Force-extension (F-x) relationships were measured for single molecules of DNA under a variety of buffer conditions, using an optical trapping interferometer modified to incorporate feedback control. One end of a single DNA molecule was fixed to a coverglass surface by means of a stalled RNA polymerase complex. The other end was linked to a microscopic bead, which was captured and held in an optical trap. The DNA was subsequently stretched by moving the coverglass with respect to the trap using a piezo-driven stage, while the position of the bead was recorded at nanometer-scale resolution. An electronic feedback circuit was activated to prevent bead movement beyond a preset clamping point by modulating the light intensity, altering the trap stiffness dynamically. This arrangement permits rapid determination of the F-x relationship for individual DNA molecules as short as -1 micron with unprecedented accuracy, subjected to both low (approximately 0.1 pN) and high (approximately 50 pN) loads: complete data sets are acquired in under a minute. Experimental F-x relationships were fit over much of their range by entropic elasticity theories based on worm-like chain models. Fits yielded a persistence length, Lp, of approximately 47 nm in a buffer containing 10 mM Na1. Multivalent cations, such as Mg2+ or spermidine 3+, reduced Lp to approximately 40 nm. Although multivalent ions shield most of the negative charges on the DNA backbone, they did not further reduce Lp significantly, suggesting that the intrinsic persistence length remains close to 40 nm. An elasticity theory incorporating both enthalpic and entropic contributions to stiffness fit the experimental results extremely well throughout the full range of extensions and returned an elastic modulus of approximately 1100 pN.

RNA polymerase (RNAP) moves along DNA while carrying out transcription, acting as a molecular motor. Transcriptional velocities for single molecules of Escherichia coli RNAP were measured as progressively larger forces were applied by a feedback-controlled optical trap. The shapes of RNAP force-velocity curves are distinct from those of the motor enzymes myosin or kinesin, and indicate that biochemical steps limiting transcription rates at low loads do not generate movement. Modeling the data suggests that high loads may halt RNAP by promoting a structural change which moves all or part of the enzyme backwards through a comparatively large distance, corresponding to 5 to 10 base pairs. This contrasts with previous models that assumed force acts directly upon a single-base translocation step.

The force produced by a single molecule of Escherichia coli RNA polymerase during transcription was measured optically. Polymerase immobilized on a surface was used to transcribe a DNA template attached to a polystyrene bead 0.5 micrometer in diameter. The bead position was measured by interferometry while a force opposing translocation of the polymerase along the DNA was applied with an optical trap. At saturating nucleoside triphosphate concentrations, polymerase molecules stalled reversibly at a mean applied force estimated to be 14 piconewtons. This force is substantially larger than those measured for the cytoskeletal motors kinesin and myosin and exceeds mechanical loads that are estimated to oppose transcriptional elongation in vivo. The data are consistent with efficient conversion of the free energy liberated by RNA synthesis into mechanical work.

Schafer et al. (Nature 352:444-448 (1991)) devised the tethered particle motion (TPM) method to detect directly the movement of single, isolated molecules of a processive nucleic acid polymerase along a template DNA molecule. In TPM studies, the polymerase molecule is immobilized on a glass surface, and a particle (e.g., a 0.23 microns diameter polystyrene bead) is attached to one end of the enzyme-bound DNA molecule. Time-resolved measurements of the DNA contour length between the particle and the immobilized enzyme (the "tether length") are made by determining the magnitude of the Brownian motion of the DNA-tethered particle using light microscopy and digital image processing. We report here improved sample preparation methods that permit TPM data collection on transcript elongation by the Escherichia coli RNA polymerase at rates (approximately 10(2)-fold higher than those previously obtained) sufficient for practical use of microscopic kinetics techniques to analyze polymerase reaction mechanisms. In earlier TPM experiments, calculation of tether length from the observed Brownian motion was based on an untested numerical simulation of tethered bead Brownian motion. Using the improved methods, we have now empirically validated the TPM technique for tether lengths of 308-1915 base pairs (bp) using calibration specimens containing particles tethered by individual DNA molecules of known lengths. TPM analysis of such specimens yielded a linear calibration curve relating observed Brownian motion to tether length and allowed determination of the accuracy of the technique and measurement of how temporal bandwidth, tether length, and other experimental variables affect measurement precision. Under a standard set of experimental conditions (0.23 microns diameter bead, 0.23 Hz bandwidth, 23 degrees), accuracy is 108 and 258 bp r.m.s. at tether lengths of 308 and 1915 bp, respectively. Precision improves linearly with decreasing tether length to an extrapolated instrumentation limit of 10 bp r.m.s. and improves proportionally to the inverse square root of measurement bandwidth (1.9 x 10(2) bp Hz-1/2 for 1090-bp tethers). Measurements on large numbers of individual polymerase molecules reveal that time-averaged single-molecule elongation rates are more variable than is predicted from the random error in TPM measurements, demonstrating that the surface-immobilized RNA polymerase molecules are kinetically heterogeneous.