Tri-modal regulation of cardiac muscle relaxation; intracellular calcium decline, thin filament deactivation, and cross-bridge cycling kinetics

Abstract

Cardiac muscle relaxation is an essential step in the cardiac cycle. Even when the contraction of the heart is normal and forceful, a relaxation phase that is too slow will limit proper filling of the ventricles. Relaxation is too often thought of as a mere passive process that follows contraction. However, many decades of advancements in our understanding of cardiac muscle relaxation have shown it is a highly complex and well-regulated process. In this review, we will discuss three distinct events that can limit the rate of cardiac muscle relaxation: the rate of intracellular calcium decline, the rate of thin-filament de-activation, and the rate of cross-bridge cycling. Each of these processes are directly impacted by a plethora of molecular events. In addition, these three processes interact with each other, further complicating our understanding of relaxation. Each of these processes is continuously modulated by the need to couple bodily oxygen demand to cardiac output by the major cardiac physiological regulators. Length-dependent activation, frequency-dependent activation, and β-adrenergic regulation all directly and indirectly modulate calcium decline, thin-filament deactivation, and cross-bridge kinetics. We hope to convey our conclusion that cardiac muscle relaxation is a process of intricate checks and balances, and should not be thought of as a single rate-limiting step that is regulated at a single protein level. Cardiac muscle relaxation is a system level property that requires fundamental integration of three governing systems: intracellular calcium decline, thin filament deactivation, and cross-bridge cycling kinetics.

Introduction

Proper cardiac muscle relaxation is of paramount importance for a healthy circulation. In between two beats, the heart muscle needs to relax to allow for ventricular filling. If the relaxation of the cardiac muscle tissue is impaired, the ventricle will be incompletely filled upon initiation of the next beat, resulting in a low volume at the beginning of contraction. Thus, even if contractile function (activation) of the heart muscle would be completely normal, slowed relaxation would lead to a lack of diastolic volume, and thus to a reduced cardiac output. As a result, despite having a good ventricular ejection fraction, insufficient amounts of oxygenated blood are circulated, and when left untreated, this can result in development of heart failure and other cardiac pathology. Clinically, aberrant relaxation is referred to as diastolic dysfunction, diastolic heart failure, or heart failure with preserved ejection fraction (HFpEF) (Borlaug and Kass 2008; Janssen and Periasamy 2007). A better understanding of how cardiac muscle relaxation is regulated is needed in order to strategize and optimize treatments for cardiac diseases where muscle relaxation impairment manifests. Although many parameters, including ventricular geometry, drugs, and pathologies are known to impact cardiac relaxation, we will specifically focus this review on the basic relaxation properties and regulation in the healthy heart muscle.

The heart is only in equilibrium once…

From its first beat in utero until death, the heart is in a dynamically changing contractile state. At no point during a normal lifespan are the governing parameters of contractile strength and kinetics in equilibrium or at steady-state. In fact, heart rate variability is a sign of a healthy heart (Counihan et al. 1993; Torres et al. 2008), and this heart rate variability is diminished with both disease and with aging (Corino et al. 2007). Thus, even under resting conditions, heart rate, wall-stress, cytosolic ion concentrations, and ion channel activities are never in equilibrium. How quickly these governing processes can respond to affect relaxation depends on the dynamic temporal nature of the individual processes. In addition, many of the rate-limiting steps of these processes are adjusted to modulate contraction and relaxation kinetics (ultimately controlling cardiac output) when the body’s demand for oxygen changes (Janssen 2010a). The strength and speed of this dynamic contraction is regulated via several mechanisms in order to adjust cardiac output to meet the bodily demand for oxygen. The three main physiological mechanisms that change cardiac muscle strength are length-dependent activation (ter Keurs et al. 1980), frequency-dependent activation (Bouchard and Bose 1989; Janssen and Periasamy 2007), and adrenergic stimulation (Bers and Ziolo 2001; Kranias and Solaro 1982). These governing mechanisms of cardiac output impact not only individual parameters that feed into cardiac muscle strength and kinetics, they also impact interactions between parameters. Thus, the cross-talk between these mechanisms further complicates the dynamic nature of cardiac inotropy and lusitropy. Most, if not all, of these parameters, interactions, and governing mechanisms impact on the relaxation phase of cardiac muscle (Brutsaert et al. 1978).

Governing of relaxation

The governing of cardiac relaxation stems from the complex interaction of a multitude of ion movements and protein interactions, each with their own temporal resolution of function. Furthermore, these processes impact on physical entities such as sarcomere length and tension/stress, that in turn feedback on the interaction between processes, as well as on themselves (Rice et al. 1999; Hofmann and Fuchs 1987; de Tombe 1998). This highly dynamic nature, where none of the interactors are in equilibrium, makes understanding of the governing processes difficult. Three interactive processes are thought to contain potentially rate-limiting properties and have put them at the forefront of investigation into governing of cardiac muscle relaxation; 1) the rate at which the calcium is lowered in the cytosol (Figure 1), 2) the rate at which the thin filament deactivates (Figure 2), and 3) the rate at which actin-myosin (cross-bridges) interact (Figure 3). In the first part of this review, we will address these main mechanisms, and their direct impact of relaxation. In the second part we discuss how these mechanisms and interactions are regulated and modified when the demand for cardiac output changes.

Figure 1.

Regulation of the rate of intracellular calcium transient decline. Left column: 3 examples (no particular order) of molecular processes that fasten the rate of intracellular calcium transient decline. PLB: phospholamban; NCX: Sodium-Calcium-Exchanger. Right column: 3 examples of molecular processes that slow down the rate of intracellular calcium transient decline.

Figure 2.

Regulation of the rate of thin filament deactivation. Left column: 3 examples (no particular order) of molecular processes that fasten the rate of thin filament deactivation. TnI: Troponin-I; TnC: Troponin-C; TnT: Troponin-T; SS: Slow Skeletal. Right column: 3 examples of molecular processes that slow down the rate of thin filament deactivation.

Figure 3.

Regulation of the rate of cross-bridge cycling. Left column: 3 examples (no particular order) of molecular processes that fasten the rate of cross-bridge cycling. MyBP-C: Myosin-binding Protein C. Right column: 3 examples of molecular processes that slow down the rate of cross-bridge cycling. RLC: Regulatory Light Chain.

1.1. Calcium transient decline

An increase in cytosolic Ca²⁺ (i.e., systolic Ca²⁺) is required for initiation of contraction. Within ventricular myocytes, this increase in Ca²⁺ is achieved by Ca²⁺ influx through L-type Ca²⁺ channels (LTCC) and Ca²⁺ expelled from the sarcoplasmic reticulum (SR) by the SR Ca²⁺ release channel (ryanodine receptor, RyR) in a process termed Ca²⁺-induced-Ca²⁺-release (CICR) (Bers 2002a). The rate at which systolic Ca²⁺ (also known as the Ca²⁺ transient) declines is an important factor that contributes to relaxation since it is the initiating event for the process, and this decline can be modulated via many molecular events (Figure 1). While LTCC and RyR do not directly contribute to this decline, the systolic [Ca²⁺]_i is a determinant of the rate of Ca²⁺ decline (Bers and Berlin 1995; Roof et al. 2011). During systole, cytosolic Ca²⁺ levels are lowered via four Ca²⁺ transport systems. These systems remove Ca²⁺ from the cytosol into the SR via the SR Ca²⁺ ATPase, the mitochondria via the Ca²⁺ uniporter and out of the myocyte via the Na⁺/Ca²⁺ exchanger (NCX) and sarcolemmal (SL) Ca²⁺ ATPase.

The SR is the major Ca²⁺ storage organelle within the myocyte. In order to maintain a normal calcium SR load over time, approximately the same amount of Ca²⁺ dispensed from the SR during CICR needs to be returned to the SR. This occurs via the cardiac SR Ca²⁺ ATPase isoform (SERCA2a). Located mostly at the longitudinal tubules of the SR, SERCA2a pumps 2 Ca²⁺ ions per ATP molecule. SERCA2a activity is regulated by its endogenous inhibitor phospholamban (PLB). PLB binding to SERCA2a decreases Ca²⁺ transport into the SR by decreasing the Ca²⁺ affinity of the pump without altering V_max. In mice, it is proposed that ~40% of the pumps are basally regulated by PLB, while it is ~60% in rabbits (Waggoner et al. 2009).

Ca²⁺ enters the mitochondria via the uniporter down a large electrochemical gradient (Williams et al. 2013). Mitochondrial Ca²⁺ uptake plays little role in decreasing cytosolic Ca²⁺ levels on a beat-to-beat basis (discussed further below) but is important in regulating mitochondrial energy production (Moravec et al. 1997).

The Na⁺/Ca²⁺ exchanger, NCX1, is located on the sarcolemma and functions by exchanging one Ca²⁺ ion for three Na⁺ ions. NCX1 is able to remove Ca²⁺ from the myocyte (forward mode) or bring Ca²⁺ into the myocyte (reverse mode) (Ottolia and Philipson 2013). During normal cardiac function, the forward mode contributes to the decline of the Ca²⁺ transient.

The SL Ca²⁺ ATPase pumps 1 Ca²⁺ ion per ATP molecule out of the myocyte. The SL Ca²⁺ ATPase plays little role in decreasing cytosolic Ca²⁺ levels (discussed further below) but is involved in modulating various signaling pathways (Bassani et al. 1995; Oceandy et al. 2007).

1.2. Role of each Ca²⁺ transport system

Each of the above Ca²⁺ transport systems contributes differently, both in timing and in quantity, to the decline of the Ca²⁺ transient. The majority of the Ca²⁺ transient decline is due to SERCA2a. There are species differences in the fraction of the Ca²⁺ transient decline via SERCA2a. For example, in mouse and rat myocytes >95% of the decline is due to SERCA2a, while in larger mammals (rabbit, dog, human), only ~70% of the decline is due to SERCA2a (Milani-Nejad and Janssen 2014). This corresponds to the number of myocyte Ca²⁺ pumps in the various species (i.e., there are more pumps in mouse/rat than rabbit/dog) (Bers 2001). Another major contributor to the decline of the Ca²⁺ transient is NCX1. To maintain normal calcium levels inside the myocyte, the Ca²⁺ that entered the myocyte through the LTCC must be removed. The vast majority of this Ca² is removed via NCX1. As with SERCA2a, there are species differences in the fraction of the Ca²⁺ transient decline that is due to NCX1 (Bers 2002b). In mouse and rat myocytes <4% of the decline is due to NCX1, while in larger mammals, ~28% of the decline is due to NCX1. This corresponds nicely to the amount of inward NCX1 current in the various species (i.e., greater NCX1 current in dog/rabbit vs. rat/mouse). The other two systems (mitochondrial Ca²⁺ uniporter and SL Ca²⁺ ATPase) together account for ~1% of the Ca²⁺ transient decline (Puglisi et al. 1996), and thus have little effect in modulating relaxation, and will not be further discussed in this review.

In addition to species differences of the various Ca²⁺ transport systems, there are shifts in the contribution of these systems in disease. For example, in human and rabbit heart failure there is a reduction in SERCA2a expression and an increase in NCX1 expression (Houser et al. 2000). These protein changes result in a reduced contribution of the SR Ca²⁺ ATPase transport system to ~50% of the Ca²⁺ transient decline, and an increase in the contribution of the NCX1 transport system to ~50% of the Ca²⁺ transient decline (Piacentino et al. 2003). Since SERCA2a has a much greater Ca²⁺ transport rate than NCX1, these protein expression changes result in a general slowing of Ca²⁺ transient decline (Ziolo et al. 2004). There is also a slowing of the Ca²⁺ transient decline with acidosis and an associated increase in diastolic [Ca²⁺]_i (Westerblad and Allen 1993; DeSantiago et al. 2004). The molecular mechanisms responsible for the slowed [Ca²⁺]_i decline are a reduction in SR Ca²⁺ uptake (SERCa2a activity) and decreased forward mode of NCX. These data demonstrate that in addition to protein expression levels, Ca²⁺ transient decline can also be acutely modulated.

1.3. Regulation of Ca²⁺ transient decline by post-translational modifications

The prototypic post-translational modification (PTM) to acutely modulate protein function is phosphorylation. In addition to being an endogenous inhibitor of SERCA2a, PLB is also a key phosphoprotein in the heart (MacLennan and Kranias 2003). PLB can be phosphorylated at Serine16 by the cAMP-dependent protein kinase (PKA) and at Threonine17 by the Ca²⁺/CaM-dependent protein kinase (CaMKII). Phosphorylation at either site relieves PLB inhibition of SERCA2a leading to a substantial increase in the Ca²⁺ pump rate to greatly hasten Ca²⁺ decline and relaxation. The role of phosphorylation to modulate NCX activity is controversial. While a study did show that PKA can upregulate NCX activity (Perchenet et al. 2000), this effect is not universally observed (Ginsburg and Bers 2005). Nevertheless, we believe if PKA can upregulate NCX activity that this will have little effect in hastening Ca²⁺ decline under physiological conditions. PKA is activated via β-adrenergic stimulation (discussed below) and with the PKA-mediated phosphorylation of PLB, the Ca²⁺ decline rate even in large mammals is almost entirely (>90%) due to SERCA2a activity (Waggoner et al. 2009).

Besides direct phosphorylation of Ca²⁺ handling proteins by PKA, an emerging area is demonstrating that other signaling pathways (in addition to β-AR stimulation) can also directly regulate PKA. For example, we have shown that neuronal nitric oxide synthase (NOS1) signaling results in increased PLB Serine16 phosphorylation to hasten Ca²⁺ transient decline (Wang et al. 2008). We further demonstrated that PKA activation was a direct, cAMP-independent effect of peroxynitrite, the signaling molecule of NOS1 (Kohr et al. 2010). In fact, we observed that NOS1 modulation of PLB phosphorylation is a key determinant of the basal (non-stimulated) Ca²⁺ transient decline rate (Roof et al. 2012). Protein phosphorylation levels are not only determined by kinase activity, but also the removal of the phosphate by phosphatases (PP) in which their activity can also be modulated. Interestingly, while low levels of peroxynitrite activate PKA, high levels of peroxynitrite activate PP resulting in the dephosphorylation of PLB and slowed Ca²⁺ decline (Kohr et al. 2008). In addition to modulating kinase and PP activity, peroxynitrite and other reactive oxygen and nitrogen species (ROS, RNS) can also directly (i.e., oxidation, S-glutathionlyation, S-nitrosylation) modulate Ca²⁺ handling proteins to alter the Ca²⁺ transient decline rate. For example, SERCA2a can be S-nitrosylated/S-glutationlated to increase activity (Bencsik et al. 2008; Lancel et al. 2009) or oxidized to decrease activity (Lancel et al. 2010; Morris and Sulakhe 1997; Scherer and Deamer 1986; Xu et al. 1997) (Figure 1). These changes in SERCA2a activity will result in a corresponding change in the Ca²⁺ transient decline rate. It has also been demonstrated that SERCA2a can undergo SUMOylation to increase activity. In HF patients, decreased SERCA2a SUMOylation contributes to the decreased SERCA2a activity in this syndrome (Kho et al. 2011).

In addition to SERCA2a, PLB is also modulated by RNS. For example, we have shown that RNS (specifically nitroxyl) modifies PLB cysteines to increase PLB pentamer formation, decreasing monomeric PLB (the form that inhibits SERCA2a) and resulting in a faster Ca²⁺ transient decline (Sivakumaran et al. 2013; Kohr et al. 2010).

While NCX phosphorylation is debatable, it has been clearly demonstrated that NCX can be oxidized leading to increased activity (Goldhaber 1996; Kuster et al. 2010; Reeves et al. 1986). While an increase in NCX activity would enhance the rate of [Ca²⁺]_i decline, one must remember that total myocyte oxidation will also result in SERCA2a oxidation to actually slow Ca²⁺ transient decline. However, the enhanced NCX activity with oxidation will however limit the increase in diastolic Ca²⁺ levels.

Since precise Ca²⁺ decline is so vital for proper relaxation, not only are protein expression levels important, the heart has constructed ways to acutely modulate Ca²⁺ transient decline via various post-translational modification (discussed further below).

2.1. The calcium-troponin interaction

While the rate of cytosolic Ca²⁺ decline is an important and initiating event in the process of relaxation, it is ultimately the removal of Ca²⁺ from troponin and subsequent deactivation of the thin filament that inhibits the interaction of myosin with actin allowing myocardial relaxation and diastolic ventricular filling. To understand how the thin filament modulates myocardial relaxation one must first understand how Ca²⁺ interacts with troponin to regulate the thin filament between the active and inactive states.

The interaction of Ca²⁺ with troponin is essential to the regulation of the thin filament. While intracellular Ca²⁺ is the signal initiating the interaction of myosin with actin, and thus contraction, Ca²⁺ itself does not directly regulate this interaction. Instead, the signaling molecule Ca²⁺ functions through the thin filament regulatory proteins; tropomyosin (Tm) and the troponin complex (troponin C (TnC), troponin I (TnI) and troponin T (TnT)) (for detailed reviews see (Kobayashi and Solaro 2005; Solaro and Westfall 2005; Tardiff 2011; Davis and Tikunova 2008).

During elevated systolic levels of intracellular free Ca²⁺, Ca²⁺ is bound to TnC of the troponin complex to maintain the activated state of the thin filament. In this activated state, TnI is bound to TnC stabilizing TnC-Ca²⁺ binding and Tm occupies a position on actin exposing myosin binding sites. As long as the thin filament is in this active state, myosin cross-bridges will freely cycle with actin and the muscle will contract.

For cardiac muscle relaxation to ensue, the thin filament must be inactivated to block the interaction of myosin with actin. As the result of intracellular Ca²⁺ decline by the mechanisms discussed above, free cytosolic Ca²⁺ eventually drops below the threshold for binding to TnC and Ca²⁺ disassociates. This disassociation of Ca²⁺ weakens TnI-TnC binding to favor TnI inhibitory binding to actin. Additional changes in TnT and Tm contribute to the movement of Tm into the “closed” position on actin causing deactivation of the thin filament. In the inactive state, these regulatory proteins sterically block the interaction of myosin with actin to promote relaxation of the cardiac muscle.

2.2. Influences on the rate of thin filament deactivation

While cardiac muscle relaxation is clearly initiated by the Ca²⁺ transient decline, the significant lack of Ca²⁺ transient and mechanical relaxation coupling in time (eg. the Ca²⁺ transient decays prior to force dissipation) indicates a role of the myofilament in the regulation of relaxation (Monasky et al. 2008; Gordon et al. 2000). The dynamics of relaxation are therefore not solely determined by the rate of the cytosolic Ca²⁺ transient decline but are therefore also determined by the rate of thin filament return to the deactivated state (Figure 2).

Force generating cross-bridges are critical to the thin filament transition from the active to the inactive state. For the thin filament to enter the inactive state, cross-bridges must release from actin such that Tm and TnI can block myosin rebinding. While the rate of cross-bridge release from actin directly contributes to the rate of relaxation (discussed below), cross-bridge detachment also indirectly decreases the affinity of TnC for Ca²⁺ and accelerates deactivation of the thin filament (Pan and Solaro 1987; Davis et al. 2007). Although the release of force producing cross-bridges is critical to deactivation, the rate of Ca²⁺ dissociation from TnC is essential for thin filament deactivation and therefore imparts a significant influence on relaxation (Davis and Tikunova 2007).

The rate of Ca²⁺ dissociation from the thin filament can be increased or decreased by troponin and Tm isoform switching, mutations and PTMs (Ertz-Berger et al. 2005; Kentish et al. 2001; Nixon et al. 2012; Liu et al. 2014; Liu et al. 2012; Davis et al. 2007; Nixon et al. 2013; Rice et al. 2010). As discussed above, transition from the active to inactive state of the thin filament and relaxation involves not only the disassociation of Ca²⁺ from TnC, but also the rebinding of TnI to actin, structural changes in TnT and Tm movement. Therefore the alteration in any of these protein-protein transitions could modulate the rate of thin filament deactivation. With the exception of Ca²⁺ disassociation from TnC, the rates for the majority of these protein transitions have not been elucidated. In the future a detailed understanding of these protein transition rates will be important to fully understand the complex nature of thin filament deactivation. It is clear however that the PTM of the regulatory proteins represents a significant mechanism to affect the rate of thin filament inactivation by altering the protein-protein interactions that modulate the rate of Ca²⁺ disassociation form TnC.

2.3. Regulation of thin filament deactivation by PTM

The PTM of myocardial proteins has evolved as a significant mechanism to rapidly modulate myocardial muscle mechanics on a beat-to-beat basis (Solaro 2001). The majority of regulatory thin filament proteins undergo PTM to rapidly alter Ca²⁺ binding to and/or disassociation from TnC to modulate the rate of relaxation (Nixon et al. 2013; Nixon et al. 2012; Liu et al. 2014). Within the thin filament a number of PTMs can occur, however phosphorylation represents the most prevalent myofilament signaling PTM to date. Phosphorylation occurs in all thin filament proteins except TnC and actin.

To discuss the role of thin-filament PTM on myocardial relaxation regulation we present the prototypical effects of cardiac TnI Ser-23 and Ser-24 phosphorylation via PKA (Figure 2). The dual phosphorylation of TnI at Ser-23/24 is a well-defined thin filament phosphorylation regulatory response (Kranias and Solaro 1982; Kentish et al. 2001; Pena and Wolska 2004; Kooij et al. 2010; Biesiadecki et al. 2007a). The phosphorylation of cardiac TnI at Ser-23/24 exists at approximately a 40% basal baseline state (Ayaz-Guner et al. 2009). Changes from this baseline state represent a critical mechanism to modulate beat-to-beat relaxation alterations in response to both physiological and pathological cardiac stress. Increases in TnI Ser-23/24 phosphorylation result in decreased Ca²⁺ binding to TnC evident experimentally as decreased TnC Ca²⁺ affinity and an acceleration in the rate of Ca²⁺ dissociation from TnC. These changes in TnC Ca²⁺ binding result in accelerated thin filament deactivation (Kentish et al. 2001; Nixon et al. 2012; Nixon et al. 2014; Walker et al. 2011). Accordingly, TnI Ser-23/24 phosphorylation and the transgenic expression of pseudo-phosphorylated TnI (Ser-23/24 mutated to Asp) in the mouse heart results in accelerated muscle contraction and heart relaxation (accelerated -dP/dt) (Kentish et al. 2001; Zhang et al. 1995; Takimoto et al. 2004; Pena and Wolska 2004; Yasuda et al. 2007). Thus, TnI Ser-23/24 phosphorylation induced decreased TnC-Ca²⁺ affinity results in in vivo acceleration of diastolic cardiac relaxation. In addition to altering relaxation through TnC Ca²⁺ affinity, TnI Ser-23/24 has also been implicated in downstream modulation of the myosin-actin cross-bridge, while others question such an effect (Turnbull et al. 2002; Strang et al. 1994; Biesiadecki et al. 2007b; Bilchick et al. 2007; Stelzer et al. 2007; Tong et al. 2008).

A number of thin filament protein residues besides TnI Ser-23/24 undergo phosphorylation. TnI can be phosphorylated at varied residues, while TnT and Tm are also phosphorylated (Buscemi et al. 2002; Perry 1999; Zhang et al. 2012; Jideama et al. 1996; Sumandea et al. 2003; Mak et al. 1978). The functional effects of the majority of these phosphorylation events have been demonstrated in isolation, however the question of their physiological integration largely remains. In response to altered myocardial demand, multiple thin filament phosphorylation events simultaneously occur in the heart. The functional effects of these integrated phosphorylation events are largely unknown.

Recent evidence has demonstrated the function of TnI Ser-23/24 phosphorylation in myocardial regulation is dependant upon other myofilament protein mutations, PTMs and TnI phosphorylations (Biesiadecki et al. 2007a; Boontje et al. 2011; Nixon et al. 2012; Deng et al. 2001; Nixon et al. 2014). Recently we demonstrated that while TnI Ser-150 phosphorylation slowed TnC Ca²⁺ disassociation, when TnI Ser-150 and Ser-23/24 phosphorylation occurred together Ca²⁺ dissociation kinetics were accelerated (Nixon et al. 2012; Nixon et al. 2014). The effect of TnI Ser-150 on TnC Ca²⁺ disassociation is therefore dependent upon its integration with TnI Ser-23/24 phosphorylation. These findings begin to demonstrate the importance of investigating thin filament phosphorylation as the integrated events that occur in response to increased myocardial demand.

Thin filament proteins can also undergo a number of other non-phosphorylation PTMs. These non-phosphorylation thin filament PTMs include modifications such as proteolysis, glycosylation, oxidation, and nitrosylation. Again, as a model we discuss TnI. In addition to phosphorylation, TnI can also undergo proteolysis and O-glycosylation. In isolation, these PTMs have been shown to directly modulate thin filament deactivation. During myocardial ischemia TnI undergoes selective proteolysis removing the 17 C-terminal amino acids that result in increased TnC Ca²⁺ affinity and slowed myofibril relaxation kinetics (Narolska et al. 2006; McDonough et al. 1999; Foster et al. 2003). On the other hand, the modification of TnI Ser-150 by O-glycosylation decreases TnC Ca²⁺ affinity (Ramirez-Correa et al. 2008). Little work has been done to investigate the integrated effects of non-phosphorylation thin filament PTMs with phosphorylation on thin filament deactivation and myocardial relaxation.

Overall it is becoming clear from our data as well as that of others that the effects of multiple thin filament protein PTMs cannot be deduced from their individual effects alone. The lack of the Ca²⁺ transient and mechanical relaxation coupling in time and our recent findings indicating the significance of TnI phosphorlyation to myocardial relaxation (Monasky et al. 2010; Monasky et al. 2013) necessitates further investigation into the role of both isolated and integrated thin filament PTMs on the regulation of myocardial relaxation.

3.1. Cross-Bridge cycling

It is necessary to keep in mind what precisely cardiac muscle is relaxing from – pressure caused by high wall stress. The stress and strains within cardiac muscle tissue is caused by forces and motions generated within the myocytes that make up the bulk of the cardiac walls. These forces and motions are generated by energy demanding interactions between the numerous interdigitating thin and thick filament proteins actin-Tm-Tn and myosin. This process, cross-bridge cycling, is modulated by many factors (Figure 3). While the removal of cytosolic Ca²⁺ and deactivation of the thin filament are necessary to inhibit cross-bridge formation, it is ultimately the structural changes specifically within the motor protein myosin that are responsible for relaxation of the myocytes (for review see (Gordon et al. 2000)).

The kinetic behavior of myosin has been proposed to possess within its cycle the rate-limiting step of cardiac isolated myofibrils relaxation (Stehle and Iorga 2010). There is ample evidence that altering (either increasing or decreasing) the rate at which cardiac muscle myosin utilizes its fuel source, ATP, can have profound effects on influencing the rates of both cardiac muscle contraction and relaxation (Gordon et al. 2000). Changes in the expression pattern between the two cardiac myosin isozymes may be the best example where a change in myosin kinetics alters both cardiac muscle contraction and relaxation and therefore the overall function of the heart (Fitzsimons et al. 1998). Not unique to cardiac muscle, classic experiments have demonstrated that different muscles (striated, smooth, fast-twitch, slow-twitch and cardiac) found across the animal kingdom exhibit an extremely wide ranging and linear relationship between the maximal speeds of muscle shortening and myosin’s ATPase rate (a mechanical event coupled to a biochemical reaction) (Barany 1967). Across numerous species and experimental conditions there is also a strong correlation between the speeds at which a cardiac muscle contracts and relaxes (Janssen 2010b). Considering myosin plays a fundamental role in both phenomenon, it would appear that myosin is at minimum tuned kinetically, if not rate-limiting, for the required mechanical performance of the heart.

Six separate polypeptide chains (two heavy, ~200kD chains and four light, ~17kD chains) form the myosin molecule (for review see (Gordon et al. 2000)). The two heavy chains coil around one another at their C-termini forming a long double helix. This long helix packs tail to tail to form a large part of each ~1um long thick filament. Protruding from the helical core of the thick filaments are the remaining heavy chains that eventually split into individual lever arms attached to separate globular heads. Each lever arm is stabilized by the binding of a single essential and regulatory light chain. The globular head contains all the necessary machinery to transfer the chemical energy of ATP into mechanical power when coupled with actin. Each myosin head can only generate ~5–10 pN of force (comparable to the weight of a single E Coli bacterium or the force generated by a HeNe laser pin shown on a surface) or move ~10nm (slightly longer than the distance across the plasma membrane) (Takagi et al. 2006). However, packed within each cardiac myocyte are approximately 2 billion myosin heads, while there are approximately 6 billion myocytes in the human left ventricle (Beltrami et al. 2001). This is more than enough myosin to build and sustain the ventricular pressure required to pump the blood throughout the body.

At any given moment toward the end of systole, there are a large number of cycling myosin strongly bound to actin (although not known, this number is probably less than 20% of the total number of myosin available within the muscle). These myosin’s are also tightly bound by adenosine diphosphate (ADP). Before the myosin can detach from the thin filament, allowing the muscle to relax and relinquish the pressure within the chamber, ADP must dissociate from the acto-myosin complex (for review see (Gordon et al. 2000)). Once this happens, one of the ample supply of cellular ATP (~10mM) nearly instantaneously binds the nucleotide free rigor head causing it to relinquish its grip on actin. Very quickly after myosin dissociates from actin, the head hydrolyzes the bound ATP into tightly bound inorganic phosphate (Pi) and ADP. The high energy stored in the terminal phosphate bond of ATP is used to swing the lever arm (and the head with it) into a pre-power stroke position - akin to cocking the hammer back on a pistol. In essence the myosin is now energized and ready to go, a state in which the majority of cardiac myosin is typically found, especially during late diastole. Due to the close proximity of the thin filament to the myosin heads (essentially a very high effective concentration of actin), myosin can quickly search for and find another actin if the thin filament is still activated. Once myosin finds another actin it re-attaches at first weakly. Soon after rebinding to actin the myosin head releases its bound Pi. Simultaneously with the release of Pi, myosin performs its powerstroke - swinging the lever arm back to its original position. This generates a force on the actin filament that if not resisted will move the thin filament and shorten the myocyte. Once again, myosin is tightly bound to actin and cannot dissipate the force until ADP dissociates. This cross-bridge cycle will continuously occur as long as a myosin can find an available actin. Both Ca²⁺-bound thin filaments and strongly bound cross-bridges increase the probability that a detached myosin head will find an available actin (for review see (Gordon et al. 2000)). In these regards, the biochemical reaction of ADP dissociation may be the rate-limiting step of the mechanical events of cardiac muscle relaxation (Siemankowski et al. 1985; Little et al. 2012)

It is not surprising then that there are numerous biochemical and mechanical influences on the rate of cardiac muscle relaxation that likewise affect ADP dissociation. Forces that resist the motion of the powerstroke (preload) slow the rate of ADP dissociation and relaxation, while forces that lower the burden on any one particular myosin help to accelerate ADP dissociation and relaxation (especially movements in the same direction of the powerstroke – i.e. other myosin powerstrokes) (Nyitrai and Geeves 2004). Intracellular environmental changes, such as elevated [ADP] and acidosis also slow the rate of ADP dissociation, whereas an increase in [Pi] accelerates relaxation in several skinned cardiac preparations (Simnett et al. 1998; Herzig et al. 1981), and in human atrial and ventricular myofibrils (Piroddi et al. 2007). As noted above, different isozymes of myosin have intrinsically different rates of ADP dissociation and rates of relaxation (Fitzsimons et al. 1998; Palmiter et al. 1999; Suzuki et al. 2009). The rate of cardiac muscle relaxation inversely scales with body size (Janssen 2010a). Similarly, the smaller the mammal, the faster the cardiac myosin releases ADP (predominately the alpha MHC lineage in small rodents and the beta MHC lineage in larger mammals) (Palmiter et al. 1999; Suzuki et al. 2009). Within a species alpha myosin has a two to five times faster rate of ADP dissociation than does beta myosin. Across species, the smaller the mammal the faster both classes of myosin release ADP. Thus, there is a clear correlation between the rates at which cardiac muscle relax to the biochemical rate of ADP dissociation.

In addition to the regulation of relaxation through the effects of Ca²⁺ concentration and thin filament deactivation, the actin-myosin cross-bridge cycling itself can be regulated to modulate cardiac muscle relaxation through thick filament associated regulatory proteins. The most significant of these include the myosin light chains, myosin binding protein C and titin. The effects of these thick filament regulatory proteins on cardiac muscle function in general have previously been reviewed (Kamm and Stull 2011; Szczesna 2003; Hernandez et al. 2007; Barefield and Sadayappan 2010; Granzier et al. 2005; LeWinter and Granzier 2010; Kruger and Linke 2011), here we focus on their contribution to the regulation of myosin cross-bridge cycling and their effects on cardiac muscle relaxation.

Directly associated with the lever arm domain of each myosin motor are two constitutively bound myosin light chains; the essential light chain (ELC) and the regulatory (phosphorylatable) light chain (RLC). Both of these myosin light chains interact with myosin in the myosin neck region and provide mechanical stability. This location is significant as the neck region is critical to myosin cross-bridge cycling and thus positions the light chains in an optimal position to directly modulate myosin cycling. Expression of the ELC in cardiac muscle consists of atrial and ventricular isoforms (Hernandez et al. 2007). The expression of these isoforms differentially modulates myosin cross-bridge kinetics with the atrial isoform exhibiting increased myosin cross-bridge cycling compared to that of the slower ventricular isoform (Hernandez et al. 2007). In normal adult ventricular myocardium the ventricular ELC is the solely expressed isoform. During cardiac disease the atrial isoform can become expressed resulting in increased actin-myosin cross-bridge cycling and altered myocardial relaxation. The modulation of cardiac muscle relaxation through the ELC is largely limited to the effects of these isoform alterations and therefore impart functional effects on a long-term basis. Similar to the ELC, the RLC is expressed as ventricular and atrial chamber specific isoforms that demonstrate different effects on cross-bridge regulation. The RLC is a phospho-protein maintained at a basal level of phosphorylation in the normal heart (Metzger et al. 1989; van der Velden et al. 2003; High and Stull 1980). Alteration of this basal phosphorylation level can modulate the actin-myosin cross-bridge on a beat-to-beat basis. Phosphorylation of the RLC by the myosin light chain kinase family (Kamm and Stull 2011) to induce direct alteration of the myosin structure resulting in its displacement away from the thick filament (Levine et al. 1998; Colson et al. 2010; Levine et al. 1996). This displacement moves the myosin head closer to actin and increases the likelihood of forming the actin-myosin cross-bridge. While this increased cross-bridge formation increases the rate of force development (Olsson et al. 2004), it results in a slowed rate of relaxation (Patel et al. 1998) as the result of the increased likelihood of cross-bridge rebinding to actin at an unaffected detachment rate. Thus through either isoform switching or specific phosphorylation, the myosin light chains are critical to the modulation of cross-bridge kinetics and cardiac relaxation.

Similar to the myosin light chains, myosin binding protein-C (MyBP-C) directly associates with the myosin head, however MyBP-C binding does not occur on every myosin head. In the ventricle MyBP-C is arranged in 7–9 “stripes” perpendicular to the long axis of the myosin filaments (Luther et al. 2008; Tong et al. 2008). While MyBP-C is expressed as three isoforms in various striated muscles, only the cardiac isoform is expressed in ventricular muscle. The location of MyBP-C contributes both to the structural organization of the myofilament and also invokes a modulatory effect on actin-myosin cross-bridge. Similar to the RLC, the cardiac MyBP-C isoform is a phospho-protein able to modulate myosin cycling on a beat-to-beat basis (Gautel et al. 1995; Yuan et al. 2008; Yuan et al. 2006). The cardiac specific phosphorylation of MyBP-C can become altered in response to cardiac stress and in cardiac disease through various signaling pathways (Kuster et al. 2012). The significance of MyBP-C phosphorylation to modulate the actin-myosin interaction has been demonstrated following PKA phosphorylation (Gautel et al. 1995). Phosphorylation of the MyBP-C PKA-sites induces a structural change in the myosin head, moving the myosin cross-bridge away from the thin filament backbone and increasing its proximity to actin (Weisberg and Winegrad 1996; Sadayappan et al. 2006). This increased proximity of the myosin to actin has been proposed as the mechanism of MyBP-C phosphorylation to increase actin-myosin cross-bridge cycling and impact on relaxation (Stelzer et al. 2007; Tong et al. 2008). Thus the dynamic phosphorylation of MyBP-C functions as a significant mechanism to modulate the actin-myosin interaction. Indeed, a truncated, non-functional form of MyBP-C in the mouse (Palmer et al. 2004) showed a significant impact on the balance between speed of contraction and speed of relaxation in isometric muscles under a variety of conditions (Janssen 2010a; Janssen 2010b), likely indicating MyBP-C as a critical and structural component in governing cardiac kinetics.

The titin molecule functions as a myofibrilar scaffolding protein spanning from the Z-disk to the M-band (Granzier and Irving 1995). In addition to this scaffolding role, titin also functions as a molecular spring contributing to the rate of cardiac relaxation. Titin contains a number of various elements that are altered during sarcomere re-lengthening to generate an elastic recoil, thus altering the passive tension of the muscle and aiding in muscle re-lengthening (LeWinter and Granzier 2010; Kruger and Linke 2011). In the normal heart, titin is co-expressed as 2 isoforms that exhibit different spring properties and therefore elastic recoil. The expression ratio of these isforms can become altered in various cardiac diseases to affect titin stiffness and cardiac relaxation (Wu et al. 2002). In addition to isoform switching titin is also a phospho-protein (Anderson and Granzier 2012; James and Robbins 2011). While a number of titin phosphorylation sites are proposed, not all function to affect relaxation (for review see (LeWinter and Granzier 2010). Two kinase specific phosphorylation’s of titin have however been demonstrated to specifically modulate cardiomyocyte passive tension and myocardial relaxation, PKA and protein kinase C (PKC). In humans, titin phosphorylation of the elastic N2B-Bus region by PKA increases the persistence length of this region, reducing passive tension resulting in decreased myocardial stiffness and improved diastolic filling (Yamasaki et al. 2002; Kruger et al. 2006; Kruger et al. 2009). Titin is also phosphorylated by PKCα in the PVEK region. Opposite to PKA phosphorylation, PKC phosphorylation reduces persistence length of the PEVK region to elevate titin-based passive tension which may also contribute to impaired myocardial relaxation (Hidalgo et al. 2009). Thus, through isoform switching and the phosphorylation of varied regions, titin functions to modulate cardiac myocyte shortening and myocardial relaxation.

4.1. Length-dependent activation

Length-dependent activation is the muscle-equivalent of the Frank Starling mechanism (de Tombe et al. 2010; Frank 1895; Starling 1918). As the ventricular volume increases (i.e. longer muscle/sarcomere length), intrinsic pressure (i.e. force) development is increased. In addition to the impact on force, the kinetics of muscle contraction and relaxation are also impacted by muscle length (Edman 1979; Allen and Kurihara 1979; Janssen and Hunter 1995). At a longer muscle length, the time needed to reach peak isometric force is longer, and the time required for the muscle to relax is likewise significantly prolonged (Kentish et al. 1986; Janssen and Hunter 1995). Often the first derivative of pressure (dP/dt) is taken as an indicator of contractile performance. Due to the increased pressure (or tension/stress in case of a linear muscle), maximal dP/dt increases, and this is often mistakenly interpreted as faster contractile kinetics. Similarly, the maximal fall of pressure/tension, the minimal value of dP/dt, is often erroneously interpreted as accelerated relaxation. When dP/dt is corrected for pressure development (i.e. divided by P), then the true kinetic timing parameter (s⁻¹) typically shows that with increased muscle length, kinetics of the contraction and relaxation are slower (Janssen 2010b). After a step-change in muscle length, the changes in kinetics of force are much more pronounced than changes in the Ca²⁺ transient decline rate (Allen and Kurihara 1982). In fact, at steady state, taken as a pure rate (s⁻¹), Ca²⁺ transient decline in isolated muscles at physiological temperature only slightly accelerates at higher length, while the decline in force is significantly decelerated (Monasky et al. 2008). In addition to these kinetic changes in the dynamic state, myofilament Ca²⁺ sensitivity is increased at longer muscle lengths (Allen and Kentish 1985; Kentish et al. 1986), largely explaining the molecular mechanism responsible for the slowed kinetics at longer sarcomere length.

Another part of length-dependent occurs via the Anrep effect. After an increase in sarcomere/muscle length, force is changed in a near-immediate step (Mateja and de Tombe 2012), followed by a much slower process that takes minutes. This latter process involves a change in the calcium transient (Alvarez et al. 1999; Luers et al. 2005), as well as changes in myofilament phosphorylation events (Monasky et al. 2010; Monasky et al. 2013; Wijnker et al. 2014). Combined, these changes further fine-tune the level of contractile activation, and prolong the relaxation at increased sarcomere/muscle length.

4.2. Frequency-dependent activation

As the heart rate increases, two distinct contractile parameters change: the force of contraction is generally increased, while the kinetics of the contraction are faster (Janssen and Periasamy 2007). Within the physiologically relevant heart rate, mammals increase force of contraction with frequency. This is most pronounced in larger mammals: humans can more than double their contractile force over their normal in vivo frequency range, while in rats this is only ~30%, and in mice often no more than 10% (Janssen and Periasamy 2007). For all species, the rate of contraction accelerates when heart rate goes up. The amplitude of contraction is mainly enhanced with frequency by enhanced Ca²⁺ cycling: with an increased number of beats, a net influx of Ca²⁺ “loads” the SR until a new “steady state” is reached, at which the cytosolic Ca²⁺ amplitude is greater. Although the amount of Ca²⁺ that enters the cell per beat is not drastically different, the number of beats per time unit is mainly causing the net increase in Ca²⁺ at higher frequency. The acceleration of contractile kinetics is much less understood, and involves changes in the kinetics of the Ca²⁺ transient, but likely also changes in the myofilament responsiveness (Varian and Janssen 2007; Varian et al. 2009; Tong et al. 2004), while changes in cross-bridge kinetics are potentially also a contributing factor. Combined, with increasing frequency of stimulation, the heart muscle accelerates, allowing for enhanced relaxation that is needed in order to allow sufficient filling prior to the initiation of the next beat. Again, acceleration is typically observed in multiple processes, Ca²⁺ transient decline, thin-filament activation, and cross-bridge kinetics, working in very close regulation to provide adequate cardiac muscle relaxation.

4.3. Adrenergic stimulation

The third main physiological regulator of cardiac pump function is beta-adrenergic stimulation. Independent of the typical increase in heart rate, covered above, β-adrenergic stimulation impacts several processes that in turn can impact on the rate of cardiac muscle relaxation. Upon adrenergic stimulation, PKA is the main enzyme responsible for phosphorylation of several proteins that then change their properties. LTCC phosphorylation will increase the amount of Ca²⁺ allowed to enter the cell each beat, and this increase in Ca²⁺ indirectly can impact the relaxation rate via Ca²⁺-depedent Serca activity. Phosphorylation of phospholamban is a major governor of the rate of Ca²⁺ transient decline (Roof et al. 2011; Kranias and Solaro 1982). Combined, this results in a very large increase in the intracellular Ca²⁺ transient. At the myofilament level, several proteins are impacted by PKA. Phosphorylation of TnI typically desensitizes the myofilaments, but is quantitatively less than the increase in the Ca²⁺ transient (i.e. the increase in Ca²⁺ outweighs the decrease in Ca²⁺ sensitivity) resulting in a net increase force production. Specifically on relaxation, the impact of phospholamban (increase speed of Ca²⁺ decline) and TnI phosphorylation (decrease in Ca²⁺ sensitivity) are synergetic, they both promote increased relaxation kinetics. Again, quantitatively the impact on Ca²⁺ transient decline and thin filament (de-)activation are rather similar, and none could be truly labeled a rate limiting step.

4.4. Integration of relaxation

The length- and frequency-dependent dissociation of the Ca²⁺ and force decline rates in the dynamic state strongly suggests that length-induced change in contractile kinetics are not solely, nor directly governed by altered Ca²⁺ transient decline, but rather at either the thin filament deactivation level, or alternatively at the level of cross-bridge kinetics. The rate of force redevelopment in intact cardiac muscle is close to the rate of thin-filament Ca²⁺ dissociation, a critical step in contractile de-activation. At the peak of contraction, which occurs at or near the systolic length in isometric contractions, cross-bridge cycling was estimated using the rate of tension redevelopment (k_tr). This k_tr was ~46 s⁻¹ in rat muscles at 37 °C (Milani-Nejad et al. 2013), virtually identical to the rate of Ca²⁺ dissociation from isolated cardiac myofibrils (~50 s⁻¹) at 37 °C as recently reported (Little et al. 2012). Moreover, the rates of these two processes are also similar to the rate at which intracellular Ca²⁺ declines in multicellular preparations (25–55 s⁻¹) at 37 °C when fluorescent ratios are calibrated and deconvoluted for speed of the dye under similar temperature and preparations (Janssen et al. 2002; Slabaugh et al. 2012). Thus, these three critical rates/processes have nearly identical rates at physiological temperature. This implies that in vivo there may not be a single step in kinetic governance which is rate limiting in the sense that acceleration of that step will produce a comparable increase in the rate of the force development (Davis et al. 2007). Thus, accelerating pressure development and decay in a beating heart may require changes in multiple kinetic steps. In contrast to acceleration, the rate could be decelerated by slowing down any single one of the contributing steps. This view would be consistent with previous finding of a tight coupling between the rate of force development and rate of relaxation and that the ratio of these rates is unaffected by load, frequency, or β-adrenergic stimulation (Janssen 2010b; Janssen 2010a).

On a cellular level, the pumping capability the heart is co-determined by the number of active cross-bridges and the speed at which they operate. Therefore, any condition that increases the rate of cross-bridge cycling can potentially enhance cardiac output. Based on our recent report demonstrating the acceleration of k_tr in intact muscles under near physiological conditions (Milani-Nejad et al. 2013) and experiments by others (Adhikari et al. 2004; Stelzer and Moss 2006; Korte and McDonald 2007), a decrease in muscle length is a candidate for such condition. Physiologically, a decrease in muscle length is encountered as the heart ejects towards the end of systole. Therefore, as the heart ejects, the rate of cross-bridge cycling is continuously accelerated which aids in increasing the amount of blood that is being pumped. Normally, cardiac output is reduced at lower preloads as dictated by the classical Frank-Starling relationship since the dramatic decline in force production outweighs an increase in cross-bridge cycling rate. It is probable that this length-dependent acceleration of cross-bridge cycling can potentially act as a system of checks and balances that acts to prevent a substantial drop in cardiac output and to partially restore the amount of blood that is being pumped by the heart at lower sarcomere lengths. This idea has been proposed by others (Hanft et al. 2008; McDonald 2011) and we believe it is a credible proposition to explain the role of accelerated cross-bridge kinetics at lower muscle lengths.

4.5. Limitation for the past and future

Quantification of the processes that impact overall cardiac muscle relaxation are unavoidably limited by the complexity of the system. The more reductionistic the method of assessment, the more accurate one can quantify a specific molecular process. Calcium transient decline, thin filament deactivation, and cross-bridge kinetics are all interrelated. Thus, the further a molecular step in any of these three processes is removed from integration with the other two, regulatory information is often lost, and the more ambiguous its interpretation for physiological relevance becomes. A careful consideration of each assessment system is warranted in light of the assessed parameter and its contribution to the overall process. Future studies should carefully weigh the impact of the degrees of reduction of the method and the experimental milieu (temperature, mechanical load, pH, etc.) of a single assessed parameter into the interpretation of its overall importance. Likewise, functional assessments in a complex system require cautions interpretation of the outcome parameter to specific underlying molecular events. To bridge the gap between individual molecular steps and complex integrative regulation, further developments of techniques that can probe specific molecular events in a complex system are needed. Enabling the investigation of a specific molecular interaction while preserving the complex integrative regulatory structure of the myocardium will ultimately unravel the regulatory contribution of each interaction in the complex nature of myocardial relaxation.

4.6. Relaxation, it is complicated: a summarizing conclusion

The relaxation of cardiac muscle is a multifaceted process (Figure 4). Although definitive quantification of separate processes can be technically achieved, the synergistic and antagonistic properties of each of the three main players in relaxation, intracellular Ca²⁺ decline, thin filament deactivation, and cross-bridge cycling kinetics, prevents the outcome of a single parameter measured in isolation to be an unambiguous quantitator. We believe that the quantitative impact of these three systems, when integrated, is so close that they each provide a nearly inseparable rate-limiting step in the overall process; if one of the three processes is sped-up by only a small amount, the other two would directly become rate-limiting. Conversely, slowing relaxation can be directly achieved by the impact of any of these three parameters, which then becomes (more) rate limiting. Relaxation is a process of intricate checks and balances, and should not be thought of as a single rate-limiting step that is regulated at a single protein level, but is a system level property that requires a fundamental integration of three governing systems: intracellular calcium decline, thin filament deactivation, and cross-bridge cycling kinetics.

Figure 4.

Cardiac muscle relaxation is a multifaceted process. Blue Squares: three main processes that heavily impact on the rate of cardiac muscle relaxation. Orange ovals: three main physiological processes that modulate the rate of cardiac muscle relaxation. Major direct interaction/impact between two processes is depicted by two-headed solid blue arrows, unresolved or minor interactions are depicted by two-headed grey dashed arrows. Green dashed arrows indicate the impact of a process on a rate that results in acceleration of the process. Red dashed arrows indicate the impact of a process on a rate that results in the slowing of the process. One-headed dashed grey arrows indicate unresolved, disputed, or minor impact. Red Pentagons: Post-translational modifications can impact each regulatory component of cardiac muscle relaxation.