Internal mechanical response of a polymer in solution

Structural Asymmetry and Kinetic Limping of Single Rotary F-ATP Synthases

F-ATP synthases use proton flow through the FO domain to synthesize ATP in the F₁ domain. In Escherichia coli, the enzyme consists of rotor subunits γεc10 and stator subunits (αβ)₃δab₂. Subunits c10 or (αβ)₃ alone are rotationally symmetric. However, symmetry is broken by the b₂ homodimer, which together with subunit δa, forms a single eccentric stalk connecting the membrane embedded FO domain with the soluble F₁ domain, and the central rotating and curved stalk composed of subunit γε. Although each of the three catalytic binding sites in (αβ)₃ catalyzes the same set of partial reactions in the time average, they might not be fully equivalent at any moment, because the structural symmetry is broken by contact with b₂δ in F₁ and with b₂a in FO. We monitored the enzyme's rotary progression during ATP hydrolysis by three single-molecule techniques: fluorescence video-microscopy with attached actin filaments, Förster resonance energy transfer between pairs of fluorescence probes, and a polarization assay using gold nanorods. We found that one dwell in the three-stepped rotary progression lasting longer than the other two by a factor of up to 1.6. This effect of the structural asymmetry is small due to the internal elastic coupling.

Entangled polymer dynamics beyond reptation

Macroscopic properties of polymers arise from microscopic entanglement of polymer chains. Entangled polymer dynamics have been described theoretically by time- and space-averaged relaxation modes of single chains occurring at different time and length scales. However, theoretical and experimental studies along this framework provide oversimplified picture of spatiotemporally heterogeneous polymer dynamics. Characterization of entangled polymer dynamics beyond this paradigm requires a method that enables to capture motion and relaxation occurring in real space at different length and time scales. Here we develop new single-molecule characterization platform by combining super-resolution fluorescence imaging and recently developed single-molecule tracking method, cumulative-area tracking, which enables to quantify the chain motion in the length and time scale of nanometres to micrometres and milliseconds to minutes. Using linear and cyclic dsDNA molecules as model systems, our new method reveals chain-position-dependent motion of the entangled linear chains, which is beyond the scope of current theoretical framework.

Conserved linear dynamics of single-molecule Brownian motion

Macromolecular diffusion in homogeneous fluid at length scales greater than the size of the molecule is regarded as a random process. The mean-squared displacement (MSD) of molecules in this regime increases linearly with time. Here we show that non-random motion of DNA molecules in this regime that is undetectable by the MSD analysis can be quantified by characterizing the molecular motion relative to a latticed frame of reference. Our lattice occupancy analysis reveals unexpected sub-modes of motion of DNA that deviate from expected random motion in the linear, diffusive regime. We demonstrate that a subtle interplay between these sub-modes causes the overall diffusive motion of DNA to appear to conform to the linear regime. Our results show that apparently random motion of macromolecules could be governed by non-random dynamics that are detectable only by their relative motion. Our analytical approach should advance broad understanding of diffusion processes of fundamental relevance.

Single Molecules Trapped by Dynamic Inhomogeneous Temperature Fields

We demonstrate a single molecule trapping concept that modulates the actual driving force of Brownian motion--the temperature. By spatially and temporally varying the temperature at a plasmonic nanostructure, thermodiffusive drifts are induced that are used to trap single nano-objects. A feedback controlled switching of local temperature fields allows us to confine the motion of a single DNA molecule for minutes and tailoring complex effective trapping potentials. This new type of thermophoretic microbeaker even provides control over a well-defined number of single molecules and is scalable to large arrays of trapping structures.

Single-molecule diffusion and conformational dynamics by spatial integration of temporal fluctuations

Single-molecule localization and tracking has been used to translate spatiotemporal information of individual molecules to map their diffusion behaviours. However, accurate analysis of diffusion behaviours and including other parameters, such as the conformation and size of molecules, remain as limitations to the method. Here, we report a method that addresses the limitations of existing single-molecular localization methods. The method is based on temporal tracking of the cumulative area occupied by molecules. These temporal fluctuations are tied to molecular size, rates of diffusion and conformational changes. By analysing fluorescent nanospheres and double-stranded DNA molecules of different lengths and topological forms, we demonstrate that our cumulative-area method surpasses the conventional single-molecule localization method in terms of the accuracy of determined diffusion coefficients. Furthermore, the cumulative-area method provides conformational relaxation times of structurally flexible chains along with diffusion coefficients, which together are relevant to work in a wide spectrum of scientific fields.

Single-molecule localization and tracking technique is widely used to visualize molecular dynamics in life science, yet it fails to detect molecular conformation. Serag et al. address this limitation via spatial quantization of temporal fluctuations in the cumulative area occupied by molecules.

Role of microscopic flexibility in tightly curved DNA

The genetic material in living cells is organized into complex structures in which DNA is subjected to substantial contortions. Here we investigate the difference in structure, dynamics, and flexibility between two topological states of a short (107 base pair) DNA sequence in a linear form and a covalently closed, tightly curved circular DNA form. By employing a combination of all-atom molecular dynamics (MD) simulations and elastic rod modeling of DNA, which allows capturing microscopic details while monitoring the global dynamics, we demonstrate that in the highly curved regime the microscopic flexibility of the DNA drastically increases due to the local mobility of the duplex. By analyzing vibrational entropy and Lipari–Szabo NMR order parameters from the simulation data, we propose a novel model for the thermodynamic stability of high-curvature DNA states based on vibrational untightening of the duplex. This novel view of DNA bending provides a fundamental explanation that bridges the gap between classical models of DNA and experimental studies on DNA cyclization, which so far have been in substantial disagreement.

Real-time calibration of a feedback trap

Feedback traps use closed-loop control to trap or manipulate small particles and molecules in solution. They have been applied to the measurement of physical and chemical properties of particles and to explore fundamental questions in the non-equilibrium statistical mechanics of small systems. These applications have been hampered by drifts in the electric forces used to manipulate the particles. Although the drifts are small for measurements on the order of seconds, they dominate on time scales of minutes or slower. Here, we show that a recursive maximum likelihood (RML) algorithm can allow real-time measurement and control of electric and stochastic forces over time scales of hours. Simulations show that the RML algorithm recovers known parameters accurately. Experimental estimates of diffusion coefficients are also consistent with expected physical properties.

Intrachain dynamics of large dsDNA confined to slitlike channels

Exploration of intrachain hydrodynamics of dsDNA within channels has been limited to indirect analysis of global coil dynamics. In this Letter, we isolate hydrodynamic interactions within single molecules of dsDNA confined to slitlike channels by making use of density covariance measurements. We show that the strength of hydrodynamic interactions in DNA is dependent on the intrachain correlation length and that screening by symmetry in slitlike confinement results in a screening length that is proportional channel height. Moreover, we directly show the partial draining nature of the blobs formed by dsDNA in slits and predict under what conditions a dsDNA blob should obey nondraining Zimm behavior.

Fluctuation modes of nanoconfined DNA

We report an experimental investigation of the magnitude of length and density fluctuations in DNA that has been stretched in nanofluidic channels. We find that the experimental data can be described using a one-dimensional overdamped oscillator chain with nonzero equilibrium spring length and that a chain of discrete oscillators yields a better description than a continuous chain. We speculate that the scale of these discrete oscillators coincides with the scale at which the finite extensibility of the polymer manifests itself. We discuss how the measurement process influences the apparent measured dynamic properties, and outline requirements for the recovery of true physical quantities.

Microfluidic systems for single DNA dynamics

Recent advances in microfluidics have enabled the molecular-level study of polymer dynamics using single DNA chains. Single polymer studies based on fluorescence microscopy allow for the direct observation of non-equilibrium polymer conformations and dynamical phenomena such as diffusion, relaxation, and molecular stretching pathways in flow. Microfluidic devices have enabled the precise control of model flow fields to study the non-equilibrium dynamics of soft materials, with device geometries including curved channels, cross-slots, and microfabricated obstacles and structures. This review explores recent microfluidic systems that have advanced the study of single polymer dynamics, while identifying new directions in the field that will further elucidate the relationship between polymer microstructure and bulk rheological properties.

Density fluctuations dispersion relationship for a polymer confined to a nanotube

DNA confined to rigid nanotubes shows density fluctuations around its stretched equilibrium conformation. We report an experimental investigation of the length-scale dependent dynamics of these density fluctuations. We find that for highly elongated molecules a Rouse description is consistent with observations at sufficiently large length scales. We further find that for strongly fluctuating molecules, or short length scales, such Rouse modes cannot be detected due to strong mixing of fluctuation modes.

Intramolecular fluorescence correlation spectroscopy in a feedback tracking microscope

We derive the statistics of the signals generated by shape fluctuations of large molecules studied by feedback tracking microscopy. We account for the influence of intramolecular dynamics on the response of the tracking system and derive a general expression for the fluorescence autocorrelation function that applies when those dynamics are linear. We show that in comparison to traditional fluorescence correlation spectroscopy, tracking provides enhanced sensitivity to translational diffusion, molecular size, heterogeneity, and long-timescale decays. We demonstrate our approach using a three-dimensional tracking microscope to study genomic lambda-phage DNA molecules with various fluorescence label configurations.

Precise characterization of the conformation fluctuations of freely diffusing DNA: beyond Rouse and Zimm

We studied the dynamics of single freely diffusing fluorescence-labeled double-stranded lambda-phage DNA molecules using dual-color 3-dimensional feedback tracking microscopy and intramolecular fluorescence correlation spectroscopy. Our technique is independently sensitive to the molecule's diffusion coefficient D and radius of gyration R(g) and is concentration insensitive, providing greater precision for characterizing the molecule's intramolecular motion than other methods. We measured D = 0.80 +/- 0.05 microm(2)/s and R(g) approximately 420 nm, consistent with the Kirkwood-Riseman prediction for a flexible polymer with strong hydrodynamic interactions (HI), but we find the statistics of intramolecular motion inconsistent with the Zimm model for such a polymer. We address a dispute in the experimental literature, finding that previous measurements on double-stranded DNA likely lacked the sensitivity to distinguish between the Zimm model and the HI-free Rouse model. Finally, we observe fluorescence fluctuations with a correlation time of over 2 s that cannot be explained by either model and propose that they may be signatures of excluded volume interactions.

Anti-Brownian traps for studies on single molecules

Until recently, Brownian motion was seen as an immutable feature of small particles in room-temperature liquids. Molecules, viruses, organelles, and small cells jiggle incessantly due to countless collisions with thermally agitated molecules of solvent. Einstein showed in 1905 that this motion is intimately linked to the tendency of every system to relax toward thermal equilibrium. In recent years, we and others have realized that Brownian motion is not as inescapable as one might think. By tracking the motion of a small particle and applying correction forces to the particle or to the measurement apparatus, one can largely suppress the Brownian motion of particles as small as a few nanometers in diameter, in aqueous solution at room temperature. This new ability to stabilize single molecules has led to a host of studies on topics ranging from the conformational dynamics of DNA to the optical properties of metal nanoparticles. In this review, we outline the physical principles behind suppression of Brownian motion. We discuss the relative merits of several systems that have been implemented. We give examples of studies performed with our anti-Brownian Electrokinetic trap (ABEL trap) as well as other anti-Brownian traps, and we discuss prospects for future research.

An optical conveyor for molecules

Trapping single ions under vacuum allows for precise spectroscopy in atomic physics. The confinement of biological molecules in bulk water is hindered by the lack of comparably strong forces. Molecules have been immobilized to surfaces, however often with detrimental effects on their function. Here, we optically trap molecules by creating the microscale analogue of a conveyor belt: a bidirectional flow is combined with a perpendicular thermophoretic molecule drift. Arranged in a toroidal geometry, the conveyor accumulates a hundredfold excess of 5-base DNA within seconds. The concentrations of the trapped DNA scale exponentially with length, reaching trapping potential depths of 14 kT for 50 bases. The mechanism does not require microfluidics, electrodes, or surface modifications. As a result, the trap can be dynamically relocated. The optical conveyor can be used to enhance diffusion-limited surface reactions, redirect cellular signaling, observe individual biomolecules over a prolonged time, or approach single-molecule chemistry in bulk water.

Atomic hydrodynamics of DNA: coil-uncoil-coil transitions in a wall-bounded shear flow

Extensive experimental work on the response of DNA molecules to externally applied forces and on the dynamics of DNA molecules flowing in microchannels and nanochannels has been carried out over the past two decades, however, there has not been available, until now, any atomic-scale means of analyzing nonequilibrium DNA response dynamics. There has not therefore been any way to investigate how the backbone and side-chain atoms along the length of a DNA molecule interact with the molecules and ions of the flowing solvent and with the atoms of passing boundary surfaces. We report here on the application of the nonequilibrium biomolecular dynamics simulation method that we developed [G. M. Wang and W. C. Sandberg, Nanotechnology 18, 4819 (2007)] to analyze, at the atomic interaction force level, the conformational dynamics of short-chain single-stranded DNA molecules in a shear flow near a surface. This is a direct atomic computational analysis of the hydrodynamic interaction between a biomolecule and a flowing solvent. The DNA molecules are observed to exhibit conformational behaviors including coils, hairpin loops, and figure-eight shapes that have neither been previously measured experimentally nor observed computationally, as far as we know. We relate the conformational dynamics to the atomic interaction forces experienced throughout the length of a molecule as it moves in the flowing solvent past the surface boundary. We show that the DNA conformational dynamics is related to the asymmetry in the molecular environment induced by the motion of the surrounding molecules and the atoms of the passing surface. We also show that while the asymmetry in the environment is necessary, it is not sufficient to produce the observed conformational dynamics. A time variation in the asymmetry, due in our case to a shear flow, must also exist. In order to contrast these results with the usual experimental situation of purely diffusive motion in thermal equilibrium we have also carried out computations with a zero shear rate. We show that in thermal equilibrium there is asymmetry and an atomic hydrodynamic coupling between DNA molecules and the solvent molecules but there is no coil-uncoil transition.

Controlling Brownian motion of single protein molecules and single fluorophores in aqueous buffer

We present an Anti-Brownian Electrokinetic trap (ABEL trap) capable of trapping individual fluorescently labeled protein molecules in aqueous buffer. The ABEL trap operates by tracking the Brownian motion of a single fluorescent particle in solution, and applying a time-dependent electric field designed to induce an electrokinetic drift that cancels the Brownian motion. The trapping strength of the ABEL trap is limited by the latency of the feedback loop. In previous versions of the trap, this latency was set by the finite frame rate of the camera used for video-tracking. In the present system, the motion of the particle is tracked entirely in hardware (without a camera or image-processing software) using a rapidly rotating laser focus and lock-in detection. The feedback latency is set by the finite rate of arrival of photons. We demonstrate trapping of individual molecules of the protein GroEL in buffer, and we show confinement of single fluorophores of the dye Cy3 in water.

Structure-fluorescence contrast relationship in cyanine DNA intercalators: toward rational dye design

The fluorescence enhancement mechanisms of a series of DNA stains of the oxazole yellow (YO) family have been investigated in detail using steady-state and ultrafast time-resolved fluorescence spectroscopy. The strong increase in the fluorescence quantum yield of these dyes upon DNA binding is shown to originate from the inhibition of two distinct processes: 1) isomerisation through large-amplitude motion that non-radiatively deactivates the excited state within a few picoseconds and 2) formation of weakly emitting H-dimers. As the H-dimers are not totally non-fluorescent, their formation is less efficient than isomerisation as a fluorescent contrast mechanism. The propensity of the dyes to form H-dimers and thus to reduce their fluorescence contrast upon DNA binding is shown to depend on several of their structural parameters, such as their monomeric (YO) or homodimeric (YOYO) nature, their substitution and their electric charge. Moreover, these parameters also have a substantial influence on the affinity of the dyes for DNA and on the ensuing sensitivity for DNA detection. The results give new insight into the development and optimisation of fluorescent DNA probes with the highest contrast.

Quantum dot photon statistics measured by three-dimensional particle tracking

We present an instrument for performing correlation spectroscopy on single fluorescent particles while tracking their Brownian motion in three dimensions using real-time feedback. By tracking CdSe/ZnS quantum dots in water (diffusion coefficient approximately 20 microm2/s), we make the first measurements of photon antibunching (at approximately 10 ns) on single fluorophores free in solution and find fluorescence lifetime heterogeneity within a quantum dot sample. In addition, we show that 2-mercaptoethanol suppresses short time-scale intermittency (1 ms to 1 s) in quantum dot fluorescence by reducing time spent in the off-state.

New directions in single-molecule imaging and analysis

Optical imaging and analysis of single molecules continue to unfold as powerful ways to study the individual behavior of biological systems, unobscured by ensemble averaging. Current expansion of interest in this field is great, as evidenced by new meetings, journal special issues, and the large number of new investigators. Selected recent advances in biomolecular analysis are described, and two new research directions are summarized: superresolution imaging using single-molecule fluorescence and trapping of single molecules in solution by direct suppression of Brownian motion.

Principal-components analysis of shape fluctuations of single DNA molecules

Thermal fluctuations agitate molecules in solution over a broad range of times and distances. By passively watching the shape fluctuations of a thermally driven biomolecule, one can infer properties of the underlying interactions that determine the motion. We applied this concept to single molecules of fluorescently labeled lambda-DNA, a key model system for polymer physics. In contrast to most other single-molecule DNA experiments, we examined the unstretched, equilibrium state of DNA by using an anti-Brownian electrokinetic trap to confine the center of mass of the DNA without perturbing its internal dynamics. We analyze the long-wavelength conformational normal modes, calculate their spring constants, and measure linear and nonlinear couplings between modes. The modes show strong signs of nonlinear hydrodynamics, a feature of the underlying equations of polymer dynamics that has not previously been reported and is neglected in the widely used Rouse and Zimm approximations.