Minimizing pulling geometry errors in atomic force microscope single molecule force spectroscopy

In atomic force microscopy-based single molecule force spectroscopy (AFM-SMFS), it is assumed that the pulling angle is negligible and that the force applied to the molecule is equivalent to the force measured by the instrument. Recent studies, however, have indicated that the pulling geometry errors can drastically alter the measured force-extension relationship of molecules. Here we describe a software-based alignment method that repositions the cantilever such that it is located directly above the molecule's substrate attachment site. By aligning the applied force with the measurement axis, the molecule is no longer undergoing combined loading, and the full force can be measured by the cantilever. Simulations and experimental results verify the ability of the alignment program to minimize pulling geometry errors in AFM-SMFS studies.     

Monte Carlo simulation for single RNA unfolding by force

Using polymer elastic theory and known RNA free energies, we construct a Monte Carlo algorithm to simulate the single RNA folding and unfolding by mechanical force on the secondary structure level. For the constant force ensemble, we simulate the force-extension curves of the P5ab, P5abc deltaA, and P5abc molecules in equilibrium. For the constant extension ensemble, we focus on the mechanical behaviors of the RNA P5ab molecule, which include the unfolding force dependence on the pulling speed, the force-hysteresis phenomenon, and the coincidence of stretching-relaxing force-curves in thermal equilibrium. We particularly simulate the time traces of the end-to-end distance of the P5ab under the constant force in equilibrium, which also have been recorded in the recent experiment. The reaction rate constants for the folding and unfolding are calculated. Our results show that the agreement between the simulation and the experimental measurements is satisfactory.     

Probing protein-protein interactions in real time

We have used a prototype small cantilever atomic force microscope to observe, in real time, the interactions between individual protein molecules. In particular, we have observed individual molecules of the chaperonin protein GroES binding to and then dissociating from individual GroEL proteins, which were immobilized on a mica support. This work suggests that the small cantilever atomic force microscope is a useful tool for studying protein dynamics at the single molecule level.     

Measuring molecular elasticity by atomic force microscope cantilever fluctuations

In single-molecule mechanics experiments the molecular elasticity is usually measured from the deformation in response to a controlled applied force, e.g., via an atomic force microscope cantilever. We have tested the validity of an alternative method based on a recently developed theory. The concept is to measure the change in thermal fluctuations of the cantilever tip with and without its coupling to a rigid surface via the molecule. The new method was demonstrated by its application to the elasticity measurements of L- and P-selectin complexed with P-selectin glycoprotein ligand-1 or their respective antibodies, which showed values comparable to those measured from the slope of the force-extension curve. L- and P-selectin were found to behave as nearly linear springs capable of sustaining large forces and strains without sudden unfolding. The measured spring constants of approximately 4 and approximately 1 pN/nm for L- and P-selectin, respectively, suggest that a physiological force of approximately 100 pN would result in an approximately 200% strain for the respective selectins.     

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.     

Development of glutathione-coupled cantilever for the single-molecule force measurement by scanning force microscopy

The accuracy and the fidelity of a single-molecule force measurement largely rely on how the molecule of interest is attached to the solid substrate surface (bead, cantilever, cover glass and etc.). A site-specific attachment of a protein without affecting its structure and enzymatic function has been a major concern. Here, we established a glutathione-coupled cantilever to which any glutathione S-transferase (GST)-fused proteins can be attached in a desired direction. The rupture force between glutathione and GST was approximately 100 pN on average. By using this cantilever, we succeeded in measuring the interaction force between importin alpha and importin beta.     

Determining Protein-Induced DNA Bending in Force-Extension Experiments: Theoretical Analysis

Computer simulations were used to investigate the possibility of determining protein-induced DNA bend angles by measuring the extension of a single DNA molecule. Analysis of the equilibrium sets of DNA conformations showed that shortening of DNA extension by a single protein-induced DNA bend can be as large as 35 nm. The shortening has a maximum value at the extending force of ∼0.1 pN. At this force, the DNA extension experiences very large fluctuations that dramatically complicate the measurement. Using Brownian dynamics simulation of a DNA molecule extended by force, we were able to estimate the observation time needed to obtain the desired accuracy of the extension measurement. Also, the simulation revealed large fluctuations of the force, acting on the attached magnetic bead from the stretched DNA molecule.     

Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization

Tendons are composed of collagen and other molecules in a highly organized hierarchical assembly, leading to extraordinary mechanical properties. To probe the cross-links on the lower level of organization, we used a cantilever to pull substructures out of the assembly. Advanced force probe technology, using small cantilevers (length <20 microm), improved the force resolution into the sub-10 pN range. In the force versus extension curves, we found an exponential increase in force and two different periodic rupture events, one with strong bonds (jumps in force of several hundred pN) with a periodicity of 78 nm and one with weak bonds (jumps in force of <7 pN) with a periodicity of 22 nm. We demonstrate a good correlation between the measured mechanical behavior of collagen fibers and their appearance in the micrographs taken with the atomic force microscope.     

Molecular mechanics modeling of azobenzene-based photoswitches

We present an extension of the generalized amber force field to allow the modeling of azobenzenes by means of classical molecular mechanics. TD-DFT calculations were employed to derive different interaction models for 4-hydroxy-4'-methyl-azobenzene, including the ground (S(0)) and S(1) excited state. For both states, partial charges and the -N = N- torsion potentials were characterized. On this basis, we pave the way to large-scale model simulations involving azobenzene molecular switches. Using the example of an isolated molecule, the mechanics of cyclic switching processes are demonstrated by classical molecular dynamics simulations.     

Multi-bead-and-spring model to interpret protein detachment studied by AFM force spectroscopy

This article deals with the detachment of molecules (fibrinogen) from a surface studied experimentally with an atomic force microscope. The detachment (or rupture) forces are measured as a function of the retraction velocity and exhibit a clear dependence on this parameter, even though the interaction between the molecules and the surface are nonspecific. To interpret these data, a mechanical multi-bead-and-spring model is developed. It consists of one to several parallel, "molecular" springs connected to an extra spring representing the cantilever that is moved at constant velocity. The free end of each molecular spring terminates with a particle that interacts with the surface through a Lennard-Jones potential. This Brownian dynamics model is used to analyze the experimental findings. In the framework of this model, it appears that the fibrinogen molecule must be ascribed a stiffness much smaller than that of the cantilever. In addition, several bonds between the molecule and the surface must be taken into account for the range of the molecule-surface interaction not to be unrealistically small. In future work, this model will be extended to more complex mechanisms such as the detachment of cells from a surface.     

Mechanical properties of external confinement modulate the rounding dynamics of cells

Many studies have demonstrated that mitotic cells can round up against external impediments. However, how the stiffness of external confinement affects the dynamics of rounding force/pressure and cell volume remains largely unknown. Here, we develop a theoretical framework to study the rounding of adherent cells confined between a substrate and a cantilever. We show that the rounding force and pressure increase exclusively with the effective confinement on the cell, which is related to the cantilever stiffness and the separation between cantilever and substrate. Remarkably, an increase of cantilever stiffness from 0.001 to 1 N/m can lead to a 100-fold change in rounding force. This model also predicts an active role of confinement stiffness in regulating the dynamics of cell volume and hydrostatic pressure. We find that the dynamic changes of cellular volume and hydrostatic pressure after osmotic shocks are opposite if the cantilever is soft, whereas the dynamic changes of cellular volume and pressure are the same if the cantilever is stiff. Taken together, this work demonstrates that confinement stiffness appears as a critical regulator in regulating the dynamics of rounding force and pressure. Our findings also indicate that the difference in cantilever stiffness need to be considered when comparing the measured rounding force and pressure from various experiments.     

Elastic properties of isolated thick filaments measured by nanofabricated cantilevers.

Using newly developed nanofabricated cantilever force transducers, we have measured the mechanical properties of isolated thick filaments from the anterior byssus retractor muscle of the blue mussel Mytilus edulis and the telson levator muscle of the horseshoe crab Limulus polyphemus. The single thick filament specimen was suspended between the tip of a flexible cantilever and the tip of a stiff reference beam. Axial stress was placed on the filament, which bent the flexible cantilever. Cantilever tips were microscopically imaged onto a photodiode array to extract tip positions, which could be converted into force by using the cantilever stiffness value. Length changes up to 23% initial length (Mytilus) and 66% initial length (Limulus) were fully reversible and took place within the physiological force range. When stretch exceeded two to three times initial length (Mytilus) or five to six times initial length (Limulus), at forces approximately 18 nN and approximately 7 nN, respectively, the filaments broke. Appreciable and reversible strain within the physiological force range implies that thick-filament length changes could play a significant physiological role, at least in invertebrate muscles.     

Adhesion forces measured between a calcium blocker drug and its receptor in living cells using atomic force microscope

The adhesion force between the tip of an atomic force microscope cantilever derivatized with nimodipine (a calcium blocker, from the dihydropyridine class, currently used in clinical medicine for hypertension) and living cells of Saccharomyces cerevisiae (unicellular eukaryotes which portray ultrastructural features characteristic of higher eukaryotic cells) was measured. This methodology allowed us to locate (and visualize) pores on the cell surface which may be responsible for calcium transportation in the living cells. The interaction of the cantilever derivatized with the calcium blocker and a pore, which can be a calcium channel, is more intense than a non-derivatized cantilever and the pore. Outside the pore (on the rest of cell surface), a derivatized or a non-derivatized cantilever has the same pattern of adhesion force. The information obtained with this method is very important for the design of new, more potent and less toxic drugs for pharmacological use.     

Interaction of Oxazole Yellow Dyes with DNA Studied with Hybrid Optical Tweezers and Fluorescence Microscopy

We have integrated single molecule fluorescence microscopy imaging into an optical tweezers set-up and studied the force extension behavior of individual DNA molecules in the presence of various YOYO-1 and YO-PRO-1 concentrations. The fluorescence modality was used to record fluorescent images during the stretching and relaxation cycle. Force extension curves recorded in the presence of either dye did not show the overstretching transition that is characteristic for bare DNA. Using the modified wormlike chain model to curve-fit the force extension data revealed a contour length increase of 6% and 30%, respectively, in the presence of YO-PRO-1 and YOYO-1 at 100 nM. The fluorescence images recorded simultaneously showed that the number of bound dye molecules increased as the DNA molecule was stretched and decreased again as the force on the complex was lowered. The binding constants and binding site sizes for YO-PRO-1 and YOYO-1 were determined as a function of the force. The rate of YO-PRO-1 binding and unbinding was found to be 2 orders of magnitude larger than that for YOYO-1. A kinetic model is proposed to explain this observation.     

Analysis of RNA flexibility by scanning force spectroscopy

Scanning force spectroscopy was used to measure the mechanical properties of double stranded RNA molecules in comparison with DNA. We find that, similar to the B–S transition in DNA, RNA molecules are stretched from the assumed A′ conformation to a stretched conformation by applying a defined force (plateau force). The force depends on the G + C content of the RNA and is distinct from that required for the B–S transition of a homologous DNA molecule. After the conformational change, DNA can be further extended by a factor of 0.7 ± 0.2 (S-factor) before melting occurs and the binding of the molecule to the cantilever is finally disrupted. For RNA, the S-factor was higher (1.0 ± 0.2) and more variable. Experiments to measure secondary structures in single stranded RNA yielded a large number of different force-distance curves, suggesting disruption and stretching of various secondary structures. Oriented attachment of the molecules to the substrate, a defined pick-up point and an increased resolution of the instrument could provide the means to analyse RNA secondary structures by scanning force spectroscopy.     

Myofibrillar creatine kinase activity inferred from a 3D model

Myofibrillar creatine kinase (CK) that buffers ATP during fluctuating muscle energy metabolism has been selected for studies of conformational changes underlying the cellular control of enzyme activity. The force field was computed for three energetic states, namely for the substrate-free CK molecule, for the molecule conjugated with the MgATP complex, and for the molecule conjugated with the pair of reactants MgATP-creatine. Without its substrates, the enzyme molecule assumes an inactive "open" form. Upon binding of the MgATP complex, the CK molecule takes up a reactive "closed" conformation. Subsequent binding of creatine yields a nonreactive "intermediary" conformation. Acid-base catalysis is considered to be the basic principle for the reversible transfer of the phosphoryl group between the substrates. The results indicate that the substrate-induced energy minimizing conformational changes do not represent a sufficient condition for CK activity and that some other essential component of physiological control at the cellular level is involved in the transition from the intermediary to the closed structure of the molecule.     

Comparing proteins by their unfolding pattern

Single molecule force spectroscopy has evolved into an important and extremely powerful technique for investigating the folding potentials of biomolecules. Mechanical tension is applied to individual molecules, and the subsequent, often stepwise unfolding is recorded in force extension traces. However, because the energy barriers of the folding potentials are often close to the thermal energy, both the extensions and the forces at which these barriers are overcome are subject to marked fluctuations. Therefore, force extension traces are an inadequate representation despite widespread use particularly when large populations of proteins need to be compared and analyzed. We show in this article that contour length, which is independent of fluctuations and alterable experimental parameters, is a more appropriate variable than extension. By transforming force extension traces into contour length space, histograms are obtained that directly represent the energy barriers. In contrast to force extension traces, such barrier position histograms can be averaged to investigate details of the unfolding potential. The cross-superposition of barrier position histograms allows us to detect and visualize the order of unfolding events. We show with this approach that in contrast to the sequential unfolding of bacteriorhodopsin, two main steps in the unfolding of the enzyme titin kinase are independent of each other. The potential of this new method for accurate and automated analysis of force spectroscopy data and for novel automated screening techniques is shown with bacteriorhodopsin and with protein constructs containing GFP and titin kinase.     

Single molecule measurements of titin elasticity

Titin, with a massive single chain of 3--4MDa and multiple modular motifs, spans the half-sarcomere of skeletal and cardiac muscles and serves important, multifaceted functions. In recent years, titin has become a favored subject of single molecule observations by atomic force microscopy (AFM) and laser optical trap (LOT). Here we review these single titin molecule extension studies with an emphasis on understanding their relevance to titin elasticity in muscle function. Some fundamental aspects of the methods for single titin molecule investigations, including the application of dynamic force, the elasticity models for filamentous titin motifs, the technical foundations and calibrations of AFM and LOT, and titin sample preparations are provided. A chronological review of major publications on recent single titin extension observations is presented. This is followed by summary evaluations of titin domain folding/unfolding results and of elastic properties of filamentous titin motifs. Implications of these single titin measurements for muscle physiology/pathology are discussed and forthcoming advances in single titin studies are anticipated.     

Mechanical Coupling between Myosin Molecules Causes Differences between Ensemble and Single-Molecule Measurements

In contracting muscle, individual myosin molecules function as part of a large ensemble, hydrolyzing ATP to power the relative sliding of actin filaments. The technological advances that have enabled direct observation and manipulation of single molecules, including recent experiments that have explored myosin's force-dependent properties, provide detailed insight into the kinetics of myosin's mechanochemical interaction with actin. However, it has been difficult to reconcile these single-molecule observations with the behavior of myosin in an ensemble. Here, using a combination of simulations and theory, we show that the kinetic mechanism derived from single-molecule experiments describes ensemble behavior; but the connection between single molecule and ensemble is complex. In particular, even in the absence of external force, internal forces generated between myosin molecules in a large ensemble accelerate ADP release and increase how far actin moves during a single myosin attachment. These myosin-induced changes in strong binding lifetime and attachment distance cause measurable properties, such as actin speed in the motility assay, to vary depending on the number of myosin molecules interacting with an actin filament. This ensemble-size effect challenges the simple detachment limited model of motility, because even when motility speed is limited by ADP release, increasing attachment rate can increase motility speed.     

UNDERSTANDING INTERCELLULAR INTERACTIONS AND CELL ADHESION: LESSONS FROM STUDIES ON PROTEIN—METAL INTERACTIONS

To understand cell—cell interactions and the interactions of cells to non-biological materials, studies on binding forces between cellular proteins and between proteins and non-biological material such as metal surfaces are essential. The adsorption of proteins to solid—water interfaces is a multifactorial and a multistep process. First steps are determined by long-range interactions where surface properties such as hydrophobicity, distribution of charged groups, ion concentrations and pH play important roles. In later steps structural rearrangements in the protein molecule and dehydration effects become more important making the adsorption process often irreversible. In the following we demonstrate that protein A and tubulin have a specific type of interaction to metal surfaces probably as an intermediate step in the adsorption process. The proteins were attached to the tip of a microfabricated cantilever in such a way that only one molecule interacts with the surface. By recording force—distance curves with an atomic force microscope the adhesion forces of single molecules binding to gold, titanium and indium—tinoxid surfaces were measured.