Rapid local compression in active gels is caused by nonlinear network response.

The actin cytoskeleton in living cells generates forces in conjunction with myosin motor proteins to directly and indirectly drive essential cellular processes. The semiflexible filaments of the cytoskeleton can respond nonlinearly to the collective action of motors. We here investigate mechanics and force generation in a model actin cytoskeleton, reconstituted in vitro, by observing the response and fluctuations of embedded micron-scale probe particles. Myosin mini-filaments can be modeled as force dipoles and give rise to deformations in the surrounding network of cross-linked actin. Anomalously correlated probe fluctuations indicate the presence of rapid local compression or draining of the network that emerges in addition to the ordinary linear shear elastic (incompressible) response to force dipoles. The anomalous propagation of compression can be attributed to the nonlinear response of actin filaments to the microscopic forces, and is quantitatively consistent with motor-generated large-scale stiffening of the gels.

Broken Detailed Balance of Filament Dynamics in Active Networks.

Myosin motor proteins drive vigorous steady-state fluctuations in the actin cytoskeleton of cells. Endogenous embedded semiflexible filaments such as microtubules, or added filaments such as single-walled carbon nanotubes are used as novel tools to noninvasively track equilibrium and nonequilibrium fluctuations in such biopolymer networks. Here, we analytically calculate shape fluctuations of semiflexible probe filaments in a viscoelastic environment, driven out of equilibrium by motor activity. Transverse bending fluctuations of the probe filaments can be decomposed into dynamic normal modes. We find that these modes no longer evolve independently under nonequilibrium driving. This effective mode coupling results in nonzero circulatory currents in a conformational phase space, reflecting a violation of detailed balance. We present predictions for the characteristic frequencies associated with these currents and investigate how the temporal signatures of motor activity determine mode correlations, which we find to be consistent with recent experiments on microtubules embedded in cytoskeletal networks.

Working strokes by single molecules of the kinesin-related microtubule motor ncd.

The ncd protein is a dimeric, ATP-powered motor that belongs to the kinesin family of microtubule motor proteins. Here we resolve single mechanochemical cycles of recombinant, dimeric, full-length ncd, using optical-tweezers-based instrumentation and a three-bead, suspended-microtubule assay. Under conditions of limiting ATP, isolated and transient microtubule-binding events exhibit exponentially distributed and ATP-concentration-dependent lifetimes. These events do not involve consecutive steps along the microtubule, quantitatively confirming that ncd is non-processive. At low loads, a single motor molecule produces ATP-triggered working strokes of about 9 nm, which occur at the ends of binding events.

Existence of a flat phase in red cell membrane skeletons.

Biomolecular membranes display rich statistical mechanical behavior. They are classified as liquid in the absence of shear elasticity in the plane of the membrane and tethered (solid) when the neighboring molecules or subunits are connected and the membranes exhibit solid-like elastic behavior in the plane of the membrane. The spectrin skeleton of red blood cells was studied as a model tethered membrane. The static structure factor of the skeletons, measured by small-angle x-ray and light scattering, was fitted with a structure factor predicted with a model calculation. The model describes tethered membrane sheets with free edges in a flat phase, which is a locally rough but globally flat membrane configuration. The fit was good for large scattering vectors. The membrane roughness exponent, zeta, defined through h alpha L zeta, where h is the average amplitude of out-of-plane fluctuations and L is the linear membrane dimension, was determined to be 0.65 +/- 0.10. Computer simulations of model red blood cell skeletons also showed this flat phase. The value for the roughness exponent, which was determined from the scaling properties of membranes of different sizes, was consistent with that from the experiments.

Short-time inertial response of viscoelastic fluids measured with Brownian motion and with active probes.

We have directly observed short-time stress propagation in viscoelastic fluids using two optically trapped particles and a fast interferometric particle-tracking technique. We have done this both by recording correlations in the thermal motion of the particles and by measuring the response of one particle to the actively oscillated second particle. Both methods detect the vortexlike flow patterns associated with stress propagation in fluids. This inertial vortex flow propagates diffusively for simple liquids, while for viscoelastic solutions the pattern spreads superdiffusively, depending on the shear modulus of the medium.

High-bandwidth viscoelastic properties of aging colloidal glasses and gels.

We report measurements of the frequency-dependent shear moduli of aging colloidal systems that evolve from a purely low-viscosity liquid to a predominantly elastic glass or gel. Using microrheology, we measure the local complex shear modulus G;{*}(omega) over a very wide range of frequencies (from 1Hzto100kHz ). The combined use of one- and two-particle microrheology allows us to differentiate between colloidal glasses and gels-the glass is homogenous, whereas the colloidal gel shows a considerable degree of heterogeneity on length scales larger than 0.5microm . Despite this characteristic difference, both systems exhibit similar rheological behaviors which evolve in time with aging, showing a crossover from a single-power-law frequency dependence of the viscoelastic modulus to a sum of two power laws. The crossover occurs at a time t_{0} , which defines a mechanical transition point. We found that the data acquired during the aging of different samples can be collapsed onto a single master curve by scaling the aging time with t_{0} . This raises questions about the prior interpretation of two power laws in terms of a superposition of an elastic network embedded in a viscoelastic background.

Twin optical traps for two-particle cross-correlation measurements: eliminating cross-talk.

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 condenser) 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.

Nonequilibrium dynamics of probe filaments in actin-myosin networks.

Active dynamic processes of cells are largely driven by the cytoskeleton, a complex and adaptable semiflexible polymer network, motorized by mechanoenzymes. Small dimensions, confined geometries, and hierarchical structures make it challenging to probe dynamics and mechanical response of such networks. Embedded semiflexible probe polymers can serve as nonperturbing multiscale probes to detect force distributions in active polymer networks. We show here that motor-induced forces transmitted to the probe polymers are reflected in nonequilibrium bending dynamics, which we analyze in terms of spatial eigenmodes of an elastic beam under steady-state conditions. We demonstrate how these active forces induce correlations among the mode amplitudes, which furthermore break time-reversal symmetry. This leads to a breaking of detailed balance in this mode space. We derive analytical predictions for the magnitude of resulting probability currents in mode space in the white-noise limit of motor activity. We relate the structure of these currents to the spatial profile of motor-induced forces along the probe polymers and provide a general relation for observable currents on two-dimensional hyperplanes.

Correlated fluctuations of microparticles in viscoelastic solutions: quantitative measurement of material properties by microrheology in the presence of optical traps.

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.

High-frequency microrheology of wormlike micelles.

We have measured the frequency-dependent shear modulus of entangled solutions of wormlike micelles by high-frequency microrheology and have compared the results with those from macrorheology experiments done on the same samples. Using optical microrheology based on laser interferometry we have measured loss and storage moduli over six decades in frequency up to about 100 kHz. We present data over a decade in concentration in the entangled regime and find good agreement between micro- and macrorheology, thus validating recently developed microrheology techniques. By collapsing data for different concentrations, we furthermore determine both the concentration scaling of the plateau modulus and a power-law exponent of the complex shear modulus at high frequencies.

Instability of myelin tubes under dehydration: deswelling of layered cylindrical structures.

We report experimental observations of an undulational instability of myelin figures. Motivated by this, we examine theoretically the deformation and possible instability of concentric, cylindrical, multilamellar membrane structures. Under conditions of osmotic stress (swelling or dehydration), we find a stable, deformed state in which the layer deformation is given by deltaR infinity r(square root[B(A)/(hB)]), where B(A) is the area compression modulus, B is the interlayer compression modulus, and h is the repeat distance of layers. Also, above a finite threshold of dehydration (or osmotic stress), we find that the system becomes unstable to undulations, first with a characteristic wavelength of order square root[xi(d)0], where xi is the standard smectic penetration depth and d0 is the thickness of dehydrated region.

Differential interference contrast microscopy using light-emitting diode illumination in conjunction with dual optical traps.

Differential interference contrast (DIC) microscopy is a common mode of biological light microscopy used to achieve maximal resolution and contrast with label-free, weakly absorbing specimens such as cells. Maintaining the polarization state of the illuminating light is essential for the technique, and this requirement can conflict with optical trapping. We describe how to optimize DIC imaging using a light-emitting diode illumination source in a microscope while integrating a dual optical trap into the set up. Every time a polarized light beam reflects off or transmits through a dichroic mirror in the beam path, its polarization state will change if it is not polarized exactly parallel (p) or perpendicular (s) to the plane of incidence. We observe wavelength-dependent optical rotation and depolarization effects in our illumination light upon reflection from/transmission through dichroic mirrors in the beam path, resulting in significant degradation of image quality. We describe a method to compensate for these effects by introducing quarter-waveplates and a laser clean-up filter into the imaging pathway. We show that this approach achieves a full recovery of image quality.

Nonequilibrium mechanics of active cytoskeletal networks.

Cells both actively generate and sensitively react to forces through their mechanical framework, the cytoskeleton, which is a nonequilibrium composite material including polymers and motor proteins. We measured the dynamics and mechanical properties of a simple three-component model system consisting of myosin II, actin filaments, and cross-linkers. In this system, stresses arising from motor activity controlled the cytoskeletal network mechanics, increasing stiffness by a factor of nearly 100 and qualitatively changing the viscoelastic response of the network in an adenosine triphosphate-dependent manner. We present a quantitative theoretical model connecting the large-scale properties of this active gel to molecular force generation.

Structural and mechanical study of a self-assembling protein nanotube.

We report a structural characterization of self-assembling nanostructures. Using atomic force microscopy (AFM), we discovered that partially hydrolyzed alpha-lactalbumin organizes in a 10-start helix forming tubes with diameters of only 21 nm. We probed the mechanical strength of these nanotubes by locally indenting them with an AFM tip. To extract the material properties of the nanotubes, we modeled the experiment using finite element methods. Our study shows that artificial helical protein self-assembly can yield very stable, strong structures that can function either as a model system for artificial self-assembly or as a nanostructure with potential for practical applications.

High-frequency stress relaxation in semiflexible polymer solutions and networks.

We measure the linear viscoelasticity of sterically entangled and chemically cross-linked networks of actin filaments over more than five decades of frequency. The high-frequency response reveals rich dynamics unique to semiflexible polymers, including a previously unobserved relaxation due to rapid axial tension propagation. For high molecular weight, and for cross-linked gels, we obtain quantitative agreement with predicted shear moduli in both amplitude and frequency dependence.