Skeletal myosins II are non-processive molecular motors that work in ensembles to produce muscle contraction while binding to the actin filament. Although the molecular properties of myosin II are well known, there is still debate about the collective work of the motors: is there cooperativity between myosin motors while binding to the actin filaments? In this study, we use high-speed AFM to evaluate this issue. We observed that the initial binding of small arrays of myosin heads to the non-regulated actin filaments did not affect the cooperative probability of subsequent bindings and did not lead to an increase in the fractional occupancy of the actin binding sites. These results suggest that myosin motors are independent force generators when connected in small arrays, and that the binding of one myosin does not alter the kinetics of other myosins. In contrast, the probability of binding of myosin heads to regulated thin filaments under activating conditions (at high Ca2+ concentration in the presence of 2 μM ATP) was increased with the initial binding of one myosin, leading to a larger occupancy of available binding sites at the next half-helical pitch of the filament. The result suggests that myosin cooperativity is observed over five pseudo-repeats and defined by the activation status of the thin filaments.

Myosin II is a non-processive molecular motor that binds to actin filaments to produce mechanical work, using the chemical free energy of adenosine triphosphate (ATP). After an initial attachment to actin, the myosin motor domain undergoes conformational changes associated with release of the ATP hydrolysis products inorganic phosphate (Pi) and ADP from the active site of myosin. In this process, a force-generating power stroke, with swing of the myosin lever arm, is generated, and there is a transition of myosin from the weak to the strong actin-binding states (Rayment et al., 1993; Fisher et al., 1995; Månsson et al., 2018; Robert-Paganin et al., 2020).

Myosin II molecules form bipolar filaments in skeletal, cardiac, and smooth muscles, and this filamentous form of myosin II allows the motors to collectively produce high forces during muscle contraction despite a low duty ratio (Finer et al., 1994; Ishijima et al., 1994; Yanagida and Ishijima, 1995; Kaya and Higuchi, 2010; Kaya et al., 2017; Pertici et al., 2018; Cheng et al., 2019; Cheng et al., 2020). The actin-attached fraction of the ATP turnover time, the duty ratio, is ∼5% (Howard, 1997), which enables high speeds of shortening (Pertici et al., 2018; Cheng et al., 2020). Although most studies looking to the mechanics of isolated myosin II have been performed with single molecules, assemblies of myosin II have been investigated in arrays developed with a small number of motors adsorbed to silica beads (Debold et al., 2005), optical fiber surfaces (Pertici et al., 2018), or with the native thick filaments (Cheng et al., 2020). These small ensemble studies show a load dependence and force–velocity relation that is similar to that observed in myofibrillar (Lowey et al., 2018) and cellular preparations (Edman and Hwang, 1977). Furthermore, these force–velocity relationships can be modeled using single molecule properties (Månsson et al., 2018; Månsson, 2019), and experimental data from single molecules (Kaya and Higuchi, 2010; Capitanio et al., 2012; Sung et al., 2015) suggesting that myosin II motors are independent force generators, as postulated decades ago (Huxley, 1957), even when they are attached to a common thick filament.

However, there are also suggestions that myosin molecules work cooperatively, and the work produced by motor assemblies is different from individual motors (Kaya et al., 2017). Accordingly, the attachment of one motor would interfere with the kinetics and attachment mechanics of other motors when working in arrays. The result casts doubt on the concept of independent force generators in motor assemblies. Cooperativity could also arise in double-headed molecules (Huxley and Tideswell, 1997; Brunello et al., 2007) or myosin motors that bind to adjacent actin sites (Caremani et al., 2013; Rahman et al., 2018). X-ray diffraction studies using muscle fiber preparations provide evidence that the coordinated movements of myosin heads may indeed regulate force generation (Irving et al., 1992; Linari et al., 2015). Finally, this form of cooperativity may arise from allosteric changes of the actin filament itself so that binding of one myosin molecule modifies the kinetics of myosin binding to nearby sites (Orlova and Egelman, 1993; Tokuraku et al., 2009; Prochniewicz et al., 2010).

Other forms of cooperativity between myosin motors involve activation of the thin filament where several cooperative phenomena have been described (Gordon et al., 2000). In skeletal muscle sarcomeres, actin–myosin interactions are regulated by Ca2+ through the regulatory proteins troponin (Tn) and tropomyosin (Tm), that form the thin filament complex with actin. Each of the Tm molecules contact seven actin monomers and is associated with the three Tn subunits: Tn-T, Tn-I, and Tn-C. Upon Ca2+ binding to Tn-C, conformational changes are triggered in the Tn–Tm complex resulting in a displacement of Tm that allows for myosin binding to actin (Galińska-Rakoczy et al., 2008; Lehman et al., 2009). We previously have shown that under relaxing conditions, thin filaments presented a combination of activated and non-activated segments along their lengths, and were not blocked from myosin; the equilibrium between blocked and closed states was defined by Ca2+-induced Tn–Tm conformational changes (Matusovsky et al., 2019). In addition, myosin binding to actin is also required for full activation, or to induce the open state of activation of the thin filament (McKillop and Geeves, 1993; Smith and Geeves, 2003; Desai et al., 2015). When myosin binds to actin, it may directly affect the regulatory system by changing the conformation of Tm, such that other myosin heads can attach to thin filaments (Geeves and Holmes, 1999; Gordon et al, 2000). Furthermore, the question remains if one or two myosin heads in a molecule are required for the full activation of the thin filament.

Therefore, cooperativity during myosin II-actin interactions can conceptually arise from two sources: cooperativity among myosin molecules within the thick filaments due to structural changes in the actin filament, or cooperativity through activation of the regulated, thin filaments. Each cooperativity source may present different mechanisms. In this study, we used high-speed atomic force microscopy (HS-AFM) to evaluate the potential cooperativity of double-headed heavy meromyosin fragments (HMM) of myosin II that were spontaneously connected to each other through the subfragment 2 (S2) tail regions, while attaching between non-regulated actin filaments, or regulated thin filaments. Because HS-AFM allows the investigation of protein dynamics with nanometer spatial and millisecond temporal resolutions (Kodera et al., 2021; Heath and Scheuring, 2018; Matusovsky et al., 2021) our experimental approach allows us to investigate important aspects of myosin cooperativity, with a better resolution than previous fluorescence microscopy studies (spatial resolution limitation of >100 nm; Desai et al., 2015). Specifically for this study, we developed a method in which independent HMM motors were spontaneously attached through their S2 regions to form a structure with up to 8–10 individual myosin heads (4–5 HMM molecules) bound to nearby sites along 2 actin filaments or 2 thin filaments (Fig. 1 and Fig. S1). The benefit of this approach is the ability to monitor the behavior of each of the HMM heads over the time of an experiment to evaluate the potential cooperative binding of HMM heads with either actin or thin filaments during the ATPase cycle. This approach also allows investigation of aspects of inter-head cooperativity as well as the potential to investigate cooperative changes along actin or thin filaments at spatial resolution similar to the inter-monomer distance along the filaments.

Proteins

Native thin filaments were purified from rabbit right and left ventricular cardiac muscle that had been glycerinated and actin was purified from acetone powder of rabbit skeletal muscle (Sigma-Aldrich), following a protocol previously used in our laboratory (Matusovsky et al., 2019). The reason of using cardiac thin filaments (cTFs) is because cTFs can be purified as a complex without disturbing the native Tm–Tn complex, while the skeletal thin filaments are usually obtained by reconstruction of purified actin, Tm and Tn, or using enzyme treatment that might affect the activity of the thin filaments. Another reason is that skeletal thin filaments are only partly activated by Ca2+ (∼20%) and rigor-bound myosins are required to complete activation (Heeley et al., 2006), while cTFs is ∼70% activated by Ca2+ alone (Houmeida et al., 2010). The double-headed skeletal myosin II was purified from rabbit psoas muscle and HMM fragments were prepared by proteolysis of the myosin with α-chymotrypsin as previously described (Cheng et al., 2019). Prior to the HS-AFM experiments, HMM, actin filaments (F-actin), and cTFs were tested for their functionality using in vitro motility and Mg2+-ATPase activity assays, as previously described (Matusovsky et al., 2019). The ethical protocol for use of animal material for the protein preparations and in HS-AFM experiments was approved by McGill University (reference number MCGL-5227).

The lipid bilayer template surface and experimental design

The lipid composition for HS-AFM imaging contained 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC), 1,2-dipalmitoyl-3-trimethylammonium-propane (DPTAP) and 1,2-dipalmitoyl-sn-glycero-3-phosphoethanolamine-N-(cap biotinyl; biotin-cap-DPPE). The lipids were purchased from Avanti Polar Lipids. DPPC:DPTAP:biotin-cap-DPPE were mixed in a weight ratio of 89:10:1. The preparation of lipid vesicles and deposition on mica substrate to form a mica-supported lipid bilayer surface (mica-SLB) has been previously described (Matusovsky et al., 2021). These lipids contain negatively and positively charged elements that allow attachment of a wide range of proteins, including actin and thin filaments, through the electrostatic interaction. Unlike mica surface, which is flat but just negatively charged, the lipid surface can be controlled by mixing charged and neutral lipids in different ratios to meet the best attachment of proteins. The attachment of filaments to the mica-SLB surface in our study was strong enough, so we could perform continuous scanning without detachment of the filaments by the HS-AFM tip.

The mica-SLB surface was rinsed with the buffer A, containing 25 mM KCl, 2 mM MgCl2, 0.25 mM EGTA, 12.5 mM imidazole-HCl, and 0.5 mM DTT, pH 7.0. Subsequently, 2.8 µl of either 7 µM non-regulated actin filaments or 1.0 µM regulated cTFs diluted in the buffer A were deposited on the mica-SLB surface. After 10 min of incubation under a wet chamber, the unbound filaments were rinsed by the assay solution. At these conditions, many filaments were attached to the surface in close proximity to each other. The optimal concentration of the filaments attached to the surface created enough space between filaments for the binding of HMM molecules, and to stabilize the distance between filaments without large variability in the spacing between them. The distance distributions between two parallel non-regulated actin filaments and regulated cTFs are shown in Fig. S2. The observed distances were enough for binding the HMM heads between two parallel filaments, allowing counting of the exact number of HMM molecules at the given time of the experiment.

The HMM heads are attached to the filaments and not stuck to the underlying surface, i.e., potentially they can be replaced by new HMM heads, in case both heads of the HMM molecule will detach from the parallel filaments. More specifically, the S2 domains of HMM are weakly connected but not firmly immobilized to the underlying lipid bilayer since we were able to analyze the myosin head displacement and visualize the lever arm motion. The displacement of the myosin heads in the presence of ATP suggests that the power stroke is occurring, and the lever arm is rotating. The cooperativity of binding of the myosin heads in F-actin–HMM or cTF–HMM complexes was studied using the following experimental conditions: (1) nucleotide-free (NF) state; (2) presence of ATP analogs (ATP-γ-S); (3) presence of ATP and Ca2+.

HS-AFM imaging of F-actin–HMM complex

After rinsing unbound actin filaments with buffer A, 3.0 µl of 8 nM HMM diluted in buffer A was placed on top of non-regulated actin filaments on the mica-SLB surface, and incubated for an additional 3 min. The F-actin–HMM complex in NF conditions was rinsed by 10 μl of buffer A, containing either NPE-caged ATP, non-caged ATP (0.5, 2, or 10 µM) or 0.5 µM non-hydrolyzable ATP-γ-S. NPE-caged ATP (adenosine 5′-triphosphate, P3-(1-(2-nitrophenyl ethyl) ester; Invitrogen) dissolved in attachment buffer was photolyzed in the AFM chamber using an UV light source at 340 nm. When at least one HMM molecule was found to be bound between two filaments, UV LED light was irradiated at the 340 nm, and the shutter remained opened for ∼5 s, which should be enough to generate 2 μM ATP from 10 μM caged ATP (Yokokawa et al., 2006; Fuijta et al., 2019). We made three separate irradiations at the beginning of our experiments to make sure that we generated at least half of ATP photolyzed from the caged ATP. A delay of ∼5–10 s was found after activation of caged ATP, likely because caged ATP molecules were in solution and required this time to attach to and get hydrolyzed in the motor domain of HMM. To ensure NF conditions, 1 U/µl of apyrase was added to the solution. Further, 1 U/ml of hexokinase and 10 mM glucose were added to the ADP solutions to remove contaminating ATP. The F-actin–HMM complex was formed on the mica-SLB surface in the buffer A with low (pCa 9.0) or high (pCa 4.5) Ca2+ concentrations to ensure similar experimental conditions as for cTFs–HMM complex.

HS-AFM imaging of cTFs–HMM complex

The procedure for imaging the cTFs–HMM complex was similar to that explained above for non-regulated actin filaments. Imaging of the cTFs–HMM complex at low Ca2+ (pCa 9.0) or high Ca2+ (pCa 4.5) concentrations, using skeletal muscle HMM was performed in the following way: 2–20 μl of TFs (1 μM) in the buffer A (relaxing conditions, absence of Ca2+) were placed on a mica-SLB surface for 10 min in the wet chamber and unbound cTFs were removed by exchanging for the buffer B, containing low or high Ca2+ concentrations. Then, 3.0 μl of skeletal muscle HMM (8 nM) in buffer A was placed on top of the mica-SLB surface with bound cTFs for 10 min in the wet chamber. Unbound HMM was washed out by buffer A followed by washing several times with appropriate buffer B with low or high Ca2+ concentrations containing 0.5–2 μM of caged or non-caged ATP as desired.

Probability of binding, fractional occupancies, and cooperativity analysis

Probability of the HMM heads binding to the non-regulated or regulated actin filaments was calculated by binomial distribution evaluated in HS-AFM experiments. This assumes that the binding situation in each frame is treated as an independent event because each myosin head is assumed to undergo independent cycling (possibly several times per frame). The bound and unbound events (0—no binding, 1—binding) were visualized directly to compute probabilities for the binding–unbinding process as a ratio of the binding events to the total number of events in each independent frame. Our experimental design allows to visualize 4–6 HMM molecules (or 8–12 individual heads) bound between two filaments. Two typical scanning views and rates were used: 150 × 75 nm2 (80 × 40 pixels2) at the 6.7–10 frames per second (fps) and 200 × 200 nm2 (120 × 120 pixels2) at the 2 fps.

Fractional occupancy (θ) is the ratio of the actin-binding sites occupied by HMM heads to the total number of the actin-binding sites experimentally observed in the given time of the experiment and calculated from:
θ=occupiedsitesoccupiedsites+unoccupiedsites.
To quantify the observed probability binding pattern in the binary system, we applied the following binomial distribution equation described a cooperative probability which is related to the probability of binding as:
C=(nk)pk(1p)nk,
where C denotes cooperative probability of binding between neighboring myosin heads, n denotes the number of total events or subsequent frames of the experiment; k denotes the number of binding events in the subsequent frames, p denotes the probability of binding, i.e., the ratio between binding events and total events, and (nk) represents the combination of total events and binding events expressed as n!/k!(nk)! (see Table S1).

We evaluated the events only for the heads which were bound between two filaments and did not consider the heads bound to the sides or top of the filaments. The events for each myosin head calculated from the reference frame, i.e., a moment when the head was bound to the filament until the end of image acquisition. The total events included both binding events (head was bound to the filament) and unbinding events (head was unbind from the filament).

Analysis of the myosin displacements

To analyze the HMM displacement, each of the HMM heads bound between two parallel non-regulated or regulated actin filaments were tracked individually in successive HS-AFM frames. The tracked parameters included the height of the HMM head used for subsequent determination of the center of mass (COM) in each myosin head. The height of the HMM heads was determined in semi-automatic mode using the x, y, and z data of the HS-AFM frames in Kodec software (v. 4.4.7.39; Ngo et al., 2015). The x and y data correspond to the lateral coordinates, while the observed z values correspond to the highest point in the center of the HMM heads. To obtain the z values for the highest point in HMM head(s) the image was automatically searched within a 5 × 5 pixels area. Next, the obtained height values and xy positions within the 5 × 5 pixels area were used to automatically calculate the COM. To obtain the accurate COM values, the height of the surface outside of the actin–HMM position was subtracted from the average COM of the HMM heads. The displacement size was initially calculated as a difference in the COM position of HMM head in the reference frame and the next frame, in successive HS-AFM frames (see Data S1). The forward (positive) and backward (negative) displacements were calculated for each myosin head and include a diverse range of displacements; very short displacements (below 1 nm), moderate displacements (2–3 nm) and longer displacements (over 4 nm), that were best fitted by sum of two Gaussians. The most frequently observed events were short and moderate displacements, while longer displacements were observed less frequently. The distributions of the forward and backward displacements were combined in one graph, each fitted by the sum of two Gaussians using similar bin sizes to avoid any deviation and mismatches in the peaks. The mean values for each peak are shown in the corresponding figure legends and in the Results. The displacement size of the upper and lower HMM heads did not differ between each other, although the frequency and binding events were not correlated between two heads within one HMM molecule. The displacement size was also not affected by the range of the ATP concentrations used in our experiments (0.2, 0.5, 2, and 10 μM), thus we averaged the data with the sampling rate of 589 events for the non-regulated actin filaments and 911 events for the regulated cTFs.

Cross-sectional analysis

Cross-sectional analysis to calculate the distance between two filaments (Fig. S2) was performed in Kodec software (Ngo et al., 2015).

HS-AFM system and cantilevers

The experiments were performed on a tapping-mode HS-AFM system (RIBM; Ando et al., 2001), equipped with an additional UV laser. The scanning frame was settled at desired pixels resolution (shown in the video and figure legends), which provided a known size in nanometers by IgorPro software (Wave Metrics, v.6.3.7.2) used to capture HS-AFM frames. Olympus cantilevers BL-AC10DS-A2 with the following parameters were used: spring constant 0.08–0.15 N/m; quality factor in water ∼1.4–1.6; resonance frequency in water 0.6–1.2 MHz. The additional carbon probe tip was fabricated on the tip of a cantilever by electron-beam deposition and sharped by plasma etcher, giving a ∼4 nm tip apex that allowed to achieve high spatial resolution (typically 2–3 nm in lateral direction and ∼0.15 nm in the vertical direction; Ando, 2018). The tip–sample loading force can be modulated and decreased by the free oscillation peak-to-peak amplitude (A0) of the cantilever set to ∼2.0 nm and the amplitude set point adjusted to more than 0.9 A0.

Data analysis and processing of HS-AFM images

To remove spike noise and to make the xy plane flat, the HS-AFM images were processed with low-pass filtering using Kodec software (4.4.7.39). The COM and cross-correlation analyses were performed in Kodec software. Fittings of equations to the observed data were performed in GraphPad Prism software (v.9.3.0). Values are reported as mean ± SD or 95% confidential intervals throughout the paper as indicated. n equals the number of independent experiments. A level of significance of P < 0.05 was used for all analyses.

Online supplemental material

Fig. S1 provides successive HS-AFM images of F-actin–HMM complex in the presence of 0.2 μM ATP. Fig. S2 provides arrangement of myosin heads between two parallel filaments. Fig S3 provides kymograph images of the F-actin–HMM and cTFs–HMM complexes at the different ATP concentrations. Fig. S4 shows the probability of binding of myosin heads to the non-regulated or regulated filaments in rigor conditions or in the presence of ATP-γ-S. Fig. S5 shows cooperative probability of the myosin heads bound to the non-regulatory F-actin Fig. S6 shows cooperative probability of the myosin heads bound to the regulatory cardiac TFs. Table S1 provides an example of the calculation of the cooperativity of binding for four neighboring HMM molecules bound to actin filaments in the presence of 10 μM ATP. Video 1 shows representative HS-AFM movies of the transient binding of skeletal HMM molecules bound between two actin filaments in the presence of 0.2 μM MgATP. Video 2 shows representative HS-AFM movies of the transient binding of skeletal HMM molecules bound between two actin filaments in the presence of 2 μM MgATP. Video 3 shows representative HS-AFM movies of the transient binding of skeletal HMM molecules bound between two actin filaments in the presence of 10 μM MgATP. Video 4 shows representative HS-AFM movies of the transient binding of skeletal HMM molecules bound between two cTFs in the presence of 0.5 or 2 μM MgATP. Data S1 provides information about the displacement size, which was initially calculated as a difference in the COM position of HMM head in the reference frame and the next frame in successive HS-AFM frames.

Experimental design to study myosin cooperativity by HS-AFM

In order to track the cooperativity behavior of the myosin heads within a sequence of successive HS-AFM images, we used an experimental approach in which pairs of HMM heads are attached to two actin filaments (Fig. 1 and Fig. S1), as explained in details in a previous study from our laboratory (Matusovsky et al., 2021). Briefly, we aimed for an experimental situation in which two non-regulated F-actin or two regulated cTFs were bound to an underlying mica-SLB surface, in parallel to each other, and with enough space for binding of double-headed HMM molecules between them. A cross-section analysis showed that the distance between two actin filaments during the experiments was 40.56 ± 9.65 nm, and the distance between cTFs was 67.69 ± 15.92 nm (Fig. S2). The observed difference in distance (27.1 ± 6.1 nm) between non-regulated F-actin and regulated cTFs did not affect the HMM binding and displacement analysis (Fig. 1 f and Fig. 2 c).

Once the filaments were found in a parallel orientation, HMM fragments were added into the HS-AFM chamber filled with an experimental solution or placed on the top of the mica-SLB surface, in a solution containing 0.2–10 μM of NPE-caged or non-caged ATP. We then searched for events where each of the two HMM heads would interact with two parallel filaments. This approach allowed us to study the intra-head and inter-heads cooperativities through successive HS-AFM frames for a given HMM head/heads over time. The design is different from that of where HMM heads are bound to one actin/thin filament and goes through attachment-detachment cycles while possibly changing position on the filament. Therefore, during probe scanning, a given binding site could be occupied by other myosin molecules, especially under weak binding conditions (presence of ATP), which would introduce uncertainties in the analysis of the cooperativity. Immediately after both HMM heads were bound between parallel filaments, we activated the NPE-caged ATP in the solution by photolysis using a UV laser (340 nm) installed into the HS-AFM system (see Materials and methods).

The HS-AFM snapshots of two parallel non-regulated F-actins or regulated cTFs showed regularly bound HMM molecules between them in the absence or in the presence of ATP (Figs. S1 and S2). The globular upper and lower heads of each HMM molecule were bound in ∼30–37 nm proximity from each other, along the actin half-helical pitch structure (Fig. 1 and Fig. S2); all conclusions on myosin cooperativity are related to this distance between myosin-binding sites. HMM heads were not bound to all the available actin-binding sites along the filaments at various experimental conditions, including rigor or in the presence of ADP in similarity to electron microscopy studies (Orlova and Egelman, 1993). This observation may be related to the immobilization of S2 regions of each HMM molecule to the underlying lipid bilayer and to the size of each HMM head, which is ∼13 nm in diameter (Matusovsky et al., 2021), to reach a maximum of ∼2–3 binding spots between neighboring actin monomers, i.e., 11 or 2 × 5.5 nm (Fig. 1 b). The ∼37 nm arrangement of myosin heads in our HS-AFM experiments is similar to the preferable binding sites of myosin heads along actin filaments (Steffen et al., 2001) and relate to the ∼37 nm hotspots for myosin head bindings along the thin filaments in the A-band of the sarcomere (Wang et al., 2021). Thus, by evaluating the binding–unbinding events of HMM heads to the filaments, we can study the intra-head cooperativity (Fig. 1, d and e; Fig. 2, a and b; and Fig. 3) and inter-head cooperativity (Figs. 4 and 5).

Kinetics of actin–myosin interaction in the non-regulated and regulated systems

We characterized functional parameters of the myosin heads bound between two parallel non-regulated F-actins or regulated cTFs, including the average backward and forward displacements (d) of myosin heads in the presence of ATP (and high Ca2+ = pCa 4.5 in the case of cTFs). The HMM displacements calculated as a change in the COM of the myosin head at the given time during the experiment (Fig. 1 c, see also Materials and methods) were in the range of 6–8 nm. The backward (towards minus end of the filament) and forward (towards plus end of the filament) HMM displacements were calculated. The size distribution of HMM displacements revealed two distinct peaks in F-actin–HMM and cTFs–HMM complexes that most likely represent the events occurring through ADP (1–3 nm displacements) and Pi releases (over 3 nm displacements) as previously described (Matusovsky et al., 2021). The sum of two peaks for backwards and forward displacements of HMM molecules were −5.84 ± 0.44 and 5.7 ± 0.35 nm on the non-regulated actin filaments, and −5.9 ± 0.91 and 5.6 ± 0.53 nm on the regulated cTFs (Fig. 1 f and Fig. 2 c).

The evaluation of displacement of myosin heads in the HS-AFM was described in detail in the Materials and methods. Briefly, the working stroke is viewed as a transition from the weak to the strong-binding states evaluated by the changes in the lever arm movement. The change in the lever arm considers a defined polarity of the actin filament. In the presence of MgATP, myosin heads detach from the filament and re-attach to the same or a new binding site, allowing us to determine the displacement of the myosin head by the change in COM. The calculated displacement in our study is slightly larger than the working stroke size of 5 nm reported for S1 (Capitanio et al., 2006) and slightly smaller than the values obtained from structural studies with single-headed myosin (∼10–12 nm; Geeves et al., 2005). It is comparable with studies performed with myosin molecules evaluated with laser tweezers (Steffen et al., 2001; Finer et al., 1994; Tyska et al., 1999) and single fiber mechanics (Piazzesi et al., 2002).

The representative binomial binding traces of the individual upper and lower myosin heads in the F-actin–HMM (Fig. 1 d; and Videos 1, 2, and 3) and in the cTFs–HMM (Fig. 2 a and Video 4) revealed that binding of one HMM head is not necessarily accompanied by the binding of the second HMM head for the given HMM molecule (M1–M4; Fig. 1 d and Fig. 2 a). To specifically investigate the coordination between two heads in a molecule we analyzed the binding events at the different ATP concentrations. Tellingly, the binding events of two heads of given HMM molecule bound between two filaments was higher at lower ATP concentrations. At the higher ATP concentrations, the binding of either one head or two heads was approximately equally distributed (Fig. 3, a–c). The amount of two heads simultaneously bound to the regulated thin filaments was increased in the presence of high Ca2+ and 0.5 μM ATP, in comparison with low Ca2+ conditions and 0.5 μM ATP. With 2 μM ATP and high Ca2+, the binding of either one head or two heads was equally distributed (Fig. 3, d–f).

Probability of HMM binding to the non-regulated and regulated actin filaments

To monitor the probability of binding events between individual myosin heads we applied a probability analysis based on a binary combination: HMM bound to the filaments equals to 1 and HMM detached from the filaments equals to 0. To use this analysis, we need to evaluate if there is any directional bias in the myosin bindings along the F-actin and cTFs, either towards the barbed plus end or the pointed minus end of the filaments. Therefore, the polarity of F-actin and cTFs complexed with HMM was determined using the morphology of the myosin heads bound to the filaments (Ngo et al., 2015). The bound myosin heads observed in the presence of MgATP, MgADP, or in the rigor state allowed us to determine the polarity of the filaments (see Figs. S1, S2, S3, and S4). According to our observations the most frequent myosin head orientation in the weak binding state (presence of MgATP-γ-S) or strong binding state (rigor state) is the one where the heads of HMM molecules are positioned toward the minus end of the filament (Fig. 1 h; Fig. 4, a and b; Fig. 5, b–d; and Fig. S4). Therefore, binding events that occurred towards to the plus end of the filament (Mn → Mn+1) for individual upper and lower myosin heads at ATP concentrations ranging from 0.2 to 10 μM were used in the analysis.

Initially, we tested binding of HMM between two filaments in rigor conditions, i.e., in the absence of ATP and Ca2+, or in the presence of ATP-γ-S, a slowly hydrolyzed analog of ATP (Fig. S4). At these conditions the HMM heads were tightly bound between two filaments with high fractional occupancies: ∼95% for the non-regulated F-actin and ∼79% for the native cTFs. The latter observation is consistent with the idea that the binding sites on cTFs in the absence of Ca2+ and ATP are present in an equilibrium between the blocked, closed, and open states (Video 4; Matusovsky et al., 2019; Risi et al., 2017; Risi et al., 2021).

The probability analyses revealed that binding of Mn myosin head to the non-regulated actin filaments did not affect the subsequent bindings of the next Mn+1 molecule (towards the plus end of the filament) in the presence of different ATP concentrations (Fig. 4, Videos 1, 2, and 3). While we can observe some random increase in the binding probabilities with 0.2 μM ATP or 2 μM ATP concentrations (Fig. 4, c and d) towards the plus end of the filament, the average fractional occupancy indicates a constant decrease in the occupancy of the binding sites with time, in all ATP concentrations used in this study (Fig. 4, c–e, right panels). These data are consistent with the results pooled from eight different experiments, suggesting that in the F-actin–HMM complex the most frequently observed events represent occupation of one binding site or no binding with the average number of occupied sites calculated as 1.27 ± 0.07 (Fig. 4 f). These results suggest that HMM molecules are frequently detached from actin in the presence of ATP due to a lower affinity of myosin to actin in comparison with the affinity to the thin filaments (Fig. S3). This idea is consistent with the different time evolutions of the number of HMM molecules with actin and thin filaments (Fig. 4 f and Fig. 5 h) in the presence of ATP. It is also consistent with findings that the fractional occupancy of actin-binding sites in the absence of ATP (rigor) or presence of slowly hydrolyzed ATP-γ-S did not change with time (Fig. S4) when HMM is bound to both actin and the thin filaments all the time, suggesting that the myosin heads did not detach from the filaments over the time of the experiment due to interaction with the scanning cantilever tip.

At the non-activating conditions with thin filaments in the blocked state (0.5 µM ATP, pCa 9.0), myosin heads revealed a similar decrease in the binding probability and fractional occupancy (Fig. 4 e) compared to the bare F-actin–HMM complex. In contrast, the probability of myosin heads binding to cTFs in the closed state under activating conditions (0.5 µM ATP, pCa 4.5) was increased (Fig. 5, f and g; and Video 4) compared to myosin heads binding to actin filaments (Fig. 4, c and d). This feature is reflected in the increased average number of attached myosin heads in the cTFs–HMM complex under activating conditions, almost doubling the average number of bound heads (Fig. 5 h) compared to the situation with the F-actin–HMM complex (Fig. 4 f). The increase in probability of binding of the myosin heads to the cTFs is also matched in the kymograph images of cTFs–HMM complex at the high [Ca2+] and different ATP concentrations, when compared to the kymograph images obtained from F-actin–HMM complex at the various ATP concentrations (Fig. S3). The random presence of activated and non-activated sites across cTFs at the relaxing (pCa > 8) or activating (pCa 4.0–4.5) conditions (Risi et al., 2017; Matusovsky et al., 2019) complicated the analysis and can explain the pattern of varied mean probabilities between HMM molecules (Fig. 5, f and g).

Cooperativity in the non-regulated and regulated actin-myosin systems

To evaluate the binding pattern probability observed in the binary system, we applied the same equation described in Materials and methods. We found no change in the probability of cooperative binding of the HMM heads to the non-regulated actin filaments. It suggests that the interaction in the F-actin–HMM complex is largely random. The linear regression slope of the cooperative probability binding between myosin heads in the F-actin–HMM complex showed no significant deviation from 0 (P = 0.295) with the Pearson’s r = 0.766 and r2 = 0.59. In contrast, the linear regression slope of the cooperative probability binding between myosin heads in the cTFs–HMM complex showed significant deviation from 0 (P = 0.022) with the Pearson’s r = 0.953 and r2 = 0.91 (Fig. 5 i). In accordance with these results, the individual fitting for each experiment demonstrated an increase in the cooperative probability of binding of the HMM heads to the regulated cTFs in comparison with that of in F-actin–HMM complex (Figs. S5 and S6). This is broadly consistent with cooperativity, although the degree of cooperative binding in the cTFs–HMM was variable between experiments as can be noticed from confidence intervals (Fig. 5 i).

In this study, we used a binomial probability analysis to evaluate the potential cooperativity between myosin motors while attached to actin or regulated thin filaments. Our experimental approach—using myosin motors that can attach between two filaments positioned in parallel on the surface—is particularly well-suited for this analysis, and we could visualize several different motors at the same time. Despite this approach has geometrical features that are distinct from those of the actin-myosin arrays operating within a muscle sarcomere, it has been recently shown that each of the double myosin heads can acquire different lever arm conformations and bind to two different thin filaments in rigor. However, this observation needs further investigation in the presence of ATP (Wang et al., 2021). This is also true when myosin attaches to actin and thin filaments in the presence of ATP, when each head may be in a different state, at a given time of the ATPase cycle (Matusovsky et al., 2021). This feature may enable myosin double heads to interact with two different thin filaments within the sarcomere, potentially maximizing muscle power and efficiency. Of particular interest, is the fact that myosin motors can be assumed as the independent force generators even when connected in small assemblies.

The displacements produced by each individual myosin head within a given HMM molecule in our experimental conditions were in the range of ∼6 nm, slightly larger than the working stroke size of 5 nm reported for myosin S1 (Capitanio et al., 2006) and slightly smaller than the values obtained from structural studies with single-headed myosin (∼10–12 nm; Geeves et al., 2005). It is comparable with studies performed with myosin molecules evaluated with laser tweezers and single fiber mechanics (Finer et al., 1994; Tyska et al., 1999; Piazzesi et al., 2002). Therefore, our results are consistent with studies utilizing different techniques.

Intra-head cooperativity in myosin motors

There are several studies suggesting that myosin molecules work cooperatively (Vilfan and Duke, 2003; Hilbert et al., 2013; Kaya et al., 2017; Hwang et al., 2021), and that the work produced by assemblies of motors is different from individual motors. For instance, a study using synthetic myosin filaments measured 4 nm stepwise actin displacements at a high load (>30 pN). Due to the fact that the mechanical work of 4 × 30 pN nm = 120 pN nm ≈ 30 kBT (kB: Bolzmann constant; T: absolute temperature) is greater than the free energy of MgATP turnover (25 kBT), the authors concluded that the steps they observed could not be produced by single motors but potentially due to coordinated force generation by several myosin motors (Kaya et al., 2017; Hwang et al., 2021). Despite the fact that theoretical analysis (Duke, 1999; Månsson, 2020) suggests that this finding is consistent with previous models of independent force generators as proposed previously (Huxley, 1957; Huxley, 1988; Hill, 1974), it cast some doubt on this concept when motors work in arrays. In this regard, the present study is consistent with fully independent force-generators along the actin filaments. Importantly, the HS-AFM approach allows us to demonstrate that this applies for neighboring actin target zones separated by ∼37 nm, appreciably shorter than possible to resolve under dynamic conditions using fluorescence microscopy (e.g., Desai et al., 2015). This result does not seem to be consistent with previous findings suggesting that binding of a myosin head allosterically affects the properties of the entire actin filament with potential changes of myosin affinity at other sites (Tokuraku et al., 2009). However, because we have only performed our studies under a limited number of specific conditions, we cannot completely exclude that such allosteric effects occur under certain conditions, e.g., at submicromolar concentrations of MgATP as in some of the experiments of Tokuraku et al. (2009). In contrast to the results with pure F-actin, we found strong evidence for cooperativity of myosin heads bound to thin filament as further considered in detail below.

Another form of cooperativity has been suggested by x-ray diffraction studies using muscle fiber preparations, indicating that the two heads of a given myosin molecule may bind sequentially to resist stretch of the active muscle (Brunello et al., 2007). Such sequential actions of the two heads have also been suggested (Edman et al., 1997; Huxley and Tideswell, 1997; Conibear and Geeves, 1998) to occur during shortening to account for rapid repriming of the myosin power stroke after a quick release, high power output during shortening and other phenomena. To the best of our knowledge, inter-head cooperativity has, however, not previously been observed experimentally under dynamic conditions in the presence of ATP. Our demonstration that binding of one myosin head increases the probability for binding of the second head is thus unique by demonstrating the potential for inter-head cooperativity where binding of one head increases the probability of binding of the second head at lower ATP concentrations. At the higher ATP concentrations, the binding of either one head or two heads was approximately equally distributed (Fig. 3).

The distance between neighboring parallel actin filaments in our study is appreciably larger than that observed in the muscle sarcomere, i.e., the design of our experiments does not necessarily reflect the sarcomere environment. However, the inter-filament distance in our study is not very different from the distances between actin filaments in the hexagonal arrangement that surrounds each thick filament in the sarcomere. In contrast to the inter-head cooperativity involving binding each of the HMM heads between two filaments, we did not study cooperativity of the double-head HMM binding to a filament (similar to in vitro motility or laser trapping), due to the uncertainty to recognize the binding of specific HMM molecules in subsequent HS-AFM frames (Matusovsky et al., 2021).

Inter-head cooperativity between myosin motors that involves activation of the thin filament

Studies have shown that myosin binding to actin is required for full activation of the thin filament (McKillop and Geeves, 1993; Smith and Geeves, 2003; Desai et al, 2015). When myosin binds to actin, it may directly affect the regulatory system by changing the conformation of Tm, such that other myosin heads can attach to thin filaments (Geeves and Holmes, 1999; Gordon, 2000; Smith and Geeves., 2003). According to this model, the transition of myosin heads from the weak to the strong binding state move Tm to an open state, making neighboring binding sites on actin available for myosin binding. Our data are consistent with this model, as we observed that the binding of one motor to the activated thin filament (pCa 4.5; Fig. 5, f and h) has changed the attachment kinetics of neighboring motors compared to non-activated thin filaments (pCa 9.0) in the blocked state or the bare actin filaments (Fig. 5 e). Most specifically, when one motor is bound to the activated thin filament at the pCa 4.5, it moves the thin filament from the closed to the open state, which allows for further motor binding at nearby sites.

In a previous study, we showed that the interaction of HMM with cTFs caused a change in the thin filament conformation, both in the absence and presence of Ca2+, and in the absence and presence of different concentrations of ATP (Matusovsky et al., 2019). Our new data strengthen those findings and corroborate the idea that cooperativity of myosin heads in striated muscles is defined by thin filaments and their state of activation. Using our experimental design with each myosin head binding to two parallel filaments, we evaluated whether one myosin head could activate the thin filament in the presence of ATP at low or high Ca2+ concentrations. Under non-activating conditions (the presence of ATP, pCa 9.0) when cTFs were in the blocked state, myosin heads were able to bind to cTFs but not able to switch the filaments from the blocked to the closed state, showing a similar decrease in the binding probability and fractional occupancy (Fig. 5 e) when compared to the F-actin–HMM complex (Fig. 4). Thus, binding of the two myosin heads are required for the transition of a thin filament from the blocked to the close state (Fig. 5) as suggested before (Desai et al., 2015; Matusovsky et al., 2019). Based on these data, we suggest that activation of thin filaments from blocked to the closed state requires binding of both myosin heads at the low Ca2+. However, the situation is changed if myosin heads bind to cTFs under activation conditions (the presence of ATP and pCa 4.5), showing an increase in the probability of binding and the relative number of motors attached to thin filaments, as a result of a first myosin binding (Fig. 4, Fig. 5 g, and Videos 3 and 4). These results suggest that one head (upper or lower heads of a given HMM molecule bound between two filaments) is able to switch a thin filament from the closed to the open state.

In addition to the cooperative phenomena considered above, our results also demonstrate higher affinity of myosin heads to the thin filaments in comparison with the actin filaments. This follows from the higher average number of the HMM heads bound (2.32 ± 0.06) to cTFs (Fig. 5 h) than to the non-regulated actin filaments (1.27 ± 0.07; Fig. 4 f) and the slower decline in the total number of available heads in the former case. These findings are broadly consistent with previous observations that both tension and the average number of attached cross-bridges was increased in actin-reconstituted skinned muscle fibers after further reconstitution with thin filament regulatory proteins (Fujita et al., 2002).

To summarize, our data suggest that cooperativity between myosin molecule along a filament is observed over five pseudo-repeats (approximately half-helical pitch of the filament) and is primarily defined by the state of thin filament activation. In contrast, we find no evidence for cooperative effects attributed to allosteric changes along pure actin filaments.

All data required for evaluation of the conclusions in the paper are present in the main body of the paper and/or in the supplemental figures, videos, Table S1, and Data S1.

Henk L. Granzier served as editor.

We thank Dr. Y.-S. Cheng for the HMM preparation.

This work was supported by the Natural Science and Engineering Research Council of Canada (to D.E. Rassier) and partly supported by Extramural Collaborative Research Grant of Cancer Research Institute, Bio-SPM, Kanazawa University (Japan; to O.S. Matusovsky). A. Månsson was supported by the Swedish Research Council (grant number 2019-03456). D.E. Rassier is a Canada Research Chair in Muscle Biophysics.

The authors declare no competing financial interests.

Author contributions: O.S. Matusovsky and D.E. Rassier designed the research; O.S. Matusovsky performed HS-AFM experiments and all authors were involved in analysis and interpretation of the data. O.S. Matusovsky, A. Månsson, D.E. Rassier wrote the paper, and all authors approved the final version of the manuscript.

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