the molecule is clamped at constant force to monitor thermal cantilever motion. Here we demonstrate that the visco-elasticity of single bio-molecules can readily be extracted from the Brownian cantilever motion during conventional force-extension measurements. It is shown that the characteristics of the cantilever determine the signal-to-noise (S/N) ratio and time resolution. Using a small cantilever, the visco-elastic properties of single dextran molecules were resolved with a time resolution of 8.3 ms. The presented approach can be directly applied to probe the dynamic response of complex bio-molecular systems or proteins in force-extension experiments. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Bound2Learn: a machine learning approach for classification of DNA-bound proteins from single-molecule tracking experiments

DNA-bound proteins are essential elements for the maintenance, regulation, and use of the genome. The time they spend bound to DNA provides useful information on their stability within protein complexes and insight into the understanding of biological processes. Single-particle tracking allows for direct visualization of protein–DNA kinetics, however, identifying whether a molecule is bound to DNA can be non-trivial. Further complications arise when tracking molecules for extended durations in processes with slow kinetics. We developed a machine learning approach, termed Bound2Learn, using output from a widely used tracking software, to robustly classify tracks in order to accurately estimate residence times. We validated our approach in silico, and in live-cell data from Escherichia coli and Saccharomyces cerevisiae. Our method has the potential for broad utility and is applicable to other organisms.     

Theoretical analysis of single-molecule force spectroscopy experiments: heterogeneity of chemical bonds

We show that the standard theoretical framework in single-molecule force spectroscopy has to be extended to consistently describe the experimental findings. The basic amendment is to take into account heterogeneity of the chemical bonds via random variations of the force-dependent dissociation rates. This results in a very good agreement between theory and rupture data from several different experiments.     

Disentangling subpopulations in single-molecule FRET and ALEX experiments with photon distribution analysis

Among the advantages of the single-molecule approach when used to study biomolecular structural dynamics and interaction is its ability to distinguish between and independently observe minor subpopulations. In a single-molecule Förster resonance energy transfer (FRET) and alternating laser excitation diffusion experiment, the various populations are apparent in the resultant histograms. However, because histograms are calculated based on the per-burst mean FRET and stoichiometry ratio and not on the internal photon distribution, much of the acquired information is lost, thereby reducing the capabilities of the method. Here we suggest what to our knowledge is a novel statistical analysis tool that significantly enhances these capabilities, and we use it to identify and isolate static and dynamic subpopulations. Based on a kernel density estimator and a proper photon distribution analysis, for each individual burst, we calculate scores that reflect properties of interest. Specifically, we determine the FRET efficiency and brightness ratio distributions and use them to reveal 1), the underlying structure of a two-state DNA-hairpin and a DNA hairpin that is bound to DNA origami; 2), a minor doubly labeled dsDNA subpopulation concealed in a larger singly labeled dsDNA; and 3), functioning DNA origami motors concealed within a larger subpopulation of defective motors. Altogether, these findings demonstrate the usefulness of the proposed approach. The method was developed and tested using simulations, its rationality is described, and a computer algorithm is provided.     

The folding pathway of a fast-folding immunoglobulin domain revealed by single-molecule mechanical experiments

The F-actin crosslinker filamin from Dictyostelium discoideum (ddFLN) has a rod domain consisting of six structurally similar immunoglobulin domains. When subjected to a stretching force, domain 4 unfolds at a lower force than all the other domains in the chain. Moreover, this domain shows a stable intermediate along its mechanical unfolding pathway. We have developed a mechanical single-molecule analogue to a double-jump stopped-flow experiment to investigate the folding kinetics and pathway of this domain. We show that an obligatory and productive intermediate also occurs on the folding pathway of the domain. Identical mechanical properties suggest that the unfolding and refolding intermediates are closely related. The folding process can be divided into two consecutive steps: in the first step 60 C-terminal amino acids form an intermediate at the rate of 55 s(-1); and in the second step the remaining 40 amino acids are packed on this core at the rate of 179 s(-1). This division increases the overall folding rate of this domain by a factor of ten compared with all other homologous domains of ddFLN that lack the folding intermediate.