Pinpointing Mechanochemical Bond Rupture by Embedding the Mechanophore into a Macrocycle

Mechanophores contain a mechanically labile bond that can be broken by an external mechanical force. Quantitative measurement and control of the applied force is possible through atomic force microscopy (AFM). A macrocycle was synthesized that contains both the mechanophore and an aliphatic chain that acts as a “safety line” upon bond breaking. This ring‐opening mechanophore unit is linked to poly(ethylene glycol) spacers, which allow investigation by single molecule force spectroscopy. The length increase upon rupture of the mechanophore was measured and compared with quantum chemical calculations.     

Mechanochemical Cycloreversion of Cyclobutane Observed at the Single Molecule Level

Mechanochemical cycloreversion of cyclobutane is known from ultrasound experiments. It is, however, not clear which forces are required to induce the cycloreversion. In atomic force microscopy (AFM) experiments, on the other hand, it is notoriously difficult to assign the ruptured bond. We have solved this problem through the synthesis of tailored macrocycles, in which the cyclobutane mechanophore is bypassed by an ethylene glycol chain of specific length. This macrocycle is covalently anchored between a glass substrate and an AFM cantilever by polyethylene glycol linkers. Upon mechanical stretching of the macrocycle, cycloreversion occurs, which is identified by a defined length increase of the stretched polymer. The measured length change agrees with the value calculated with the external force explicitly included (EFEI) method. By using two different lengths for the ethylene glycol safety line, the assignment becomes unambiguous. Mechanochemical cycloreversion of cyclobutane is observed at forces above 1.7 nN.     

Mechanically activated rupture of single covalent bonds: evidence of force induced bond hydrolysis

We have used temperature-dependent single molecule force spectroscopy to stretch covalently anchored carboxymethylated amylose (CMA) polymers attached to an amino-functionalized AFM cantilever. Using an Arrhenius kinetics model based on a Morse potential as a one-dimensional representation of covalent bonds, we have extracted kinetic and structural parameters of the bond rupture process. With 35.5 kJ mol(-1), we found a significantly smaller dissociation energy and with 9.0 × 10(2) s(-1) to 3.6 × 10(3) s(-1) also smaller Arrhenius pre-factors than expected for homolytic bond scission. One possible explanation for the severely reduced dissociation energy and Arrhenius pre-factors is the mechanically activated hydrolysis of covalent bonds. Both the carboxylic acid amide and the siloxane bond in the amino-silane surface linker are in principle prone to bond hydrolysis. Scattering, slope and curvature of the scattered data plots indicate that in fact two competing rupture mechanisms are observed.     

Bond rupture force measurement by means of a quartz resonator

Methods to measure the bond rupture force are considered. It is proposed to use a quartz resonator as an active element rather than simply a sensor. When the surface oscillation amplitude of an AT quartz resonator increases smoothly (rupture event scanning), a particle attached to the quartz surface is removed by inertial forces, and from their values it is easy to obtain the bond dissociation value. This procedure provides reliable measurements of the rupture force of about 10 pN. As the atomic force microscopy method, the rupture event scanning does not apply electromagnetic radiation, but has simpler instrumental set-up. The scanning requires minimum sample preparation, can be performed in various media (vacuum, air, liquid), and takes only a few minutes.     

Forced dissociation of a biomolecular complex under periodic and correlated random forcing

The dissociation of a biomolecular complex under the action of periodic and correlated random forcing is studied theoretically. The former is characterized by the period tau p and the latter by the correlation time tau r. The rupture rates are calculated by overdamped Langevin dynamics and three distinct regimes are identified for both cases by comparison to local relaxation time tau R and bond lifetime T. For periodic forcing, the adiabatic approximation cannot be applied in the regime tau p相似文献   

Functionalized self-assembled monolayers for measuring single molecule lectin carbohydrate interactions

The specific interactions between sugar-binding proteins (lectins) and their complementary carbohydrates mediate several complex biological functions. There is a great deal of interest in uncovering the molecular basis of these interactions. In this study, we demonstrate the use of an efficient one-step amination reaction strategy to fabricate carbohydrate arrays based on mixed self-assembled monolayers. These allow specific lectin carbohydrate interactions to be interrogated at the single molecule level via AFM. The force required to directly rupture the multivalent bonds between Concanavalin A (Con A) and mannose were subsequently determined by chemical force microscopy. The mixed self-assembled monolayer provides a versatile platform with active groups to attach a 1-amino-1-deoxy sugar or a protein (Con A) while minimizing non-specific adhesion enabling quick and reliable detection of rupture forces. By altering the pH of the environment, the aggregation state of Con A was regulated, resulting in different dominant rupture forces, corresponding to di-, tri- and multiple unbinding events. We estimate the value of the rupture force for a single Con A-mannose bond to be 95 ± 10 pN. The rupture force is consistent even when the positions of the binding molecules are switched. We show that this synthesis strategy in conjunction with a mixed SAM allows determination of single molecules bond with high specificity, and may be used to investigate lectin carbohydrate interactions in the form of carbohydrate arrays as well as lectin arrays.     

Adhesion from tethered ligand-receptor bonds with microsecond lifetimes

According to classical thermodynamics, biological ligand-receptor bonds should have a median lifetime of about 2 ms, and nearly half should have lifetimes of nanoseconds to microseconds. As a result, it is clear that many "weak" bonds are indispensable for cellular adhesion, signaling, and other critical events. However, the forces required to rupture such weak bonds and the adhesion they provide between surfaces are largely unknown because of their propensity to dissociate rapidly from a measuring probe. To measure such weak bond forces quantitatively, we followed nature's example of adhering surfaces with many weak ligand-receptor bonds. Analogously to how multiplicity promotes stronger adhesion between cellular membranes, multiple bonds created significant adhesion between model cellular surfaces. Specifically, we used an automated surface forces apparatus to measure the adhesion between complementary surfaces bearing dense populations of streptavidin receptors and flexible PEG tethers that each anchored a weakly binding ligand (HABA, or 2-(4-hydroxyphenylazo) benzoic acid). We show that this short-lived bond (<100 mus) leads to low forces of dissociation and only a small fraction being simultaneously bound. These results are significant because the HABA-streptavidin bond energy ( approximately 10.5kBT) is similar to the average found in nature (14.7kBT). The measurements exemplify how a single ligand-receptor bond may fall apart and rejoin many times before completing a cellular function yet can still exhibit strength in numbers.     

Measurement of the unwinding force of a DNA double helix

The review is devoted to measurement methods of bond rupture forces in complex biological molecules, namely, the unwinding forces of a DNA double helix. Mechanical methods not affecting electromagnetically a system under study, which is especially significant for biological systems, are considered. We describe two main methods: atomic force microscopy and rupture event scanning. The latter is a new method also based on the mechanical action but it has a much simpler instrumental implementation. The capabilities of both methods are compared and they are shown to be promising to investigate chemical bond rupture forces in biological systems. The application of these methods to study the strength of chemical bonds is associated with overcoming numerous technical difficulties in both performance of measurements themselves and chemical modification of conjugated surfaces. We demonstrate the applicability of these methods not only for fundamental studies of the strength of chemical bonds determining the stability and the related possibility of functioning of three-dimensional biomolecular complexes, but also for the design of biosensors based on the mechanical effect (quartz crystal microbalance, QCM), e.g., with an opportunity of rapid analysis of DNA.     

Single-molecule measurement of the strength of a siloxane bond

Increasing the mechanical stability of artificial polymer materials is an important task in materials science, and for this a profound knowledge of the critical mechanoelastic properties of its constituents is vital. Here, we use AFM-based single-molecule force spectroscopy measurements to characterize the rupture of a single silicon-oxygen bond in the backbone of polydimethylsiloxane as well as the force-extension behavior of this polymer. PDMS is not only a polymer used in a large variety of products but also an important model system for highly flexible polymers. In our experiments, we probe the entire relevant force range from low forces dominated by entropy up to the rupture of the covalent Si-O bonds in the polymer backbone at high forces. The resulting rupture-force histograms are investigated with microscopic models of bond rupture under load and are compared to density functional theory calculations to characterize the free-energy landscape of the Si-O bond in the polymer backbone.     

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 approximately 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 (approximately 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.     

Anomalously increased lifetimes of biological complexes at zero force due to the protein-water interface

A number of biological bonds show dramatically increased lifetimes at zero-force conditions, compared to lifetimes when even a small tensile force is applied to the ligand. The discrepancy is so great that it cannot be explained by the traditional receptor-ligand binding models. This generic phenomenon is rationalized here by considering the interaction of water with the receptor-ligand complex. It is argued that the water-protein interaction creates an energy barrier that prevents the ligand unbinding in the absence of the force. The properties of the interaction are such that even application of a relatively low force results in a dramatic drop of the bond lifetime due to the alteration of the water-receptor and water-ligand interaction network. The phenomenon is described by the presence of a second shallow interaction energy minimum for the bound ligand followed by a wide receptor-ligand dissociation barrier. The general analysis is applied quantitatively to the actin-myosin system, which demonstrates the gigantic drop of the bond lifetime at small forces and catch behavior (an increase in the lifetime) at moderate forces. The base hypothesis proposed to explain the small-force abnormal drop in the bond lifetime suggests that the majority of biological bonds may exhibit this phenomenon irrespectively whether they behave as slip or catch-slip bonds.     

On the detection of single bond ruptures in dynamic force spectroscopy by AFM

Force spectroscopy is a novel tool in physical chemistry and biophysics. This methodology is aimed at providing kinetic parameters of dissociation at a single-molecule level by rupturing molecular bonds subjected to different loading rates. One persistent problem in the implementation of this methodology is a question about the single-bond nature of the rupture events detected in experiments based on atomic force microscopy. Here we address this question by considering the probability that the nearly simultaneous rupture of two molecular bonds might appear as a single bond rupture in the experimental data, complicating the data analysis and contributing to systematic errors in the extracted kinetic parameters. An approximate analytical model predicts that such events might be common in experiments employing soft cantilever force sensors and short tethers to immobilize the interacting molecules. These findings are confirmed by a more elaborate numerical model providing valuable guidelines on performing single-molecule force spectroscopy experiments.     

Dynamic strength of the silicon-carbon bond observed over three decades of force-loading rates

The mechanical strength of individual Si-C bonds was determined as a function of the applied force-loading rate by dynamic single-molecule force spectroscopy, using an atomic force microscope. The applied force-loading rates ranged from 0.5 to 267 nN/s, spanning 3 orders of magnitude. As predicted by Arrhenius kinetics models, a logarithmic increase of the bond rupture force with increasing force-loading rate was observed, with average rupture forces ranging from 1.1 nN for 0.5 nN/s to 1.8 nN for 267 nN/s. Three different theoretical models, all based on Arrhenius kinetics and analytic forms of the binding potential, were used to analyze the experimental data and to extract the parameters fmax and D(e) of the binding potential, together with the Arrhenius A-factor. All three models well reproduced the experimental data, including statistical scattering; nevertheless, the three free parameters allow so much flexibility that they cannot be extracted unambiguously from the experimental data. Successful fits with a Morse potential were achieved with fmax = 2.0-4.8 nN and D(e) = 76-87 kJ/mol, with the Arrhenius A-factor covering 2.45 x 10(-10)-3 x 10(-5) s(-1), respectively. The Morse potential parameters and A-factor taken from gas-phase density functional calculations, on the other hand, did not reproduce the experimental forces and force-loading rate dependence.     

Dynamic strength of molecularly bonded surfaces

This study reports a theoretical analysis of the forced separation of two adhesive surfaces linked via a large number of parallel noncovalent bonds. To describe the bond kinetics, we implement a three-state reaction model with kinetic rates obtained from a simple integral expression of the mean first passage time for diffusive barrier crossing in a pulled-distance-dependent potential. We then compute the rupture force for the separation of adhesive surfaces at a constant rate. The results correspond well with a Brownian dynamics simulation of the same system. The separation rate relative to the intrinsic relaxation time of the bonds defines three loading regimes and the general dependence of the adhesion on kinetic or thermodynamic parameters of the bonds. In the equilibrium regime, the rupture force asymptotically approaches the equilibrium rupture force, which increases linearly with the equilibrium bond energy. In the near-equilibrium regime, the rupture force increases with the separation rate and increasingly correlates with the bond rupture barrier. In the far-from-equilibrium regime where rebinding is irrelevant, the rupture force varies linearly with the rupture barrier.     

Evidence of Splitting 1,2,3‐Triazole into an Alkyne and Azide by Low Mechanical Force in the Presence of Other Covalent Bonds

The cycloaddition reaction of an alkyne and azide to form a 1,2,3‐triazole is widely used in many areas. However, the stability of the triazole moiety under mechanical stress is unclear. To see if a triazole could be selectively split into an alkyne and azide in the presence of other typical covalent bonds, a mica surface functionalized with a molecule containing a triazole moiety in the middle and an activated ester at the end was prepared. An atomic force microscope (AFM) tip with amino groups on its surface was ramped over the mica surface at predefined locations, which could temporarily link the tip to the surface through amide bond formation. During retraction, the triazole or another bond in the linkage broke, and a force was recorded. The forces varied widely at different ramps from close to 0 pN to 860 pN due to nonspecific adhesions and to the inherent inconsistency of single bond rupture. If some of the forces were from triazole cycloreversion, there would be alkynes at the predefined ramping locations. The surface was reacted with an azide carboxylic acid followed by labeling with amino Au nanoparticles (AuNPs). AFM imaging revealed AuNPs at the predicted locations, which provided evidence that under certain conditions triazole could be split selectively in the presence of other bonds at forces below 860 pN.     

Off-center Mechanophore Activation in Block Copolymers

Block copolymers (BCPs) are used in numerous applications in modern materials science. Yet, like homopolymers, BCPs can undergo covalent bond scission when mechanically stressed (mechanochemistry), which could lead to unexpected consequences in such applications. BCPs’ heterogeneity may affect force transduction, perhaps changing force distribution and localization. To verify this, a gem-dichlorocyclopropane (gDCC) embedded linear chain is prepared and extended with a poly(methyl methacrylate) block. When stressed in solution, the mechanochemical ring-opening of gDCC is accelerated compared to homopolymers, even though the mechanophores are at the chain ends. Moreover, a higher mechanophore activation selectivity is obtained. These results indicate that mechanochemical response outside, and even far from the chain center is quite prominent in BCPs, and that forces along the polymer chain can efficiently activate multi-mechanophores regions, even when far from the polymer midchain.     

Calculation of normal vibrations as applied to the study of properties of inorganic compounds

Using the Morse potential and spectroscopic constants it has been shown for diatomic molecules that the force constant of the bond (Kq) is proportional to its dissociation energy (D) so that Kq can be regarded as a measure of the bond strength. An analysis of K_MA of a series of complexes clearly indicates the correlation between the force constants K_MA and the MA bond length, thermodynamic constants of the MA bond dissociation, and reaction rates of the MA bond rupture.     

C2 in a Box: Determining Its Intrinsic Bond Strength for the X1Σg+ Ground State

The intrinsic bond strength of C₂ in its ¹Σ_g⁺ ground state is determined from its stretching force constant utilizing MR‐CISD+Q(8,8), MR‐AQCC(8,8), and single‐determinant coupled cluster calculations with triple and quadruple excitations. By referencing the CC stretching force constant to its local counterparts of ethane, ethylene, and acetylene, an intrinsic bond strength half way between that of a double bond and a triple bond is obtained. Diabatic MR‐CISD+Q results do not change this. Confinement of C₂ and suitable reference molecules in a noble gas cage leads to compression, polarization, and charge transfer effects, which are quantified by the local CC stretching force constants and differences of correlated electron densities. These results are in line with two π bonds and a partial σ bond. Bond orders and bond dissociation energies of small hydrocarbons do not support quadruple bonding in C₂.     

Force and Stress along Simulated Dissociation Pathways of Cucurbituril-Guest Systems

The field of host-guest chemistry provides computationally tractable yet informative model systems for biomolecular recognition. We applied molecular dynamics simulations to study the forces and mechanical stresses associated with forced dissociation of aqueous cucurbituril-guest complexes with high binding affinities. First, the unbinding transitions were modeled with constant velocity pulling (steered dynamics) and a soft spring constant, to model atomic force microscopy (AFM) experiments. The computed length-force profiles yield rupture forces in good agreement with available measurements. We also used steered dynamics with high spring constants to generate paths characterized by a tight control over the specified pulling distance; these paths were then equilibrated via umbrella sampling simulations and used to compute time-averaged mechanical stresses along the dissociation pathways. The stress calculations proved to be informative regarding the key interactions determining the length-force profiles and rupture forces. In particular, the unbinding transition of one complex is found to be a stepwise process, which is initially dominated by electrostatic interactions between the guest's ammoniums and the host's carbonyl groups, and subsequently limited by the extraction of the guest's bulky bicyclooctane moiety; the latter step requires some bond stretching at the cucurbituril's extraction portal. Conversely, the dissociation of a second complex with a more slender guest is mainly driven by successive electrostatic interactions between the different guest's ammoniums and the host's carbonyl groups. The calculations also provide information on the origins of thermodynamic irreversibilities in these forced dissociation processes.