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Proc Natl Acad Sci U S A. Jul 31, 2007; 104(31): 12714–12719.
Published online Jul 18, 2007. doi:  10.1073/pnas.0705525104
PMCID: PMC1924791
Biochemistry

A closer look at energy transduction in muscle

Abstract

Muscular force is the sum of unitary force interactions generated as filaments of myosins move forcibly along parallel filaments of actins, understanding that the free energy required comes from myosin-catalyzed ATP hydrolysis. Using results from conventional biochemistry, our own mutational studies, and diffraction images from others, we attempt, in molecular detail, an account of a unitary interaction, i.e., what happens after a traveling myosin head, bearing an ADP-Pi, reaches the next station of an actin filament in its path. We first construct a reasonable model of the myosin head and actin regions that meet to form the “weakly bound state”. Separately, we consider Holmes' model of the rigor state [Holmes, K. C., Angert, I., Kull, F. J., Jahn, W. & Schröder, R. R. (2003) Nature 425, 423–427], supplemented with several heretofore missing residues, thus realizing the “strongly bound state.” Comparing states suggests how influences initiated at the interface travel elsewhere in myosin to discharge various functions, including striking the actins. Overall, state change seems to occur by attachment of a hydrophobic triplet (Trp-546, Phe-547, and Pro-548) of myosin to an actin conduit with a hydrophobic guiding rail (Ile-341, Ile-345, Leu-349, and Phe-352) and the subsequent linear movement of the triplet along the rail.

Keywords: actin, ATPase, mutation, myosin

Here, we attempt a molecular account of the central interactions that occur when muscle contracts or sustains tension. Because of a peculiar structural organization of muscle, the contractile apparatus can be thought of as effectively a linear filament of myosin molecules forcibly advancing along a parallel filament of actin molecules, the process being thermodynamically paid for by losing free energy of myosin-bound ATP hydrolysis (1). In this sense, contraction is an instance of transducing chemical (free) energy into mechanical work. For our purposes, however, it is simpler to consider our task to be explaining how a traveling myosin head, bearing a partly hydrolyzed ATP, on reaching interaction distance to an actin pair, fastens to it, first weakly and later strongly, and then, how it, in a remarkable cooperation with the actins, casts off the terminal phosphate of ATP and delivers a mechanical impulse to the actins.

The account that follows is put together by using reports from many laboratories. These are of three general kinds, conventional biochemical [e.g., Scheme 1,§ showing the time-dependence of forming complexes of myosin and actin (24)]; mutational [e.g., recent works identifying myosin surface loops engaged in complexing with actin (5, 6)]; and x-ray diffraction [e.g., studies of Rayment (710), of Cohen (11), and of their pioneering associates]. Application of diffraction techniques has dramatically improved resolution and has shown that a globular head of myosin has specialized “organs,” like an enzyme pocket in which to conduct ATP hydrolysis, a long, stiff α-helix (“relay helix”) to transmit linear force, a converter to turn it into a rotation, and a lever arm to deliver a mechanical impulse to (at the time attached) actins (Fig. 1). In addition, from fitting crystal structures of actin and the myosin head to the 3D structure reconstructed from cryoEM pictures of actin filaments decorated with S1 (an isolated single myosin head), Rayment et al. (7) have suggested that ionic and hydrophobic residues, which are possibly involved in actin binding, are localized at one end of the myosin head, which is far from either the enzyme pocket or the converter (Fig. 1). At the end of the head, the so-called “actin-binding” cleft separates the 50-kDa domain into two parts, named the upper and lower subdomains, both of which are involved in actin binding (7, 12). Because the enzyme pocket was connected to the apex of the cleft, they proposed that actin binding causes the cleft closure, resulting in opening the enzyme pocket and accelerating product releases. However, the precise mechanism is not yet clear, because of limited information on the weakly bound complex, which is initially formed when a traveling myosin head encounters two actins. Recently, many functional tests have been carried out with expressed myosin mutants at sites thought from crystallography to be a patch for binding actins and demonstrated that some residues are mainly engaged in the formation of the weakly bound complex, whereas other residues are mainly engaged in the transition from the weakly-to-strongly bound complex (Table 1). Here, based on knowledge from these tests, we construct a reasonable model of the myosin and actin regions that meet to form weak binding. Comparing our model with a rigor complex model (12), we suggest how influences initiated at the actin–myosin interface travel elsewhere in myosin to discharge various functions, including cleft closure, Pi release, and a mechanical impulse.

Fig. 1.
Specialized “organs” of myosin. The N-terminal 25-kDa (residues 2–202), the upper 50-kDa (207–468), the lower 50-kDa (469–651), and the C-terminal 20-kDa (652–791) segments of the myosin motor domain heavy ...
Table 1.
Functional tests of myosins mutated at sites thought to be a patch for actin binding

Results and Discussion

Modeling of the Weakly Bound Complex of Fibrous Actin (F-Actin) and M.ADP.Pi.

A model of the weakly bound state to be constructed must have some properties like those of its predecessor, some properties that draw it to both members of the complex, and some properties that move it toward its successor. We assume that, on entry, the myosin active site continues to be posthydrolytic and that complex formation is mainly driven by the relatively long-range electrostatic attractions between myosin and the two actins. To form such a model of the weakly bound complex, we use the crystal structure of a Dictyostelium myosin motor domain complexed with MgADP.VO4, which has been proposed to be an analog of the transient state or the posthydrolytic state by Smith and Rayment (10), and dock it to an atomic model of F-actin. As shown in a stereoview of Fig. 2, four positively charged segments of myosin fit well spatially to four negatively charged segments of the two actins, respectively; Lys-652 and Lys-653 of myosin fit to Asp-24 and Asp-25 of the first actin, Arg-530 of myosin to the negatively charged cluster between Asp-1 and Glu-4 (Residues 1, 2, and 3 are missing in the crystal structure of rabbit skeletal actin) of the first actin, Lys-573 of myosin to Glu-99 and Glu-100 of the second actin, and Lys-576 and Lys-578 of myosin to Glu-93 of the second actin. This is consistent with previous studies using a zero-length cross-linker that bridges a carboxylic group and lysine (16, 17). In these studies, a myosin head was cross-linked to two distinct actins at its lower 50-kDa subdomain and at its C-terminal 20-kDa domain. In our model, Asp-374 at the so-called “loop 4” of myosin also fits well to Lys-326 of the first actin. Many recent kinetic studies with actin mutants (1820) or myosin mutants (5, 6, 21, 22) also show that the foregoing residues are involved in forming the weakly bound complex.

Fig. 2.
Stereoview of the weakly bound AM.ADP.Pi complex. The same colors are used for segments of the myosin heavy chain as in Fig. 1, whereas the first actin and the second actin are colored cyan and dark green, respectively. The direction of the pointed end ...

Interestingly, our model suggests that before cleft closure, both Trp-546 and Phe-547 in the hydrophobic triplet of myosin are already close to Ile-345 and Leu-349 of the first actin, although a surface loop bearing Pro-534 and Pro-535 (“proline-rich loop”) is not as yet close to either Leu-349 or Phe-352 of the first actin. In this early stage, Val-409 and Gly-410 at the cardiomyopathy loop of myosin are also close to Pro-332, Pro-333, and Glu-334 of the first actin, but this loop seems to move freely to either side on the actin surface. Therefore, we speculate that the myosin head in this complex does not yet completely orient on the actin filament and that this complex can easily dissociate into actin and M.ADP.Pi.

Involvement of Four Surface Loops in the Transition from the Weakly-to-Strongly Bound State.

Functional tests of mutants suggest that in contrast to the early stage, four surface loops of myosin are involved in the later Pi-leaving stage of the actin-activated ATPase reaction (Table 1). One loop bears a hydrophobic triplet of residues, the second is the proline-rich loop, the third is the loop 2, and the fourth is the cardiomyopathy loop. Because the fluorescence of F-actin (whose Cys-374 is labeled with pyrene-iodoacetamide) is quenched by ≈ 80% on complexing with wild-type myosin (23), measurements of pyrene–actin fluorescence have been often used to detect formation of a rigor complex. In an immediately preceding paper (6), we reported that triplet-compromised mutants (W546A, F547A, and P548A) had a reduced extent of fluorescence quenching when complexed with pyrene-labeled F-actin, whereas the maximum extents of quenching by double-headed myosin fragments (HMMs) mutated at the C terminus of loop 2 or the cardiomyopathy loop were identical to that obtained with wild-type HMM. From this result and data listed in Table 1, we conclude that, although all three loops work together in cleft closure and actin activation, the triplet-bearing loop is somehow different from two other loops in the route by which it communicates with its specific target elsewhere in myosin. As described below, we also think that the proline-rich loop contact with the first actin is engaged in closing the cleft.

Comparison Between Two Complex Models.

To know what happens at the actin–myosin interface when the weakly bound state converts into the strongly bound state, we compare our weakly bound complex model with the acto-S1 rigor complex model published by Holmes et al. (12), by superimposing their actins with ours. The myosin head has rotated upward (toward the first actin), suggesting that its binding with the first actin is strengthened (arrow a in Fig. 3), whereas that with the second actin is weakened (arrow b in Fig. 3). This is consistent with our previous results with HMMs mutated lysines of interest here into alanines, suggesting that two lysines (Lys-652 and Lys-653) at the C terminus of loop 2 are involved either in the weakly bound AM.ADP.Pi-forming stage or in the later Pi-releasing stage and that two lysines (Lys-576 and Lys-578) at the second actin-binding loop are also involved in the former stage but not in the latter stage (Table 1).

Fig. 3.
Comparison between myosin heads in our weakly bound complex model (colors are same as those in Fig. 1) and in the rigor complex model (cyan) reported by Holmes et al. (12). Actins of two models are superimposed, and movements of the myosin head are shown ...

To deduce the role of Lys-652 and Lys-653 more precisely, we must know their exact locations in the rigor complex. In Holmes' rigor complex model (12); however, the entire loop 2 is missing, so we cannot use it to find the location of the two lysines. We supplement his model with 9 aa residues including these lysines, using the crystal structure of Dictyostelium myosin motor domain with MgADP.VO4 (10). We do this by superimposing their connecting helices and β-sheet strands (Fig. 4A). The distances of these lysines to Asp-24 or Asp-25 of the first actin (Lys-652 α-carbon to Asp-24 α-carbon, 4.8 Å and Lys-653 α-carbon to Asp-25 α-carbon, 6.4 Å) are now closer than those in the weakly bound state (5.4 and 6.5 Å), suggesting that electrostatic interactions between these charged residues may have important roles different from those functioned in the weakly bound complex. Lys-652 and Lys-653 are, in one direction, connected to the third strand of the seven-stranded β-sheet via a helix named “HW” by Coureux et al. (24); in another direction, they reach a part (a segment from Pro-604 to Val-628) of the upper 50-kDa subdomain, via a loop called a “strut” by Sutoh (25). Therefore, it is natural to assume that the contact of the C terminus of loop 2 with the first actin (a in Fig. 4A) is very important in positioning the backbone β-sheet, on which both the upper 50-kDa subdomain and the N-terminal 25-kDa domain are carried. In the rigor state, the cardiomyopathy loop, which has moved freely toward either side in the weakly bound state, is caught by a dead-end surface or “ditch” (surrounded by residues Ala-26, Pro-27, Ala-29, Val-30, Tyr-337, and Tyr-338) of the first actin (b in Fig. 4A). So, this loop can no longer move freely on the actin surface. In fact, the Holmes' model shows an overlap of masses around the contact of the cardiomyopathy loop of myosin and the first actin (12). We conclude that the rigor myosin head, particularly the upper 50-kDa subdomain and the N-terminal 25-kDa domain, orients at a specific angle to the actin filament by making use of the two anchors described above. We also conclude that this stereospecific attachment is necessary before both actin activation and delivery of the mechanical impulse, because the mutation of Lys-652 or Lys-653, or of the cardiomyopathy loop (Ile-407, Asp-412, or Val-414), into an alanine significantly reduces actin-activated ATPase and in vitro motility (6).

Fig. 4.
The rigor complex of acto-S1. Structures shown in A and B are derived from the same structure reported by Holmes et al. (12). Segments of the myosin heavy chain and the first actin are colored the same as in Fig. 1 or or2,2, but the second actin ...

A Driving Force for the Movement of the Lower 50-kDa Subdomain.

To close the actin-binding cleft, the lower 50-kDa subdomain must move differently from the upper 50-kDa subdomain or the N-terminal 25-kDa domain. What force causes the lower subdomain to move so? From previous results that mutations of the hydrophobic triplet most remarkably weakened the affinity of HMM for F-actin (6), we assume that, upon cleft closure, the strongest contact with the first actin is that of the triplet-bearing loop. Residues between Lys-336 and Phe-352 of actin form a surface α-helix (Fig. 4A), and among them, residues Ile-341, Ile-345, Leu-349, and Phe-352 are exposed on the binding interface for myosin (Fig. 4B). These four residues, properly aligned, form a “conduit” along which the hydrophobic triplet of myosin moves, the side chains of the residues form a guiding rail that preserves direction. We also assume that the movement along the conduit occurs when the cleft closes. In Holmes' rigor model, this α-helix is aligned antiparallel to the α-helix of Ile-515 to Cys-545 (adjacent to the triplet Trp-546–Phe-547–Pro-548) of myosin, and there are two bridges, with mainly hydrophobic interactions, between the two helices. Trp-546 and Phe-547 of the triplet contact the hydrophobic conduit of the first actin, just as in the weakly bound complex (a in Fig. 4B). But in the rigor complex, they hold on to a node between Ile-341 and Ile-345** of the conduit but not to the node between Ile-345 and Leu-349. Thus, the attached triplet linearly slides by one turn along the axis of the α-helix of actin when the complex converts from the weakly into the strongly bound state. From these observations, we think that the approach of the triplet of myosin to the conduit of actin, and its slide along the conduit, triggers several important movements in the myosin head. These movements close the cleft, resulting in Pi release and a mechanical impulse. This explains why triplet-compromised mutations cause serious damage in both actin activation and motility (5, 6).

The proline-rich loop of smooth muscle or Dictyostelium myosin, composed of residues between Glu-529 and Gly-536, projects from the center of a long α-helix composed of residues Ile-515 to Cys-545 of the myosin (10, 11). Because Holmes' rigor model used skeletal muscle S1 as the binding partner of actins, Thr-532–Asn-533–Pro-534–Pro-535 were substituted by only a methionine (12). To compare Holmes' model with ours, we supplement his model with six residues in the proline-rich loop using the same Dictyostelium myosin structure (10), superimposing the connecting α-helices. Pro-534 and Pro-535 in this loop, just like Met-530 of skeletal muscle S1, fit well to Leu-349 and Phe-352 at the end of the hydrophobic conduit of the first actin (b in Fig. 4B). This hydrophobic interaction network has not yet appeared in the weakly bound complex, so we speculate that the new formation of these hydrophobic interactions moves the triplet along the conduit of the first actin, leading finally to stabilizing the actin–myosin interaction. Our view agrees well with various proposals (7, 27, 28), namely that hydrophobic interaction networks at the actin–myosin interface expand during the weak-to-strong conversion. Previously, we reported that Vmax values of smooth muscle mutants at Thr-532–Asn-533–Pro-534–Pro-535 substituted by one methionine or one lysine were ≈ 2-fold greater or 1/2 of that of the wild-type, respectively (5). So, we suggest that this proline-rich loop is important for the rate of cleft closure (and thus the rate of Pi release), because this loop has an important role in forming the second hydrophobic interaction network with the first actin. In the rigor complex, Arg-530 of myosin, a part of the proline-rich loop, is rather far from Glu-4 of the first actin (although they, behind the proline-rich loop, are not seen in Fig. 4B); nevertheless, they may electrostatically interact with each other, if the side chain of Arg-530 is twisted, or if missing N-terminal residues (Asp-1, Glu-2, and Asp-3) are added to Glu-4 of the first actin. Because this arginine has already made contact with N-terminal negatively charged residues of the first actin in the early, weakly bound state (Fig. 2), this flexible bridge may assist the proline-rich loop to approach the end of the conduit of the attached actin.

How Do Events Initiated at the Interface Transmit Their Influences to the Cleft, the Pocket, and the Lever Arm?

It is widely believed that the mechanical impulse to actins is delivered somewhere in the reaction steps from AM.ADP.Pi to the rigor complex (4). Because we have obtained snapshots of the pre- and postpower-stroke states, we now try to infer what occurs in between the two states. Our approach (constructing a weakly bound complex and then comparing it with the rigor complex) per se does not permit time sequencing of events in the interval. However, together with conventional biochemical and mutational studies, we can make a reasonable guess as described in the following. We assume that an attachment of the triplet of myosin to the conduit of actin and the subsequent run of the triplet along the conduit initiate various paths of influence within the myosin head in three distinct stages. In the first stage (step 2 of Fig. 5), the approach of the triplet to the conduit releases the myosin head from the second actin and rotates it toward the first actin (two curved arrows colored black in Fig. 5). The C terminus of loop 2 keeps contact with the first actin. The cardiomyopathy loop begins to move on the actin surface toward the dead end. Then the cleft begins to close, and the bound myosin head orients to a fixed angle to the axis of the actin filament.

Fig. 5.
A serial diagram depicting, step 1, the initial contact between a myosin head and two actins (first, cyan and second, dark green) of a filament; step 2, rotating the myosin head toward the first actin that follows the weak-to-strong transition; step 3, ...

In the second stage (step 3 of Fig. 5), the linear movement of the triplet along the conduit and the formation of the second hydrophobic interaction network force the lower 50-kDa subdomain to rotate (curved arrow colored ocher in Fig. 5). Within the lower subdomain, a four-stranded β-sheet (residues Lys-568 to Lys-571, Glu-580 to Leu-584, Lys-589 to Ala-594, and Glu-473 to Phe-477) behaves as a stiff connector, which is especially important in transmitting displacements to two other functional organs. One is the enzyme pocket, and the other is the converter. The last strand of the four-stranded β-sheet is connected to switch 2 of the enzyme pocket via a short loop, so the twisted rotation of the β-sheet (curved arrow near b of Fig. 4B) moves switch 2 away from the γ-phosphate of ATP, without deforming other parts of the pocket. These movements break the salt bridge between Arg-247 (on switch I) and Glu-470 (on switch II), and open the so-called “back door” to accelerate Pi release (29). The foregoing explains why actin facilitates the rate of Pi release from myosin and also why myosin releases products in a sequence [first Pi and then ADP, even when the myosin head binds F-actin (4)].

The rotational movement of the lower subdomain initiated by the linear movement of the triplet also causes the rotation of the relay helix, but this small rotation does not fully explain the rotation of ≈70° of the converter around the principal axis of the SH1 helix. X-ray crystallographic studies of myosin motor domain complexes with various ATP analogs suggested that opening of switch 2 triggers structural changes of force-transmitting devices between the switch and the converter (9, 11, 30). After these changes, the relay helix, which has been bent at its center when switch 2 has been closed, releases from the seven-stranded β-sheet and straightens. Straightening out of the relay helix enhances the converter rotation by additionally twisting the distal half of the relay helix and the SH1 helix as described in refs. 30 and 31. By this mechanical cascade, the linear movement of the triplet finally converts into a large rotation of the converter and then of the rigidly attached lever arm (curved arrow colored violet in Fig. 5). By the rotation, the lever arm, lying distal to the actin filament, strikes the actins upward (toward the pointed end of the filament) so as to advance myosin toward the next station of the actin filament. The cardiomyopathy loop is also important in delivering the mechanical impulse, as this loop has to be anchored to the first actin during the power stroke. Functional importance of this loop is supported by Sutoh's clever experiments showing that mutagenic deletion of the cardiomyopathy loop abolishes the strong binding between myosin and actin, in actin-activated ATPase and in vitro motility (32).

In the final stage of the power stroke (step 4 of Fig. 5), the upper 50-kDa subdomain largely rotates on an axis passing around strands 5, 6, and 7 of the seven-stranded β-sheet (curved arrow colored red in Fig. 5). We think that this is a result of complicated global changes, within both the upper 50-kDa subdomain and the N-terminal 25-kDa domain; it is also initiated by the linear movement of the triplet. The extreme movement of the relay helix finally results in a distortion of the seven-stranded β-sheet bearing the upper subdomain, because this helix is connected with the first two strands of the β-sheet via hydrophobic bridges. At the same time, however, the movement of the upper subdomain is restricted at two peripheral points (a and b in Fig. 4A) by anchoring to the first actin. As a result, the upper subdomain rolls away from the N-terminal 25-kDa domain. This forces the enzyme pocket to open, and ADP is ready to be released from the pocket. When a new ATP enters, the pocket closes again by forces attracting both sides, and the upper subdomain is returned to its original orientation. Because the cardiomyopathy loop, which has functioned as an anchor during the power stroke, is now detached from the first actin, the myosin head as a whole dissociates from the actins and travels to the next station of the actin filament (step 5 in Fig. 5). During traveling, the conformation of the myosin head returns to the prepower-stroke state, and ATP is hydrolyzed into ADP and Pi. This step becomes the restoring action (“reverse stroke”) necessary for the start of the next power stroke (30). The myosin head bearing ADP-Pi then rebinds to the actin filament, and the cycle starts again (step 1 in Fig. 5).

In summary, the foregoing findings account for the central events of muscle contraction in totally molecular terms, explaining the event cycle inferred by Lymn and Taylor (4) from kinetic observations. Although our reasoning has yet to be confirmed by computer simulations or precise docking programs, we can now plausibly visualize the difference between weakly (prepower-stroke) and strongly (postpower-stroke) -bound states of the contractile system. Comparison between states suggests that in the transition between two bound states, the actin–myosin interface has a large expansion of hydrophobic interaction networks. If this result is interpreted as a large increase in configurational entropy of the system, then it can be considered consistent with the Van't Hoff analyses of force development (28).

Methods

Docking Crystal Structures of Myosin to a 3D Model of F-Actin.

Models of the rigor complex (rigor_complex.pdb), F-actin (3actin.pdb), and the myosin motor domain (motor_domain.pdb), and the crystal structure of Dictyostelium myosin motor domain with MgADP.VO4 (1VOM.pdb) were downloaded from the Protein Database. Docking was performed visually by using RasTop ver. 2.0.0.0, replacing atoms with balls with a Van der Walls radius.

Abbreviation

HMM
double-headed myosin fragment.

Footnotes

The authors declare no conflict of interest.

§A, M, and Pi are actin, a myosin head, and orthophosphate, respectively. Improved resolution indicates that the myosin head interacts with two actins of an actin filament (see below); the 1 : 1 ratio pictured in the scheme should for now be taken as a kinetics approximation. Also to be noted is the distinction between “A” and “A”. This simply reminds one that after a myosin completes an interaction ending with AM, it reacts with a new ATP and is thus freed to travel to the next station, where it forms A.ADP.Pi (A and A, of course, are chemically identical but are distinguishable because of their separate locations on the actin filament).

This loop has been first reported by using cardiac myosin to participate functionally in the actomyosin interaction (13). Recently a study mutating Glu-365 at the loop 4 of Dictyostelium myosin (corresponding to Asp-374 of smooth muscle myosin) into glutamine suggested that this residue has an important role in the actomyosin interaction particularly in the weakly bound state [a late abstract Pos-L96 in the 50th Biophysical Society Annual Meeting (February 22, 2006)].

Although the amino acid sequence of proteins is different in various organisms (or in different major tissues of the same organism), the residues of interest here are highly conserved. Throughout, we use the sequence numeration appropriate for smooth muscle myosin, as extracted from chicken gizzard (14). We note that Arg-247, Asp-374, Val-409, Gly-410, Asp-412, Val-414, Glu-470, Arg-530, Thr-532–Asn-533–Pro-534–Pro-535, Trp-546–Phe-547–Pro-548, Glu-557, Lys-573, Lys-576–Lys-578, and Lys-652–Lys-653 correspond to rabbit skeletal Arg-245, Glu-372, Val-408, Gly-409, Glu-411, Val-413, Glu-468, Lys-528, Met-530, Met-541–Phe-542–Pro-543, Gln-552, Lys-569, Lys-572–Lys-574, and Lys-641–Lys-642, respectively, and to Dictyostelium discoideum Arg-238, Glu-365, Ala-400, Gly-401, Asp-403, Val-405, Glu-459, Arg-520, Gln-521–Pro-522–Pro-523, Val-534–Phe-535–Pro-536, Thr-545, Arg-562, Lys-565, and Lys-622–Lys-623, respectively. We also use the rabbit skeletal sequence numeration for actin (15).

**Yeast actin mutants with alanine replacing Ile-341 or Ile-345 grow normally, although the mutant with alanines or lysines replacing both isoleucines does not survive (26). So we suppose that a remaining isoleucine can still support the linear sliding of the hydrophobic triplet of myosin, although the movement may not be so smooth as that obtained by a pair of isoleucines.

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