|Home | About | Journals | Submit | Contact Us | Français|
The myosin superfamily of molecular motors utilizes energy from ATP hydrolysis to generate force and motility along actin filaments in a diverse array of cellular processes. These motors are structurally, kinetically, and mechanically tuned to their specific molecular roles in the cell. Optical trapping techniques have played a central role in elucidating the mechanisms by which myosins generate force and in exposing the remarkable diversity of myosin functions. Here, we present thorough methods for measuring and analyzing interactions between actin and non-processive myosins using optical trapping techniques.
Myosins are cytoskeletal motors that use the energy from ATP hydrolysis to generate force and movement along actin filaments. Humans express thirty-eight myosin motor proteins (1) with diverse biochemical and mechanical properties that enable them to function in a wide-array of cellular processes, including muscle contraction, cell migration, mechanosensing, intracellular transport, generating membrane dynamics, and cellular signaling (2–4). Mutations in myosin genes can result in cardiomyopathies, hearing loss, blindness, cancer, and developmental defects (5).
Despite their diverse functions, all characterized myosins follow a similar ATPase and mechanochemical cycles (4). The rate and equilibrium constants that define the ATPase pathway vary substantially across the myosin family, resulting in differences in the steady-state populations and lifetimes of intermediates that confer diverse mechanical functions to the motors. It has been a substantial challenge to the field to determine how the biochemical intermediates on the myosin ATPase pathway are linked to structural changes that ultimately lead to force generation. Additionally, it has been a challenge to determine how divergent biochemical properties lead to mechanical differences among different myosins isoforms, how mechanical loads affect myosin power output, and how myosin mutations affect motor function in disease.
Single-molecule techniques, in conjunction with biochemical, spectroscopic, and structural studies, have been incredibly powerful in their ability to elucidate the molecular mechanisms of molecular motors (6, 7). Notably, optical tweezers have served as an indispensable tool for discovering the mechanisms of myosin function. Pioneering work by the laboratory of Dr. James Spudich led to the development of an assay to probe the properties of non-processive myosin motors (i.e., motors that only take a single step on actin before detaching), dubbed the three-bead assay (8). In this assay, an actin filament is suspended between two optically trapped beads, tensed, and then lowered onto a pedestal bead that is sparsely coated with myosin (Fig. 1). The myosin motor can then bind to the actin, displacing the beads. From these displacements, it is possible to extract information about the myosin working stroke, attachment lifetime, and magnitude of force generation. The three-bead assay has also been used to probe the kinetics and mechanics of processive myosins (9, 10). It is worth noting that other geometries have also been employed to study single non-processive motors (11–13).
To conduct the three-bead assay, one must (1) couple beads to actin, (2) prepare flow cells with pedestal beads, (3) attach myosins to the pedestal, and (4) identify single-molecule interactions between myosin and actin. In this chapter, we describe the procedures for performing this assay along with techniques for measuring myosin’s force-dependent kinetics and stiffness. We also describe techniques for data analysis. Our optical trapping setup is briefly described in Subheading 3.9 below. For detailed instructions on building a dual-beam optical trap for the three-bead assay, the reader is directed to an excellent chapter by the Spudich laboratory (14). For single-bead assays, the reader is referred to experiments in Chaps. 5, 17, and 18.
In the three-bead geometry, an actin filament is stretched between two optically trapped beads and then lowered on to a pedestal bead that is sparsely coated with myosin (Fig. 1). Therefore, before starting, one must: (1) purify actin and myosin, (2) functionalize beads so that they can stick to actin, and (3) assemble and load flow cells with the necessary components. Here, we provide protocols for each of these procedures.
Optical trapping assays require purified actin and myosin. The purification of myosin will depend on the specific myosin construct being used. Myosin can be tissue purified or produced recombinantly using an appropriate eukaryotic expression system (15–19).
While various systems are used to prepare myosin, actin can be prepared in large quantities from rabbit back muscle (20). In the first part of this preparation, muscle is ground and washed with both aqueous and organic solvents to form an “acetone powder”. This powder can be stored for long periods at −20 °C and can be used for a simple actin-extraction preparation (Subheading 3.2 and Note 19). The procedure for generating acetone powder is the following:
The procedure for purifying actin from acetone powder is the following:
Building a stable and well-defined bead-actin-bead dumbbell is crucial for measuring single-molecule attachment events. The dumbbell consists of two optically-trapped beads and a single actin filament, and the actin filament must remain stably associated with the beads (i.e., it must not dissociate or slip) in the presence of mechanical tension. Several methods have been developed to couple actin filaments to polystyrene beads. Here, we will describe three different reagents for creating actin-bead attachments: N-ethylmaleimide modified myosin, neutravidin-biotin, and a HaloTagged, actin-binding domain from α-actinin (HT-ABD).
N-ethylmaleimide (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. Perform the following steps:
Biotinylated-actin binding to neutravidin- (or streptavidin-) coated beads is an easily implemented, high-affinity linkage that is very stable to applied tension, tolerant of a wide-range of solution conditions, and insensitive to physiological MgATP concentrations. The disadvantages of the linkage are that it requires covalent modification of actin, and that it cannot be used if myosin is adhered to pedestals using a biotin-neutravitin/streptavidin attachment strategy. Biotinylated actin can be prepared by the experimenter or purchased from commercial sources (see Note 8). Perform the following steps:
Recently, our lab attached beads to the actin-binding domain of α-actinin fused to a HaloTag (22). This strategy generates an ATP-insensitive bead-to-actin linkage that does not interfere with other biotin-streptavidin linkages in solution. 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-histadine tag for purification is described in detail elsewhere (22). The procedure is the following:
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:
In the three-bead geometry, silica beads are adhered to the surface of the cover glass to act as myosin-binding pedestals. Pedestal beads are coated with nitrocellulose to aid with protein binding to the flow cell surface and to adhere the beads to the cover glass. Here, we describe the assembly of flow cells for the three-bead assay (Fig. 2):
Place the flow cell at a ~30° angle by resting its the top on an elevated surface (we use the petri dish that was used for storing the cover glass after drying, Fig. 2c). Add solutions to the top of the flow cell and ensure that all liquid flows through the flow cell. If necessary, use absorbent filter paper or cotton-tipped applicators to wick the solutions at the bottom of the flow chamber while being careful not to over draw the solution through the chamber. Perform the following steps:
Dumbbells are formed by stringing an actin filament between two optically trapped beads. Therefore, a dual-beam optical trap must be employed (14). Our optical trapping instrument has been described previously (23). In our system, a 1064 nm solid-state laser beam is split into two polarization-separated beams using a half wave plate and a polarizing beam splitter (Fig. 3). These two beams can be independently steered by acoustic optical deflectors (AODs), enabling the manipulation of the beads necessary to form bead-actin-bead dumbbells. The beams are recombined in a prism, expanded, and then relayed through the objective to the sample plane. The detection of the optically-trapped beads occurs at the back-focal plane where movements of the optically-trapped beads relative to the center of the optical trap are detected using polarization separated quadrant photodiodes (QPDs). Back-focal plane detection measures forces (i.e., the relative displacement of the bead from the center of the optical trap) and not the absolute position of the beads in space. To identify single-molecule interactions, perform the following steps:
Several methods have been developed to detect actomyosin-binding interactions (Fig. 4). Most of these methods rely on changes in the Brownian motion of the optically-trapped beads when myosin binds to actin (e.g., (8, 23, 26–28)). The variance in the position of the beads is reduced when myosin binds to actin. The variance can be calculated over a sliding time window and a variance threshold can be chosen to discriminate bound and unbound states (29, 30). Alternatively, a sinusoidal waveform can be actively applied to one of the optically-trapped beads and the passive response of the second bead can be measured (31, 32). This methodology increases the temporal resolution by magnifying the difference in the variance between the bound and unbound states.
For our data analysis, we prefer using a covariance threshold since it utilizes information from both optically trapped beads (27, 33), which requires the simultaneous detection of forces on both beads (i.e., two QPDs are necessary; Fig. 3). In the absence of myosin binding, the two optically trapped beads are mechanically coupled through the actin filament. When myosin binds to actin, the coupling between the beads is reduced. The covariance, a measurement of bead motion coupling, is high in the absence of myosin binding and low when myosin binds. The covariance is calculated over a sliding time window (Fig. 4b) and a histogram of covariance values for the data trace can be calculated (Fig. 4d). The histogram should show two distributions with a peak of lower covariance corresponding to the actin-myosin bound state and a peak of higher covariance corresponding to the unbound state. The separation between the peaks will depend on the pretension of the actin filament and the stiffness of the myosin. These peaks can be used to select bound and unbound states.
To achieve good separation between the covariance distributions, there must be a measurable change in the covariance during a binding interaction over the averaging window. As such, increasing the pretension on the bead-actin-bead dumbbell will increase the separation between the peaks. Moreover, the size of the sliding window used to calculate the covariance can be increased. While increasing the size of the window will increase the separation between the covariance distributions, it will also make it impossible to detect binding events with durations smaller than the size of the window. Therefore, when analyzing a data set, there is a tradeoff between better covariance peak separation and temporal resolution.
The selection of binding events is based on the distribution of the covariances. One could define a binding event as one in which the covariance drops below a given threshold for at a user-specified amount of time (see Note 31). With good separation between the bound and unbound covariance peaks, it is useful to select the minimum value between the two peaks as the covariance threshold. These selection criteria will maximize the temporal resolution, but it will result in the identification of more “false positives”. Alternatively, one could require a binding event to start when the covariance value transitions from the value of the unbound peak to the value of the bound peak and then end once the covariance transitions from the value of the bound peak to the value of the unbound peak. This methodology limits the number of detected “false positive” events, but it also reduces the temporal resolution.
Once binding events are identified, it is possible to determine the lifetime of the bound states from the distribution of individual attachment durations. Several methods have been developed to determine actin-attachment lifetimes, but we prefer utilizing maximum likelihood estimation (MLE) of the data (34). MLE determines the optimum parameters of a model-dependent probability density function (PDF) from the data without the need for binning. This technique is appropriate for the analysis of single-molecule data for several reasons. Most importantly, single-molecule data are often not normally distributed, which is what is required in traditional least-squares fitting. Additionally, in experiments where the duration of short-lived binding interactions is similar to the dead time of the instrument, techniques such as averaging and fitting functions to histograms will lead to an over-estimate of the attachment lifetime. MLE does not have these limitations.
The interpretation of the data will depend on the number of processes observed. Statistical methods should be used when fitting models of increasing complexity to the data to justify model selection. When using MLE, the ratio of the log-likelihoods can be compared to a chi-squared distribution (35).
The displacement of the bead-actin-bead dumbbell during the myosin working stroke is often of the same magnitude as the variance in bead position due to thermally-driven motions of the dumbbell. Therefore, determining the magnitude of the myosin-driven displacement is not trivial. However, several methods have been utilized to measure this displacement, and some of these techniques have been successful in detecting and quantifying working-stroke sub-steps as has been seen in some myosin isoforms (10, 22, 32, 33, 36, 37). Here, we describe three of these techniques.
Myosins adjust their motile properties in response to mechanical forces on the lever arm, and several optical trapping techniques using the three-bead geometry have been used to measure the effects of these loads on actomyosin attachment durations. Some techniques use active force- or position- feedback loops to apply loads to myosin by steering the trapping beam using an acousto-optic deflector (AOD; Fig. 3). Other techniques apply forces without active feedback. Selected examples of these techniques are discussed below.
Active force feedback upon engagement of actomyosin relies on detecting a change in trap motion to identify binding events (e.g., variance) (8). Once a detection threshold is crossed for a given amount of time, the feedback is engaged. Active feedback loops can work by increasing the trap stiffness or moving the trap once a binding interaction is identified. Drawbacks of these techniques are that the feedback loops are necessarily slower since calculations must be done before engaging the feedback loop, and one must account for nonlinear series compliances in the bead-actin attachments. Techniques to speed up the feedback loops have been implemented where the bead-actin-bead dumbbell is oscillated, increasing the ability to distinguish binding interactions and activate the feedback loop (37, 42).
The isometric optical clamp is an active feedback loop developed by the Goldman and Shuman Laboratories (23, 43). This technique uses an active feedback loop in which one of the optically trapped beads (motor bead) is actively moved to maintain the other optically trapped bead (transducer bead) at a constant position. This is achieved using an AOD to steer the motor bead. This technique has the advantage that the feedback is always engaged and thus there is not a delay time beyond the time-constant of the feedback loop itself. Also, one need not correct for system compliances since the position of the transducer bead is held constant. The procedure for collecting data using the isometric optical clamp is similar to the procedure used to collect data in the absence of feedback. Before an experiment, the time constant of the feedback loop is adjusted to the desired value by forming a bead-actin-bead dumbbell, applying a square wave to the transducer bead, and then watching the time response of the motor bead. After the feedback loop time constant is set and a single active myosin on the surface is identified, the feedback loop is engaged and data are collected. Actin filaments have polarity and thus the feedback loop direction might need to be reversed to ensure that the applied forces oppose the myosin’s working stroke. Binding interactions are identified post acquisition using the covariance thresholding described earlier, and the attachment durations and the force on the myosin (exerted by the motor bead) can be measured.
The Spudich Laboratory implemented a novel method for measuring the force dependence of myosin interactions in which the stage is oscillated during an actomyosin attachment, resulting in the force of the stage oscillations being transferred to the myosin and the optically-trapped beads (44). This technique, dubbed harmonic force spectroscopy, has the advantage that the force is applied to the myosin rapidly, no feedback loops are required, and forces are not applied by expensive and difficult-to-align optical components. This method is well-suited for single force-dependent transitions that limit detachment over the range of all probed forces. However, this technique has the limitation that analysis of complex force-dependent processes will not be straightforward. For example this technique would not have allowed for the determination of the force-dependent mechanism of Myo1c or Myo6 (22, 45).
An ultra-fast feedback system was developed by the Capitanio Laboratory to enable the detection of binding events with sub-millisecond resolution (28). In this setup, force is applied to one of the optically-trapped beads, causing it to move at a constant velocity when no myosin is bound. When myosin binds, the force that was applied to the first bead is rapidly transferred to the myosin. By observing changes in the velocity of the beads, one can determine, with sub-millisecond resolution, when binding occurs. This technique gives excellent temporal resolution (28), but it is technically challenging to implement.
To analyze the force-dependence of actomyosin detachment and attachment durations are measured over a range of forces. According to Arrhenius transition theory, force affects the rate of a transition by (46):
where k0 is the rate in the absence of force, F is the force, kB is Boltzmann’s constant, T is the temperature, and d is the distance to the force-dependent transition state, also known as the distance parameter. Note that k(F) changes exponentially with the vector quantity d (i.e., it depends on the direction of the applied force). A larger d is indicative of a more force-sensitive transition. The probability density function is given by:
As a consequence, if a single transition limits actomyosin dissociation at a given force, the distribution of attachment durations will be exponentially distributed at each force.
For data best fit by a simple exponential function, the reciprocal value of the mean attachment duration will equal the characteristic rate. Therefore, one method of analyzing the data is to plot the mean detachment rate at each force as a function of force and then fit Eq. 1 to the data using least-squares fitting to obtain the force dependence of the detachment rate. If the data are not exponentially distributed, this methodology will not work since the reciprocal value of the mean attachment duration will not equal the characteristic rate. There are two important situations where the data will not be exponentially distributed.
As described earlier (Subheading 3.11), these caveats mean that simple least-squares fitting of the mean values will not give the correct answer and MLE must be used (34, 47). To determine the errors in the MLE fitting and the sensitivity of the data to outliers, bootstrapping simulations can be used. In this method, a data set with N points is randomly resampled to generate a new data set with N points and then MLE is used to determine the values of the fitting parameters. By conducting a large number of simulations, it is possible to determine the uncertainty in each of the fit parameters.
The abilities of myosin to generate and sense forces depend on the stiffness of the myosin. Several methodologies have been developed to measure myosin’s stiffness using the three-bead geometry. Here, we discuss selected methods. In one technique, a sinusoidal oscillation is applied to one bead and the passive response of the second optically-trapped bead is recorded (31). In the absence of myosin binding, the passive bead will follow the actively driven bead. When myosin binds to actin, the myosin acts as an additional elastic element in the system, damping the response of the passive bead to the active oscillations. By measuring the force on the actively driven bead and the position response of the passive bead, it is possible to measure the stiffness of the myosin. A method developed by the Sleep Laboratory uses a slow triangular wave applied to both optically-trapped beads (48). When the myosin binds to the actin, the myosin is stretched and a force-extension curve can be generated. A similar technique was applied to study muscle myosin-II filaments and the actin extension was corrected by measuring the position of a quantum dot covalently attached to the actin (49). In another method, passive response of the beads to Brownian motion in the presence and absence of myosin is measured (27, 48). As described earlier, when myosin binds to actin, the covariance between the two optically-trapped beads is reduced in proportion to the stiffness of the myosin. The correlation coefficient or the cross power spectral densities can be calculated to give the stiffness of the myosin.
The authors wish to acknowledge grants from the National Institutes of Health (R01GM057247 and P01GM087253 to E.M.O. and R00HL123623 to M.J.G.).
1Tissue can be obtained from fresh rabbit skeletal muscle or from commercially available cryoground tissue (Pel-Freez Biologicals) (50).
2Buffer A can be prepared in a 100x stock and stored at −20°C. If preparing a 100x stock, omit the calcium chloride from the stock and add the calcium chloride when preparing the 1x solution.
3We find the glass-ball-type Dounce homogenizers to be preferable to Teflon-coated homogenizers.
4This buffer can be prepared as a 5x stock and frozen at −20°C.
5This solution can be aliquoted and frozen at −20°C.
6NEM is highly reactive, so it should be stored dessicated, and aqueous solutions should be made immediately before use.
7This myosin can be purified from rabbit back muscle using established protocols (51).
8Biotinylated actin can be purchased from commercial sources (Cytoskeleton AB07) or prepared from purified actin (52).
9This should be stored at −20°C in an amber microcentrifuge tube.
10PMSF should be prepared fresh in ethanol.
11This reagent can be stored as 100 mM in DMSO at −80°C.
12This is only necessary if using streptavidin to attach biotinylated myosin to the coverslip surface.
13As in any kinetic experiment, the concentration of ATP should be checked spectrophotometrically by measuring the absorbance at 259 nm. The extinction coefficient for ATP is equal to 15,400 M−1cm−1. This solution can be frozen at −20°C. ATP should not be stored with magnesium since magnesium accelerates its hydrolysis.
14This is a 100x stock that can be frozen at −20°C in 100 μL aliquots.
15This should be stored at −20°C in an amber microcentrifuge tube.
16For some myosins, weak-binding light chains (e.g., calmdodulin) will need to be included at an appropriate concentration (53).
17Prepare this solution immediately before loading into the flow cell, since the myosin will stick to the tube and the effective concentration will change with longer incubations.
18This buffer should be prepared right before loading the flow cell. The concentration of actin should be checked before loading the flow cell by examining the fluorescence of individual filaments. There should be approximately one filament per 50 x 50 μm field of view.
19All steps of this protocol should be conducted at 4°C and in a cold room if possible.
20Filter paper or cheesecloth can also be placed on top of the powder to prevent it from blowing away or becoming contaminated.
210.5 g of acetone powder will produce more than enough actin for 1 month of experiments.
22When placed under tension in the optical trapping assay, actin will sometimes break. The frequency of breakage increases with the age of the actin. If breaking is problematic, prepare fresh actin.
23The 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.
24BSA-coating minimizes adsorption of beads to the tubes.
25The percentage of biotinylated actin can be optimized by the experimenter, as 25% is generally the upper limit.
26It is difficult to get a homogenous suspension, and vigorous mixing is required. Over time, the amyl acetate from the stock is lost due to its low vapor pressure and additional amyl acetate can be added.
27Always check to see whether the coating looks uniform. If there are bare patches on the glass or if the liquid is not evenly spread, the cover glass should be discarded.
28We tape plastic pipet tips to the bottom of a petri dish and then let the bead-coated cover glass dry while resting at an angle on the tip.
29It is best to transfer a small volume beads to a fresh tube before sonicating to avoid sonicating the stock suspension.
30Higher pretensions increase the temporal resolution but increase the probability of actin breakage.
31In our experiments with myosin-I isoforms, this is usually set to 10 milliseconds.