Graphical method for force analysis: macromolecular mechanics with atomic force microscopy

We present a graphical method for a unifying, quantitative analysis of molecular bonding-force measurements by atomic force microscopy (AFM). The method is applied to interpreting a range of phenomena commonly observed in the experimental AFM measurements of noncovalent, weak bonds between biological macromolecules. The analysis suggests an energy landscape underlying the intermolecular force and demonstrates that many observations, such as "snaps-on," "jumps-off," and hysteresis loops, are different manifestations of a double-well energy landscape. The analysis gives concrete definitions for the operationally defined "attractive" and "adhesive" forces in terms of molecular parameters. It is shown that these operationally defined quantities are usually functions of the experimental setup, such as the stiffness of the force probe and the rate of its movement. The analysis reveals a mechanical instability due to the multistate nature of molecular interactions and provides new insight into macromolecular viscosity. The graphical method can equally be applied to a quantitative analysis of multiple unfolding of subunits of the giant muscle protein titin under AFM.     

Energy landscape roughness of the streptavidin-biotin interaction

Molecular interactions between receptors and ligands can be characterized by their free energy landscape. In its simplest representation, the energy landscape is described by a barrier of certain height and width that determines the dissociation rate of the complex, as well as its dynamic strength. Some interactions, however, require a more complex landscape with additional barriers and roughness along the reaction coordinate. This roughness slows down the dissociation kinetics of the interaction and contributes to its dynamic strength. The streptavidin-biotin complex has been extensively studied due to its remarkably low dissociation kinetics. However, single molecule measurements from independent experiments showed scattered and disparate results. In this work, the energy landscape roughness of the streptavidin-biotin interaction was estimated to be in the range of 5-8kBT using dynamic force spectroscopy (DFS) measurements at three different temperatures. These results can be used to explain both its slow dissociation kinetics and the discrepancies in the reported force measurements.     

Effects of multiple-bond ruptures on kinetic parameters extracted from force spectroscopy measurements: revisiting biotin-streptavidin interactions

Force spectroscopy measurements of the rupture of the molecular bond between biotin and streptavidin often results in a wide distribution of rupture forces. We attribute the long tail of high rupture forces to the nearly simultaneous rupture of more than one molecular bond. To decrease the number of possible bonds, we employed hydrophilic polymeric tethers to attach biotin molecules to the atomic force microscope probe. It is shown that the measured distributions of rupture forces still contain high forces that cannot be described by the forced dissociation from a deep potential well. We employed a recently developed analytical model of simultaneous rupture of two bonds connected by polymer tethers with uneven length to fit the measured distributions. The resulting kinetic parameters agree with the energy landscape predicted by molecular dynamics simulations. It is demonstrated that when more than one molecular bond might rupture during the pulling measurements there is a noise-limited range of probe velocities where the kinetic parameters measured by force spectroscopy correspond to the true energy landscape. Outside this range of velocities, the kinetic parameters extracted by using the standard most probable force approach might be interpreted as artificial energy barriers that are not present in the actual energy landscape. Factors that affect the range of useful velocities are discussed.     

Model energy landscapes and the force-induced dissociation of ligand-receptor bonds

We discuss models for the force-induced dissociation of a ligand-receptor bond, occurring in the context of cell adhesion or single molecule unbinding force measurements. We consider a bond with a structured energy landscape which is modeled by a network of force dependent transition rates between intermediate states. The behavior of a model with only one intermediate state and a model describing a molecular zipper is studied. We calculate the bond lifetime as a function of an applied force and unbinding forces under an increasing applied load and determine the relationship between both quantities. The dissociation via an intermediate state can lead to distinct functional relations of the bond lifetime on force. One possibility is the occurrence of three force regimes where the lifetime of the bond is determined by different transitions within the energy landscape. This case can be related to recent experimental observations of the force-induced dissociation of single avidin-biotin bonds.     

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

     

Measuring the folding landscape of a harmonically constrained biopolymer

Pioneering studies have shown that the probability distribution of opening length for a DNA hairpin, recorded under constant force using an optical trap, can be used to reconstruct the energy landscape of the transition. However, measurements made under constant force are subject to some limitations. Under constant force a system with a sufficiently high energy barrier spends most of its time in the closed or open conformation, with relatively few statistics collected in the transition state region. We describe a measurement scheme in which the system is driven progressively through the transition by an optical trap and an algorithm is used to extract the energy landscape of the transition from the fluctuations recorded during this process. We illustrate this technique in simulations and demonstrate its effectiveness in experiments on a DNA hairpin. We find that the combination of this technique with the use of short DNA handles facilitates a high-resolution measurement of the hairpin's folding landscape with a very short measurement time.     

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.     

Energy landscape of streptavidin-biotin complexes measured by atomic force microscopy

The dissociation of ligand and receptor involves multiple transitions between intermediate states formed during the unbinding process. In this paper, we explored the energy landscape of the streptavidin-biotin interaction by using the atomic force microscope (AFM) to measure the unbinding dynamics of individual ligand-receptor complexes. The rupture force of the streptavidin-biotin bond increased more than 2-fold over a range of loading rates between 100 and 5000 pN/s. Moreover, the force measurements showed two regimes of loading in the streptavidin-biotin force spectrum, revealing the presence of two activation barriers in the unbinding process. Parallel experiments carried out with a streptavidin mutant (W120F) were used to investigate the molecular determinants of the activation barriers. From these experiments, we attributed the outer activation barrier in the energy landscape to the molecular interaction of the '3-4' loop of streptavidin that closes behind biotin.     

Atomic force microscope studies of the fusion of floating lipid bilayers

This study investigated the fusion of apposing floating bilayers of egg L-alpha-phosphatidylcholine (egg PC) or 1,2-dimyristoyl-sn-glycero-3-phosphocholine. Atomic force microscope measurements of fusion forces under different compression rates were acquired to reveal the energy landscape of the fusion process under varied lipid composition and temperature. Between compression rates of approximately 1000 and approximately 100,000 pN/s, applied forces in the range from approximately 100 to approximately 500 pN resulted in fusion of floating bilayers. Our atomic force microscope measurements indicated that one main energy barrier dominated the fusion process. The acquired dynamic force spectra were fit with a simple model based on the transition state theory with the assumption that the fusion activation potential is linear. A significant shift in the energy landscape was observed when bilayer fluidity and composition were modified, respectively, by temperature and different cholesterol concentrations (15% < or = chol < or = 25%). Such modifications resulted in a more than twofold increase in the width of the fusion energy barrier for egg PC and 1,2-dimyristoyl-sn-glycero-3-phosphocholine floating bilayers. The addition of 25% cholesterol to egg PC bilayers increased the activation energy by approximately 1.0 k(B)T compared with that of bilayers with egg PC alone. These results reveal that widening of the energy barrier and consequently reduction in its slope facilitated membrane fusion.     

Single-molecule unfolding force distributions reveal a funnel-shaped energy landscape

The protein folding process is described as diffusion on a high-dimensional energy landscape. Experimental data showing details of the underlying energy surface are essential to understanding folding. So far in single-molecule mechanical unfolding experiments a simplified model assuming a force-independent transition state has been used to extract such information. Here we show that this so-called Bell model, although fitting well to force velocity data, fails to reproduce full unfolding force distributions. We show that by applying Kramers' diffusion model, we were able to reconstruct a detailed funnel-like curvature of the underlying energy landscape and establish full agreement with the data. We demonstrate that obtaining spatially resolved details of the unfolding energy landscape from mechanical single-molecule protein unfolding experiments requires models that go beyond the Bell model.     

Probing the energy landscape of the membrane protein bacteriorhodopsin

The folding and stability of transmembrane proteins is a fundamental and unsolved biological problem. Here, single bacteriorhodopsin molecules were mechanically unfolded from native purple membranes using atomic force microscopy and force spectroscopy. The energy landscape of individual transmembrane alpha helices and polypeptide loops was mapped by monitoring the pulling speed dependence of the unfolding forces and applying Monte Carlo simulations. Single helices formed independently stable units stabilized by a single potential barrier. Mechanical unfolding of the helices was triggered by 3.9-7.7 A extension, while natural unfolding rates were of the order of 10(-3) s(-1). Besides acting as individually stable units, helices associated pairwise, establishing a collective potential barrier. The unfolding pathways of individual proteins reflect distinct pulling speed-dependent unfolding routes in their energy landscapes. These observations support the two-stage model of membrane protein folding in which alpha helices insert into the membrane as stable units and then assemble into the functional protein.     

Adsorption characteristics of P(3HB) depolymerase as evaluated by surface plasmon resonance and atomic force microscopy

Molecular recognition of poly[(R)-3-hydroxybutyrate] (P(3HB)) depolymerase from Ralstonia pickettii T1 to the surfaces of biodegradable aliphatic polyesters such as P(3HB) and poly(L-lactic acid) (PLLA) was examined from the viewpoints of kinetics and dynamics. To determine the kinetic parameters on the interaction between the substrate-binding domain (SBD) of P(3HB) depolymerase and various polymer substrates with different chemical structures, surface plasmon resonance (SPR) measurements were performed. On the other hand, using an atomic force microscopic (AFM) cantilever tip functionalized with the SBD of P(3HB) depolymerase, the mechanical parameters such as unbinding force to the polymer surfaces were measured. Both the SPR and AFM measurements showed that the SBD has a high affinity to P(3HB) and PLLA. From the results of kinetics and dynamics, the energy potential landscape of SBD-polymer interaction was disclosed on the basis of a phenomenological model, and the mechanism of the interaction was discussed.     

Looking inside molecular bonds at biological interfaces with dynamic force spectroscopy

Weak non-covalent interactions between large molecules govern interfacial structure and adhesion in biology. Because of thermal activation, these bonds have modest lifetimes and bond lifetimes are progressively shortened under application of external force. Theory predicts that bond survival time depends on how fast the force is applied and the expected survival time specifies the most likely breakage force (strength) at a given loading rate (force/time). Plotted as a function of log(e) (loading rate), the dynamic spectrum of bond strength provides an image of the prominent barriers traversed in the energy landscape along the unbinding pathway, which establishes a direct link between measurements of bond force and molecular-scale chemistry. Experimentally, the challenge is to measure bond strength over several orders of magnitude in loading rate. With a recently designed probe technique, we have measured strengths of single receptor-ligand bonds and receptor-membrane anchoring over an enormous range of loading rates from 10(-1) pN/s to 10(5) pN/s, which reveals an inner view of the complexity of these interactions.     

Probing binding pocket of serotonin transporter by single molecular force spectroscopy on living cells

The serotonin transporter (SERT) terminates neurotransmission by removing serotonin from the synaptic cleft. In addition, it is the site of action of antidepressants (which block the transporter) and of amphetamines (which induce substrate efflux). The interaction energies involved in binding of such compounds to the transporter are unknown. Here, we used atomic force microscopy (AFM) to probe single molecular interactions between the serotonin transporter and MFZ2-12 (a potent cocaine analog) in living CHOK1 cells. For the AFM measurements, MFZ2-12 was immobilized on AFM tips by using a heterobifunctional cross-linker. By varying the pulling velocity in force distance cycles drug-transporter complexes were ruptured at different force loadings allowing for mapping of the interaction energy landscape. We derived chemical rate constants from these recordings and compared them with those inferred from inhibition of transport and ligand binding: koff values were in good agreement with those derived from uptake experiments; in contrast, the kon values were scaled down when determined by AFM. Our observations generated new insights into the energy landscape of the interaction between SERT and inhibitors. They thus provide a useful framework for molecular dynamics simulations by exploring the range of forces and energies that operate during the binding reaction.     

Energetics of the native energy landscape of a two-domain calcium sensor protein: distinct folding features of the two domains

The protein folding energy landscape allows a thorough understanding of the protein folding problem which in turn helps in understanding various aspects of biological functions. Characterizing the cooperative unfolding units and the intermediates along the folding funnel of a protein is a challenging task. In this paper, we investigated the native energy landscape of EhCaBP, a calcium sensor, belonging to the same EF-hand superfamily as calmodulin. EhCaBP is a two-domain EF-hand protein consisting of two EF-hands in each domain and binding to four Ca2+ cations. Native-state hydrogen exchange (HX) was used to assess the folding features of the landscape and also to throw light on the structure-folding function paradigm of calcium sensor proteins. HX measurements under the EX2 regime provided the thermodynamic information about the protein folding events under native conditions. HX studies revealed that the unfolding of EhCaBP is not a two-state process. Instead, it proceeds through cooperative units. The C-terminal domain exhibits less denaturant dependence than the N-terminal domain, suggesting that the former is dominated by local fluctuations. It is interesting to note that the N- and C-terminal domains of EhCaBP have distinct folding features. In fact, these observed differences can regulate the domain-dependent target recognition of two-domain Ca2+ sensor proteins.     

Point mutations in membrane proteins reshape energy landscape and populate different unfolding pathways

Using single-molecule force spectroscopy, we investigated the effect of single point mutations on the energy landscape and unfolding pathways of the transmembrane protein bacteriorhodopsin. We show that the unfolding energy barriers in the energy landscape of the membrane protein followed a simple two-state behavior and represent a manifestation of many converging unfolding pathways. Although the unfolding pathways of wild-type and mutant bacteriorhodopsin did not change, indicating the presence of same ensemble of structural unfolding intermediates, the free energies of the rate-limiting transition states of the bacteriorhodopsin mutants decreased as the distance of those transition states to the folded intermediate states decreased. Thus, all mutants exhibited Hammond behavior and a change in the free energies of the intermediates along the unfolding reaction coordinate and, consequently, their relative occupancies. This is the first experimental proof showing that point mutations can reshape the free energy landscape of a membrane protein and force single proteins to populate certain unfolding pathways over others.     

Probing Position-Dependent Diffusion in Folding Reactions Using Single-Molecule Force Spectroscopy

Folding of proteins and nucleic acids involves a diffusive search over a multidimensional conformational energy landscape for the minimal-energy structure. When examining the projection of conformational motions onto a one-dimensional reaction coordinate, as done in most experiments, the diffusion coefficient D is generally position dependent. However, it has proven challenging to measure such position-dependence experimentally. We investigated the position-dependence of D in the folding of DNA hairpins as a simple model system in two ways: first, by analyzing the round-trip time to return to a given extension in constant-force extension trajectories measured by force spectroscopy, and second, by analyzing the fall time required to reach a given extension in force jump measurements. These methods yielded conflicting results: the fall time implied a fairly constant D, but the round-trip time implied variations of over an order of magnitude. Comparison of experiments with computational simulations revealed that both methods were strongly affected by experimental artifacts inherent to force spectroscopy measurements, which obscured the intrinsic position-dependence of D. Lastly, we applied Kramers’s theory to the kinetics of hairpins with energy barriers located at different positions along the hairpin stem, as a crude probe of D at different stem positions, and we found that D did not vary much as the barrier was moved along the reaction coordinate. This work underlines the difficulties faced when trying to deduce position-dependent diffusion coefficients from experimental folding trajectories.