Length-dependent Ca²⁺ activation in cardiac muscle: some remaining questions

Abstract

The steep relationship between systolic force and end diastolic volume in cardiac muscle (Frank–Starling relation) is, to a large extent, based on length-dependent changes in myofilament Ca²⁺ sensitivity. How sarcomere length modulates Ca²⁺ sensitivity is still a topic of active investigation. Two general themes have emerged in recent years. On the one hand, there is a large body of evidence indicating that length-dependent changes in lattice spacing determine changes in Ca²⁺ sensitivity for a given set of conditions. A model has been put forward in which the number of strong-binding cross-bridges that are formed is directly related to the proximity of the myosin heads to binding sites on actin. On the other hand, there is also a body of evidence suggesting that lattice spacing and Ca²⁺ sensitivity are not tightly linked and that there is a length-sensing element in the sarcomere, which can modulate actin–myosin interactions independent of changes in lattice spacing. In this review, we examine the evidence that has been cited in support of these viewpoints. Much recent progress has been based on the combination of mechanical measurements with X-ray diffraction analysis of lattice spacing and cross-bridge interaction with actin. Compelling evidence indicates that the relationship between sarcomere length and lattice spacing is influenced by the elastic properties of titin and that changes in lattice spacing directly modulate cross-bridge interactions with thin filaments. However, there is also evidence that the precise relationship between Ca²⁺ sensitivity and lattice spacing can be altered by changes in protein isoform expression, protein phosphorylation, modifiers of cross-bridge kinetics, and changes in titin compliance. Hence although there is no unique relationship between Ca²⁺ sensitivity and lattice spacing the evidence strongly suggests that under any given set of physiological circumstances variation in lattice spacing is the major determinant of length-dependent changes in Ca²⁺ sensitivity.

Appendix

Some of the papers cited in this review raise the question of whether there is a need for the muscle research community to arrive at some consensus as to the most appropriate means to quantitate change in Ca²⁺ sensitivity. In the case of skinned fiber studies the great majority of investigators have expressed Ca²⁺ sensitivity in terms of the pCa at which normalized force is half-maximal (pCa₅₀); the difference at, for example, two different lengths would be ΔpCa₅₀. In the papers of Konhilas et al., Ca²⁺ sensitivity is expressed in terms of the absolute Ca²⁺ concentration needed for half maximal force (EC₅₀; μM) and the length-related difference is then ΔEC₅₀. While one would hope to arrive at the same qualitative answer regardless of which measure is used, in actual practice this is not always the case, as is seen in the paper on ssTnI substitution and PKA phosphorylation (Konhilas et al., 2003). With ssTnI substitution the ΔEC₅₀ changed from 0.41 to 0.26, a statistically significant difference, but the ΔpCa₅₀ did not change at all (0.12 vs. 0.13). With PKA treatment of wild type fibers the ΔEC₅₀ was increased from 0.41 to 0.79 but the ΔpCa₅₀ was the same (0.12) for both phosphorylated and non-phosphorylated fibers. In the paper comparing cardiac, and fast and slow skeletal muscle (Konhilas et al., 2002c) the ΔEC₅₀ values followed the order 0.65 (cardiac), 0.42 (fast skeletal), and 0.25 (slow skeletal). The ΔpCa₅₀ values followed the order 0.09 (cardiac), 0.08 (fast skeletal), and 0.05 (slow skeletal). That is, by one measure cardiac muscle had greater length sensitivity than fast skeletal muscle but by another measure there was no discernible difference.

One consideration when comparing EC₅₀ (absolute [Ca²⁺]) and pCa₅₀ (the –log [Ca²⁺]) may be the question of which parameter exhibits a Gaussian (normal) or non-Gaussian distribution in a population of fibers. When either parameter is estimated by fitting the population data with the Hill equation (as in Figure 1) the estimate of fit is normally distributed and is characterized by an estimated mean value and the corresponding standard error. In contrast, a histogram of EC₅₀ or pCa₅₀ values from fits to force-[Ca²⁺] data from several individual fibers may or may not be normally distributed, raising the question of which is the preferred characterization; to our knowledge this comparison has not appeared in the literature. On the other hand, even if (as could be expected) either EC₅₀ or pCa₅₀ exhibits a normal distribution and the other does not, the central tendencies of both can be recovered through an appropriate statistical estimate which would be normally distributed. It is not clear that these considerations would influence the conclusions regarding the effects of length on EC₅₀ or pCa₅₀ described above.

Which is the more valid measure of length sensitivity, ΔEC₅₀ or ΔpCa₅₀? An advantage of ΔpCa₅₀ as the preferred measure is that its value is independent of where the [Ca²⁺] lies on the absolute scale. To take an admittedly extreme case, let us suppose that Muscle A has EC₅₀ values at long and short sarcomere length of 1.0 and 2.0 μM, respectively, and Muscle B has corresponding values of 10 and 20 μM. The ΔEC₅₀ values differ by a factor of 10 but the ΔpCa₅₀ value in both cases is 0.3, reflecting the fact that in each case the ratio of EC₅₀ at the two lengths is identical. In both cases an equivalent degree of stretch produces a two-fold increase in Ca²⁺ sensitivity. The question then becomes one of absolute change versus relative change and which one is more physiologically meaningful. Put another way, a significant difference in a pair of ΔpCa₅₀ values will always be associated with a significant difference in ΔEC₅₀, but the converse is not always true. Thus while both measures may have a legitimate use it could be argued that the ΔpCa₅₀ provides a less ambiguous measure of a change in sensitivity.