We describe a high-resolution, high-bandwidth technique for determining the local viscoelasticity of soft materials such as polymer gels. Loss and storage shear moduli are determined from the power spectra of thermal fluctuations of embedded micron-sized probe particles, observed with an interferometric microscope. This provides a passive, small-amplitude measurement of rheological properties over a much broader frequency range than previously accessible to microrheology. We study both F-actin biopolymer solutions and polyacrylamide (PAAm) gels, as model semiflexible and flexible systems, respectively. We observe high-frequency ω 3/4 scaling of the shear modulus in F-actin solutions, in contrast to ω 1/2 scaling for PAAm.PACS numbers: 61.30. Cz, 64.70.Md, 83.70.Jr The local analysis of viscoelasticity can explore the small-scale structure of complex fluids. It can also potentially measure bulk viscoelastic quantities in small samples. Experiments have been done to characterize the local viscoelasticity of materials since at least the 1920s, when magnetic particles in gelatin were manipulated by field gradients [1]. Crick used a similar technique to study living cells [2]. With the recent advent of methods for force generation, detection, and manipulation of particles on sub-micrometer scales, experimental possibilities have expanded greatly, and interest in microrheology has grown substantially [3][4][5][6][7][8]. Here we report an optical technique for high resolution and high bandwidth observations of the thermal fluctuations of particles embedded in soft materials. Using dispersion relations from linear response theory, the frequency-dependent loss and elastic storage shear moduli are both calculated from the fluctuation power spectra, which we measure with a resolution of 2Åfrom 0.1 Hz to 20 kHz. This frequency range exceeds that of video-based microrheological experiments (although large-volume rheometers can reach frequencies up to 500 kHz [9]) and allowed us to observe high-frequency ω 3/4 scaling of the shear modulus for entangled, semiflexible solutions. These dynamics differ fundamentally from those of flexible polymer systems.We have studied F-actin solutions as a model semiflexible polymer, and polyacrylamide (PAAm) gels as a flexible polymer control. Actin is one of the primary components of the cytoskeleton of plant and animal cells and is largely responsible for the viscoelastic response of cells [10]. Actin is a particularly accessible model system because individual filaments can be hundreds of microns in length. Viscoelastic properties of entangled F-actin solutions in vitro have been measured using conventional macroscopic rheology [11][12][13][14][15]. Actin has also been the subject of recent microrheological studies [3][4][5][6].The relationship between thermal motion and hydrodynamic response is well-known in the context of Brownian motion in simple viscous fluids. Less obviously, the bulk viscoelastic properties of complex fluids can also be determined from thermal motion. Such a passi...

We have developed a new technique to measure viscoelasticity in soft materials such as polymer solutions, by monitoring thermal fluctuations of embedded probe particles using laser interferometry in a microscope. Interferometry allows us to obtain power spectra of fluctuating beads from 0.1 Hz to 20 kHz, and with subnanometer spatial resolution. Using linear response theory, we determined the frequency-dependent loss and storage shear moduli up to frequencies on the order of a kHz. Our technique measures local values of the viscoelastic response, without actively straining the system, and is especially suited to soft biopolymer networks. We studied semiflexible F-actin solutions and, as a control, flexible polyacrylamide (PAAm) gels, the latter close to their gelation threshold. With small particles, we could probe the transition from macroscopic viscoelasticity to more complex microscopic dynamics. In the macroscopic limit we find shear moduli at 0.1 Hz of G ′ = 0.11±0.03 Pa and 0.17±0.07 Pa for 1 and 2 mg/ml actin solutions, close to the onset of the elastic plateau, and scaling behavior consistent with G * (ω) ∼ ω 3/4 at higher frequencies. For polyacrylamide we measured plateau moduli of 2.0, 24, 100 and 280 Pa for crosslinked gels of 2, 2.5, 3 and 5% concentration (weight/volume) respectively, in agreement to within a factor of two with values obtained from conventional rheology. We also found evidence for scaling of G * (ω) ∼ ω 1/2 , consistent with the predictions of the Rouse model for flexible polymers.

Fis, the most abundant DNA-binding protein in Escherichia coli during rapid growth, has been suspected to play an important role in defining nucleoid structure. Using bulk-phase and single-DNA molecule experiments, we analyze the structural consequences of non-specific binding by Fis to DNA. Fis binds DNA in a largely sequence-neutral fashion at nanomolar concentrations, resulting in mild compaction under applied force due to DNA bending. With increasing concentration, Fis first coats DNA to form an ordered array with one Fis dimer bound per 21 bp and then abruptly shifts to forming a higher-order Fis-DNA filament, referred to as a low-mobility complex (LMC). The LMC initially contains two Fis dimers per 21 bp of DNA, but additional Fis dimers assemble into the LMC as the concentration is increased further. These complexes, formed at or above 1 microM Fis, are able to collapse large DNA molecules via stabilization of DNA loops. The opening and closing of loops on single DNA molecules can be followed in real time as abrupt jumps in DNA extension. Formation of loop-stabilizing complexes is sensitive to high ionic strength, even under conditions where DNA bending-compaction is unaltered. Analyses of mutants indicate that Fis-mediated DNA looping does not involve tertiary or quaternary changes in the Fis dimer structure but that a number of surface-exposed residues located both within and outside the helix-turn-helix DNA-binding region are critical. These results suggest that Fis may play a role in vivo as a domain barrier element by organizing DNA loops within the E. coli chromosome.

Motivated by results from an earlier Brownian dynamics simulation for the collapse of a single, stiff polymer in a poor solvent ͓B. Schnurr, F. C. MacKintosh, and D. R. M. Williams, Europhys. Lett. 51, 279 ͑2000͔͒ we calculate the conformational energies of the intermediate ͑racquet͒ states suggested by the simulations. In the absence of thermal fluctuations ͑at zero temperature͒ the annealed shapes of these intermediates are welldefined in certain limits, with their major structural elements given by a particular case of Euler's elastica. In appropriate units, a diagram emerges that displays the relative stability of all states, tori, and racquets. We conclude that, in marked contrast to the collapse of flexible polymers, the condensation of semiflexible or stiff polymers generically proceeds via a cascade through metastable intermediates, the racquets, towards a ground state, the torus or ring, as seen in the dynamical simulations.