Supplementary Information

Transcription

1 Supplementary Information Switching of myosin-v motion between the lever-arm swing and Brownian search-and-catch Keisuke Fujita 1*, Mitsuhiro Iwaki 2,3*, Atsuko H. Iwane 1, Lorenzo Marcucci 1 & Toshio Yanagida 1,3 1 Soft Biosystem Group, Laboratories for Nanobiology, Graduate School of Frontier Biosciences, Osaka University, 1-3 Yamadaoka, Suita, Osaka , Japan. 2 Graduate School of Medicine, Osaka University, 1-3 Yamadaoka, Suita, Osaka , Japan. 3 Laboratory for Cell Dynamics Observation, Quantitative Biology Center, RIKEN, OLABB, 6-2-3, Furuedai, Suita, Osaka , Japan. *These authors contributed equally to this work. Correspondence and requests for materials should be addressed to M.I. ( iwaki@fbs.osaka-u.ac.jp) or to T.Y. ( yanagida@fbs.osaka-u.ac.jp). Supplementary Figures S1-S5 Supplementary Tables S1 Supplementary Discussion

2 Supplementary Figure S1. Typical trace of an optically-trapped myosin-v molecule. (a) Processive steps at 3 μm ATP. Data were low-pass filtered at 5 Hz with 12.8 Hz of sampling rate. Because the time interval (78 ms) is comparable to the duration of state 3, the intermediate state was rarely detected. The trace was corrected by an attenuation factor (Methods). (b) Dwell time distribution. The histogram was fitted to an auto-convolution of tk 2 exp (-kt) excluding the data in the white bar because the dwell times < 150 ms could be missed. k=2.4 s -1, N=218. (c) Step size distribution. Mean step sizes were determined by the central position of a single Gaussian curve (77 ± 1.9 nm, mean ± s.e.m). N=195.

3 Supplementary Figure S2. Langevin simulation of the Brownian head tethered to an optically-trapped bead via a DNA handle. (a) Model for the simulation. The bead is treated as an over-damped particle with drag coefficient γ B =1800 pnns/nm (derived by Stokes law assuming the radius of the bead is 105 nm and the viscosity of water at 25 C is pnms/nm 2 ), trapped by a linear spring of stiffness K trap = pn/nm, and attached via a DNA handle to a detached myosin head. The force-extension

4 curve of the DNA handle is a modified version of a freely jointed chain model 44. The length of the DNA, x, is given by x = L 0 [coth( 2FL p k B T ) k T B ](1+ F ) 2FL p K 0 where F is force; k B T, thermal energy; L 0, contour length under zero tension; L p, persistence length; and K o, elastic modulus. The detached head is treated as an over-damped particle with drag coefficient γ h =72.4 pnns/nm 33 and linked to the firmly attached forward head. The protein structure is simplified as an elastic cord of stiffness K protein =0.01 pn/nm (one-head bound state), where the value was estimated from directly observing the Brownian search by using a gold nano-particle attached to the myosin-v head (ref 34, unpublished result). The position of the attached head is varied to simulate experimental force values ( pn). The system of Langevin equations is numerically simulated by an Euler- Maruyama method. (b) Example of the simulated head (red) and bead (black) motion. The position of the detached head is simulated until it reaches the target position 57 nm forward its equilibrium position where it stops. (c) Dwell times between 20 nm and 57 nm sub-steps. (left) Experimental data at 3 μm ATP. The histogram was fitted by a single exponential with a rate constant of 8.1 s -1 excluding the data in the white bar because the dwell times < 50 ms could be missed. N=52. (right) Simulated distribution of the first-passage time with a time constant of 50 ms, which is comparable with the experimental value (123 ms). The discrepancy between the two is due to simplifications in the simulation like the detached head always attaching during its first passage. This assumption is based on biochemical data 27,45 that indicate a weak to strong transition (32 s -1 ) occurs in 95 % of the heads, while the weak to detach transition (1.63 s -1 ) occurs in just 5%. Shown values refer to the entire range of simulated forces. (d) Load dependence of the bead variance when myosin-v is in the observed one-headed bound state (red circles), observed two-headed bound state (blue circles), and simulated oneheaded bound state (orange circles). (e) Load dependence of the first-passage time for

5 the Brownian head to reach a forward (57 nm) actin target. Red circles are observed dwell times between 20 nm and 57 nm; black circles are simulated dwell times.

6 a b Supplementary Figure S3. Geometry between myosin-v and the bead. Illustrations show the geometry between the rear head and the linked bead (a) before and (b) after detachment of the rear head. Electron micrograph images of myosin-v are from Oke et al 35. (a) The depression angle (θ) was calculated by using the radius of the bead (105 nm) and the length of the DNA (60 nm) including the length of the modification (10

7 nm) due to the antibody and neutravidin. (b) The depression angle (39 o ) and the length of the lever-arm were derived from the micrograph. These calculations indicate that displacement of the bead due to detachment is negligible (~3 nm).

8 Supplementary Figure S4. Schematic diagram for myosin-v motility in a handover-hand mechanism (a) and inchworm-like mechanism (b). (a) Initially, both heads are in the ADP bound state and span the actin half helical pitch 36 nm apart (state 1). The rear head detaches from actin upon ATP binding and binds to the forward actin target 72 nm ahead, resulting in a 36 nm displacement by the tail (state 1-2, 2-3). Thus, myosin-v requires one ATP for each 36 nm tail displacement. (b) Initially, the rear head is the nucleotide-free state and the lead head is the ADP state (state 1). In an inchworm-like mechanism, the rear head detaches from actin upon ATP binding and

9 binds to the forward actin target next to, but ahead of the lead head, while the position of the tail remains unchanged (state 1-2). A 36 nm displacement by the tail couples with the lever-arm swing upon ADP release by the original lead head while in the adjacent head binding state (state 2-3). The original lead head detaches from actin upon ATP binding again, binds to the forward actin target such that both heads span the 36 nm actin half helical pitch (state 3-4). A second identical cycle then emerges (state 4-7). Thus, myosin-v requires two ATP for each 36 nm tail displacement.

10 Supplementary Figure S5. Simulation of an optically-trapped bead tagged to myosin-v via the C-terminus. (a) The maximum stall force generated by the kinetic parameters reported in Table 1 was simulated assuming conventional myosin nanometry. A bead with drag coefficient γ B =1800 pnnm/ns (see Fig. S2a) is trapped in a system with stiffness K trap = pn/nm and rigidly attached to the myosin-v C- terminus. The lever-arm of Head 1 can swing between the pre- and post- powerstroke states with reaction rates k swing and k reversal and detach at rates k detach1 and k detach2. To simulate k catch, Head 2 is simulated as an over-damped particle (drag coefficient, γ B =72 pnnm/ns 33 ) by using a numerical approximation corresponding to the Langevin equations described in Supplementary Figure S2. Here, the Brownian search and catch mechanism neglects the probability of backward steps (attachment to rear position R). Attachment to the forward position F occurs as soon as Head 2 reaches it. This

11 assumption is based on biochemical data 27,45 (see Fig. S2c). Protein stiffness, K p =0.2 pn/nm 37, and k B T=4.12 pnnm. The simulation stops when detachment occurs. (b) Simulated traces of bead motion. All simulations begin at approximately 1 pn of external force and stop when detachment occurs (from time when lines show no variance). Backward steps of 20 nm corresponding to lever-arm reversal are also observed (arrows). (c) Distribution of the stall force. The distribution shows a peak around 2.7 pn, showing that the kinetic parameters described in Figure 4c are compatible with previously reported stall forces from conventional nanometry studies 4,8.

12 Supplementary Table S1. Kinetic parameters obtained from the model analysis ΔG [k B T] d [nm] -3.3 ± ± 1.0

13 Supplementary Discussion The 65 nm peak in Figure 2a. When the 20 nm swing cannot be resolved, the observed step component should measure 77 nm. When the 20 nm step can be resolved, the step component should be observed as two substeps, a 20 nm component and a 57 nm component. Therefore, that both 77 and 57 nm steps are detectable suggests the 65 nm peak in Figure 2a is a result of a convolution of the two. Discrepancy between our results and others 32. Sellers and Veigel obtained higher rates for the swing and reversal transition than we did. However, they likely overestimated the swing and reversal rates because they neglect the detachment pathway when calculating the swing and reversal rates. Whereas they defined the lever arm-swing and reversal rate as the reciprocal of the average dwell time in the pre- and post-state, respectively, we obtained the lever arm-swing and reversal rate by considering other rates such as the detachment and catch rate from the reciprocals of the average dwell times. When the reactant can pass through multiple pathways, the increasing rate of each product equals the sum of each rate. This is derived from the model shown below. We start from the hypothesis that the events follow a reaction of the type:

14 where no reverse reactions are considered. In this case the concentration of C follows the differential equation: dc(t) dt = k 1 C k 2 C = k ( 1 + k 2 )C which can be solved analytically to obtain: C(t) = C 0 exp[ ( k 1 + k 2 )t] where C 0 is the initial concentration. Here, the cumulative frequencies of events is described by ( ) C(t 1 + dt) C(t 1 ) = C(t 1 )exp [ ( k 1 + k 2 )dt] 1 where t 1 is the dwell time. C also has the property: dc i (t) dt = k i Ct () where i=1, 2. Integrating gives, ( [ ]) C i (t) = C 0k i 1 exp ( k k 1 + k 1 + k 2 )t 2 Therefore, the product concentration increases exponentially with the sum of k 1 +k 2. Similarly, referring to Figure 3d in ref 32, can be rewritten to give,

15 Here, the decay rate of the dwell time of the post-lever-arm swing state equals k reversal +k detach1, and the decay rate of the dwell time of the pre-lever-arm swing state equals k swing +k detach2. However, Sellers and Veigel calculated the swing and reversal rate directly from the decay rate of the dwell time. In order to estimate the swing and reversal rates more accurately, the detachment rate should be subtracted from the apparent decay rate, a rate they did not calculate. Because they reported, The majority (60 70%) of final transitions before detachment were reversals at all forces, the detachment rate from the pre-lever-arm swing state should be larger than that of the post state. So the swing rate at the pre-state is more overestimated than the reversal rate at the post-state. Consequently, the reported 4 pn where the swing and reversal rates meet is too high. Another possible explanation, as Sellers and Veigel themselves suggest, is a difference in the force application geometry. Because they attached myosin monomers to the bead nonspecifically, the directions of the external force vary, which reduces the effective force on the lever arm swing (see cartoon a). This too would cause an overestimation. On the other hand, in our geometry, the bead follows the direction of the myosin movement, which means the direction of force is always opposite the walking direction and the lever arm swing (see cartoon b).

16 Supplementary References 44. Smith, S.B., Cui, Y. & Bustamante, C. Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules. Science 271, (1996). 45. Hannemann, D.E., Cao, W., Olivares, A.O., Robblee, J.P. & De La Cruz, E.M. Magnesium, ADP, and actin binding linkage of myosin V: evidence for multiple myosin V-ADP and actomyosin V-ADP states. Biochemistry 44, (2005).