We use silicon strip detectors (originally developed for the CLEO III high energy particle physics experiment) to measure fluid particle trajectories in turbulence with temporal resolution of up to 70,000 frames per second. This high frame rate allows the Kolmogorov time scale of a turbulent water flow to be fully resolved for 140 ≥ R λ ≥ 970. Particle trajectories exhibiting accelerations up to 16,000 m s −2 (40 times the rms value) are routinely observed. The probability density function of the acceleration is found to have Reynolds number dependent stretched exponential tails. The moments of the acceleration distribution are calculated. The scaling of the acceleration component variance with the energy dissipation is found to be consistent with the results for low Reynolds number direct numerical simulations, and with the K41 based Heisenberg-Yaglom prediction for R λ ≥ 500. The acceleration flatness is found to increase with Reynolds number, and to exceed 60 at R λ = 970. The coupling of the acceleration to the large scale anisotropy is found to be large at low Reynolds number and to decrease as the Reynolds number increases, but to persist at all Reynolds numbers measured. The dependence of the acceleration variance on the size and density of the tracer particles is measured. The autocorrelation function of an acceleration component is measured, and is found to scale with the Kolmogorov time τ η .

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport[1, 2], processes in stirred chemical reactors and combustion systems [3], and in the industrial production of nanoparticles[4]. The perspective of particle trajectories has been used successfully to describe mixing and transport in turbulence[3, 5], but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations [6,7], based on the 1941 scaling theory of Kolmogorov[8, 9] (K41). Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that universal K41 scaling of the acceleration variance is attained at high Reynolds numbers. Our data show strong intermittency-particles are observed with accelerations of up to 1,500 times the acceleration of gravity (40 times the root mean square value). Finally, we find that accelerations manifest the anisotropy of the large scale flow at all Reynolds numbers studied.In principle, fluid particle trajectories are easily measured by seeding a turbulent flow with minute tracer particles and following their motions with an imaging system. In practice this can be a very challenging task since we must fully resolve particle motions which take place on times scales of the order of the Kolmogorov time, τ η = (ν/ǫ) 1/2 where ν is the kinematic viscosity and ǫ is the turbulent energy dissipation. This is exemplified in Fig. 1, which shows a measured three-dimensional, time resolved trajectory of a tracer particle undergoing violent accelerations in our turbulent water flow, for which τ η = 0.3 ms. The particle enters the detection volume on the upper right, is pushed to the left by a burst of acceleration and comes nearly to a stop before being rapidly accelerated (1200 times the acceleration of gravity) upward in a cork-screw motion. This trajectory illustrates the difficulty in following tracer particles-a particle's acceleration can go from zero to 30 times its rms value and back to zero in fractions of a millisecond and within distances of hundreds of micrometers.Conventional detector technologies are effective for low Reynolds number flows[10, 11], but do not provide adequate temporal resolution at high Reynolds numbers. However, the requirements are met by the use of silicon strip detectors as optical imaging elements in a particle tracking system. The strip detectors employed in our experiment (See Fig. 2a) were developed to measure particle tracks in the vertex detector of the CLEO III experiment operating at the Cornell Electron Positron Collider [12]. When applied to particle tracking in turbulence (See Fig. 2b) each detector measures a one-dimensional projection of the image of the tracer particles. Using a data acquisition system designed for the turbulence expe...

Transcriptional pausing by RNA polymerase (RNAP) plays an important role in the regulation of gene expression. Defined, sequence-specific pause sites have been identified biochemically. Single-molecule studies have also shown that bacterial RNAP pauses frequently during transcriptional elongation, but the relationship of these "ubiquitous" pauses to the underlying DNA sequence has been uncertain. We employed an ultrastable optical-trapping assay to follow the motion of individual molecules of RNAP transcribing templates engineered with repeated sequences carrying imbedded, sequence-specific pause sites of known regulatory function. Both the known and ubiquitous pauses appeared at reproducible locations, identified with base-pair accuracy. Ubiquitous pauses were associated with DNA sequences that show similarities to regulatory pause sequences. Data obtained for the lifetimes and efficiencies of pauses support a model where the transition to pausing branches off of the normal elongation pathway and is mediated by a common elemental state, which corresponds to the ubiquitous pause.

We describe an apparatus that can measure the instantaneous angular displacement and torque applied to a quartz particle which is angularly trapped. Torque is measured by detecting the change in angular momentum of the transmitted trap beam. The rotational Brownian motion of the trapped particle and its power spectral density are used to determine the angular trap stiffness. The apparatus features a feedback control that clamps torque or other rotational quantities. The torque sensitivity demonstrated is ideal for the study of known biological molecular motors.

By using single-molecule measurements, we demonstrate that the elongation kinetics of individual Escherichia coli RNA polymerase molecules are remarkably homogeneous. We find no evidence of distinct elongation states among RNA polymerases. Instead, the observed heterogeneity in transcription rates results from statistical variation in the frequency and duration of pausing. When transcribing a gene without strong pause sites, RNA polymerase molecules display transient pauses that are distributed randomly in both time and distance. Transitions between the active elongation mode and the paused state are instantaneous within the resolution of our measurements (<1 s). This elongation behavior is compared with that of a mutant RNA polymerase that pauses more frequently and elongates more slowly than wild type.T ranscription elongation is a processive but discontinuous process, with active synthesis of mRNA punctuated by transient pauses (1-4). Both bacteria and eukaryotes control gene expression in vivo by regulating pausing at specific sites on the DNA template (5, 6). Several regulatory pauses lead to long-lived isomerizations of the elongation complex, allowing transcription factors to bind the paused RNA polymerase (RNAP) and modify subsequent elongation (6-8). However, not all hesitation by the RNAP is thought to be regulatory; transcription of any naturally occurring template reveals numerous pauses with short half-lives, reflecting a distinct type of pausing that is inherent to the RNAP enzyme mechanism. At present, little is known about the RNAP configurations during these brief pauses or what governs the transition from active elongation to a paused state in the absence of specific regulatory signals.These dynamic aspects of elongation are obscured when studying a population of RNAP molecules in which the asynchronous behavior of individual RNAPs is smeared into an ensemble-average. Analyzing the motion of single RNAP molecules in real time eliminates the complication of population dynamics, revealing the kinetic interplay between active elongation and nonproductive states (9-12). Furthermore, continuous tracking of individual RNAPs exposes any variation in the behavior of single RNAP molecules as well as the differences that exist between RNAPs.There is more asynchrony during transcription elongation than would be generated by an enzymatic reaction with a single rate-limiting step, but the mechanisms leading to the additional asynchrony have yet to be clearly defined (13). Transcriptional pausing, where a fraction of RNAP stop at discrete sites for a variable duration, is known to induce dispersion of the population. However, whether or not the stochastic behavior of a structurally homogeneous population is sufficient to generate the observed levels of asynchrony, or if one must also invoke alternate stable RNAP conformations is a subject of debate. A recent study of single RNAP molecules suggests that an elongating RNAP population is composed of RNAPs in distinct states that elongate at different intrinsic ...