Actomyosin

The GNP images were quickly localized by radial symmetry based on the particle localization method^{51 (link)} (the software is available in the reference) and screened to exclude GNPs that showed unpredictable behaviour from the geometry of the complex (Supplementary Fig. 5). We considered the excluded GNP to bind non-specifically to the glass surface or not firmly tether to the DNA origami rod-myosin-actin complex. After screening, the GNPs were localized by Gaussian distribution fitting^{20 (link)}, and the trajectory in the direction of the major axis was analysed by an inference method using a hidden Markov model^{39 (link)} assuming two states (binding and detached states). We estimated the displacement caused by the actomyosin generation process from the inferred distance between the two states (Fig. 4d).
To evaluate hidden states in the detached state, we used nonparametric Bayesian inference based on a hidden Markov model^{41 (link)}, which is capable of detecting hidden molecular states without defining the number of states beforehand. We downloaded and used Matlab files, especially “iHmmNormalSampleBeam.m”, with the following assumptions. First, a trajectory in each state was normally distributed. Second, we assumed one detached state and infinite binding states, and that the binding states share the same emission distribution. The standard deviations of the two emission distributions of the detached state and binding states were fixed at 12.5 nm and 4.7 nm, respectively. The fixed values were obtained by calculating the standard deviations of all points and the points of the strong binding states in the analyzed trajectories. The data used for the inference included 10,000 points (400 ms). The probability of a transition from a binding state to another binding state was fixed to 0. The inferred states whose points were <1% of the analyzed trajectories or had dwell times <40 μs were excluded from the analysis. Finally, the positions of the inferred binding states were defined as the relative positions from the inferred detached position. We performed the inference 1000 times, in which the iteration of the Markov chain Monte Carlo algorithm was set to 1000 (Fig. 6a). Among the inferred states, states whose positions were within the peaks ± 1 SD were used to calculate the accessibility and the dwell time in Fig. 7a. To test the detection accuracy, we produced simulated data assuming 4 or 8 transient binding states and a detached state with the standard deviations (12.5 nm and 4.7 nm) obtained from the experimental data as described above.
The time course of the fluorescence intensity from Cy3-EDA-ATP was analyzed to calculate the ATP waiting time. Briefly, the time course was acquired by averaging the intensity of a 7 × 7 pixels region of interest (ROI) in each frame. The center of the ROI was defined by the scattering image of the GNP attached to a myosin. A correction of background noise was performed by calculating the average intensity of the perimeter around the ROI^{52 (link)}. We measured the on-time by fitting the data to a double exponential decay and defined the slower rate as the ATP binding rate, thus giving a complete ATPase cycle^{53 (link)}. The ATP binding rate of Cy3-EDA-ATP was corrected to the rate of normal ATP by a factor of 2.8^{54 (link)}.

Myosin II was purified from
rabbit skeletal muscle and fluorescently labeled with DyeLight 488
(Invitrogen, Carlsbad, CA, USA) according to Alvarado and Koenderink.^{66 (link)} Labeled
and unlabeled myosin II were stored separately in myosin storage buffer
(300 mM KCl, 25 mM KH₂PO₄, 0.5 mM DTT, 50% (v/v)
glycerol, pH 6.5), where the high ionic strength prevents myosin self-assembly
into bipolar filaments. For experiments, myosin II was dialyzed overnight
in glycerol-free myosin buffer (300 mM KCl, 20 mM imidazol, 4 mM MgCl₂, 1 mM DTT, pH 7.4) and controlled self-assembly into bipolar
filaments was induced by adjusting a KCl concentration of 50 mM via
mixing with myosin polymerization buffer (20 mM imidazol, 1.6 mM MgCl₂, 1 mM DTT, 1.2 mM Trolox, pH 7.4). After an incubation time
of 10 min at 20 °C, the bipolar myosin II filaments were immediately
used for contractile experiments. For the contraction experiments,
the F-actin networks were transferred into an actomyosin buffer by
a 10-fold buffer exchange (50 mM KCl, 20 mM imidazol, 2 mM MgCl₂, 1 mM DTT, 1 mM Trolox, pH 7.4). The reorganization of the
networks was performed at a final ATP concentration of 0.1 mM combined
with an ATP-regeneration system of creatine phosphate (10 mM)/creatine
kinase (0.1 mg/mL)^{66 (link)} and a myosin II concentration
of 0.4 μM.

To measure the apical and basal tissue recoil velocities after ablation, laser ablations were performed using an inverted laser scanning microscope (LSM880 NLO, Carl Zeiss) equipped with a multi-photon Ti::Sapphire laser (Mai Tai HP DeepSee, Spectra-Physics). Ablations were performed in 14–24 hAPF pupae expressing the utrABD::GFP actin or Ecad::3xGFP AJ markers mounted with medial coverslip flattening and imaged in single-photon bidirectional scan mode every 1 s for 30 s with a 40×/1.3 OIL DICII PL APO (UV) VIS-IR (420762-9800) objective. A region of interest (ROI) corresponding to a 34.5 × 17.25 µm rectangle along the AP axis and centered on the medial or lateral neck region was ablated as previously described^{69 (link),74 (link),75 (link)}. Apical and basal ablations were sequentially performed in the same pupa. The initial tissue recoil velocity, which is proportional to the stress^{33 (link)} was determined between t = 1 s and t = 7 s after ablation. No differences in the recoil velocities were found upon changing the order of sequential ablations of the apical and basal domains (Supplementary Fig. 6i, j). To measure AP and ML tension simultaneously, either basally or apically, a small 8.6 × 8.6 µm circular ROI was ablated in 22 hAPF-old pupae and imaged every 0.25 s. The initial recoil velocity was measured between 0.25 s and 1.25 s following ablation. Note that recoil velocities after ablation indicate tensions only up to a prefactor (which is typically a dissipation factor). They can be considered as reasonable proxies of tensions^{33 (link),42 (link)}, while absolute tension values are not measured.
The same microscope set-up was used to measure recoil velocity along the apical-basal axis after lateral ablation. Ablations were performed in 21–22 hAPF Ecad::3xGFP pupae. Before ablation, a 21 × 21 µm stack (50–60 z-planes, 0.5 µm apart) centered on the boundary between the thorax and neck was acquired to visualize the apical AJ Ecad::GFP signal and the weaker basal Ecad::GFP signal. Ablation was then performed in a 21 × 21 µm ROI located at a z-plan equidistant from apical and basal tissue surfaces. The 21 × 21 µm stack (50–60 z-planes, 0.5 µm apart) was subsequently acquired 30 s after ablation. The lateral membrane recoil velocity was determined by measuring the distance between apical and basal tissue domains before and 30 s after ablation. Since this laser power is sufficient to ablate the actomyosin network of the tissue at a deeper position to trigger tissue recoil, we can safely consider that this regime is sufficient to ablate the lateral cortex to estimate recoil velocity.