Semiflexible polymers are of great biological importance in determining the mechanical properties of cells. Techniques collectively known as microrheology have recently been developed to measure the viscoelastic properties of solutions of submicroliter volumes. We employ one such technique, which uses a focused laser beam to trap a micron-sized silica bead and interferometric photodiode detection to measure passively the position fluctuations of the trapped bead with nanometer resolution and high bandwidth. The frequency-dependent complex shear modulus G*(f) can be extracted from the position fluctuations via the fluctuation-dissipation theorem and the generalized Stokes-Einstein relation. Using particle tracking microrheology, we report measurements of shear moduli of solutions of fd viruses, which are filamentous, semiflexible, and monodisperse bacteriophages, each 0.9 microm long, 7 nm in diameter, and having a persistence length of 2.2 microm. Recent theoretical treatments of semiflexible polymer dynamics provide quantitative predictions of the rheological properties of such a model system. The fd samples measured span the dilute, semidilute, and concentrated regimes. In the dilute regime G*(f) is dominated by (rigid rod) rotational relaxation, whereas the high-frequency regime reflects single-semiflexible filament dynamics consistent with the theoretical prediction. Due to the short length of fd viruses used in this study, the intermediate regime does not exhibit a well-developed plateau. A dynamic scaling analysis gives rise to a concentration scaling of c(1.36) (r=0.99) in the transition regime and a frequency scaling of f(0.63) (r=0.98) at high frequencies.

The Brownian motions of microscopic particles in viscous or viscoelastic fluids can be used to measure rheological properties. This is the basis of recently developed one- and two-particle microrheology techniques. For increased temporal and spatial resolution, some microrheology techniques employ optical traps, which introduce additional forces on the particles. We have systematically studied the effect that confinement of particles by optical traps has on their auto- and cross-correlated fluctuations. We show that trapping causes anticorrelations in the motion of two particles at low frequencies. We demonstrate how these anticorrelations depend on trap strength and the shear modulus of viscoelastic media. We present a method to account for the effects of optical traps, which permits the quantitative measurement of viscoelastic properties in one- and two-particle microrheology over an extended frequency range in a variety of viscous and viscoelastic media.

The correlated motions of two micron-sized particles reflect the ͑micro-͒ rheological properties of a fluid and can be conveniently detected using two optical traps in combination with interferometric displacement detection. When the correlations become small, cross-talk between the two beams becomes important. We have used dual optical traps created by either two orthogonally polarized laser beams derived from one laser source, or by two independent lasers of different wavelengths for microrheology experiments. High numerical aperture lenses ͑objective and condenser͒ in the optical path can introduce depolarization, and polarizing beam splitters are not perfect, both of which can lead to optical cross-talk. We have characterized the cross-talk in our setup and demonstrate that the use of two independent laser eliminates cross-talk entirely.

We report on the construction of colloidal stars: 1 microm polystyrene beads grafted with a dense brush of 1 microm long and 10 nm wide charged semiflexible filamentous viruses. The pair interaction potentials of colloidal stars are measured using an experimental implementation of umbrella sampling, a technique originally developed in computer simulations in order to probe rare events. The influence of ionic strength and grafting density on the interaction is measured. Good agreements are found between the measured interactions and theoretical predictions based upon the osmotic pressure of counterions.

Semiflexible polymers are of great biological importance in determining the mechanical properties of cells. We have used optical tweezers to trap pairs of micron-sized silica spheres in solutions of semiflexible polymers, and laser interferometry to detect their thermal motions with high bandwidth. Frequency-dependent complex shear moduli were extracted from the auto-and cross-correlated bead motions, with the response functions being derived from position-fluctuation data using dispersion relations from linear response theory.