An expanding explanation for the ascending limb of muscle’s active force-length relationship

Many readers of this article will have taken, or perhaps taught, a systems-based physiology class. These often cover the material at a fast pace. As an example, at the University of Kentucky, I am allotted two hours to teach the medical students “all” of muscle physiology. We cover muscle’s length-tension relationship on slide seven. I explain that active force drops as filament overlap decreases on the descending limb, and that there is a plateau where the effective overlap does not change because of the thick filaments’ bare zones. I also explain that the ascending limb is critically important for cardiac muscle and, while the mechanism is poorly understood, likely reflects actin filaments from one half-sarcomere interfering with those from the other. It was not until I read the fascinating work of Rockenfeller, Günther, and Hooper in this issue of Biophysical Journal (1) that I realized that some of my teaching has been completely wrong (or, if my Chair is reading this just before my annual performance review, “potentially incomplete.”)

Rockenfeller et al.’s manuscript starts with a penetrating analysis of the existing literature and previous explanations for the active force-length relationship. They cite more than 150 papers and point out that there is little experimental justification for fitting the ascending limb with a piece-wise linear function. The authors are equally skeptical of mechanisms that attribute the ascending limb to thin filaments protruding through the M-line and being pushed back by oppositely polarized myosin heads. Instead, Rockenfeller et al.’s careful reading of the literature points them toward the potential roles of lattice spacing and electrostatic forces.

The authors go on to develop a detailed and mathematically rigorous model that is extremely novel and exceptionally interesting. The first point the authors make is that the myofibrillar lattice is a constant volume system. Consequently, as the muscle shortens, the myofilaments move further apart. While this behavior is widely recognized, personally, I had not realized the magnitude of the effect. Rockenfeller et al. calculate that the actin to myosin surface to surface distance increases from 7 to 22 nm as sarcomeres shorten from 150 to 50% of their reference length (measured near the force-length plateau.) This variation seems likely to impact the probability of a myosin head coming within range of a binding site on actin.

The second feature considered by Rockenfeller at al. is the electrostatic field between the myofilaments. The authors note that each myosin head carries a net positive charge, and that the thick and thin filaments are negatively charged. They also postulate that the negative charges on actin are screened by tropomyosin in fully relaxed muscle and exposed in fully activated muscle. In Rockenfeller et al.’s view, thin filament activation alters the electrostatic field between the filaments, and thus the radial displacement at which myosin heads have a minimum potential energy. These relationships are, of course, dependent on the interfilamentary spacing, and thereby the sarcomere length. The authors develop analytical expressions for the potentials and invoke statistical mechanics to derive the probability of a myosin head being attracted to the thin filament (where it can attach and generate force) at different sarcomere lengths and levels of activation.

The authors then fit their analytical model to experimental data collated from the literature. Importantly, the model reproduces the rightward shift of the active-length tension curve as thin filament activation is decreased. I was excited by this result and think that it may have implications for the length-dependent shift in Ca²⁺ sensitivity that contributes to the Frank-Starling relationship in cardiac muscle. Looking at the model fits, I was also surprised to see that many of the experimental datasets collated by Rockenfeller et al. show force rising with length over the “plateau” region that Gordon et al.’s famous paper attributed to the thick filament bare zone (2). Here again, Rockenfeller et al. deserve great credit for their rigorous analysis of the literature.

Rockenfeller et al.’s manuscript is interesting and important, but some aspects of the work may not appeal to every muscle biophysicist. As an example, the modeling probably oversimplifies some of the structural aspects of the interacting heads motif of myosin (3,4) and does not account for the force-dependent changes in the relative populations of superrelaxed and disordered relaxed heads (5). The potential effects of myosin binding protein-C are not considered (6). Since I spent many hours as a PhD student puzzling over Gordon et al.’s description of their spot-follower technique, I also expected to see more discussion of the potential confounding effects of series compliance and sarcomere length inhomogeneities (2,7).

Nevertheless, I consider this paper to be a fantastic achievement. The authors have looked at an old problem with fresh eyes and developed an entirely new way of thinking about muscle’s active force-length relationship. The fits of the authors’ model to the datasets are incredibly compelling. As scientists pursuing better quantitative understanding of biology, we should all be grateful for their efforts.

Rockenfeller et al. end their manuscript by stating their model “is, for now, a better explanation of the ascending arm.” I agree. I am still not sure how to teach “all” of muscle physiology in two hours, but one thing is for sure—I will be updating slide seven for next year’s class.