- Email: [email protected]
A giant step for myosin
JAMES R. SELLERS AND EARL HOMSHER
MACROMOLECULAR STRUCTURES
A giant step for myosin The ra,ging debate about the step size involved in the myosin/actin motor has been fueled by some more conflicting results. The classical crossbnidge model (Fig. 1, left) for the mechanism by which myosin movesactin filaments suggests that a myosin head, charged with the energy from an ATP molecule, attaches strongly to an actin subunit within the lilament. The myosin then exerts force (transduction) by bending Norrotating, displaces the actin by about lOnm, releases its reaction products, then binds another molecule of A.TP and detaches from the translocated actin Went. The myosin head then ‘recocks’ to its initial position and repeats the process. The myosin heads are thought to ;act asynchronously in a stochastic fashion. The 10 nm displacement or ‘step’ per ATP hydrolysed is inferred from the chord length of the myosin head (2Onm) and is :supported by mechanical studies. This model is analogous to a two-stroke piston engine in which there is a drive stroke and a recovery exhaust stroke. However, the recent development of in vitro assays capable of measuring quantal force and motile events force the re-evaluation of the crossbridge.
There have been many attempts to measure the displacement of actin filaments per ATP hydrolysed, in muscle fibres and in in vitro motility assay systems. Step-size estimations have generally relied on measurements of net distance moved, ATP hydrolysed, and the fraction of crossbridges attached. The results from several sys terns, summarized in Table 1, have yielded a wide range of step-size estimates. Those less than 4Onm per ATP molecule are consistent with the classical model of crossbridge action, whereas those in which the movement exceeds 40 nm per ATP are not. All of these measurements depend crucially on an estimation of the number of attached crossbridges per unit length of actin. Even using similar in vitro motility assays, in which the movement of fluorescently labelled actin filaments over a surface coated with myosin is visualized using video microscopy, two groups have arrived at very different values for the step size [l-3]. This discrepancy is, in part, related to the higher translocation rate observed by one of the groups
Fig. 1. Three cross-bridge mechanisms. Myosin heads are shown projecting from a thick filament and actin monomers are shown as numbered spheres. Dark red myosin heads have just hydrolysed ATP, have maximal free energy content, and are ready to generate force. Green myosin headls are at the end of their working stroke and close to detachment. White myosin heads have released all their free energy and must bind and hydrolyse another ATP to be ready to generate force again. Dragged cross-bridges are shown in blue with extended S-2 portions; they are assumed to have dissipated their free energy. In the large step-size model, the cross-bridges in each panel show a displacement of the thin filament and the concomitant loss of energy derived from the hydrolysis of ATP. The progressive loss of colour represents the incremental loss of free energy from the cross-bridge as it undergoes multiple displacements of actin; between steps 3 and 4 a new ATP molecule is bound and the cycle begins again.
Volume 1
Number 6
1991
347
and also to other possible differences, as Huxley [4].
by
discussed
filaments tend to diffuse rapidly away from the surface if not bound by myosin. This behavior is consistent with solution kinetic results which suggest that myosin spends only about 5% of its cycle time in a strongly bound state. The observation of myosin-mediated motility at this myosin density depends on the inclusion of a viscous polymer, methylcellulose, in the assay medium, which decreases the lateral diffusion of the actin filament and allows it to remain near the surface for short periods of time, even when no myosin heads are bound.
The controversy has been continued by three papers that appeared together in Nature [5-71. Higuchi and Goldman [6] measured the stiffness (a reflection of number of attached crossbridges) and distance shortened by skinned muscle fibres during isotonic shortening following photogeneration of a known amount of ATP. The step size obtained is dependent on the shortening velocity, which is itself a function of the applied load. Estimated step-size ranges from a lower limit of 20nm at intermediate loads to > 40 nm at low loads. Higuchi and Goldman account for the large step size by postulating that, in addition to work-producing crossbridge interactions, crossbridges may attach and be dragged along without producing net work (Fig. 1, center). Such a mechanism would be analogous to a four stroke piston engine. The other two papers in the trilogy circumvent the limitations inherent in the study of the transduction process assayed in systems with a large ensemble of myosins; for example, the behavior of a single muscle fibre represents the concerted action of > 109 myosin molecules. Both Ishijima et al. [7] and Uyeda et al. [ 51 introduce exciting new in vitro methods to examine the mechanical behavior produced by small numbers of working myosin molecules. In so doing, they use analytical approaches that have been previously exploited by electrophysiologists studying the electrical behavior of single membrane channels. However, me conclusions drawn from these two novel approaches concerning the step size and the fraction of time a myosin molecule spends in a strongly attached force-generating state during the ATP hydrolysis cycle (termed the duty ratio) are vety different. Uyeda et al. [5] examine the step-size issue by visualizing me movement of single fluorescently labelled actin filaments over myosin bound to a surface at very low densities, such that the actin filament is in contact with only a few myosin heads. Previous work from this laboratory had shown that under these conditions the actin
Frog Frog
sartorius sartorius
0°C v,,,
PI
OT,
psoas fibre
[61
myofibrils
1101
5°C
[31
22°C 30°C 30°C
Rabbit Skinned Crab
[sl
Motility Moti I ity Motility
assays assays assays
Motility Motility
assays assays
0.5
<510
0.3 v,,,
v,,,
From knowledge of the unitary velocity (0.33 f.un/s> and an assumption that the cycle time of myosin bound to the surface at low dilution is the same as that measured for densely populated surfaces, Uyeda et al. [5] calculate a step size of 5 nm per ATP molecule hydrolysed. Taking the stance of devil’s advocate, they conclude that even when all possible inaccuracies are compounded, the maximal step size is still considerably less
~82
Calculation assumes all crossbridges attached during shortening (dividing total actin length per gram of muscle by total myosin S-l molecules per gram). The value then is portional to the fraction of S-l strongly attached at a given time.
>40 >20
Corrected stiffness
v,,,
7-O”Cvnm 20-c,
Each video frame of a filament’s movement was analysed and the centroid position of the actin filament determined with subpixel accuracy. The displacement of the actin filament was plotted against time and regions in which the actin filament was moving uniformly for at least seven consecutive video frames (200 ms) were selected. Histograms of the velocity distributions of these movements were plotted. where no myosin is bound to the surface, the actin tiaments exhibit Brownian movement along their long axis and the resulting velocity distribution is Gaussian. But when myosin is bound to the surface at low density, there is a peak in the velocity distribution at 0.33 pm/s and sometimes a smaller peak at about twice this value. This result is interpreted as etidence for quantal movement of a&n by myosin. The second peak at about 0.66 mn,/s is expected if two myosin molecules are interacting with the same actin filament. The doubling of the velocity is due to the asynchronous nature of the interaction of the two myosins with actin and to the small fraction of time any given head is actually translocating actin compared to the overall cycle time for ATP hydrolysis.
for fraction of Sl is directly proportional
bound to actin to the fraction
assuming of S-l
muscle bound.
600 123 25 8 ~28 5
See
*Unless otherwise noted, step size, is calculated from the equation, length of actin in assay, V is ATPase ,rate (molecules/second/assay) attached myosin molecules.
reference
for
assumptions
made
in calculation.
Step size =(v~ L)/(V. 1) where v is filament velocity L is and 1 is the minimum filament length between adjacent
@ 1991 Current Biology
than the geometric constraint of 40nm imposed by the size of the myosin head and probably less than 20nm. This approach, unlike (earlier studies of the step size using in vitro motility assays, does not depend directly on a knowledge of the length of the moving actin filament or on measurement of the ATPase activity of the sample under the microscope. In the Ishijima et al. [7’] paper, a single actin filament is attached to a stiff glass micro-needle, calibrated so that its measured displacement can be expressed as an-applied force. The actin lilament is then allowed to interact with a small numbser of myosin molecules attached to a glass surface and the force and frequency of the observed force fluctuations are measured. Using a fast Fourier transform to convert the data from the time to the frequency domain and iassuming a simple ‘on*lY crossbridge model, they evdiuate the kinetics of the force-generating process. Two important generalizations can be made from their results: the force fluctuations observed in their recordings are consistent with the notion that myosin attachment, foace exertion, and detachment are stochastic processes; and the power density spectrum of the force fluctuations are consistent with the known isometric actomyosin ATPasserate. Further interpretation of the data on the basis of a simple ‘on-off model, suggests that in the isometric ATPase cycle the crossbridge stays attached to the thin filament for 30% of the ATPase cycle. In addition, using longer actin filaments or micro-needles of reduced stiness, Ishijima et al. are able to examine the behavior of force as an actin filament is propelled at velocities up to 50% of the maximum. Here they find that the amplitude and frequency of force fluctuations during thin filament translocation are much reduced. These results suggest that during rapid filament sliding, the crossbridge remains attached. and exerting net force for up to 90% of the ATPase cycle. This conclusion is diametrically opposed to the conclusions of Uyeda et al. with regard to both the step-size and the fraction of time the myosin spends in a force-producing state. The results of Higuchi and Goldman [6] are consistent with multiple actomyosin interactions for one ATP molecule, but these interactions could be working or nonworking (dragging>. The conclusion of lshijima et al. fits with their concept that myosin is a motor that &eases its free energy in discrete quanta during interaction with several different actins. According to this view, du.ring rapid shortening the crossbridge attaches to one actin and exerts an amount of force to displace it a short distance then rapidly detaches and reattaches to another actin subunit and displaces it a short distance, and so on (Fig. 1, right). In this case, the myosin motor is analogous to a clock mainspring with an escapement mechanism, allowing the energy from a single ATP molecule to be: parcelled out in small discrete amounts. The energy myosin obtains from hydrolysis of ATP may be transferred to actin, which parcels it out in repeated cycles. This type of mechanism would also be consistent with an ‘apparent’ large step size. Regardless of the model proposed for the crossbridge motor, it is useful to recall a simple thermodynamic constraint that applies to any proposed mechanism. The
Volume 1
Number 6
1991
free energy (that energy which can be converted to useful work) available from the hydrolysis of a single ATP molecule (assuming 100% efficiency) is 8 X lo-20 J/molecule. If the average force exerted on the actin filament by a myosin head as it moves through its power stroke is 1 X lo-lzN/head, then the greatest distance over which it can exert that force must be less than 80 X lo-pm. Longer power strokes require a reduction in the average force exerted per myosin head. Thus, the trilogy, although not resolving the question of crossbridge step-size, has produced new physiological approaches to examining the molecular nature of the motor mechanism and has introduced alternative hypotheses to account for the observed behaviors. The insights from these studies have benefitted from study of other molecular motors such as kinesin and dynein 1111, and should stimulate further such studies. Contrary to what some may believe, the crossbridge mechanism is far from being understood. Acknowledgements: We would like to helpful commentson the manuscript.
thank
Kathleen
Collins
for
References 1.
TOYOSHIMA
YY, KRON SJ, SPUDICH Jk The myosin step size: the unit displacement per ATP hydrolyzed in an in vitm assay. Pm Nati Acad Sci USA 1990, 87:7130-7134. UYEDA TQP, KRON SJ, SPUDICH JA: Myosinstep size:Estimation from slow sliding movement of actin over low densitiesof heavy meromyosin. J MoZ Biol 1990, 214699-710. HARAOA Y, SAKURADA K, AOKI T, THOMAS DD, YANAGIDA T: Mechanochemicalcoupling in actomyosin energy transduction studied by in vitro movement assay.J Mol Biol 1990, 216:4M8. HUXLEY SE: Sliding filaments and molecular motile systems. J Biol Cbem 1990, 265:8347-8350. UYEDA TQP, WARRICK HM, KRON SJ, SPLJDICH JA: Quantized velocities at low myosin densities in an in vitro motility assay. Nature 1991, 352:307-311. HXGUCHI H, GOLDMAN YE: Sliding distance between actin and myosin filaments per ATP molecule hydrolyzed in skinned muscle fibres. Nature 1991, 352:352-354. ISHIJIMA A, DOI T, SAKURADA K, YANAGIDA T: Sub-piconewton force fluctuations of actomyosin in vitro. Nature 1991, 352:301-306. HOMSHER E, IRVING M, WALLNER A: High-energy phosphate metabolism and energy liberation associated with rapid shortening in frog skeletal muscle. J Physiol 1981, 321:423-436. HOMSHER E, YAMADA T, WALUVER A, TSAI J: Energy balance studies in tiog skeletal muscle shortening at one-half maximal velocity. J Gen Pbysid 1984, 84347-359. YANAGIDA T, ARATA T, OOSAWA F: Sliding distance of actin filament induced by a myosin crossbridge during one ATP hydrolysis cycle. Nahcre 1985, 316366369. HOWARD J, HEDSPETH AJ, VALE R: Movement of microtubules by single kinesin molecules.Nature 1989, %2:15&158.
Measurement of
2.
3.
4. 5.
6.
7.
8.
9
10
11
James R. Sellers, Laboratory of Molecular Cardiology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA. Earl Homsher, Department of Physiology, School of Medicine, University of California, Los Angeles, California 90024, USA.
349
MACROMOLECULAR STRUCTURES
A giant step for myosin The ra,ging debate about the step size involved in the myosin/actin motor has been fueled by some more conflicting results. The classical crossbnidge model (Fig. 1, left) for the mechanism by which myosin movesactin filaments suggests that a myosin head, charged with the energy from an ATP molecule, attaches strongly to an actin subunit within the lilament. The myosin then exerts force (transduction) by bending Norrotating, displaces the actin by about lOnm, releases its reaction products, then binds another molecule of A.TP and detaches from the translocated actin Went. The myosin head then ‘recocks’ to its initial position and repeats the process. The myosin heads are thought to ;act asynchronously in a stochastic fashion. The 10 nm displacement or ‘step’ per ATP hydrolysed is inferred from the chord length of the myosin head (2Onm) and is :supported by mechanical studies. This model is analogous to a two-stroke piston engine in which there is a drive stroke and a recovery exhaust stroke. However, the recent development of in vitro assays capable of measuring quantal force and motile events force the re-evaluation of the crossbridge.
There have been many attempts to measure the displacement of actin filaments per ATP hydrolysed, in muscle fibres and in in vitro motility assay systems. Step-size estimations have generally relied on measurements of net distance moved, ATP hydrolysed, and the fraction of crossbridges attached. The results from several sys terns, summarized in Table 1, have yielded a wide range of step-size estimates. Those less than 4Onm per ATP molecule are consistent with the classical model of crossbridge action, whereas those in which the movement exceeds 40 nm per ATP are not. All of these measurements depend crucially on an estimation of the number of attached crossbridges per unit length of actin. Even using similar in vitro motility assays, in which the movement of fluorescently labelled actin filaments over a surface coated with myosin is visualized using video microscopy, two groups have arrived at very different values for the step size [l-3]. This discrepancy is, in part, related to the higher translocation rate observed by one of the groups
Fig. 1. Three cross-bridge mechanisms. Myosin heads are shown projecting from a thick filament and actin monomers are shown as numbered spheres. Dark red myosin heads have just hydrolysed ATP, have maximal free energy content, and are ready to generate force. Green myosin headls are at the end of their working stroke and close to detachment. White myosin heads have released all their free energy and must bind and hydrolyse another ATP to be ready to generate force again. Dragged cross-bridges are shown in blue with extended S-2 portions; they are assumed to have dissipated their free energy. In the large step-size model, the cross-bridges in each panel show a displacement of the thin filament and the concomitant loss of energy derived from the hydrolysis of ATP. The progressive loss of colour represents the incremental loss of free energy from the cross-bridge as it undergoes multiple displacements of actin; between steps 3 and 4 a new ATP molecule is bound and the cycle begins again.
Volume 1
Number 6
1991
347
and also to other possible differences, as Huxley [4].
by
discussed
filaments tend to diffuse rapidly away from the surface if not bound by myosin. This behavior is consistent with solution kinetic results which suggest that myosin spends only about 5% of its cycle time in a strongly bound state. The observation of myosin-mediated motility at this myosin density depends on the inclusion of a viscous polymer, methylcellulose, in the assay medium, which decreases the lateral diffusion of the actin filament and allows it to remain near the surface for short periods of time, even when no myosin heads are bound.
The controversy has been continued by three papers that appeared together in Nature [5-71. Higuchi and Goldman [6] measured the stiffness (a reflection of number of attached crossbridges) and distance shortened by skinned muscle fibres during isotonic shortening following photogeneration of a known amount of ATP. The step size obtained is dependent on the shortening velocity, which is itself a function of the applied load. Estimated step-size ranges from a lower limit of 20nm at intermediate loads to > 40 nm at low loads. Higuchi and Goldman account for the large step size by postulating that, in addition to work-producing crossbridge interactions, crossbridges may attach and be dragged along without producing net work (Fig. 1, center). Such a mechanism would be analogous to a four stroke piston engine. The other two papers in the trilogy circumvent the limitations inherent in the study of the transduction process assayed in systems with a large ensemble of myosins; for example, the behavior of a single muscle fibre represents the concerted action of > 109 myosin molecules. Both Ishijima et al. [7] and Uyeda et al. [ 51 introduce exciting new in vitro methods to examine the mechanical behavior produced by small numbers of working myosin molecules. In so doing, they use analytical approaches that have been previously exploited by electrophysiologists studying the electrical behavior of single membrane channels. However, me conclusions drawn from these two novel approaches concerning the step size and the fraction of time a myosin molecule spends in a strongly attached force-generating state during the ATP hydrolysis cycle (termed the duty ratio) are vety different. Uyeda et al. [5] examine the step-size issue by visualizing me movement of single fluorescently labelled actin filaments over myosin bound to a surface at very low densities, such that the actin filament is in contact with only a few myosin heads. Previous work from this laboratory had shown that under these conditions the actin
Frog Frog
sartorius sartorius
0°C v,,,
PI
OT,
psoas fibre
[61
myofibrils
1101
5°C
[31
22°C 30°C 30°C
Rabbit Skinned Crab
[sl
Motility Moti I ity Motility
assays assays assays
Motility Motility
assays assays
0.5
<510
0.3 v,,,
v,,,
From knowledge of the unitary velocity (0.33 f.un/s> and an assumption that the cycle time of myosin bound to the surface at low dilution is the same as that measured for densely populated surfaces, Uyeda et al. [5] calculate a step size of 5 nm per ATP molecule hydrolysed. Taking the stance of devil’s advocate, they conclude that even when all possible inaccuracies are compounded, the maximal step size is still considerably less
~82
Calculation assumes all crossbridges attached during shortening (dividing total actin length per gram of muscle by total myosin S-l molecules per gram). The value then is portional to the fraction of S-l strongly attached at a given time.
>40 >20
Corrected stiffness
v,,,
7-O”Cvnm 20-c,
Each video frame of a filament’s movement was analysed and the centroid position of the actin filament determined with subpixel accuracy. The displacement of the actin filament was plotted against time and regions in which the actin filament was moving uniformly for at least seven consecutive video frames (200 ms) were selected. Histograms of the velocity distributions of these movements were plotted. where no myosin is bound to the surface, the actin tiaments exhibit Brownian movement along their long axis and the resulting velocity distribution is Gaussian. But when myosin is bound to the surface at low density, there is a peak in the velocity distribution at 0.33 pm/s and sometimes a smaller peak at about twice this value. This result is interpreted as etidence for quantal movement of a&n by myosin. The second peak at about 0.66 mn,/s is expected if two myosin molecules are interacting with the same actin filament. The doubling of the velocity is due to the asynchronous nature of the interaction of the two myosins with actin and to the small fraction of time any given head is actually translocating actin compared to the overall cycle time for ATP hydrolysis.
for fraction of Sl is directly proportional
bound to actin to the fraction
assuming of S-l
muscle bound.
600 123 25 8 ~28 5
See
*Unless otherwise noted, step size, is calculated from the equation, length of actin in assay, V is ATPase ,rate (molecules/second/assay) attached myosin molecules.
reference
for
assumptions
made
in calculation.
Step size =(v~ L)/(V. 1) where v is filament velocity L is and 1 is the minimum filament length between adjacent
@ 1991 Current Biology
than the geometric constraint of 40nm imposed by the size of the myosin head and probably less than 20nm. This approach, unlike (earlier studies of the step size using in vitro motility assays, does not depend directly on a knowledge of the length of the moving actin filament or on measurement of the ATPase activity of the sample under the microscope. In the Ishijima et al. [7’] paper, a single actin filament is attached to a stiff glass micro-needle, calibrated so that its measured displacement can be expressed as an-applied force. The actin lilament is then allowed to interact with a small numbser of myosin molecules attached to a glass surface and the force and frequency of the observed force fluctuations are measured. Using a fast Fourier transform to convert the data from the time to the frequency domain and iassuming a simple ‘on*lY crossbridge model, they evdiuate the kinetics of the force-generating process. Two important generalizations can be made from their results: the force fluctuations observed in their recordings are consistent with the notion that myosin attachment, foace exertion, and detachment are stochastic processes; and the power density spectrum of the force fluctuations are consistent with the known isometric actomyosin ATPasserate. Further interpretation of the data on the basis of a simple ‘on-off model, suggests that in the isometric ATPase cycle the crossbridge stays attached to the thin filament for 30% of the ATPase cycle. In addition, using longer actin filaments or micro-needles of reduced stiness, Ishijima et al. are able to examine the behavior of force as an actin filament is propelled at velocities up to 50% of the maximum. Here they find that the amplitude and frequency of force fluctuations during thin filament translocation are much reduced. These results suggest that during rapid filament sliding, the crossbridge remains attached. and exerting net force for up to 90% of the ATPase cycle. This conclusion is diametrically opposed to the conclusions of Uyeda et al. with regard to both the step-size and the fraction of time the myosin spends in a force-producing state. The results of Higuchi and Goldman [6] are consistent with multiple actomyosin interactions for one ATP molecule, but these interactions could be working or nonworking (dragging>. The conclusion of lshijima et al. fits with their concept that myosin is a motor that &eases its free energy in discrete quanta during interaction with several different actins. According to this view, du.ring rapid shortening the crossbridge attaches to one actin and exerts an amount of force to displace it a short distance then rapidly detaches and reattaches to another actin subunit and displaces it a short distance, and so on (Fig. 1, right). In this case, the myosin motor is analogous to a clock mainspring with an escapement mechanism, allowing the energy from a single ATP molecule to be: parcelled out in small discrete amounts. The energy myosin obtains from hydrolysis of ATP may be transferred to actin, which parcels it out in repeated cycles. This type of mechanism would also be consistent with an ‘apparent’ large step size. Regardless of the model proposed for the crossbridge motor, it is useful to recall a simple thermodynamic constraint that applies to any proposed mechanism. The
Volume 1
Number 6
1991
free energy (that energy which can be converted to useful work) available from the hydrolysis of a single ATP molecule (assuming 100% efficiency) is 8 X lo-20 J/molecule. If the average force exerted on the actin filament by a myosin head as it moves through its power stroke is 1 X lo-lzN/head, then the greatest distance over which it can exert that force must be less than 80 X lo-pm. Longer power strokes require a reduction in the average force exerted per myosin head. Thus, the trilogy, although not resolving the question of crossbridge step-size, has produced new physiological approaches to examining the molecular nature of the motor mechanism and has introduced alternative hypotheses to account for the observed behaviors. The insights from these studies have benefitted from study of other molecular motors such as kinesin and dynein 1111, and should stimulate further such studies. Contrary to what some may believe, the crossbridge mechanism is far from being understood. Acknowledgements: We would like to helpful commentson the manuscript.
thank
Kathleen
Collins
for
References 1.
TOYOSHIMA
YY, KRON SJ, SPUDICH Jk The myosin step size: the unit displacement per ATP hydrolyzed in an in vitm assay. Pm Nati Acad Sci USA 1990, 87:7130-7134. UYEDA TQP, KRON SJ, SPUDICH JA: Myosinstep size:Estimation from slow sliding movement of actin over low densitiesof heavy meromyosin. J MoZ Biol 1990, 214699-710. HARAOA Y, SAKURADA K, AOKI T, THOMAS DD, YANAGIDA T: Mechanochemicalcoupling in actomyosin energy transduction studied by in vitro movement assay.J Mol Biol 1990, 216:4M8. HUXLEY SE: Sliding filaments and molecular motile systems. J Biol Cbem 1990, 265:8347-8350. UYEDA TQP, WARRICK HM, KRON SJ, SPLJDICH JA: Quantized velocities at low myosin densities in an in vitro motility assay. Nature 1991, 352:307-311. HXGUCHI H, GOLDMAN YE: Sliding distance between actin and myosin filaments per ATP molecule hydrolyzed in skinned muscle fibres. Nature 1991, 352:352-354. ISHIJIMA A, DOI T, SAKURADA K, YANAGIDA T: Sub-piconewton force fluctuations of actomyosin in vitro. Nature 1991, 352:301-306. HOMSHER E, IRVING M, WALLNER A: High-energy phosphate metabolism and energy liberation associated with rapid shortening in frog skeletal muscle. J Physiol 1981, 321:423-436. HOMSHER E, YAMADA T, WALUVER A, TSAI J: Energy balance studies in tiog skeletal muscle shortening at one-half maximal velocity. J Gen Pbysid 1984, 84347-359. YANAGIDA T, ARATA T, OOSAWA F: Sliding distance of actin filament induced by a myosin crossbridge during one ATP hydrolysis cycle. Nahcre 1985, 316366369. HOWARD J, HEDSPETH AJ, VALE R: Movement of microtubules by single kinesin molecules.Nature 1989, %2:15&158.
Measurement of
2.
3.
4. 5.
6.
7.
8.
9
10
11
James R. Sellers, Laboratory of Molecular Cardiology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA. Earl Homsher, Department of Physiology, School of Medicine, University of California, Los Angeles, California 90024, USA.
349