High-Speed Optical Traps Address Dynamics of Processive and Non-Processive Molecular Motors

Abstract

Interactions between biological molecules occur on very different time scales, from the minutes of strong protein–protein bonds, down to below the millisecond duration of rapid biomolecular interactions. Conformational changes occurring on sub-ms time scales and their mechanical force dependence underlie the functioning of enzymes (e.g., motor proteins) that are fundamental for life. However, such rapid interactions are beyond the temporal resolution of most single-molecule methods. We developed ultrafast force-clamp spectroscopy (UFFCS), a single-molecule technique based on laser tweezers that allows us to investigate early and very fast dynamics of a variety of enzymes and their regulation by mechanical load. The technique was developed to investigate the rapid interactions between skeletal muscle myosin and actin, and then applied to the study of different biological systems, from cardiac myosin to processive myosin V, microtubule-binding proteins, transcription factors, and mechanotransducer proteins. Here, we describe two different implementations of UFFCS instrumentation and protocols using either acousto- or electro-optic laser beam deflectors, and their application to the study of processive and non-processive motor proteins.

1. Introduction

1.1. Background

Optical trapping techniques have evolved into widely adopted procedures in biophysical labs for mechanical measurements on individual molecules and assemblies, as is clear from the collection of contributions to this volume. A limitation of most optical trapping experiments is the detection of very short events and the dynamics and mechanics in these short interactions. In this chapter, we describe an approach to circumvent this limitation for processive and non-processive myosin isoforms, we term ultrafast force-clamp spectroscopy (UFFCS). This method is a variant of the optical trap 3-bead assay originally introduced by the Spudich group [1] (Fig. 1a, b), where a polymer, such as an actin filament, a microtubule, or DNA strand, is suspended between two polystyrene beads in dual optical traps forming a “dumbbell” geometry. The filament is brought in close proximity to a larger pedestal bead on the microscope slide surface that has been sparsely coated with the motor or enzyme.

Fig. 1.

Schematic of UFFCS applied to myosin motors and position signal examples. (a) A single myosin-5B molecule is attached to a glass bead pedestal through a streptavidin-biotin link. A single actin filament is trapped by suspending it between α-actinin coated beads (the so called “three-bead” geometry). Black arrows represent the force clamped on the right and left bead, red arrow represents the net force (F = ΔF) on the dumbbell. F is alternated back and forth to maintain the dumbbell within a limited oscillation range when myosin is not bound to actin. (b) The same geometry of (a) can be adopted for myosin-II S1 subfragment. In this case, a single myosin-II subfragment is attached to a glass bead pedestal through aspecific interaction with the nitrocellulose on the glass coverslip surface. (c) Example trace showing displacement and force during the corresponding phases of dumbbell oscillation, myosin-5B attachment, and processive runs under assistive (push) and hindering(pull) loads. (d) Example trace of myosin II interactions with actin. Top: record of force F = ΔF applied to the right (red) and left bead (black). Bottom: record of trap position. In the trace in figure, the direction of the force is inverted by the feedback systems when the trap displacement reaches 200 nm. The flat portion of the trace, highlighted by vertical dotted lines, represents an interaction. When the motor protein binds to the cytoskeletal filament, the net force F = ΔF is transferred to the surface-coupled motor protein. The dumbbell exponentially reaches an equilibrium position and stops (i.e., the velocity of the trapped bead drops to zero). (This figure has been modified from [4, 14])

Brief interaction events between myosin and actin or other molecular motors with their cognate cytoskeletal filament or nucleic processing enzymes with DNA or RNA are usually detected by a decrease in thermal fluctuations [1–3]. In the three-bead assay, the mean squared amplitude of Brownian motions of the dumbbell, due to random impulses of water molecule is given by:

$${{\sigma }_{\text{d}}}^2=\langle x^2\rangle =K_{\text{B}}T/2k_{\text{t}}$$ (1)

where σ_d² is the variance of the free dumbbell position along the filament axis, the ⟨ ⟩ symbols indicate averaging, x is the deflection from the mean bead position, K_B is Boltzman’s constant, T is the temperature in Kelvin, and k_t is the trap stiffness. 2k_t is the system stiffness given before interactions by the sum of the two trap stiffnesses (assuming a rigid dumbbell). When the motor or enzyme binds to the filament, its stiffness, k_m, adds to the total system stiffness causing the variance of the Brownian motions to decrease during attachment according to:

$${{\sigma }_{\text{a}}}^2=\langle x^2\rangle =K_{\text{B}}T/\left(2k_{\text{t}}+k_{\text{m}}\right)$$ (2)

which can be detected when a running variance signal decreases below a threshold set according to the relative trap and motor stiffness values. A lower limit of the event duration detectable by this method (the dead time) is determined by a time-averaging window required to calculate the variance reliably enough to minimize spurious false positive events and loss of real events, false negatives. At a more fundamental level, a lower limit of the dead time is set by the cutoff frequency of the dumbbell plus myosin system,

$$f_{\text{c}}=\left(2k_{\text{t}}+k_{\text{m}}\right)/(2\pi \beta )$$ (3)

where β is the viscous drag on each bead given by Stokes equation. In fact, most of the change in the position variance between the free and bound dumbbell occurs at frequencies well below f_c, and is abolished as the cutoff frequency is approached [4]. Thus, the averaging window must be large enough to include substantial energy at frequencies below f_c. In practical terms, for typical trap setups and biological filaments or DNA strands, the dead time is 5–15 ms, thereby limiting the shortest events detectable to approximately this duration.

Other methods to improve event detection depend on correlation between the motions of the two beads. Being mechanically connected to each other through the filament causes the bead fluctuations to be coupled. The extent of coupling between beads “a” and “b” is given by the covariance (σ_ab),

$${\sigma }_{\text{ab}}=\langle x_{\text{a}}{x}_{\text{b}}\rangle =\frac{k_{\text{L}}^2{K}_{\text{B}}T}{{\left(k_{\text{t}}+k_{\text{L}}\right)}^2\left(2k_{\text{t}}{k}_{\text{L}}/\left(k_{\text{t}}+k_{\text{L}}\right)\right)}$$ (4)

where k_L is the stiffness linking each bead to the filament plus the stiffness of half of the filament length, the reciprocal of its mechanical compliance, usually mostly due to lateral vibrations [5]. Attachment of the motor or enzyme to the filament “shunts” the bead-to-bead coupling to the fixed pedestal bead on the slide, thereby reducing the attached covariance to,

$${\sigma }_{\text{ab}}=\langle x_{\text{a}}{x}_{\text{b}}\rangle =\frac{k_{\text{L}}^2{K}_{\text{B}}T}{{\left(k_{\text{t}}+k_{\text{L}}\right)}^2\left(k_{\text{m}}+2k_{\text{t}}{k}_{\text{L}}/\left(k_{\text{t}}+k_{\text{L}}\right)\right)}$$ (5)

To increase the coupling signal at relatively high frequency (about 1 kHz), a small sinusoidal motion can be imparted onto one of the beads and the coupling between them detected by the amplitude of the sinusoidal motion transferred to the other bead. Attachment of a pedestal bead bound motor reduces the coupling by a similar amount as the thermal fluctuations [6, 7]. These methods improve the reliably detectable minimum event duration to few ms.

Due to the thermal fluctuations of position in the detached dumbbell, the exact position at the moment of attachment is variable causing the amplitude of any given stroke to vary [8]. The amplitude of these fluctuations is on the order or greater than the stoke itself. For instance, with a combined stiffness of the two traps at 0.1 pN/nm, the width of the distribution of fluctuating positions, $\sqrt{{\sigma }_{\text{d}}^2}$, is ±6.3 nm, whereas the working stroke of cardiac myosin is ~5 nm. The stroke and its dynamics are expected to depend strongly on the force on the actomyosin crossbridge. The recorded positions of the displacements for a group of events gives the average stroke, but this value represents the displacement over a range of forces. Various feedback schemes for adjusting the force during attachments or varying it purposefully during the events have been devised to estimate the force dependence of the event lifetimes [1, 7–9], but these do not directly reveal the stroke itself, except in the average from many events.

When myosin attaches to actin, the working stroke that displaces the actin filament takes place within ~1 ms. Thus, direct observation of the timing and load-dependence of this crucial event has not been feasible with the variance and covariance methods described above. Actomyosin events shorter than the 5–15 ms limit are common and many other systems have even faster kinetics [10]. This situation prompted one of our labs to develop a different approach to detecting events, monitoring the position of the dumbbell starting very early after attachment and controlling the force and, thus, the strain as an independent variable [4]. This technique, named ultrafast force-clamp spectroscopy (UFFCS), made it possible to reveal force-dependent fast kinetic events that were previously inaccessible due to the limited time resolution [4, 11–13]. It introduced the ability to study the dependence of mechanochemical properties of enzymes on both the intensity and the direction of the applied strains during the entire duration of short and long interactions, which is crucial in the case of processive motors [14].

This system has been applied to the study of muscle myosin [4], cardiac muscle myosin [11], DNA-binding proteins [13], processive myosin-5B [14, 15], microtubule-binding proteins [16, 17], and mechanotransducer proteins [18]. In this chapter, we describe the UFFCS system, its further development since its introduction and its particular application to processive and non-processive myosin proteins.

1.2. Ultrafast Optical Trapping

A dual-beam, force-clamp optical trapping system described by Capitanio et al. [4] is capable of independently maintaining a constant force on each bead in a bead-actin-bead dumbbell while the dumbbell position changes within a spatial range of several hundred nanometers. The system modulates the positions of the traps to maintain a constant force on each bead as detected by back-focal-plane interferometry of the trapping laser light scattered by the beads [19]. This signal is a direct indication of the force exerted on the bead, not the absolute bead position. During an experiment, an actin dumbbell is brought close to a myosin molecule on the surface of a pedestal bead affixed to a glass coverslip (Fig. 1a, b). The actin dumbbell is pre-stretched to approximately 3–5 pN of tension (−F₁ and F₁) from both beads, which limits the series mechanical compliance of the assembly. The feedback system is activated and the force setpoint for the left bead is set to −F₁, while for the right bead to F₁′ = F₁ + ΔF (Fig. 1a, b). The system quickly applies this excess force to the right bead by moving the position of the trap, resulting in an unbalanced force on the dumbbell assembly. The dumbbell then moves rightward at a constant velocity such that the net force is balanced by hydrodynamic drag on the moving dumbbell. During this motion, the forces on both beads are maintained at their constant setpoints (−F₁ and F₁′) by the feedback loops. The dumbbell continues to travel at this constant velocity until the traps have moved a prespecified distance (~100 nm), at which point the setpoint for each bead is triggered to change to −F₁′ = −F₁ − ΔF and F₁, switching the net force to the left direction, and leading to motion at a constant velocity in the opposite direction (Fig. 1c, d).

The applied force and direction of motion continue to alternate back and forth until the myosin interacts with the actin filament, at which point the force of the hydrodynamic drag is transferred to the myosin molecule within ~10–100 μs (depending on the viscous drag and stiffness of the myosin+dumbbell), which becomes loaded with the excess force, + or − ΔF. This transfer of force abruptly stops the dumbbell’s motion, while the total forces on both beads are maintained constant by the feedback system (Fig. 1c, d). While the myosin interacts with actin, the applied force is held constant, and the motion of the actin filament is recorded from the position of the two traps. Thus, the force-producing displacement of the power stroke can be observed under various predetermined loads. When the myosin dissociates from actin, the dumbbell resumes its earlier motion, and the excess force is transferred back to hydrodynamic drag (Fig. 1c, d). In a single 30-s-long recording, the actin dumbbell switches its direction of travel thousands of times and myosin attaches to actin in dozens of interactions, depending on the particular myosin isoform and various experimental parameters. The principal advantages of the ultrafast optical trap system are (1) that the predetermined force is applied to the myosin very rapidly after attachment, so that the working stroke takes place under this load and (2) the events detected can be much shorter (>100 μs) than with other methods (≥5 ms) due to the facile detection of the sudden stop of bead motion when the myosin attaches.

To implement the ultrafast force-clamp method, four key components are required: (1) a stable dual-beam optical trap setup, (2) high bandwidth force detection electronics, (3) a high-speed feedback control system, and (4) low-latency, high precision beam steering. The response time of the force-clamp feedback loop must be very rapid (≤10 μs) to investigate processes such as the myosin power stroke and targeting of DNA-binding proteins, as it must maintain constant forces on both beads while the actin dumbbell is in motion.

To stably maintain the mean force on the beads to within 5% of the set points under these conditions, we found it necessary to generate a feedback loop update rate less than 10 μs. This includes the time to (1) detect the current force on the beads, (2) perform the feedback calculations, and (3) update the position of the trapping beam. We optimized each of these three components of the setup to reach the 10 μs loop time. The force on each bead is monitored by back-focal-plane interferometry of the 1064 nm trapping laser on two silicon quadrant photodiodes which can achieve a rise time for the force detection system of ~2 μs. We utilize a National Instruments Multifunction I/O module equipped with a Field-Programmable Gate Array (FPGA) to perform the feedback calculations, based on the QPD signals and the force setpoint, to update the control signal for the beam deflectors. The feedback calculations are performed at the same rate as the data acquisition rate, 200–250 kHz, leading to the feedback update time of 4–5 μs.

In the original ultrafast optical trap instrument in Florence [4], the infrared beams steering devices were acousto-optical deflectors (AODs) driven by direct digital synthesizers and power amplifiers. These produce a relatively wide variation of deflection angle (40 mrad) and switch angles within ~3–10 μs. The speed is determined by the propagation of the ultrasonic acoustic wave in the optical crystal across the light beam. By positioning a narrow beam at the driving piezoelectric transducer side of the crystal, the speed is optimized, but the resolution of deflection and collimation of the beam are also affected by the beam size, so it is difficult to obtain better than 3 μs response time of the AOD. This is adequate for 10 μs overall feedback response.

The setup in Philadelphia initially used AODs, but, contrary to what was observed in Florence, we found spurious oscillations of the dumbbell position that were caused by slight unexpected variations of the beam angle as functions of the input frequency [20]. These nonlinear fluctuations had been described earlier and ascribed to low amplitude standing waves in the AOD crystal [21]. We switched to electro-optic deflectors (EODs), which do not exhibit this problem. EODs are faster (1 μs, limited by the drive electronics) but have a smaller maximum deflection angle (3 mrad) than AODs. Nevertheless, the deflection angle is large enough to produce the feedback driven 100–200 nm triangle wave motions required in the ultrafast technique, but larger deflections (e.g., pre-tensioning the dumbbell) are done with mechanical mirrors. Moreover, large filament displacements, such as those produced by processive motors on cytoskeletal filaments or nucleic acids, require the wide deflection angles provided by AODs.

The procedures for preparing samples, assembling apparatus, conducting and analyzing experiments are described in detail in the other chapters for a range of biophysical systems. Here, we give details of different methodologies for actin-bead assembly (biotin-streptavidin link, NEM or α-actinin coated beads) and for processive (myosin V) and non-processive (myosin II) motors. The provided protocols can be easily adapted to different motor proteins. Protocols for measuring kinetics of actomyosin interactions and strain dependence of steps in actin translocation by myosin are given in Greenberg et al. [22] and Gardini et al. [23]. For completeness, some of the details of these protocols are repeated here. Another implementation of UFFCS, using an x-y AOD and position sensing instead of back-focal-plane force detection and optimized for studying motions of microtubule-associated proteins, is described by Tripathy et al. in this volume, Chap. 22.

2. Materials

2.1. Beads Functionalization

2.1.1. Neutravidin Beads

Biotinylated Latex Beads

1. 0.9 μm carboxylated latex beads 10% solids (Sigma, CLB9).

2. 0.5 μm fluorescent microspheres 1% solids (Bangs Labs, Dragon green FS03F).

3. Phosphate Buffer (PB): 50 mM, pH 7.0 (KH₂PO₄/K₂HPO₄ from powder, Sigma P5379/P8281) (see Note 1).

4. Crosslinker EDC (N-(3-Dimethylaminopropyl)-N′-ethylcarbodiimide hydrochloride) (Sigma, E-6383).

5. 2 mg/mL biotin-x-cadaverine (Molecular Probes, A1594) in DMSO (Sigma, D8418) (see Note 2).

6. 1% NaN₃ in ultrapure water (from powder, Sigma, S2002).

Neutravidin-Coated Fluorescent Latex Beads

1. Biotinylated 0.5 μm fluorescent microspheres or 0.9 μm biotinylated latex beads (Subheading “Biotinylated Latex Beads”).

2. PB.

3. 1 M glycine in ultrapure water (from powder, Sigma, G7126).

4. 5 mg/mL neutravidin protein in PB (Pierce, 31000, 10 mg) (see Note 2).

5. 5 mg/mL streptavidin Alexa532 in PB (Thermo Fisher, S-11224) (see Note 2).

2.1.2. N-Ethylmaleimide (NEM) Modified Beads

1. High salt buffer (HSB): 500 mM KCl, 4 mM MgCl₂, 1 mM EGTA, and 20 mM KH₂PO₄, pH 7.2.

2. KMg25 buffer: 25 mM KCl, 60 mM MOPS, pH 7.0, 1 mM EGTA, 1 mM MgCl₂, and 1 mM DTT (see Note 3).

3. 1 mL of 1 M Dithiothreitol (DTT) (see Note 4).

4. 50 mM N-ethylmaleimide (Sigma, 04259–5G) in water prepared fresh (see Note 5).

5. Skeletal muscle myosin in glycerol (see Note 6).

6. Glycerol (Sigma, G7893).

7. Polystyrene beads (1.1 μm diameter, 10% solids, Sigma, LB-11).

8. Bovine serum albumin (BSA) (Fisher, 50–230-3400).

2.1.3. α-Actinin-Coated Fluorescent Beads

Purification of HaloTagged, Actin-Binding Domain of α-Actinin (HT-ABD)

1. Lysis buffer (LB): 25 mM Tris, pH 7.5, 20 mM Imidazole, 300 mM NaCl, 0.5 mM EGTA, 0.5% Igepal (Sigma, CA-630), 1 mM beta-mercaptoethanol, 1 mM PMSF, and 0.01 mg/mL aprotinin and leupeptin (see Note 7).

2. Wash buffer (WB): same as LB minus Igepal.

3. Elution buffer (EB): 12 mM imidazole, 300 mM NaCl, 25 mM Tris, pH 7.5, 1 mM EGTA, and 1 mM EDTA.

4. FPLC buffer A: 10 mM Tris, pH 7.5, 50 mM KCl, 1 mM DTT, and 1 mM EGTA.

5. FPLC buffer B: same as FPLC buffer A except 1 M KCl.

6. KMg25 buffer.

Coupling HT-ABD to Beads

1. 1 μm diameter Polybead amino microspheres (Polysciences, 17010–5).

2. BSA.

3. HaloTag succinimidyl-ester (O₂) ligand (Promega, P1691) (see Note 8).

4. Actin-binding domain of human α-actinin 1 (ACTN1; residues 30–253) (see Note 9).

5. PBS.

6. KMg25 buffer.

Fluorescent Labeling of Beads

1. Rhodamine BSA (Molecular Probes, A23016).

2. PB.

2.2. Silica Beads

1. Silica beads, 1.54 μm diameter 10% solids, or 1.21 μm 10% solids (Bangs Labs, SS04N).

2. Acetone (Sigma, 32201).

3. Pentyl acetate solution (Sigma, 46022–250ML-F).

4. Nitrocellulose 1%: 10 mg nitrocellulose 0.45 μm pore size (Sigma, N8267) dissolved in 1 mL penyl acetate solution or amyl acetate (Sigma, S 109584).

2.3. Rhodamine F-Actin & Biotinylated Actin

2.3.1. F-Actin

1. G-actin protein (Cytoskeleton, AKL99 1 mg), reconstituted to 10 mg/mL from powder following manufacturer instructions, final buffer: 5 mM Tris–HCl, pH 8.0, 0.2 mM CaCl₂, 0.2 mM ATP, 5% (w/v) sucrose and 1% (w/v) dextran (see Note 2).

2. 10× actin polymerization buffer: 100 mM Tris–HCl, 20 mM MgCl₂, 500 mM KCl, 10 mM ATP, and 50 mM guanidine carbonate, pH 7.5) (Cytoskeleton, BSA02) (see Note 2).

3. dl-Dithiothreitol (DTT) 1 M in ultrapure water (from powder, Sigma, 43819) (see Note 3).

4. 250 μM rhodamine phalloidin (Phalloidin–Tetramethylrhodamine B isothiocyanate) in methanol (from powder, Sigma, P1951) (see Note 3).

5. Milli-Q ultrapure water.

2.3.2. Biotinylated F-Actin

1. Reagents 1–6 as in Subheading 2.3.1.

2. Biotinylated G-actin protein (Cytoskeleton, AB07), reconstituted to 10 mg/mL from powder following manufacturer instructions, final buffer: 5 mM Tris–HCl, pH 8.0, 0.2 mM CaCl₂, 0.2 mM ATP, 5% (w/v) sucrose, and 1% (w/v) dextran (see Note 2).

2.4. Flow Cell

1. Pure Ethanol (Sigma, 02860).

2. Nitrocellulose + silica beads (1.54/1.21 μm) solution (Subheading 3.4 for silica bead preparation).

3. Double-sided sticky tape (~60 μm thick).

4. Glass coverslips: 24 × 24 mm and 60 × 24 mm, ~150 μm thick.

5. Glass slides: 26 × 76 mm, 1 mm thick.

2.5. Myosin-V Experiments

1. M5B buffer: 10 mM MOPS, pH 7.3, 0.5 M NaCl, 0.1 mM EGTA, and 3 mM NaN₃ with 2 μM Calmodulin (CaM, 208783, Merck).

2. dl-Dithiothreitol (DTT) 1 M in ultrapure water (from powder, Sigma, 43819) (see Note 3).

3. Streptavidin protein 1 mg/mL (ThermoFisher, 21122).

4. AB buffer: 25 mM KCl, 4 mM MgCl₂, 25 mM MOPS, and 1 mM EGTA, pH 7.2 (see Note 1).

5. Purified biotinylated myosin-5B heavy meromyosin (see Note 10).

6. BSA 50 mg/mL in AB buffer (from powder, Sigma, B4287) (see Note 2).

7. 1 μm diameter α-actinin coated fluorescent beads (Subheading 2.1.3).

8. Rhodamine F-actin (Subheading 2.3.1).

9. 100 mM ATP, pH 7.0 in ultrapure distilled water (see Note 3).

10. 5 mg/mL glucose oxidase from Aspergillus niger in AB buffer (from powder, Sigma, G7141) (see Note 2).

11. 5 mg/mL catalase from bovine liver in AB buffer (from powder, Sigma, C40) (see Note 2).

12. 250 mg/mL glucose in AB buffer (from powder, Sigma, G7528) (see Note 11).

13. 1 M creatine phosphate disodium salt tetrahydrate in AB buffer (from powder, Sigma, 27920) (see Note 12).

14. 10 mg/mL creatine phosphokinase from rabbit muscle in AB buffer (from powder, Sigma, C3755) (see Note 12).

15. Imaging Buffer (IB): AB buffer with 1.2 μM glucose oxidase, 0.2 μM catalase, 17 mM glucose, 20 mM DTT, 2 μM CaM and ATP at the concentration needed for the experiment.

16. High vacuum silicone grease heavy (Merck Millipore, 107921).

2.6. Myosin-II Experiments

1. AB buffer.

2. 2×S1 buffer: 200 mM NH₄Ac and 3 mM MgAc, pH 7.6 (see Note 1).

3. Streptavidin protein 1 mg/mL (ThermoFisher, 21122).

4. Purified non-processive myosin protein. In the experiments reported below, myosin-II S1 subfragment from mouse muscle fibers type 2B in S1 buffer was used (see Note 13).

5. 50 mg/mL BSA in AB buffer (from powder, Sigma, B4287) (see Note 2).

6. Functionalized trapping beads (Subheadings 2.1.1–2.1.3).

7. Rhodamine F-actin (Subheading 2.3.1) or Rhodamine F-biotinylated actin (Subheading 2.3.2).

8. 100 mM ATP, pH 7.0 in ultrapure water (see Note 3).

9. 5 mg/mL glucose oxidase from Aspergillus niger in AB buffer (from powder, Sigma, G7141) (see Note 2).

10. 5 mg/mL catalase from bovine liver in AB buffer (from powder, Sigma, C40) (see Note 2).

11. 250 mg/mL glucose in AB buffer (from powder, Sigma, G7528) (see Note 11).

12. 1 M creatine phosphate disodium salt tetrahydrate in AB buffer (from powder, Sigma, 27920) (see Note 12).

13. 10 mg/mL creatine phosphokinase from rabbit muscle in AB buffer (from powder, Sigma, C3755) (see Note 12).

14. 1 M DL-Dithiothreitol (DTT) in ultrapure water (from powder, Sigma, 43819) (see Note 3).

15. Deoxygenating system: 20 mM DTT, 200 μg/mL glucose oxidase, 50 μg/mL catalase, 3 mg/mL glucose in AB buffer.

16. ATP regenerating system: 2 mM creatine phosphate, 100 μg/mL creatine phosphokinase in AB buffer.

17. High vacuum silicone grease heavy (Merck Millipore, 107921).

2.7. Optical Trap Instrument (AOD Configuration)

The experimental setup (Fig. 2) is based on a dual-beam optical trapping system which utilizes a custom-made inverted microscope with a force measurement module and combined with brightfield and fluorescence imaging. Two optical traps are formed by splitting the input beam into two beams with orthogonal polarizations using a polarizing beam splitter (PBS1). The position of each trap can be independently controlled by two 1-dimensional AODs. Both beams are deflected by a corresponding AOD in the horizontal plane (parallel to the optical table) such that the two traps in the focal plane of the objective are freely movable along the same line. The light scattered by the trapped particles is collected by the condenser and the force is measured using back-focal-plane (BFP) interferometry.

Fig. 2.

AOD-based experimental setup. AOD-based experimental setup. Trapping control unit contains elements for controlling the positions of the traps. Fluorescence and brightfield units provide corresponding imaging systems to visually control the experiment. Trap detection unit performs measurement of the optical force. M mirror, FM flipping mirror, WP half-wave plate, AOD acousto-optic deflector, PBS polarizing beam splitter, L lens, OI optical isolator, DM dichroic mirror, FF fluorescence filter, HL halogen lamp, QPD quadrant photodetector, CMOS complementary metal-oxide-semiconductor camera, HM-CMOS high-magnification CMOS camera, DDS direct digital synthesizer, FPGA field-programmable gate array

2.7.1. Trapping Control Unit

The optical isolator (OI) eliminates possible instabilities in the laser output due to a back-reflected light. The laser beam is split by PBS1 into two beams with orthogonal polarization. A half-wave plate WP1 provides control over the power distribution between two beams. Each beam passes through its own AOD (AOD1 and AOD2) and both beams are recombined by PBS2. Half-wave plates WP2 and WP3 change the polarization state of the beams to fit the requirements of the AODs for optimal operation and to ensure a correct recombination of the beams after the beam polarization is rotated 90° by the AOD. The AODs are controlled by a direct digital synthesizer (DDS) block, which contains two synchronized synthesizers (one for each AOD) that are programmed by the FPGA module. The AODs change the angle of the outgoing beam depending on the frequency of the acoustic wave in the AOD crystal. The lens L1 serves to convert the angular displacement into lateral displacement and, therefore, is placed at its focal distance from both AODs. The lens L2 collimates both beams and it is placed at its focal distance from the objective back aperture. The optical traps are formed in the focal plane of the objective. We measured 8 μs response time of the feedback system, defined as the time from when command signals are sent from the FPGA to the DDS, plus the time the AODs spend to move the traps, plus the rise time (10–90%) of the QDP position signals [23]. The mechanical relaxation time of the dumbbell-myosin system was about 10 μs using fast skeletal myosin II and neutravidin-biotin actin-bead links; the dead time was about 100 μs [4]. In the optical setup in Florence, with the particular AODs and optical configuration used, only slight “wiggling” effect was observed [24], and no detectable position instabilities during the force-clamp as reported at UPenn [20].

2.7.2. Imaging Unit

Fluorescence imaging consists of an EM-CCD camera, the excitation laser (EXC), appropriate emission filter (FF) and excitation dichroic mirror (DM2). Brightfield imaging is achieved by two CMOS cameras, which allow observation of the trapping region with different fields of view (FOV). For both fluorescence and brightfield imaging systems the image is formed by the objective and the tube lens L3. The camera with a higher magnification (HM-CMOS) is used in the stage mechanical feedback loop as a position detector of the fixed particle. A motorized flip mirror (FM) provides convenient switching between brightfield and fluorescent modules.

2.7.3. Detection Unit

BFP interferometry is used to measure forces acting on trapped particles. This method relies on the measurements of the relative position of the trapped particle with respect to the laser beam by tracking the centroid of the scattered light intensity in the BFP of the condenser. The force in each trap is measured separately by splitting the beams with orthogonal polarization using PBS3. The lenses L5, L6, L7 are aligned to image the BFP of the condenser onto a corresponding QPD (see Note 14).

2.8. Optical Trap Instrument (EOD Configuration)

The control signal from the feedback calculations must move the position of the beam in the sample chamber precisely and rapidly. AODs were initially used in the UPenn setup, as described above, because of their fast response time (<10 μs), and moderate deflection angle, e.g., 30 mrad (1.7°) [23]. However, we found that the AODs introduced distortions to the laser beams which had detrimental consequences for the feedback loops. Slight intensity variations in the deflected beam as the deflection angle was changed, likely due to a small standing wave component of ultrasound in the AOD crystal led to artifactual jumps in the position signals that were difficult to separate from motions due to the biological sample. This led us to attempt the experiments with EODs, which did not exhibit such effects and improved the reliability of the system. EODs offer a smaller deflection range of only 3 mrad (0.17°), but afford greater transmission and more uniform modulation of the beam angle as well as faster response time (2 μs) [23, 24]. Each of these deflector systems was optimized to reposition the beam in less than 4 μs from the command signal input, allowing us to achieve the required 10 μs loop time (2 μs force detection +4 μs feedback calculation +4 μs beam steering).

This loop update time is much faster than the trapped bead’s response time in solution (~160 μs), as indicated from the power spectrum of bead displacement, which has a corner frequency near 2 kHz. While it has previously been shown that a position-clamp feedback loop running faster than the time response of the bead can increase the effective trap stiffness, our feedback loop operates in the force-clamp mode. This causes a decrease in the effective stiffness of the trap (since the trap follows the bead rather than restraining it). The (reduced) effective stiffness in solution is not highly relevant to the experiments as the primary interest is the dynamics of the actin filament motions during interactions with myosin. In this situation, the effective stiffness of the entire system becomes much greater than that of the trap, mostly due to the myosin’s stiffness on the order of 1 pN/nm. The ultrafast system is capable of detecting halting of the actin within about 100 μs (see Subheading 3.9.1) of myosin attachment under the conditions of our experiments [11] and subsequent displacements of the actin filament can also be resolved within few ten of μs (see Subheading 3.9.3).

The EOD setup in Philadelphia (Fig. 3) is very similar to the AOD one in Florence. The main differences are the deflectors and their driving electronics, which are high voltage amplifiers instead of ultrasonic frequency synthesizers, and extra lenses shown in Fig. 3 that narrow the beam for transit through the EODs.

Fig. 3.

EOD-based experimental setup. The optics and electronics are similar to the AOD version, although extra lenses are required to narrow the infrared beam sufficiently to traverse the long, narrow deflection crystal. Dashed blue lines indicate planes conjugate to the objective back focal plane. L7 is necessary to create a conjugate plane at Picomotor Mirror 1 (PM1) to properly control the position of EOD B’s beam relative to EOD A’s beam. A similar lens (L6) is included after EOD A to maintain homogeneity between the beam paths. Half-wave plate (HWP) A rotates the polarization of the incoming light to horizontal as required for deflection. A pair of lenses in front of each EOD (L2–L4, and L3–L5) reduce the beam diameter for transit through the long, narrow EOD crystals. PBS1 controls the total intensity of both traps to be by diverting energy into a beam block (black box). PBS polarizing beam splitter, M mirror, L lens, HV Amp high voltage amplifier, QPD quadrant photodiode. The microscope is also equipped for TIRF illumination and single molecule fluorescence detection via an EMCCD camera, which are not shown here

The 1064 nm solid-state trapping laser beam is split into two orthogonally polarized beams using a half-wave plate and a polarizing beam splitter (Fig. 3). These two beams are independently steered by the EODs, enabling the manipulation of the beads necessary to form bead-actin-bead dumbbells. The beams are recombined in a polarizing prism, expanded, and then relayed through the objective to the sample plane. The detection of the optically trapped beads occurs at the BFP where movements of the optically trapped beads relative to the center of the optical trap are detected using polarization separated QPDs. BFP detection measures forces (i.e., the product of the relative displacement of the bead from the center of the optical trap and the stiffness) and not the absolute position of the beads in space. A real-time drift and slope correction (DSC) system was included to improve stability and accuracy of the force signals caused by thermal drifts and other variations [11]. In brief, the feedback system was paused intermittently (for 2 ms at 10 ms intervals) to probe the baseline force signals for drift. The amount of detected drift is used to correct the set points of the feedback loops to maintain accurate forces relative to the baselines.

The reduced angular displacement of the EODs and the location of the effective center of the deflection within the EOD device required special consideration in the optical path design. The 3 mrad deflection of the laser beam by the EOD in our system corresponds to several hundred nanometers of trap translation at the sample, which is sufficient for the feedback experiments. However, to form actin dumbbells from filaments of various lengths that are pre-tensioned to ~5 pN, >3 μm of beam travel is required. This is accomplished via a remote-controlled gimbal mounted mirror (PM1 in Fig. 3) placed at another position conjugate to the BFP of the objective. Angular changes at this mirror produce displacement at the sample. The effective center of deflection of the EOD, which also needs to be conjugate to the BFP of the objective, is located approximately 2 cm inside the 10 cm EOD device, measured from the exit aperture. To ensure both this center of deflection and the PM1 mirror are conjugate to each other, a short focal length relay lens is used to image the center of rotation of the EOD onto the mirror as a 4f optical relay. While only one of the traps is manipulated by this conjugate mirror, both traps contain corresponding relay lenses (L6 and L7 in Fig. 3) to produce similar beam characteristics once they are recombined.

3. Methods

3.1. Trapping Beads Functionalization

3.1.1. Neutravidin-Coated Beads

In this preparation, volumes and centrifuge times refer to 0.9 μm diameter beads and, within square brackets, 0.5 μm diameter beads. Smaller beads allow higher temporal resolution, but they tend to cluster and complicate trapping. We suggest optimizing measurement protocols using 0.9 μm beads and then switch to 0.5 μm beads for optimal temporal resolution.

Biotinylated Latex Beads

1. In a 0.5 mL tube, mix 25 μL 0.9 μm carboxylated beads and 475 μL PB [100 μL 0.5 μm microspheres and 400 μL PB].

2. Centrifuge at 19,400 × g for 2 min [8 min] at 4 °C.

3. Discard supernatant very carefully and resuspend the pellet in 500 μL PB by pipetting, vortexing, and brief sonication (see Note 15).

4. Centrifuge a second time at 19,400 × g for 2 min [8 min] at 4 °C.

5. Discard supernatant very carefully and resuspend the pellet in 80 μL PB (see Note 15).

6. Prepare 74 mg/mL EDC in PB, EDC should be prepared fresh and it must be used within 15 min after preparation (see Note 16).

7. To the beads resuspended at step 5, add 10 μL 74 mg/mL EDC and 10 μL 2 mg/mL biotin-x-cadaverine.

8. Incubate at room temperature for 30 min. Mix gently occasionally.

9. Wash beads three times as follows: centrifuge at 19,400 × g for 2 min [8 min] at 4 °C, discard supernatant, resuspend the pellet in 500 μL PB (see Note 15).

10. After the third centrifugation, discard supernatant and resuspend the bead pellet (see Note 15) in 98 μL PB + 2 μL 1% NaN₃ (see Note 17).

Neutravidin Fluorescent Beads

In this preparation, volumes and centrifuge times refers to preparation of 0.9 μm diameter beads. Entries in square brackets are for 0.5 μm diameter beads.

1. Use 12.5 μL 0.9 μm biotinylated latex beads [12.5 μL 0.5 μm biotinylated latex beads] (Subheading “Biotinylated Latex Beads”).

2. Add 175 μL PB.

3. Centrifuge at 19,400 × g for 2 min [8 min] at 4 °C.

4. Discard supernatant very carefully and resuspend the pellet in 100 μL PB [800 μL PB] (see Note 15).

5. Add 10 μL [100 μL] 1 M glycine, 10 μL [100 μL] 5 mg/mL neutravidin and 0.5 μL 5 mg/mL streptavidin-alexa532 [no streptavidin-alexa532].

6. Incubate at room temperature for 20 min. Gently mix the solution every 5 min.

7. Centrifuge at 19,400 × g for 2 min [8 min] at 4 °C, then discard supernatant and resuspend the pellet in 200 μL PB (see Note 15).

8. Repeat step 7 two more times (see Note 18).

3.1.2. Preparation of N-Ethylmaleimide Modified Myosin Beads

N-ethyl maleimide (NEM) modifies reactive sulfhydryl residues in myosin, resulting in a non-enzymatically active motor domain that binds strongly to actin. NEM-myosin bound to beads has been shown to be highly effective for creating stable dumbbells for experiments performed at low ATP concentrations. However, at ATP concentrations >100 μM, we find that the linkages between the actin and the NEM-myosin slip when the dumbbell is placed under tension.

1. Dilute 0.8 mg of rabbit skeletal myosin to ~1 mg/mL in water to a final volume of 0.8 mL. Myosin will start to form filaments once the salt is lowered below 200 mM KCl and the final salt concentration should be less than 25 mM after dilution with water. If the initial stock of myosin is dilute, then dilute 0.8 mg of myosin into a solution than contains less than 25 mM salt, concentrate, and proceed as described below.

2. Centrifuge at 15,000 × g for 30 min at 4 °C in a benchtop centrifuge. Discard the supernatant and save the myosin pellet.

3. Resuspend the pellet in 110 μL HSB. The high salt depolymerizes filamentous myosin.

4. Add 12 μL of 50 mM NEM to the myosin. Incubate 90 min at room temperature (see Note 19).

5. Add 1 mL of water and DTT to 20 mM to quench the reaction and polymerize the myosin.

6. Centrifuge at 15,000 × g for 30 min at 4 °C using a benchtop centrifuge. Discard the supernatant and save the myosin pellet.

7. Resuspend the pellet in 200 μL HSB and add 200 μL glycerol. Add DTT to 10 mM. NEM-modified myosin can be stored up to 1 month at −20 ° C.

8. Wash 2 μL of polystyrene beads two times with 250 μL Milli-Q H₂O to remove surfactants. Centrifuge at 15,000 × g for 2 min at 4 °C using the benchtop centrifuge. Remove the supernatant. If a well-formed pellet is not formed, remove some supernatant and centrifuge again.

9. Resuspend the beads in ~15 μL Milli-Q H₂O and sonicate for 30 s.

10. Add 80 μL of NEM-modified myosin to the beads and let mixture equilibrate for 2 h at 4 °C or overnight on ice.

11. Prepare BSA-coated 1.5 mL microcentrifuge tubes during the incubation above. Prepare two tubes with 1 mL HSB containing 1 mg/mL BSA and two tubes with 1 mL KMg25 containing 1 mg/mL BSA. Equilibrate at room temperature for at least 30 min (see Note 20).

12. After 2 h, add 1 mL of HSB to the beads and then centrifuge in the BSA-coated tubes at 10,000 × g for 8 min using the benchtop centrifuge. Repeat wash.

13. Wash beads one time in 1 mL KMg25. Centrifuge in a BSA-coated tube at 10,000 × g for 8 min using the benchtop centrifuge.

14. Resuspend the pellet in 200 μL KMg25 (without BSA) and transfer to the last BSA-coated tube (after removing the BSA solution from the tube).

15. Store NEM-myosin-coated beads at 4 °C for up to 10 days.

3.1.3. α-Actinin Coated Fluorescent Beads

Purification of HaloTagged, Actin-Binding Domain of α-Actinin (HT-ABD)

This strategy generates an ATP-insensitive bead-to-actin linkage that does not interfere with other biotin-streptavidin linkages in solution, which is necessary, for example, when coupling biotinylated myosin-Vb HMM to the surface (see Subheading 3.7.1). The preparation is more complicated than the methods described above, and it requires bacterial expression and purification of a recombinant protein. The sequence details of the HT-ABD construct containing a hexa-histidine tag for purification are described in detail elsewhere [25].

1. Express HT-ABD using the pLT36 plasmid available from the Ostap Lab in Rosetta2(DE3) pLysS cells using standard techniques. Expression is induced with 0.1 mM IPTG after cells reach a density of 0.6–0.8 OD and then the cells are grown for 3 h. The cell pellet can be stored at −80 °C.

2. For each liter of cells, resuspend in 50 mL LB on ice using a homogenizer.

3. Sonicate cells five times for 15 s using a probe-tip sonicator.

4. Centrifuge at 25,000 × g for 30 min at 4 °C. Save the supernatant.

5. Load the supernatant onto a 2 mL nickel-NTA column at 1 mL/min using a peristaltic pump.

6. Wash the column five times with 3 mL of WB.

7. Add 5 mL EB to the column. Let sit for 30 min.

8. Elute the protein and then repeat steps 6 and 7.

9. Dialyze the eluant into FPLC buffer A overnight at 4 °C.

10. Use FPLC with a MonoQ column to purify the protein with a gradient of FPLC buffers A and B.

11. Concentrate protein using centrifugal filter units (Millipore UFC901024), dialyze into 1 L KMg25 overnight, and then freeze rapidly and store in liquid nitrogen in 50 μL aliquots.

Bead-Actin Linkages: Coupling of HT-ABD to Beads

The HT-ABD construct is linked to beads to create an ATP-insensitive actin-linkage. Amino-functionalized beads are linked via a succinimidyl ester to a chloroalkane group. The chloroalkane covalently links to the HaloTag gene-product fused to the α-actinin actin-binding domain. Perform the following steps:

1. Use a bath sonicator to disperse 50 μL of amino microspheres in 1 mL of water.

2. Wash beads three times in 1 mL water. Centrifuge at 10,000 × g for 8 min in the benchtop centrifuge after each wash to pellet the beads.

3. Resuspend the beads in 200 μL of phosphate buffered saline. Split this volume into 40 μL aliquots and sonicate the beads using a bath sonicator for 20 min.

4. Add 2 μL of 100 mM succinimidyl-ester ligand to each aliquot. Sonicate beads for 30 min in a bath sonicator. Let the beads sit for 30 min. During the incubation, the succinimidyl ester becomes covalently linked to the amino groups on the beads.

5. Prepare BSA-coated 1.5 mL Eppendorf tubes while you wait. Prepare two tubes of 1 mL KMg25 + 1 mg/mL BSA. Let sit at room temperature for at least 30 min.

6. Combine all of the bead aliquots into a BSA-coated tube and then wash beads three times with 1 mL PBS. Centrifuge at 10,000 × g for 8 min at 4 °C in the benchtop centrifuge after each wash.

7. Resuspend the beads in 200 μL of PBS. Split this volume into 40 μL aliquots and sonicate the beads using a bath sonicator for 20 min with added ice to prevent the temperature from rising.

8. Add 50 μL of HT-ABD to each aliquot. Let sit in a water bath at 37 °C for 1 h.

9. Combine all of the bead aliquots in a BSA-coated tube and then wash beads three times with 1 mL PBS. Centrifuge at 10,000 × g for 8 min at 4 °C in the benchtop centrifuge after each wash.

10. After the final wash, resuspend the beads in 1 mL of KMg25. Aliquot the beads into 20 μL aliquots, snap freeze in liquid nitrogen, and store in liquid nitrogen or in a −80 °C freezer.

Labeling of HT-ABD Beads

1. Incubate 200 μL beads solution with Rhodamine BSA at 5 μg/mL final concentration for 10 min.

2. Wash with PB 50 mM three times (see Note 21).

3. After final wash resuspend in 500 μL 50 mM PB (see Notes 22 and 23).

3.2. Preparation of Silica Beads

1. Dissolve 20 μL 1.2 μm or 1.5 μm 10% solid silica beads (according to the experimental needs (see Note 24)) in 1–1.5 mL of acetone.

2. Vortex the beads and sonicate for 30 s.

3. Centrifuge at 18,500 × g for 2 min at room temperature.

4. Discard supernatant very carefully (see Note 15) and resuspend in 1–1.5 mL acetone.

5. Centrifuge again at 18,500 × g for 2 min at room temperature.

6. Discard supernatant very carefully and let acetone evaporate for 2–5 min in vented hood.

7. Resuspend the pellet in 1 mL pentyl acetate.

8. Centrifuge at 18,500 × g for 2 min at room temperature.

9. Discard supernatant very carefully.

10. Repeat steps 6 and 7 and resuspend the pellet in 100 μL nitrocellulose 1% + 900 μL pentyl acetate or amyl acetate (see Note 25).

3.3. Fluorescent and Biotinylated F-Actin

3.3.1. F-Actin

1. In a 0.5 mL tube mix 69 μL ultrapure water, 10 μL 10× actin polymerization buffer, 20 μL G-actin 10 mg/mL, and 1 μL DTT 1 M (see Note 26).

2. Put on ice for >1 h. Actin polymerizes at the higher ionic strength.

3. In a new 0.5 mL tube take 25 μL of polymerized F-actin and add 19.5 μL ultrapure water, 2.5 μL 10× actin polymerization buffer, 1 μL 1 M DTT, and 2 μL 250 μM rhodamine phalloidin.

4. Leave on ice overnight (see Note 27).

3.3.2. Biotinylated F-Actin

1. In a 0.5 mL tube mix 6 μL ultrapure water, 1 μL actin polymerization buffer 10×, 2 μL 10 mg/mL biotinylated G-actin protein and 1 μL 1 M DTT (see Note 26).

2. Put on ice for >1 h.

3. Take 10 μL polymerized biotinylated F-actin and add 6 μL ultrapure water, 1 μL 10× actin polymerization buffer, 1 μL 100 mM DTT and 2 μL 250 μM rhodamine phalloidin.

4. Leave on ice overnight (see Note 27).

3.4. Flow Cell Preparation

1. Take a glass coverslip (24 × 24 mm) and cleanse it carefully with paper soaked with pure ethanol. Then rinse it directly with pure ethanol, while handling it carefully with clean tweezers. Dry it under a gentle flow of nitrogen. No visible residues should be left on the glass surface. If perfect cleaning is not reached after a first cleaning, repeat the cleaning procedure.

2. Take the tube containing the silica beads stock (Subheading 3.2), vortex and briefly sonicate it for ~30 s.

3. Smear 2–4 μL silica bead solution on one surface of the coverslip by means of a second clean coverslip (24 × 60 mm) or plastic pipette tip, and wait for it to dry completely (see video article [26]).

4. Take a microscope slide (26 × 76 mm) and clean it carefully with paper soaked with pure ethanol. Dry it under a gentle flow of nitrogen to remove coarse residues on both surfaces.

5. Cut two narrow strips of double-sided sticky tape (~3 mm large, 60–100 μm thick) and carefully attach them on one side of the microscope slide in order to create a chamber of about 20–30 μL final volume, as shown in Fig. 4a.

6. (optional) Apply vacuum grease on the glass next to the sides of the tape using a syringe (Fig. 4c) to provide a better seal. Ensure that the lines of grease are continuous.

7. Handling the coverslip (prepared at step 3) with clean tweezers, close the chamber with the nitrocellulose + bead layer facing the inside of the chamber, as shown in Fig. 4a, by pressing the coverslip carefully with a plastic tip.

Fig. 4.

Flow cell assembly. (a) A glass coverslip, smeared with silica beads, is attached onto a microscope slide through double sticky tape stripes to form a flow cell about 20 μL volume. (b) Side view of the assembled flow cell. (c) Top view of the flow cell. Solutions are flown from one side of the chamber with a pipette and sucked from the other side through a filter paper to create a flow in the arrow direction

3.5. Optical Trap Alignment (AODs)

3.5.1. AOD Alignment

1. Align AOD1 (Fig. 2) such that the beam is aligned at the center of the objective at the central frequency (75 MHz).

2. Align the second beam which is controlled by AOD2 to follow the same path after recombination at the PBS.

3. Place the lens L1 at the focal distance from both AODs. This lens will transfer the angular displacement of the beam into a lateral, parallel displacement. This lens should be placed in a position where the distance between the centers of both beams after AODs is constant.

4. Position the lens L2 to collimate the diverging beams after the lens L1.

5. A fine alignment can be achieved by monitoring the back-reflected light from the slide in the focal plane of the objective. When properly aligned, the center of the spot does not change its lateral position when the objective scanner is moved up and down. Also, the spot should look symmetrical at different objective heights (Fig. 5) (see Note 28).

Fig. 5.

Back-reflected light pattern from the coverslip-water interface appears symmetrical at different imaging planes

3.5.2. EOD Alignment

A similar process to the one described above for AODs is used for EODs with the following differences:

1. The middle position of the trapping beam occurs when no voltage is applied to the EOD and the beam is undeflected.

2. Because of the low maximum deflection angle possible with an EOD, one of the beam paths includes a controllable mirror (PM1 In Fig. 3) to alter the distance between the two beams in the trapping chamber for capturing and pre-tensioning filaments. This mirror should be optically conjugate to the center of rotation in the EODs (approximately 1/3 of the length of the distance of the EOD from the exit aperture. A 4f lens system can be used to produce this setup (L7, Fig. 3). To maintain consistent beam paths for both traps, a similar lens should be placed at the other EOD (L6, Fig. 3).

3. The aperture and crystal face of EODs are often much smaller than those of AODs, so the beam diameter is reduced and very carefully aligned to pass through the EOD. The alignment is assisted by using a high quality 6-axis mount for the EODs.

3.6. System Calibration (Table 1)

Table 1.

Calibrations of the system

Camera calibration		AOD or EOD calibration			QPD calibration
X-Y	Z	Trap position (MHz to nm)	Power (MHz vs W)	Stiffness (MHz vs pN/nm)	B (V to nm)
Used in mechanical stabilization system. Matches the position in pixels (X-Y) and axial		Calibration of the trap position. Used in the force-clamp feedback to calculate an appropriate frequency change in AODs or voltage on the EODs	Calibration of the optical power variations for different deflection angles	Relates AOD or EOD frequency roll-off to the trap stiffness. Used to set the optical force acting on the trapped particle	Used in the force-clamp feedback control to convert measured voltage from detectors to relative displacement in nm

The bold frame shows the calibration parameters that are calculated from a single set of measurements spectral measurements of thermal fluctuations

3.6.1. Calibration of the nm-Stabilization System (z and x-y Stabilization)

X-Y localization

1. Prepare a sample chamber with silica beads attached to the coverslip. See Subheading 3.4.

2. Image a fixed single particle on a camera.

3. Move a piezo stage across the FOV in short steps and record the position of the particle in pixels at each step (see Note 29) (Fig. 6b).

4. Perform a linear fit to the recorded data and calculate the calibration constant of the camera in nm/pixel (see Note 30).

Fig. 6.

(a) Step response of the mechanical stabilization system with different gain values. (b) X-Y calibration. A set of images with particle been displaced 400 nm at each frame along the X-axis. Red dot represents the measured center of the particle. (c) Z calibration. A set of images with particle been displaced 200 nm at each frame along the Z-axis. Red represents the measured center of the particle. Red circle shows the circle used in the z-value calculation

Z localization

1. Image a single particle on the camera for mechanical feedback.

2. Find X-Y position of the particle (see Note 30) (Fig. 6c).

3. Calculate Z-value (see Note 31).

4. Move objective with a scanning piezo stage.

5. Repeat 2–4 for a range of ±1 μm,

6. Perform a linear fit of the position–Z-value data and find the Z calibration constant (see Notes 32 and 33) (Fig. 6a).

3.6.2. Trap Position (MHz to nm or V to nm)

1. Prepare a flow chamber with silica beads attached on the coverslip surface (Subheading 3.4) and floating polystyrene beads (use trapping beads prepared as in Subheading 3.1).

2. To calibrate the nm/pixel of the brightfield camera focus a silica bead on the coverslip surface slightly decentered (about 5 μm) from the center of the FOV and acquire an image of the FOV.

3. Move the bead by 10 μm toward the FOV center using the piezo stage and acquire a second image.

4. By using a centroid algorithm calculate the center of the bead in the two images and calculate the distance in pixels between the two beads to obtain the nm/pixel calibration of the brightfield camera.

5. For the AOD setup, trap a single floating particle in one trap and move the trap using AOD in small steps (0.2 MHz).

6. Acquire an image of the particle and the corresponding frequency of the AOD for each step.

7. Calculate the position of the particle in the FOV by using the centroid algorithm as before and convert it into nm by using the nm/pixel calibration obtained in the previous step.

8. Perform a linear fit to the frequency-position data and calculate the calibration constant in nm/MHz.

9. Repeat calibration for the second trap.

10. A similar procedure is used to calibrate the EODs, with the step sizes of the changes in input signals dependent on the particular EOD and high voltage drivers.

3.6.3. Power and Stiffness (MHz vs. W), QPD (MHz vs. pN/nm)

Power and stiffness calibration of AODs and calibration of QPDs can be calculated from a single set of measurements. One benefit of a properly aligned EOD setup is the following procedures do not need to be performed regularly as the power and stiffness is very consistent across the EOD’s range.

1. Prepare a sample with floating trapping neutravidin beads.

2. Trap a single particle in each trap.

3. Move both traps using corresponding AOD in small steps (0.2 MHz) and record a Brownian motion of the particle in both traps with QPD and the corresponding frequency of the AOD (Fig. 7).

4. Calculate an average power on the detectors at each position.

5. Find trap stiffness and QPD calibration constant beta by fitting a Lorentzian function to a power spectrum of the recorded Brownian motion (see Notes 34 and 35).

Fig. 7.

Power spectrum of the QPD signal of a trapped particle

3.7. Sample Preparation

3.7.1. Processive Myosin V

1. Prepare a flow cell as described in Subheading 3.4.

2. Incubate with 1 mg/mL biotinylated BSA for 5 min (see Note 36).

3. Wash with AB buffer supplemented with 1 mM DTT.

4. Incubate with 1 mg/mL streptavidin at for 5 min.

5. Wash carefully with AB buffer supplemented with 1 mM DTT.

6. Incubate biotinylated myosin-5B heavy meromyosin at 3 nM concentration in M5B buffer with 2 μM CaM for 5 min on the surface (see Note 37).

7. Wash with three volumes of biotinylated BSA at 1 mg/mL supplemented with 2 μM CaM in AB and incubate for 3 min.

8. While incubating prepare Reaction Mix (RM): 0.005% α-actinin functionalized beads (Subheading 3.1.3), 1 nM rhodamine phalloidin F-Actin (Subheading 3.3.1) in IB.

9. Wash with RM with the desired ATP concentration.

10. Close the chamber carefully with silicone grease and put the sample onto the microscope (see Note 38).

3.7.2. Non-Processive Myosin II

1. Prepare a flow cell as described in Subheading 3.4.

2. If the myosin will be attached to the surface via biotin-streptavidin linkages, add 50 μL of 1 mg/mL streptavidin to the flow cell surface and incubate for 5 min. If myosin will be adsorbed to the surface directly, add it now and skip steps 4 and 5.

3. Wash with three volumes of 1 mg/mL BSA in AB and incubate last volume for 5 min.

4. During this incubation, prepare the myosin-II S1 subfragment at 1 μg/mL in AB buffer.

5. Flow ~50 μL of myosin and incubate for 1 min (see Notes 37–39).

6. While incubating, prepare Reaction Mix (RM). According to experimental needs, proceed in one of the two following ways:

   1. Prepare RM with pre-mixed low concentration trapping beads and F-actin. RMi: functionalized trapping beads at ~0.002% solids, 1–2 nM biotinylated rhodamine-labeled F-actin (Subheading 3.3.2), ATP at the desired concentration, deoxygenating system, and ATP regenerating system in AB buffer (see Note 40).

   2. prepare RM with F-actin only and add a “high” concentration trapping beads by filling a small portion of the chamber right before closing it. RMii: 0.2 nM biotinylated rhodamine-labeled F-actin (Subheading 3.3.2), ATP at the desired concentration, deoxygenating system and ATP regenerating system in AB buffer (see Note 40).

7. Wash with either RMi or RMii at the desired ATP concentration.

8. (only in case (b)) After washing with RMii, briefly sonicate functionalized trapping beads (<5 s) in a bath sonicator and add ~4 μL to the flow cell to fill ~1/3 of the flow cell volume.

9. Close the chamber carefully with silicone grease and put the sample onto the microscope.

3.8. Measurement Protocol

1. Move the sample using long-range translators until a bead floating in solution is visible.

2. Switch on one of the two traps and trap one bead.

3. Move close to the coverslip surface to prevent unwanted trapping of multiple beads in the same trap. Repeat steps 1 and 2 to trap another bead in the second trap.

4. Adjust the power of the AODs acoustic waves to get the same stiffness in both traps. Trap stiffness in the range of 0.03–0.14 pN/nm is usually used in these experiments. Smaller stiffness values are useful to have better sensitivity at low forces. For EODs the power should be adjusted before the experimenting using the half-wave plate that proceeds the EODs.

5. Switch to fluorescence microscopy. The two trapped beads will be visible in fluorescence microscopy.

6. Move the sample using long-range translators to find an actin filament floating in solution (see Notes 40 and 41). Move the sample so that one end of the filament comes close to one of the beads until they attach (Fig. 8).

7. Regulate the distance between the beads roughly equal to the filament length by changing the frequency of the acoustic wave in the AODs or using the controllable mirror if using EODs.

8. Rapidly move the stage in the direction of the second bead, which is not linked to the actin filament. The liquid flow will stretch the actin filament in the direction of the second bead and the filament will eventually attach to it (Fig. 8).

9. Once the actin filament is stably attached to both beads, shutter the fluorescence excitation to prevent photobleaching of the actin.

10. Zero the position of the beams on the QPDs.

11. Record 5 s of data at 20 kHz, filtered at 10 kHz to measure the power spectral density (PSD) of the trapped beads ([22], Fig. 5). A Lorentzian function can be fit to the PSD to calculate the trap stiffness and the conversion between V and pN:

    $$\mathrm{PSD}(f)=\frac{4\beta K_{\text{B}}T}{C^2\left(1+\frac{f^2}{f_{\text{c}}^2}\right)}+y_0$$ (6)

    where β is the viscous drag coefficient, K_B is Boltzmann’s constant, T is the temperature, C is the calibration constant for pN/V, f is the frequency, f_c is the corner frequency, and y₀ is the noise floor. The viscous drag coefficient for a bead is given by β = 6πηr where r is the radius of the bead and η is the viscosity of water. The trap stiffness, k_t, is related to the corner frequency by k_t = 2πβf_c.

12. Slowly separate the traps to stretch the filament until the tension reaches about 2–5 pN. Test the rigidity of the complex by oscillating one trap in a triangular wave and checking that the triangular wave motion is precisely transferred to the other bead.

13. Move the stage and place the dumbbell in proximity of a silica bead stuck onto the coverslip surface. Adjust the height of the trapped bead centers at or slightly below the silica bead diameter, to allow contact between the filament and proteins attached onto the silica bead surface.

14. Switch on the ultrafast force-clamp with 2–3 pN net force and 100–200 nm oscillation amplitude and start scanning the bead (laterally across the direction of the filament axis) in discrete steps of about 20–30 nm. For each step, look for interactions for about 30 s. Binding events are identified by stopping of the velocity in the trap position signals (Fig. 9). If binding events are not observed, then step ahead.

15. Locate the position and height where the largest number of interactions are observed and start the stage nanometer-stabilization feedback.

16. Record data.

Fig. 8.

Experimental procedure for dumbbell assembly. (a) Fishing for a single fluorescent actin filament in solution with the left bead. (b) By rapidly moving the stage in the direction of the second bead, the actin filament is stretched by the liquid flow and (c) eventually attaches to the right bead. Trapped bead diameter is 1 μm. (Figure reproduced from [23])

Fig. 9.

Position signals under constant positive (a) and negative (b) force (top) and dumbbell velocity (bottom). Velocity distribution (right) perfectly fits the sum of two Gaussian functions, one cantered on zero (bound state), the other one cantered on v = Ftot/γ (unbound state). Binding and unbinding events (black dotted lines) were detected with a threshold (green dotted line) chosen to assure <1% false events. (Figure reproduced from [4])

3.9. Data Analysis

Here we describe the analysis of data from ultrafast force-clamp experiments to detect interactions between the motor protein and the cytoskeletal filament at high temporal resolution, separate multiple interaction kinetics, and measure sub-ms dynamics of the working stroke under load. Finally, for the case of processive motors, we describe the analysis of the motor’s steps and processive runs.

3.9.1. Event Detection

Attachment of a motor protein to its filament is detected from the derivative of the position signal (the dumbbell velocity), as it drops to zero upon binding (see Fig. 9, where positive and negative forces are separated for independent analysis). Velocity change upon myosin binding occurs with the same short relaxation time τ = 2β/(2k_t + k_m) as the time constant of force application to the myosin (see Eq. 3), so that interactions lasting for few tens of microseconds can potentially be detected. However, to prevent detection of false events due to thermal noise, the velocity record is smoothed using a σ = 25–800 μs width Gaussian filter that increases the signal-to-noise ratio (SNR) but also the dead time. The amount of smoothing is set so that the number of false events is estimated to be <1% of all detected events based on statistical estimates [27, 28]. The smoothing varies with the applied force but is constant across experimental conditions. Because higher net loads lead to faster motion of the actin, less smoothing is required and shorter events can be detected at higher loads.

Moreover, in our method, the dead time for the detection of binding events (Td_b) is larger than for unbinding events (Td_u), since transitions are detected by threshold crossing with a threshold closer to the bound state, as explained in the step-by-step protocol below. In summary, for a given motor protein (i.e., k_m) and bead radius (i.e., β), the dead time varies with both force and type of event to be detected.

Typical dead times for the detection of skeletal muscle myosin binding events using 500 nm diameter beads are Td_b ≈ 100 μs at ~5 pN and ~35 μs at ~12 pN [4]. Detection of unbinding events displays shorter dead times, with Td_u ≈ 30 μs at ~5 pN and ~12.5 μs at ~12 pN. Below is a step-by-step protocol for implementing the detection method:

1. Separate positive and negative force records and separately apply the following protocol to the two data sets.

2. From the trap position of the leading bead (the bead with the higher magnitude of force applied), calculate velocity by two-point difference. The trap position for the leading bead should be taken as the position of the actin filament as there is less influence of nonlinear end compliance on this more highly loaded bead and better SNR.

3. Apply a Gaussian filter with standard deviation σ to smooth velocity data. Start by setting σ ≈ 1 ms for ~1 pN force and lower values of σ for higher forces, up to ~25 μs at ~10 pN.

4. Calculate the velocity distribution and fit it with a double Gaussian function to respectively get peak velocities (v₁, v₂), amplitudes (A₁, A₂), and standard deviations (σ₁, σ₂) of the unbound and bound states (see Fig. 9, right panels).

5. Calculate the optimal threshold to separate bound and unbound events as,

   $$\varphi =\frac{\frac{{\upsilon }_1}{{\sigma }_1}+\frac{{\nu }_2}{{\sigma }_2}}{\frac{1}{{\sigma }_1}+\frac{1}{{\sigma }_2}}$$ (7)

   In this way, the probability per unit time of threshold crossing due to thermal noise is the same from the bound to the unbound state and vice versa [4]. Since the stiffness of the system is higher in the bound state, σ₂ is smaller than σ₁, and ϕ is closer to the velocity of the bound state v₂ (see Fig. 9, right panels).

6. Estimate the number of false events due to threshold crossing by thermal noise as

   $$F_{\text{B}}=T_{\text{U}}\cdot k\cdot f_{\text{C}}\cdot \text{exp}\left[-\frac{{\left({\nu }_1-\varphi \right)}^2}{2{\sigma }_1^2}\right]$$ (8)

   and

   $$F_{\text{U}}=T_{\text{B}}\cdot k\cdot f_{\text{C}}\cdot \text{exp}\left[-\frac{{\left({\nu }_2-\varphi \right)}^2}{2{\sigma }_2^2}\right]$$ (9)

   where $T_{\text{B}}=\frac{T}{1+A_1{\sigma }_1/A_2{\sigma }_2}$ and $T_{\text{U}}=\frac{T}{1+A_2{\sigma }_2/A_1{\sigma }_1}$ are, respectively, the time the protein spends in the bound and unbound state during the recording time T; f_c is the cutoff frequency of the Gaussian filter; k depends on the filter response and the noise spectrum (k = 0.849 for a Gaussian filter and white noise) [27]. Increase or decrease the filter width σ and repeat steps 3–6 until F_B and F_U become around ~1%.
7. Once the optimal σ and ϕ have been set, locate binding (t_b*) and unbinding (t_u*) times when the threshold is crossed. t_b* and t_u* differ from the true binding and unbinding times (t_b and t_u), since the optimal threshold is closer to the bound state velocity [4]. Corrected binding times are obtained as:

   $$t_b=t_b^{*}-\sqrt{2}\sigma er{f}^{-1}\left(\frac{{\nu }_1+{\nu }_2-2\varphi }{{\nu }_1-{\nu }_2}\right)$$ (10)

   and

   $$t_{\text{u}}=t_{\text{u}}^{*}+\sqrt{2}\sigma {\text{erf}}^{-1}\left(\frac{{\nu }_1+{\nu }_2-2\varphi }{{\nu }_1-{\nu }_2}\right)$$ (11)

   where erf is the error function. Additional corrections should be applied for interactions that are so short that the velocity cannot fully switch from one state to the other [4].
8. The dead times are calculated as [4]:

   $${\text{Td}}_{\text{b}}=2\sigma \sqrt{2}{\mathrm{erf}}^{-1}\left(\frac{{\nu }_1-\varphi }{{\nu }_1-{\nu }_2}\right)$$ (12)

   and

   $${\text{Td}}_{\text{u}}=2\sigma \sqrt{2}{\mathrm{erf}}^{-1}\left(\frac{\varphi -{\nu }_2}{{\nu }_1-{\nu }_2}\right)$$ (13)

3.9.2. Duration Analysis

Analysis of distribution of event durations from ultrafast force-clamp experiments on myosin motors reveals the presence of multiple unbinding kinetics from actin. It is therefore important to separate the kinetics of those states, which is usually possible by fitting the distribution of event durations with multiple exponentials. This not only allows the quantification of the kinetics of the different actomyosin states but, as explained in the next section, also the measurement of conformational changes occurring between those states.

1. Calculate the cumulative frequency distribution of bound events. Cumulative rather than frequency distribution is preferable as it does not depend on the subjective choice of a bin size.

2. Fit the graph of the cumulative frequency distribution with an exponential function of the form:

   $$C_{\text{f}}(\tau )=1-\sum _i^N{A}_i\text{exp}\left(-k_i\tau \right)$$ (14)

   Here we assume that the motor detaches from the filament independently from each of the N states, the jth state detaches from the filament with a rate k_j and is populated by a fraction $A_j/\sum _i^N{A}_i$ of events. The fraction of lost events owing to limited time resolution is given by $\sum _i^N{A}_i/\left(\sum _i^N{A}_i-1\right)$.

3. Find the number of states N that best-fit data. This is usually a tricky task, which can be accomplished by visually comparing fits to data and from residual analysis. Since increasing N usually results in lower residuals, it is not always easy to judge whether an additional state is required and significantly enhance data fitting. A less subjective approach consists in using a log-likelihood ratio test with a p-value cutoff to determine if, for example, triple and/or double exponential distributions are statistically justified. We devised a computational tool (MEMLET) to this end [29]. Figure 10 shows examples in which single, double, and triple exponentials were needed to fit cumulative frequency distributions of bound events in actin–myosin interactions. See also [4, 11].

4. A_i and k_i are obtained from the best-fit parameters.

5. To separate events in which the motor protein detached from the structural state i with rate k_i from events in which it detached from state j with rate k_j, calculate:

   $$t_{ij}=\text{ln}\left(100\frac{A_j}{A_i}\right)/\left(k_j-k_i\right)$$ (15)

   If k_i < k_j, it follows that events with durations t > t_ij detached from state i with 99% confidence [4].

Fig. 10.

Typical cumulative frequency distributions of the duration of actin-myosin interactions with 10 μM ATP for forces of 0 pN (n = 37), +3.1 pN (n = 215) and +5.5 pN (n = 329). The distributions show a single-exponential fit (1-exp fit) under zero force, two-exponential fit (2-exp fit) under low force and three-exponential fit (3-exp fit) under high force. k1 < k3 < k2 are detachment rates from different myosin structural states obtained from data fitting. (Figure reproduced from [4])

3.9.3. Analysis of the Motor Protein Working Stroke

The amplitude and temporal development of the motor protein working stroke can be measured from ensemble averages of single-molecule interactions [7, 30]. In this method, the beginnings of the events are aligned based on their detected time of binding and time-averaged point-by-point. Ensemble averaging increases spatial resolutions by scaling position noise as sqrt(N) (N is the number of interactions) allowing for Angstrom resolution when N ~ 1000 [4, 7, 30]. Temporal resolution depends on the uncertainty of binding time (σ_A), which increases proportionally with the filter width and inversely with SNR:

$${\sigma }_{\text{A}}=\frac{{\sigma }_1+{\sigma }_2}{{\nu }_1-{\nu }_2}2\sqrt{\pi }\sigma$$ (16)

The value of σ_A is thus smaller (better temporal resolution) for larger forces. For the interaction between fast skeletal muscle myosin and actin, σ_A was in the range 10–50 μs [4]. For cardiac myosin the average value of σ_t varied from 0.5 ms for 1.5 pN to ~72 μs for 4.5 pN. Below is a step-by-step protocol to calculate ensemble averages:

1. Obtain a linear fit of the rising or falling position signal preceding the beginning of each event when the myosin attaches (see Fig. 11b).

2. Align the events at their detected time of binding t_b along the horizontal time axis (Eq. 10), and at the value of the fitted pre-event line at time t_b along the vertical position axis (Fig. 11b).

3. Set the event ending as t_u-σ_A or t_u-2σ_A as obtained from Eqs. (11) and (16). This procedure gives high confidence that the last position value remains within the bound event period.

4. Extend the last position value of each event to match the length of the longest event (Fig. 11b).

5. Time-average the events point-by-point (Fig. 11b).

Fig. 11.

Ensemble averages: analysis of conformational changes of molecular motors. (a) A single interaction can be modeled as a sequence of conformations which determines the motor working stroke. Here, the motor protein goes through three sequential conformations (B0, B1, B2) with average lifetimes τ0, τ1, τ2. B0 is a pre-powerstroke state; the transition from B0 to B1 produces a first step δ1; and the transition from B1 to B2 a second step δ2. (b) Ensemble averages (black trace) are built by aligning single interactions (blue, red, and green traces) at their beginning along both the horizontal time and vertical position axes, extending the last position value of each event to match the length of the longest event (dotted lines), and time-averaging the events point-by-point. (c) Examples of experimental actin–myosin interactions under hindering load. Magenta arrowheads indicate actin–myosin binding, green arrowheads myosin working stroke and cyan arrowheads actin–myosin detachment. d) Ensemble average of 191 actin-myosin interactions with durations >1.5 ms under +3.2 pN force. t = 0 is time of binding. Before binding, the dumbbell moved at constant velocity against viscous drag (v = −178 nm ms⁻¹). After binding, myosin produced a ~4 nm working stroke in the opposite direction in a few milliseconds. Development of the working stroke was fitted by a bi-exponential function (magenta curve). (Figure reproduced from [4])

3.9.4. Quantification of the Ensemble Averages

To compare the characteristics of the ensemble averages across various experimental conditions, perform the following analysis (as described in detail in [11]):

1. Vertically offset the ensemble average so that the minimum position of the ensemble average within the first millisecond after actin binding is the baseline of zero displacement.

2. From the unfiltered average, determine the magnitude of the initial displacement by taking maximum position value reached within a given time window. This time window may need to be adjusted based on the kinetics of the myosin being studied and the experimental conditions (1.2 ms was used for β-cardiac myosin at forces above 1.5 pN, whereas 5 ms was used at 1.5 pN as the displacement was observed to be slower).

3. The time between when the ensemble average is at its minimum and its initial maximum is recorded as t_intit.

4. To calculate the kinetics of the initial displacement, normalize the ensemble average by scaling the position signal by the maximum initial displace so that it ranges from 0 to 1.

5. Determine the time, t_20–80, it takes for the normalized signal to cross from 0.2 to 0.8, and convert this to a rate constant (k) assuming a single-exponential process: k = (ln(0.8) − ln(0.2))/t_20–80%.

6. To quantify the size and timing of any subsequent dips of the ensemble average (which may be indicative of power stroke reversals), determine the initial stroke size by averaging 100 μs of data on either side of t_init.

7. Determine the location and position of any subsequent dip after the detected binding time using a 1 ms moving average of the ensemble and find the minimum point between t_init and the remaining time during the event, up to a maximum time (15 ms for β-cardiac myosin, based on crossbridge kinetics and visual inspection of the ensemble averages).

8. The amplitude and timing of the dip is reported as the difference between the time and displacement of initial stroke and the minimum dip, respectively.

9. The total displacement of the ensemble average is quantified as the average position over the last 200 μs of the ensemble average.

3.9.5. Analysis of Processive Runs

The analysis method described in the previous sections can be adapted to detect steps of processive motors and measure the step size, run length, and velocity, as previously described [14] (Fig. 12). The detection of steps in processive runs is based on the change in velocity, as caused by myosin stepping.

1. Apply steps 1–6 in Subheading 3.9.1 to find the optimal filter width and threshold.

2. Get binding (t_b*) and unbinding (t_u*) times when the threshold is crossed. Differently from non-processive motors, here, allow threshold crossing in both directions, for both positive and negative velocities. By doing this, forward and backward steps following myosin binding are detected. In fact, as the processive motor steps or backsteps, an abrupt rise and fall in velocity occurs, which is detected as if it is a rapid unbinding and rebinding by crossing across the velocity threshold. Obtain true binding and unbinding times (t_b and t_u), as before from Eqs. (10) and (11).

3. Assign apparent unbinding-rebinding events as steps of a motor run when they are rapid (<3 ms) and of reasonable amplitude (we used step size <90 nm for myosin-5B to include two consequent steps occurring within the time resolution of the step detection method). Unbinding-rebinding events outside these limits are considered as true unbinding and rebinding of the motor from the filament, rather than steps of an attached motor.

Fig. 12.

Position record showing myosin-5B processive runs and the step and run detection algorithm. Detected beginning and end of each run are indicated by green and cyan vertical lines, respectively. Red horizontal lines indicate the detected steps. [ATP] = 100 μM. (Figure reproduced from [14])

3.9.6. Run Length Correction for Pushing Forces

The peculiarity of the UFFCS protocol, which automatically reverses the force when the bead reaches the pre-set edge of the excursion range, must be taken into account when analyzing processive runs of motor proteins. In fact, when the force is applied in the same direction of motor stepping (assisting force), it can happen that the motor moves up to the edge of the excursion range where the force is reversed, so that the myosin run under assisting force is interrupted (arrows in Fig. 13). On the other hand, when the force is directed against myosin stepping (hindering force), the edge of the excursion range where the force is reversed is never reached by stepping, because myosin moves in the opposite direction (Fig. 13, hindering force). Thus, processive runs under hindering force are not limited by the excursion range.

Fig. 13.

Force inversion during myosin runs. When myosin binds and moves the filament in the positive direction under assisting assistive force (push), it can happen that it reaches the edge of the oscillation range where the force is reversed (indicated by the arrows), so that the myosin run under assistive assisting force is interrupted. Contrary, under hindering opposing force (pull), myosin processive stepping prevents the dumbbell from reaching the force inversion point. Therefore, run lengths are not limited by the oscillation range for hindering opposing forces. (Figure reproduced from [14])

In these cases, run lengths under assisting force are corrected by calculating the true run length RL from the expected (measured) average run length ⟨RL_m⟩ under our experimental constrains. Assuming exponentially distributed run lengths (see Fig. 14), the survival function (i.e., the probability of run longer than x) is given by

$$F_{\text{RL}}=e^{-\frac{x}{\text{RL}}}$$ (17)

Fig. 14.

Myosin-5B run length under hindering force is exponentially distributed. Histogram of myosin-5B run lengths under 1.2 pN resisting hindering force and 100 μM [ATP]. Red curve is the exponential fit to the data. (Figure reproduced from [14])

Assuming that myosin binding to actin is equally probable along actin excursion between 0 and D, and zero elsewhere, the associated survival function is given by

$$F_x=\{\begin{array}{l}1-\frac{x}{D},x\le D\hfill \\ 0,x>D\hfill \end{array}$$ (18)

The probability that myosin generates a run longer than x is given by the product between Eqs. (17) and (19):

$$F_{\text{RL}}\cdot F_x=\{\begin{array}{l}{e}^{-\frac{x}{\text{RL}}}\left(1-\frac{x}{D}\right),x\le D\hfill \\ 0,x>D\hfill \end{array}$$ (19)

from which the probability density function is derived

$$p(x)=\{\begin{array}{l}{e}^{-\frac{x}{\text{RL}}}\left(\frac{1}{\text{RL}}+\frac{1}{D}-\frac{x}{D\cdot \text{RL}}\right),x\le D\hfill \\ 0,x>D\hfill \end{array}$$ (20)

From the probability density function we can finally derive the expected run length value ⟨RL_m⟩

$$\langle {\text{RL}}_{\text{m}}\rangle ={\int }_{-\infty }^{+\infty }x\cdot p(x)\text{d}x=\frac{1}{D}\left[{\text{RL}}^2\left(e^{-\frac{D}{\text{RL}}}-1\right)+\text{RL}\cdot D\right]$$ (21)

In summary, given the measured average run length ⟨RL_m⟩, the true run length RL is calculated by numerically solving Eq. (21).

4. Notes

1. Filter-sterilize buffers with 200 nm filters.

2. Aliquot into experiment-sized portions and store it at −80 °C.

3. This buffer can be prepared as a 5× stock and frozen at −20 °C.

4. This solution can be aliquoted and frozen at −20 °C.

5. NEM is highly reactive, so it should be stored dessicated, and aqueous solutions should be made immediately before use.

6. This myosin can be purified from rabbit back muscle using established protocols [31].

7. PMSF should be prepared fresh in ethanol.

8. This reagent can be stored as 100 mM in DMSO at −80 °C.

9. The cDNA sequence for the actin-binding domain of human α-actinin 1 (ACTN1) (residues 30–253) containing a 5′ NdeI site and a 3′ BamH1 site was inserted into the pET28a vector. The pET28a vector also contains a N-terminal hexahistadine tag for protein purification. The HaloTag cDNA sequence was cut from the pFC20A vector (Promega) between the BamH1 and HindIII sites and inserted into the pET vector containing the α-actinin gene insert. This vector was transfected into BL21(DE3) cells and expressed via IPTG induction. The protein was purified by running the cell lysate over a NiNTA column followed by a FLPC MonoQ column (0–1-M KCl gradient) [25].

10. Myosin-5B DNA constructs, protein production, and purification: a cDNA construct encoding for amino acids 1–1095 of murine myosin-5B heavy meromyosin (MW 127 kDa) with a C-terminal Avi-tag was inserted in a modified pFastBac1 vector encoding a C-terminal Flag-tag with standard cloning techniques. Untagged rat CaM cDNA (Accession number NP_114175.1; 17 kDa) that is at the protein level 100% identical with murine CaM was expressed from pFastBac1. Recombinant baculovirus generation and gene expression were performed as recommended by the manufacturer (ThermoFisher Scientific). For protein production, Sf9 insect cells were infected with recombinant baculoviruses encoding myosin-5B and CaM. Avi-tag myosin-5B heavy meromyosin was purified via Flag capture [14] followed by size exclusion chromatography on a HiLoad Superdex 16/600 pg column (GE Healthcare Life Sciences). Biotinylation reaction was performed on the Flag-resin through incubation with BirA biotin ligase and d-biotin (Avidity) [14, 32].

11. Prepare ~1.5 mL solution in an Eppendorf, close it with parafilm and store it at 4 ° C for many months.

12. This enzyme should be prepared fresh daily.

13. Different type of myosins can be used in the high-speed optical tweezers (S1 subfragments or full-length non-processive myosins). Here we describe experimental procedures and data analysis for non-processive motors only. Extraction/expression and purification protocols vary between myosins. In the experiments reported here, myosin II from mouse muscle fibers type 2B was extracted and purified, and S1 subfragments were obtained from pure myosin sample as described [33].

14. Mechanical stability of the whole system is a crucial part of the force measurements. To assure an appropriate reduction the mechanical noise level in the system, a combination of techniques is used:

    • The setup is built on an optical table on a pressurized support that provides filtering of the ambient vibrations.

    • All components of the setup are enclosed to prevent any disturbance of the laser beam by ambient air flows. The cover of the setup is divided into smaller compartments to discourage the formation of convective flows inside the enclosure.

    • Inverted microscope is placed on elastomeric isolators which provide an additional vibration isolation of the most noise-sensitive part of the setup.

    • The piezo stage (X-Y) and objective piezo scanner (Z) operate in a closed-loop regime and thus provide an active stabilization to the system.

    • Another low frequency noise source arises from the thermal drift in optical components. To compensate for the drift an additional active stabilization system is realized through a feedback loop using a CMOS camera (HM-CMOS in Fig. 2). In this system a spherical particle is attached to the slide and provides a reference for the drift correction in the imaging system. The particle is imaged on the camera and a custom-made Labview script detects the position of the particle and corrects the position of the piezo stages to keep the particle in the same location during measurements with nm precision.

15. To discard supernatant, use small volume tips (≤200 μL) and pay careful attention not to disturb the pellet. Resuspended beads must be vortexed and sonicated briefly for ~30 s.

16. Once opened EDC is very unstable even at −20 °C. For this reason, small vials should be preferred (in the case of Sigma the smallest size available is 1 G). Upon opening, a vial should be used within a week.

17. Beads can be stored for 2–3 months at 4 °C.

18. Beads can be store at 4 °C and used in trapping experiments for 1 week.

19. The amount of NEM added may need to be adjusted depending on the age of the myosin. Older (>6 months) myosin preparations lose activity and may require less NEM to render the myosin inactive.

20. BSA-coating minimizes adsorption of beads to the tubes.

21. Washing consists in the following steps: centrifuge at 6797 × g for 5 min at room temperature, then carefully discard supernatant.

22. Prior to proceeding to trapping experiments, check beads under the microscope that they are not aggregated.

23. Beads can be aliquoted and stored at −80 °C for several months.

24. Volumes and centrifuge parameters are equivalent for both sized beads. Smaller silica beads can be used with 0.5 μm neutravidin beads. Smaller silica beads allow trapping of shorter actin filaments without interfering with the force-clamp and the nm-stabilization feedback.

25. Silica beads can be stored 4 °C for 2–3 months in Eppendorf tubes closed with parafilm pellicle. After 3 months, beads display fluorescence, probably produced by contaminants present in the parafilm and/or plastic tubes. Batters et al. suggest storage in small glass tubes to avoid contamination [34].

26. Mix gently without pipetting.

27. Rhodamine F-Actin can be stored on ice and used in the trap for ~1 week.

28. The laser beam should be positioned as close as possible to the piezo element in each AOD. This will minimize a reaction time in the AOD feedback loop and improve time resolution of the force-clamp system.

29. The X-Y position of the particle is calculated by finding a weighted centroid of the image.

    $$[X;\Upsilon ]=\left[\frac{\sum _{ij}{x}_{ij}{I}_{ij}}{\sum _{ij}{I}_{ij}};\frac{\sum _{ij}{y}_{ij}{I}_{ij}}{\sum _{ij}{I}_{ij}}\right]$$

    where I_ij is the intensity of ijth pixel. It may be necessary to remove the background from the image. This can be performed by applying some threshold to each pixel and set all values below the threshold to zero.

30. X-Y calibration constant of the camera (pixels to nm) usually remains constant and, unless any optical element has been changed or moved, there is no need for a recalibration.

31. The axial position of the particle is measured as the following ratio:

    $$Z=\frac{S_{\text{in}}^R}{S_{\text{out}}^R}$$

    where $S_{\text{in}}^R$, $S_{\text{out}}^R$ are the sums of all pixels inside and outside the circle of a radius R, which is centered at the X-Y position of the particle. The radius R should be approximately equal to the radius of the imaged particle to provide sufficient sensitivity to the changes in position.

32. Z calibration constant highly depends on the particle, illumination, current position of the objective, etc. Therefore, it is recommended to perform this calibration with each particle that is used in the experiment and at the position where the experiment will be performed.

33. The nm-stabilization system counteracts low frequency noises and drift of the microscope image plane due to temperature changes in the optical elements of the setup. The gain is set empirically for each axis individually by examining the step response of the system. The gain that creates the steepest step in the position of the particle (without overshoots) is set as the optimal gain. Figure 6a shows an example of the step response of X-axis at three different gains. According to the described parameters, the optimal gain for this stabilization system is g = 0.25. This adjustment must be repeated for Y and Z axes.

34. This calibration defines the performance of the force-clamp feedback system. It is recommended to repeat this calibration for the whole range of AOD frequencies each week to ensure reliability of the AOD feedback system. Also, it is important to repeat calibration with each new sample to have correct force calibration for the measurements (this can be performed within the frequencies used during measurement). For weekly calibrations—scan all the frequencies that can be used during experiments.

35. AODs performance in the displacement of the beam is linear and is less prone to slight misalignments. Therefore, this calibration can be well described for a wide range of frequencies by the slope of the position-frequency plot and does not require frequent recalibration.

36. The solutions in the flow chamber are applied by adding from one side with a pipette while wicking by capillary action from the other side with filter paper. If desired, the flow cell can be inclined at a ~30° angle by resting its top on an elevated surface (such as the petri dish that was used for storing the cover glass after drying).

37. The incubation time in this step must be very precise, since the duration of the incubation, together with the protein concentration in solution, determine the protein density on the glass surface. Under these conditions, approximately 1 in 3 silica beads interact with the actin filament, providing evidence that few of the beads contain more than one myosin-5B molecule. To ensure single-molecule conditions, only 1 in 10 beads should give binding interactions. At this density, the likelihood that a given bead has more than one myosin that can interact with the actin is less than 5% [35]. Adjust the concentration of myosin to achieve these conditions.

38. Experiments are usually performed at room temperature (22 °C).

39. The concentration indicated here can vary with the protein investigated. The optimal concentration of S1 to be used must be determined through optical trap experiments as the concentration that leads to detectable actomyosin interactions every two to three silica beads investigated. It is therefore a good practice to start with higher protein concentration and progressively decrease it until the above-mentioned condition is fulfilled.

40. The optimal bead and actin concentration should be carefully adjusted. Low bead concentration reduces the probability of trapping multiple beads in a trap during the experiment, but, on the other hand, may slow down bead searching. Similarly, low actin concentration prevents attachment of multiple filaments to the trapped beads but can, as well, slow down actin searching. We suggest optimizing the experimental conditions at low ATP concentrations (5 μM) because myosin interactions are slowed and easily detected.

41. The length of the actin filament should be >3 μm. Shorter filaments will introduce distortions in the position signals when the traps are near the silica bead. Moreover, the nm-stabilization feedback could also be disturbed if the trapped beads are visible within the image of the silica bead.