Pairwise Interactions between Linear Alkanes in Water Measured by AFM Force Spectroscopy

Pairwise interactions between n-alkanes from decane to octadecane in water have been studied by single-molecule force spectroscopy. The interacting molecules are covalently tethered to the glass substrate and to the probe of an atomic force microscope by water-soluble linkers to facilitate single-molecule detection. However, the measured distribution of rupture forces deviates significantly from the distribution predicted by theoretical models for rupture of individual bonds. To describe the statistics of rupture forces, an analytical model that considers near-simultaneous rupture of two bonds loaded by tethers with different lengths is introduced. The common most probable force analysis approach is used for comparison. In both data analyses, the possible systematic errors due to nonlinear elasticity of polymeric tethers and variations in the shape of the potential of mean force were considered. Experimental distributions of rupture forces are well-fit by the two-bond rupture model using a single set of kinetic parameters for different experiments, while the most probable force approach yields parameters that vary significantly for different samples. The measured activation energies for dissociation of alkanes are close to the free energies predicted by cavity models of hydrophobic interactions. The surface free-energy density is estimated to be ∼21 kJ/(mol nm^2) and is close to the upper limit of free energies used in the computer simulations of hydrophobic interactions in proteins. In contrast to the predictions of the cavity models, the measured activation energy does not increase monotonically with increase in alkane chain size. To explain this discrepancy and the measured distance to the transition-state barrier (∼0.6 nm), it is suggested that alkanes undergo conformational transition to the collapsed state upon dimerization. Change in the alkane conformation from extended to helical has been observed previously for binding of alkanes in water to hydrophobic synthetic receptors. Here, however, conformational change is suggested without geometrical constraints imposed by small cavitands. The proposed collapsed state of the alkane dimers has implications for the kinetics of self-assembly of surfactant micelles

Effects of Multiple-Bond Ruptures in Force Spectroscopy Measurements of Interactions between Fullerene C_(60) Molecules in Water

Interactions between fullerene C_(60) molecules in water were measured by force spectroscopy. Fullerene molecules were covalently connected to bifunctional water-soluble poly(ethylene glycol) (PEG) linkers and subsequently tethered to the substrate and to the tip of the atomic force microscope to facilitate single molecule detection and avoid spurious surface effects. The distributions of rupture forces for substrates prepared with different incubation times of C_(60)-PEG-NH_2 exhibit high rupture forces that cannot be explained by the theoretical distribution of single molecule binding. Moreover, the relative amplitude of the high force peak in the histogram increases with incubation time. These observations are explained by attributing the measured high forces to the rupture of multiple bonds between fullerene molecules. Force spectroscopy data analysis based on the most probable forces gives significantly different dissociation rates for samples that exhibit different amplitudes of the high force peak. An approximate analytical model that considers ruptures of two bonds that are simultaneously loaded by tethers with different lengths is proposed. This model successfully fits the distributions of the rupture forces using the same set of kinetic parameters for samples prepared with different grafting densities. It is proposed that this model can be used as a common tool to analyze the probability distributions of rupture forces that contain peaks or shoulders on the high force side of the distribution

Anisotropy of Pairwise Interactions between Hexadecanes in Water Measured by AFM Force Spectroscopy

The pulling coordinate dependence of hexadecane dimer dissociation in water was studied using AFM-based single molecule force spectroscopy. Hexadecanes were covalently bound to both the AFM cantilever and to the glass substrates through hydrophilic poly-(ethylene glycol) tethers. The polymer tether was attached either to the end of hexadecane or in the middle of the molecule. Experimentally studied configurations of hexadecanes tethered to the AFM probe and to the glass substrate include a symmetric end-attached configuration (EE), an asymmetric end-attached vs middle-attached configuration (ME), and a symmetric middle-attached configuration (MM). Kinetic parameters of the distance to the transition state barrier (barrier width) and activation energy of dissociation were extracted from the statistical analysis of double tether rupture events. The rupture force analysis employs a recently introduced two-bond model that corrects for errors induced by potential multiple simultaneous rupture events and accounts for the tether stiffening effects. Effects of the shape of intermolecular potential were considered by using the Bell−Evans and Hummer−Szabo force spectroscopy models. The activation energies to dissociation were similar for all configurations while the barrier width was significantly shorter for the MM and ME configurations than for EE configurations. Primitive models that include touching or merging spherical or cylindrical shapes were considered. These models were inconsistent with the extracted kinetic parameters. It is suggested that the observed anisotropy may be a result of conformational transition of hexadecane from extended to collapsed state during dimerization. A flexible four-bead model of hexadecane was introduced to account for conformational flexibility. Using the length and solvent accessible surface area of hexadecane, the four-bead model gave molecular dissociation parameters consistent with the experimental data. This suggests that conformational flexibility is an important factor in hydrophobic interactions between alkane chains

Pairwise Interactions between Linear Alkanes in Water Measured by AFM Force Spectroscopy

Pairwise interactions between n-alkanes from decane to octadecane in water have been studied by single-molecule force spectroscopy. The interacting molecules are covalently tethered to the glass substrate and to the probe of an atomic force microscope by water-soluble linkers to facilitate single-molecule detection. However, the measured distribution of rupture forces deviates significantly from the distribution predicted by theoretical models for rupture of individual bonds. To describe the statistics of rupture forces, an analytical model that considers near-simultaneous rupture of two bonds loaded by tethers with different lengths is introduced. The common most probable force analysis approach is used for comparison. In both data analyses, the possible systematic errors due to nonlinear elasticity of polymeric tethers and variations in the shape of the potential of mean force were considered. Experimental distributions of rupture forces are well-fit by the two-bond rupture model using a single set of kinetic parameters for different experiments, while the most probable force approach yields parameters that vary significantly for different samples. The measured activation energies for dissociation of alkanes are close to the free energies predicted by cavity models of hydrophobic interactions. The surface free-energy density is estimated to be ∼21 kJ/(mol nm^2) and is close to the upper limit of free energies used in the computer simulations of hydrophobic interactions in proteins. In contrast to the predictions of the cavity models, the measured activation energy does not increase monotonically with increase in alkane chain size. To explain this discrepancy and the measured distance to the transition-state barrier (∼0.6 nm), it is suggested that alkanes undergo conformational transition to the collapsed state upon dimerization. Change in the alkane conformation from extended to helical has been observed previously for binding of alkanes in water to hydrophobic synthetic receptors. Here, however, conformational change is suggested without geometrical constraints imposed by small cavitands. The proposed collapsed state of the alkane dimers has implications for the kinetics of self-assembly of surfactant micelles

Anisotropy of Pairwise Interactions between Hexadecanes in Water Measured by AFM Force Spectroscopy

The pulling coordinate dependence of hexadecane dimer dissociation in water was studied using AFM-based single molecule force spectroscopy. Hexadecanes were covalently bound to both the AFM cantilever and to the glass substrates through hydrophilic poly-(ethylene glycol) tethers. The polymer tether was attached either to the end of hexadecane or in the middle of the molecule. Experimentally studied configurations of hexadecanes tethered to the AFM probe and to the glass substrate include a symmetric end-attached configuration (EE), an asymmetric end-attached vs middle-attached configuration (ME), and a symmetric middle-attached configuration (MM). Kinetic parameters of the distance to the transition state barrier (barrier width) and activation energy of dissociation were extracted from the statistical analysis of double tether rupture events. The rupture force analysis employs a recently introduced two-bond model that corrects for errors induced by potential multiple simultaneous rupture events and accounts for the tether stiffening effects. Effects of the shape of intermolecular potential were considered by using the Bell−Evans and Hummer−Szabo force spectroscopy models. The activation energies to dissociation were similar for all configurations while the barrier width was significantly shorter for the MM and ME configurations than for EE configurations. Primitive models that include touching or merging spherical or cylindrical shapes were considered. These models were inconsistent with the extracted kinetic parameters. It is suggested that the observed anisotropy may be a result of conformational transition of hexadecane from extended to collapsed state during dimerization. A flexible four-bead model of hexadecane was introduced to account for conformational flexibility. Using the length and solvent accessible surface area of hexadecane, the four-bead model gave molecular dissociation parameters consistent with the experimental data. This suggests that conformational flexibility is an important factor in hydrophobic interactions between alkane chains

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