Identifying Multiple Populations from Single‐Molecule Lifetime Distributions

A major advantage of single‐molecule methods over ensemble‐averaging techniques involves the ability to characterize heterogeneity through the identification of multiple molecular populations. It can be challenging, however, to determine absolute values of dynamic parameters (and to relate these values to those determined from a conventional method) because characteristic timescales of various populations may vary over many orders of magnitude, and under a given set of experimental conditions instrumental sensitivity to various populations may be unequal. Using data obtained from the single‐molecule tracking microscopy of fibrinogen protein adsorption and desorption, it is shown that by performing a combined analysis of molecular trajectories obtained using a range of acquisition times, it is possible to extract quantitative absolute values of multiple population fractions and residence times (with well‐defined uncertainties), even when these values span many orders of magnitude. In particular, as many as six distinct populations are rigorously identified, exhibiting characteristic timescales that vary over nearly three orders of magnitude with population fractions as small as one part in a thousand. This approach will lead to better comparability between single‐molecule experiments and may be useful in connecting single‐molecule to ensemble‐averaged observations.     

Power-law blinking in the fluorescence of single organic molecules.

The blinking behavior of perylene diïmide molecules is investigated at the single‐molecule level. We observe long‐time scale blinking of individual multi‐chromophoric complexes embedded in a poly(methylmethacrylate) matrix, as well as for the monomeric dye absorbed on a glass substrate at ambient conditions. In both these different systems, the blinking of single molecules is found to obey analogous power‐law statistics for both the on and off periods. The observed range for single‐molecular power‐law blinking extends over the full experimental time window, covering four orders of magnitude in time and six orders of magnitude in probability density. From molecule to molecule, we observe a large spread in off‐time power‐law exponents. The distributions of off‐exponents in both systems are markedly different whereas both on‐exponent distributions appear similar. Our results are consistent with models that ascribe the power‐law behavior to charge separation and (environment‐dependent) recombination by electron tunneling to a dynamic distribution of charge acceptors. As a consequence of power‐law statistics, single molecule properties like the total number of emitted photons display non‐ergodicity.     

Effects of solute-solvent proton exchange on polypeptide chain dynamics: a constant-pH molecular dynamics study

A method for performing implicit-solvent molecular dynamics simulations at constant pH was applied to a pentapeptide acetyl-Ala-Asp-Ala-Lys-Ala-amide at pH 4. As a reference, molecular dynamics simulations were done for the same peptide with two variants of its fixed protonation patterns expected to dominate at pH 4, i.e., with a protonated and a deprotonated side chain of the Asp residue and the protonated Lys residue in both cases. The dynamic trajectories of the peptide were used to discuss the problem of the significance of the solute-solvent proton exchange phenomena for the dynamics and structural distributions of the polypeptide chain. The Asp-Lys distance was used as a probe of the overall molecular structure of the investigated pentapeptide. To characterize the dynamics, distributions of the "waiting" times for a transition from a "short" distance conformation to a "long" distance conformation were constructed, based on the generated molecular dynamics trajectories. We show that the relaxation time for the transitions, derived from the constant-pH simulations, is very close to the relaxation time characterizing a permanently protonated molecule, although the average protonation probability of the short-distance conformation is close to zero. However, the distribution of the Asp-Lys distances obtained from constant-pH simulations cannot be reproduced as a linear combination of the distributions resulting from the simulations with fixed protonation states.     

Molecular weight dependence of emission intensity and emitting sites distribution within single conjugated polymer molecules

We investigated exciton migration, trapping and emission processes occurring within a single conjugated polymer molecule by means of superresolution fluorescence localization microscopy. This methodology allowed us to locate the spatial distribution of emitting sites within single chains with nanometre precision. The study was done on individual poly[2-methoxy-5-(2'-ethyl-hexyloxy)-1,4-phenylene vinylene] (MEH-PPV) molecules with average molecular weights ranging from 215,000 to 1,440,000 and with narrow weight distributions. We found that the mean emission intensity increases proportionally to the polymer molecular weight. The localization experiments suggest that the emitting sites are distributed nearly uniformly within a single chain and that the sites are on average 10 nm apart, irrespective of the molecular weight of the polymer. Furthermore, spatial contours formed by all the combined emitting sites within one chain show elongated shapes, in agreement with a rod-like structure of MEH-PPV in a collapsed state.     

Identifying mechanisms of interfacial dynamics using single-molecule tracking

The "soft" (i.e., noncovalent) interactions between molecules and surfaces are complex and highly varied (e.g., hydrophobic, hydrogen bonding, and ionic), often leading to heterogeneous interfacial behavior. Heterogeneity can arise either from the spatial variation of the surface/interface itself or from molecular configurations (i.e., conformation, orientation, aggregation state, etc.). By observing the adsorption, diffusion, and desorption of individual fluorescent molecules, single-molecule tracking can characterize these types of heterogeneous interfacial behavior in ways that are inaccessible to traditional ensemble-averaged methods. Moreover, the fluorescence intensity or emission wavelength (in resonance energy transfer experiments) can be used to track the molecular configuration and simultaneously directly relate this to the resulting interfacial mobility or affinity. In this feature article, we review recent advances involving the use of single-molecule tracking to characterize heterogeneous molecule-surface interactions including multiple modes of diffusion and desorption associated with both internal and external molecular configuration, Arrhenius-activated interfacial transport, spatially dependent interactions, and many more.     

Angular intensity distribution of a molecular oxygen beam scattered from a graphite surface

The scattering of the oxygen molecule from a graphite surface has been studied using a molecular beam scattering technique. The angular intensity distributions of scattered oxygen molecules were measured at incident energies from 291 to 614 meV with surface temperatures from 150 to 500 K. Every observed distribution has a single peak at a larger final angle than the specular angle of 45° which indicates that the normal component of the translation energy of the oxygen molecule is lost by the collision with the graphite surface. The amount of the energy loss by the collision has been roughly estimated as about 30-41% based on the assumption of the tangential momentum conservation during the collision. The distributions have also been analyzed with two theoretical models, the hard cubes model and the smooth surface model. These results indicate that the scattering is dominated by a single collision event of the particle with a flat surface having a large effective mass. The derived effective mass of the graphite surface for the incoming oxygen is 9-12 times heavier than that of a single carbon atom, suggesting a large cooperative motion of the carbon atoms in the topmost graphene layer.     

Spatial imaging of individual vibronic states in the interior of single molecules

Selective excitations of specific vibronic modes in position space are realized in single naphthalocyanine molecules adsorbed on an ultrathin alumina film by a scanning tunneling microscope at low temperature. Distinct spatial distributions are imaged for the different vibronic modes, which are in accordance with spectra recorded over different points of the molecule and its orbital structure. These distinct vibronic images, together with the differential conductance images and calculated molecular orbitals, lead to vibrational excitations that are associated with the doubly degenerate lowest unoccupied molecular orbitals (LUMO)--LUMO-α and LUMO-β. These results reveal the presence of different molecular conformations on the surface and the nature of the electron-vibrational coupling.     

Distinct and long-lived activity states of single enzyme molecules

Individual enzyme molecules have been observed to possess discrete and different turnover rates due to the presence of long-lived activity states. These stable activity states are thought to result from different molecular conformations or post-translational modifications. The distributions in kinetic activity observed in previous studies were obtained from small numbers of single enzyme molecules. Due to this limitation, it has not been possible to fully characterize the different kinetic and equilibrium binding parameters of single enzyme molecules. In this paper, we analyze hundreds of single beta-galactosidase molecules simultaneously; using a high-density array of 50,000 fL-reaction chambers, we confirm the presence of long-lived kinetic states within a population of enzyme molecules. Our analysis has isolated the source of kinetic variability to kcat. The results explain the kinetic variability within enzyme molecule populations and offer a deeper understanding of the unique properties of single enzyme molecules. Gaining a more fundamental understanding of how individual enzyme molecules work within a population should provide insight into how they affect downstream biochemical processes. If the results reported here can be generalized to other enzymes, then the stochastic nature of individual enzyme molecule kinetics should have a substantial impact on the overall metabolic activity within a cell.     

LSPR Imaging: Simultaneous Single Nanoparticle Spectroscopy and Diffusional Dynamics

A wide-field localized surface plasmon resonance (LSPR) imaging method using a liquid crystal tunable filter (LCTF) is used to measure the scattering spectra of multiple Ag nanoparticles in parallel. This method provides the ability to characterize moving Ag nanoparticles by measuring the scattering spectra of the particles while simultaneously tracking their motion. Consequently, single particle diffusion coefficients can be determined. As an example, several single Ag nanoprisms are tracked, the LSPR scattering spectrum of each moving particle is obtained, and the single particle diffusion coefficient is determined from its trajectory. Coupling diffusion information with spectral information in real time is a significant advance and addresses many scientific problems, both fundamental and biological, such as cell membrane protein diffusion, functional plasmonic distributions, and nanoparticle growth mechanisms.     

The probe rules in single particle tracking

Single particle tracking (SPT) enables light microscopy at a sub-diffraction limited spatial resolution by a combination of imaging at low molecular labeling densities and computational image processing. SPT and related single molecule imaging techniques have found a rapidly expanded use within the life sciences. This expanded use is due to an increased demand and requisite for developing a comprehensive understanding of the spatial dynamics of bio-molecular interactions at a spatial scale that is equivalent to the size of the molecules themselves, as well as by the emergence of new imaging techniques and probes that have made historically very demanding and specialized bio-imaging techniques more easily accessible and achievable. SPT has in particular found extensive use for analyzing the molecular organization of biological membranes. From these and other studies using complementary techniques it has been determined that the organization of native plasma membranes is heterogeneous over a very large range of spatial and temporal scales. The observed heterogeneities in the organization have the practical consequence that the SPT results in investigations of native plasma membranes are time dependent. Furthermore, because the accessible time dynamics, and also the spatial resolution, in an SPT experiment is mainly dependent on the luminous brightness and photostability of the particular SPT probe that is used, available SPT results are ultimately dependent on the SPT probes. The focus of this review is on the impact that the SPT probe has on the experimental results in SPT.     

Free energy of binding of a small molecule to an amorphous polymer in a solvent

Crystallization is a commonly used purification process in industrial practice. It usually begins with heterogeneous nucleation on a foreign surface. The complicated mechanism of heterogeneous nucleation is not well understood, but we hypothesize that a possible correlation between binding affinity to a surface and nucleation enhancement might exist. Amorphous polymers have been used in controlling crystallization. However, to our knowledge, no attempt has been made to calculate the free energy of binding of a small molecule to an amorphous polymer in a solvent, and to characterize the binding sites/conformations of this system at a molecular level. We developed a two-step approach, first using Adsorption Locator to identify probable binding sites and molecular dynamics to screen for the best binding sites and then using the Blue-Moon Ensemble method to compute the free energy of binding. A system of ethylene glycol, polyvinyl alcohol (PVA), and heavy water (D(2)O) was used for validation, since experimental data exists on a related system. Looking at four independently constructed surfaces, we found that ethylene glycol binds to an indentation on the surface or in a hole beneath the surface. We focused on the indentation binding sites because they are easily accessible and do not have large free energy barriers. The closest system for which experimental data on binding energetics exists is ethylene glycol on PVA in aqueous solutions/gels, and the magnitudes of the free energy of binding to the three best indentation binding sites are close to the experimental value, 0.4-3.7 kcal/mol higher. Our approach offers a way to compute the free energy of binding and characterize the binding sites/conformations, and is general enough to apply to other small molecule/amorphous polymer/solvent systems.     

Influence of isomerization on nonlinear optical properties of molecules

The influence of rotational and geometrical isomerism on the nonlinear optical (NLO) properties, specifically the first-order hyperpolarizability beta, of chromophores of current interest has been investigated with density functional theory (DFT). In the first of this two-part study, the rotational isomerism of a linear chromophore was explored. Calculation of the torsion potentials about two of the rotatable and conformation-changing single bonds in a chromophore demonstrated the near equality of the molecular energies at 0 degrees and 180 degrees rotational angles. To explore the consequences of this near conformational energy degeneracy to NLO behavior, the eight low energy rotational isomers of FTC [Robinson, B. H.; et al. Chem. Phys. 1999, 245, 35] were investigated. This study provides the first-reported DFT-based calculation of the statistical mechanical average of beta over the conformational space of a molecule having substantial nonlinear optical behavior. The influence of the solvent reaction field on rotameric populations and on the beta tensor is reported. In the second part, two molecules having two donors and two acceptors bonded respectively in ortho and meta positions on a central benzene ring are shown to have substantially different beta tensors. These two so-called molecular Xs have different highest occupied molecular orbital to lowest unoccupied molecular orbital (HOMO-LUMO) distributions, and consistent with expectations, it is found that the larger beta(zzz) is associated with a large spatial asymmetry between the HOMOs and LUMOs. Large hyperpolarizability correlates with the HOMO concentrated on the donor groups and the LUMO on the acceptor groups.     

Tracking Surface Glycans on Live Cancer Cells with Single‐Molecule Sensitivity

Using a combination of metabolically labeled glycans, a bioorthogonal copper(I)‐catalyzed azide–alkyne cycloaddition, and the controlled bleaching of fluorescent probes conjugated to azide‐ or alkyne‐tagged glycans, a sufficiently low spatial density of dye‐labeled glycans was achieved, enabling dynamic single‐molecule tracking and super‐resolution imaging of N‐linked sialic acids and O‐linked N‐acetyl galactosamine (GalNAc) on the membrane of live cells. Analysis of the trajectories of these dye‐labeled glycans in mammary cancer cells revealed constrained diffusion of both N‐ and O‐linked glycans, which was interpreted as reflecting the mobility of the glycan rather than to be caused by transient immobilization owing to spatial inhomogeneities on the plasma membrane. Stochastic optical reconstruction microscopy (STORM) imaging revealed the structure of dynamic membrane nanotubes.     

Quantum state-resolved CO2 collisions at the gas-liquid interface: surface temperature-dependent scattering dynamics

Energy transfer dynamics at the gas-liquid interface are investigated as a function of surface temperature both by experimental studies of CO2 + perfluorinated polyether (PFPE) and by molecular dynamics simulations of CO2 + fluorinated self-assembled monolayers (F-SAMs). Using a normal incident molecular beam, the experimental studies probe scattered CO2 internal-state and translational distributions with high resolution infrared spectroscopy. At low incident energies [Einc = 1.6(1) kcal/mol], CO2 J-state populations and transverse Doppler velocity distributions are characteristic of the surface temperature (Trot approximately Ttrans approximately TS) over the range from 232 to 323 K. In contrast, the rotational and translational distributions at high incident energies [Einc = 10.6(8) kcal/mol] show evidence for both trapping-desorption (TD) and impulsive scattering (IS) events. Specifically, the populations are surprisingly well-characterized by a sum of Boltzmann distributions where the two components include one (TD) that equilibrates with the surface (TTD approximately TS) and a second (IS) that is much hotter than the surface temperature (TIS > TS). Support for the superthermal, yet Boltzmann, nature of the IS channel is provided by molecular dynamics (MD) simulations of CO2 + F-SAMs [Einc = 10.6 kcal/mol], which reveal two-temperature distributions, sticking probabilities, and angular distributions in near quantitative agreement with the experimental PFPE results. Finally, experiments as a function of surface temperature reveal an increase in both sticking probability and rotational/translational temperature of the IS component. Such a trend is consistent with increased surface roughness at higher surface temperature, which increases the overall probability of trapping, yet preferentially leads to impulsive scattering of more highly internally excited CO2 from the surface.     

Light-activatable molecular beacons with a caged loop sequence

We have synthesized molecular beacons with caged nucleobases in the loop region. These constructs remain non-fluorescent in the presence of their target RNA but can be fully activated by light (366 or 405 nm) in vitro and in HEK293 cells. We suggest that this technology will be useful for single molecule RNA tracking in living cells.     

Rainbow scattering of CO and N2 from LiF(001)

The angular intensity distributions of CO and N(2) molecules scattered from a LiF(001) surface have been measured as functions of surface temperature, incident translational energy, and incident azimuthal direction affecting surface corrugation at a high resolution. Although both molecules have the same molecular mass and linear structure, only the CO molecule shows a rainbow feature in its scattering pattern, while the N(2) molecule shows a single peak distribution. From the comparisons of the obtained results with the calculated predictions based on the newly developed classical theory of the ellipsoid-washboard model, the differences in scattering distribution are attributed to the effects of molecular anisotropy and center-of-mass position. With an increase in the extent of the molecular anisotropy such as that of N(2) and CO as compared with rare-gas atoms, the summation of several scattering distributions depending on molecular orientation results in smearing the rainbow scattering on the corrugated surface. This smearing effect, however, attenuates when center-of-mass position deviates from the molecular center, as that for CO.     

Molecular Recognition‐Mediated Transformation of Single‐Chain Polymer Nanoparticles into Crosslinked Polymer Films

We describe single‐chain polymer nanoparticles (SCNPs) possessing intramolecular dynamic covalent crosslinks that can transform into polymer films through a molecular recognition‐mediated crosslinking process. The SCNPs utilise molecular recognition with surface‐immobilised proteins to concentrate upon a substrate, bringing the SCNPs into close spatial proximity with one another and allowing their dynamic covalent crosslinkers to undergo intra‐ to interpolymer chain crosslinking leading to the formation of polymeric film. SCNPs must possess both the capacity for specific molecular recognition and a dynamic nature to their intramolecular crosslinkers to form polymer films, and an investigation of the initial phase of film formation indicates it proceeds from features which form upon the surface then grow predominantly in the xy directions. This approach to polymer film formation presents a potential method to “wrap” surfaces displaying molecular recognition motifs—which could potentially include viral, cellular and bacterial surfaces or artificial surfaces displaying multivalent recognition motifs—within a layer of polymer film.     

Single‐Molecule Measurement of Adsorption Free Energy at the Solid–Liquid Interface

Adsorption plays a critical role in surface and interface processes. Fractional surface coverage and adsorption free energy are two essential parameters of molecular adsorption. However, although adsorption at the solid–gas interface has been well‐studied, and some adsorption models were proposed more than a century ago, challenges remain for the experimental investigation of molecular adsorption at the solid–liquid interface. Herein, we report the statistical and quantitative single‐molecule measurement of adsorption at the solid–liquid interface by using the single‐molecule break junction technique. The fractional surface coverage was extracted from the analysis of junction formation probability so that the adsorption free energy could be calculated by referring to the Langmuir isotherm. In the case of three prototypical molecules with terminal methylthio, pyridyl, and amino groups, the adsorption free energies were found to be 32.5, 33.9, and 28.3 kJ mol^?1, respectively, which are consistent with DFT calculations.     

A theoretical study of molecular conduction. III. A nonequilibrium-Green's-function-based Hartree-Fock approach

Many recent experimental and theoretical studies have paid attention to the conductivity of single molecule transport junctions, both because it is fundamentally important and because of its significance in the development of molecular-based electronics. In this paper, we discuss a nonequilibrium Green's function (NEGF)-based Hartree-Fock (HF) approach; the NEGF method can appropriately accommodate charge distributions in molecules connected to electrodes. In addition, we show that a NEGF-based density matrix can reduce to an ordinary HF density matrix for an isolated molecule if the molecule does not interact with electrodes. This feature of the NEGF-based density matrix also means that NEGF-based Mulliken charges can be reduced to ordinary Mulliken charges in those cases. Therefore, the NEGF-based HF approach can directly compare molecules that are connected to electrodes with isolated ones, and is useful in investigating complicated features of molecular conduction. We also calculated the transmission probability and conduction for benzenedithiol under finite electrode biases. The coupling between the electrodes and molecule causes electron transfer from the molecule to the electrodes, and the applied bias modifies this electron transfer. In addition, we found that the molecule responds capacitively to the applied bias, by shifting the molecular orbital energies.