Strain Dependence of the Elastic Properties of Force-Producing Cross-Bridges in Rigor Skeletal Muscle

Abstract

Stretch and release experiments carried out on skinned single fibers of frog skeletal muscle under rigor conditions indicate that the elastic properties of the fiber depend on strain. For modulation frequencies below 1000 Hz, the results show an increase in Young's modulus of 20% upon a stretch of 1 nm/half-sarcomere. Remarkably, the strain dependence of Young's modulus decreases at higher frequencies to about 10% upon a 1-nm/half-sarcomere stretch at a modulation frequency of 10 kHz. This suggests that the cause of the effect is less straightforward than originally believed: a simple slackening of the filaments would result in an equally large strain dependence at all frequencies, whereas strain-dependent properties of the actin filaments should show up most clearly at higher frequencies. We believe that the reduction of the strain dependence points to transitions of the cross-bridges between distinct force-producing states. This is consistent with the earlier observation that Young's modulus in rigor increases toward higher frequencies.

Do Actomyosin Single-Molecule Mechanics Data Predict Mechanics of Contracting Muscle?

“…Naturally, such corrections introduce uncertainties, independent of approach used (cf. [ 67 , 167 , 192 , 198 , 220 , 221 , 222 ]). However, interestingly the resulting estimate of Y xb of 5.2 nm in skinned rabbit psoas muscle fibers at 19 °C [ 199 ] is very similar to 4.5 nm calculated from isometric cross-bridge force and stiffness from single-molecule data (see above).…”

“…Despite the above arguments, there is no consensus as to whether the cross-bridge elasticity is indeed non-linear in the muscle cell. Some authors have presented evidence for non-linear elasticity in muscle cells under rigor conditions [ 198 , 222 ] and in active contraction [ 167 , 194 ]. However, it is not clear whether this non-linearity is an artefact, e.g., due to slackening of filaments [ 198 , 245 ], or whether it is attributed to the myofilaments or to the cross-bridges [ 222 ].…”

“…Some authors have presented evidence for non-linear elasticity in muscle cells under rigor conditions [ 198 , 222 ] and in active contraction [ 167 , 194 ]. However, it is not clear whether this non-linearity is an artefact, e.g., due to slackening of filaments [ 198 , 245 ], or whether it is attributed to the myofilaments or to the cross-bridges [ 222 ]. Additionally, some other authors have, on the basis of their experimental findings [ 199 , 245 ], argued strongly against any non-linearity whether in the myofilaments or in the cross-bridges [ 227 , 245 , 246 ].…”

Poorly Understood Aspects of Striated Muscle Contraction

“…An issue that has severely complicated the interpretation of a large number of muscle mechanical studies is the possibility of a nonlinear (non-Hookean) elasticity of the cross-bridges [ 67 , 111 , 237 ] and/or myofilaments [ 33 , 238 – 242 ] or the presence of a time-invariant parallel-elastic element, possibly attributed to a fixed number of cross-bridges [ 243 ]. These issues (reviewed in [ 222 ]) have been considered further recently [ 244 ] but are not yet resolved making it challenging to interpret stiffness data in terms of the number of attached cross-bridges.…”

Nonlinear Actomyosin Elasticity in Muscle?

“…The existence of the elastic elements has been verified in experimental studies from both muscle cells ( 4 , 8 , 9 , 10 , 11 ) and single molecules ( 12 , 13 ), and the elasticity has key roles in recent models of actin-myosin based contractility ( 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 ). Although the cross-bridge elasticity is generally assumed to be linear (Hookean; e.g., ( 3 , 4 , 10 , 22 )), this idea was challenged by experimental results from skinned muscle fibers ( 23 , 24 ) more than 20 years ago. Recently, the idea of nonlinear cross-bridge elasticity was taken up again based on theoretical considerations ( 25 ).…”