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.

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.

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.

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.

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.

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.

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.

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.

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 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.

Nanoindentation studies of full and empty viral capsids and the effects of capsid protein mutations on elasticity and strength.

The elastic properties of capsids of the cowpea chlorotic mottle virus have been examined at pH 4.8 by nanoindentation measurements with an atomic force microscope. Studies have been carried out on WT capsids, both empty and containing the RNA genome, and on full capsids of a salt-stable mutant and empty capsids of the subE mutant. Full capsids resisted indentation more than empty capsids, but all of the capsids were highly elastic. There was an initial reversible linear regime that persisted up to indentations varying between 20% and 30% of the diameter and applied forces of 0.6-1.0 nN; it was followed by a steep drop in force that is associated with irreversible deformation. A single point mutation in the capsid protein increased the capsid stiffness. The experiments are compared with calculations by finite element analysis of the deformation of a homogeneous elastic thick shell. These calculations capture the features of the reversible indentation region and allow Young's moduli and relative strengths to be estimated for the empty capsids.

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.

Rapid chiral assembly of rigid DNA building blocks for molecular nanofabrication.

Practical components for three-dimensional molecular nanofabrication must be simple to produce, stereopure, rigid, and adaptable. We report a family of DNA tetrahedra, less than 10 nanometers on a side, that can self-assemble in seconds with near-quantitative yield of one diastereomer. They can be connected by programmable DNA linkers. Their triangulated architecture confers structural stability; by compressing a DNA tetrahedron with an atomic force microscope, we have measured the axial compressibility of DNA and observed the buckling of the double helix under high loads.

Short-time inertial response of viscoelastic fluids: observation of vortex propagation.

We probe the response of viscous and viscoelastic fluids on micrometer and microsecond length and time scales using two optically trapped beads. In this way we resolve the flow field, which exhibits clear effects of fluid inertia. Specifically, we resolve the short-time vortex flow and the corresponding evolution of this vortex, which propagates diffusively for simple liquids. For viscoelastic fluids, this propagation is shown to be faster than diffusive and the displacement correlations reflect the frequency-dependent shear modulus of the medium.

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.

Bacteriophage capsids: tough nanoshells with complex elastic properties.

The shell of bacteriophages protects the viral DNA during host-to-host transfer and serves as a high-pressure container storing energy for DNA injection into a host bacterium. Here, we probe the mechanical properties of nanometer-sized bacteriophage phi 29 shells by applying point forces. We show that empty shells withstand nanonewton forces while being indented up to 30% of their height. The elastic response varies across the surface, reflecting the arrangement of shell proteins. The measured Young's modulus (approximately 1.8 GPa) is comparable with that of hard plastic. We also observe fatigue and breakage of capsids after probing them repetitively. These results illustrate the mechanoprotection that viral shells provide and also suggest design principles for nanotechnology.

Deformation and collapse of microtubules on the nanometer scale.

We probe the local mechanical properties of microtubules at the nanometer scale by radial indentation with a scanning force microscope tip. We find a linear elastic regime that can be described by both thin-shell theory and finite element methods, in which microtubules are modeled as hollow tubes. We also find a nonlinear regime and catastrophic collapse of the microtubules under large loads. The main physics of protein shells at the nanometer scale shows simultaneously aspects of continuum elasticity in their linear response, as well as molecular graininess in their nonlinear behavior.

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.

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.

Imaging microtubules and kinesin decorated microtubules using tapping mode atomic force microscopy in fluids.

The atomic force microscope has been used to investigate microtubules and kinesin decorated microtubules in aqueous solution adsorbed onto a solid substrate. The netto negatively charged microtubules did not adsorb to negatively charged solid surfaces but to glass covalently coated with the highly positively charged silane trimethoxysilylpropyldiethylenetriamine (DETA) or a lipid bilayer of 1,2-dipalmitoyl-3-dimethylammoniumpropane. Using electron beam deposited tips for microtubules adsorbed on DETA, single protofilaments could be observed showing that the resolution is up to 5 nm. Under conditions where the silane coated surfaces are hydrophobic, microtubules opened, presumably at the seam, whose stability is lower than that of the bonds between the other protofilaments. This led to a "sheet" with a width of about 100 nm firmly attached to the surface. Microtubules decorated with a stoichiometric low amount of kinesin molecules in the presence of the non-hydrolyzable ATP-analog 5'-adenylylimidodiphosphate could also be adsorbed onto silane-coated glass. Imaging was very stable and the molecules did not show any scan-induced deformation even after hundreds of scans with a scan frequency of 100 Hz.