Rupture force of single supramolecular bonds in associative polymers by AFM at fixed loading rates

Atomic-force-microscopy-based single-molecule force spectroscopy (AFM-SMFS) was used to study the bond strength of self-complementary hydrogen-bonded complexes based on the 2-ureido-4[1H]-pyrimidinone (UPy) quadruple H-bond motif in hexadecane (HD). The unbinding force corresponding to single UPy-UPy dimers was investigated at a fixed piezo retraction rate in the nonequilibrium loading rate regime. The rupture force of bridging supramolecular polymer chains formed between UPy-functionalized substrates and AFM tips in the presence of a bis-UPy derivative was found to decrease with increasing rupture length. The rupture length was identified as the chain length of single, associating polymers, which allowed us to determine the number of supramolecular bonds (N) at rupture. The rupture force observed as a function of N was in quantitative agreement with the theory on uncooperative bond rupture for supramolecular linkages switched in a series. Hence, the value of the dimer equilibrium constant Keq=(1.3+/-0.5) x 10(9) M(-1), which is in good agreement with previously estimated values, was obtained by SMFS of supramolecular polymers at a single loading rate.     

Forced Kramers escape in single-molecule pulling experiments

The pulling-induced rupture of noncovalent bonds is studied by the overdamped Kramers theory with full account of a time-varying barrier. Mechanic pulling reduces the energy barrier and leads to loading-rate dependence of the rupture force F(u)(F(t)). Tested against Langevin dynamics, four distinct regimes are identified, including kinetic dominant, weak pulling, strong pulling, and mechanic pulling dominant. Asymptotic analyses show that F(u) approximately ln F(t) in weak pulling regime and becomes 1-(F(u)F(c)) approximately [ln(F(t))E(b)](23) in strong pulling regime. Kinetic informations such as activation energy E(b) and critical force F(c) were extracted from pulling experiments for biotin-streptavidin complex.     

Pattern-dependent tunable adhesion of superhydrophobic MnO2 nanostructured film

Tuning the adhesive force on a superhydrophobic MnO(2) nanostructured film was achieved by fabricating different patterns including meshlike, ball cactus-like, and tilted nanorod structures. The marvelous modulation range of the adhesive forces from 130 to nearly 0 μN endows these superhydrophobic surfaces with extraordinarily different dynamic properties of water droplets. This pattern-dependent adhesive property is attributed to the kinetic barrier difference resulting from the different continuity of the three-interface contact line. This finding will provide the general strategies for the adhesion adjustment on superhydrophobic surfaces.     

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   

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.     

Remote C-H bond functionalization reveals the distance-dependent isotope effect

Iodination of remote aryl C-H bonds has been achieved using palladium acetate as the catalyst and iodoacetate (IOAc) as the oxidant. Systematic kinetic isotope studies imply a mechanistic regime shift as the number of bonds separating the directing heteroatom and the target C-H bond increases. Both isotope and electronic effects observed in remote C-H bond activation are consistent with an electrophilic palladation pathway in which the initial palladation is slower than the C-H bond cleavage.     

Reactivity of chemisorbed oxygen atoms and their catalytic consequences during CH4-O2 catalysis on supported Pt clusters

Kinetic and isotopic data and density functional theory treatments provide evidence for the elementary steps and the active site requirements involved in the four distinct kinetic regimes observed during CH(4) oxidation reactions using O(2), H(2)O, or CO(2) as oxidants on Pt clusters. These four regimes exhibit distinct rate equations because of the involvement of different kinetically relevant steps, predominant adsorbed species, and rate and equilibrium constants for different elementary steps. Transitions among regimes occur as chemisorbed oxygen (O*) coverages change on Pt clusters. O* coverages are given, in turn, by a virtual O(2) pressure, which represents the pressure that would give the prevalent steady-state O* coverages if their adsorption-desorption equilibrium was maintained. The virtual O(2) pressure acts as a surrogate for oxygen chemical potentials at catalytic surfaces and reflects the kinetic coupling between C-H and O═O activation steps. O* coverages and virtual pressures depend on O(2) pressure when O(2) activation is equilibrated and on O(2)/CH(4) ratios when this step becomes irreversible as a result of fast scavenging of O* by CH(4)-derived intermediates. In three of these kinetic regimes, C-H bond activation is the sole kinetically relevant step, but occurs on different active sites, which evolve from oxygen-oxygen (O*-O*), to oxygen-oxygen vacancy (O*-*), and to vacancy-vacancy (*-*) site pairs as O* coverages decrease. On O*-saturated cluster surfaces, O*-O* site pairs activate C-H bonds in CH(4) via homolytic hydrogen abstraction steps that form CH(3) groups with significant radical character and weak interactions with the surface at the transition state. In this regime, rates depend linearly on CH(4) pressure but are independent of O(2) pressure. The observed normal CH(4)/CD(4) kinetic isotope effects are consistent with the kinetic-relevance of C-H bond activation; identical (16)O(2)-(18)O(2) isotopic exchange rates in the presence or absence of CH(4) show that O(2) activation steps are quasi-equilibrated during catalysis. Measured and DFT-derived C-H bond activation barriers are large, because of the weak stabilization of the CH(3) fragments at transition states, but are compensated by the high entropy of these radical-like species. Turnover rates in this regime decrease with increasing Pt dispersion, because low-coordination exposed Pt atoms on small clusters bind O* more strongly than those that reside at low-index facets on large clusters, thus making O* less effective in H-abstraction. As vacancies (*, also exposed Pt atoms) become available on O*-covered surfaces, O*-* site pairs activate C-H bonds via concerted oxidative addition and H-abstraction in transition states effectively stabilized by CH(3) interactions with the vacancies, which lead to much higher turnover rates than on O*-O* pairs. In this regime, O(2) activation becomes irreversible, because fast C-H bond activation steps scavenge O* as it forms. Thus, O* coverages are set by the prevalent O(2)/CH(4) ratios instead of the O(2) pressures. CH(4)/CD(4) kinetic isotope effects are much larger for turnovers mediated by O*-* than by O*-O* site pairs, because C-H (and C-D) activation steps are required to form the * sites involved in C-H bond activation. Turnover rates for CH(4)-O(2) reactions mediated by O*-* pairs decrease with increasing Pt dispersion, as in the case of O*-O* active structures, because stronger O* binding on small clusters leads not only to less reactive O* atoms, but also to lower vacancy concentrations at cluster surfaces. As O(2)/CH(4) ratios and O* coverages become smaller, O(2) activation on bare Pt clusters becomes the sole kinetically relevant step; turnover rates are proportional to O(2) pressures and independent of CH(4) pressure and no CH(4)/CD(4) kinetic isotope effects are observed. In this regime, turnover rates become nearly independent of Pt dispersion, because the O(2) activation step is essentially barrierless. In the absence of O(2), alternate weaker oxidants, such as H(2)O or CO(2), lead to a final kinetic regime in which C-H bond dissociation on *-* pairs at bare cluster surfaces limit CH(4) conversion rates. Rates become first-order in CH(4) and independent of coreactant and normal CH(4)/CD(4) kinetic isotope effects are observed. In this case, turnover rates increase with increasing dispersion, because low-coordination Pt atoms stabilize the C-H bond activation transition states more effectively via stronger binding to CH(3) and H fragments. These findings and their mechanistic interpretations are consistent with all rate and isotopic data and with theoretical estimates of activation barriers and of cluster size effects on transition states. They serve to demonstrate the essential role of the coverage and reactivity of chemisorbed oxygen in determining the type and effectiveness of surface structures in CH(4) oxidation reactions using O(2), H(2)O, or CO(2) as oxidants, as well as the diversity of rate dependencies, activation energies and entropies, and cluster size effects that prevail in these reactions. These results also show how theory and experiments can unravel complex surface chemistries on realistic catalysts under practical conditions and provide through the resulting mechanistic insights specific predictions for the effects of cluster size and surface coordination on turnover rates, the trends and magnitude of which depend sensitively on the nature of the predominant adsorbed intermediates and the kinetically relevant steps.     

Correction of systematic errors in single-molecule force spectroscopy with polymeric tethers by atomic force microscopy

Single-molecule force spectroscopy has become a valuable tool for the investigation of intermolecular energy landscapes for a wide range of molecular associations. Atomic force microscopy (AFM) is often used as an experimental technique in these measurements, and the Bell-Evans model is commonly used in the statistical analysis of rupture forces. Most applications of the Bell-Evans model consider a constant loading rate of force applied to the intermolecular bond. The data analysis is often inconsistent because either the probe velocity or the apparent loading rate is being used as an independent parameter. These approaches provide different results when used in AFM-based experiments. Significant variations in results arise from the relative stiffness of the AFM force sensor in comparison with the stiffness of polymeric tethers that link the molecules under study to the solid surfaces. An analytical model presented here accounts for the systematic errors in force-spectroscopy parameters arising from the nonlinear loading induced by polymer tethers. The presented analytical model is based on the Bell-Evans model of the kinetics of forced dissociation and on the asymptotic models of tether stretching. The two most common data reduction procedures are analyzed, and analytical expressions for the systematic errors are provided. The model shows that the barrier width is underestimated and that the dissociation rate is significantly overestimated when force-spectroscopy data are analyzed without taking into account the elasticity of the polymeric tether. Systematic error estimates for asymptotic freely jointed chain and wormlike chain polymer models are given for comparison. The analytical model based on the asymptotic freely jointed chain stretching is employed to analyze and correct the results of the double-tether force-spectroscopy experiments of disjoining "hydrophobic bonds" between individual hexadecane molecules that are covalently tethered via poly(ethylene glycol) linkers of different lengths to the substrates and to the AFM probes. Application of the correction algorithm decreases the spread of the data from the mean value, which is particularly important for measurements of the dissociation rate, and increases the barrier width to 0.43 nm, which might be indicative of the theoretically predicted hydrophobic dewetting.     

Mechanisms of reductive eliminations in square planar Pd(II) complexes: nature of eliminated bonds and role of trans influence

The trans influence of various phosphine ligands (L) in direct as well as dissociative reductive elimination pathways yielding CH(3)CH(3) from Pd(CH(3))(2)L(2) and CH(3)Cl from Pd(CH(3))(Cl)L(2) has been quantified in terms of isodesmic reaction energy, E(trans), using the MPWB1K level of density functional theory. In the absence of a large steric effect, E(trans) correlated linearly with the activation barrier (E(act)) of both direct and dissociation pathways. The minimum of molecular electrostatic potential (V(min)) at the lone pair region of phosphine ligands has been used to assess their electron donating power. E(trans) increased linearly with an increase in the negative V(min) values. Further, the nature of bonds that are eliminated during reductive elimination have been analyzed in terms of AIM parameters, viz. electron density (ρ(r)), Laplacian of the electron density (?(2)ρ(r)), total electron energy density (H(r)), and ratio of potential and kinetic electron energy densities (k(r)). Interestingly, E(act) correlated inversely with the strength of the eliminated metal-ligand bonds measured in terms of the bond length or the ρ(r). Analysis of H(r) showed that elimination of the C-C/C-Cl bond becomes more facile when the covalent character of the Pd-C/Pd-Cl bond increases. Thus, AIM details clearly showed that the strength of the eliminated bond is not the deciding factor for the reductive elimination but the nature of the bond, covalent or ionic. Further, a unified picture showing the relationship between the nature of the eliminated chemical bond and the tendency of reductive elimination is obtained from the k(r) values: the E(act) of both direct and dissociative mechanisms for the elimination of CH(3)CH(3) and CH(3)Cl decreased linearly when the sum of k(r) at the cleaved bonds showed a more negative character. It means that the potential electron energy density dominates over the kinetic electron energy density when the bonds (Pd-C/Pd-Cl) become more covalent and the eliminated fragments attain more radical character leading to the easy formation of C-C/C-Cl bond.     

Influences of linkage stiffness on rupture rate in single-molecule pulling experiments

In the dissociation of a noncovalent biomolecular bond by external pulling, the bonded site is often connected to the force-acting site by a linkage. The role of the linkage stiffness on the rupture of a ligand-receptor complex under constant force is investigated by overdamped Langevin dynamics for the elastically coupled ligand and probe. The effects on the bond lifetime include effective ligand diffusivity, force fluctuations, and violation of adiabatic condition. The rupture rate declines with increasing linkage stiffness. For soft linkage, the effect associated with the spring and probe can be ignored, and the true rupture rate can be extracted. On the other hand, for stiff linkage, the diffusivity of the probe has to be accounted for and, thus, leads to a lower rupture rate, depending on the diffusivity ratio between the probe and ligand. Nevertheless, the energy barrier height can be reasonably extracted by constant pulling experiments, regardless of the linkage stiffness.     

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.     

Investigating the specific interactions between carbonic anhydrase and a sulfonamide inhibitor by single-molecule force spectroscopy

In this communication, we report on the interaction landscape of an active site-specific enzyme-inhibitor complex by single-molecule force spectroscopy. Electrostatic immobilization was employed to orient a carbonic anhydrase enzyme on a positively charged surface so its active site is pointing upward. This approach to immobilization effectively increases the number of specific interactions measured between the zinc ion of the active site on carbonic anhydrase and a sulfonamide inhibitor tethered to an atomic force microscope (AFM) probe. Further, it reduces the time required for data collection and thereby minimizes the possible mechanical damage to the probe and contamination of the enzyme surface. The rupture force measured at various loading rates is interpreted in terms of a single energy barrier for the carbonic anhydrase enzyme-sulfonamide inhibitor complex from which the kinetic and thermodynamic parameters were estimated on the basis of microscopic models and were compared to the Bell-Evans model. The dissociation rate for the enzyme-inhibitor complex was found to be significantly faster (~35 times) than the natural spontaneous dissociation rate.     

Polypeptide friction and adhesion on hydrophobic and hydrophilic surfaces: a molecular dynamics case study

Using all-atomistic MD simulations including explicit water, the mobility and adhesion of a mildly hydrophobic single polypeptide chain adsorbed on hydrophobic and hydrophilic diamond surfaces is investigated by application of lateral and vertical pulling forces. Forced motion on the hydrophilic surface exhibits stick-slip due to breaking and reformation of hydrogen bonds; in contrast, on the hydrophobic surface, the motion is smooth. By carefully tuning the driving force magnitude, the linear-response regime is reached on a hydrophobic surface and equilibrium values for mobility and adhesive strength are obtained. On the hydrophilic surface, on the other hand, slow hydrogen-bond kinetics prevents equilibration and only upper bounds for adhesion force and mobility can be estimated. Whereas the desorption force is rather comparable on the two surfaces and differs at most by a factor of 2, the mobility on the hydrophilic surface is at least 30-fold reduced compared to the hydrophobic one. A simple model based on a single particle diffusing in a corrugated potential landscape suggests that cooperativity is rather limited and that the small mobility on a hydrophilic surface can be rationalized in terms of incoherently moving monomers. The experimentally well-known peptide mobility in bulk water is quantitatively reproduced in our simulations, which serves as a sensitive test on our methodology employed.     

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.     

Nanoscale high-frequency contact mechanics using an AFM tip and a quartz crystal resonator

The transmission of high-frequency shear stress through a microscopic contact between an AFM tip and an oscillating quartz plate was measured as a function of vertical pressure, amplitude, and surface properties by monitoring the MHz component of the tip's deflection. For dry surfaces, the transmission of shear stress is proportional to the vertical load across the contact. This provides a measure of the forces of adhesion between the substrate and the tip. When stretching soft polymeric fibers created by pulling on the surface of a pressure sensitive adhesive, the transmitted shear stress decreased linearly with extension over the entire range of pulling. This contrasts with the static adhesive force, which remained about constant until it discontinuously dropped at the point of rupture.     

On the possibility of detecting low barrier hydrogen bonds with kinetic measurements

Recent experimental evidence has pointed to the possible presence of a short, strong hydrogen bond in the enzyme-substrate transition states in some biochemical reactions. To date, most experimental measures of these short, strong hydrogen bonds have monitored their equilibrium properties. In this work we show that kinetic measurements can also be used to detect the presence of short, strong hydrogen bonds. In particular, we find nontrivial differences among rate constant ratios of protonated to deuterated hydrogen bonds between strong and weak hydrogen bonds for proton transfer between donor-acceptor sites. We quantify this kinetic isotope effect by performing dynamical calculations of these rate constants by computing reactive flux through a dividing surface. This reactive flux is computed by evolving trajectories on an effective quantum mechanical potential energy surface.     

Probing multivalent interactions in a synthetic host-guest complex by dynamic force spectroscopy

Multivalency is present in many biological and synthetic systems. Successful application of multivalency depends on a correct understanding of the thermodynamics and kinetics of this phenomenon. In this Article, we address the stability and strength of multivalent bonds with force spectroscopy techniques employing a synthetic adamantane/β-cyclodextrin model system. Comparing the experimental findings to theoretical predictions for the rupture force and the kinetic off-rate, we find that when the valency of the complex is increased from mono- to di- to trivalent, there is a transition from quasi-equilibrium, with a constant rupture force of 99 pN, to a kinetically dependent state, with loading-rate-dependent rupture forces from 140 to 184 pN (divalent) and 175 to 210 pN (trivalent). Additional binding geometries, parallel monovalent ruptures, single-bound divalent ruptures, and single- and double-bound trivalent ruptures are identified. The experimental kinetic off-rates of the multivalent complexes show that the stability of the complexes is significantly enhanced with the number of bonds, in agreement with the predictions of a noncooperative multivalent model.     

Dwell time analysis of a single-molecule mechanochemical reaction

Force-clamp spectroscopy is a novel technique for studying mechanochemistry at the single-bond level. Single disulfide bond reduction events are accurately detected as stepwise increases in the length of polyproteins that contain disulfide bonds and that are stretched at a constant force with the cantilever of an atomic force microscope (AFM). The kinetics of this reaction has been measured from single-exponential fits to ensemble averages of the reduction events. However, exponential fits are notoriously ambiguous to use in cases of kinetic data showing multiple reaction pathways. Here we introduce a dwell time analysis technique, of widespread use in the single ion channel field, that we apply to the examination of the kinetics of reduction of disulfide bonds measured from single-molecule force-clamp spectroscopy traces. In this technique, exponentially distributed dwell time data is plotted as a histogram with a logarithmic time scale and a square root ordinate. The advantage of logarithmic histograms is that exponentially distributed dwell times appear as well-defined peaks in the distribution, greatly enhancing our ability to detect multiple kinetic pathways. We apply this technique to examine the distribution of dwell times of 4488 single disulfide bond reduction events measured in the presence of two very different kinds of reducing agents: tris-(2-carboxyethyl)phosphine hydrochloride (TCEP) and the enzyme thioredoxin (TRX). A different clamping force is used for each reducing agent to obtain distributions of dwell times on a similar time scale. In the case of TCEP, the logarithmic histogram of dwell times showed a single peak, corresponding to a single reaction mechanism. By contrast, similar experiments done with TRX showed two well-separated peaks, marking two distinct modes of chemical reduction operating simultaneously. These experiments demonstrate that dwell time analysis techniques are a powerful approach to studying chemical reactions at the single-molecule level.     

Failure of elastomeric polymers due to rate dependent bond rupture

A new cohesive zone model is developed in order to study the mechanisms of adhesive and cohesive failures of soft rubbery materials. The fracture energy is estimated here using a strategy similar to that of Lake and Thomas (LT) by considering the dissipation of stored elastic energy followed by the extension and relaxation of polymer chains. The current model, however, departs from that of LT in that the force needed to break an interfacial bond does not have a fixed value; instead, it depends on the thermal state of the system and the rate at which the force is transmitted to the bond. While the force required to rupture a chain is set by the rules of thermomechanically activated bond dissociation kinetics, extension of a polymer chain is modeled within both the linear and nonlinear models of chain elasticity. Closed form asymptotic solutions are obtained for the dependence of crack propagation speed on the energy release rate, which are valid in two regimes: (I) slow crack velocity or short relaxation time for bond dissociation; (II) fast crack velocity or long relaxation time for bond dissociation. The rate independent and the zero temperature limit of this theory correctly reduces to the fracture model of LT. Detailed comparisons are made with a previous work by Chaudhury et al. which carried out an approximate analysis of the same problem.     

QM/MM studies of the enzyme-catalyzed dechlorination of 4-chlorobenzoyl-CoA provide insight into reaction energetics

The conversion of 4-chlorobenzoyl-CoA to 4-hydroxybenzoyl-CoA catalyzed by 4-chlorobenzoyl-CoA dehalogenase is investigated using combined QM/MM approaches. The calculated potential of mean force at the PM3/CHARMM level supports the proposed nucleophilic aromatic substitution mechanism. In particular, a Meisenheimer intermediate was found, stabilized by hydrogen bonds between the benzoyl carbonyl of the ligand and two backbone amide NHs at positions 64 and 114. Mutation of Gly113 to Ala significantly increases the barrier by disrupting the hydrogen bond with the Gly114 backbone. The formation of the Meisenheimer complex is accompanied by significant charge redistribution and structural changes in the substrate benzoyl moiety, consistent with experimental observations. Theoretical results suggest that the reaction rate is limited by the formation of the Meisenheimer complex, rather than by its decomposition. A kinetic model based on the calculated free energy profile is found to be consistent with the experimental time course data.