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Register a new userHigh-resolution detection of Brownian motion for quantitative Optical Tweezers experiments
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We have developed a new 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. Next, 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 then 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.
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Viscosity is an important property of out-of-equilibrium systems such as active biological materials and driven non-Newtonian fluids, and for fields ranging from biomaterials to geology, energy technologies and medicine. However, noninvasive viscosity measurements typically require integration times of seconds. Here we demonstrate a four orders-of-magnitude improvement in speed, down to twenty microseconds, with uncertainty dominated by fundamental thermal noise for the first time. We achieve this using the instantaneous velocity of a trapped particle in an optical tweezer. To resolve the instantaneous velocity we develop a structured-light detection system that allows particle tracking with megahertz bandwidths. Our results translate viscosity from a static averaged property, to one that may be dynamically tracked on the timescales of active dynamics. This opens a pathway to new discoveries in out-of-equilibrium systems, from the fast dynamics of phase transitions, to energy dissipation in motor molecule stepping, to violations of fluctuation laws of equilibrium thermodynamics.
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Diffusive transport in many complex systems features a crossover between anomalous diffusion at short times and normal diffusion at long times. This behavior can be mathematically modeled by cutting off (tempering) beyond a mesoscopic correlation time the power-law correlations between the increments of fractional Brownian motion. Here, we investigate such tempered fractional Brownian motion confined to a finite interval by reflecting walls. Specifically, we explore how the tempering of the long-time correlations affects the strong accumulation and depletion of particles near reflecting boundaries recently discovered for untempered fractional Brownian motion. We find that exponential tempering introduces a characteristic size for the accumulation and depletion zones but does not affect the functional form of the probability density close to the wall. In contrast, power-law tempering leads to more complex behavior that differs between the superdiffusive and subdiffusive cases.
We have simulated the motion of a bead subjected to a constant force while embedded in a network of semiflexible polymers which can represent actin filaments. We find that the bead displacement obeys the power law x ~ t^alfa. After the initial stage characterized by the exponent alfa=0.75 we find a new regime with alfa=0.5. The response in this regime is linear in force and scales with the polymer concentration as c^(-1.4). We find that the polymers pile up ahead of the moving bead, while behind it the polymer density is reduced. We show that the force resisting the bead motion is due to steric repulsion exerted by the polymers on the front hemisphere of the bead.
We study the 2D motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.
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