Micro-mechanical response and power-law exponents from the longitudinal fluctuations of F-actin solutions.

We investigate the local fluctuations of filamentous actin (F-actin), with a focus on the skeletal thin filament, using single-particle optical trapping interferometry. This experimental technique allows us to detect the Brownian motion of a tracer bead immersed in a complex fluid with nanometric resolution at the microsecond time-scale. The mean square displacement, loss modulus, and velocity autocorrelation function (VAF) of the trapped microprobes in the fluid follow power-law behaviors, whose exponents can be determined in the short-time/high-frequency regime over several decades. We obtain 7/8 subdiffusive power-law exponents for polystyrene depleted microtracers at low optical trapping forces. Microrheologically, the elastic modulus of these suspensions is observed to be constant up to the limit of high frequencies, confirming that the origin of this subdiffusive exponent is the local longitudinal fluctuations of the polymers. Deviations from this value are measured and discussed in relation to the characteristic length scales of these F-actin networks and probes' properties, and also in connection with the different power-law exponents detected in the VAFs. Finally, we observed that the thin filament, composed of tropomyosin (Tm) and troponin (Tn) coupled to F-actin in the presence of Ca2+, shows exponent values less dispersed than that of F-actin alone, which we interpret as a micro-measurement of the filament stabilization.

Filamentous and step-like behavior of gelling coarse fibrin networks revealed by high-frequency microrheology.

By a micro-experimental methodology, we study the ongoing molecular process inside coarse fibrin networks by means of microrheology. We made these networks gelate around a probe microbead, allowing us to observe a temporal evolution compatible with the well-known molecular formation of fibrin networks in four steps: monomer, protofibril, fiber and network. Thanks to the access that optical-trapping interferometry provides to the short-time scale on the bead's Brownian motion, we observe a Kelvin-Voigt mechanical behavior from low to high frequencies, range not available in conventional rheometry. We exploit that mechanical model for obtaining the characteristic lengths of the filamentous structures composing these fibrin networks, whose obtained values are compatible with a non-affine behavior characterized by bending modes. At very long gelation times, a ω7/8 power-law is observed in the loss modulus, theoretically related with the longitudinal response of the molecular structures.

Resonances arising from hydrodynamic memory in Brownian motion.

Observation of the Brownian motion of a small probe interacting with its environment provides one of the main strategies for characterizing soft matter. Essentially, two counteracting forces govern the motion of the Brownian particle. First, the particle is driven by rapid collisions with the surrounding solvent molecules, referred to as thermal noise. Second, the friction between the particle and the viscous solvent damps its motion. Conventionally, the thermal force is assumed to be random and characterized by a Gaussian white noise spectrum. The friction is assumed to be given by the Stokes drag, suggesting that motion is overdamped at long times in particle tracking experiments, when inertia becomes negligible. However, as the particle receives momentum from the fluctuating fluid molecules, it also displaces the fluid in its immediate vicinity. The entrained fluid acts back on the particle and gives rise to long-range correlations. This hydrodynamic 'memory' translates to thermal forces, which have a coloured, that is, non-white, noise spectrum. One hundred years after Perrin's pioneering experiments on Brownian motion, direct experimental observation of this colour is still elusive. Here we measure the spectrum of thermal noise by confining the Brownian fluctuations of a microsphere in a strong optical trap. We show that hydrodynamic correlations result in a resonant peak in the power spectral density of the sphere's positional fluctuations, in strong contrast to overdamped systems. Furthermore, we demonstrate different strategies to achieve peak amplification. By analogy with microcantilever-based sensors, our results reveal that the particle-fluid-trap system can be considered a nanomechanical resonator in which the intrinsic hydrodynamic backflow enhances resonance. Therefore, instead of being treated as a disturbance, details in thermal noise could be exploited for the development of new types of sensor and particle-based assay in lab-on-a-chip applications.

Synchrotron infrared microspectroscopy detecting the evolution of Huntington's disease neuropathology and suggesting unique correlates of dysfunction in white versus gray brain matter.

Huntington's disease (HD), caused by a mutation of the corresponding gene encoding the protein huntingtin (htt), is characterized by progressive deterioration of cognitive and motor functions, paralleled by extensive loss of striatal neurons. At the cellular level, pathogenesis involves an early and prolonged period of neuronal dysfunction followed by neuronal death. Understanding the molecular events driving these deleterious processes is critical to the successful development of therapies to slow down or halt the progression of the disease. Here, we examined biochemical processes in a HD ex vivo rat model, as well as in a HD model for cultured neurons using synchrotron-assisted Fourier transform infrared microspectroscopy (S-FTIRM). The model, based on lentiviral-mediated delivery of a fragment of the HD gene, expresses a mutant htt fragment in one brain hemisphere and a wild-type htt fragment in the control hemisphere. S-FTIRM allowed for high spatial resolution and distinction between spectral features occurring in gray and white matter. We measured a higher content of ß-sheet protein in the striatal gray matter exposed to mutant htt as early as 4 weeks following the initiation of mutant htt exposure. In contrast, white matter tracts did not exhibit any changes in protein structure but surprisingly showed reduced content of unsaturated lipids and a significant increase in spectral features associated with phosphorylation. The former is reminiscent of changes consistent with a myelination deficiency, while the latter is characteristic of early pro-apoptotic events. These findings point to the utility of the label-free FTIRM method to follow mutant htt's ß-sheet-rich transformation in striatal neurons ex vivo, provide further evidence for mutant htt amyloidogenesis in vivo, and demonstrate novel chemical features indicative of white matter changes in HD. Parallel studies in cultured neurons expressing the same htt fragments showed similar changes.

Monitoring ligand-receptor interactions by photonic force microscopy.

We introduce a method for the acquisition of single molecule force measurements of ligand-receptor interactions using the photonic force microscope (PFM). Biotin-functionalized beads, manipulated with an optical trap, and a streptavidin-functionalized coverslip were used to measure the effect of different pulling forces on the lifetime of individual streptavidin-biotin complexes. By optimizing the design of the optical trap and selection of the appropriate bead size, pulling forces in excess of 50 pN were achieved. Based on the amplitude of three-dimensional (3D) thermal position fluctuations of the attached bead, we were able to select for a bead-coverslip interaction that was mediated by a single streptavidin-biotin complex. Moreover, the developed experimental system was greatly accelerated by automation of data acquisition and analysis. In force-dependent kinetic measurements carried out between streptavidin and biotin, we observed that the streptavidin-biotin complex exhibited properties of a catch bond, with the lifetime increasing tenfold when the pulling force increased from 10 to 20 pN. We also show that silica beads were more appropriate than polystyrene beads for the force measurements, as tethers, longer than 200 nm, could be extracted from polystyrene beads.

Persistent correlation of constrained colloidal motion.

We have investigated the motion of a single optically trapped colloidal particle close to a limiting wall at time scales where the inertia of the surrounding fluid plays a significant role. The velocity autocorrelation function exhibits a complex interplay due to the momentum relaxation of the particle, the vortex diffusion in the fluid, the obstruction of flow close to the interface, and the harmonic restoring forces due to the optical trap. We show that already a weak trapping force has a significant impact on the velocity autocorrelation function C(t)=v(t)v(0) at times where the hydrodynamic memory leads to an algebraic decay. The long-time behavior for the motion parallel and perpendicular to the wall is derived analytically and compared to numerical results. Then, we discuss the power spectral densities of the displacement and provide simple interpolation formulas. The theoretical predictions are finally compared to recent experimental observations.

Motion of a colloidal particle in an optical trap.

Thermal position fluctuations of a colloidal particle in an optical trap are measured with microsecond resolution using back-focal-plane interferometry. The mean-square displacement and power spectral density are in excellent agreement with the theory for a Brownian particle in a harmonic potential that accounts for hydrodynamic memory effects. The motion of a particle is dominated at short times by memory effects and at longer times by the potential. We identify the time below which the particle's motion is not influenced by the potential, and find it to be approximately tau(k)/20 , where tau(k) is the relaxation time of the restoring force of the potential. This allows us to exclude the existence of free diffusive motion, proportional to t, even for a sphere with a radius as small as 0.27 microm in a potential as weak as 1.5 microN/m. As the physics of Brownian motion can be used to calibrate an optical trap, we show that neglecting memory effects leads to an underestimation of more than 10% in the detector sensitivity and the trap stiffness for an experiment with a micrometer-sized particle and a sampling frequency above 200kHz . Furthermore, these calibration errors increase in a nontrivial fashion with particle size, trap stiffness, and sampling frequency. Finally, we present a method to evaluate calibration errors caused by memory effects for typical optical trapping experiments.

Single potassium niobate nano/microsized particles as local mechano-optical Brownian probes.

Perovskite alkaline niobates, due to their strong nonlinear optical properties, including birefringence and the capability to produce second-harmonic generation (SHG) signals, attract a lot of attention as potential candidates for applications as local nano/microsized mechano-optical probes. Here, we report on an implementation of photonic force microscopy (PFM) to explore the Brownian motion and optical trappability of monocrystalline potassium niobate (KNbO3) nano/microsized particles having sizes within the range of 50 to 750 nm. In particular, we exploit the anisotropic translational diffusive regime of the Brownian motion to quantify thermal fluctuations and optical forces of singly-trapped KNbO3 particles within the optical trapping volume of a PFM microscope. We also show that, under near-infrared (NIR) excitation of the highly focused laser beam of the PFM microscope, a single optically-trapped KNbO3 particle reveals a strong SHG signal manifested by a narrow peak (λ(em) = 532 nm) at half the excitation wavelength (λ(ex) = 1064 nm). Moreover, we demonstrate that the thus induced SHG emission can be used as a local light source that is capable of optically exciting molecules of an organic dye, Rose Bengal (RB), which adhere to the particle surface, through the mechanism of luminescence energy transfer (LET).

Accounting for inertia effects to access the high-frequency microrheology of viscoelastic fluids.

We study the Brownian motion of microbeads immersed in water and in a viscoelastic wormlike micelles solution by optical trapping interferometry and diffusing wave spectroscopy. Through the mean-square displacement obtained from both techniques, we deduce the mechanical properties of the fluids at high frequencies by explicitly accounting for inertia effects of the particle and the surrounding fluid at short time scales. For wormlike micelle solutions, we recover the 3/4 scaling exponent for the loss modulus over two decades in frequency as predicted by the theory for semiflexible polymers.

Contact angle at the leading edge controls cell protrusion rate.

Plasma membrane tension and the pressure generated by actin polymerization are two antagonistic forces believed to define the protrusion rate at the leading edge of migrating cells [1-5]. Quantitatively, resistance to actin protrusion is a product of membrane tension and mean local curvature (Laplace's law); thus, it depends on the local geometry of the membrane interface. However, the role of the geometry of the leading edge in protrusion control has not been yet investigated. Here, we manipulate both the cell shape and substrate topography in the model system of persistently migrating fish epidermal keratocytes. We find that the protrusion rate does not correlate with membrane tension, but, instead, strongly correlates with cell roundness, and that the leading edge of the cell exhibits pinning on substrate ridges-a phenomenon characteristic of spreading of liquid drops. These results indicate that the leading edge could be considered a triple interface between the substrate, membrane, and extracellular medium and that the contact angle between the membrane and the substrate determines the load on actin polymerization and, therefore, the protrusion rate. Our findings thus illuminate a novel relationship between the 3D shape of the cell and its dynamics, which may have implications for cell migration in 3D environments.

Selective transport control on molecular velcro made from intrinsically disordered proteins.

The selectivity and speed of many biological transport processes transpire from a 'reduction of dimensionality' that confines diffusion to one or two dimensions instead of three. This behaviour remains highly sought after on polymeric surfaces as a means to expedite diffusional search processes in molecular engineered systems. Here, we have reconstituted the two-dimensional diffusion of colloidal particles on a molecular brush surface. The surface is composed of phenylalanine-glycine nucleoporins (FG Nups)--intrinsically disordered proteins that facilitate selective transport through nuclear pore complexes in eukaryotic cells. Local and ensemble-level experiments involving optical trapping using a photonic force microscope and particle tracking by video microscopy, respectively, reveal that 1-µm-sized colloidal particles bearing nuclear transport receptors called karyopherins can exhibit behaviour that varies from highly localized to unhindered two-dimensional diffusion. Particle diffusivity is controlled by varying the amount of free karyopherins in solution, which modulates the multivalency of Kap-binding sites within the molecular brush. We conclude that the FG Nups resemble stimuli-responsive molecular 'velcro', which can impart 'reduction of dimensionality' as a means of biomimetic transport control in artificial environments.

Hydrodynamic and subdiffusive motion of tracers in a viscoelastic medium.

We investigate the diffusive motion of micron-sized spherical tracers in a viscoelastic actin filament network over the time span of 8 orders of magnitude using optical-tweezers single-particle tracking. The hydrodynamic interactions of a tracer with the surrounding fluid are shown to dominate at microsecond time scales, while subdiffusive scaling due to viscoelastic properties of the medium emerges at millisecond time scales. The transition between these two regimes is analyzed in the frame of a minimal phenomenological model which combines the Basset force and the generalized Stokes force. The resulting Langevin equation accounts for various dynamical features of the thermal motion of endogenous or exogenous tracers in viscoelastic media such as inertial and hydrodynamic effects at short times, subdiffusive scaling at intermediate times, and eventual optical trapping at long times. Simple analytical formulas for the mean-square displacement and velocity autocorrelation function are derived.

High-resolution detection of Brownian motion for quantitative optical tweezers experiments.

We have developed an in situ method to calibrate optical tweezers experiments and simultaneously measure the size of the trapped particle or the viscosity of the surrounding fluid. The positional fluctuations of the trapped particle are recorded with a high-bandwidth photodetector. We compute the mean-square displacement, as well as the velocity autocorrelation function of the sphere, and compare it to the theory of Brownian motion including hydrodynamic memory effects. A careful measurement and analysis of the time scales characterizing the dynamics of the harmonically bound sphere fluctuating in a viscous medium directly yields all relevant parameters. Finally, we test the method for different optical trap strengths, with different bead sizes and in different fluids, and we find excellent agreement with the values provided by the manufacturers. The proposed approach overcomes the most commonly encountered limitations in precision when analyzing the power spectrum of position fluctuations in the region around the corner frequency. These low frequencies are usually prone to errors due to drift, limitations in the detection, and trap linearity as well as short acquisition times resulting in poor statistics. Furthermore, the strategy can be generalized to Brownian motion in more complex environments, provided the adequate theories are available.

Three-dimensional force measurements in optical tweezers formed with high-NA micromirrors.

The three-dimensional trap stiffness of optical tweezers formed with high-NA micromirrors is investigated by back-focal-plane interferometry and power spectrum analysis. Normalized stiffness values of kappaxy/Ptrap=1.2(microN/m)/mW and kappaz/Ptrap=0.52(microN/m)/mW in the transverse and axial directions, respectively, have been measured for polystyrene spheres with a radius of 1.03 microm. Compared with high-NA microscope objectives, micromirrors achieve much better trapping performances, particularly in the axial direction.

Anisotropic memory effects in confined colloidal diffusion.

The motion of an optically trapped sphere constrained by the vicinity of a wall is investigated at times where hydrodynamic memory is significant. First, we quantify, in bulk, the influence of confinement arising from the trapping potential on the sphere's velocity autocorrelation function C(t). Next, we study the splitting of C(t) into C_{parallel}(t) and C_{perpendicular}(t), when the sphere is approached towards a surface. Thereby, we monitor the crossover from a slow t{-3/2} long-time tail, away from the wall, to a faster t{-5/2} decay, due to the subtle interplay between hydrodynamic backflow and wall effects. Finally, we discuss the resulting asymmetric time-dependent diffusion coefficients.

Stiffness alterations of single cells induced by UV in the presence of nanoTiO2.

Nanocrystalline titanium dioxide (nanoTiO2) has been reported to generate reactive oxygen species (ROS) under UV illumination. In our studies, changes in mechanical properties of human skin fibroblasts, exposed to the oxidative stress induced in the presence of nanoTiO2 and UV light, were studied using atomic force microscopy (AFM). The exposure of cells to the action of ROS was performed at low TiO2 concentration (4 microg/mL) and under illumination with low-intensity UVA (8 and 20 mW/cm2) or UVC (0.1 mW/ cm2). AFM measurements of the cell stiffness were carried out immediately after exposure of cells to the oxidative stress. The data suggest that under illumination with low-intensity UVA nanoTiO2 generates ROS, which, in turn, damage cellular and subcellular structures. This process was detected by AFM as a marked drop in the cellular stiffness of ca. 30-75%, which occurred rapidly, in the time frame of 1 min. The photo-oxidative stress inducing the decrease of cell stiffness was cancelled in the presence of a well-established antioxidant, beta-carotene. The results highlight the sensitivity of AFM to detect early changes in mechanical properties of cells exposed to oxidative stress.

Friction force microscopy as an alternative method to probe molecular interactions.

Friction force microscopy was applied to study protein-carbohydrate interactions that are important in many cellular recognition processes. The expression and structure of carbohydrates can be investigated using lectins as molecular probes since they recognize different types of sugar molecules. Lectins (concanavalin A and lentil lectin, recognizing mannose-type carbohydrates) were attached to the probing tip and carboxypeptidase Y (possessing complementary carbohydrates) was immobilized on a modified glass surface using microcontact printing. The results obtained from friction force maps and dependencies on the loading rate (measured in a physiological buffer) were divided in two distinct groups. The first group of results obtained for lectin-protein complexes was assigned to molecular recognition events, whereas the other including all control measurements was attributed to nonspecific interaction. All results presented here indicate that friction force microscopy can be successfully employed to study recognition processes.

Catalytically grown carbon nanotubes of small diameter have a high Young's modulus.

Experimental studies of carbon nanotubes (CNTs) obtained through different synthesis routes show considerable variability in their mechanical properties. The strongest CNTs obtained so far had a high Young's modulus of 1 TPa but could only be produced in gram scale quantities. The synthesis by catalytic chemical vapor deposition, a method that holds the greatest potential for large-scale production, gives CNTs with a high defect density. This leads to low Young's modulus values below 100 GPa for multiwall CNTs. Here we performed direct measurements of the mechanical properties of catalytically grown CNTs with only a few walls and find a Young's modulus of 1 TPa. This high value is confirmed for CNTs grown under two different growth conditions where the synthesis parameters such as the hydrocarbon source, catalyst material, and the synthesis temperature were varied. The results indicate that the observed difference in the Young's modulus for the catalytically grown CNTs with high and low numbers of walls is probably related to the growth mechanism of CNT.

Mechanical properties of single motor molecules studied by three-dimensional thermal force probing in optical tweezers.

A new method combining three-dimensional (3D) force measurements in an optical trap with the analysis of thermally induced (Brownian) position fluctuations of a trapped probe was used to investigate the mechanical properties of a single molecule, the molecular motor kinesin. One kinesin molecule attached to the probe was bound in a rigorlike state to one microtubule. The optical trap was kept weak to measure the thermal forces acting on the probe, which were mainly counterbalanced by the kinesin tether. The stiffness of kinesin during stretching and compression with respect to its backbone axis were measured. Our results indicate that a section of kinesin close to the motor domain is the dominating element in the flexibility of the motor structure. The experiments demonstrate the power of 3D thermal fluctuation analysis to characterize mechanical properties of individual motor proteins and indicate its usefulness to study single molecule in general