We examine the formation and concomitant rotation of electrodynamically bound dimers (EBD) of 150 nm diameter Ag nanoparticles trapped in circularly polarized focused Gaussian beams. The rotation frequency of an EBD increases linearly with the incident beam power, reaching mean values of ∼4 kHz for relatively low incident powers of 14 mW. Using a coupled-dipole/effective polarizability model, we reveal that retardation of the scattered fields and electrodynamic interactions can lead to a “negative torque” causing rotation of the EBD in the direction opposite to that of the circular polarization. This intriguing opposite-handed rotation due to negative torque is clearly demonstrated using electrodynamics-Langevin dynamics simulations by changing particle separations and thus varying the retardation effects. Finally, negative torque is also demonstrated in experiments from statistical analysis of the EBD trajectories. These results demonstrate novel rotational dynamics of nanoparticles in optical matter using circular polarization and open a new avenue to control orientational dynamics through coupling to interparticle separation.Keywords: angular momentum; negative optical torque; optical torque; optical trapping; Optical tweezers; plasmonic nanoparticles;

An extension of the Maxwell–Faraday law of electromagnetic induction to optical frequencies requires spatially appropriate materials and optical beams to create resonances and excitations with curl. Here we employ cylindrical vector beams with azimuthal polarization to create electric fields that selectively drive magnetic responses in dielectric core–metal nanoparticle “satellite” nanostructures. These optical frequency magnetic resonances are induced in materials that do not possess spin or orbital angular momentum. Multipole expansion analysis of the scattered fields obtained from electrodynamics simulations show that the excitation with azimuthally polarized beams selectively enhances magnetic vs electric dipole resonances by nearly 100-fold in experiments. Multipolar resonances (e.g., quadrupole and octupole) are enhanced 5-fold by focused azimuthally versus linearly polarized beams. We also selectively excite electric multipolar resonances in the same identical nanostructures with radially polarized light. This work opens new opportunities for spectroscopic investigation and control of “dark modes”, Fano resonances, and magnetic modes in nanomaterials and engineered metamaterials.Keywords: cylindrical vector beams; FDTD simulations; meta-atom; multipolar resonances; Optical magnetism; plasmonic nanocluster;

We present a general method for detecting and correcting biases in the outputs of particle-tracking experiments. Our approach is based on the histogram of estimated positions within pixels, which we term the single-pixel interior filling function (SPIFF). We use the deviation of the SPIFF from a uniform distribution to test the veracity of tracking analyses from different algorithms. Unbiased SPIFFs correspond to uniform pixel filling, whereas biased ones exhibit pixel locking, in which the estimated particle positions concentrate toward the centers of pixels. Although pixel locking is a well-known phenomenon, we go beyond existing methods to show how the SPIFF can be used to correct errors. The key is that the SPIFF aggregates statistical information from many single-particle images and localizations that are gathered over time or across an ensemble, and this information augments the single-particle data. We explicitly consider two cases that give rise to significant errors in estimated particle locations: undersampling the point spread function due to small emitter size and intensity overlap of proximal objects. In these situations, we show how errors in positions can be corrected essentially completely with little added computational cost. Additional situations and applications to experimental data are explored in SI Appendix. In the presence of experimental-like shot noise, the precision of the SPIFF-based correction achieves (and can even exceed) the unbiased Cramér–Rao lower bound. We expect the SPIFF approach to be useful in a wide range of localization applications, including single-molecule imaging and particle tracking, in fields ranging from biology to materials science to astronomy.

We introduce a general theoretical framework to study the shape dynamics of actively growing and remodeling surfaces. Using this framework we develop a physical model for growing bacterial cell walls and study the interplay of cell shape with the dynamics of growth and constriction. The model allows us to derive constraints on cell wall mechanical energy based on the observed dynamics of cell shape. We predict that exponential growth in cell size requires a constant amount of cell wall energy to be dissipated per unit volume. We use the model to understand and contrast growth in bacteria with different shapes such as spherical, ellipsoidal, cylindrical and toroidal morphologies. Coupling growth to cell wall constriction, we predict a discontinuous shape transformation, from partial constriction to cell division, as a function of the chemical potential driving cell wall synthesis. Our model for cell wall energy and shape dynamics relates growth kinetics with cell geometry, and provides a unified framework to describe the interplay between shape, growth and division in bacterial cells.

A central challenge in nano- and mesoscale materials research is facile formation of specific structures for catalysis, sensing, and photonics. Self-assembled equilibrium structures, such as three-dimensional crystals or ordered monolayers, form as a result of the interactions of the constituents. Other structures can be achieved by imposing forces (fields) and/or boundary conditions, which Whitesides termed “self-organization”. Here, we demonstrate contact line pinning on locally curved surfaces (i.e., a self-assembled monolayer of SiO2 colloidal particles) as a boundary condition to create extended arrays of uniform rings of Au nanoparticles (NPs) on the SiO2 colloids. The mechanism differs from the well-known “coffee-ring” effect; here the functionalized NPs deposit at the contact line and are not driven by evaporative transport. Thus, NP ring formation depends on the hydrophobicity and wetting of the SiO2 colloids by the chloroform solution, ligands on the NPs, and temperature. The NP rings exhibit size scaling behavior, maintaining a constant ratio of NP ring-to-colloid diameter (from 300 nm to 2 μm). The resultant high-quality NP ring structures are expected to have interesting photonic properties.Keywords: contact line; nanoparticle rings; scaling behavior; SiO2 monolayer; wetting

Mirrors and optical cavities can modify and enhance matter–radiation interactions. Here we report that chemically synthesized Au nanoplates can serve as micrometer-size mirrors that enhance electrodynamic interactions. Because of their plasmonic properties, the Au nanoplates enhance the brightness of scattered light from Ag nanoparticles near the nanoplate surface in dark-field microscopy. More importantly, enhanced optical trapping and optical binding of Ag nanoparticles are demonstrated in interferometric optical traps created from a single laser beam and its reflection from individual Au nanoplates. The enhancement of the interparticle force constant is ≈20-fold more than expected from the increased intensity due to standing wave interference. We show that the additional stability for optical binding arises from the restricted axial thermal motion of the nanoparticles that couples to and reduces the fluctuations in the lateral plane. This new mechanism greatly advances the photonic synthesis of ultrastable nanoparticle arrays and investigation of their properties.

Optical forces acting on metallic nanoparticles can be used to organize mesoscale arrays for various applications. Here, we show that silver nanoparticles can be deposited as ordered arrays and chains on chemically modified substrates using a simple and facile optical trapping approach that we term “optical printing”. The deposited patterns show preferred separations between nanoparticles resulting from their electrodynamic coupling (i.e., optical binding) in the electromagnetic field of the optical trapping beam. Centrosymmetric optical traps readily allow simultaneous deposition of nanoparticle pairs and triples maintaining the interparticle geometries present in solution. Repositioning an optical line trap with small intercolumn separations allows selectively sampling low and high energy parts of the interparticle potentials. We find that the preferred particle arrangements controllably change from rectangular and triangular to near-field aggregates as one forces the separation to be small. The separation affects the interactions. Interpretation of the results is facilitated by electrodynamic simulations of optical forces. This optical printing approach, which enables efficient fabrication of dense nanoparticle arrays with nanoscale positional precision, is being employed for quantum optics and enhanced sensing measurements.

Uncovering the quantitative laws that govern the growth and division of single cells remains a major challenge. Using a unique combination of technologies that yields unprecedented statistical precision, we find that the sizes of individual Caulobacter crescentus cells increase exponentially in time. We also establish that they divide upon reaching a critical multiple (≈1.8) of their initial sizes, rather than an absolute size. We show that when the temperature is varied, the growth and division timescales scale proportionally with each other over the physiological temperature range. Strikingly, the cell-size and division-time distributions can both be rescaled by their mean values such that the condition-specific distributions collapse to universal curves. We account for these observations with a minimal stochastic model that is based on an autocatalytic cycle. It predicts the scalings, as well as specific functional forms for the universal curves. Our experimental and theoretical analysis reveals a simple physical principle governing these complex biological processes: a single temperature-dependent scale of cellular time governs the stochastic dynamics of growth and division in balanced growth conditions.

We quantitatively analyzed particle tracking data on insulin granules expressing fluorescent fusion proteins in MIN6 cells to better understand the motions contributing to intracellular transport and, more generally, the means for characterizing systems far from equilibrium. Care was taken to ensure that the statistics reflected intrinsic features of the individual granules rather than details of the measurement and overall cell state. We find anomalous diffusion. Interpreting such data conventionally requires assuming that a process is either ergodic with particles working against fluctuating obstacles (fractional Brownian motion) or nonergodic with a broad distribution of dwell times for traps (continuous-time random walk). However, we find that statistical tests based on these two models give conflicting results. We resolve this issue by introducing a subordinated scheme in which particles in cages with random dwell times undergo correlated motions owing to interactions with a fluctuating environment. We relate this picture to the underlying microtubule structure by imaging in the presence of vinblastine. Our results provide a simple physical picture for how diverse pools of insulin granules and, in turn, biphasic secretion could arise.

Optical “nano-manipulation” to control small objects with nanoscale precision requires strongly localized optical fields that are usually based on user-imposed shaping of the incident optical beam. Here we report an in situ approach to reshape and enhance electromagnetic (EM) fields using scattering and interference that is concomitant with “dynamic self-assembly” of nanoparticle arrays using simple (unstructured) applied EM fields. We show that Ag nanoparticles (∼140 nm diameter) illuminated by coherent light can form linear chains with nanometer precision via strong optical binding interactions. The chains, in turn, create highly shaped EM fields via coherent scattering from the particles, allowing less polarizable particles to be “co-trapped” in both intermediate-scale and near-field regimes. These less polarizable particles include quantum dots (CdSe/ZnS or CdSe/CdZnS core/shell nanocrystals; both are smaller than 10 nm, while the latter are further coated by ∼30 nm thick silica shells) and small Ag nanoparticles (60 nm diameter). This hierarchical optical-field-induced assembly is a starting point for photonically building artificial nanomaterials.Keywords: dynamic self-assembly; Ag nanoparticles; light-matter interaction; optical binding; optical tweezers; plasmonics;

Optical manipulation of metal nanowires offers the possibility to control the position, orientation, and associated motions of individual nanowires, particularly by utilizing their plasmonic properties. Here, we demonstrate that the orbital angular momentum of photons in Laguerre–Gauss (optical vortex) beams can induce rotation of single silver (Ag) nanowires with lengths of over 10 μm that are lying on (in molecular proximity to) a dielectric surface. We show that the rotation dynamics are governed by plasmonic interactions of the Ag nanowires with linearly polarized light, which yield a sinusoidal optical torque that causes angular acceleration. These results provide important information to understand the angular dependence of plasmonic nanowire–light interactions and extend the repertoire to realize applications in plasmonic lab-on-a-chip systems.Keywords: Ag nanowires; optical manipulation; optical vortex; orbital angular momentum; plasmonics;

Understanding whether noble-metal nanostructures can be trapped optically and under what conditions will enable a range of applications that exploit their plasmonic properties. However, there are several nontrivial issues that first need to be resolved. A major one is that metal particles experience strong radiation pressure in optical beams, while stable optical trapping requires an attractive force greater than this radiation pressure. Therefore, it has generally been considered impossible to obtain sufficiently strong gradient forces using single-beam optical tweezers to trap relatively large metal nanostructures in three dimensions. Here we demonstrate that a single, tightly focused laser beam with a wavelength of 800 nm can achieve three-dimensional optical trapping of individual gold (Au) nanowires with lengths over 2 μm. Nanowires can be trapped by the beam at one of their ends, in which case they undergo significant angular fluctuations due to Brownian motion of the untrapped end. They can also be trapped close to their midpoints, in which case they are oriented approximately perpendicular to the light polarization direction. The behavior is markedly different from that of Ag nanowires with similar length and diameter, which cannot be trapped in three dimensions by a single focused Gaussian beam. Our results, including electrodynamics simulations that help to explain our experimental findings, suggest that the conventional wisdom, which holds that larger metal particles cannot be trapped, needs to be replaced with an understanding based on the details of plasmon resonances in the particles.Keywords: Au nanowires; nanophotonics; optical manipulation; optical tweezers; plasmonics

We demonstrate assembly of spheroidal Ag nanoparticle clusters, chains and arrays induced by optical binding. Particles with diameters of 40 nm formed ordered clusters and chains in aqueous solution when illuminated by shaped optical fields with a wavelength of 800 nm; specifically, close-packed clusters were formed in cylindrically symmetric optical traps, and linear chains were formed in line traps. We developed a coupled-dipole model to calculate the optical forces between an arbitrary number of particles and successfully predicted the experimentally observed particle separations and arrangements as well as their dependence on the polarization of the incident light. This demonstrates that the interaction between these small Ag particles and light is well described by approximating the particles as point dipoles, showing that these experiments extend optical binding into the Rayleigh regime. For larger Ag nanoparticles, with diameters of approximately 100 nm, the optical-binding forces become comparable to the largest gradient forces in the optical trap, and the particles can arrange themselves into regular arrays or synthetic photonic lattices. Finally, we discuss the differences between our experimental observations and the point dipole theory and suggest factors that prevent the Ag nanoparticles from aggregating as expected from the theory.Keywords: Ag nanoparticles; light−matter interaction; optical binding; optical tweezers; Rayleigh regime; self-assembly

We report the first experimental realization of all-optical trapping and manipulation of plasmonic nanowires in three dimensions. The optical beam used for trapping is the Fourier transform of a linearly polarized Bessel beam (termed FT-Bessel). The extended depth of focus of this beam enables the use of a retroreflection geometry to cancel radiation pressure in the beam propagation direction, making it possible to trap highly scattering and absorbing silver nanowires. Individual silver nanowires with lengths of several micrometers can be positioned by the trapping beam with a precision better than 100 nm and are oriented by the polarization of the trapping light with a precision of approximately 1°. Multiple nanowires can be trapped simultaneously in spatially separated maxima of the trapping field. Since trapping in the interferometric FT-Bessel potential is robust in bulk solution and near surfaces, it will enable the controlled assembly of metal nanowires into plasmonic nanostructures.

Resonant-pump polarizability response spectroscopy (RP-PORS) is based on an optical heterodyne detected transient grating (OHD-TG) method with an additional resonant pump pulse. In RP-PORS, the resonant pump pulse excites the solute–solvent system and the subsequent relaxation of the solute–solvent system is monitored by the OHD-TG spectroscopy. RP-PORS is shown to be an excellent experimental tool to directly measure the solvent responses in solvation. In the present work, we extended our previous RP-PORS (Park et al., Phys. Chem. Chem. Phys., 2011, 13, 214–223) to measure time-dependent transient solvation polarizability (TSP) spectra with Coumarin153 (C153) in acetonitrile. The time-dependent TSP spectra showed how the different solvent intermolecular modes were involved in different stages of the solvation process. Most importantly, the inertial and diffusive components of the solvent intermolecular modes in solvation were found to be spectrally and temporally well-separated. In a dipolar solvation of C153, high-frequency inertial solvent modes were found to be driven instantaneously and decay on a subpicosecond timescale while low-frequency diffusive solvent modes were induced slowly and decayed on a picosecond timescale. Our present result is the first experimental manifestation of frequency-dependent solvent intermolecular response in a dipolar solvation.

We demonstrate controlled trapping and manipulation of single silver (Ag) nanowires in two dimensions at a surface using structured light fields generated with a spatial light modulator. The Ag nanowires are attracted toward the regions of maximal optical intensity along the surface when the trapping laser light is linearly polarized and are repelled toward the minima of optical intensity when the light is circularly polarized. For linearly polarized light, stably trapped nanowires are oriented perpendicular to the polarization direction due to a torque induced by an asymmetrical response of the nanowire to the electric field. The attractive interactions with linearly polarized trapping laser light, which is at 800 nm for all measurements, enable stable trapping and translation of Ag nanowires in the antinodes of optical gratings and in zero-order Bessel beams. Trapped nanowires can be positioned and oriented on a transparent dielectric substrate, making possible the nonmechanical assembly of plasmonic nanostructures for particular functions.Keywords: Ag nanowires; optical manipulation; optical tweezers; plasmonics; structured light

We demonstrate the plasmon-selective and driven deposition of (bipyramidal) Au nanoparticles on transparent substrates (glass coverslips) utilizing total internal reflection (TIR) illumination. Near-IR laser light undergoing TIR at a glass–water interface causes colloidal Au bipyramids to irreversibly deposit onto the glass surface. We demonstrate that the deposition process has particle (i.e., shape) selectivity that is associated with resonant plasmon excitation. Specifically, the deposition is selective for the bipyramids over spheroidal particles that are also present in solution due to the former’s surface plasmon resonance in the near-IR region. Our measurements, finite difference time domain simulations, and the results of an analytical model show that the optical (i.e., scattering and gradient) forces that act on the particles are large and cause the observed acceleration and directed motion of the bipyramids. These directional forces play a major role in the spatial pattern of particle deposition that is observed. In addition, the resonant photothermal heating of the Au bipyramids causes an irreversible loss in colloidal stability, thus allowing them to adhere to the surface. Structural (i.e., scanning electron microscopy) characterization of the deposited bipyramids reveals a slight reduction in aspect ratio relative to the ensemble, consistent with the proposed (heating) mechanism. To our knowledge this is the first demonstration of the plasmon-selective deposition of metal nanoparticles from a heterogeneous mixture.

Resonant pump polarizability response spectroscopy (RP-PORS) was used to study the isotropic and anisotropic solvent structural relaxation in solvation. RP-PORS is the optical heterodyne detected transient grating (OHD-TG) spectroscopy with an additional resonant pump pulse. A resonant pump excites the solute–solvent system and the subsequent relaxation of the solute–solvent system is monitored by the OHD-TG spectroscopy. This experimental method allows measuring the dispersive and absorptive parts of the signal as well as fully controlling the beam polarizations of incident pulses and signal. The experimental details of RP-PORS were described. By performing RP-PORS with Coumarin 153(C153) in CH3CN and CHCl3, we have successfully measured the isotropic and anisotropic solvation polarizability spectra following electronic excitation of C153. The isotropic solvation polarizability responses result from the isotropic solvent structural relaxation of the solvent around the solute whereas the anisotropic solvation polarizability responses come from the anisotropic translational relaxation and orientational relaxation. The solvation polarizability responses were found to be solvent-specific. The intramolecular vibrations of CHCl3 were also found to be coupled to the electronic excitation of C153.

We resolve information about the dynamics of simple liquids that has been obscured in prior frequency and time-domain measurements by way of full field-resolved polarization emission time (FR-PET) measurements of carbon disulfide. The amplitude and phase of the field-resolved transient-grating signal is used to calculate a spectrogram of the signal field at each delay between the transient-grating (TG) pump and probe pulses. The temporal maximum of the spectrogram, defined to be the signal emission time, varies with pump−probe delay; it follows the convolution of the TG pulses while the pulses overlap and exhibits recurrences at times when the nuclear dynamics are the main component of the liquid material response. Since this is a third-order nonlinear spectroscopic method, the isotropic and anisotropic signals are constructed from the polarization tensor components. The frequency-integrated anisotropic component of the signal is equivalent to the signal measured in optical Kerr Effect (OKE) experiments. The FR-PET determination of the signal emission times is a direct measurement of the third-order nonlinear (polarizability) polarization and, hence provides new strong constraints on appropriate models of the liquid dynamics. Models for the material response function are used to calculate the signal emission times. In particular, we show that the proper treatment of the time-correlation function for orientational motion gives the best fit to the FR-PET data for rotational diffusional motion. We also establish that librational motion is not a short-time (coherent) motion that leads to rotational diffusion. Finally, we find that the Bucaro−Litovitz form for interaction-induced dynamics is not entirely correct for the CS2 liquid we study. We suggest that the failing may result from the implicit assumption of two-body interactions, which is only appropriate for gases.

Three-dimensional finite-difference time-domain simulations were performed to explore the excitation of surface plasmon resonances in long silver (Ag) nanowires. In particular, we show that it is possible to generate plasmonic wave packets that can propagate along the nanowire by exciting superpositions of surface plasmon resonances. By using an appropriately chirped pulse, it is possible to transiently achieve localization of the excitation at the distal end of the nanowire. Such designed coherent superpositions will allow realizing spatiotemporal control of plasmonic excitations for enhancing nonlinear responses in plasmonic “circuits”.

Traditionally, microscopic fluctuations of molecules have been probed by measuring responses of an ensemble to perturbations. Now, single-molecule experiments are capable of following fluctuations without introducing perturbations. However, dynamics not readily sampled at equilibrium should be accessible to nonequilibrium single-molecule measurements. In a recent study [Qu, X. et al. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 6602−6607], the efficiency of fluorescence resonance energy transfer (FRET) between probes on the L18 loop and 3′ terminus of the 260 nucleotide RNase P RNA from Bacillus stearothermophilus was found to exhibit complex kinetics that depended on the (periodically alternating) concentration of magnesium ions ([Mg2+]) in solution. Specifically, this time series was found to exhibit a quasi-periodic response to a square-wave pattern of [Mg2+] changes. Because these experiments directly probe only one of the many degrees of freedom in the macromolecule, models are needed to interpret these data. We find that Hidden Markov Models are inadequate for describing the nonequilibrium dynamics, but they serve as starting points for the construction of models in which a discrete observable degree of freedom is coupled to a continuously evolving (hidden) variable. Consideration of several models of this general form indicates that the quasi-periodic response in the nonequilibrium experiments results from the switching (back and forth) in positions of the minima of the effective potential for the hidden variable. This switching drives oscillation of that variable and synchronizes the population to the changing [Mg2+]. We set the models in the context of earlier theoretical and experimental studies and conclude that single-molecule experiments with periodic peturbations can indeed yield qualitatively new information beyond that obtained at equilibrium.

Time- and wavelength-resolved pump−probe measurements are performed on the conductive, primary and secondary doped, forms of polyaniline in solution to investigate the relaxation dynamics of photoexcited polarons. Contrasting dynamics observed in the two forms allow investigation of electronic (and structural) relaxation of this material. Pump pulse at 800 nm photoexcites an electron from the valence to polaron band, and subsequent relaxation dynamics are probed by a white light continuum pulse. Three distinct features are observed in the primary doped sample: (1) absorption near time zero in the 900−1025 nm probe wavelength region; (2) delayed absorption from 850 to 1025 nm; (3) pronounced oscillations with frequencies of 165 and 210 cm−1. The first two features are associated with intraband absorptions to higher-lying states in the polaron band from the initial excited and conformationally changed intermediate states. The oscillations reflect torsional motions associated with photoexcitation and relaxation. In the secondary doped material, only bleaching and stimulated emission are observed throughout the whole spectral region; neither transient absorption signals nor oscillatory dynamics are observed. Kinetic modeling is performed to establish the mechanism of relaxation. We propose that the excited polaron relaxes nonradiatively to the ground state through an intermediate state(s) with a twisted geometry. Our measurements and analysis allow us to describe the structure of the polaron bands for primary and secondary doped polyaniline; they are in the small and large polaron limits, respectively, and are consistent with a bandgap for the primary doped form and without a bandgap (i.e., metallic) for the secondary doped material.

The evolution of RNA conformation with Mg²⁺ concentration ([Mg²⁺]) is typically determined from equilibrium titration measurements or nonequilibrium single [Mg²⁺]-jump measurements. We study the folding of single RNA molecules in response to a series of periodic [Mg²⁺] jumps. The 260-residue catalytic domain of RNase P RNA from Bacillus stearothermophilus is immobilized in a microfluidic flow chamber, and the RNA conformational changes are probed by fluorescence resonance energy transfer (FRET). The kinetics of population redistribution after a [Mg²⁺] jump and the observed connectivity of FRET states reveal details of the folding pathway that complement and transcend information from equilibrium or single-jump measurements. FRET trajectories for jumps from [Mg²⁺] = 0.01 to 0.1 mM exhibit two-state behavior whereas jumps from 0.01 mM to 0.4 mM exhibit two-state unfolding but multistate folding behavior. RNA molecules in the low and high FRET states before the [Mg²⁺] increase are observed to undergo dynamics in two distinct regions of the free energy landscape separated by a high barrier. We describe the RNA structural changes involved in crossing this barrier as a “hidden” degree of freedom because the changes do not alter the detected FRET value but do alter the observed dynamics. The associated memory prevents the populations from achieving their equilibrium values at the end of the 5- to 10-sec [Mg²⁺] interval, thereby creating a nonequilibrium steady-state condition. The capability of interrogating nonequilibrium steady-state RNA conformations and the adjustable period of [Mg²⁺]-jump cycles makes it possible to probe regions of the free energy landscape that are infrequently sampled in equilibrium or single-jump measurements.

We present a comprehensive study that integrates experimental and theoretical nonequilibrium techniques to map energy landscapes along well defined pull-axis specific coordinates to elucidate mechanisms of protein unfolding. Single-molecule force-extension experiments along two different axes of photoactive yellow protein combined with nonequilibrium statistical mechanical analysis and atomistic simulation reveal energetic and mechanistic anisotropy. Steered molecular dynamics simulations and free-energy curves constructed from the experimental results reveal that unfolding along one axis exhibits a transition-state-like feature where six hydrogen bonds break simultaneously with weak interactions observed during further unfolding. The other axis exhibits a constant (unpeaked) force profile indicative of a noncooperative transition, with enthalpic (e.g., H-bond) interactions being broken throughout the unfolding process. Striking qualitative agreement was found between the force-extension curves derived from steered molecular dynamics calculations and the equilibrium free-energy curves obtained by Jarzynski–Hummer–Szabo analysis of the nonequilibrium work data. The anisotropy persists beyond pulling distances of more than twice the initial dimensions of the folded protein, indicating a rich energy landscape to the mechanically fully unfolded state. Our findings challenge the notion that cooperative unfolding is a universal feature in protein stability.

The equilibrium folding of the catalytic domain of Bacillus subtilis RNase P RNA is investigated by single-molecule fluorescence resonance energy transfer (FRET). Previous ensemble studies of this 255-nucleotide ribozyme described the equilibrium folding with two transitions, U-to-Ieq-to-N, and focused on the Ieq-to-N transition. The present study focuses on the U-to-Ieq transition. Comparative ensemble measurements of the ribozyme construct labeled with fluorescein at the 5′ end and Cy3 at the 3′ end show that modifications required for labeling do not interfere with folding and help to define the Mg2+ concentration range for the U-to-Ieq transition. Histogram analysis of the Mg2+-dependent single-molecule FRET efficiency reveals two previously undetermined folding intermediates. The single-molecule FRET trajectories exhibit non-two-state and nonergodic behaviors at intermediate Mg2+ concentrations on the time scale of seconds. The trajectories at intermediate Mg2+ concentrations are classified into five classes based on three FRET levels and their dynamics of interconversion within the measured time range. This heterogeneity, together with the observation of “nonsudden jump” FRET transitions, indicates that the early folding steps of this ribozyme involve a series of intermediates with different degrees of kinetic isolation and that folding occurs under kinetic control and involves many “local” conformational switches. A free energy contour is constructed to illustrate the complex folding surface.

Fitting the image of a single molecule to the point spread function of an optical system greatly improves the precision with which single molecules can be located. Centroid localization with nanometer precision has been achieved when a sufficient number of photons are collected. However, if multiple single molecules reside within a diffraction-limited spot, this localization approach does not work. This paper demonstrates nanometer-localized multiple single-molecule (NALMS) fluorescence microscopy by using both centroid localization and photobleaching of the single fluorophores. Short duplex DNA strands are used as nanoscale “rulers” to validate the NALMS microscopy approach. Nanometer accuracy is demonstrated for two to five single molecules within a diffraction-limited area. NALMS microscopy will greatly facilitate single-molecule study of biological systems because it covers the gap between fluorescence resonance energy transfer-based (<10 nm) and diffraction-limited microscopy (>100 nm) measurements of the distance between two fluorophores. Application of NALMS microscopy to DNA mapping with <10-nm (i.e., 30-base) resolution is demonstrated.

The process of large RNA folding is believed to proceed from many collapsed structures to a unique functional structure requiring precise organization of nucleotides. The diversity of possible structures and stabilities of large RNAs could result in non-exponential folding kinetics (e.g. stretched exponential) under conditions where the molecules have not achieved their native state. We describe a single-molecule fluorescence resonance energy transfer (FRET) study of the collapsed-state region of the free energy landscape of the catalytic domain of RNase P RNA from Bacillus stearothermophilus (Cthermo). Ensemble measurements have shown that this 260 residue RNA folds cooperatively to its native state at ≥1 mM Mg2+, but little is known about the conformational dynamics at lower ionic strength. Our measurements of equilibrium conformational fluctuations reveal simple exponential kinetics that reflect a small number of discrete states instead of the expected inhomogeneous dynamics. The distribution of discrete dwell times, collected from an “ensemble” of 300 single molecules at each of a series of Mg2+ concentrations, fit well to a double exponential, which indicates that the RNA conformational changes can be described as a four-state system. This finding is somewhat unexpected under [Mg2+] conditions in which this RNA does not achieve its native state. Observation of discrete well-defined conformations in this large RNA that are stable on the seconds timescale at low [Mg2+] (<0.1 mM) suggests that even at low ionic strength, with a tremendous number of possible (weak) interactions, a few critical interactions may produce deep energy wells that allow for rapid averaging of motions within each well, and yield kinetics that are relatively simple.

We perform single-molecule spatial tracking measurements of a DNA repair protein, the C-terminal domain of Ada (C-Ada) from Escherichia coli, moving on DNA extended by flow. The trajectories of single proteins labeled with a fluorophore are constructed. We analyze single-protein dwell times on DNA for different flow rates and conclude that sliding (with essentially no hopping) is the mechanism of C-Ada motion along stretched DNA. We also analyze the trajectory results with a drift-diffusion Langevin equation approach to elucidate the influence of flow on the protein motion; systematic variation of the flow enables one to estimate the microscopic friction. We integrate the step-size probability distribution to obtain a version of the fluctuation theorem that articulates the relation between the entropy production and consumption under the adjustable drag (i.e., bias) from the flow. This expression allows validation of the Langevin equation description of the motion. Comparison of the rate of sliding with recent computer simulations of DNA repair suggests that C-Ada could conduct its repair function while moving at near the one-dimensional diffusion limit.

Resonant pump polarizability response spectroscopy (RP-PORS) was used to study the isotropic and anisotropic solvent structural relaxation in solvation. RP-PORS is the optical heterodyne detected transient grating (OHD-TG) spectroscopy with an additional resonant pump pulse. A resonant pump excites the solute–solvent system and the subsequent relaxation of the solute–solvent system is monitored by the OHD-TG spectroscopy. This experimental method allows measuring the dispersive and absorptive parts of the signal as well as fully controlling the beam polarizations of incident pulses and signal. The experimental details of RP-PORS were described. By performing RP-PORS with Coumarin 153(C153) in CH3CN and CHCl3, we have successfully measured the isotropic and anisotropic solvation polarizability spectra following electronic excitation of C153. The isotropic solvation polarizability responses result from the isotropic solvent structural relaxation of the solvent around the solute whereas the anisotropic solvation polarizability responses come from the anisotropic translational relaxation and orientational relaxation. The solvation polarizability responses were found to be solvent-specific. The intramolecular vibrations of CHCl3 were also found to be coupled to the electronic excitation of C153.

Resonant-pump polarizability response spectroscopy (RP-PORS) is based on an optical heterodyne detected transient grating (OHD-TG) method with an additional resonant pump pulse. In RP-PORS, the resonant pump pulse excites the solute–solvent system and the subsequent relaxation of the solute–solvent system is monitored by the OHD-TG spectroscopy. RP-PORS is shown to be an excellent experimental tool to directly measure the solvent responses in solvation. In the present work, we extended our previous RP-PORS (Park et al., Phys. Chem. Chem. Phys., 2011, 13, 214–223) to measure time-dependent transient solvation polarizability (TSP) spectra with Coumarin153 (C153) in acetonitrile. The time-dependent TSP spectra showed how the different solvent intermolecular modes were involved in different stages of the solvation process. Most importantly, the inertial and diffusive components of the solvent intermolecular modes in solvation were found to be spectrally and temporally well-separated. In a dipolar solvation of C153, high-frequency inertial solvent modes were found to be driven instantaneously and decay on a subpicosecond timescale while low-frequency diffusive solvent modes were induced slowly and decayed on a picosecond timescale. Our present result is the first experimental manifestation of frequency-dependent solvent intermolecular response in a dipolar solvation.