Analyzing single-bond experiments: influence of the shape of the energy landscape and universal law between the width, depth, and force spectrum of the bond

Membrane Tubulation with a Biomembrane Force Probe

Tubulation is a common cellular process involving the formation of membrane tubes ranging from 50 nm to 1 µm in diameter. These tubes facilitate intercompartmental connections, material transport within cells and content exchange between cells. The high curvature of these tubes makes them specific targets for proteins that sense local geometry. In vitro, similar tubes have been created by pulling on the membranes of giant unilamellar vesicles. Optical tweezers and micromanipulation are typically used in these experiments, involving the manipulation of a GUV with a micropipette and a streptavidin-coated bead trapped in optical tweezers. The interaction forms streptavidin/biotin bonds, leading to tube formation. Here, we propose a cost-effective alternative using only micromanipulation techniques, replacing optical tweezers with a Biomembrane Force Probe (BFP). The BFP, employing a biotinylated erythrocyte as a nanospring, allows for the controlled measurement of forces ranging from 1 pN to 1 nN. The BFP has been widely used to study molecular interactions in cellular processes, extending beyond its original purpose. We outline the experimental setup, tube formation and characterization of tube dimensions and energetics, and discuss the advantages and limitations of this approach in studying membrane tubulation.

Characterizing cell adhesion by using micropipette aspiration

We have developed a technique to directly quantify cell-substrate adhesion force using micropipette aspiration. The micropipette is positioned perpendicular to the surface of an adherent cell and a constant-rate aspiration pressure is applied. Since the micropipette diameter and the aspiration pressure are our control parameters, we have direct knowledge of the aspiration force, whereas the cell behavior is monitored either in brightfield or interference reflection microscopy. This setup thus allows us to explore a range of geometric parameters, such as projected cell area, adhesion area, or pipette size, as well as dynamical parameters such as the loading rate. We find that cell detachment is a well-defined event occurring at a critical aspiration pressure, and that the detachment force scales with the cell adhesion area (for a given micropipette diameter and loading rate), which defines a critical stress. Taking into account the cell adhesion area, intrinsic parameters of the adhesion bonds, and the loading rate, a minimal model provides an expression for the critical stress that helps rationalize our experimental results.

Force dependence of energy barriers in atomic friction and single-molecule force spectroscopy: critique of a critical scaling relation

Friction force microscopy and single-molecule force spectroscopy are experimental methods to explore multistable energy landscapes by means of a controlled reduction of the energy barriers between adjacent potential minima. This affects the system's interstate transition rates proportional to e(-ΔE(f)/kBT), with ΔE(f) being the barrier height, k(B)T the thermal energy, and f the elastic force applied. It is often assumed that, at large forces, the barrier height scales as (f(c) - f)(3/2), where f(c) is the critical force, at which the barrier vanishes. We show that, for the elastic forces produced by a pulling device of finite stiffness κ, this scaling relation is actually incorrect. Rather, the barrier is a double-valued function of force of the form E(f) ∝ (κ/κ(c) ±√1 − f/f(0))(3), where f(0) is the maximal force that the system potential can generate, and the characteristic stiffness κ(c) is not necessarily much larger than κ. In particular, for finite κ, the barrier vanishes at a certain force f(κ) < f(0), but, in view of the double-valuedness of ΔE(f), the maximal force f0 can still be reached. We derive the relation between the most probable force at the moment of transition, fm, and the pulling velocity, v. The usually assumed scaling f(m) ∝ (ln v)(2/3) is recovered as the κ → 0 limit of our more general result, but becomes increasingly worse as κ grows. We introduce a new data analysis method that allows one to quantitatively characterize the system potential and evaluate the stiffness of the pulling device, κ, which is usually not known beforehand. We demonstrate the feasibility of our method by analyzing the results of a numerical experiment based on the standard Prandtl-Tomlinson model of nanoscale friction.

Mechanochemitry: a molecular biomechanics view of mechanosensing

Molecular biomechanics includes two themes: the study of mechanical aspects of biomolecules and the study of molecular biology of the cell using mechanical tools. The two themes are interconnected for obvious reasons. The present review focuses on one of the interconnected areas-the mechanical regulation of molecular interaction and conformational change. Recent conceptual developments are summarized, including catch bonds, regulation of molecular interaction by the history of force application, and cyclic mechanical reinforcement. These studies elucidate the mechanochemistry of some of the candidate mechanosensing molecules, thereby providing a natural connection to mechanobiology.

Fibers with integrated mechanochemical switches: minimalistic design principles derived from fibronectin

Inspired by molecular mechanisms that cells exploit to sense mechanical forces and convert them into biochemical signals, chemists dream of designing mechanochemical switches integrated into materials. Using the adhesion protein fibronectin, whose multiple repeats essentially display distinct molecular recognition motifs, we derived a computational model to explain how minimalistic designs of repeats translate into the mechanical characteristics of their fibrillar assemblies. The hierarchy of repeat-unfolding within fibrils is controlled not only by their relative mechanical stabilities, as found for single molecules, but also by the strength of cryptic interactions between adjacent molecules that become activated by stretching. The force-induced exposure of cryptic sites furthermore regulates the nonlinearity of stress-strain curves, the strain at which such fibers break, and the refolding kinetics and fraction of misfolded repeats. Gaining such computational insights at the mesoscale is important because translating protein-based concepts into novel polymer designs has proven difficult.

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.

Force measurement enabling precise analysis by dynamic force spectroscopy

Dynamic force spectroscopy (DFS) makes it possible to investigate specific interactions between two molecules such as ligand-receptor pairs at the single-molecule level. In the DFS method based on the Bell-Evans model, the unbinding force applied to a molecular bond is increased at a constant rate, and the force required to rupture the molecular bond is measured. By analyzing the relationship between the modal rupture force and the logarithm of the loading rate, microscopic potential barrier landscapes and the lifetimes of bonds can be obtained. However, the results obtained, for example, in the case of streptavidin/biotin complexes, have differed among previous studies and some results have been inconsistent with theoretical predictions. In this study, using an atomic force microscopy technique that enables the precise analysis of molecular interactions on the basis of DFS, we investigated the effect of the sampling rate on DFS analysis. The shape of rupture force histograms, for example, was significantly deformed at a sampling rate of 1 kHz in comparison with that of histograms obtained at 100 kHz, indicating the fundamental importance of ensuring suitable experimental conditions for further advances in the DFS method.

Reconsideration of dynamic force spectroscopy analysis of streptavidin-biotin interactions

To understand and design molecular functions on the basis of molecular recognition processes, the microscopic probing of the energy landscapes of individual interactions in a molecular complex and their dependence on the surrounding conditions is of great importance. Dynamic force spectroscopy (DFS) is a technique that enables us to study the interaction between molecules at the single-molecule level. However, the obtained results differ among previous studies, which is considered to be caused by the differences in the measurement conditions. We have developed an atomic force microscopy technique that enables the precise analysis of molecular interactions on the basis of DFS. After verifying the performance of this technique, we carried out measurements to determine the landscapes of streptavidin-biotin interactions. The obtained results showed good agreement with theoretical predictions. Lifetimes were also well analyzed. Using a combination of cross-linkers and the atomic force microscope that we developed, site-selective measurement was carried out, and the steps involved in bonding due to microscopic interactions are discussed using the results obtained by site-selective analysis.

Model accounting for the effects of pulling-device stiffness in the analyses of single-molecule force measurements

Single-molecule force spectroscopy provides a powerful approach for investigating molecular transitions along specific reaction coordinates. Here, we present a general analytical model for extracting the intrinsic rates and activation free energies from force measurements on single molecules that is applicable to a broad range of pulling speeds and device stiffnesses. This model relaxes existing limitations to perform force measurements with soft pulling devices for proper theoretical analyses and, in fact, allows experiments to specifically exploit device stiffness as a control parameter in addition to pulling speed for a reliable estimation of energetic and kinetic parameters.

Energy landscape, structure and rate effects on strength properties of alpha-helical proteins

The strength of protein domains is crucial to identify the mechanical role of protein domains in biological processes such as mechanotransduction, tissue mechanics and tissue remodeling. Whereas the concept of strength has been widely investigated for engineered materials, the strength of fundamental protein material building blocks and how it depends on structural parameters such as the chemical bonding, the protein filament length and the timescale of observation or deformation velocity remains poorly understood. Here we report a systematic analysis of the influence of key parameters that define the energy landscape of the strength properties of alpha-helical protein domains, including energy barriers, unfolding and refolding distances, the locations of folded and unfolded states, as well as variations of the length and pulling velocity of alpha-helical protein filaments. The analysis is facilitated by the development of a double-well mesoscale potential formulation, utilized here to carry out a systematic numerical analysis of the behavior of alpha-helices. We compare the results against widely used protein strength models based on the Bell model, one of the simplest models used to characterize the strength of protein filaments. We find that, whereas Bell-type models are a reasonable approximation to describe the rupture of alpha-helical protein domains for a certain range of pulling speeds and values of energy barriers, the model ceases to hold for very large energy barriers and for very small pulling speeds, in agreement with earlier findings. We conclude with an application of our mesoscale model to investigate the effect of the length of alpha-helices on their mechanical strength. We find a weakening effect as the length of alpha-helical proteins increases, followed by an asymptotic regime in which the strength remains constant. We compare strand lengths found in biological proteins with the scaling law of strength versus alpha-helix filament length. The mesoscale model reported here is generally applicable to other protein filaments that feature a serial array of domains that unfold under applied strain, where a similar length-dependent strength could be observed.

Force spectroscopy of a single artificial biomolecule bond: the Kramers' high-barrier limit holds close to the critical force

We use a minimal system with a single micron-size bead trapped with optical tweezers to investigate the kinetics of escape under force. Surprisingly, the exponential decay of the off rate with the barrier energy is still valid close to the critical force. Hence, the high viscosity approximation derived by Kramers in the case of a high energy barrier holds even for an energy barrier close to the thermal energy. Several recent models describe a single biomolecule bond by a smooth single-barrier energy profile. When this approach is accurate enough, our result justifies the use of Kramers' approximation in the high-force regime, close to the critical force of the system, as done in recent single biomolecule bond studies.

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.

Statistics of forced thermally activated escape events out of a metastable state: most probable escape force and escape-force moments

The dynamics of a number of experimental systems can be described as thermally activated escape out of a metastable state over a potential barrier, whose height is being constantly reduced in time by an increasing external force. In such systems, one can distinguish two loading regimes: for slow loading, the distribution of the force values at which escape occurs is a monotonically decreasing function, while for fast loading, the escape-force distribution has a maximum at some nonzero force value. In this work, an approximate relation between the most probable escape force and the first two moments thereof is derived for fast loading, and the expression for the first two force moments vs loading rate is obtained for slow loading. Then, for a special but physically well-motivated functional form of the escape rate, the most probable escape force is found analytically as a function of the loading rate. The high accuracy of these expressions is confirmed by comparing them with numerical results for realistic parameter values.