Molecular Investigations into the Mechanics of Actin in Different

Dec 9, 2010 - Nucleotides regulate the mechanical hierarchy between subdomains of the nucleotide binding domain of the Hsp70 chaperone DnaK. Daniela ...
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J. Phys. Chem. B 2011, 115, 186–195

Molecular Investigations into the Mechanics of Actin in Different Nucleotide States Ji Y. Lee, Tyler M. Iverson, and Ruxandra I. Dima* Department of Chemistry, UniVersity of Cincinnati, Cincinnati, Ohio 45221, United States ReceiVed: August 30, 2010; ReVised Manuscript ReceiVed: NoVember 17, 2010

Actin plays crucial roles in the mechanical response of cells to applied forces. For example, during cell adhesion, under the action of forces transmitted through integrins, actin filaments (F-actin) induce intracellular mechanical movements leading to changes in the cell shape. Muscle contraction results from the interaction of F-actin with the molecular motor myosin. Thus, understanding the origin of actin’s mechanical flexibility is required to understand the basis of fundamental cellular processes. F-actin results from the polymerization of globular actin (G-actin), which contains one tightly bound nucleotide (ATP or ADP). Experiments revealed that G-actin is more flexible than F-actin, but no molecular-level understanding of this differential behavior exists. To probe the basis of the mechanical behavior of actin, we study the force response of G-actin bound with ATP (G-ATP) or ADP (G-ADP). We investigate the global unfolding of G-actin under forces applied at its ends and its mechanical resistance along the actin-actin and actin-myosin bonds in F-actin. Our study reveals that the nucleotide plays an important role in the global unfolding of actin, leading to multiple unfolding scenarios which emphasize the differences between the G-ATP and G-ADP states. Furthermore, our simulations show that G-ATP is more flexible than G-ADP and that the actin-myosin interaction surface responds faster to force than the actin-actin interaction surface. The deformation of G-actin under tension revealed in our simulations correlates very well with experimental data on G-actin domain flexibility. Introduction Actin is the monomeric subunit of microfilaments and thin filaments. The microfilament is one of the three major components of the cytoskeleton, and the thin filament is part of the contractile apparatus in muscle cells. Therefore, actin plays important roles in cellular processes such as muscle contraction, cell motility, cell division and cytokinesis, vesicle and organelle movement, and the establishment and maintenance of cell junctions and cell shape.1-3 Monomeric actin (G-actin) consists of 375 residues and 1 tightly bound nucleotide (ADP or ATP). The atomic resolution structure of actin4 shows that it consists of two domains separated by a deep cleft, which serves as the nucleotide binding site. Each domain is subdivided into two subdomains: subdomains 1 and 2 form the small domain, and subdomains 3 and 4 form the large domain (Figure 1). In addition, the DNase I-binding loop (DB loop, residues 40-48) adopts a disordered loop structure in G-actin with ATP (G-ATP), while it forms a short R-helix in G-actin with ADP (G-ADP).5 The nucleotidefree state of G-actin is believed to consist of a number of structures with similar energy that are readily interconverted,6 with subdomain 2 being the main region of the chain responsible for this conformational variability. Upon the spontaneous polymerization of G-actin into F-actin, ATP is hydrolyzed to ADP, with a slower release of Pi (k ) 5.8 × 10-4 s-1).7 The most common F-actin architecture corresponds to a helical structure consisting of 13 actin molecules per 6 left-handed turns and morphologically appears as two right-handed steep helices that twist slowly around each other.8,9 However, alternative F-actin structural states have been detected.6,10,11 For example, Schutt et al.12 reported the existence of an untwisted F-actin. * To whom correspondence should be addressed. E-mail: Ruxandra.Dima@ uc.edu. Phone: +1 513 5563961. Fax: +1 513 5569239.

Figure 1. Crystal structure of G-ADP from the PDB.5 The subdomains 1, 2, 3, and 4 are shown in ice blue, magenta, orange, and cyan, respectively. The red, green, and blue spheres at the top (bottom) represent residues 41-45 (166-169), 202-204 (286-289), and 243, 244 (322-325), respectively. Positions with the same color are pairs at the interface between actin molecules along the longitudinal direction of F-actin. Black spheres represent residues 4, 24, 25, 99, 100, 341, 345, 349, 352 in subdomain 1 and 144, 332, 333 in subdomain 3 and form the actin-myosin interaction surface.

Muscle contraction results from a sliding force between F-actin and myosin13 and forces generated within the cell through such actomyosin interactions play crucial roles in cell growth and division. Therefore, understanding the structural dynamics of the interactions between myosin and actin is crucial for deciphering the origin of fundamental cellular processes such as contraction. Single molecule experiments employing laser optical tweezers (LOTs) have been conducted to measure the process of forced unbinding of myosin and actin binding proteins (ABPs) such as filamin and R-actinin from F-actin.14,15 They

10.1021/jp108249g  2011 American Chemical Society Published on Web 12/09/2010

Mechanics of Actin in Different Nucleotide States revealed that forces required to rupture ABPs from the F-actin lattice range between 50 and 100 pN under moderate loading rates of up to 260 pN/s. Scaling of this value at the typical atomic force microscopy (AFM) loading rates of ∼5000-10 000 pN/s results in forces of up to 500 pN to break myosin from F-actin. This value resembles the forces measured by Kojima and co-workers16 for breaking apart F-actin. Thus, a natural question to ask is whether the rupture of myosin and other ABPs from F-actin will be accompanied by breaking/unfolding processes inside F-actin. As part of the cytoskeleton, F-actin actively experiences forces. For example, during cell adhesion forces get transmitted to F-actin through integrins.17,18 Thus, to gain insight into the functions of F-actin, a good understanding of its mechanical properties is needed. Kojima et al.16 measured the stiffness of a 1 µm long F-actin as 43.7 pN/nm. More recently, Liu et al.19 reported a similar stiffness but also found a second value of 5.8 pN/nm. They proposed that this may be due to a different connection between actin and the lever or to the different F-actin structural state with higher compliance proposed by Schutt et al.12 Studies have also measured that the length-tension relation in F-actin is linear in the 50-230 pN range,19 while the force required to break the filament is 320-600 pN.20 Neutron scattering experiments revealed that the dynamics of G- and, respectively, F-actin do not coincide,17 with G-actin being the more flexible state of actin. While the authors attributed this change in behavior to the structural diversity of the states, no investigation has been conducted to pinpoint the molecular-level changes that give rise to the overall measured differences. To shed light into the above issues, i.e., to determine the connection between the mechanical response of F-actin and the behavior of its actin subunits, we employ molecular simulations of a coarse-grained description of the chain, the self-organized polymer (SOP) model.21 Previously, SOP led us to unravel the details of the force-unfolding scenarios in the green fluorescent protein (GFP) and tubulin in agreement with experimental measurements.21-23 Furthermore, this model has been successfully employed to understand the mechanical control of molecular motors24 and the details of large scale allosteric transformations in GroEL.25 We start with the study of the global unfolding of G-actin under forces applied at the ends of the chain to determine the basis of the flexibility of the molecule which can be modulated by its interactions with neighboring actins or with ABPs in the filament. Next, we investigate the stretching stiffness and the structural changes in G-actin under forces applied along the actin-actin and, respectively, the actin-myosin interaction interfaces in F-actin. These simulations, performed both in the absence and in the presence of the nucleotide(s), enable us to characterize the actin unfolding mechanisms along various directions of the applied force that are functionally relevant. Our study of the effect of the nucleotide on the mechanical behavior of actin aligns well with very recent investigations into the role of nucleotides in the structure of F-actin26 and its interaction with cofilin.27 By relating our results to a variety of experimental studies, we can provide molecular-level structural interpretation for the existing data. Our most important finding is that the nucleotide state has a dramatic effect on the global unfolding of G-actin under forces applied to its ends, while it induces only modest variations into the mechanical behavior of the actin monomer inside F-actin. We propose that the experimental finding that the presence of the nucleotide affects the mechanical properties of F-actin actually refers to the

J. Phys. Chem. B, Vol. 115, No. 1, 2011 187 interactions between monomers in the filament rather than to the internal behavior of the monomers. Methods Self-Organized Polymer (SOP) Model. We used a topologybased model for actin in which each amino acid is represented by its CR atom.21-23 The detailed description of the model and the total energy function that have been presented in our previous publications is provided in the Supporting Information. Simulations. We used Brownian dynamics simulations at T ) 300 K28 to generate the mechanical unfolding trajectories. To estimate the simulation time scale, we used h ) 0.16 τH, where τH ) (ζεh)/(kBT)τL with τL ) 2 ps and ζ ) 50 (the unitless friction coefficient which accounts for the high friction regime) for the overdamped limit. The value for εh (2 kcal/mol), which denotes the strength of the van der Waals interactions between amino acids, was chosen as in studies of GroEL25 and tubulin23 dynamics. These choices led to an integration time step h ∼ 50 ps. It is important to note that this value is short enough to prevent any large fluctuations in covalent bonds that could lead to divergence of the covalent part of the energy function, i.e., of the FENE potential from eq 1 in the Supporting Information. To mimic the AFM experimental setup, the N-term end (or groups at one end of the monomer) was stretched at constant pulling speed (V ) 1.9 µm/s) while the C-term end (or groups at the other end) was fixed. The pulling direction was chosen as the direction between the N-term and the C-term (or between the centers of masses of the pulled and fixed groups). The cantilever spring constant was ks ) 35 (180) pN/nm in the global unfolding (filament) simulations. The 180 pN/nm value was selected from the microfabricated cantilever experiments of F-actin flexibility.19 To probe the global unfolding in G-actin, we simulated 12 trajectories for each nucleotide state. In the case of unfolding in F-actin, we simulated 24 trajectories for G-ATP and G-ADP in the absence of the nucleotide. In the presence of the nucleotide, we simulated 24 trajectories for pulling each of the nucleotide states along the actin-actin interactions, and 12 trajectories for each nucleotide state pulled along the actomyosin bonds. Structures. We took the structures for G-actin with ADP and ATP from the protein data bank (PDB),29 1J6Z5 and 1NWK,30 respectively. Since there are missing residues (40-51) in the DB loop of 1NWK, we reconstructed this region using the corresponding part of the G-ATP structure from 1ATN. Figure 1 depicts 1J6Z. G-ADP has an R-helix structure for the DB loop (residues 40-48 around the red spheres in subdomain 2). G-actin consists of four subdomains: subdomain 1 (1A: 1-32, 1B: 70-144, 1C: 338-375), subdomain 2 (33-69), subdomain 3 (3A: 145-180, 3B: 270-337), and subdomain 4 (181-269). Details regarding the secondary structure elements from each protein are provided in Table S1 from the Supporting Information. Overlap Function Change. To monitor the progress of the deformation from the initial PDB conformation, we calculated the overlap function change for each residue (i). The overlap o function is defined as χi(t) ) (1/N)Σj N-1 ) 1Θ(R0 - |ri, j - ri, j|). Here, ri, j, ri,o j, R0, and N are the same as in eq 1 from the Supporting Information, and Θ(x) is the Heaviside step function. χi(t) ) 1 means that the structure at time t is identical to the PDB structure, while a 0 or a small value means that the structure is very deformed compared to the PDB. To account for the thermal noise, we chose a maximum time period ∆t, and we calculated the average value θi(t) ) 〈χi(t)〉 over ∆t. The overlap function change is defined as ∆θi(t) ) θi(t + ∆t) -

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Figure 2. Global unfolding pathway for G-ADP in the absence of the nucleotide. (A) FEC and (B) force versus time. The three experimentally detectable peaks P1, P2, and P3 are indicated, and the corresponding structures are drawn on the right. (C) Overlap function change, (D) velocity, and (E) tension for each peak. The time interval corresponding to each line color in (C) to (E) of each line is depicted in (B). The green dotted line in (A) corresponds to a simulation in the presence of the nucleotide. The numbering system is described in the Methods section.

θi(t). We used ∆t ) 26.5 (21.2) ns for the global unfolding simulations (for the filament simulations). Tension Propagation. To monitor the progress of tension propagation from the point of application of force inside the chain, we calculated the force on each covalent bond between residues i and i + 1 and we assigned it to residue i. The force is obtained from the covalent part of the potential energy function of the SOP model, i.e., from the FENE potential (shown in the SOP model) as described in ref 31 according to

(

o fi(t) ) k(ri,i+1 - ri,i+1 )

1-

1 o (ri,i+1 - ri,i+1 )2 R20

)

Here, ri, i+1, ri,o i+1, R0, and k are the same as in eq 1 from the Supporting Information. Similar to the overlap function change, we computed a time averaged tension 〈fi〉 over the same time period (∆t) used to determine the overlap function change. Velocity. To monitor the movement of each residue (i), we calculated its average velocity over the time interval ∆t used to determine the overlap function change. The velocity is Vi(t) - Rti|, where, Rti is time averaged position over ) (1/∆t)|Rt+∆t i ∆t at time t, that is, Rti1 ) (1/∆t)Σt t1)+∆tt1 ri (here ri is position vector of residue i). Throughout the paper we report the x component of velocity (Vx) because in our simulations this is the pulling direction. Results and Discussion Global Unfolding of G-actin. Our investigations into the mechanical behavior of actin first followed the global dynamics

of the molecule resulting from applying a net external force at the ends of the chain. To mimic the AFM experimental setup,32 we pulled on the N-term end while keeping the C-term end fixed. In vitro experiments found that nucleotide-free G-actin (NFA) denatures without stabilizing agents such as sucrose.33 However, in vivo the NFA state can be stabilized by ABPs such as profilin that promote nucleotide exchange during treadmilling.30 In contrast, F-actin is stable in a nucleotide-free state.33 In light of these findings and of the importance of the nucleotide (ATP or ADP) for the function of actin, to decipher its contribution to the mechanical response of actin, we performed simulations both in the absence and in the presence of the nucleotide. Previously, the SOP model with explicit description of ATP/ADP has been successfully used to determine the nature of conformational transitions in GroEl25 and in protein kinase A.34 Due to the above-discussed structural variability exhibited by NFA, and in the absence of a known three-dimensional structure, we worked under the assumption that the structures resulting from the removal of the respective nucleotide from the X-ray structures of G-ATP and G-ADP are the most likely populated conformations of the NFA. This assumption is supported by our results, detailed below, which show the presence of a unique mechanical unfolding pathway and very similar critical forces when starting from either of these two conformations. Unfolding in the Absence of the Nucleotide. We found a unique unfolding pathway in the absence of the nucleotide, depicted in the force extension curve (FEC) from Figure 2A for G-ADP and Figure 3A for G-ATP. For G-ADP the unfolding peaks present critical forces in the 200-260 pN range, while G-ATP is somewhat more flexible responding to 150-210 pN

Mechanics of Actin in Different Nucleotide States

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Figure 3. Global unfolding pathway for G-ATP. Similar to Figure 2 for G-ADP, we represent the (A) FEC and (B) force versus time. In (A), the black curve corresponds to the simulations in the absence of ATP, while the green dotted line corresponds to the simulations with ATP. (C) ∆θ values, (D) velocity (x component), and (E) tension are plotted separately for each of the three peaks.

forces. The other difference between the two G-actin states is in the first unfolding peak: while in G-ADP P1 is well-defined, in G-ATP we found a plateau instead of a peak. This suggests that, in G-ATP, the unfolding in P1 is noncooperative, while the same process becomes cooperative in G-ADP. To delineate the origin of each unfolding event (peak), in addition to the survey of the configurational state(s) corresponding to each peak, we computed three parameters described in detail in the Methods section. For example, by following the time evolution of ∆θ from Figure 2C for G-ADP, we determined that the unfolding process leading to the formation of peak P1 occurs at the boundary between regions 1C and 3B because of its large negative value of ∆θ. This region consists of the β-strand S18 and the second half of the R-helix H14 (see Table S1 for the definitions of S18 and H14). Interestingly, Figure 2C indicates that other regions of the chain also experience perturbations in their structural arrangement during P1, but these initial perturbations do not lead to subsequent unfolding. This is the case with the N-term part of the chain (1A, 2, and 1B subdomains), which, initially (magenta and green curves) loses contacts at the same pace as the C-term part. The corresponding graph in G-ATP from Figure 3C shows that this time the initial level of perturbation in the N-term part of the chain is even greater than in G-ADP. For the second half of the DB-loop (positions 44-47), the ∆θ values are negligible, while both flanking positions present large ∆θ values. This is indicative of a lack of tension propagation through this part of the chain, which is a loop in G-ATP, in contrast to the ease of propagation of perturbations in G-ADP where this segment is an R-helix for which the ∆θ values are nonzero and equal. Also, there are more native contacts between the N-term (1-30) and the C-term (320-345) regions in G-ADP than in G-ATP. Thus, we

hypothesize that the lack of unfolding cooperativity in P1 for G-ATP results from the reduced contacts between the N-term and the C-term regions and the lack of tension propagation through the DB-loop. Analysis of the velocity of each position in the chain along the direction of the applied force (x) shown in Figure 2D for G-ADP indicates that the left side of R1 moves along the pulling direction (from the C-term to the N-term), while its right side shrinks as a result of a decrease in tension. The transition point is 337 which has constant velocity. Thus, at the end of peak P1 (black curve), H14 is fully unfolded and the 337-372 region is fully stretched. This conclusion is further enforced by the plot of the tension stored in the chain around P1 in Figure 2E because the tension in the left part of R1 increases from 0 to 100 pN, which is indicative of the unfolding of this region. Peak P2 in Figure 2A corresponds to the separation of the small and large domains, while P3 occurs from the breaking of the small domain into subdomains. As seen in Figure 2C, the separation between the small and the large domains in P2 induces substantial structural perturbations in distant regions of the molecule. The only other detectable peak, P6 (Figure S1), corresponds to the separation of the large domain into two subdomains, 3A and 3B+4 (subdomains 3B and 4) which differ from the structural subdomains present in the PDB structure. No other unfolding events that appear in our simulations are going to be experimentally detectable as, with the exception of P6, after peak P3, in excess of 50% of hydrophobic residues in each subdomain are exposed to the solvent and the lifetime of any other state than the fully unfolded one would be too short for experimental detection.21,22 In summary, the unfolding of G-ADP along the global reaction coordinate corresponding to its end-to-end distance proceeds through three intermediates

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Lee et al. TABLE 1: Extension Stiffness (kstiff) and the First Rupture Force (F1st) for G-ADP and G-ATPa kstiff (pN/nm) G-ADP G-ATP

AA AM AAM AA AM AAM

521 252 462 404 204 354

( ( ( ( ( (

33 24 38 66 28 52

(611 (313 (535 (568 (269 (451

( ( ( ( ( (

F1st (pN) 120) 99) 133) 98) 63) 87)

748 520 702 668 558 743

( ( ( ( ( (

26 17 28 30 16 36

(753 (586 (768 (633 (713 (803

( ( ( ( ( (

32) 65) 55) 51) 94) 42)

a AA, AM, and AAM represent the actin-actin, actin-myosin, and actin-actin-myosin unfolding scenarios, respectively. The stiffness was obtained by linearly fitting the initial period from 0 to 1 ms in the FECs from all the 24 trajectories. The first set of numbers represent those extracted from the normal pulling, while the values in the parentheses correspond to the reversal pulling.

Figure 4. New global unfolding pathways for (A) G-ADP and (B) G-ATP from the simulations in the presence of the nucleotide. In (A) the structural snapshot corresponding to peak P2 is shown, and in (B) the snapshot corresponding to the unique unfolding peak, P1, is depicted. This now represents the major unfolding pathway for G-ATP in the presence of the nucleotide.

representing the unraveling of the C-term end of the chain, the rupture of the interface between the small and the large domains, and the further separation of the small domains into its two subdomains. The major difference between the two nucleotide states is that, in the G-ATP case, the initial unfolding event at the C-term end of the chain does not give rise to an unfolding intermediate. Unfolding in the Presence of the Nucleotide. The presence of the nucleotide results in multiple unfolding scenarios: two for G-ADP and three for G-ATP. In G-ADP, 10 trajectories (83%) follow the same pathway as in the absence of the nucleotide from Figure 2A (compare the thick green dotted curve for simulations with the nucleotide with the black curve corresponding to the simulations in the absence of the nucleotide). However, the corresponding FEC (green dotted curve in Figure 2A) shows that P1 and P2 are much more pronounced than in the absence of the nucleotide corresponding now to rupture forces of 250 pN and, respectively, 330 pN. As a result, peaks P2 and P3 from above are now part of a single broad and tall peak. In the remaining two trajectories (17%), G-ADP unfolds according to a different pathway depicted in Figure 4A: while P1 corresponds to the same unfolding event as in the major pathway, P2 results from the unfolding of the large domain without initially separating from the small domain. The last detectable peak along this trajectory, at an end-to-end distance of ∼85 nm, corresponds to peak P3 from the major pathway. In the G-ATP simulations, two trajectories (17%) and four trajectories (33%) follow the major and, respectively, the minor pathways from the G-ADP case. Importantly, in the G-ATP case, the FEC of the major pathway from G-ADP in the presence of the nucleotide is substantially different from the one discussed above. Namely, P1 is now a high peak (force ∼280 pN) and P2 and P3 are completely merged into one tall peak (see green dotted curve in Figure 3A). So, in the presence of the nucleotide, this pathway presents two intermediates, one corresponding to the cooperative unfolding of the C-term region of the chain and the second one to the rupture of the interface between the small and the large domains accompanied by the separation of the small domain into two subdomains. Even more surprisingly, in

G-ATP, 50% of trajectories follow an entirely new pathway (see Figure 4B) according to which the first unfolding event (peak P1 at f ∼ 270 pN) now corresponds to the unraveling of the chain from its N-terminal end. The only other experimentally detectable peak along this pathway corresponds to peak P6 from above, i.e., to the separation of the large domain into two subdomains. Thus, the presence of the nucleotide leads to the stabilization of intermediates resulting in a multitude of unfolding pathways. We found this to be particularly true in G-ATP which exhibits a dramatic shift in the pathway population compared with the simulations in the absence of the nucleotide. This behavior results from the larger number of contacts between ATP and actin than between ADP and actin and the fact that the presence of the ATP induces the DB-loop to transmit tension (this time, only position 47 has a vanishing ∆θ). In conclusion, the major effects of the nucleotide are that it induces cooperativity in the mechanical unfolding of G-actin, it facilitates tension propagation through the DB-loop in the ATP state, and it increases the resistance of the chain to rupture. Unfolding of G-actin in Filaments. Previous studies have shown that proteins behave anisotropically under force.35 We expect that this is especially true in actin because, in contrast to other globular proteins, the choice of the direction of application of a pulling force can be directly related to its functional roles. That is, in addition to the application of the force at the ends of the chain, there are at least two other force directions which are crucial for the role of actin in filamentous form. As discussed in the Introduction, these are the direction of the longitudinal axis of F-actin and the direction of the actomyosin bond(s). Thus, to probe the degree of mechanical rigidity for actin in its functional forms, we conducted pulling experiments along these additional directions. In a recent MD study of F-actin in the two nucleotide states, Voth and collaborators found that the major effects of the conformational transition of the DB-loop from the loop state in F-ATP to the R-helix state in F-ADP are to disrupt the nonbonded contacts between the DB-loop and the plug-in loop (positions 264-271) from neighboring actin monomers.36 Thus, for our analysis of the behavior of actin monomers in F-actin, we focused on the set of contact pairs shared by the two nucleotide states of the filament. The resulting stiffness and first rupture force values from all the G-ADP and G-ATP simulations are in Table 1. Actin-Actin Interaction. We investigated the response of G-ADP to a force applied along the longitudinal direction of F-actin, i.e., at the interface between neighboring actin molecules in the filament. Starting from the list of residues that are in contact between actin monomers in F-actin,9 we selected the most solvent-exposed positions (see Figure 1), and we applied the force at the pointed end interface, while positions at the

Mechanics of Actin in Different Nucleotide States

Figure 5. Unfolding pathway for G-ADP under a force applied along the actin-actin interaction interface in the filament. In the simulation, the residues at the bottom (barbed end) are fixed while the residues at the top (pointed end) are pulled. The chosen positions are described in Figure 1. (A) FEC and (B) force versus time. The structures corresponding to the two experimentally detectable peaks, P1 and P2, are shown in the right panel. (C) Overlap function change in each peak. The pulled and fixed residues are marked by arrows and squares, respectively, right over the residue number.

barbed end interface were kept fixed (see Figure 5). We found a unique unfolding pathway with two peaks in the FEC (Figure 5). As depicted in Figure 5C, P1 results from the extension of the entire subdomain 4, while P2 is due to the extension of subdomains 1A, 2, and 1B. Both peaks correspond to forces that far exceed the critical forces during the global unfolding of G-actin (∼700-850 pN) indicating that the molecule is far more rigid along the F-actin axis. Analysis of the time evolution of the ∆θ values (Figure 5C) shows that the unfolding of subdomain 4 from peak P1 is very localized. However, the events leading to the formation of peak P2 are accompanied by substantial perturbations in the 3B and 1C regions of the molecule. The corresponding investigation for G-ATP revealed that the unfolding process is very similar to the one in G-ADP (see below Figure 8A-C). Differences between the behavior of the two G-actin states appear in the value of the rupture force which is lower in G-ATP (∼650 pN) and in the fact that the unfolding in peak P2 of G-ATP is very localized. Actin-Myosin Interaction. To investigate the response of G-actin to a force applied along the actin-myosin interface while the monomer is part of the filament, we fixed the positions at the actin-myosin interface and we applied a force on positions at the actin-actin interface toward the pointed end of the filament. All the trajectories show the same unfolding pathway characterized by two peaks in the FEC from Figure 6A for G-ADP and in Figure 8D for G-ATP. Unfolding of subdomain 4 results in the formation of the first peak (P1), while

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Figure 6. Similar to Figure 5, an illustration of the unfolding pathway for G-ADP under a force applied along the bonds from the actin-myosin interaction surface in F-actin.

peak P2 corresponds to the unraveling of the R-helices from subdomain 3. While the P1 unfolding process resembles closely the first unfolding step in the actin-actin pulling simulations, the unfolding in P2 is completely different because this time the small domain does not unravel. Since position 25 is fixed and the region between residues 25 and 40 is already stretched during the initial (harmonic) part of the trajectory, the ∆θ values corresponding to the small domain (including 1A, 1B, 1C, and 2) are negligible for peak P2 (Figure 6C and Figure 8F), signaling that the unfolding along the actin-myosin direction is a highly localized process. We note that the stiffness (Table 1) is much smaller than in the actin-actin case, indicating that G-actin is more flexible along the actin-myosin interaction interface than along the actin-actin interaction surface, although in the both cases the first rupture event occurs in the same region of the chain. Actin-Actin-Myosin Interaction. Another force application scenario for an actin molecule when part of the filament is for actin to experience pulling forces along the actin-actin and the actin-myosin interfaces simultaneously.20 Upon pulling actin at the positions along the pointed end interface, while keeping fixed the positions at the barbed-end interface and at the actin-myosin interface, we found only one unfolding pathway in all our simulations. The corresponding FEC depicted in Figure 7A for G-ADP (Figure 8G for G-ATP) indicates that, unlike the unraveling along the actin-actin and the actin-myosin directions, the current unfolding process does not involve any intermediates because only one force peak, P1, is detectable. The part of the molecule that unfolds to give rise to this peak

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Lee et al. pN/nm), while for the reversal pulling they are large (99-133 pN/nm). A similar trend is found in G-ATP (the normal pulling standard deviations are 28-66 pN/nm, while the reversal pulling ones are 63-98 pN/nm). Moreover, in the G-ATP case the most dramatic change induced by the reversal of the pulling direction is the 30% increase in the value of the stiffness compared with the normal pulling case. Thus, G-ATP exhibits unfolding directionality when pulled along the actin-myosin interface which is reminiscent of the recently found behavior of a component of the sarcomere Z-disk, the titin-telethonin complex.37 Conclusions

Figure 7. Unfolding pathway for the pulling of G-ADP along both the actin-actin and the actin-myosin bonds. In this set of simulations, the residues at the bottom (both actin-actin and actin-myosin contacts) are fixed, while the residues at the top are pulled. (A) FEC and (B) time dependent force change. The structural snapshot corresponding to the unfolding event in each peak is drawn on the right. (C) ∆θ values for each peak.

is subdomain 4, similar to the first unfolding event in both the actin-actin and the actin-myosin cases. The lack of a secondary force peak is due to the fact that the contacts with myosin prevent the stretching of subdomain 2 and the contacts with neighboring actin molecules prevent, for the most part, the stretching of subdomain 3. The extension stiffness resulting from our trajectories is 462 ( 38 pN/nm for G-ADP (354 ( 52 pN/ nm for G-ATP), and it lies in between the values obtained in the actin-actin and the actin-myosin cases. Similar to the pulling at the ends of the G-actin molecule, we ran actin stretching simulations along the actin-actin and the actin-myosin directions in the presence of the nucleotide (ATP or ADP). However, in these cases, the presence of the nucleotide did not result in changes in the unfolding of the molecule. Reversal Pulling on Actin Monomers in F-actin. The actin filament has orientation, possessing a barbed and a pointed end. Thus, because we are interested in the mechanical response of actin monomers when part of the filament, we also simulated the pulling of G-actin along the longitudinal axis of the filament but in the opposite direction from the one above, i.e., from the pointed end to the barbed end. The resulting values for the stiffness and first rupture force are reported in Table 1. While in G-ADP for the reversal pulling the average values of the stiffness are slightly higher than for the normal pulling, the most noticeable difference is in the standard deviation. Namely, for the normal pulling the standard deviations are modest (24-38

An important finding resulting from studying the response of F-actin to forces applied along its longitudinal axis is that, at an extension of 0.5% for a 1 µm long filament, 62% of the data correspond to a stiffness of 34.5 pN/nm, while 35% of the data points lead to only 5.8 pN/nm stiffness.19 Using our extracted stiffness values of the response of G-ADP to a force applied along the same direction as in Liu et al.’s experiments19 of kG ) 521 (611) pN/nm, we estimated the stiffness coefficient of a 1 µm long filament as kF ) 5.7-6.7 pN/nm. We used the equation kF ) kG/(LF/LG) × 2, where LG ) 5.5 nm and LF ) 1 µm. The multiplication by 2 is due to the presence of 2 parallel strands in the ribbon state of F-actin envisioned by Schutt et al.12 Our estimated stiffness resembles closely the 5.8 pN/nm from Liu et al.’s experiments. Because in our simulations we did not consider the twisted structure of F-actin, the agreement between our estimate and the experimental measurement enforces the proposal that the reduced stiffness is due to the alternative, ribbonlike structure of F-actin reported by Schutt et al.12 in which the two strands are suggested to be untwisted while still maintaining the main actin-actin intersubunit contacts from the Holmes model.9 Another important comparison between our results and the existing experimental results is in the value of the critical unfolding force for actin monomers in a filament. In the Liu and Pollack study,19 forces up to ∼280 pN (maximal physiological tension) do not lead to F-actin rupture and, in the 50-230 pN regime, the length-tension relation is usually linear. However, in some experimental traces, a nonlinear behavior, characterized by sudden changes of the length-tension graph, appears at forces exceeding 150 pN. In our simulations, we measured forces of ∼750 pN (650 pN) for the first unfolding event in G-ADP (G-ATP) under conditions of the experiment.19 Our cantilever stiffness (k ) 180 pN/nm) and pulling speed (1.9 µm/s) result in a loading rate of 342 000 pN/s. In LOT15,38 experiments, the loading rates are 10-1000 pN/s. Thus, if we extrapolate our unfolding forces to the experimental regime, considering the typical experimental loading rate to be 100 pN/s and a logarithmic dependence of the rupture force on the loading rate,39 i.e., the Bell-Evans model, we get a value of ∼92 (80) pN for the unfolding force of an actin monomer in a singlestranded filament. Considering that F-actin is double stranded, the net force applied on F-actin that leads to the unfolding of a monomer becomes 180 (160) pN, which is well below the actin-actin bond breaking force of 600 pN.20 This coincides with the value at which Liu and Pollack19 reported nonlinearity in the length-tension behavior, strongly suggesting that partial unfolding of actin monomers inside the filament contributes to the experimental behavior. These results are reminiscent of the differences between LOT and AFM experiments. For example, LOT15 and AFM experiments32 performed to study the rupture of the actin-filamin complex lead to seemingly contradictory

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Figure 8. Unfolding pathways of G-ATP when pulled according to the actin-actin, actin-myosin, and actin-actin-myosin scenarios. The left, middle, and right columns are the data from the actin-actin, actin-myosin, and actin-actin-myosin scenarios, respectively. FEC (A, D, G), force versus time (B, E, H), and ∆θ values (C, F, I) are shown.

results. Namely, the extrapolation of the higher loading rate AFM results to the level of the LOT loading rates would result into an unfolding force for filamin of ∼50 pN. However, the LOT experiments only detect unbinding of filamin from F-actin at this force value.15 Further LOT experiments, employing increased loading rates, revealed unfolding of filamin prior to unbinding from F-actin strongly suggesting that the rupture mechanism depends critically on the loading rate: at low loading rates only unbinding takes place, while at high loading rates unfolding precedes unbinding.15,38 Thus, our results indicate that the behavior of F-actin under a force applied along its longitudinal axis is primarily harmonic at modest loading rates (∼up to 200 pN/s) leading directly to filament rupture, while at large loading rates (exceeding 1000 pN/s) it will be nonlinear due to partial unfolding of actin monomers before filament rupture, in agreement with experimental predictions.19 In our simulations targeted at probing the force response of an actin monomer in F-actin, we discovered a high degree of anisotropy manifested through an increased resistance to force along the longitudinal axis of the filament as compared with the actin-myosin direction which is approximately perpendicular to the axis of the filament. Thus, the actin-myosin interaction surface responds faster to force than the actin-actin interaction surface. This result is consistent with the transient character of the actin-myosin interaction versus the more permanent aspect of the actin-actin interaction. Our measured critical unfolding force for G-actin pulled along the actin-myosin interactions from Table 1 is ∼550 pN. If we extrapolate this value to the loading rate used in the LOT experiments that probed the rupture of the actomyosin bonds,14 the resulting force is 95 pN. This value is very similar to the maximal actomyosin bond rupture

force indicating that nature selected similar forces for both unfolding and unbinding. Thus, as pointed out for F-actin-filamin complexes,38 both unfolding and unbinding are important mechanisms for controlling cytoskeletal mechanics. Two factors account for the differential behavior of actin during the normal and the reversal pulling in F-actin. First, due to the nonequilibrium character of mechanical unfolding in the overwhelming majority of AFM and LOT experiments and in simulations, the finite speed of propagation of the force from the application point through the whole structure is reflected in the force-extension curve. For example, in our simulations, in the normal pulling direction the force is applied directly to subdomains 2 and 4, while keeping subdomains 1 and 3 fixed, resulting in a lower stretching stiffness for either of the pulled subdomains than when the force is applied to subdomains 1 and 3 even if subdomains 2 and 4 are unfolding this time as well. This is a consequence of the delay in the propagation of the applied force to the unfolding regions in subdomains 2 and 4. Because in force ramp induced unfolding the force is proportional to time, the time delay leads to an increase in the force and stiffness constant during the reverse pulling case. Second, due to the presence of contacts between subdomains 1 and 3, versus the absence of contacts between subdomains 2 and 4, the normal and the reverse pulling setups are not exactly each others’ counterparts. For example, for the normal actin-actin pulling, because subdomains 2 and 4 do not interact with each other and therefore can unravel independently of each other, the overwhelming majority of trajectories start with the unfolding of subdomain 4 (peak 1 in Figure 5), which is the weakest part of the molecule. Importantly, this unfolding event does not perturb the interface between subdo-

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mains 1 and 3. However, during reverse pulling, because subdomains 2 and 4 are fixed, the fixed positions constrain them to move together and unfolding of any of these two subdomains can only occur by pushing down on subdomains 1 and 3. In more detail, as depicted in Figure S2, the unfolding starting with subdomain 4 results in breaking ∼70% of the contacts between subdomains 1 and 3 (Figure S2(A)). In contrast, when unfolding starts with subdomain 2, only ∼10% of the contacts between subdomains 1 and 3 break (Figure S2(B)). This leads to an increase in the resistance of the molecule to unfolding from subdomain 4 manifested in a dramatic switch in the percentage of trajectories that start unfolding from this subdomain. For G-ADP, 100% of trajectories for normal pulling unfold from subdomain 4, while this pathway is found in 63% of the reverse pulling trajectories. The remaining 37% of trajectories unfold starting from subdomain 2. For G-ATP, while 83% of the normal pulling trajectories unfold from subdomain 4, no reverse pulling trajectory follows this pathway; i.e., 100% of reverse pulling trajectories unravel from subdomain 2. In turn, this switch in the probabilities of the unfolding pathways leads to the increase in the standard deviation of the stiffness. In conclusion, the larger standard deviation in the critical force value for the reversal pulling means more variety among the trajectories compared with the normal pulling case. Thus, the orientation of the filament is not only due to the differential organization of monomers at the two ends but also has a basis in the intrinsic flexibility of the monomers. A wealth of experimental data exists regarding domain flexibility in G-actin (summarized in Figure S3) that can be compared with the order of unfolding in our simulations. For example, Page et al.40 reported the existence of a rigid core in each domain (indicated by the E1 line in Figure S3) while subdomains 2 and 4 are flexible, with one R-helix in subdomain 4 presenting the largest average deviation value among all the secondary structures (E2 line in Figure S3). They also reported that subdomains 3 and 4, unlike subdomains 1 and 2, are not free to rotate independently of one another. In addition, in the Holmes F-actin model,9 subdomain 2 executes a large movement between G-actin and F-actin (E3 line in Figure S3). As presented above, in our simulations of the global unfolding of G-actin, the first unfolding events occur at regions found at the boundary between subdomains 3B and 1C, 1B and 3A, and 2 and 1B (denoted first, second, and third in Figure S3). Because subdomains 1 and 2 detach prior to the separation of subdomains 3 and 4, our results agree with the experimental report that, unlike subdomains 1 and 2, subdomains 3 and 4 are not free to rotate independently. We found that subdomains 2 and 4 unfold without leading to the formation of a peak in our simulations of the global unfolding of G-actin, which can be easily understood in light of the experimental data that these two subdomains are flexible.40 This behavior is further illustrated in our actin simulations in a filament in which, along all the directions of an applied force, the relevant unfolding events occur primarily in subdomain 4. Our simulations in the presence of the nucleotide reveal that only the global unfolding of G-actin is affected by the nucleotide. The main effects are an increase in unfolding cooperativity manifested in higher and fewer peaks in the FECs, stabilization of intermediates to the point of introducing kinetic partitioning for unfolding, stabilization of the small domain which always opens first in the absence of the nucleotide, and, most importantly, emphasizing the difference between G-ATP and G-ADP. These results offer structural details regarding the proposal of Pollard and collaborators that the bound nucleotide

Lee et al. is not essential for the polymerization of actin, instead being crucial for stabilizing G-actin.33 In addition, our finding that the presence of the nucleotide does not induce any changes into the mechanical behavior of actin monomers when part of the filament is in perfect agreement with the experimental result that F-actin is stable even in the absence of the nucleotide.33 Our result that G-ATP is more flexible than G-ADP in all the forced-unfolding scenarios adds to the growing body of evidence that the increased stiffness of F-ATP compared with F-ADP41 is likely to be due to the behavior of the bonds at the actin-actin interface rather than to the behavior of the actin monomers themselves.36,42 Acknowledgment. This work was partially supported in part by the National Science Foundation grant MCB-0845002. Supporting Information Available: Additional details regarding the model energy function and the secondary structure elements of the two nucleotide states of actin; also, figures depicting additional intermediates populated during the global unfolding of G-actin, the pathways present during the reverse unfolding of G-ADP along the actin-actin interface, and the comparison between our simulated rupture regions with the experimentally measured domain flexibility. This material is available free of charge via the Internet at http://pubs.acs.org/. References and Notes (1) Mofrad, M. R. K.; Kamm, R. D. Cytoskeletal Mechanics: Models and Measurements; Cambridge University Press: Cambridge, MA, 2007. (2) Carballido-Lopez, R. Microbiol. Mol. Biol. ReV. 2006, 70, 888– 909. (3) Doherty, G. J.; McMahon, H. T. Annu. ReV. Biophys. 2008, 37, 65–95. (4) Kabsch, W.; Mannherz, H. G.; Suck, D.; Pai, E. F.; Holmes, K. C. Nature 1990, 347, 37–44. (5) Otterbein, L. R.; Graceffa, P.; Dominguez, R. Science 2001, 293, 708–711. (6) Reisler, E.; Egelman, E. H. J. Biol. Chem. 2007, 282, 36133–36137. (7) Belmont, L. D.; Orlova, A.; Drubin, D. G.; Egelman, E. H. Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 29–34. (8) Egelman, E. H. J. Muscle Res. Cell Motil. 1985, 6, 129–151. (9) Holmes, K. C.; Popp, D.; Gebhard, W.; Kabsch, W. Nature 1990, 347, 44–49. (10) Orlova, A.; Prochniewicz, E.; Egelman, E. H. J. Mol. Biol. 1995, 245, 598–607. (11) Galkin, V. E.; Orlova, A.; Lukoyanova, N.; Wriggers, W.; Egelman, E. H. J. Cell Biol. 2001, 153, 75–86. (12) Schutt, C. E.; Lindberg, U. Proc. Natl. Acad. Sci. U.S.A. 1992, 89, 319–323. (13) Huxley, H. E. Science 1969, 164, 1356–1366. (14) Guo, B.; Guilford, W. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 9844–9849. (15) Ferrer, J. M.; Lee, H.; Chen, J.; Pelz, B.; Nakamura, F.; Kamm, R. D.; Lang, M. J. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 9221–9226. (16) Kojima, H.; Ishijima, A.; Yanagida, T. Proc. Natl. Acad. Sci. U.S.A. 1994, 91, 12962–12966. (17) Fujiwara, S.; Plazanet, M.; Matsumoto, F.; Oda, T. Biophys. J. 2008, 94, 4880–4889. (18) Evans, E. A.; Calderwood, D. A. Science 2007, 316, 1148–1154. (19) Liu, X.; Pollack, G. H. Biophys. J. 2002, 83, 2705–2715. (20) Tsuda, Y.; Yasutake, H.; Ishijima, A.; Yanagida, T. Proc. Natl. Acad. Sci. U.S.A. 1996, 93, 12937–12942. (21) Hyeon, C.; Dima, R. I.; Thirumalai, D. Structure 2006, 14, 1633– 1645. (22) Mickler, M.; Dima, R. I.; Dietz, H.; Hyeon, C.; Thirumalai, D.; Rief, M. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 20268–20273. (23) Dima, R. I.; Joshi, H. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 15743–15748. (24) Hyeon, C.; Onuchic, J. N. Proc. Natl. Acad. Sci. U.S.A. 2007, 104, 17382–17387. (25) Hyeon, C.; Lorimer, G. H.; Thirumalai, D. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 18939–18944. (26) Pfaendtner, J.; Lyman, E.; Pollard, T. D.; Voth, G. A. J. Mol. Biol. 2010, 396, 252–263.

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