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Force Generation and Shortening in Skeletal Muscle

Richard J. Podolsky, Mark Schoenberg

10.1002/cphy.cp100106

Source: Supplement 27: Handbook of Physiology, Skeletal Muscle

Originally published: 1983

Published online: January 2011

Full Article on Wiley Online Library



Abstract

The sections in this article are:

1 Experimental Preparations
2 States of the Fiber
3 Properties of Activated Fibers
3.1 Force‐Velocity Relation
3.2 Viscoelastic Theory
3.3 Fenn Effect
3.4 Quick Releases
3.5 Discovery of Sliding Filaments and Cross Bridges
3.6 Force‐Length Relation
3.7 Kinetic Properties of Cross Bridges
3.8 Cross‐Bridge Model of A. F. Huxley
3.9 High‐Time‐Resolution Mechanical Measurements
3.10 Force Steps
3.11 Length Steps
4 Muscle Biochemistry
4.1 Other Experiments: Some Puzzling Results
4.2 Recent Biochemical Studies
4.3 Hill Formalism
4.4 Application of Hill Formalism
5 Current Frontiers
6 Conclusion
Figure 1. Figure 1.

Double array of myofilaments in a sarcomere. Array of thick filaments in center of sarcomere forms the A band. Thin filaments extend into the thick‐filament array from the dense Z line. The part of the thin‐filament array that does not interdigitate with thick filaments forms the I band. The part of the thick‐filament array that does not interdigitate with thin filaments forms the H zone. × 67,000. [From Huxley 36.]
Figure 2. Figure 2.

Length‐tension relation and filament dispositions at various sarcomere lengths. Upper diagram: length‐tension relation for frog muscle. Middle diagram: sarcomere—a, thick‐filament length; b, thinfilament length; c, length of central bare region of thick filament; Z, width of the Z band. Lower diagrams: filament dispositions at various striation spacings. Number at left of each diagram corresponds to numbered parts of length‐tension relation. Note that 1,2,3, and 5 are close to discontinuities in length‐tension relation. [From Gordon et al. 18.]
Figure 3. Figure 3.

Force‐pCa relation for skinned frog muscle fiber. [From Hellam and Podolsky 23.]
Figure 4. Figure 4.

Contraction kinetics of a skinned frog muscle fiber at different free‐calcium concentrations. Top trace, displacement; middle trace, force; bottom trace, zero force. Fiber is fully activated at pCa 5 and half‐activated at pCa 6.4. Dashed line on displacement trace is back extrapolation of steady motion. The 2 displacement traces, which are juxtaposed in inset, are almost the same. [From Gulati and Podolsky 20.]
Figure 5. Figure 5.

Rate functions for cross‐bridge interaction in the 1957 model of A. F. Huxley. Here f is the rate function for cross‐bridge formation, g is the rate function for cross‐bridge dissociation, x is the distance between the actual position of the actin site and the actin position at which the cross bridge exerts zero force, and h is the value of x at which f reaches a maximum value.

From Huxley 30, © 1957, with permission from Pergamon Press, Ltd
Figure 6. Figure 6.

Cross‐bridge distributions at different steady speeds. Note that area of distribution function (and therefore instantaneous number of cross bridges) decreases as contraction speed increases.

From Huxley 30, © 1957, with permission from Pergamon Press, Ltd
Figure 7. Figure 7.

Cross‐bridge mechanism in which force is generated by a very rapid configurational change. The S1 moiety of the myosin molecule is attached to the thick filament at M through a flexible region that can be extended to length l0 by thermal energy. It is assumed that S1 attaches to an actin site A in one configuration (solid line) and then very rapidly and irreversibly changes to another configuration (broken line) that can stretch the flexible region beyond l0 and produce force. A: change in state stretches the flexible region to length l and force is proportional to l‐l0. B: flexible region is not completely extended when S1 attached to A, and stretched length of flexible region is less than l. C: stretched length of flexible region is l0 and force is zero. D: change in configuration of S1 moiety does not stretch flexible region beyond l0 and force is zero. If S1 remains attached to A, flexible region can be stretched by motion of the thin filament; negative force is produced when x/h < −0.8. E: force function for this mechanism. Note that stiffness is not a measure of number of attached cross bridges in this mechanism, because cross bridges in flat region of force curve do not show stiffness.
Figure 8. Figure 8.

Response of frog muscle fibers to sudden changes in load at 3°C. Lower traces, force records; upper traces, displacement. a, Isometric tension; b, record after sudden change in load, slow time scale; c‐k, changes in load, rapid time scale. Force step as fraction of P0 is given along side force trace. Arrows mark points at which actual motion intersects back extrapolation of steady motion. Note that force is steady ∼2–6 ms after force step, but displacement transient lasts 10–40 ms. Displacement scale bar is 4 nm per half sarcomere in panels c through g and 8 nm per half sarcomere in the other panels. [From Civan and Podolsky 3.]
Figure 9. Figure 9.

Rate functions for cross‐bridge interaction in the model of Podolsky and Nolan. Upper panel: f is rate function for cross‐bridge formation; g is rate function for cross‐bridge dissociation. Lower panel: k is force function for cross bridge.

From Podolsky and Nolan 52, © 1971, reprinted by permission of Prentice‐Hall, Inc., Englewood Cliffs, NJ
Figure 10. Figure 10.

Cross‐bridge distributions in forcestep experiments. Top panel shows distribution during isometric contraction. When load is suddenly changed to P < P0, isometric distribution shifts to the left as shown in lower panels. Steady‐state distribution for each load is given by solid line. Note that area of steady‐state distribution function (and therefore instantaneous number of cross bridges) increases as load decreases and contraction speed increases.

From Podolsky and Nolan 52, © 1971, reprinted by permission of Prentice‐Hall, Inc., Englewood Cliffs, NJ
Figure 11. Figure 11.

Transient changes in tension exerted by a stimulated frog muscle fiber when suddenly stretched (top panel) or shortened (middle panels). Bottom panel shows typical release. Number next to each record shows size of corresponding length change per half sarcomere (in nm). [From Huxley 31.]
Figure 12. Figure 12.

Relation between velocity transient and tension transient. Phase 1 represents an instantaneous elasticity. Phase 2 is a rapid shortening in velocity transient or a rapid tension recovery in tension transient. Phase 3 is a marked reduction of either shortening speed or tension recovery. Phase 4 is steady shortening in the velocity transient or a very slow recovery of tension in the tension transient. Note that duration of phases is not the same in the two types of transient. Phases 1 and 2 of the tension transient are shown on a faster time scale in Figure 11. [From Huxley 31.]
Figure 13. Figure 13.

Behavior of the cross‐bridge head and compliance (spring) in the model of Huxley and Simmons during tension development and during an isometric transient. There are 3 attached states: state 1 (A), state 2(B and C), and state 3(D). Step length change of muscle occurs between B and C.

Adapted from Huxley and Simmons 35
Figure 14. Figure 14.

Effect of step amplitude size on T1 (extreme tension) and T2 (tension approached during rapid recovery phase), both as a fraction of To, which is isometric tension immediately before the step. [From Huxley 31.]
Figure 15. Figure 15.

One possible free‐energy diagram corresponding to the biochemical cycle AMD·Pi AM MT MD·Pi AMD·Pi shown in text. Free‐energy levels of unattached states are independent of x, a measure of strain in an attached cross bridge, more rigorously defined in Cross‐Bridge Model of A. F. Huxley, p. 177. Free‐energy curves of attached states are parabolas. Minimum free energy of AM state is to left of that for state AMD·Pi under the assumption that equilibrium configuration for AM state is more acutely angled than that for AMD·Pi (i.e., equilibrium configuration for AMD·Pi looks like Fig. 13B and AM more like Fig. 13D). Other states, such as M and AMT, are considered unimportant in this simple model.

Adapted from Eisenberg and Hill 10


Figure 1.

Double array of myofilaments in a sarcomere. Array of thick filaments in center of sarcomere forms the A band. Thin filaments extend into the thick‐filament array from the dense Z line. The part of the thin‐filament array that does not interdigitate with thick filaments forms the I band. The part of the thick‐filament array that does not interdigitate with thin filaments forms the H zone. × 67,000. [From Huxley 36.]



Figure 2.

Length‐tension relation and filament dispositions at various sarcomere lengths. Upper diagram: length‐tension relation for frog muscle. Middle diagram: sarcomere—a, thick‐filament length; b, thinfilament length; c, length of central bare region of thick filament; Z, width of the Z band. Lower diagrams: filament dispositions at various striation spacings. Number at left of each diagram corresponds to numbered parts of length‐tension relation. Note that 1,2,3, and 5 are close to discontinuities in length‐tension relation. [From Gordon et al. 18.]



Figure 3.

Force‐pCa relation for skinned frog muscle fiber. [From Hellam and Podolsky 23.]



Figure 4.

Contraction kinetics of a skinned frog muscle fiber at different free‐calcium concentrations. Top trace, displacement; middle trace, force; bottom trace, zero force. Fiber is fully activated at pCa 5 and half‐activated at pCa 6.4. Dashed line on displacement trace is back extrapolation of steady motion. The 2 displacement traces, which are juxtaposed in inset, are almost the same. [From Gulati and Podolsky 20.]



Figure 5.

Rate functions for cross‐bridge interaction in the 1957 model of A. F. Huxley. Here f is the rate function for cross‐bridge formation, g is the rate function for cross‐bridge dissociation, x is the distance between the actual position of the actin site and the actin position at which the cross bridge exerts zero force, and h is the value of x at which f reaches a maximum value.

From Huxley 30, © 1957, with permission from Pergamon Press, Ltd


Figure 6.

Cross‐bridge distributions at different steady speeds. Note that area of distribution function (and therefore instantaneous number of cross bridges) decreases as contraction speed increases.

From Huxley 30, © 1957, with permission from Pergamon Press, Ltd


Figure 7.

Cross‐bridge mechanism in which force is generated by a very rapid configurational change. The S1 moiety of the myosin molecule is attached to the thick filament at M through a flexible region that can be extended to length l0 by thermal energy. It is assumed that S1 attaches to an actin site A in one configuration (solid line) and then very rapidly and irreversibly changes to another configuration (broken line) that can stretch the flexible region beyond l0 and produce force. A: change in state stretches the flexible region to length l and force is proportional to l‐l0. B: flexible region is not completely extended when S1 attached to A, and stretched length of flexible region is less than l. C: stretched length of flexible region is l0 and force is zero. D: change in configuration of S1 moiety does not stretch flexible region beyond l0 and force is zero. If S1 remains attached to A, flexible region can be stretched by motion of the thin filament; negative force is produced when x/h < −0.8. E: force function for this mechanism. Note that stiffness is not a measure of number of attached cross bridges in this mechanism, because cross bridges in flat region of force curve do not show stiffness.



Figure 8.

Response of frog muscle fibers to sudden changes in load at 3°C. Lower traces, force records; upper traces, displacement. a, Isometric tension; b, record after sudden change in load, slow time scale; c‐k, changes in load, rapid time scale. Force step as fraction of P0 is given along side force trace. Arrows mark points at which actual motion intersects back extrapolation of steady motion. Note that force is steady ∼2–6 ms after force step, but displacement transient lasts 10–40 ms. Displacement scale bar is 4 nm per half sarcomere in panels c through g and 8 nm per half sarcomere in the other panels. [From Civan and Podolsky 3.]



Figure 9.

Rate functions for cross‐bridge interaction in the model of Podolsky and Nolan. Upper panel: f is rate function for cross‐bridge formation; g is rate function for cross‐bridge dissociation. Lower panel: k is force function for cross bridge.

From Podolsky and Nolan 52, © 1971, reprinted by permission of Prentice‐Hall, Inc., Englewood Cliffs, NJ


Figure 10.

Cross‐bridge distributions in forcestep experiments. Top panel shows distribution during isometric contraction. When load is suddenly changed to P < P0, isometric distribution shifts to the left as shown in lower panels. Steady‐state distribution for each load is given by solid line. Note that area of steady‐state distribution function (and therefore instantaneous number of cross bridges) increases as load decreases and contraction speed increases.

From Podolsky and Nolan 52, © 1971, reprinted by permission of Prentice‐Hall, Inc., Englewood Cliffs, NJ


Figure 11.

Transient changes in tension exerted by a stimulated frog muscle fiber when suddenly stretched (top panel) or shortened (middle panels). Bottom panel shows typical release. Number next to each record shows size of corresponding length change per half sarcomere (in nm). [From Huxley 31.]



Figure 12.

Relation between velocity transient and tension transient. Phase 1 represents an instantaneous elasticity. Phase 2 is a rapid shortening in velocity transient or a rapid tension recovery in tension transient. Phase 3 is a marked reduction of either shortening speed or tension recovery. Phase 4 is steady shortening in the velocity transient or a very slow recovery of tension in the tension transient. Note that duration of phases is not the same in the two types of transient. Phases 1 and 2 of the tension transient are shown on a faster time scale in Figure 11. [From Huxley 31.]



Figure 13.

Behavior of the cross‐bridge head and compliance (spring) in the model of Huxley and Simmons during tension development and during an isometric transient. There are 3 attached states: state 1 (A), state 2(B and C), and state 3(D). Step length change of muscle occurs between B and C.

Adapted from Huxley and Simmons 35


Figure 14.

Effect of step amplitude size on T1 (extreme tension) and T2 (tension approached during rapid recovery phase), both as a fraction of To, which is isometric tension immediately before the step. [From Huxley 31.]



Figure 15.

One possible free‐energy diagram corresponding to the biochemical cycle AMD·Pi AM MT MD·Pi AMD·Pi shown in text. Free‐energy levels of unattached states are independent of x, a measure of strain in an attached cross bridge, more rigorously defined in Cross‐Bridge Model of A. F. Huxley, p. 177. Free‐energy curves of attached states are parabolas. Minimum free energy of AM state is to left of that for state AMD·Pi under the assumption that equilibrium configuration for AM state is more acutely angled than that for AMD·Pi (i.e., equilibrium configuration for AMD·Pi looks like Fig. 13B and AM more like Fig. 13D). Other states, such as M and AMT, are considered unimportant in this simple model.

Adapted from Eisenberg and Hill 10
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Article Title: Force Generation and Shortening in Skeletal Muscle
 

How to Cite

Richard J. Podolsky, Mark Schoenberg. Force Generation and Shortening in Skeletal Muscle. Compr Physiol 2011, Supplement 27: Handbook of Physiology, Skeletal Muscle: 173-187. First published in print 1983. doi: 10.1002/cphy.cp100106