Relating the microscopic and macroscopic response of a polymeric fluid in a shearing flow.

The microscopic and macroscopic response of a polymer solution in start-up shear flow was investigated using fluorescence microscopy of single molecules, bulk viscosity measurements, and Brownian dynamics simulations. An overshoot in viscosity was observed upon flow inception and understood via the observed molecular extension and by simulation findings. Increasing the polymer concentration up to six times the overlap concentration ( C(*)) has no effect on the character of the dynamics of individual molecules.

A single-molecule study of RNA catalysis and folding.

Using fluorescence microscopy, we studied the catalysis by and folding of individual Tetrahymena thermophila ribozyme molecules. The dye-labeled and surface-immobilized ribozymes used were shown to be functionally indistinguishable from the unmodified free ribozyme in solution. A reversible local folding step in which a duplex docks and undocks from the ribozyme core was observed directly in single-molecule time trajectories, allowing the determination of the rate constants and characterization of the transition state. A rarely populated docked state, not measurable by ensemble methods, was observed. In the overall folding process, intermediate folding states and multiple folding pathways were observed. In addition to observing previously established folding pathways, a pathway with an observed folding rate constant of 1 per second was discovered. These results establish single-molecule fluorescence as a powerful tool for examining RNA folding.

Single-polymer dynamics in steady shear flow.

The conformational dynamics of individual, flexible polymers in steady shear flow were directly observed by the use of video fluorescence microscopy. The probability distribution for the molecular extension was determined as a function of shear rate, gamma;, for two different polymer relaxation times, tau. In contrast to the behavior in pure elongational flow, the average polymer extension in shear flow does not display a sharp coil-stretch transition. Large, aperiodic temporal fluctuations were observed, consistent with end-over-end tumbling of the molecule. The rate of these fluctuations (relative to the relaxation rate) increased as the Weissenberg number, gamma;tau, was increased.

Effect of anisotropy of the bending rigidity on the supercoiling free energy of small circular DNAs.

In principle, the supercoiling free energy of a small circular DNA will be enhanced by increasing the anisotropy of its bending potential at constant persistence length. The magnitude of this effect is investigated by Monte Carlo simulation using an extension of a previously proposed algorithm. The supercoiling free energy at 298 K is simulated for circular DNAs containing N = bp with torsion constant alpha = 5.8 X 10(-12) dyne cm, persistence lengths P = 500 A and 10,000 A, and a range of anisotropies of the bending potential from rho = 1.0 to 16.0. The apparent torsion constants, reckoned from these supercoiling free energies by assuming an isotropic bending potential, are found to increase by less than 3% as the input anisotropy increases from 1.0 to 16.0 When P = 500 A, the apparent torsion constant never rises significantly above the input value over the entire range of input anisotropies. When P = 10,000 A, the apparent torsion constant rises only about 3% above the input value for anisotropies rho = 8.0 and 16.0. Evidently, anisotropy of the bending potential cannot account for the fact that the torsion constants reported for small circular DNAs exceed those reported for long linear DNAs by a factor of 1.6 or more.

A test of the model-free formulas. Effects of anisotropic rotational diffusion and dimerization.

The effects of anisotropy of rotational diffusion and extent of dimerization on the performance of the simple and extended model-free formulas are investigated. Numerically exact 15N NMR R1, R2, and NOE data are simulated for cylindrically symmetric species and also for mixtures of spherical monomers and dimers with the same internal dynamics. The relevant internuclear vectors are assumed to move in isotropic deflection potentials fixed at different orientations in the molecule and to exhibit a single relaxation time in their internal correlation functions. The simple model-free formula is fitted to these simulated data in order to obtain the best-fit order parameter and internal relaxation time for each nucleus. Fitting is accomplished by the standard data-analysis protocol, in which a single common global correlation time is adjusted, and also by an alternative protocol, in which the global correlation time is adjusted separately for each nucleus. The extended model-free formula is likewise fitted to these same data. With noise-free data, the simple model-free formula and standard protocol yield remarkably good best-fit internal motion parameters up to moderate anisotropies (r = D parallel/D perpendicular = 2.0), but some or many of the NMR relaxation data are not fitted well even for quite modest anisotropies (r = 1.3). The extended model-free formula yields an improved fit to the NMR data, but predicts substantial amplitudes of nonexistent slow internal motions (tau approximately greater than 0.2 ns) for many of the nuclei for all r > or = 1.3. The simple model-free formula with the alternate protocol yields even better internal motion parameters than the standard protocol and also an excellent fit to the NMR relaxation data. The best-fit global correlation time for each nucleus corresponds very closely to the theoretical correlation time defined herein. Knowledge of these times would allow one not only to estimate the anisotropy of diffusion but also in favorable cases to infer the existence of slow internal motions. Inclusion of typical statistical errors in R1, R2, and NOE, or modest exchange contributions to R2, seriously degrades the performance of the simple model-free formula with either protocol, especially in regard to the internal relaxation times, which can exhibit very large deviations from their input value even for spherical diffusors. When the fraction of monomers existing as dimers lies in the range 0.1 < or = fd < or = 0.8, none of the three model-free approaches tested yields reliable internal motion parameters.