Single‐Molecule 3D Orientation Imaging Reveals Nanoscale Compositional Heterogeneity in Lipid Membranes

In soft matter, thermal energy causes molecules to continuously translate and rotate, even in crowded environments, thereby impacting the spatial organization and function of most molecular assemblies, such as lipid membranes. Directly measuring the orientation and spatial organization of large collections (>3000 molecules μm^?2) of single molecules with nanoscale resolution remains elusive. In this paper, we utilize SMOLM, single‐molecule orientation localization microscopy, to directly measure the orientation spectra (3D orientation plus “wobble”) of lipophilic probes transiently bound to lipid membranes, revealing that Nile red's (NR) orientation spectra are extremely sensitive to membrane chemical composition. SMOLM images resolve nanodomains and enzyme‐induced compositional heterogeneity within membranes, where NR within liquid‐ordered vs. liquid‐disordered domains shows a ≈4° difference in polar angle and a ≈0.3π sr difference in wobble angle. As a new type of imaging spectroscopy, SMOLM exposes the organizational and functional dynamics of lipid‐lipid, lipid‐protein, and lipid‐dye interactions with single‐molecule, nanoscale resolution.     

Trajectory analysis of single molecules exhibiting non-brownian motion

Four techniques for analyzing single molecule tracking data--confinement level analysis, time series analysis and statistical analysis of lateral diffusion, multistate kinetics, and a newly developed method, radius of gyration evolution analysis--are compared using a set of sample fluorophore trajectories obtained from the lipophilic carbocyanine dye 1,1'-dioctadecyl-3,3,3'3'-tetramethylindocarbocyanine, DiIC(18), partitioned into surface tethered poly(n-isopropylacrylamide). The purpose here is two-fold: first to test that these techniques can be applied to single molecules trajectories, which typically contain a smaller total number of frames than those obtained from other particles, e.g. quantum dots or gold nanoparticles; and second to critically compare the information obtained from each method against the others. A set of five SMT trajectories, ranging in length from 41 to 273 steps with a 30 ms frame transfer exposure, were all successfully analyzed by all four techniques, provided two important criteria were met: enough steps to define the motion were acquired in the trajectory, generally on the order of 50 steps, and the fast and slow diffusion coefficients differ by at least a factor of 5. Beyond that the four trajectory analysis methods studied provide partially confirmatory and partially complementary information. SMT data resulting from more complex physical behavior may well benefit from using these techniques in succession to identify and sort populations.     

Molecular dynamics simulations of a liquid crystalline molecule in the smectic A and E phases and in vacuum

Molecular dynamics simulations are performed in this work at 393 and 323 K for a mesogenic molecule ( R )-1-methylheptyl 4\[4-(2-allyloxyethoxy)biphenyl-4-carbonyloxy]benzoate in the simulated smectics A and E, respectively, and in a vacuum at 300 K, for a period of 1.0ns. The trajectories obtained from molecular dynamics simulations allow us to investigate the dynamical behaviour of this mesogenic molecule in the simulated smectic phases. This dynamical behaviour of a single molecule is presented using the distributions of dihedral angles and rotational diffusion around the C-axis defined by the simulated cells. Simulation results indicate that, except for the bonds near the end of the spacer segment, the dihedral angles all exhibit a single Gaussian-like distribution in the smectic A and E phases. Fluctuations of a dihedral angle about its mean value are more restricted in the smectics A and E than in those simulated in a vacuum. The average value of the fluctuations of the dihedral angles at the bonds in the spacer is found to be about 2 fold larger than that of fluctuations in the tail of the same molecule in the smectic A and E phases. In the smectic A phase, the distribution of orientations of a molecule about its long axis in a 36 molecule cell in which the outer molecules are fixed is found to have three distinct peaks. This result shows that the orientational fluctuations of single molecules are limited by confinement due to neighbouring molecules, i.e. that the layers have short-range structural correlations. The orientational distributions show larger fluctuations at the ends of the molecules.     

On the orientation of a designed transmembrane peptide: toward the right tilt angle?

The orientation of the transmembrane peptide WALP23 under small hydrophobic mismatch has been assessed through long-time-scale molecular dynamics simulations of hundreds of nanoseconds. Each simulation gives systematically large tilt angles (>30 degrees). In addition, the peptide visits various azimuthal rotations that mostly depend on the initial conditions and converge very slowly. In contrast, small tilt angles as well as a well-defined azimuthal rotation were suggested by recent solid-state 2H NMR studies on the same system. To optimally compare our simulations with NMR data, we concatenated the different trajectories in order to increase the sampling. The agreement with 2H NMR quadrupolar splittings is spectacularly better when these latter are back-calculated from the concatenated trajectory than from any individual simulation. From these ensembled-average quadrupolar splittings, we then applied the GALA method as described by Strandberg et al. (Biophys J. 2004, 86, 3709-3721), which basically derives the peptide orientation (tilt and azimuth) from the splittings. We find small tilt angles (6.5 degrees), whereas the real observed tilt in the concatenated trajectory presents a higher value (33.5 degrees). We thus propose that the small tilt angles estimated by the GALA method are the result of averaging effects, provided that the peptide visits many states of different azimuthal rotations. We discuss how to improve the method and suggest some other experiments to confirm this hypothesis. This work also highlights the need to run several and rather long trajectories in order to predict the peptide orientation from computer simulations.     

Identification and quantitative analysis of the intermediate phase in a linear high-density polyethylene

The observation of chain conformation and mobility in polyethylene by solid-state ¹³C magic angle spinning (MAS) nuclear magnetic resonance (NMR) permits unambiguous identification and quantitative analysis of an intermediate phase. The carbon-carbon bonds in the intermediate phase adopt, on the average, an all-trans conformation and are more mobile than in the crystalline state (room temperature rate of reorientation ≈ 10⁷ Hz). Comparisons of crystallinities by differential scanning calorimetry, wide-angle x-ray diffraction, and NMR support the high orientation of the intermediate phase and suggest a lower heat of fusion than for the crystals. Results from ¹³C spin-lattice relaxation and ¹H spin diffusion show that the mass fractions are ≈ 20% and the domain sizes ≈ 36 Å. Both change with crystallization and annealing conditions. © 1994 John Wiley & Sons, Inc.     

Single-Molecule 3D Orientation Imaging Reveals Nanoscale Compositional Heterogeneity in Lipid Membranes

In soft matter, thermal energy causes molecules to continuously translate and rotate, even in crowded environments, thereby impacting the spatial organization and function of most molecular assemblies, such as lipid membranes. Directly measuring the orientation and spatial organization of large collections (>3000 molecules μm⁻²) of single molecules with nanoscale resolution remains elusive. In this paper, we utilize SMOLM, single-molecule orientation localization microscopy, to directly measure the orientation spectra (3D orientation plus “wobble”) of lipophilic probes transiently bound to lipid membranes, revealing that Nile red's (NR) orientation spectra are extremely sensitive to membrane chemical composition. SMOLM images resolve nanodomains and enzyme-induced compositional heterogeneity within membranes, where NR within liquid-ordered vs. liquid-disordered domains shows a ≈4° difference in polar angle and a ≈0.3π sr difference in wobble angle. As a new type of imaging spectroscopy, SMOLM exposes the organizational and functional dynamics of lipid-lipid, lipid-protein, and lipid-dye interactions with single-molecule, nanoscale resolution.     

On the relationships between kinetic schemes and two-state single molecule trajectories

Trajectories of a signal that fluctuates between two states which originate from single molecule activities have become ubiquitous. Common examples are trajectories of ionic flux through individual membrane channels and of photon counts collected from diffusion, activity, and conformational changes of biopolymers. By analyzing the trajectory, one wishes to deduce the underlying mechanism, which is usually described by a multisubstate kinetic scheme. In previous works [O. Flomenborn, J. Klafter, and A. Szabo, Biophys. J. 88, 3780 (2005); O. Flomenbom and J. Klafter, Acta Phys. Pol. B 36, 1527 (2005)], we divided kinetic schemes that generate two-state trajectories into two types: reducible schemes and irreducible schemes. A full characterization of the reducible ones was given. We showed that all the information in trajectories generated from reducible schemes is contained in the waiting time probability density functions (PDFs) of the two states. It follows that reducible schemes with the same waiting time PDFs are not distinguishable; namely, such schemes lead to identical two-state trajectories in the statistical sense. In this work, we further characterize the topologies of kinetic schemes, now of irreducible schemes, and further study two-state trajectories from the two types of scheme. We suggest various methods for extracting information about the underlying kinetic scheme from the trajectory (e.g., calculate the binned successive waiting times PDFs and analyze the ordered waiting time trajectories), and point out the advantages and disadvantages of each. We show that the binned successive waiting times PDFs are not only more robust than other functions when analyzing finite trajectories, but contain, in most cases, more information about the underlying kinetic scheme than other functions in the limit of infinitely long trajectories. For some cases, however, analyzing the ordered waiting times trajectory may supply unique information about the underlying kinetic scheme.     

Spectral Diffusion of Single Molecules in a Hierarchical Energy Landscape

Spectral diffusion as a result of both the transitions between different molecular conformers and the ′′molecular softness′′ of quasi‐free perylene diimides on a SiO₂ surface is investigated by means of single‐molecule spectroscopy, which reveals the time dependence of both the fluorescence spectra and the three‐dimensional orientation. Spectral wavelengths of all single emitters cover a wide energy range of about 0.27 eV, which is due to different types of conformers with large differences in optical transition energy. Time‐dependent spectral trajectories of single emitters within this wavelength manifold are evaluated with a model transcribed from the analysis of spatial diffusion. Spectral diffusion processes are closely correlated with fluorescence emission and excitation power. The overall analysis of spectral diffusion reveals, similar to proteins, a hierarchy of energy barriers in a broad energy landscape.     

Force driven separation of drops by deterministic lateral displacement

We investigate the separation of drops in force-driven deterministic lateral displacement (f-DLD), a promising high-throughput continuous separation method in microfluidics. We perform scaled-up macroscopic experiments in which drops settle through a square array of cylindrical obstacles. These experiments demonstrate the separation capabilities-and provide insight for the design-of f-DLD for drops of multiple sizes, including drops that are larger than the gaps between cylinders and exhibit substantial deformation as they move through the array. We show that for any orientation of the driving force relative to the array of obstacles, the trajectories of the drops follow selected locking directions in the lattice. We also found that a simple collision model accurately describes the average migration angles of the drops for the entire range of sizes investigated here, and for all forcing directions. In addition, we found a difference of approximately 20° between the critical angles at which the smallest and largest drops first move across a line of obstacles (column) in the array, a promising result in terms of potential size resolution of this method. Finally, we demonstrate that a single line of cylindrical obstacles rotated with respect to the driving force is capable of performing binary separations. The critical angles obtained in such single line experiments, moreover, agree with those obtained using the full array, thus validating the assumption in which the trajectory (and average migration angle) of the drops is calculated from individual obstacle-drop collisions.     

An investigation of the stable orientations of orthorhombic particles in a thin film and their effect on its critical failure pressure

The effects of shape and contact angle on the behaviour of orthorhombic particles at an interface and in thin films were investigated using Surface Evolver. It is shown that the energetically stable orientations of the particle change with its aspect ratio. Long, wide, flat particles with low contact angles are more stable in flat orientations, i.e. with two faces parallel to the flat film surface. More cubic particles with higher contact angles are more stable in twisted orientations, where the opposite sides of the film can be drawn together at the sharp edges of the particle. The combination of contact angle and orientation has been found to have a large effect on the capillary pressure required to rupture the film. A film containing a particle in a flat orientation will rupture at a capillary pressure up to three times greater than one containing an identical particle in a twisted orientation. Wider, flatter particles with low contact angles stabilise thin liquid films to a greater extent than cubic particles with high contact angles.     

Theoretical Studies of Single Molecule Spectroscopy at Room Temperature

This talk is motivated by recent room-temperature single molecule experiments, which measure the optical spectrum along single molecular trajectories and monitor the molecular dynamics and chemical kinetics of individual reactive systems. These experiments contain new information that requires theoretical models and interpretations. Several aspects of single molecule spectroscopy are analyzed:(1) Event-averaged single molecule quantities are calculated, with the prediction of the echo signal in the joint event probability distribution function^[1]. Similar to the photon echo phenomenon, the single molecule echo signal measures solvent effects on chemical kinetics. (2) The statistics of single molecule blinking events are often correlated to underlying quantum mechanisms. The distribution functions of waiting-time sequences are examined for several quantum processes, including electron transfer, solvent relaxation, laser-induced emission, and single quantum-dot blinking^[2]. (3) Single molecule measurements of heterogeneous diffusion reveal deviations from the Gaussian distribution of Brownian motion. As a quantitative measure, the non-Gaussian indicator decays asymptotically to zero according to 1/t for finite time correlation, but saturates at a plateau value for power-law correlation.     

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.     

NON-REACTIVE ORIENTATIONS OF MOLECULES AT SURFACES

The role of the orientation of a molecule in its interaction with a surface is examined for the specific case of NO interaction with Pt(111). For this system molecular chemisorption occurs, mediated by a strong chemisorption well. Experimental results concerning sticking, angular distributions of scattered molecules, steric effects in scattering, and rotational excitation will be presented. Classical trajectory calculations using a model potential energy hypersurface can reproduce most experimental findings. Analysis of the trajectories shows that there is a strong orientation dependence of rotational excitation and sticking. The O-end of the molecule turns out to be non-reactive. The N-end of the molecule is very reactive. Its behaviour can almost be described using statistical methods.     

Expansion of differential cross sections determined from classical trajectory studies in a series of legendre polynomials

A novel method to compute differential cross sections from classical trajectory studies is presented. The cross section is expanded exactly in a series of Legendre polynomials. The series coefficients are computed directly from the deflection angles determined from each trajectory. Model calculations presented here show that 3000 trajectories are often enough to give very accurate differential cross sections.     

High throughput single molecule tracking for analysis of rare populations and events

High throughput single molecule tracking methods were developed to perform quantitative analyses of rare molecular populations. An optimization strategy for single molecule tracking at interfaces is described that allowed tracking of ~10(6) unique trajectories. These large statistical datasets were analyzed in order to identify and characterize distinct molecular populations based on their characteristic dynamic behavior (residence time or surface diffusion) and/or their spatial distribution. Cumulative (i.e. integrated) probability distributions were found to be several orders of magnitude more sensitive to rare populations than were raw probability distributions. Mapping using Accumulated Probe Trajectories (MAPT) was used to characterize molecular populations associated with rare surface heterogeneities. Importantly, large sample sizes were found to result in a dramatic enhancement in the ability to identify rare populations and to resolve their dynamic and spatial parameters.     

Semiclassical nonadiabatic dynamics based on quantum trajectories for the O(3P,1D) + H2 system

The O(3P,1D) + H2 --> OH + H reaction is studied using trajectory dynamics within the approximate quantum potential approach. Calculations of the wave-packet reaction probabilities are performed for four coupled electronic states for total angular momentum J = 0 using a mixed coordinate/polar representation of the wave function. Semiclassical dynamics is based on a single set of trajectories evolving on an effective potential-energy surface and in the presence of the approximate quantum potential. Population functions associated with each trajectory are computed for each electronic state. The effective surface is a linear combination of the electronic states with the contributions of individual components defined by their time-dependent average populations. The wave-packet reaction probabilities are in good agreement with the quantum-mechanical results. Intersystem crossing is found to have negligible effect on reaction probabilities summed over final electronic states.     

Role of Emissive and Non‐Emissive Complex Formations in Photoinduced Electron Transfer Reaction of CdTe Quantum Dots

Bimolecular photoinduced electron transfer (PET) from excited state CdTe quantum dot (QD*) to an electron deficient molecule 2,4‐dinitrotoluene (DNT) is studied in toluene. We observed two types of QD‐DNT complex formations; (i) non‐emissive complex, in which DNT is embedded deep inside the surface polymer layer of QD and (ii) emissive complex, in which DNT molecules are attached to QDs but approach to the QD core is shielded by polymer layer. Because of its non‐emissive nature, the lifetime of QD is not affected by dark complex formation, though the steady‐state emission is greatly quenched. However, emissive complex formation causes both, lifetime and steady‐state emission quenching. In our fitting model, consideration of Poisson distribution of the attached quencher (DNT) molecules at QD surface enables a comprehensive fitting to our time resolved data. QD‐DNT complex formation was confirmed by an isothermal titration calorimetry (ITC) study. Fitting to the time resolved data using a stochastic kinetic model shows moderate increase (0.05 ns^?1 to 0.072 ns^?1) of intrinsic quenching rate with increasing the QD particle size (from ≈3.2 nm to ≈5.2 nm). Our fitting also reveals that the number of DNT molecules attached to a single QD increases from ≈0.1–0.2 to ≈1.2–1.7, as the DNT concentration is increased from ≈1 mm to 17.5 mm . Complex formation at higher quencher concentration assures that the observed PET kinetics is a thermodynamically controlled process where solvent diffusion has no role on it.     

The application of multiple linear regression to the measurement of the median particle size of drugs and pharmaceutical excipients by near-infrared spectroscopy.

A number of powdered drugs and pharmaceutical excipients were used to demonstrate the ability of near-infrared spectroscopy to measure median particle size (d50). Sieved fractions and bulk samples of aspirin, anhydrous caffeine, paracetamol, lactose monohydrate and microcrystalline cellulose were particle sized by forward angle laser light scattering (FALLS) and scanned by fibre-optic probe FT-NIR spectroscopy. Two-wavenumber multiple linear regression (MLR) calibrations were produced using: NIR reflectance; absorbance and Kubelka-Munk function data with each of median particle size, reciprocal median particle size and the logarithm of median particle size. Best calibrations were obtained using reflectance data versus the logarithm of median particle size (NIR predicted lnd50 versus ln(FALLS d50) for microcrystalline cellulose and lactose monohydrate sieve fraction calibrations: r = 0.99 in each case). Working calibrations for lactose monohydrate (median particle size range: 19.2-183 microns) and microcrystalline cellulose (median particle size range: 24-406 microns) were set-up using combinations of machine sieve-fractions and bulk samples. This approach was found to produce more robust calibrations than just the use of sieved fractions. The method has been compared with single wavenumber quadratic least squares regression using reflectance and mean-corrected reflectance data with median particle size. Correlation between NIR predicted and FALLS values was significantly better using the MLR method.     

Study of sulfur heterogeneous nucleation from supersaturated vapor on tungsten oxide and sodium chloride seed particles. Determination of contact angle of critical sulfur nuclei

A procedure has been developed for determining the contact angle of a critical nucleus formed on seed particles during the heterogeneous nucleation of a vapor in a flow chamber. The procedure comprises the determination of the fraction of enlarged particles, as well as the selective separation of nanoparticles over sizes to locate the zone of intense nucleation. The concentration and size distribution of aerosol particles have been measured with a diffusion spectrometer of aerosols. Vapor concentration distributions and supersaturation fields have been determined by solving the mass-transfer problem. The calculated supersaturation fields are in good agreement with the location of the intense nucleation zone experimentally found with the help of selective separation. The fractions of enlarged particles have been determined as functions of supersaturation in the chamber. A formula has been derived for calculating the fraction and size distribution function of enlarged particles at known supersaturation and temperature fields and a preset contact angle. The contact angles are selected in a manner such that the calculated fraction of enlarged particles coincides with that measured experimentally. It has been revealed that the contact angle of critical sulfur nuclei formed on tungsten oxide seed particles with average radii 〈R _p〉 ≈ 5.8?4.4 nm is in a range of 21.2?20.5°, while, in the case of sodium chloride seed particles with 〈R _p〉 ≈ 6.0?4.4 nm, the contact angle is 20.4?17.4°. The size of a critical nucleus has been found to be proportional to calculated average radius of a seed particle 〈R _p〉 in both cases.