Processive Nanostepping of Formin mDia1 Loosely Coupled with

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Processive nano-stepping of formin mDia1 loosely coupled with actin polymerization Hiroaki Kubota, Makito Miyazaki, Taisaku Ogawa, Togo Shimozawa, Kazuhiko Kinosita, and Shin'ichi Ishiwata Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.8b03277 • Publication Date (Web): 25 Sep 2018 Downloaded from http://pubs.acs.org on September 26, 2018

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Processive nano-stepping of formin mDia1 loosely coupled with actin polymerization Hiroaki Kubota1, ¶, Makito Miyazaki1, §, *, Taisaku Ogawa1, #, Togo Shimozawa2, ‡,

Kazuhiko Kinosita, Jr.1, †, and Shin’ichi Ishiwata1, *

1

Department of Physics, Faculty of Science and Engineering, Waseda University, 3-4-1 Okubo,

Shinjuku-ku, Tokyo 169-8555, Japan

2

Department of Life Science and Medical Bioscience, Faculty of Science and Engineering,

Waseda University, 2-2 Wakamatsuchou, Shinjuku-ku, Tokyo 162-8480, Japan

¶

Present address: Department of Microbiology, Tokyo Metropolitan Institute of Public Health,

3-24-1 Hyakunincho, Shinjuku-ku, Tokyo 169-0073, Japan

§

Present address: The Hakubi Center for Advanced Research, Kyoto University, Sakyo-ku, Kyoto

606-8501, Japan, and Department of Physics, Graduate School of Science, Kyoto University, Sakyo-ku, Kyoto 606-8501, Japan

#

Present address: Laboratory for Integrative Omics, RIKEN Quantitative Biology Center (QBiC),

6-2-3 Furuedai, Suita, Osaka 565-0874, Japan

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ACS Paragon Plus Environment

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‡

Present address: Technical division, Graduate School of Science, The University of Tokyo, 7-3-1

Hongo, Bunkyo-ku, Tokyo 113-0033, Japan

†

Deceased

*

To whom the correspondence may be addressed: [email protected] (MM) or

[email protected] (SI)

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ABSTRACT Formins are actin-binding proteins that construct a nanoscale machinery with the growing barbed end of actin filaments and serve as key regulators of actin polymerization and depolymerization. To maintain the regulation of actin dynamics, formins have been proposed to processively move at every association or dissociation of a single actin molecule toward newly-formed barbed ends. However, the current models for the motile mechanisms were established without direct observation of the elementary processes of this movement. Here, using optical tweezers, we demonstrate that formin mDia1 moves stepwise, observed at nanometer spatial resolution. The movement comprised forward and backward steps with unitary step sizes of 2.8 and –2.4 nm, respectively, which nearly equaled actin subunit length (~2.7 nm), consistent with the generally accepted models. However, in addition to steps equivalent to the length of a single actin subunit, those equivalent to the length of two or three subunits were frequently observed. Our findings suggest that the coupling between mDia1 stepping and actin polymerization is not tight but loose, which may be achieved by the multiple binding states of mDia1, providing insights into the synergistic functions of biomolecules for efficient construction and regulation of nanofilaments.

Keywords: Formin, actin, single molecule, optical tweezers, individual steps, cytoskeleton.

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The actin cytoskeleton is a key regulator of diverse cellular functions, including morphological change, motility, and division. These processes are regulated by various actin-binding proteins. Formins are bound to the barbed ends of actin filaments and regulate actin polymerization dynamics. Formin-mediated actin polymerization is affected by various factors, including another actin-binding protein, profilin, and mechanical force. Profilin dramatically enhances the regulation of actin polymerization dynamics 1–3. An appropriate concentration ratio of profilin to G-actin accelerates actin filament elongation from the formin-bound barbed end by more than tenfold, while excess profilin (more than tenfold the concentration of ATP–G-actin, or equivalent to the concentration of ADP–G-actin) induces depolymerization 3–8. Mechanical force applied to formins strongly modulates actin polymerization dynamics 6, 8–11. While stretching force was revealed to affect the regulation by pioneering studies using microfluidics 6, 9, a recent study using magnetic tweezers showed that torque was also a key factor 10. In addition, our previous study demonstrated that mechanical force coordinates the effects of profilin on the regulation of formin-mediated actin polymerization dynamics 8. One of the most unique features of formins is “processive capping.” Formins processively move and track the growing barbed end during the elongation of actin filaments. The molecular structure of formins is related to this mechanism. Formins are generally composed of formin homology domains 1 and 2 (FH1 and FH2) and other domains, with FH2 as the actin-binding domain. Crystallography showed that the semicircular FH2 domain forms a ring-like structure via dimerization 12, 13, and this ring-like FH2 dimer holds an actin trimer, of which the conformation 4


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is considered the structure of the formin–actin complex at the barbed end 13, allowing the association and dissociation of actin monomer at the barbed end. The molecular mechanism of “processive capping” has been described based on the crystal structure of the formin–actin complex 13. Given the symmetric structure, two FH2 dimer halves are thought to alternately move with the addition of a new actin monomer to the barbed end. In more detail, the two stable positions (pre- and post-translocated positions) of the FH2 dimer halves are considered to be in rapid equilibrium. Immediately after the association of an actin monomer to the barbed end, one FH2 dimer half is fixed in the translocated position. Then, the other half is released to achieve rapid equilibrium. This molecular mechanism is known as the “stair-stepping” model 13. The “stepping-second” model, in which the detachment of formin from the barbed end is taken into account, was later proposed 14. Both models are based on the alternate movements of the FH2 dimer halves at every association or dissociation of one actin monomer. In other words, the two models assume that the movement of formins is “tightly” coupled with actin polymerization and depolymerization. However, the movement of formins has not been directly observed with such a high spatiotemporal resolution. For decades, optical tweezers have been extensively used for the observation of movement of molecular motors at nanometer and millisecond spatiotemporal resolution, especially for resolving linear movements into elementary steps 15–17. Here, we employed optical tweezers to investigate the movement of formin mDia1 in single actin monomer resolution. If mDia1 moves as expected, based on the present stair-stepping or stepping-second models 13, 14, the step sizes of mDia1 5


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should be correlated with the size of actin subunits in the structural model of actin filaments (~2.7 nm). This prediction was largely consistent with our results; however, step sizes corresponding to two or three actin subunits were also detected, suggesting that the coupling between mDia1 stepping and actin polymerization is not tight, but loose (mDia1 does not always translocate at every association or dissociation of a single actin monomer).

Detection of the unitary steps of mDia1. To detect the stepwise movement of mDia1, we utilized the actin dumbbell method used in our previous study 8 (Fig. 1). Two beads were linked by a single actin filament. The barbed end of the actin filament was associated with the FH2 dimer of mDia1, whose FH1 domain was immobilized on one of the beads via interaction between an N-terminal glutathione S-transferase (GST)-tag on mDia1 and glutathione on the bead surface. The other side of the actin filament (pointed-end) was attached to the neutravidin-conjugated surface of the second bead via biotinylated actin monomers assembled onto the pointed-end region. This geometry allowed the detection of mDia1 movement, through which it was possible to measure the length change of actin filament due to the polymerization– depolymerization dynamics at the barbed end.

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Fig. 1 Actin dumbbell method for the detection of processive stepping of mDia1. (a) Both ends of an elongating single actin filament from mDia1 were linked by an mDia1-immobilized bead and avidin bead. The two beads were trapped by optical tweezers. The trap center for the mDia1 bead was manipulated to apply stretching tension to the filament, while the trap center for the avidin bead was fixed and used for the measurement of applied tension. The pointed-end region of the filament (< 1 µm) was 10% biotinylated and allowed to attach to the avidin bead. (b) mDia1 (FH1FH2) was tethered to the glutathione–BSA-coated bead surface via N-terminal GST-tag. (c) Phase-contrast images of the two beads, to which a single actin filament was tethered, 7


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are shown. The actin filament was not visible. A stretching–relaxation cycle was repeated three times. Black open arrowheads and magenta arrows in c and d show the timing of stretching of the actin filament by manipulation of a lower trap center and the duration of relaxation due to actin polymerization, respectively. (d) The centroids of the two beads were measured, and the trajectory of actin filament elongation was calculated from the time courses of the distance between the centroids of the two beads.

To detect the elementary processes of mDia1 movement, we employed low concentrations of G-actin in solution to slow down the actin polymerization reaction (40 and 75 nM). Actin filaments were maintained for stretching through manipulation of the two beads by optical tweezers in order to decrease the noise due to thermal bending fluctuation of the filaments. Although mDia1-mediated actin polymerization is force-dependent 6, 8–11, the rate of elongation of the actin filament by mDia1 was almost constant in the stretching force range examined in this analysis (4–6 pN) as shown in our previous study 8. In contrast, Yu et al. 10 showed that the elongation rate was not saturated at 4–6 pN; however, they mentioned that the force-dependent acceleration of polymerization was strongly affected by the method of mDia1 immobilization. In the present study, we simply considered that the elongation rate was constant at 4–6 pN because the immobilization method used here was the same as that used in our previous study 8. In addition, the bead-to-bead distance underwent force-dependent but actin 8


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polymerization-independent changes, as mentioned in previous reports 8, 18. Thus, the actin polymerization-independent changes were subtracted from raw data to extract the trajectories of mDia1 movement originating from actin polymerization (Supplementary Figs. 1 and 2). The time courses of the elongation of bead-to-bead distance were resolved to stepwise increments at 40 and 75 nM of G-actin (Fig. 2). Steps determined by a step-finding algorithm 19 included several-nanometer forward and backward steps (Fig. 2, colored lines). Forward steps indicate movement toward the direction of filament elongation. The frequency of the forward steps was much higher than that of the backward steps, indicating that the actin filaments were elongated at 40 and 75 nM. Of note, the G-actin concentrations used in this study (40 and 75 nM) were slightly lower than or comparable to the critical concentration for polymerization of G-actin estimated based on single actin filaments without formin (64 nM) 20. However, this value was obtained as the sum of polymerization at the pointed and barbed ends, so the critical concentration for polymerization at the barbed end only should be lower than 64 nM.

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Fig. 2 Typical examples of the trajectories of actin filament elongation at 40 and 75 nM G-actin. Gray trajectories represent the elongation after subtracting the actin polymerization-independent length change and 0.1-s median filtering. Steps in these trajectories were detected using the step-finding algorithm (colored lines; for details, see Materials and Methods). Detected backward steps are specified by arrowheads.

Step size analysis. First, we compared the detected step sizes with the magnitude (SD) of fluctuation during the dwell time. More than 95% or 80% of steps were one or two times larger than the SD of fluctuation, respectively, indicating that the spatial resolution in our analysis was sufficient to detect steps from the trajectories (Fig. 3a). 10


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Histograms of the step sizes appeared to have several peaks in the range between ± 0 and ± 10 nm (Fig. 3b). If it is assumed that the unitary step size of mDia1 is equivalent to the size of a single actin subunit in actin filament (~2.7 nm), the range of 1–10 nm includes the sizes corresponding to one to three actin subunits (ideally, 2.7, 5.4, and 8.1 nm). Hence, we fitted the histograms using triple Gaussian functions. The conventional models for the processive movement of formins assume that the step size is equivalent to the size of an actin subunit (~2.7 nm) 13, 14. As expected, the histograms fitted with triple Gaussian functions indicated that the step sizes of mDia1 were correlated with actin filament subunits for both forward and backward steps. Namely, the peaks of Gaussian functions obtained by global fitting were 2.8, 4.9, and 8.7 nm for forward steps and –2.4, –5.2, and –8.7 nm for backward steps. Although the third peak (–8.7 nm) was unclear in the histograms of backward steps (especially for 40 nM G-actin), they were fitted with triple Gaussian functions for consistency with the forward steps.

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Fig. 3 Step sizes and dwell times of mDia1 stepping. (a) The ratios of the step size to the magnitude of fluctuation (SD) at plateau before steps are plotted against the step sizes. The proportions of steps with sizes larger than once or twice the SD are shown. (b) Average step sizes were determined using a triple Gaussian function: 2.8, 4.9, and 8.7 nm for forward steps, and –2.4, –5.2, and –8.7 nm for backward steps. Forward and backward steps were individually fitted, but steps at different actin concentrations (40 and 75 nM G-actin) were globally fitted. Single, double, and triple arrowheads indicate the steps that are suggested to be correlated with one, two, and three actin monomers, respectively. Computed curves for individual Gaussian functions are drawn in solid lines, while the original triple Gaussian function curves are indicated by dashed lines. Proportions of the area of each Gaussian curve are shown in parentheses. (c) Dwell times of

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forward and backward steps in one trajectory are defined as schematically shown. After separating the original trajectory (upper) into two trajectories for forward (middle) and backward (lower) steps, the dwell times were calculated from the separated trajectories. Open and closed arrowheads indicate forward and backward steps, respectively. (d) Histograms of dwell times are fitted with Eq. 1 (Materials and Methods). Time constants, k, obtained by the fitting are shown.

Dwell time analysis. Assuming that the forward and backward steps were coupled with association and dissociation of actin monomers on the barbed end, respectively, the forward and backward steps are expected to independently occur. Accordingly, we separated the forward and backward steps from the trajectories (Fig. 3c) and analyzed their dwell times. The histograms were monotonically decayed (Fig. 3d). Since the histograms of step size were fitted with triple Gaussian functions (Fig. 3b), the data of single reactions (association or dissociation of one actin monomer) and sequential reactions (subsequent association or dissociation of two or three actin monomers) could coexist in the dwell time histograms. Hence, the dwell time histograms were fitted with Eq. 1 (see Materials and Methods), which produced the sum of single and sequential reactions. The ratio of these three reactions was estimated from the area of three Gaussian functions of step size (Fig. 3b), and the values were used as the coefficients of three reactions in Eq. 1 (‫ܣ‬, ‫ܤ‬, and ‫) ܥ‬. As a result, the time constants for the forward steps depended on G-actin concentration (0.92 s-1 for 40 nM and 1.4 s-1 for 75 nM G-actin) (Fig. 3d), whereas the time 13


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constants for the backward steps were almost independent of G-actin concentration (0.56 s-1 for 40 nM and 0.62 s-1 for 75 nM G-actin) (Fig. 3d).

Here, we have detected the stepwise length change of actin filaments through tracking the stepwise movement of formin mDia1 along actin filaments at nanometer spatial resolution. The pointed-end region of actin filaments containing biotinylated actin subunits was fixed to an avidin bead through avidin–biotin interaction so that the polymerization and depolymerization at the pointed end did not contribute to the changes in bead-to-bead distance. On the other hand, the position of the mDia1 bead was designed to be equivalent to that of the barbed end of an actin filament. Of note, the trajectories indicated the centroid of two FH2 dimer halves because mDia1 was tethered to the surface of the bead via two FH1 domains. When one FH2 dimer half moves and the other is stationary, half of the length of translocation is detected as one step size. The unitary step sizes of forward and backward steps of mDia1 were determined to be 2.8 and – 2.4 nm, respectively. These results indicated that the step size of mDia1 is equivalent to the length of the actin subunit in actin filaments (~2.7 nm), as suggested by a structural model in which the half pitch of a double helical actin filament constructed by 13 actin subunits is 36 nm. A recent study by Young et al. 21 using interferometric scattering microscopy showed the actin filament dynamics at single-actin-monomer resolution and revealed that the length change of actin filaments caused by association or dissociation of one actin monomer was ~2.7 nm. Taken together, the stepping motion of mDia1 detected in this study directly indicated that the movement 14


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of mDia1 is correlated with the structure of actin filaments. On the other hand, the dwell time analysis also indicated that mDia1 stepping is coupled with actin polymerization dynamics. The actin polymerization rate is generally expressed using two reaction rate constants, namely, actin association and dissociation rates. The actin association rate depends on the actin concentration, while the dissociation rate is independent of actin concentration. Our experimental results, in which the dwell time of forward steps of mDia1 depended on actin concentration but that of backward steps was independent, strongly suggested that the movement of mDia1 directly correlates with the stepwise polymerization and depolymerization of actin. Double- and triple-sized steps (4.9 and 8.7 nm for forward steps, and –5.2 and –8.7 nm for backward steps) were detected. Although these steps could be due to the limitation of the spatiotemporal resolution, we confirmed that the spatial resolution was sufficient for the detection of single-sized steps as revealed by the comparison of step sizes with the noise level at the dwell time (Fig. 3a). The temporal resolution in our experiment was considered equal to the reciprocal of the recording rate (1/300 frames per second (fps) = 0.003 s) or the window size of the median filter (0.1 s). Compared with the experimental values of the rate constants of forward steps (0.92 and 1.4 s-1 at 40 and 75 nM G-actin, respectively), our temporal resolution was also sufficient to individually detect the single-sized steps. The relationships between the temporal resolution and the probabilities of the detection of single-, double-, and triple-sized steps according to Eqs. 3–5 (Materials and Methods) are summarized in Fig. 4. The probabilities of double- and triple-sized steps experimentally obtained were significantly larger than the computed values at the reciprocal 15


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of the recording rate (0.003 s) and the window size of the median filter (0.1 s), indicating that these steps are not artifacts but naturally occur irrespective of the temporal resolution. The same discussion was also applicable to the backward steps (Supplementary Fig. 3). The presence of these plural steps indicates that the stepping movement of mDia1 is not tightly, but loosely coupled with actin polymerization dynamics.

Fig. 4 Estimation of the probabilities of the detection of multiple-sized forward steps. (a) Apparent probabilities of single-, double-, and triple-sized forward steps against temporal resolution were computed using the rate constants obtained from the dwell time histograms (0.92 and 1.4 s-1 for 40 and 75 nM G-actin, respectively, as in Fig. 3d). (b) Computed probabilities of double- and triple-sized steps at 0.003 s (the reciprocal of the recording rate) and 0.1 s (the 16


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window size of the median filter) were compared with the experimentally obtained values, for which the proportions of the areas of Gaussian functions in the step size histograms (Fig. 3b) were used.

The fact that steps of mDia1 corresponding to multiple actin subunits were observed suggests the existence of novel pathways of mDia1 stepping (Fig. 5). The processive movement of formins has been generally considered to comprise one single-sized step per actin monomer association, in accordance with the symmetric structure of FH2 dimer and actin filaments 13, 14. However, we demonstrated that one double-sized step of mDia1 can occur after the association or dissociation of two actin monomers. This result contradicts the generally accepted models. Hence, we propose a new model in which mDia1 occasionally remains at the same position when one actin monomer associates or dissociates, and it moves only after the occurrence of the second association or dissociation of actin monomer, which results in the double-sized stepping movements of both FH2 dimer halves.

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Fig. 5 Proposed model of mDia1 stepping. A stepping model was proposed referring to the stair-stepping model 13. The standard structure of a double-helical actin filament is shown in dark gray, while the unstable structure held by the FH2 dimer observed by crystallography is shown in light gray. Post/lasso and Knob sites of FH2 dimer halves are represented by squares and triangles, respectively. Numbers of actin subunits are shown as , , and . In the generally accepted pathway of the open/closed transition theory, two FH2 dimer halves alternately move at every association or dissociation of actin monomer to the barbed end, with 2.7-nm step size as the moving distance of the centroid of the two FH2 dimer halves (shown by dashed blue lines). 18


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Single-sized forward and backward steps are shown as with dashed arrows. Here, we present another pathway (shown as ), in which FH2 dimer halves remain stationary even after the association or dissociation of the actin monomer, due to newly assumed configurations (represented by magenta and orange actin subunits in * and ** states, respectively). These states are achieved by newly proposed processes: association and dissociation of actin monomers at the blocked and accessible states, respectively. After the second association or dissociation of actin monomer, both FH2 dimer halves move to return to the generally accepted pathway (). The movement of two FH2 dimer halves in one step corresponds to the double-sized step (5.4 nm).

Although we do not have direct evidence, the double-sized step might be composed of two events of ultrafast successive stair-stepping. This is because the observed triple-sized steps require at least one event of switching of the FH2 dimer half in the preceding position (namely, stair-stepping), so that it would be natural to expect that the multiple-sized steps are achieved by the combination of ultrafast stair-stepping. These proposed pathways require intermediate states shown by * and ** in Fig. 5, which deviate from the structural basis observed by crystallography 13, and are assumed to exist as energetically unfavorable configurations. The effects of profilin on mDia1 stepping were not examined in this study. In typical conditions, profilin accelerates the formin-mediated actin polymerization by interacting with the FH1 domain

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to increase the local concentration of actin monomers near the FH2 dimer. Thus, we suggest that profilin does not directly affect mDia1 stepping but decreases the dwell time of individual steps. Shemesh et al. 22 proposed two modes for formin stepping to solve the “rotation paradox” 23. One is the normal stair-stepping and the other is the second screw mode; in the second mode, formin rotates in reverse to release torsional stress accumulated by the general stair-stepping mode due to actin polymerization. Thus, the torsional stress seemed to affect how mDia1 chooses single-sized or double-sized steps as the next step, as the double-sized steps are possibly involved in the second mode. However, we cannot accept this idea because optically trapped beads are generally considered to be free from rotational restriction, so that mDia1 can freely spin during actin polymerization and depolymerization without accumulating torsional stress. Therefore, the double-sized steps observed in this study would not correspond to the second screw mode proposed by Shemesh et al. 22. The mechanism for the selection of two step sizes should be elucidated in the future. In contrast to the single-sized steps explained by the previous model 13 (Fig. 5, upper), double-sized steps require additional pre-stepping intermediate states before the 5.4 nm-forward or backward steps (* and ** in Fig. 5). The intermediate states for the double-sized forward step are based on the conformation in which the forefront actin subunit at the barbed end does not completely interact with FH2 domains (* in Fig. 5). This conformation may allow the forefront subunit to interact with other barbed-end associated proteins, such as capping protein (CP). A previous study demonstrated a “decision complex” that comprised the simultaneous 20


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binding of CP and mDia1 to the barbed end 24. The authors supposed that the simultaneous binding was achieved by the accessible state in the stair-stepping model, because they speculated that this conformation blocks only one protofilament end and thus one of the two CP subunits can associate with the other protofilament end. Our model provides an alternative explanation that the forefront actin subunit at the barbed end is completely or partially free from being occupied by mDia1 at the intermediate states (* in Fig. 5), so that other barbed-end associated proteins can freely interact with the barbed end. In summary, the loose coupling between actin polymerization and the stepping motion of mDia1 makes it possible to realize a synergistic function of mDia1 and other barbed-end associated proteins in the regulation of actin polymerization.

Materials and Methods Protein preparation. Truncated mDia1 composed of FH1 and FH2 domains was expressed and purified as an N-terminal GST-tagged protein using a bacterial cell system 8. G-actin was purified from rabbit skeletal muscle 25. All procedures conformed to the Guidelines for Proper Conduct of Animal Experiments approved by the Science Council of Japan, and the experiments were performed according to the Regulations for Animal Experimentation of Waseda University.

Microscopy. The same microscope system was used as in our previous studies 8, 26, 27. Briefly, dual-trap optical tweezers and a high-speed digital camera (BOBCAT ICL-B0620M; Imperx, 21


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Boca Raton, FL, USA) were equipped on an inverted microscope (IX71, Olympus, Tokyo, Japan). Phase-contrast and fluorescence images were obtained simultaneously at 30 fps. For the high-resolution observation of optically trapped beads, phase-contrast images were recorded by the high-speed digital camera at 300 fps, where 1 pixel was equal to 37 nm. Green (532 nm) and red (633 nm) lasers were used for distinguishing the two types of beads to construct the actin dumbbell 8. The stiffness of the optical tweezers was determined by moving the microscope stage at a constant speed and measuring the displacement of beads from the trap center (F = 6πηrv, where η, r, and v represent the coefficient of viscosity, bead radius, and speed of stage movement, respectively) 8, 28.

Actin dumbbell method. The actin dumbbell was constructed according to our previous report 8. Two 1-µm polystyrene beads were linked by a single actin filament. The barbed end was attached to the mDia1-immobilized bead, while the pointed end was attached to the avidin bead through biotin–avidin interaction (the pointed-end region of the filament was biotinylated). Glutathione-conjugated BSA was adsorbed to the bead surface to form glutathione–GST interaction for immobilization of N-terminal GST-tagged mDia1 on the bead surface. Avidin beads were fluorescently labeled by IC5-conjugated BSA prepared with IC5–maleimide (Dojindo, Kumamoto, Japan) and excited by 633-nm laser light to distinguish them from mDia1 beads during construction of the actin dumbbell.

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Elongation of actin filaments was measured in basic buffer (10 mM imidazole–HCl pH 7.4, 50 mM KCl, 1 mM MgCl2, 1 mM EGTA, and 50 µM CaCl2) containing 10 mM DTT, 1 mM ATP, non-labeled ATP–G-actin (40 or 75 nM), and an oxygen-scavenging system (0.22 mg mL-1 glucose oxidase, 0.036 mg mL-1 catalase, and 4.5 mg mL-1 glucose). Two beads were individually trapped by two IR laser beams. To apply tensile force to an actin filament, the trap center of the mDia1 bead was shifted to extend the distance between the two trap centers. Transposition of the mDia1 bead was repeated to maintain the tension at 4 to 6 pN. Phase-contrast images of the two beads were recorded using the high-speed digital camera at 300 fps. Thirty-three and 55 actin dumbbells for the experiments involving 40 and 75 nM G-actin, respectively, were examined. All experiments were performed at 26 ± 1°C. The stiffness of the optical tweezers for measurements was 0.081 or 0.073 pN nm-1.

Data analysis. The recorded images were analyzed using the Particle Track and Analysis plug-in (developed by Yoshiyuki Arai, Osaka University) in ImageJ software (National Institutes of Health, Bethesda, MD, USA) to determine the positions of the two beads. As in our previous study 8, an increase in the bead-to-bead distance involved actin polymerization-independent but force-dependent change. This length change did not originate from the extension of the actin filament because the stiffness of actin filaments is high (300 pN nm-1 per micron actin filament length) 18, so the distance was corrected assuming the force-dependent bead rotation 18. Prior to the measurement of actin polymerization, force-dependent length changes were calibrated for 23


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each actin dumbbell (by stretching more than three times at >1 pN), and they were fitted by equations expressing the length change due to force-dependent bead rotation (Eqs. 5, 6, 19, and 20 indicated by Dupuis et al. 18), where the flexural rigidity ‫ ܫܧ‬of actin dumbbells was the fitting parameter. Using the fitting curve, force-dependent length change was subtracted from the observed bead-to-bead distance. After median filtering (0.1 s), time courses of the subtracted bead-to-bead distance were split into 10,000 plots (equal to ~30 sec) and applied to the step-finding algorithm 19

. Detected steps at a force range between 4 to 6 pN were collected for the step size and dwell

time analysis. Dwell times are defined as the periods of plateau before steps. Forward and backward steps were separately analyzed; in other words, one dwell time of the forward step was regarded as the period between two forward steps even if backward steps were included during this period (cf., Fig. 3c). To determine the step size of mDia1 movement, the step size histograms of 40 and 75 nM G-actin were globally fitted by a triple Gaussian function, assuming that the centers of three peaks were common fitting parameters between the two different actin concentrations. After calculation of the areas of the Gaussian functions for each peak, the dwell time histograms were fitted by one, two, and three sequential reactions as follows:

ܽ‫ି ݁ܣ‬௞௧ + ܽ‫ି ݁ݐ݇ܤ‬௞௧ + ܽ‫ ݇ܥ‬ଶ ‫ ݐ‬ଶ ݁ ି௞௧

(1),

where ‫ܣ‬, ‫ܤ‬, and ‫ ܥ‬are the areas of three Gaussian functions obtained from the step size analysis in the order of smallest to largest, and ܽ, ݇, and ‫ ݐ‬are the coefficient, time constant, and dwell time, respectively. 24


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Estimation of the probabilities of the detection of multiple-sized steps When the time required for one step was longer than the temporal resolution, a single-sized step was detected. If two or three steps occurred too quickly to be separately detected, double- or triple-sized steps were detected. Here, if it is assumed that the unitary steps of mDia1 occur according to a single reaction, the probability that mDia1 does not step until ‫ ݐ‬was expressed with the rate constant ݇ as

ܲሺ‫ݐ‬ሻ = ݁ ି௞௧

(2).

The probability of the detection of a single-sized step ‫݌‬ୱ୧୬୥୪ୣ at the temporal resolution ܶ was expressed as

‫݌‬ୱ୧୬୥୪ୣ = ݁ ି௞்

(3).

On the other hand, when the first stepping of mDia1 occurred before ܶ, the first step was not detected as an individual step. This first stepping must be merged into the following second or third steps to be detected as a double- or triple-sized step. A double-sized step was detected when the total time required for the first and second steps exceeded ܶ. Hence, the probability of detection of a double-sized step ‫݌‬ୢ୭୳ୠ୪ୣ was described as ௌୀ்

‫݌‬ୢ୭୳ୠ୪ୣ = ‫׬‬ௌୀ଴ −

ௗ௉ሺ௧ሻ ௗ௧

ቚ

௧ୀௌ

× ܲ ሺܶ − ܵሻ݀ܵ = ݇ܶ݁ ି௞்

(4).

A triple-sized step was detected when the total time required for the first and second steps was shorter than ܶ. The probability of detection of a triple-sized step ‫୲݌‬୰୧୮୪ୣ was described as ௌୀ்

‫୲݌‬୰୧୮୪ୣ = ‫׬‬ௌୀ଴ −

ௗ௉ሺ௧ሻ ௗ௧

ቚ

௧ୀௌ

× ሼ1 − ܲሺܶ − ܵሻሽ݀ܵ = 1 − ݁ ି௞் − ݇ܶ݁ ି௞் 25


(5),

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where steps larger than triple-sized steps were ignored because the experimental data indicated that they are rare events. The sum of the probabilities of single-, double-, and triple-sized steps was 1.

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SUPPORTING INFORMATION Supplementary Figs. 1 and 2 show the details of the actin dumbbell method for observation of the stepping motion of mDia1, estimated from the bead-to-bead distance. Supplementary Fig. 3 demonstrates the computed probabilities of the detection of multiple-sized backward steps.

AUTHOR CONTRIBUTIONS H.K., M.M., K.K., and S.I. designed and H.K. performed the experiments and data analysis. H.K., M.M., and S.I. wrote the manuscript. M.M. and T.S. set up the microscope. T.O. prepared glutathione-conjugated BSA. All authors discussed the results.

ACKNOWLEDGMENTS We thank Y. Arai for providing the Particle Track and Analysis plug-in. This work was supported by Grants-in-Aid for Specially Promoted Research (grant no. 21000011), Scientific Research (S) (grant nos. 22227005 and 26221102), Young Scientists (B) (grant nos. 24740294 and 15K21444), Scientific Research on Innovative Areas (grant no. 26115715), and Scientific Research (B) (Generative Research Fields) (grant no. 16KT0077) from the Ministry of Education, Culture, Sports, Science, and Technology, Japan; Waseda University Grants for Special Research Projects (grant nos. 2015B-295 and 2015K-214); Takeda Science Foundation; and The Hakubi project of Kyoto University. 27


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CONFLICT OF INTERESTS The authors declare no competing financial interest.

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Processive Nanostepping of Formin mDia1 Loosely Coupled with

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