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37), while the strongly bound state time, t s , determines the velocity at which movement occurs (16 18). Thus, the elevated ATPase is not a reflection of a change in t s and thus is not relevant to velocity considerations. Importantly, we can conclude that none of the mutated myosins have been hampered in their ability to hydrolyze ATP, which we take as an indication that the mutations did not have generally deleterious effects on the myosin. The mutant and wild-type myosins were then subjected to an in vitro sliding filament motility assay (32, 33, 41). The sliding velocities increased with increasing number of light chain binding sites for wild-type and mutant myosins (Fig. 4 Left), consistent with the swinging neck-lever model. Most significantly, the 2xELCBS mutant form moved faster than the wild-type myosin (the range was 21 33% faster in four experiments), and the most straightforward interpretation of making the enzyme move faster is that the neck behaves like a lever arm. If one makes the further (undoubtedly oversimplified) assumptions that, first, all of the stroke derives from the movement of a relatively rigid lever arm that rotates about some fulcrum point, and, second, that the 2xELCBS mutant has a lever arm that is elongated by the linear insertion of one extra ELC binding domain, then one can extrapolate the points in Fig. 4 Left back to zero lever arm length. This ``fulcrum point'' in the structure is shown by the red dot in Fig. 1, and the sliding velocities are now proportional to the length of lever arm when the same set of data is replotted against the length measured from this putative fulcrum point (Fig. 4 Right). Milligan and colleagues (13, 14) provided complementary evidence for a fulcrum point in this region by comparing helically reconstituted actomyosin structures between the ADP-bound and rigor (no nucleotide) states. Interestingly, this putative fulcrum point is very near to what has been called the reactive thiol region in skeletal muscle myosin, which undergoes dramatic changes in structure during the ATPase cycle (38, 39). There are other, albeit more complicated, explanations for the velocity results shown in Fig. 4. For example, it is possible that there is another minor but independent mechanism to generate movement, such as a change in binding angle between actin and the myosin head at the actin myosin binding face, as has been long postulated (40). Thus, the fulcrum point of the swinging motion of the lever arm may be to the right of the red dot in Fig. 1 Upper, closer to the ELC binding domain. Another possibility is that t s is linearly related to the number of light chain binding sites, and this contributes to the changes in velocity since v d t s . This possibility can be tested in the future. For example, the feedback-enhanced laser trap assay (6) can be used to determine t s directly as a measure of the duration time of the myosin displacement. In summary, the linear relationship between sliding velocity and the neck length strongly supports the swinging neck-lever model. It is particularly noteworthy that we were able to create a mutant motor that moves faster than the wild type in a way the model predicts. An interesting point to consider (see Appendix) is that this lever arm of the S1 will have a certain bending stiffness and may be the structural equivalent of the elastic element that has long been known to be part of the actin myosin system, as elucidated by tension-transient experiments using muscle fibers (40). APPENDIX: Is the lever arm of myosin a molecular elastic element? J ONATHON H OWARD * AND J AMES A. S PUDICH *Department of Physiology and Biophysics, University of Washington, Seattle, WA 98195-7290; and Department of Biochemistry, Stanford University School of Medicine, Stanford, CA 94305 The classic experiments of Huxley and Simmons (40) defined an elastic element in muscle that has been attributed to the myosin molecule. They measured the tension drop when a stimulated muscle held at a fixed length is rapidly shortened through a small distance and found that a component of the system behaves like a linear spring. Such an elastic element is fundamental to force generation because it allows strain to develop within the motor prior to movement of the cargo; relief of this strain then drives the relative displacement of the motor and the track along which it moves. While diagrammatic representations often show this elastic spring as being part of the myosin rod beyond the light-chain binding domain of the molecule, we consider here that the elastic element is the light-chain binding domain itself and may account quantitatively for the cross-bridge stiffness observed in muscle experiments. The head domain of myosin, commonly called subfragment 1 or S1, is the only part of the myosin molecule required for movement in vitro (33) and for production of force similar to that seen in intact muscle (9, 42). An unusual structural feature of S1 is the 8-nm-long light-chain binding domain that is at F IG . 4. Sliding velocities of mutant and wild-type myosins. Bars indicate standard deviation. (Left) Sliding velocity as a function of the number of light chain binding sites. These data are representative of four independent experiments with different preparations of proteins over a period of a year. (Right) The same set of data is replotted against the length of the putative lever arm. The lever arm lengths for wild type and each mutant were measured from the fulcrum point shown as a red dot in Fig. 1 to the 90 bend at the C terminus of the long heavy chain -helix (shown in violet in Fig. 1) that makes up the neck domain--these lengths are 3-D computer-graphic measurements based on the crystal structure (2). 4462 Biophysics: Uyeda et al. Proc. Natl. Acad. Sci. USA 93 (1996) the C terminus of the S1 moiety (2, 3). It has been suggested that this region of the myosin head could serve as a lever arm to amplify smaller conformational changes elsewhere in the motor domain (5, 13 15, 19 21, 43, and this paper). Indeed, fluorescence polarization experiments have shown that the light-chain binding region changes orientation by a minimum of 3 relative to the filament axis in muscle in response to quick length changes and during the transitions between states of the cross-bridge cycle associated with active force production (15). While this angle change would appear to be too small to account for a unitary displacement of several nanometers (6), it is a minimum value for technical reasons, and two other complementary studies strongly support the lever arm hypothesis. First, electron microscopy of decorated actin filaments showed that a rotation of the light-chain binding domain through 23 accounts well for the two different conformations that S1 adopts depending on whether ADP is bound at the active site; the difference could account for as much as 3.5 nm of movement of the far C terminus of S1 (13, 14). Second, this paper used molecular genetic approaches to shorten, and importantly, to elongate the lever arm and demonstrate a linear relationship between the lever arm length and the velocity with which the myosin moves in vitro. We argue here that the lever arm could also be the elastic element referred to above, since the elasticity of the light-chain binding domain is expected to be comparable to that measured in the rapid shortening experiments. Furthermore, the nature of the light chains and their interaction with the 8-nm-long -helical stretch of the heavy chain at the C terminus of S1 may determine the spring constant of the light-chain binding domain and therefore affect the force that the molecular motor can produce. Consider a very simple model of the lever arm as a clamped beam of length L and flexural rigidity (the resistance to bending forces) equal to EI. If a transverse force F is applied at the free end, then this end will move through a distance x such that: F 3EI L 3 x (44). In other words, the beam has a stiffness 3EI L 3 3kTL p L 3 , where L p EI kT is the persistence length (45), k is the Boltzmann constant, and T is temperature. The light-chain binding domain has a length of 8 nm. It seems reasonable to consider that the lever arm, which has two light chains wrapped around the long -helix, has a rigidity similar to that of a coiled coil, which has two -helices wrapped around each other. The persistence length of a coiled coil is 100 nm (J.H., unpublished measurements derived from the coiled-coil myosin rod domain). For comparison, the L p of DNA, which has a dimension similar to these two protein structures, is 50 nm (46). Substituting L 8 nm, L p 100 nm, and kT 4 pN nm, we obtain 2 pN nm. On the other hand, the rapid shortening experiments indicate a muscle stiffness equal to 0.27 pN nm when normalized to the total number of myosin heads per half sarcomere [a shortening of 6 nm per half sarcomere drops the force from 1.6 pN per head to zero (47)]. Since only about half the compliance in muscle resides in the myosin heads and the other half resides in the actin filaments (e.g., see ref. 48), this value for the stiffness needs to be doubled to 0.5 pN nm per myosin head. If only a quarter of the myosin heads were attached during isometric contraction (duty ratio of 0.25; refs. 6 and 16), then the stiffness per attached head would be 2 pN nm, equal to that derived above! Clearly, this equality could be fortuitous given the large uncertainties in both the experimental and theoretical stiffnesses. The assumptions made, however, are not unreasonable, and the calculations do show that it is quite plausible that the elasticity of myosin resides within the light-chain binding domain, which corresponds to the lever arm. Indeed, one expects the light-chain binding domain to contribute some compliance to the myosin molecule. There are three interesting predictions that follow from the hypothesis that the lever arm is the elastic element. (i) The motor force should be inversely proportional to the square of the length of the lever arm. To see this, let the force-generating conformational change be a rotation, through an angle , of the insertion point of the lever into the motor domain. Thus, in the absence of a restoring force, the tip of the lever arm (the C terminus of S1) would move through a distance x L , On the other hand if there were a restoring force (F max ) that prevented the C terminus of the lever arm from moving, then F max 3kTL p L 3 x 3kTL p L 3 L 3kTL p L 2 . Since the angular change is independent of the length of the lever arm, it follows that the maximum force is proportional to L 2 . On the other hand, if the lever arm acted as a rigid rod and the elasticity were due to a pivotal spring (49) located at the point of insertion into the motor domain, then the maximum force would depend on L 1 . (ii) The maximum work should be inversely proportional to the lever length (L 1 ). To see this, note that if the restoring force (F o ) is less than the maximum force, then the tip will move through a distance x F o (the working stroke), and the amount of work done will equal W F o x F o F o x F o2 . The maximum work occurs when F o F max 2, and W max F max x 4 3 4 kTL p 2 L. That is, the maximum work is inversely proportional to the lever length. This leads to a paradox at the shortest lever arm lengths where the work might get so large as to exceed the theoretical maximum force. Presumably a motor with a very short lever arm will fail at high forces (the rotation through would not take place). (iii) The maximum force will depend on the stiffness of the lever arm. For example, if the link between the ELC and the catalytic domain of S1 and or the link between the ELC and RLC domains were flexible, we would expect a smaller stiffness and thus a smaller force. Thus, the properties of the light chains may affect the flexural rigidity of the lever arm, thereby regulating the force produced by a particular myosin isoform. The establishment of laser trap technologies to measure directly the force and work produced by a single myosin molecule (6, 50) and systems that allow genetic engineering of the molecular motor myosin to produce myosins with different lever arm lengths (this paper) should allow critical testing of whether force production is inversely proportional to the lever arm length squared, as predicted by the elastic lever arm model. The same approaches should allow testing of the concept that the nature of the light chains modulates the spring constant of the elastic lever arm and therefore the amount of force that can be produced by different isoforms of myosin, Biophysics: Uyeda et al. Proc. Natl. Acad. Sci. USA 93 (1996) 4463 which have different light chains. Indeed, even skeletal myosin binds two alternate forms of RLC, for reasons that have been unclear. Moreover, myosin light chains are altered by posttranslational modifications, such as phosphorylation in the case of smooth muscle myosin and Dictyostelium myosin (for a review, see ref. 51) and binding of Ca 2 in the case of scallop myosin (52). One goal then is to use molecular genetics and laser trap technology to gain detailed molecular information about the physiological relevance of altered myosin types. We thank members of the Spudich laboratory for stimulating discussions and advice, and K. Zaita for technical assistance. 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