Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications

Abstract

Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.

Figure 1.

Schematic of optical trap with components needed for microrheology experiments. Components highlighted in red are those referred to in the text. Back focal plane force detection is achieved via a condenser and position sensing detector (PSD). Precision movement of the trap relative to the sample is achieved via a piezoelectric stage and/or mirror (GM-1). The mercury arc lamp, fluorescence filter cubes, 1064 nm dichroic, and CMOS camera are needed for fluorescence imaging. The polarization beam splitters (PBS), the second mirror (GM-2), and second PSD are needed for two traps. The remaining components are standard for optical tweezers.

Figure 2.

Linear oscillatory microrheology. (A) An optically trapped microsphere is sinusoidally displaced through the sample while the force exerted on the bead is measured. (B) Sample data showing the position of the stage (which moves the trap relative to the sample) and the measured force during oscillation. The stage amplitude x_max, force amplitude F_max, and phase shift Δϕ between the two curves for each frequency ω are measured to compute the linear viscoelastic moduli. (C) G′(ω) (closed symbols) and G″(ω) (open symbols) measured using this method for 1 mg/mL linear DNA of varying lengths (listed in legend). Data is reproduced with permission from ref 19. Copyright 2014 ACS. (D) Equations relating measured quantities to viscoelastic moduli for a microsphere of a given radius R.

Figure 3.

Nonlinear mesoscale microrheology. (A) A trapped bead is moved at a constant speed v over a large distance x as the force F the sample exerts on the bead is measured. An effective differential modulus K = dF/dx and viscosity η can be determined from the measured F(x) curves (table column 1). All quantities for a given bead radius R can be converted to those used in macrorheology (table column 2). (B–G) Data for entangled networks of actin (left) and DNA (right). (B, C) Force curves for varying strain rates (or Wi) as displayed in legends in D and E. (D) K(x) determined from F(x) curves in B. Dashed lines correspond to actin relaxation time scales.(E) K(γ) determined from σ(γ) curves in C. B–E are reproduced with permission from references and . Copyright 2014 APS and Copyright 2015 RSC, respectively.

Figure 4.

Measuring local stress relaxation following mesoscale strains. (A) Following trap displacement (red), the trap is held fixed and the relaxation of the force exerted on the trapped bead (blue) is measured over time. (B) Force relaxation for entangled actin (same system as Figure 3) for varying $\dot{\gamma }$ listed in legend. The force is normalized by the value at the beginning of relaxation F₀. The data show a crossover from exponential to power-law relaxation at a strain rate of ~3 s⁻¹. The black line represents power-law scaling with the exponent listed. (C) Following trap displacement (blue), the bead is held in the trap for a specific wait time t_w, after which the trap is turned off and the trajectory of the released bead is tracked (red). The force on the bead during strain, proportional to the bead displacement from the trap center (black), is recorded during Strain and Wait Time. (D) The decay rate β of the bead recoil as a function of wait time t_w for varying Wi (legend in inset and Figure 3E) for entangled DNA (same system as Figure 3). β, normalized by the disengagement rate τ_D⁻¹ of the system, is determined by fitting each recoil trajectory r (inset) to a single exponential. Solid lines through Wi > 20 data are power-laws with exponents of 0 and −0.6. Solid line through Wi < 20 data is an exponential decay function. Inset: Recoil trajectories as a function of time t. Figures reproduced from references and . Copyright 2015 RSC and Copyright 2014 APS, respectively.

Figure 5.

Active macromolecular-tracking microrheology couples mechanical response to polymer mobility. (A, B) An optically trapped microsphere is displaced a distance x (red) while the force F (green) exerted on the bead is measured before, during and following the strain. Concurrent with force measurements, mobility and deformations of single discretely labeled polymers (blue) are imaged and tracked. (C) Each measurement results in a force (green) and an average polymer velocity and displacement (blue) in varying regions of the network (blue box, B). (D) Spatially resolved polymer velocity vectors map the deformation field surrounding the strain to characterize stress propagation dynamics and length scales.

Figure 6.

Time-resolved microrheology during triggered activity of nonequilibrium materials. (A) Microfluidic device used to change buffer conditions without mechanical disruption or loss of the sample. The cartoon shows actin filaments and microspheres sealed in the central sample chamber, flanked by membranes that are permeable to small molecules but not macromolecules.^, Buffer channels connected to capillary tubing allow for existing buffer to be pulled out of the chamber while the desired buffer is pulled in. Prior to experiments, buffer channels are filled with the buffer that matches that of the sample. To change the chemical environment of the sample, a digitally controlled syringe pump pulls the existing buffer from the flanking channels while the new desired buffer is pulled in. The membrane thickness and flow rate are set so that the new buffer is able to diffuse into the sample chamber while the existing buffer diffuses out.^, (B, C) Time-dependent elastic moduli G′(ω) of actin networks during depolymerization (disassembly, B) and subsequent repolymerization (reassembly, C) of actin filaments triggered by varying concentrations of MgCl₂, CaCl₂, and ATP. Red and blue curves are ω-averaged values for networks with (red) and without (blue) 2% biotin-NeutrAvidin crosslinkers. Solid black lines are (B) fits to single exponentials with time constants listed in min, and (C) linear fits with slopes listed in mPa-min⁻¹. Data is reproduced from reference .