Refined procedure of evaluating experimental single-molecule force spectroscopy data

Gamma estimator of Jarzynski equality for recovering binding energies from noisy dynamic data sets

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions. The Jarzynski equality forms a theoretical basis in recovering the free energy difference between two states from exponentially averaged work performed to switch the states. In practice, the exponentially averaged work value is estimated as the mean of finite samples. Numerical simulations have shown that samples having thousands of measurements are not large enough for the mean to converge when the fluctuation of external work is above 4 k_BT, which is easily observable in biomolecular interactions. We report the first example of a statistical gamma work distribution applied to single molecule pulling experiments. The Gibbs free energy of surface adsorption can be accurately evaluated even for a small sample size. The values obtained are comparable to those derived from multi-parametric surface plasmon resonance measurements and molecular dynamics simulations.

Measuring interaction energies from experimentally measured single-molecular interactions is challenging. Here, the authors report a gamma work distribution applied to single molecule pulling events for estimating peptide absorption free energy.

Longer collagen fibers trigger multicellular streaming on soft substrates via enhanced forces and cell-cell cooperation

Grouped cells often leave large cell colonies in the form of narrow multicellular streams. However, it remains unknown how collective cell streaming exploits specific matrix properties, like stiffness and fiber length. It is also unclear how cellular forces, cell-cell adhesion and velocities are coordinated within streams. To independently tune stiffness and collagen fiber length, we developed new hydrogels and discovered invasion-like streaming of normal epithelial cells on soft substrates coated with long collagen fibers. Here, streams arise owing to a surge in cell velocities, forces, YAP activity and expression of mesenchymal marker proteins in regions of high-stress anisotropy. Coordinated velocities and symmetric distribution of tensile and compressive stresses support persistent stream growth. Stiff matrices diminish cell-cell adhesions, disrupt front-rear velocity coordination and do not promote sustained fiber-dependent streaming. Rac inhibition reduces cell elongation and cell-cell cooperation, resulting in a complete loss of streaming in all matrix conditions. Our results reveal a stiffness-modulated effect of collagen fiber length on collective cell streaming and unveil a biophysical mechanism of streaming governed by a delicate balance of enhanced forces, monolayer cohesion and cell-cell cooperation.This article has an associated First Person interview with the first authors of the paper.

Single-Molecule Force Spectroscopy: Experiments, Analysis, and Simulations

The mechanical properties of cells and of subcellular components are important to obtain a mechanistic molecular understanding of biological processes. The quantification of mechanical resistance of cells and biomolecules using biophysical methods matured thanks to the development of nanotechnologies such as optical and magnetic tweezers, the biomembrane force probe, and atomic force microscopy (AFM). The quantitative nature of force spectroscopy measurements has converted AFM into a valuable tool in biophysics. Force spectroscopy allows the determination of the forces required to unfold protein domains and to disrupt individual receptor/ligand bonds. Molecular simulations as a computational microscope allow investigation of similar biological processes with an atomistic detail. In this chapter, we first provide a step-by-step protocol of force spectroscopy experiments using AFM, including sample preparation, measurements, and analysis and interpretation of the resulting dynamic force spectrum in terms of available theories. Next, we present the background for molecular dynamics (MD) simulations focusing on steered molecular dynamics (SMD) and the importance of bridging computational tools with experimental techniques.

Bayesian Uncertainty Quantification for Bond Energies and Mobilities Using Path Integral Analysis

Dynamic single-molecule force spectroscopy is often used to distort bonds. The resulting responses, in the form of rupture forces, work applied, and trajectories of displacements, are used to reconstruct bond potentials. Such approaches often rely on simple parameterizations of one-dimensional bond potentials, assumptions on equilibrium starting states, and/or large amounts of trajectory data. Parametric approaches typically fail at inferring complicated bond potentials with multiple minima, while piecewise estimation may not guarantee smooth results with the appropriate behavior at large distances. Existing techniques, particularly those based on work theorems, also do not address spatial variations in the diffusivity that may arise from spatially inhomogeneous coupling to other degrees of freedom in the macromolecule. To address these challenges, we develop a comprehensive empirical Bayesian approach that incorporates data and regularization terms directly into a path integral. All experimental and statistical parameters in our method are estimated directly from the data. Upon testing our method on simulated data, our regularized approach requires less data and allows simultaneous inference of both complex bond potentials and diffusivity profiles. Crucially, we show that the accuracy of the reconstructed bond potential is sensitive to the spatially varying diffusivity and accurate reconstruction can be expected only when both are simultaneously inferred. Moreover, after providing a means for self-consistently choosing regularization parameters from data, we derive posterior probability distributions, allowing for uncertainty quantification.

Piezoelectric tuning fork biosensors for the quantitative measurement of biomolecular interactions

The quantitative measurement of biomolecular interactions is of great interest in molecular biology. Atomic force microscopy (AFM) has proved its capacity to act as a biosensor and determine the affinity between biomolecules of interest. Nevertheless, the detection scheme presents certain limitations when it comes to developing a compact biosensor. Recently, piezoelectric quartz tuning forks (QTFs) have been used as laser-free detection sensors for AFM. However, only a few studies along these lines have considered soft biological samples, and even fewer constitute quantified molecular recognition experiments. Here, we demonstrate the capacity of QTF probes to perform specific interaction measurements between biotin-streptavidin complexes in buffer solution. We propose in this paper a variant of dynamic force spectroscopy based on representing adhesion energies E (aJ) against pulling rates v (nm s(-1)). Our results are compared with conventional AFM measurements and show the great potential of these sensors in molecular interaction studies.

Haptotaxis is cell type specific and limited by substrate adhesiveness

Motile cells navigate through tissue by relying on tactile cues from gradients provided by extracellular matrix (ECM) such as ligand density or stiffness. Mesenchymal stem cells (MSCs) and fibroblasts encounter adhesive or 'haptotactic' gradients at the interface between healthy and fibrotic tissue as they migrate towards an injury site. Mimicking this phenomenon, we developed tunable RGD and collagen gradients in polyacrylamide hydrogels of physiologically relevant stiffness using density gradient multilayer polymerization (DGMP) to better understand how such ligand gradients regulate migratory behaviors. Independent of ligand composition and fiber deformation, haptotaxis was observed in mouse 3T3 fibroblasts. Human MSCs however, haptotaxed only when cell-substrate adhesion was indirectly reduced via addition of free soluble matrix ligand mimetic peptides. Under basal conditions, MSCs were more contractile than fibroblasts. However, the presence of soluble adhesive peptides reduced MSC-induced substrate deformations; increased contractility may contribute to limited migration, but modulating cytoskeletal assembly was ineffective at promoting MSC haptotaxis. When introduced to gradients of increased absolute ligand concentrations, 3T3s displayed increased contractility and no longer haptotaxed. These data suggest that haptotactic behaviors are limited by adhesion and that although both cell types may home to tissue to aid in repair, fibroblasts may be more responsive to ligand gradients than MSCs.

Interplay of matrix stiffness and protein tethering in stem cell differentiation

Stem cells regulate their fate by binding to, and contracting against, the extracellular matrix. Recently, it has been proposed that in addition to matrix stiffness and ligand type, the degree of coupling of fibrous protein to the surface of the underlying substrate, that is, tethering and matrix porosity, also regulates stem cell differentiation. By modulating substrate porosity without altering stiffness in polyacrylamide gels, we show that varying substrate porosity did not significantly change protein tethering, substrate deformations, or the osteogenic and adipogenic differentiation of human adipose-derived stromal cells and marrow-derived mesenchymal stromal cells. Varying protein-substrate linker density up to 50-fold changed tethering, but did not affect osteogenesis, adipogenesis, surface-protein unfolding or underlying substrate deformations. Differentiation was also unaffected by the absence of protein tethering. Our findings imply that the stiffness of planar matrices regulates stem cell differentiation independently of protein tethering and porosity.

Cooperation of binding sites at the hydrophilic domain of cell-surface sulfatase Sulf1 allows for dynamic interaction of the enzyme with its substrate heparan sulfate

BACKGROUND

Sulf1 is a cell-surface sulfatase removing internal 6-O-sulfate groups from heparan sulfate (HS) chains. Thereby it modulates the activity of HS-dependent growth factors. For HS interaction Sulf1 employs a unique hydrophilic domain (HD).

METHODS

Affinity-chromatography, AFM-single-molecule force spectroscopy (SMFS) and immunofluorescence on living cells were used to analyze specificity, kinetics and structural basis of this interaction.

RESULTS

Full-length Sulf1 interacts broadly with sulfated glycosaminoglycans (GAGs) showing, however, higher affinity toward HS and heparin than toward chondroitin sulfate or dermatan sulfate. Strong interaction depends on the presence of Sulf1-substrate groups, as Sulf1 bound significantly weaker to HS after enzymatic 6-O-desulfation by Sulf1 pretreatment, hence suggesting autoregulation of Sulf1/substrate association. In contrast, HD alone exhibited outstanding specificity toward HS and did not interact with chondroitin sulfate, dermatan sulfate or 6-O-desulfated HS. Dynamic SMFS revealed an off-rate of 0.04/s, i.e., ~500-fold higher than determined by surface plasmon resonance. SMFS allowed resolving the dynamics of single dissociation events in each force-distance curve. HD subdomain constructs revealed heparin interaction sites in the inner and C-terminal regions of HD.

CONCLUSIONS

Specific substrate binding of Sulf1 is mediated by HD and involves at least two separate HS-binding sites. Surface plasmon resonance KD-values reflect a high avidity resulting from multivalent HD/heparin interaction. While this ensures stable cell-surface HS association, the dynamic cooperation of binding sites at HD and also the catalytic domain enables processive action of Sulf1 along or across HS chains.

GENERAL SIGNIFICANCE

HD confers a novel and highly dynamic mode of protein interaction with HS.

Application of atomic force microscopy for characteristics of single intermolecular interactions

Atomic force microscopy (AFM) can be used to make measurements in vacuum, air, and water. The method is able to gather information about intermolecular interaction forces at the level of single molecules. This review encompasses experimental and theoretical data on the characterization of ligand-receptor interactions by AFM. The advantage of AFM in comparison with other methods developed for the characterization of single molecular interactions is its ability to estimate not only rupture forces, but also thermodynamic and kinetic parameters of the rupture of a complex. The specific features of force spectroscopy applied to ligand-receptor interactions are examined in this review from the stage of the modification of the substrate and the cantilever up to the processing and interpretation of the data. We show the specificities of the statistical analysis of the array of data based on the results of AFM measurements, and we discuss transformation of data into thermodynamic and kinetic parameters (kinetic dissociation constant, Gibbs free energy, enthalpy, and entropy). Particular attention is paid to the study of polyvalent interactions, where the definition of the constants is hampered due to the complex stoichiometry of the reactions.

Demonstration of specific binding of heparin to Plasmodium falciparum-infected vs. non-infected red blood cells by single-molecule force spectroscopy

Glycosaminoglycans (GAGs) play an important role in the sequestration of Plasmodium falciparum-infected red blood cells (pRBCs) in the microvascular endothelium of different tissues, as well as in the formation of small clusters (rosettes) between infected and non-infected red blood cells (RBCs). Both sequestration and rosetting have been recognized as characteristic events in severe malaria. Here we have used heparin and pRBCs infected by the 3D7 strain of P. falciparum as a model to study GAG-pRBC interactions. Fluorescence microscopy and fluorescence-assisted cell sorting assays have shown that exogenously added heparin has binding specificity for pRBCs (preferentially for those infected with late forms of the parasite) vs. RBCs. Heparin-pRBC adhesion has been probed by single-molecule force spectroscopy, obtaining an average binding force ranging between 28 and 46 pN depending on the loading rate. No significant binding of heparin to non-infected RBCs has been observed in control experiments. This work represents the first approach to quantitatively evaluate GAG-pRBC molecular interactions at the individual molecule level.

Long lifetime of hydrogen-bonded DNA basepairs by force spectroscopy

Electron-tunneling data suggest that a noncovalently-bonded complex of three molecules, two recognition molecules that present hydrogen-bond donor and acceptor sites via a carboxamide group, and a DNA base, remains bound for seconds. This is surprising, given that imino-proton exchange rates show that basepairs in a DNA double helix open on millisecond timescales. The long lifetime of the three-molecule complex was confirmed using force spectroscopy, but measurements on DNA basepairs are required to establish a comparison with the proton-exchange data. Here, we report on a dynamic force spectroscopy study of complexes between the bases adenine and thymine (A-T, two-hydrogen bonds) and 2-aminoadenine and thymine (2AA-T, three-hydrogen bonds). Bases were tethered to an AFM probe and mica substrate via long, covalently linked polymer tethers. Data for bond-survival probability versus force and the rupture-force distributions were well fitted by the Bell model. The resulting lifetime of the complexes at zero pulling force was ~2 s for two-hydrogen bonds (A-T) and ~4 s for three-hydrogen bonds (2AA-T). Thus, DNA basepairs in an AFM pulling experiment remain bonded for long times, even without the stabilizing influence of base-stacking in a double helix. This result suggests that the pathways for opening, and perhaps the open states themselves, are very different in the AFM and proton-exchange measurements.

Interaction of an anticancer peptide fragment of azurin with p53 and its isolated domains studied by atomic force spectroscopy

p28 is a 28-amino acid peptide fragment of the cupredoxin azurin derived from Pseudomonas aeruginosa that preferentially penetrates cancerous cells and arrests their proliferation in vitro and in vivo. Its antitumor activity reportedly arises from post-translational stabilization of the tumor suppressor p53 normally downregulated by the binding of several ubiquitin ligases. This would require p28 to specifically bind to p53 to inhibit specific ligases from initiating proteosome-mediated degradation. In this study, atomic force spectroscopy, a nanotechnological approach, was used to investigate the interaction of p28 with full-length p53 and its isolated domains at the single molecule level. Analysis of the unbinding forces and the dissociation rate constant suggest that p28 forms a stable complex with the DNA-binding domain of p53, inhibiting the binding of ubiquitin ligases other than Mdm2 to reduce proteasomal degradation of p53.

Functional characterization of a supramolecular affinity switch at the single molecule level

Surface-immobilized and switchable resorcin[4]arene receptor molecules were quantitatively investigated with atomic force microscopy (AFM) and AFM-single molecule force spectroscopy (AFM-SMFS). The upper rim of the supramolecular receptor cavities was modified with two photodimerizable anthracene moieties. The molecular constitution can be externally switched and controlled by exposure to ultraviolet (UV) light and heat. The topography as well as the complexation affinity against small ammonium guest ions of the two isomers were investigated at the single molecule level. Our results demonstrate the feasibility to externally control the supramolecular receptor's affinity and simultaneously quantify and associate these binding properties with the structural change of the resorcin[4]arenes structure on the basis of the measured molecule corrugation height.

Antibody-unfolding and metastable-state binding in force spectroscopy and recognition imaging

Force spectroscopy and recognition imaging are important techniques for characterizing and mapping molecular interactions. In both cases, an antibody is pulled away from its target in times that are much less than the normal residence time of the antibody on its target. The distribution of pulling lengths in force spectroscopy shows the development of additional peaks at high loading rates, indicating that part of the antibody frequently unfolds. This propensity to unfold is reversible, indicating that exposure to high loading rates induces a structural transition to a metastable state. Weakened interactions of the antibody in this metastable state could account for reduced specificity in recognition imaging where the loading rates are always high. The much weaker interaction between the partially unfolded antibody and target, while still specific (as shown by control experiments), results in unbinding on millisecond timescales, giving rise to rapid switching noise in the recognition images. At the lower loading rates used in force spectroscopy, we still find discrepancies between the binding kinetics determined by force spectroscopy and those determined by surface plasmon resonance-possibly a consequence of the short tethers used in recognition imaging. Recognition imaging is nonetheless a powerful tool for interpreting complex atomic force microscopy images, so long as specificity is calibrated in situ, and not inferred from equilibrium binding kinetics.

Single-molecule force spectroscopy of cartilage aggrecan self-adhesion

We investigated self-adhesion between highly negatively charged aggrecan macromolecules extracted from bovine cartilage extracellular matrix by performing atomic force microscopy (AFM) imaging and single-molecule force spectroscopy (SMFS) in saline solutions. By controlling the density of aggrecan molecules on both the gold substrate and the gold-coated tip surface at submonolayer densities, we were able to detect and quantify the Ca(2+)-dependent homodimeric interaction between individual aggrecan molecules at the single-molecule level. We found a typical nonlinear sawtooth profile in the AFM force-versus-distance curves with a molecular persistence length of l(p) = 0.31 ± 0.04 nm. This is attributed to the stepwise dissociation of individual glycosaminoglycan (GAG) side chains in aggrecans, which is very similar to the known force fingerprints of other cell adhesion proteoglycan systems. After studying the GAG-GAG dissociation in a dynamic, loading-rate-dependent manner (dynamic SMFS) and analyzing the data according to the stochastic Bell-Evans model for a thermally activated decay of a metastable state under an external force, we estimated for the single glycan interaction a mean lifetime of τ = 7.9 ± 4.9 s and a reaction bond length of x(β) = 0.31 ± 0.08 nm. Whereas the x(β)-value compares well with values from other cell adhesion carbohydrate recognition motifs in evolutionary distant marine sponge proteoglycans, the rather short GAG interaction lifetime reflects high intermolecular dynamics within aggrecan complexes, which may be relevant for the viscoelastic properties of cartilage tissue.

Identifying single bases in a DNA oligomer with electron tunnelling

It has been proposed that single molecules of DNA could be sequenced by measuring the physical properties of the bases as they pass through a nanopore. Theoretical calculations suggest that electron tunnelling can identify bases in single-stranded DNA without enzymatic processing, and it was recently experimentally shown that tunnelling can sense individual nucleotides and nucleosides. Here, we report that tunnelling electrodes functionalized with recognition reagents can identify a single base flanked by other bases in short DNA oligomers. The residence time of a single base in a recognition junction is on the order of a second, but pulling the DNA through the junction with a force of tens of piconewtons would yield reading speeds of tens of bases per second.

Reconstruction of potential energy profiles from multiple rupture time distributions

We explore the mathematical and numerical aspects of reconstructing a potential energy profile of a molecular bond from its rupture time distribution. While reliable reconstruction of gross attributes, such as the height and the width of an energy barrier, can be easily extracted from a single first passage time (FPT) distribution, the reconstruction of finer structure is ill-conditioned. More careful analysis shows the existence of optimal bond potential amplitudes (represented by an effective Peclet number) and initial bond configurations that yield the most efficient numerical reconstruction of simple potentials. Furthermore, we show that reconstruction of more complex potentials containing multiple minima can be achieved by simultaneously using two or more measured FPT distributions, obtained under different physical conditions. For example, by changing the effective potential energy surface by known amounts, additional measured FPT distributions improve the reconstruction. We demonstrate the possibility of reconstructing potentials with multiple minima, motivate heuristic rules-of-thumb for optimizing the reconstruction, and discuss further applications and extensions.

Single-molecule force spectroscopy: a method for quantitative analysis of ligand–receptor interactions

The quantitative analysis of molecular interactions is of high interest in medical research. Most methods for the investigation of ligand–receptor complexes deal with huge ensembles of biomolecules, but often neglect interactions with low affinity or small subpopulations with different binding properties. Single-molecule force spectroscopy offers fascinating possibilities for the quantitative analysis of ligand–receptor interactions in a wide affinity range and the sensitivity to detect point mutations. Furthermore, this technique allows one to address questions about the related binding energy landscape. In this article, we introduce single-molecule force spectroscopy with a focus on novel developments in both data analysis and theoretical models for the technique. We also demonstrate two examples of the capabilities of this method.

Maximum likelihood estimation of protein kinetic parameters under weak assumptions from unfolding force spectroscopy experiments

Single molecule force spectroscopy (SMFS) is extensively used to characterize the mechanical unfolding behavior of individual protein domains under applied force by pulling chimeric polyproteins consisting of identical tandem repeats. Constant velocity unfolding SMFS data can be employed to reconstruct the protein unfolding energy landscape and kinetics. The methods applied so far require the specification of a single stretching force increase function, either theoretically derived or experimentally inferred, which must then be assumed to accurately describe the entirety of the experimental data. The very existence of a suitable optimal force model, even in the context of a single experimental data set, is still questioned. Herein, we propose a maximum likelihood (ML) framework for the estimation of protein kinetic parameters which can accommodate all the established theoretical force increase models. Our framework does not presuppose the existence of a single force characteristic function. Rather, it can be used with a heterogeneous set of functions, each describing the protein behavior in the stretching time range leading to one rupture event. We propose a simple way of constructing such a set of functions via piecewise linear approximation of the SMFS force vs time data and we prove the suitability of the approach both with synthetic data and experimentally. Additionally, when the spontaneous unfolding rate is the only unknown parameter, we find a correction factor that eliminates the bias of the ML estimator while also reducing its variance. Finally, we investigate which of several time-constrained experiment designs leads to better estimators.

Quantitative analysis of single-molecule RNA-protein interaction

RNA-binding proteins impact gene expression at the posttranscriptional level by interacting with cognate cis elements within the transcripts. Here, we apply dynamic single-molecule force spectroscopy to study the interaction of the Arabidopsis glycine-rich RNA-binding protein AtGRP8 with its RNA target. A dwell-time-dependent analysis of the single-molecule data in combination with competition assays and site-directed mutagenesis of both the RNA target and the RNA-binding domain of the protein allowed us to distinguish and quantify two different binding modes. For dwell times <0.21 s an unspecific complex with a lifetime of 0.56 s is observed, whereas dwell times >0.33 s result in a specific interaction with a lifetime of 208 s. The corresponding reaction lengths are 0.28 nm for the unspecific and 0.55 nm for the specific AtGRP8-RNA interactions, indicating formation of a tighter complex with increasing dwell time. These two binding modes cannot be dissected in ensemble experiments. Quantitative titration in RNA bandshift experiments yields an ensemble-averaged equilibrium constant of dissociation of KD = 2 x 10(-7) M. Assuming comparable on-rates for the specific and nonspecific binding modes allows us to estimate their free energies as DeltaG0 = -42 kJ/mol and DeltaG0 = -28 kJ/mol for the specific and nonspecific binding modes, respectively. Thus, we show that single-molecule force spectroscopy with a refined statistical analysis is a potent tool for the analysis of protein-RNA interactions without the drawback of ensemble averaging. This makes it possible to discriminate between different binding modes or sites and to analyze them quantitatively. We propose that this method could be applied to complex interactions of biomolecules in general, and be of particular interest for the investigation of multivalent binding reactions.

Controlling atomic joints between carbon nanotubes by electric current

Using a transmission electron microscope and a nanomanipulator, we explored the early head-to-head coalescence of two capped carbon nanotubes (CNTs) under induction of electric current. We measured detaching forces for coalesced CNTs, showing discrete identifiable values attributable to van der Waals interaction, single sp2-like bonds, and double sp3-like bonds by comparing them with forces obtained using molecular dynamics simulations. Our results underscore the feasibility of atomically controlled junctions of CNTs tuned by the amount of the electrical current.

Dynamic force spectroscopy of the Helicobacter pylori BabA-Lewis b binding

The binding strength of the Helicobacter pylori adhesin-receptor complex BabA-ABO/Lewis b has been analyzed by means of dynamic force spectroscopy. High-resolution measurements of rupture forces were performed in situ on single bacterial cells, expressing the high-affinity binding BabA adhesin, by the use of force measuring optical tweezers. The resulting force spectra revealed the mechanical properties of a single BabA-Leb bond. It was found that the bond is dominated by one single energy barrier and that it is a slip-bond. The bond length and thermal off-rate were assessed to be 0.86+/-0.07 nm and 0.015+/-0.006 s(-1), respectively.