Interrogating biology with force: single molecule high-resolution measurements with optical tweezers

Abstract

Single molecule force spectroscopy methods, such as optical and magnetic tweezers and atomic force microscopy, have opened up the possibility to study biological processes regulated by force, dynamics of structural conformations of proteins and nucleic acids, and load-dependent kinetics of molecular interactions. Among the various tools available today, optical tweezers have recently seen great progress in terms of spatial resolution, which now allows the measurement of atomic-scale conformational changes, and temporal resolution, which has reached the limit of the microsecond-scale relaxation times of biological molecules bound to a force probe. Here, we review different strategies and experimental configurations recently developed to apply and measure force using optical tweezers. We present the latest progress that has pushed optical tweezers' spatial and temporal resolution down to today's values, discussing the experimental variables and constraints that are influencing measurement resolution and how these can be optimized depending on the biological molecule under study.

Figure 1

Force exerted by optical tweezers. (a) A dielectric microsphere is stably trapped near the laser beam focus. A lateral displacement of the bead (x_bead) is opposed by a restoring force F. (b) For small displacements of the bead from the trap center (x_bead), the force exerted by optical tweezers grows linearly with x_bead. Beyond the linear region, a near-constant force region follows, after which the force rapidly drops to zero.

Figure 2

Configurations for the measurement of force and displacement with optical tweezers. (a) Single bead or single trap geometry. The trap is static and the bead displacement x_bead measures protein displacement. (b) Three-bead assay. Both traps are static and the trapped beads displacement (x_bead) measures protein displacement. (c) Two-bead or double trap assay. The left trap is stationary and measures the force applied to the polymer. The right bead moves in steps or ramps and, for each displacement, the forces applied to the polymer and its extension are measured. (d) Force-clamp or isotonic clamp. A feedback system moves the trap to keep force on the bead constant. Trap displacements (x_trap) measure protein displacements. (e) Position-clamp or isometric clamp. The left bead detects movements of the dumbbell (x_bead), whereas the right bead moves using an AOD to oppose the detected movements. The right bead measures the force applied by the motor protein (F_motor). (f) Dynamic force spectroscopy. The molecular bond is subjected to constant loading rates and rupture forces and bond lifetimes are measured.

Figure 3

Parameters affecting thermal noise and spatial resolution. (a) k_trap is the trap stiffness and k_motor comprises the motor protein stiffness in series with the stiffness of the linkages connecting the protein to the bead and the coverslip surface. γ_bead is the bead viscous drag coefficient. (b) Position fluctuations. Drawing of the position signal of a bead linked to a compliant (k₁) or stiff system (k₂). (c) Power density spectrum of the bead position. When the stiffness of the system increases (k₂ > k₁), the noise amplitude decreases at low frequencies (f << f_C) (turquoise area), but it is unchanged at high frequencies (pink area). When the viscous drag decreases (γ₂ < γ₁), the low-frequency noise decreases, whereas the high-frequency noise increases. The area under the power spectrum stays constant (d) The measured bead displacement (x_bead) depends on the motor protein displacement (x_motor) and on the values of the trap and protein stiffness.

Figure 4

Strategies to reduce instrumental noise. (a) Active stabilization of a surface coupled assay (67). A laser beam (green) was focused on a fiducial mark (transparent cylinder) bound to the coverslip to measure stage drifts, which were compensated by a feedback system driving a piezo stage. (b) To demonstrate the resolution of the system illustrated in panel a, the stage was moved in 0.34-nm increments (blue) such that the apparent DNA contour length changed. A step-fitting algorithm found steps (black) at 0.33 ± 0.08 nm. Data filtered at 5 Hz (light green) and 0.2 Hz (dark green). (c) A pairwise distance distribution of the 0.2-Hz data from panel b show a peak at 0.31 ± 0.09 nm. (d) Passive stabilization via a suspended double-trap assay. The picture represents the experiment by Abbondanzieri et al. (40), in which a single molecule of RNA polymerase (blue) was attached to the left bead held in the trap and tethered via the upstream DNA to the right bead held in a second trap. (e) Representative records from Abbondanzieri et al. (40) for single molecules of RNAP transcribing <18 pN of assisting load, median-filtered at 50 ms (pink) and 750 ms (black). Horizontal lines (dotted) are spaced at 3.4 Å intervals. (f) In Abbondanzieri et al. (40), the position histograms for 37 segments derived from transcription records for 28 individual RNAP molecules were computed and the autocorrelation function was calculated for each of these. The power spectral density of the averaged autocorrelation function showed a peak at the dominant spatial frequency, corresponding to the inverse of the fundamental step size, 3.7 ± 0.6 Å.

Figure 5

Ultrafast force-clamp spectroscopy. (a) Schematic of the operational principle of the method illustrating constant F_tot = ΔF applied to molecule B through two feedback systems clamping the force on the left to −F and on the right bead to F+ΔF. The force is measured using quadrant detector photodiodes and kept constant by moving the traps via AODs. (b) Position of the dumbbell. The net force is switched between +ΔF and −ΔF to keep the dumbbell within a confined spatial interval (±200 nm). The dumbbell stops when A binds to B. (c) Mechanical model for actin-myosin and DNA-LacI interaction. (d) Relaxation times calculated from the models in panel c using 500-nm diameter beads (78). (e) Actin-myosin interactions longer than 1 ms showed that the myosin working stroke is developed 0.2–1 ms after attachment. (Filled arrowheads pointing down) Myosin working stroke. (f) Submillisecond single actin-myosin interactions detected with ultrafast force-clamp spectroscopy. (Filled arrowheads pointing up) Actin-myosin binding. (Open arrowheads pointing down) Actin-myosin detachment.