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LETTERS |
We would like to thank the authors of the letter to the editor for bringing up some interesting points of discussion, and we will attempt in the following to address some of the more important issues. The general conclusion of the authors of the letter is that nothing new was provided in the Topical Review (Herzog et al. 2006), that many of the cited papers suffer from limits of accuracy and additional obvious problems, and that the whole collection of observations is readily explained by non-uniformities of half-sarcomere lengthening.
In the Topical Review we challenge the view that sarcomere length non-uniformity can readily explain residual force enhancement observed in muscles, single fibres and myofibril preparations. Our arguments centre primarily on the observations that force enhancement is observed on the ascending part of the force–length relationship, can exceed the forces observed for purely isometric contractions on the plateau of the force–length relationship, and occurs in the presence of sarcomere clamping in single fibres (e.g. Edman et al. 1982). Furthermore, we review literature and show recent evidence that sarcomere and half-sarcomere lengths are stable on the descending limb of the force–length relationship (e.g. Rassier et al. 2003; Telley et al. 2006), and demonstrate that in single myofibrils, individual (half-) sarcomeres show force enhancement and (half-) sarcomere lengths are non-uniform prior to and after stretch, and if anything, seem to be more uniform following a stretch compared to before, in agreement with suggestions by Edman et al. (1982) and Telley et al. (2006).
Regarding some specific comments, in the section on ‘Excess tension’ the authors of the letter question the results that ‘tension after stretch can ... exceed the tension in a fixed-end contraction at the initial length ...’ However, as pointed out in the Topical Review, we define residual force enhancement as the increase in steady-state, isometric force following active muscle (fibre, myofibril) stretching compared to the force for a purely isometric contraction at the same length. Therefore, our comparisons are not made with respect to the initial length, but with respect to the length after the stretch. This is the accepted definition for residual force enhancement (Edman et al. 1982), as it does not make sense to expect isometric forces to be the same at different muscle length.
The second point of controversy surrounds whether there is force enhancement on the ascending part of the force–length relationship. Such force enhancement has been observed frequently by groups other than ours (e.g. Abbott & Aubert, 1952; Cook & McDonagh, 1995; and De Ruiter et al. 2000 for whole muscle preparations; and Sugi, 1972 for fibre bundles). In fact, force enhancement on the ascending limb of the force–length relationship has also been observed by proponents of the sarcomere length non-uniformity theory. For example, Fig. 1 was scanned and redrawn from Morgan et al. (2000 – their Fig. 3) where it was stated that they did not observe force enhancement on the ascending part of the force–length curve, while in actuality it was present. For the longest stretches, they observed higher forces on 10 out of 11 conditions (one was the same force with and without stretch), the average force enhancement on the ascending limb of the force–length relationship (estimated from their figure) was 5.7%, and the maximum force enhancement at the plateau was about 15%. Our published values on the same preparation are similar to those shown by Morgan et al. (2000), except that our interpretation was that these results (which were observed consistently) are not caused by noise or inaccuracies in measurements, but are real. With a resolution of our force measurement system of 0.02 N (or about 0.1% of the total soleus force in a cat), we can easily resolve force enhancement of 5–15%. The average force enhancement above plateau force shown in Fig. 3 of our Topical Review was about 6% for 10 fibres. However, the stretch conditions (a 10% stretch from the ascending limb onto the plateau) shown in that figure do not maximize force enhancement. Nevertheless, force enhancement was observed in all 10 fibres used in that experiment (Peterson et al. 2004). Therefore, suggesting that our results might only show force enhancement beyond optimum length, and that force enhancement was ‘insignificantly above optimum tension’ is, at least from a statistical point of view, incorrect. Needless to say, all our equipments can resolve force differences of much smaller than 1%, and therefore consistent force enhancement of 5% or 10% above the plateau forces cannot be dismissed with arguments based on limits of accuracy.
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Arguably, the only preparation in which sarcomere dynamics and force can be studied is a single myofibril, as in this preparation sarcomeres are arranged mechanically in series, and therefore, the forces measured at the end of the myofibril also represent the instantaneous sarcomere forces. In myofibrils (half-) sarcomere length ratios differ prior to and following stretching of myofibrils on the descending limb of the force–length relationship, and there is distinct force enhancement in this preparation, which exceeds the isometric plateau forces. In Fig. 2, we show an active myofibril with six sarcomeres stretched from an initial average sarcomere length of 2.7 µm to a final average length of 3.1 µm. The following observations regarding the sarcomere length non-uniformity theory seem particularly important. First, there is clear force enhancement; second, sarcomere lengths do not become non-uniform during stretch, but they are non-uniform in the initial isometric contraction and they remain non-uniform throughout and after the stretch. Third, the shortest, and according to the non-uniformity theory strongest, sarcomere is stretched the most, and becomes the longest (and thus the weakest) sarcomere and should now be stretched beyond myofilament overlap, whereas, if anything, it is shortening towards the end of the contraction at the expense of the shortest (following stretch) and thus presumably strongest sarcomere. All these observation are utterly incompatible with the sarcomere length non-uniformity theory, and similar results to the one shown here have been published by Rassier et al. (2003) and Telley et al. (2006).
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In the section non-uniformity of sarcomere strength, we are asked to consider three half-sarcomeres (upper panel of Fig. 1 of letter to the editor) of a fibre or myofibril with non-uniform strengths. Based on the reviewer's arguments, the weakest half-sarcomere is then ‘rapidly’ and ‘uncontrollably’ stretched beyond actin–myosin overlap, and will be caught by passive forces at a very long sarcomere length. However, published data (Telley et al. 2006; Rassier et al. 2003), and Fig. 2 shown here, do not support such a scenario. Furthermore, in a myofibril, it is not possible to have three half-sarcomeres with different strength, as suggested by the authors of the letter, as half-sarcomeres in a myofibril are strictly in series and must support the same force. Also, if one argues that the weakest half-sarcomere is stretched, then the remaining two half-sarcomeres (or at least one of them) need to shorten, and therefore the force supported by the shortening sarcomere would be smaller than the isometric force indicated on the force–length graph, because of the force–velocity properties (Hill, 1938) and again the contention of the authors of the letter would not hold.
Regarding the section on damage, it is argued that the increase in passive tension observed in whole muscle following stretch is caused by injury contractures of fibres, and thus is not seen in single fibre preparations. However, passive force enhancement has been reported in single fibres by our group, and even if not specifically pointed out, can be seen in force traces obtained by other groups following deactivation of single fibres (e.g. Edman et al. 1982; their Figs 4 and 6). In addition, if passive force enhancement was caused by damage, one would expect that it could not be abolished instantaneously, as muscle or fibre damage would not be expected to disappear instantaneously. However, passive force enhancement can be completely abolished by simply releasing a muscle to its prestretched length and stretching it back to its original length (e.g. Herzog et al. 2003). Although our group was the first to describe passive force enhancement (Herzog & Leonard, 2002) and study its properties (Herzog et al. 2003), careful evaluation of earlier works shows many beautiful examples of passive force enhancement that were not mentioned by the original authors (e.g. Josephson & Stokes, 1999 – their Fig. 1; Morgan et al. 2000 – their Fig. 5B; Edman et al. 1982 – their Fig. 6).
Regarding stiffness measurements, the authors of the letter to the editor are mistaken when stating that increases in stiffness have not been observed in single fibres for the force enhanced state. For example, we found an increase in stiffness in the force enhanced state of 9% and 14% for stretches of 5% and 10% of fibre length, respectively, in single fibres of the lumbrical muscles of frog (Rassier & Herzog, 2005). These values were comparable, albeit slightly smaller, than the corresponding values of the force enhancement (13 and 18%, respectively). Furthermore, the force–time traces shown in Fig. 1B of the letter to the editor do not show a situation of residual force enhancement for two reasons: first, the contraction is only held for 0.1 s following the stretch, and in view of their previous comments, we are sure that the authors of the letter to the editor would agree that steady-state has not been reached and that force and stiffness values obtained at that instant in time should not be used in this argument when there are perfectly good results available for the steady-state situation. Second, the authors do not compare the stiffness measurements to stiffness obtained at the same length but refer it to the length prior to stretch, which is questionable, especially since the sarcomere lengths prior to and after the stretch are not known. Thus Fig. 1 in the letter to the editor, although depicting a perfectly good experiment, is misleading in the current context where comparisons at the same length and for steady-state situations are required. Finally, it would be fair to acknowledge that the results in Fig. 1 of the letter to the editor do not agree with results found by others. For example, Linari et al. (2000) show an increase in stiffness during and shortly after stretch, in contrast to the results presented by the authors of the letter. Although the authors refer to the data shown as ‘The best measurements of stiffness during a stretch’, that is a rather confident assessment of a result that is in conflict with others in the literature.
We agree with the authors of the letter that it will be difficult to show how stretch might modify actin–myosin interactions, as we have suggested in the Topical Review. However, in his classic article Andrew Huxley (1957) already points out that stretching might affect the kinetics of ATP hydrolysis (although Huxley does not refer to ATP, but rather to a high-energy phosphate compound). Furthermore, in non-muscle myosins (myosin V and myosin VI), it has been shown that a ‘stretching’ force affects the processivity of these motors, presumably by influencing the on–off rates of ADP in the hydrolysis cycle (e.g. Rief et al. 2000; Altman et al. 2004; Veigel et al. 2005; Purcell et al. 2005). Finally, in pilot work with Dr J. Spudich at Stanford University, we found that dwell times and duty ratios of attached cross-bridges were changed by pushing or stretching forces (Mehta et al. 2006). So, although we agree with the authors of the letter that it might be difficult to reconcile our ideas within the framework of the sliding filament (Huxley & Niedergerke, 1954; Huxley & Hanson, 1954) and cross-bridge theory (Huxley, 1957), it is possible with today's technology to test such hypotheses, and it seems to us that theories should not be accepted or rejected based on the difficulty of testing them.
In concluding, we would like to emphasize, as we have in the Topical Review, that the mechanisms underlying force enhancement are not known. Our idea of a passive and an active component to residual force enhancement is based on work that has emerged primarily in the past five years. In light of this evidence, it seems difficult to maintain that sarcomere length non-uniformity is the mechanism underlying residual force enhancement. However, we acknowledge that in all preparations, sarcomere lengths are non-uniform, but what effect these non-uniformities have on muscle contraction in general and force enhancement specifically remains a matter of debate.
1 Faculty of Kinesiology, University of CalgaryCalgary, AB T2N 1 N4, Canada
References
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