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.     

Influence of pulling handles and device stiffness in single-molecule force spectroscopy

In single-molecule force spectroscopy, individual molecules and complexes are often stretched by pulling devices via intervening molecular handles. Accurate interpretation of measurements from such experiments in terms of the underlying energy landscape, defined by activation barriers and intrinsic rates of transition, relies on our understanding, and proper theoretical treatment, of the effects of the pulling device and handle. Here, we present a framework based on Kramers' theory that elucidates the dependence of measured rupture forces and rates on the pulling device stiffness and attributes of the handle, contour length and persistence length. We also introduce a simple analytic model that improves prediction of activation barriers and intrinsic rates for all device stiffnesses and handle properties, thus allowing for a more reliable interpretation of experiments. Our analyses also suggests intuitive ways of displaying the measured force spectra for proper prognosis of device and handle effects and provides the range of device and handle attributes over which these effects can be neglected.     

Springs and speeds in free energy reconstruction from irreversible single-molecule pulling experiments

The nonequilibrium work relation allows for the calculation of equilibrium free energy differences between states based on the exponential average of accumulated work from irreversible transitions. Here, we compare two distinct approaches of calculating free energy surfaces from unidirectional single-molecule pulling experiments: the stiff spring approximation and the Hummer-Szabo method. First, we perform steered molecular dynamics simulations to mechanically stretch the model peptide deca-alanine using harmonic potentials with different spring stiffnesses and at various constant pulling velocities. We then calculate free energy surfaces based on the two methods and their variants, including the first and second cumulant expansion of the exponentially weighted work and the Gaussian position approximation for the delta function in Hummer and Szabo's expression. We find that with large harmonic force constants, the second cumulant expansion performs well in conjunction with either the stiff spring approximation or the Hummer-Szabo method. When interpreting dynamic force spectroscopy (pullings at different speeds), the second cumulant expansion of the stiff spring approximation performs the best when pulling velocities are similar, but variants of the Hummer-Szabo perform the best when they are spread over a large spectrum. While these conclusion are not definitive for all systems, the insights should prove useful for scientists interpreting nonequilibrium pulling experiments.     

Photobleaching pathways in single-molecule FRET experiments

To acquire accurate structural and dynamical information on complex biomolecular machines using single-molecule fluorescence resonance energy transfer (sm-FRET), a large flux of donor and acceptor photons is needed. To achieve such fluxes, one may use higher laser excitation intensity; however, this induces increased rates of photobleaching. Anti-oxidant additives have been extensively used for reducing acceptor's photobleaching. Here we focus on deciphering the initial step along the photobleaching pathway. Utilizing an array of recently developed single-molecule and ensemble spectroscopies and doubly labeled Acyl-CoA binding protein and double-stranded DNA as model systems, we study these photobleaching pathways, which place fundamental limitations on sm-FRET experiments. We find that: (i) acceptor photobleaching scales with FRET efficiency, (ii) acceptor photobleaching is enhanced under picosecond-pulsed (vs continuous-wave) excitation, and (iii) acceptor photobleaching scales with the intensity of only the short wavelength (donor) excitation laser. We infer from these findings that the main pathway for acceptor's photobleaching is through absorption of a short wavelength photon from the acceptor's first excited singlet state and that donor's photobleaching is usually not a concern. We conclude by suggesting the use of short pulses for donor excitation, among other possible remedies, for reducing acceptor's photobleaching in sm-FRET measurements.     

Linker dependent bond rupture force measurements in single-molecule junctions

We use a modified conducting atomic force microscope to simultaneously probe the conductance of a single-molecule junction and the force required to rupture the junction formed by alkanes terminated with four different chemical link groups which vary in binding strength and mechanism to the gold electrodes. Molecular junctions with amine, methylsulfide, and diphenylphosphine terminated molecules show clear conductance signatures and rupture at a force that is significantly smaller than the measured 1.4 nN force required to rupture the single-atomic gold contact. In contrast, measurements with a thiol terminated alkane which can bind covalently to the gold electrode show conductance and force features unlike those of the other molecules studied. Specifically, the strong Au-S bond can cause structural rearrangements in the electrodes, which are accompanied by substantial conductance changes. Despite the strong Au-S bond and the evidence for disruption of the Au structure, the experiments show that on average these junctions also rupture at a smaller force than that measured for pristine single-atom gold contacts.     

Extraction of kinetic information from single-molecule experiments.

We discuss two possible approaches for extracting kinetic information from single-molecule experiments. The first approach is based on computing correlation functions from measured fluorescence signals, and the second on studying the statistics of on and off times of the same fluorescence signal. We show that in both cases it is possible to extract kinetic information about the nature of intramolecular fluctuations of the single molecule. We show that for single-molecule kinetics the intramolecular fluctuations produce stochastic memory effects which lead to new dynamic features that do not exist in traditional chemical kinetics. In particular, we investigate a new type of chemical oscillations in correlation functions observed experimentally by Edman and Rigler (Proc. Natl. Acad. Sci. USA 2000, 97, 8266).     

Estimating equilibrium ensemble averages using multiple time slices from driven nonequilibrium processes: theory and application to free energies, moments, and thermodynamic length in single-molecule pulling experiments

Recently discovered identities in statistical mechanics have enabled the calculation of equilibrium ensemble averages from realizations of driven nonequilibrium processes, including single-molecule pulling experiments and analogous computer simulations. Challenges in collecting large data sets motivate the pursuit of efficient statistical estimators that maximize use of available information. Along these lines, Hummer and Szabo developed an estimator that combines data from multiple time slices along a driven nonequilibrium process to compute the potential of mean force. Here, we generalize their approach, pooling information from multiple time slices to estimate arbitrary equilibrium expectations. Our expression may be combined with estimators of path-ensemble averages, including existing optimal estimators that use data collected by unidirectional and bidirectional protocols. We demonstrate the estimator by calculating free energies, moments of the polymer extension, the thermodynamic metric tensor, and the thermodynamic length in a model single-molecule pulling experiment. Compared to estimators that only use individual time slices, our multiple time-slice estimators yield substantially smoother estimates and achieve lower variance for higher-order moments.     

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.     

Adsorption of polyelectrolyte versus surface charge: in situ single-molecule atomic force microscopy experiments on similarly, oppositely, and heterogeneously charged surfaces

We have studied the effect of the pH and surface charge of mica on the adsorption of the positively charged weak polyelectrolyte (PE) poly(2-vinylpyridine) (P2VP) using atomic force microscopy (AFM) single-molecule experiments. These AFM experiments were performed in situ directly under aqueous media. If the mica's surface and the PE are oppositely charged (pH > 3), the PE forms a flat adsorbed layer of two-dimensionally (2D) equilibrated self-avoiding random walk coils. The adsorbed layer's structure remains almost unchanged if the pH is decreased to pH 3 (the mica's surface is weakly charged). At pH 2 (the mica surface is decorated by spots of different electrical charges), the polyelectrolyte chains take the form of a 2D compressed coil. In this pH range, at an increased P2VP concentration in solution, the PE segments preferentially adsorb onto the top of previously adsorbed segments, rather than onto an unoccupied surface. We explain this behavior as being caused by the heterogeneous character of the charged surface and the competitive adsorption of hydronium ions. The further increase of polymer concentration results in a complete coverage of the mica substrate and the charge overcompensation by P2VP chains adsorbed on the similarly charged substrate, due to van der Waals forces.     

Prompt gamma as a fluence rate monitor in neutron beam experiments

An accurate measurement of the neutron lifetime requires a determination of neutron fluence rate to an accuracy of a few tenths of a percent. The¹⁰B(n,)⁷ Li reaction offers the possibility of achieving this uncertainty. The thermal cross section is large and its departure from 1/v behavior is about 3 parts in 10000. The principal alpha branch is to the first excited state of⁷Li which then decays by emission of a 478 keV gamma ray. The measurement of the gamma branch can be made with boron samples that totally absorb thermal neutrons, allowing greater sensitivity and eliminating the uncertainty of target thickness. The absolute efficiency of the gamma detector can be determined by an alpha-gamma coincidence technique. Preliminary investigations of this method are presented with a discussion of the problems that must be overcome to achieve the desired uncertainty.Work supported in part by the Department of Energy     

Determination of nucleation rate in polymers using isothermal crystallization experiments and computer simulation

Within the frame of overall kinetics of crystallization, polymer crystallization is characterized by only three parameters: the initial density of potential nucleiN ₀, their activation frequencyq and the growth rateG. The growth rateG is rather easy to measure, whereas the nucleation parameters are generally unknown. Our purpose is to determine bothN ₀ andq using experimental isothermal two-dimensional crystallizations and computer simulation. Both these parameters are deduced from the rate of appearance of spherulites expressed as a function of the transformed surface fraction. The activation times of the spherulites are deduced from the shape of the boundaries between spherulites at the end of the transformation. When the growth rateG is known, the evolution of the transformed surface fraction is rebuilt using a computer simulation, so that only one observation of the final stage of the crystallization is needed.     

Dependence of single-molecule conductance on molecule junction symmetry

The symmetry of a molecule junction has been shown to play a significant role in determining the conductance of the molecule, but the details of how conductance changes with symmetry have heretofore been unknown. Herein, we investigate a naphthalenedithiol single-molecule system in which sulfur atoms from the molecule are anchored to two facing gold electrodes. In the studied system, the highest single-molecule conductance, for a molecule junction of 1,4-symmetry, is 110 times larger than the lowest single-molecule conductance, for a molecule junction of 2,7-symmetry. We demonstrate clearly that the measured dependence of molecule junction symmetry for single-molecule junctions agrees with theoretical predictions.     

Origins of blinking in single-molecule Raman spectroscopy

We observe spectral and intensity fluctuations in Raman scattering from single molecules of 4-mercaptopyridine (4-Mpy) adsorbed on textured silver surfaces. We present evidence that the root cause of these fluctuations is thermal. Analysis of the spectra shows that in some cases the spectral changes are associated with molecular reorientation and in others with chemical reactions of the 4-Mpy. Analogous surfaces fully covered with 4-Mpy exhibit similar behavior, indicating that monolayer Raman spectra are dominated by a few molecules at most.     

Bond rupture in highly drawn nylon 6 fibers influence of strain rate on radical concentration and permanent deformation

Summary In high-drawn nylon 6 fibers the radical concentration caused by the rupture of the tie molecules was measured by ESR at different strains and strain rates, viz. 2.5-500% min^–1.The spectral shape of the radical was temperature-dependent. This was tentatively explained from the fact that the -methylene protons of the secondary radical of nylon 6, (-CO-NH-(aHa-CoH2a) stop rotating at liquid nitrogen temperature.Furthermore the radical concentration depends on the strain rate, and consequently on time, which is explained by assuming that the tie molecules have a length distribution. So it follows that the process is of a viscoelastic nature and has little to do with thermally activated bond rupture. The assumption that the tie molecules have a length distribution is also supported by the value of the elastic modulus which, in contrast with what is sometimes assumed (28), is already accounted for by the relatively few taut tie molecules.Permanent deformation which, like chain rupture also an irreversible process, has been measured as a function of strain and strain rate. Roughly, a linear correlation seems to be present between the number of radicals and the magnitude of the permanent deformation.

---

Zusammenfassung In hochverstreckten Nylon-6-Fasern wurde die durch das Zerreißen von Molekülketten entstandene Radikalkonzentration mit Hilfe von ESR bei einer unterschiedlichen Dehnung und bei Dehnungsgeschwindigkeiten zwischen 2,5 und 500% min^–1 gemessen. Die Form des Radikalspektrums war temperaturabhängig. Dies ließ sich aus der Tatsache erklären, daß die -Methylenprotonen des sekundären Radikals von Nylon 6, (-CO-NH-CH_ga-CßH₂), bei der Temperatur von flüssigem Stickstoff zu rotieren aufhören.Weiter ist die Radikalkonzentration von der Dehnungsgeschwindigkeit und somit von der Zeit abhängig. Dies konnte aus der Annahme erklärt werden, daß die Tie-Moleküle eine Längenverteilung haben.So folgt, daß der Prozeß viskoelastischer Natur ist und er wenig mit thermisch aktivierter Bindungsspaltung zu tun hat. Das Vorhandensein einer Längenverteilung für die Tie-Moleküle wird auch durch den Wert des elastischen Moduls unterstützt, der anders, als manchmal angenommen wird (28), schon aus den relativ wenig gespannten Verbindungsmolekülen erklärt werden kann.Die bleibende Deformation, ebenso wie die Kettenspaltung ein irreversibler Prozeß, wurde als Funktion von Dehnung und Dehnungsgeschwindigkeit gemessen. Annähernd gibt es eine lineare Korrelation . zwischen der Radikalkonzentration und der Größe der bleibenden Deformation.

---

---

With 6 figures 2 tables     

Analysis of single-molecule dynamics in liquid HF

The center-of-mass velocity autocorrelation function of liquid HF is examined by means of a velocity field approach, originally developed for monatomic liquids and subsequently tested for liquid water. The basic ingredients of the approach (the wavevector-dependent current correlations) are evaluated by computer simulations in a model HF system using a recently developed intermolecular potential. The theory is found to reproduce the relevant features of self-dynamics in HF. The main advantage of the approach is the decomposition of single-molecule motion into longitudinal and transverse contributions, which provides information clarifying the origin of the peculiarities of HF dynamics. A comparison with the results for H₂O is presented, with the aim of stressing the different behavior of these two hydrogen-bonded systems.