Abstract
The regulation of actin dynamics is essential for various cellular processes. Former evidence suggests a correlation between the function of non-conventional myosin motors and actin dynamics. We investigate the contribution of the catch-bond myosin1b to actin dynamics using sliding motility assays. We observe that sliding on myosin1b immobilized or bound to a fluid bilayer enhances actin depolymerization at the barbed end, while sliding on the weak catch-bond myosin II has no effect. Our theoretical model shows the pivotal impact of the catch-bond behavior of a motor on depolymerization of sliding actin filaments. The catch-bond prolongs the attachment time of the motor at the barbed end due to the friction force exerted by the sliding filament; thereby this motor exerts a sufficient force on this end to promote depolymerization. This work reveals a non-conventional myosin motor as a new type of depolymerase.
Actin filaments (F-actin) form a variety of dynamical architectures that govern cell morphology and cell movements. The dynamics of the actin networks are regulated in space and time by the assembly and disassembly of actin polymers under the control of regulatory proteins. Cortical actin organizes lateral movement of transmembrane proteins and participates in membrane signaling by interacting transiently with the plasma membrane 1. One class of actin-associated molecular motors, the single-headed myosin 1 proteins, bridges cortical actin to the plasma membrane. Polymerization of actin filaments at the plasma membrane generates forces on the membrane as well as on their membrane linkers. Inversely myosin 1 can exert and sustain pN forces on F-actin 2.
This important class of myosins contains a motor domain at its N-terminus that binds F-actin in response to ATP hydrolysis, a light chain binding domain (LCBD) that binds calmodulin (in most cases), and a Tail domain at the C-terminus (Fig. 1A) 3. The Tail domain encompasses a tail homology domain (TH1) with a pleckstrin homology motif (PH) that binds phosphoinositides (Fig. 1A). Beside the involvement of myosin 1 proteins in a large variety of cellular processes including cell migration and membrane trafficking 3, manipulation of myosin 1 expression has revealed a correlation between these myosins and actin network architecture 4, 5, 6, 7. In particular, under- or overexpression of one of these myosins, myosin 1b (Myo1b), affects the organization of the actin cytoskeleton in the juxtanuclear region of HeLa cells 4 and in growth cones of cortical neurons 6. However, the role of these motors in actin dynamics remains to be explored.
When bound to a substrate and in contact with F-actin, Myo1b has different configurations over time as a function of the ATP hydrolysis stage. When attached, Myo1b performs a first power-stroke and propels the actin filament over a distance d1 towards the minus-end (being a plus-end motor) and depending on the applied force, it performs a second power stroke over a distance d2. Myo1b being a catch bound motor (the time Myo1b remains bound to F-actin strongly increases with an applied load), it thus remains attached to the filament for a time that depends on the applied force F. It eventually detaches independently of the force but depending on the ATP concentration with a rate 9 (Fig. 1B). Due to its mechanosensitive behavior, Myo1b could in turn exert a force on actin filaments 8, 9 and thus affect their polymerization. In this paper, we use in vitro F-actin gliding assays (Fig. 1C) and total internal reflection fluorescence (TIRF) microscopy to study the effect of Myo1b on actin polymerization dynamics, with the motors either immobilized on a solid substrate (Fig. 1C, III) or bound to a fluid supported bilayer, which mimics cell membranes (Fig. 1C, IV).
The sliding velocity vf of single stabilized F-actin on Myo1b immobilized on a glass coverslip (Fig. S1A, top and Movie S1), the sliding velocity vf and the polymerization rate vp (expressed in actin sub-unit/s, with the length of an actin subunit being equal to 2.7 nm) of single F-actin (Fig. S1A, bottom and Movie S1) (Materials and Methods), both in the presence of 0.3% methylcellulose for keeping the filaments in the TIRF field, were measured by image analysis. At high Myo1b density (8000 µm−2) (for the motor density measurement, see Materials and Methods and Fig. S1B), both stabilized and polymerizing filaments move with the same average sliding velocity vf = 56.4 ± 15.4 nm.s−1 and vf = 53.9 ± 5.5 nm.s−1, respectively (Fig. 2A, Fig.2B, Movie S1 and Table S1) in the presence of 2 mM ATP (above saturation for motor activity) 10. In both cases, this velocity decreases by about a factor two when decreasing the Myo1b density by a factor of twenty (Fig. S2B, S2C, Table S1) or when reducing the ATP level to 0.2 mM (Fig. 2A,B, Movies S2, S3) below saturation for Myo1b, but not affecting actin polymerization (Table S2).
To describe the actin filament sliding on Myo1b taking into account the force and ATP dependence, we extend the two state cross-bridge model 11 to a three-state cross-bridge model in order to explicitly include the two distinct sub-steps observed by Laksoo et al. 9; (Fig. 1B, Material and Methods). Increasing the ATP concentration increases the filament sliding velocity vf, while the fraction of motors in the ATP-dependent sub-step 2 decreases; however it lowers the catch-bond dependent transition rate, ω1-2(Fig. 1B). This in turn increases the time that the catch-bond motor spends in the ADP state, as compared to what happens for a weakly catch-bond motor such as myosin II (Fig. S3E). By matching the force-dependent transition rate (ω1-2) and the ATP dependent detachment rate (ωdet) we calculate the stationary sliding velocity of the filament, at the two measured ATP concentrations (vf ≈ 55 nm/s at CATP = 2mM and vf ≈ 25 nm/s at CATP = 0.2mM, Fig. S3F) for Myo1b as well as for MyoII (vf ≈ 255 mm/s at CATP = 2mM). This model describes accurately the effect of the catch-bond on the sliding velocity (Fig. S3F).
We next investigated the impact of Myo1b on actin polymerization upon filament sliding. The actin assembly-disassembly kinetics are an order of magnitude faster at the barbed (plus) end than at the pointed (minus) end 12. Thus, we measured the elongation ΔL of F-actin at the barbed-end versus time (Fig. 2C). Strikingly, filament sliding on Myo1b decreases the actin polymerization rate vp, as compared to actin polymerization in the absence of Myo1b (Fig. 2D and Movie S3). This effect is stronger for high filament sliding velocity (in the presence of 2 mM ATP) and weaker at lower Myo1b density on the substrate (Figs. S2B, S2D, Movie S3 and Table S2). We also measured the dynamics of the pointed (minus) end by detecting the relative movement of this extremity compared to a fiducial point on the filament. In contrast with the barbed end, we did not observe any filament length variation (Fig. S2A and Movie S4), thus filament sliding on the motors reduces the actin polymerization rate at the barbed-end only. As a control, we tested the impact on actin polymerization of free Myo1b present only in the bulk, or immobilized on the surface but inactivated (Figs. S2B,D and Movie S5); we did not observe any effect on polymerization (Fig. S2E). Moreover, although actin filaments slide five-fold faster on non-or weak catch-bond myosins such as muscle myosin II (MyoII) 13, at the same bulk monomeric-actin (G-actin) concentration (Fig. 2A,B and Movie S6), the actin polymerization rate remains similar to the control (Fig. 2C, D). These observations demonstrate that an immobilized myosin motor with intact activity and a catch-bond behavior reduces the actin polymerization rate at the barbed-end up to a factor two (Fig. 2D and Table S2), in contrast to a weak catch-bound myosin such as muscle MyoII.
Dynamics at the barbed-end results from a balance between the rate of association of G-actin kon and the rate of dissociation koff; steady state is obtained at the critical concentration Cc+. Classically, these dynamical parameters are deduced from the measurement of the variation of the polymerization rate vp with G-actin concentration Cm: vp = konCm − koff. By varying the G-actin bulk concentration from 0.1 to 1 µM in the presence of either 0.2 mM and 2 mM ATP, we observed that the slope corresponding to kon is unchanged when F-actin slides over Myo1b, whereas Cc+ which is the ratio between koff and kon increases (Fig. 2D) demonstrating that koff increases under these conditions (Fig. 2D and Table S2). Still, in the absence of G-actin in the bulk, filaments depolymerize faster when they slide over Myo1b (Fig. S2F, G and Movie S7). Interestingly, the dissociation rate is weakly affected when reducing Myo1b density (Fig. S2E and Table S2). The decrease of the dissociation rate is due to a lower sliding velocity of the filament. As expected, the sliding velocity of the filament decreases weakly with the motor density. In our model, this effect is associated with the impact of the external hydrodynamic drag on the filament, which eventually slows down the motors. In contrast, while sliding on MyoII is much faster, this myosin has no influence on koff at the barbed-end of the filament (Fig. 2D and Table S2). Together, these observations indicate that the catch-bond Myo1b is an actin depolymerase.
One possible mechanism for this depolymerase activity is that Myo1b induces actin depolymerization by modulating the torsion of the filaments 14. In this case, the polymerization kinetics is expected to depend on the filament length with a twist gradient inversely proportional to the length. However this is not what we observe (Fig. S2H), excluding an explicit role of filament torsion due to motor attachment along the filament.
We thus developed a theoretical model for actin polymerization when filaments slide on motors depending on their catch-bond properties (Fig. 1B, Fig. 2E, and Materials and Methods). Due to the catch-bond behavior of Myo1b, the transition rate between sub-step 1 and sub-step 2 in Fig. 1B decreases with increasing filament sliding velocity. Thus, the motors remain in the ADP state for an increased time, inducing a larger friction on the sliding filaments as compared to non-catch-bond motors such as MyoII. We assume that this friction between the motor and the filament increases the attachment time of the single molecular motor at the barbed end and thus this motor induces a force Fmot at this extremity sufficient to promote depolymerization (Fig. 2E). We have quantified this effect by assessing the impact of the friction force on the increase of the actin dissociation rate. For this we have introduced an exponential decay of the dissociation rate with the force on the filament over a characteristic force f* 15 (Materials and Methods Eq. SE10). This characteristic force quantifies the force sensitivity of the depolymerization rate of actin koff. Using our model we have determined 3.5pN < f < 4.5pN (Fig. S5A). f ≫ 5pN would make the actin filament insensitive to forces applied by the motor (Fig. S5A). f ≪ 3pN would impact the dissociation at low ATP concentration, precluding the stability of the filaments in the presence of motors (Fig. S5A). This model shows that the catch-bond behavior of Myo1b strongly increases the F-actin depolymerization at the barbed-end while a weakly-catch bond MyoII motor barely impacted F-actin depolymerization in agreement with our experiments.
In cells, Myo1b is bound to the fluid plasma membrane lipid bilayer through the interaction of its PH domain with PI(4,5)P2 16, and thus it is not immobilized (Fig. 3A). We mimic experimentally these cellular conditions by analyzing the impact of Myo1b on actin dynamics when bound to a glass-supported lipid bilayer (SLB) composed of 79.5% POPC, 20% L-α-phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) and 0.5% Rhodamine-PE or Atto488-DOPE (mol/mol) (Fig. 1C and Fig. 3) (Materials and Methods). We checked using fluorescence recovery after photobleaching (FRAP) that membrane fluidity was preserved in the SLB with bound Myo1b (Fig. 3A and Fig. S6). The lipid diffusion coefficient was in agreement with data published on SLBs composed of pure POPC 17. After recruitment on the SLB, Myo1b diffuses freely in the plane of the membrane (Fig. 3A). We did not observe any difference between experiments with or without methylcellulose in the bulk (Fig. 3A). In addition, the lipids continue to diffuse freely even when Myo1b diffusion is strongly decreased by a dense actin network (Fig. 3A) due to an emerging coupling when a filament bridges multiples motors. The diffusion coefficients are close to those measured in cell membranes (Fig. 3A), showing that in our in vitro experiments, the fluidity of the membrane is preserved. As previously reported 18, myosin 1 proteins bound to a lipid bilayer exert a force strong enough to propel actin filaments in spite of the fluidity of the support. We confirmed that in the presence of 2 mM ATP and at a similar Myo1b density as when immobilized (8500 µm−2), stabilized and polymerizing F-actin slides on Myo1b bound to SLBs, although with a velocity reduced by about 25%: vf = 37.6 ± 7.3nm.s−1 and vf = 39.3 ± 8.2nm.s−1 respectively (Fig. 3B, Fig. 3C, Movie S8 and Table S1).
We have calculated the relative contributions of the viscous drag of the bulk and of the lipid bilayer on the motion of the filaments. First, we have considered F-actin moving in water (ηb = 10−3Pa. s) above Myo1b bound to a SLB (Fig. 3D). We estimate that, since the in-plane viscous drag between the motor and the lipid bilayer is much larger than the bulk viscosity experienced by the actin filaments, the velocity of the filament-motor couple, vm, practically vanishes. Thus, filaments slide with a velocity vf similar to that measured for immobilized motors: vf ≈ vf (Fig. S7). Including the increased viscosity of the bulk in the presence of methylcellulose (10−2 Pa.s at 0.3%, product information Sigma) and crowding effects between nearby filaments reduces the effective sliding speed of the filament vf since part of the sliding is dissipated by in-plane motion of the motors in the bilayer (Fig. S7). This can explain why in our experiments, F-actin moves over SLB-bound Myo1b but with a slightly reduced velocity as compared to immobilized Myo1b (Fig. 3C, Table S1). This is in line with the results by Grover et al 19 showing a decreased gliding velocity of membrane-anchored kinesins due to their slippage in the lipid bilayer.
In these experimental conditions, we observed a significant increase of the actin depolymerization rate at the barbed end koff when filaments slide on Myo1b bound to a SLB, although weaker than for immobilized Myo1b, while keeping the polymerization rate unchanged (Fig. 3E, Fig. 3F and Table S2). We conclude that the dissipation of sliding filaments in SLBs is low enough to let Myo1b exert a significant dissociation force even when bound to a fluid membrane (See force balance in Fig. 3G).
As previously shown, MyoII induces actin network contraction, potentially leading to filament buckling and breaking 20, 21. However, we show here that muscle MyoII which is a weak catch-bond 13 in the pN force range, does not affect actin polymerization dynamics. Different actin-binding proteins are already known for preventing actin polymerization (capping protein) 12, enhancing it (formin) 22, 23 or depolymerizing actin (ADF/cofilin) 24, 25 at the barbed end. Also, some kinesin motors, e.g., kinesins 8 and 13, have been shown to depolymerize microtubules 26, 27. We show here for the first time that increasing the sliding speed of the actin filaments through increasing the ATP-concentration strongly impacts the actin dissociation rate koff at the barbed-end in a significant way only for catch-bond motors (Tables S1 and S2). Note that the catch-bond effect on the actin growth is due to the longer attachment time of the Myo1b motor, but other molecular mechanisms that increase the duty ratio would potentially lead to a similar effect on actin dissociation. Another Myosin 1 (Myosin 1c) that is also a catch-bond, might regulate actin dynamics at the barbed-end. Nevertheless, the lifetime of its attachment to actin under load is ten times lower than for Myo1b 28, thus we expect its impact on actin dynamics to be moderate as compared to Myo1b, but this remains to be tested.
Experimental evidence supports a role of several Myosin 1 proteins in membrane remodeling 3. Similarly to capping proteins 29, Myo1b and perhaps other Myosin 1 proteins could shape membranes by regulating the growth of filaments at the plasma membrane. Further experiments need to be performed in the future to determine the relative contribution of Myo1b with respect to the other binding proteins. Alternatively, Myo1b could shape membranes by inducing stresses in the cortical actin. Indeed, Myo1b induces actin movement and reduces actin growth when bound to supported bilayers, as shown in our experiments. Since the fluidity of our synthetic membranes and of cellular membranes are similar (Fig. 3A), we propose that Myo1b has the same function in cells. Collectively, these motors could drive the sliding of actin filaments at the membrane surface, which could create stresses that relax by deforming the cortex and the attached membrane. Interestingly, when Myo1b is bound to a deformable giant liposome, we observed that it produces membrane invaginations in presence of stabilized actin filaments (Fig. S8).
Myo1b’s influence on actin dynamics can control the organization of actin networks, as reported in growth cones 6. An actin network can be impacted by Myo1b in different ways. It can reduce the length of actin filaments, as shown by this work, and thus change the mesh-size, or the cortical thickness and consequently the cortical contractibility 30. Whether or not it can affect the Arp2/3-dependent branched actin network and/or formin-dependent actin bundles remains to be explored. Moreover, since Myo1b is specifically present at the interface between the plasma membrane and the cortical actin, Myo1b may coordinate receptor signaling by arranging the cytoskeleton 31.
Besides myosin II and myosin 1 proteins, myosin VI has also been reported to influence the actin architecture during, e.g. spermatid individualization in Drosophila 32 or around melanosomes 33. It might be time now to take a fresh look on the involvement of non-conventional myosins in actin dynamics and organization.
Materials and Methods
Protein purification
Actin was purified from rabbit muscle and isolated in monomeric form in G buffer (5 mM Tris-HCl, pH 7.8, 0.1 mM CaCl2, 0.2 mM ATP, 1 mM DTT and 0.01% NaN3). Actin was labeled with Alexa 594 succimidyl ester-NHS 34.
Myosin II was purified from rabbit muscle as previously described 35.
Expression and purification of Myosin 1b: FLAG-myo1b was expressed in HEK293-Flp-In cells cultured in Dulbecco’s modified Eagle medium supplemented with 10% fetal bovine serum and 0.18 mg ml−1 hygromycine in a spinner flask at 37 °C under 5% CO2, and collected by centrifugation (1,000 g, 10min, 4 °C) to obtain a 4–5 g of cell pellet. The pellet was lysed in FLAG Trap binding buffer (30 mM HEPES, pH 7.5, 100 mM KCl, 1 mM MgCl2, 1mM EGTA, 1 mM ATP, 1 mM DTT, 0.1% protease inhibitor cocktail (PIC), 1% Triton X-100) for 30 min at 4 °C and centrifuged at 3,400 g for 10 min at 4 °C. The collected supernatant was then ultracentrifuged (250,000 g, 60 min, 4 °C). The solution between pellet and floating lipid layer was incubated with 150 µl of anti-FLAG beads for 2 h at 4 °C. The beads were collected by centrifugation (1,000 g, 5 min, 4 °C). After a washing step, FLAG-myo1b was then eluted by incubating with 0.24 mg ml−1 of 3X FLAG peptide in 300 µl elution buffer (binding buffer without Triton X-100 supplemented with 0.1% methylcellulose) for 3 h at 4 °C. After removal of the beads by centrifugation (1,000 g, 3 min, 4 °C), the protein solution was dialyzed against elution buffer overnight at 4 °C to remove the 3X FLAG peptide. Myo1b was fluorescently labeled using Alexa Fluor 488 5-SDP ester 36. Inactivated Myo1b was removed by ultracentrifugation (90,000 rpm, 20 min, 4 °C) with 10 µM F-actin in presence of 2 mM ATP. Inactivated Myo1b was then dissociated from F-actin by incubating the pellet collected after untracentrifugation in elution buffer (30 mM HEPES, pH 7.5, 100 mM KCl, 1 mM MgCl2, 1mM EGTA, 1 mM ATP, 1 mM DTT and 0.1% methylcellulose) supplemented with 1 M NaCl and collected in the supernatant after a second centrifugation (90,000 rpm, 20 min, 4 °C).
Supported lipid bilayer (SLB) preparation
SLBs were formed by fusion of small unilamellar vesicles (SUVs) prepared as follows. Lipid mixtures containing 79.5 % POPC, 20 % L-α-phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) and 0.5 % Rhodamine-PE or Atto488-DOPE (mol/mol) were mixed together in a glass vial, dried with N2, placed in vacuum desiccator for 1 hour, then rehydrated with Fluo F buffer (5 mM Tris-HCl-pH 7.8, 100 mM KCl, 1 mM MgCl2, 0.2 mM EGTA, 0.2 mM or 2 mM ATP, 10 mM DTT, 1 mM DABCO, 0.01% NaN3) for 30 min at room temperature, to a final lipid concentration of 2 mg/mL. After rehydration, the glass vial was vortexed to detach the liposomes. SUVs were formed by sonication, aliquoted and stored at −20 °C. For SLB formation by fusion, CaCl2 was added to a final concentration of 5 mM, with 50 µl of SUVs. The solution was incubated in the chamber for 20 min and washed 5 times with Fluo F buffer 0.1 % BSA. The quality of the SLB was checked by FRAP.
Giant unilamellar vesicle (GUV) preparation
Lipid compositions for GUVs were 79.7 % POPC, 20 % L-α-phosphatidylinositol-4,5-bisphosphate (PI(4,5)P2) and 0.3 % Texas Red DHPE. GUVs were prepared by using polyvinyl alcohol (PVA) gel-assisted method in a 200 mM sucrose buffer at room temperature for 2 hour as described previously 37.
Myosin 1b surface density
We measured the protein surface density (number of proteins per unit area) on solid surfaces or on SLBs by using a previously established procedure 38, 39. It is calculated from a labeled proteins/lipids calibration. We first measure the fluorescence of POPC SLBs containing predefined amounts of Atto488-DOPE fluorescent lipids (DOPE*) to establish the relationship between the density of DOPE* nDOPE* and the corresponding fluorescence intensity IDOPE*SLB (Fig. S1Ba). Assuming an area per POPC of 0.68 nm2, we derive the calibration coefficient A corresponding to the slope of this curve. Note that A depends on the illumination and recording settings of the microscope.
Since Myo1b is labeled with Alexa488 and not Atto488, we have to correct this value by the ratio of fluorescence of the two fluorescent dyes in bulk deduced from the slope of the titration curves (Fig. S1Bb and c). We then obtained the surface density of the protein deduced from the measurement of the Myo1b-Alexa488 intensity IMyo1b* as: where Z is the degree of labeling for the protein of interest (Here, Z=1). In our experiments, the calibration factor is equal to 0.278.
Single-filament TIRF microscopy assays
The kinetics of single filament assembly was monitored by TIRF microscopy (Eclipse Ti inverted microscope, 100X TIRF objectives, Quantem 512SC camera). The experiments were controlled using the Metamorph software. Coverslips and glass slides were sequentially cleaned by sonication with H2O, ethanol, acetone for 10 min, then 1M KOH for 20 min and H2O for 10 min. In the case of supported lipid bilayer, first the coverslips and glass slides were cleaned by sonication with Hellmanex III (Hellma Analytics) for 30 min. Flow chambers were assembled with a coverslip bound to a glass slide with two parallel double-stick tapes. The chamber was incubated with 100 nM anti-myo1b antibody in G buffer (5 mM Tris-HCl, pH 7.8, 0.1 mM CaCl2, 0.2 mM ATP, 1 mM DTT and 0.01% NaN3) for 10 min at room temperature. The chamber was rinsed three times with buffer G 0.1 % BSA and incubated 5 min at room temperature. Then the chamber was incubated with 300 nM Alexa488-labeled myo1b in Fluo F buffer (5 mM Tris-HCl, pH 7.8, 100 mM KCl, 1 mM MgCl2, 0.2 mM EGTA, 0.2 mM or 2 mM ATP, 10 mM DTT, 1 mM DABCO, 0.01% NaN3) for 10 min at room temperature. Assays were performed in Fluo F buffer, containing 0.2 or 2 mM constant ATP, supplemented with 0.3% methylcellulose (Sigma) and with G-actin (10 % Alexa594) or F-actin (stabilized with phalloidin-Alexa594) at indicated concentrations. To maintaining a constant concentration of ATP in this assay an ATP regenerating mix, including 2 mM ATP, 2 mM MgCl2, 10 mM creatine phosphate and 3.5 U/mL creatine phosphokinase, which constantly re-phosphorylates ADP into ATP to maintain a constant concentration of free ATP, was added.
The sliding and elongation velocities of actin filaments were analyzed by using Kymo Tool Box plugin of Image J software (https://github.com/fabricecordelieres/IJ_KymoToolBox). Only filaments longer than 20 pixels are analyzed. When filaments slide on myosins, only those moving directionally during the whole sequence are selected. On each image of a sequence, a segmented line is manually drawn over a single filament, which generates a 10 pixel wide band. The plugin flattens the curved filaments and generates a kymograph. The accuracy on the displacement and the length of the filaments is of the order of the pixel size (160 nm). We consider that each actin subunit contributes to 2.7 nm of the filament length.
FRAP methods
For diffusion measurements, Fluorescence Recovery After Photobleaching (FRAP) experiments were performed through a X100 or X60 oil immersion objective on an inverted spinning disk confocal microscope (Nikon eclipse Ti-E equipped with a Prime 95B™ Scientific CMOS camera, Photometrics) equipped with a FRAP unit. Recovery curves (average of 5 independent experiments, performed on different circular regions of the SLB using the same bleaching conditions) were normalized to the initial intensity and fitted with a single exponential function. We derive the τ1/2 time corresponding to the time at which the fluorescence signal has recovered 50% of its value before bleach. We calculated the diffusion coefficient using the Soumpasis equation 40:
, where r is the radius of the bleached region.
Theoretical model for filament sliding: Myosin1b as a catch bond motor
Myosin 1b motor
Myo1b is identified as a molecular motor with a catch-bond detachment rate: it responds to small resisting loads by dramatically increasing its duty ratio 9. Single molecule experiments have established that the motor cycle of Myo1b contains two distinctive steps. In sub-step 1, the motor performs a first power stroke of size d1 = 5.1 nm. From sub-step 1, the motor transits to sub-step 2 (Fig. 1B). After the transition, the motor relaxes its stress 9 and it performs a second power stroke of size d2 = 3.3nm. The transition rate between sub-step 1 and 2, ω1-2(F) depends on the applied force on the motor, F, and shows a catch-bond behavior (Fig. 1B). As found in the single molecule experiments by Laakso et al. this step was force sensitive in the direction of forcing. However, in the motility assays experiments, the force on the motor occurs in both directions, in the direction of sliding, during the power stroke, and opposing the direction of sliding. We define here the powerstroke as the period of the motor cycle where the strain of the motor is positive and pushes the motor in the gliding direction. In this paper, we assume the force sensitivity is equal on both direction. In other words, the transition rate, ω1-2(F) is proportional to the absolute value of the force applied on the motor,
Here, ωi is the force independent transition rate observed at large force, ω0, the force-dependent transition rate at vanishing force, b, the distance quantifying the strain sensitivity of the motor and kBT the thermal energy. After the first power-stroke, because of the catch-bond, the motor remains attached to the gliding filament. To prevent unphysical stretching of the motors, they relax their strain and transit to sub-step 2 behind a critical stretching length of the motor lmax = vftmax36, where tmax is the maximal attachement time corresponding to a filament sliding at a speed vf. Behind an extension larger than lmax, the motor spring is non linear and the spring strongly stiffens, hence behind this threshold, the transition rate to sub-step 2 becomes infinite. Eventually, after performing a second power-stroke, the motor detaches from the filament with a rate that depends on ATP concentration, CATP, ωdet(CATP), and follows Michaelis-Menten kinetics, where ωsat is the detachment rate at saturated ATP concentrations and C* the characteristic value above which the rate ωdet saturates.
Three-state crossbridge model
To describe the actin filament sliding over Myo1b motors and to include the force and ATP dependences of the motor cycle, we extend the classical cross-bridge model 11,41 by explicitly including the force-and ATP dependent sub-steps of the motor cycle as depicted in Fig.1b. This model is valid for a filament sliding at constant velocity vf and in the limit of a large number of molecular motors propelling the filament.
An actin filament sliding at speed vf is transiently attached to a motor in either of the sub-steps 1 or 2, discussed in the previous paragraph (Fig. 1b). We assume here that the two powerstrokes are instantaneous. While the motor is in sub-step 1, it exerts a force on the filament: where kcb is the cross-bridge stiffness of the motor and τ1 is the time since attachment to the filament (the “age” of the motor in sub-step 1) and d1 the amplitude of the powerstroke. Similarly, while the motor is in sub-step 2, it exerts a force on the filament of magnitude, where τ2 is now the age of the motor in sub-step 2, i.e. the time since the transition to sub-step 2. The fraction of attached motors along the filament, both in sub-step 1, ρ1, and in sub-step 2, ρ2, as function of their respective ages, τ1 and τ2, evolve according to the following kinetic equations where δ(τ1) is the Dirac delta function, ωon is the attachment rate and nd is the fraction of detached motors. Note that we assume that during the powerstroke, the motor does not detach, i.e., ω1-2(τ < d1/vf) = 0. We also ignore here, in a mean field approximation, the effect of thermal fluctuations upon attachment of the motors and during the transition between state 1 and state 2. Still, during the transition between states 1 and 2, the thermal fluctuations play an important role in relaxing the strain created on the motro during state 1. Equivalently, ρ2 evolves as,
Solving this set of equations requires the determination of the total fraction of detached motors, nd, which is obtained by summing the two populations of attached motors,
The time-averaged force exerted by a single molecular motor along the filament is the sum of the contributions of the motors in sub-steps 1 and 2,
In Fig. S3 A,B we plot the integrands of the two contributions as functions of the motor ages in the corresponding sub-steps for (A) CATP = 0.2 mM and (B) CATP = 2 mM. We use here the kinetic and mechanical parameters given in Table I, (see next section for the choice of these parameters). This figure shows that, initially, when τ < d/vf the motor is under positive strain and exerts a positive (propelling) force due to the power stroke, while for τ > d/vf the motor is nuder negative strain and exerts an opposing frictional force. Note that is implies that the motor can transit to sub-step 2 during the power stroke as well as after the power-stroke. Since the time the motor spends performing the power stroke is small < d1/vf ≈ 0.25s, motors rarely transit to sub-step 2 without completing their power-stoke. Moveover, we choose a maximal extension of the motor of 50 - 125nm, which, at a sliding speed of 25nm/s, correpsonds to a maximal transition time tmax ≈ 2−5sec. This value has been based on maximal extensions in single molecule experiments on muscle motor myoII42. Morever note that, as can be seen in Fig.S3A, only a tiny fraction < 10−3 are still attached at this attachment times.
Depending on the relative values of the kinetic parameters, we identify two regimes. In the limit ω1-2(F) ≫ ωdet(CATP), the ATP dependent detachment is the limiting step and the motor mainly resides in sub-step 2 (Fig. S3C). This typically corresponds to low ATP concentrations. When ω1-2(F) ≪ ωdet(CATP), the motor mainly resides in sub-step 1 and the force dependent (catch-bond) transition between sub-steps 1 and 2 impacts the detachment: this can be seen through the long tail in the force exerted by motors in sub-step 2 in Fig S3B. To emphasize the role of the motor kinetics we show in Fig. S3D that a larger attachment rate ωon increases the fraction of motors attached to the filament and also the fraction of motors in the force dependent sub-step 1, n1. A larger value of ωon increases the fraction of time that the motor resides in the force dependent sub-step 1 and therefore the impact of the catch-bond on the filament sliding becomes more important.
To further illustrate the role of the catch bond on the motor cycle, we plot the fraction of motors in sub-step 1, n1, and sub-step 2, n2, and compare a catch-bond motor as described above with a slip-bond motor where the transition rate is force independent ω1-2 = ωi + ω0. We indeed observe that upon increasing the ATP concentration the fraction of motors in sub-step 1 remains constant for the slip-bond motor, in contrast to the catch-bond motor for which n1 increases. The fraction of motors in sub-step 2 naturally decreases upon increasing CATP. The increased fraction of motors in sub-step 1 increases the friction between the filament and the motor, decreasing the sliding velocity, relative to the velocity for a slip-bond motor (Fig. S3F).
Determination of the Myo1b transition and detachment rates
In this section, we estimate the kinetic rates and mechanical parameters of the Myo1b motor at the ATP concentrations used in our experiments. The values reported for the (un)-binding kinetics in Laakso et al. 9 were obtained at significantly lower ATP concentrations (CATP = 50µM) than reported here (CATP = 0.2 − 2 mM). Using these values would imply attachment times up to 10-100 seconds, which are not compatible with sliding speeds of the order of 50nm/s; indeed they would imply stretching the Myo1b motor up to microns. Moreover it is worth noting that the detachment rates reported in Laakso et al. 9 are the combined kinetic rates of the two sub-steps (sub-step 1 - 2) and (sub-step 2 - detached). Therefore we use the measured sliding velocities at the two ATP concentrations of our experiments to determine ωi, ω0 and ωsat (See SE1 and SE2). As already stressed earlier, given the measured speeds we consider that the transition and detachment rates cannot be larger that one second, since otherwise this would imply motor extension larger than 50nm.
To match ωsat, ω0 and ωi, we calculate the difference of the predicted and measured sliding speed at vf(CATP = 0.2 mM): vf = 25nm/s and vf(CATP = 2 mM): vf = 55nm/s,
By calculating an error map as a function of ωi and ω0 for a range of ωsat values we found that ωsat ≈ 25s−1 provides optimal matches in sliding speed relative to our experiments (Fig. S4A and S4B). In Fig. S4C and S4E we show the respective values of the error for ωsat = 10 s−1 and ωsat = 40 s−1 are much higher relative to the ωsat ≈ 25s−1 plot (Fig. S4D).
Globally, this analysis provides a band of values that match the sliding velocities at ATP concentrations of 0.2 and 2 mM. This range of values that match the sliding velocities at both ATP concentrations (Indicated in Red in Fig S4D) and corresponds to two regimes: weakly catch bond (ω0/ωi ≈ 1) and strong catch-bonds (ω0/ωi ≫ 1). The strength of the catch-bond is characterized by the ratio between ω0 (which is the transition ratio at vanishing force, Eq. SE1) and ωi (which is the transition rate at high force, Eq. SE1). For our further analysis we choose values as indicated in Table I.
Filament sliding enhances actin depolymerization
We showed in the previous section that due to the catch-bond characteristic of Myo1b, the motor spends a larger time in catch-bond sub-step 1. Here we hypothesise that the prolonged attachment time of the last Myo1b motor to the barbed end of the filament induces a transient stress, and enhances the depolymerization. Experimentally (Fig. 2D), we show that, while the polymerization rate remains unaltered for filaments sliding over Myo1b, the depolymerization rate of the actin filament increases. This effect can be described by the average force dependent depolymerization rate 15, where is the depolymerization rate in the absence of applied force and f* is the characteristic scale for the force sensitivity of the depolymerization rate. Since in the experiment, the filaments slide over catch-bond motors, the effective opposing frictional force on the filament is increased, enhancing the force at the plus-end and hence the depolymerization. Using SE10 we estimate the predicted increase in depolymerization rate as a function of ATP concentration for various values of the characteristic force, f* (Fig. S5A). Note also that, depending on f* this depolymerization rate may diverge in our theoretical model. We find that for ωon = 100 s−1, 3.5 < f*< 4.5 pN matches best our experimentally observed depolymerization rates.
The value of the attachment rate ωon (detached - sub-step 1) is a parameter that does not impact the sliding velocity at vanishing external force Fmot = 0. However, increasing ωon, increases the fraction of motors in sub-step 1 and sub-step 2 as depicted in Fig S3D. Indeed, an increase of ωon leads to a larger number of motor cycles per unit time and therefore to a larger total time that the motor spends in the catch-bond sub-step ρ1. However, particularly at high ATP concentration, it shifts the equilibrium fraction from a sub-step, primarily dominated by the ATP dependent sub-step 2, to a sub-step dominated by the force dependent catch bond sub-step 1 (Fig. S3E). Choosing a value for ωon in the range of 10 − 103 does not qualitatively impact the results at the experimental ATP concentrations as we show in Fig. S5B.
Identifying that myoII is a weak catch bond motor, we model it with a single force-independent rate (ω0 = ωi = 0), a power-stroke d = 5.0 nm and a cross-bridge stiffness kcb = 0.4 pN/nm 11. In Fig. 2b we observe that at CATP = 2.0mM, the sliding velocity is vf ≈ 255nm/s. We calculate ωsat that matches this sliding velocity: ωsat ≈ 82 s−1. Using this value, we plot the effect of the motors on the depolymerization rate of actin as a function of ωon and find a small enhancement of the depolymerization rate < 10% for ωon = 1 − 102 s−1, in agreement with our experimental data.
Taken together our model shows two interesting features. First, since the filaments are sliding on catch-bond Myo1b motors, their sliding speed decreases while the effective friction exerted by the motors on the filament increases. Second, increasing the sliding velocity by e.g. increasing the ATP concentration increases the time that the motor spend under tension; it increases therefore the total friction force experienced by the filament and hence enhances the depolymerization.
In order to explicitly account for the density of motors along the actin filament, we now derive the sliding velocity of the filament in the gliding assay from the balance between the motor driving force, Fmot, and the drag force on the filament due to its surrounding NFmot = ξvf (N is the total number of motors along the filament). Depending on the magnitude of the friction coefficient, ξ, a decrease of the number of motors along the filament slows down the filament sliding vf. This rationalizes the decrease of sliding velocity observed upon lowering the density of motors in the gliding assay (Fig. S2C, Table S1). In addition, a decrease of the motor density along the filament lowers the enhancement of depolymerization since the motors spend less time in the catch-bond sub-step 1 (Fig. S3E), in agreement with our measurements (Table S2).
Filament sliding on a lipid bilayer
In order to estimate how the motor force is transmitted to the filament when the molecular motors are immersed in a lipid bilayer, instead of being rigidly anchored to a solid surface, we write a simplified force balance between the viscous friction force of the motor/filament and the force exerted by the molecular motors nFmot where n = ρℓ is the number of attached motors along the filament of length ℓ, where ξm is the in-plane friction coefficient of the motor complex in the lipid bilayer, vm, the speed of a molecular motor, ξf, the friction coefficient between the filament and the surrounding solution and , the speed of the filament in the assay. The first equation is the force balance on the filament and the second equation is the force balance on the filament and motors complex. We use here a simplified expression for the motor force estimated in Eq. SE 8, i.e., 41, where fs is the stall force of one motor and v0 the motor speed at vanishing external force (fs ≈ O(1) pN and v0 ≈ 50nm/s as calculated before with the more detailed model). The friction between the filament and the solution can be estimated as ξf ≈ 2πηb/(log ℓ/bf) ≈ O(10−8) Pa.s.m, where we use the bulk viscosity of water ηb = O(10−3) Pa.s and as a cut-off lengthscale, the size of the filament ℓ = O(10−5)m. Note however that the effective bulk viscosity can be significantly larger since the filament slides close to a surface. The friction between the motor complex and the lipid membrane is ξm ≈ 4πηm/ log(l0/L) ≈ O(10−9) Pa.s.m 43, where L is the size of the membrane and l0 the size of a motor (we estimate the membrane viscosity as ηm ≈ O(10−10) Pa.s. 4 and log(L/l0) ≈ O(1)). Solving equations SE 11 and SE 12 gives the following values for the velocity of the filament, , relative to the velocity at zero external force on a solid substrate, v0, and for the velocity of the motor, vm,
For realistic values of the friction coefficient of water and typical force values we obtain a filament speed which is very close to the filament speed on a solid substrate , indicating that, since the in-plane membrane friction of the motor is larger than the filament friction with the fluid, the motors are effectively immobile. However, upon increasing the viscous friction between the filament and the bulk by one/two orders of magnitude, potentially due to inter-filament friction (at high filament density) or to the addition of methylcellulose, the sliding speed of the filament diminishes significantly (Fig. S7). Also decreasing the density of motors along the filament impacts the sliding speed since the effective friction between membrane and motor is proportional to the density of motors.
Author contributions
P.B and E.C. designed the study. J.P. and A.M. performed TIRF experiments and analyzed data; J.P. and T.L. conducted FRAP experiments; H.B. purified Myosin 1b. R.K. and J.-F.J. developed the model. P.B, E.C., J.P., R.K. and J.-F.J. wrote the paper.
Competing interests
The authors declare no competing interests.
Acknowledgments
We thank B. Goud for insightful discussions, C. Le Clainche (I2BC, Gif-sur-Yvette, France) for providing actin and Myosin II and critically reading the manuscript, F.-C. Tsai for SLB preparation, L. Blanchoin, C. Leduc, J. Prost, M. Henderson for carefully reading the manuscript. The authors greatly acknowledge the Cell and Tissue Imaging (PICT-IBiSA), Institut Curie, member of the French National Research Infrastructure France-BioImaging (ANR10-INBS-04). This work was supported by Institut Curie, Centre National de la Recherche Scientifique (CNRS), the European Research Council (ERC) (J.F.J., P.B. and E.C are partners of the advanced grant, project 339847 and their groups belong to the CNRS consortium CellTiss, the Labex CelTisPhyBio (ANR-11-LABX0038) and Paris Sciences et Lettres (ANR-10-IDEX-0001-02). J.P. and R.K. were funded by the ERC project 339847.