The mechanism of the force enhancement by MgADP under simulated ischaemic conditions in rat cardiac myocytes

Abstract

In this study, the effects of MgADP and/or MgATP on the Ca²⁺-dependent and Ca²⁺-independent contractile force restoration were determined in order to identify the origin of the tonic force increase (i.e. ischaemic contracture) which develops during advanced stages of ischaemia. Experiments were performed at 15 °C during simulated ischaemic conditions in Triton-skinned right ventricular myocytes from rats. In the presence of 5 mm MgATP the maximal Ca²⁺-dependent force (P_o) of 39 ± 2 kN m⁻² (mean ± s.e.m.) under control conditions (pH 7.0, 15 mm phosphocreatine (CP)) decreased to 8 ± 1 % during simulated ischaemia (pH 6.2, 30 mm inorganic phosphate (P_i), without CP). This change was accompanied by a major reduction in Ca²⁺ sensitivity (pCa₅₀ 4.10 vs. 5.62). Substitution of MgADP for MgATP restored isometric force production and its Ca²⁺ sensitivity (pCa₅₀ 4.74 at 4 mm MgADP and 1 mm MgATP). In addition, it shifted the MgATP threshold concentration of Ca²⁺-independent force development to higher levels in a concentration-dependent manner. However, Ca²⁺-independent force was facilitated less by MgADP than Ca²⁺-dependent force. The MgADP-induced increase in force was accompanied by marked reductions in the velocity of unloaded shortening and the rate of tension redevelopment. These data and simulations using a model of cross-bridge kinetics suggest that the ischaemic force is not a consequence of a reduction in intracellular MgATP concentration, but identify MgADP as a key modulator of the cross-bridge cycle under simulated ischaemic conditions in cardiac muscle, with a much lower inhibition constant (0.012 ± 0.003 mm) than in skeletal muscle. Therefore, MgADP has a high potential to stabilize the force-generating cross-bridge state and to facilitate the development of ischaemic contracture, possibly involving a Ca²⁺ activation process in the ischaemic myocardium.

Previous investigations on the mechanical effects of ATP, its breakdown products and other metabolites have contributed greatly to our understanding of the actomyosin interaction in skeletal (e.g. Bremel & Weber, 1972; Cooke & Pate, 1985; Hibberd et al. 1985) and cardiac muscle preparations (e.g. Fabiato & Fabiato, 1975, 1978). However, most of our knowledge concerning the effects of MgADP on muscle mechanics originates from experiments performed on skeletal muscle preparations at physiological pH in the absence of inorganic phosphate (P_i; Siemankowski et al. 1985; Cooke & Pate, 1985; Hoar et al. 1987; Westerblad et al. 1998; Lu et al. 2001).

The effects of MgADP on the cross-bridge cycle in cardiac tissue are particularly of interest during advanced stages of cardiac ischaemia when intracellular P_i and H⁺ accumulation diminish force generation (Elliott et al. 1992). It has been suggested that after the depletion of the phosphocreatine (CP) store, MgATP hydrolysis increases MgADP significantly in the myofibrillar compartment at the expense of MgATP. Thus MgADP may potentially contribute to the development of ischaemic contracture (Ventura-Clapier & Veksler, 1994; Veksler et al. 1997; Stapleton & Allshire, 1998). However, in the presence of P_i and low pH, quantitative data on the effects of [MgADP] on cardiac force generation and on the cross-bridge cycle are sparse.

We therefore decided to investigate the interactions between [MgATP], [MgADP] and both Ca²⁺-dependent and Ca²⁺-independent force production under simulated ischaemic conditions (pH 6.2 and 30 mm P_i). Progression of the metabolic disturbance during ischaemia was mimicked by substituting MgADP for MgATP ([MgATP] + [MgADP] = 5 mm) in a concentration-dependent manner. In additional experiments the effects of a decrease in MgATP concentration without an increase in MgADP concentration were tested to isolate the MgADP-dependent component of ischaemic force restoration.

The interpretation of skinned fibre experiments in the presence of MgADP and the absence of CP is complicated by intracellular adenine nucleotide gradients caused by ATP hydrolysis and diffusion of the reactants (e.g. Cooke & Pate, 1985). In order to minimize the intracellular concentration gradients, isolated Triton-permeabilized myocytes were used in this study. In addition, model calculations were employed to evaluate the influence of the adenine nucleotide concentration profiles inside the cardiomyocytes.

The MgADP-specific changes in the kinetics of cross-bridge interaction were assessed by measuring the unloaded shortening velocity (V_o) and rate constant of tension redevelopment (k_tr). These parameters allowed the recognition of the dominant role of MgADP on cross-bridge transition rates in the presence of P_i, low pH and [MgATP], and the determination of a significantly lower inhibitory constant (K_i) of MgADP for myofibrillar ATPase in cardiac muscle than in skeletal muscle (Sleep & Glyn, 1986).

In the Appendix, a cross-bridge model is presented which accounts for the influence of the MgADP and MgATP concentrations on the isometric force under ischaemic conditions in cardiac muscle. This model is based on the formalism described by Pate & Cooke (1989) and incorporates more recent experimental (Kawai et al. 1993) and theoretical developments (Slawnynch et al. 1994). These modelling efforts suggest that the enhancement of the force-promoting role of MgADP under ischaemic conditions is a natural consequence of thermodynamic changes in the free energy profiles of the different cross-bridge states.

Thus, experimental results and model calculations both indicate that MgADP accumulation may result in a more pronounced tonic force increase under ischaemic conditions than under physiological conditions in the myocardium.

Methods

Myocyte isolation and experimental set-up

Experiments were performed in accordance with local ethical guidelines. Myocytes were isolated mechanically as described previously (Van der Velden et al. 1998). Briefly, hearts of Na-pentobarbitone-anaesthetized (20-35 mg (kg body weight)⁻¹, i.p., Sanofi, Libourne, France) Wistar rats (300-600 g) of either sex were rapidly excised. After excision, the hearts were perfused according to Langendorff with Tyrode solution (equilibrated with 95 % O₂-5 % CO₂) containing (mm): NaCl 128.3, KCl 4.7, CaCl₂ 1.36, MgCl₂ 1.05, NaHCO₃ 20.2, NaH₂PO₄ 0.42, glucose monohydrate 11.1 and 2,3-butanedione monoxime (BDM) 30 (Sigma, St Louis, MO, USA) (20 °C). The free right ventricular wall was then immersed in relaxing solution for cell isolation and mechanically disrupted within 5–10 s, using a tissue homogenizer. The resultant suspension of small clumps of myocytes, single myocyte-sized preparations and cell fragments was permeabilized with 0.3 % Triton X-100 (Sigma) for 5 min, washed and kept in relaxing solution for cell isolation at 0 °C for 6–24 h. A single myocyte was attached with silicone adhesive (100 % silicone, Dow Corning) to two thin stainless-steel needles while viewed by means of an inverted microscope. One needle was attached to a force transducer (SensoNor, Horten, Norway) and the other to a piezoelectric motor (Physike Instrumente, Waldbrunn, Germany), both connected to joystick-controlled micromanipulators. After curing for 50 min, the preparation was transferred from the mounting area to a small temperature-controlled well (volume 68 μl) containing control relaxing solution (Table 1), from which the myocyte could be transferred to a similar temperature-controlled well containing activating solution. During cell attachment and subsequent force measurements, myocytes were viewed at a magnification of × 320. Images were captured by means of a charged coupling device (CCD) video camera and stored on a personal computer. The average sarcomere length was determined by means of a spatial Fourier transform as described previously (Fan et al. 1997) and adjusted to 2.2 μm. The diameters of the preparation were measured microscopically, in two perpendicular directions. Cross-sectional area was calculated by assuming an elliptical cross-section. All chemicals were obtained from Merck (Darmstadt, Germany), unless indicated otherwise.

Table 1.

Compositions of the solutions

	pCa	Na2ATP(mM)	MgCl2(mM)	Ionic strength(mM)
Control solutions, MgATP 5mM; CP 15mM; pH 7.0; Pi 0mM
Relaxing	10.00	6.75	9.46	207
Activating	4.73	6.80	6.32	182
Ischaemic solutions, MgATP 5 mM; CP 0mM; pH 6.2; Pi 30mM
Relaxing	10.00	7.98	6.75	200
Activating	4.56	8.07	6.68	184
Ischaemic solutions, MgATP 5 mM; CP 0 mM; pH 6.2; Pi 30mM
Relaxing	10.00	20.51	6.74	198
Activating	4.54	20.58	6.67	182
Ischaemic solutions, MgATP 5 mM; CP 15 mM; pH 6.2; Pi 30mM
Relaxing	10.00	8.03	6.98	199
Activating	3.40	9.24	6.90	184
Ischaemic solutions, MgATP 0.01 mM; CP 15 mM; pH 6.2; Pi 30mM
Relaxing	10.00	0.016	2.00	198
Activating	3.40	0.018	1.93	184

All solutions contained, in addition, BES (100 mM). Relaxing solutions contained 7 mM BAPTA and activating solutions contained 7 mM CaBAPTA. CaBAPTA was made by mixing equimolar amounts of CaCO₃ and BAPTA. The ionic equivalent of the solutions was adjusted to 133 mM with 1,6-diaminohexane-N,N,N′,N′-tetraacetic acid. pH was adjusted with KOH.

Solutions

The composition of the solution used for cell isolation was (mm): MgCl₂ 1, KCl 100, EGTA 2, Na₂ATP 4 and imidazole 10 (pH 7.0, adjusted with KOH). All solutions for force measurements contained 1,2-bis(2-aminophenoxy)ethane-N,N,N'N'-tetraacetic acid (BAPTA; Acros Organics, Fairlawn, NJ, USA) as a Ca²⁺ buffer, because its Ca²⁺-chelating properties are less affected by low pH than those of EGTA. The purity of the BAPTA was determined as described by Harrison & Bers (1987) and was found to be 97.3 %. The compositions of the solutions for force measurements (shown in Table 1) were calculated as described previously (Stienen et al. 1999), using the stability constants listed by Brooks & Storey (1992) with appropriate temperature and ionic equivalent corrections (Harrison & Bers, 1989). The calculated free Mg²⁺ and total MgATP and MgADP concentrations of solutions were 1 and 5 mm, respectively, unless indicated otherwise. Physiological conditions were mimicked by applying solutions with a pH of 7.0 in the presence of CP (15 mm) and in the absence of P_i. Ischaemic conditions were simulated by decreasing the pH from 7.0 to 6.2 and by including 30 mm KH₂PO₄. Phosphocreatine was also omitted from the ischaemic solutions used to study the effects of MgADP (in combination with MgATP). The ionic strength of the solutions varied slightly (between 207 and 182 mm, depending on the solution type; see Table 1). Solutions with intermediate free Ca²⁺ concentrations were obtained by mixing the activating and relaxing solutions. To achieve maximal Ca²⁺ activation in the ischaemic activating solutions, appropriate amounts of CaCl₂ were added to cover the Ca²⁺ concentration range up to pCa 3.0. Total [ATP] and [ADP] were increased to account for the simultaneous Ca²⁺ binding to adenine nucleotides.

Force measurements

Isometric force was measured after the preparation had been transferred from the relaxing to the activating solution, by moving the stage of the inverted microscope. When a steady force was reached, the length of the myocyte was reduced by 20 % within 2 ms using the piezoelectric motor (slack test). As a result of this intervention, the force first dropped to zero and then started to redevelop. The rate of tension redevelopment was determined from the force signals after the myocyte had been restretched to its original length (L_o; see below). About 3 s after the onset of force redevelopment the myocyte was returned to the relaxing solution, where a slack test with a long slack duration (10 s) was performed to assess the passive force level. The active isometric force was calculated by subtracting the passive force from the total peak isometric force. Force redevelopment after the restretch was fitted to a single exponential to estimate the rate constant of force redevelopment (k_tr) at saturating Ca²⁺ levels under both control (pCa 4.73) and ischaemic conditions (pCa 3.4; Fig. 4B). The duration of the slack period was 21 ms under the control conditions. Similarly short slack durations did not provide good estimates of k_tr during simulated ischaemia and in the presence of MgADP. The slack duration was therefore increased to 900 ms in these latter measurements. The unloaded shortening velocity (V_o) was determined under ischaemic conditions (at pCa 3.2) using slack tests with a duration of 2.7 s, whereas the amplitude of the length changes was varied between 19 and 23 % of L_o (in five steps). V_o was derived from the slope of the linear regression line between the relative length change and the duration of unloaded shortening (Fig. 4A).

Figure 4. Reduction in cross-bridge cycling by [MgADP] under simulated ischaemic conditions.

A, the slack times increased more with increasing slack amplitudes (expressed as percentages of L_o) in the presence of 4 mm MgADP (and 1 mm MgATP, right) than in the presence of 2.5 mm MgADP (and 2.5 mm MgATP, left) at pCa 3.2. This reflects a decrease in the rate of unloaded shortening velocity (V_o). Length changes are shown schematically at the top and an expanded view of the corresponding force signals at the bottom. The zero force levels reached at different amplitudes of length changes are indicated by dashed lines, and are shifted vertically for illustrative purposes. End-points of slack times are connected by continuous straight lines. B, rates of tension redevelopment (k_tr) were determined by the exponential fitting of tension traces after restretching of the myocyte (as depicted at the top) to L_o at the end of slack tests from 80 % L_o. ○, control data obtained at pCa 4.73; ▪, recordings in the presence of 4 mm MgADP (and 1 mm MgATP) at pCa 3.4 under ischaemic conditions. Differences in k_tr are illustrated by superimposed results of exponential fits (dashed lines). A dash on the left indicates a zero force level. C, V_o and k_tr values (means ± s.e.m.) for various MgATP and MgADP concentration pairs (n = 5-15). An estimate for V_o (2 L_o s⁻¹) under control conditions is indicated by ▾. The curve fitted to V_o data (dashed line) resulted a K_i of 0.012 mm for MgADP.

Force and length signals were monitored by using an analogue pen recorder and were stored in a personal computer. The sampling rate during experiments was 20 Hz, while during slack tests it was 1 kHz.

Experimental protocol

The temperature during the measurements was set to 15 °C in order to maintain the mechanical stability of the permeabilized myocyte preparations. During the initial stage of the experiment, nonischaemic control parameters were determined. The first contracture was performed at saturating Ca²⁺ concentration (pCa 4.73). Thereafter, the sarcomere length was readjusted to 2.2 μm, if necessary. The second measurement at pCa 4.73 was used as a measure of the maximal force output (P_o) of the preparation. The next three to five test measurements were carried out under various experimental conditions, followed by another nonischaemic control activation at pCa 4.73. Measurements were continued unless maximal force output (P_o) declined below 70 %. The force production at submaximal levels of activation was normalized to the nearest reference force value obtained at maximal activation.

Mathematical modelling

In the absence of CP, the intracellular MgATP and MgADP concentrations depend on the interplay between ATP hydrolysis (resulting in MgATP breakdown and MgADP production) and diffusion. During simulated ischaemia the myokinase inhibitor P¹,P⁵-di(adenosine-5′) pentaphosphate (Boehringer Mannheim, Mannheim, Germany) did not modify the force recordings (see Results), so the myokinase activity was neglected in our calculations. Hence, with the assumptions of cylindrical geometry for the myocyte, with a radius (r_o) of 10 μm (average radius of myocytes), and equal diffusion constants for MgATP and MgADP (Cooke & Pate, 1985), the MgATP concentration (y) at a distance r from the centre of the myocyte at a given time t is determined by the following differential equation:

(1)

where D denotes the diffusion coefficient (20 μm² s⁻¹ inside the myocyte (Cooke & Pate, 1985) and 270 μm² s⁻¹ in the unstirred medium outside the myocyte (Yoshizaki et al. 1987)), a is the rate of MgATP consumption by myosin (0.2 mm s⁻¹ at infinite MgATP concentration; Ebus et al. 2001), K_m (10 μM) is the Michaelis-Menten constant for MgATP binding (Ebus et al. 2001) and K_i is the inhibition constant for MgADP, assuming competitive inhibition for the same binding site. Calculations were performed with two different values of K_i: 0.2 mm, determined in skeletal muscle (Cooke & Pate, 1985), and 0.012 mm, estimated on the basis of the V_o values measured in this study. [MgATP] (and [MgADP] = 5 mm – [MgATP]) was calculated by numerically solving Eqn (1) from r = 0 (the centre of the myocyte) to an outer radius (r_∞), set at 150 μm, with a maximal step size of 0.2 μm. This takes the possible influence of an unstirred layer around the myocyte into account. As a boundary condition at t = 0, the intracellular concentrations were considered to be equal to the nominal concentrations of the surrounding medium. At t = 0, ATPase activity started and consequently MgATP and MgADP concentration gradients developed, which became approximately stationary in less than 60 s. The rate of ATP hydrolysis and the diffusion constant for MgADP in solution were estimated as described by Ebus et al. (2001) and Yoshizaki et al. (1987), respectively, after appropriate correction for temperature. These simulations, as well as the model calculations described in the Appendix, were performed using Mathematica 4 (Wolfram Reseach, Inc., Champaign, IL, USA).

Data analysis

The relation between force and pCa was fitted to a modified Hill equation:

(2)

where P_Ca is the steady-state force, P_o is the steady isometric force at saturating Ca²⁺ concentration, the Hill coefficient (n_H) is a measure of the steepness of the relationship, Ca₅₀ (or pCa₅₀) is the midpoint of the relation, and P_-Ca is defined as the isometric force recorded at pCa 10.

Values are given as means ± s.e.m. for n myocytes obtained from at least five different hearts. Differences were tested by means of Student's unpaired t test at a 0.05 level of significance (P < 0.05).

Results

MgADP promotes force production under simulated ischaemic conditions in the absence and presence of Ca²⁺

The effect of MgADP on myocardial force production was studied under simulated ischaemic conditions in skinned myocardial cells (Fig. 1) at a sarcomere length of 2.2 μm and 15 °C. Peak isometric force recorded at pH 7.0 in the absence of P_i (control conditions) at saturating [Ca²⁺] (pCa 4.73) was defined as control P_o. This control P_o served as a reference (Fig. 1a) for the effects of simulated ischaemia (pH 6.2, 30 mm P_i; Fig. 1b) and subsequent alterations in MgADP concentrations (Fig. 1c and d).

Figure 1. Substitution of MgADP for MgATP enhances isometric force production under simulated ischaemic conditions.

The maximal isometric force (P_o) recorded in an isolated myocyte at pH 7.0 without added P_i (control) at saturating Ca²⁺ concentration (pCa 4.73; a) dropped after lowering of the pH to 6.2 and elevation of P_i to 30 mm (simulated ischaemia, indicated by a bold horizontal line) at pCa 3.4 in the presence of 5 mm MgATP (b). Subsequent partial substitution of MgADP for MgATP enhanced P_o (c) and induced force generation in the relaxing solution (at pCa 10, d and e). The total [MgATP] + [MgADP] was kept constant at 5 mm. During protocol a, the CP concentration was 15 mm; CP was not present during measurements b-d. The short-dashed line indicates zero force level. The long-dashed line at ≈7 % of the control P_o indicates the passive force level.

The first two contractures in Fig. 1 reveal a marked reduction in peak isometric force from a control of 41.1 kN m⁻² to 1.9 kN m⁻² under simulated ischaemic conditions at saturating [Ca²⁺] in the presence of 5 mm [MgATP]. Subsequent activation in the presence of 1 mm MgATP and 4 mm MgADP demonstrated (as illustrated by Fig. 1c) that the ischaemic force production was greatly enhanced, to 23.6 kN m⁻², in this case. When the myocyte was exposed to the same mixture at pCa 10 (i.e. in the relaxing solution; Fig. 1d) the force development was relatively small (4.1 kN m⁻²). This force component (P_-Ca) was obtained after subtraction of the passive force level as indicated in the Methods. Hence, it was most probably a consequence of the altered [MgATP] : [MgADP] ratio. Figure 1e illustrates that P_-Ca was further increased (i.e. to 11 kN m⁻²) at 4.5 mm MgADP and 0.5 mm MgATP.

A decrease in [MgATP] in combination with a rise in [MgADP] promotes ischaemic force development more effectively than low [MgATP] alone

The adenine nucleotide concentration dependences of ischaemic P_o and ischaemic P_-Ca were obtained by using a range of MgATP concentrations (Fig. 2). In one series of measurements, a range of MgATP concentrations (between 5 and 0.1 mm) was applied, while the total adenine nucleotide concentration ([MgADP] + [MgATP]) was kept constant at 5 mm (Fig. 2A). Another series of measurements was performed in which only [MgATP] was varied (from 5 to 0.01 mm) (Fig. 2B) in order to isolate the pure [MgATP] dependence of the isometric force. In these experiments, intracellular MgADP accumulation due to actomyosin ATPase was avoided by the inclusion of 15 mm phosphocreatine.

Figure 2. The isometric force is greatly enhanced by [MgADP] under simulated ischaemic conditions.

A, the peak isometric force (expressed as a fraction of the control P_o) increased both at saturating [Ca²⁺] (pCa 3.4, •) and in the relaxing solution (pCa 10, ○) when the reduction of [MgATP] was accompanied by an increase in [MgADP] (from a [MgATP] of 2.5 mm downwards). B, in the absence of MgADP the isometric force was enhanced only at lower [MgATP], either in the presence of Ca²⁺ (pCa 3.4, ▪, below [MgATP] = 0.25 mm) or in the absence of Ca²⁺ (pCa 10, ▪, below [MgATP] = 0.1 mm). Symbols indicate means ± s.e.m. (n = 6-20). All data resulted from simulated ischaemia experiments. Data in A were recorded in the absence of CP. In contrast, data in B were obtained in the presence of CP (15 mm). The continuous lines indicate the cross-bridge simulations based on the model described in the Appendix.

Figure 2 demonstrates that the originally minute ischaemic force values present at 5 mm MgATP gradually increased towards the nonischaemic reference value (i.e. towards 1) at low [MgATP]. It is also apparent that, in the presence of MgADP, the isometric force increased to higher levels than in its virtual absence. Comparison of the means of the ischaemic force values at identically high Ca²⁺ concentrations (P_o; • vs. ▪, pCa 3.4) and low Ca²⁺ concentrations (P_-Ca; ○ vs. ▪, pCa 10) indicated that, in the presence of MgADP, P_o and P_-Ca were both enhanced at intermediate MgATP concentrations. Comparison of the forces in the absence and presence of Ca²⁺ revealed that P_o is more sensitive than P_-Ca to a decrease in MgATP. Furthermore, in the presence of MgADP the force levels became elevated at significantly higher MgATP concentrations than in its absence. In summary, MgADP contributed greatly to the increase in ischaemic force when [MgATP] was less than 5 mm (up to 0.1 mm MgATP) at pCa 3.4. This increase in ischaemic force up to a [MgATP] of 0.5 mm was chiefly due to enhancement of the Ca²⁺-activated force.

Figure 2 also presents computer simulations based on the cross-bridge model described in the Appendix. It can be seen that the simulations agree well with the data at saturating Ca²⁺ concentrations. Hence the model provides an adequate explanation of the enhanced force-promoting role of MgADP under mimicked ischaemic conditions.

MgADP partly restores the Ca²⁺ sensitivity of force production under ischaemic conditions

To gain further insight into the MgADP-associated recovery of ischaemic force, the Ca²⁺ sensitivities of the isometric force (Fig. 3) under control and simulated ischaemic conditions (at [MgATP] = 5 mm) were compared with the Ca²⁺ sensitivity observed under ischaemic conditions in the presence of MgADP. To assess the effect of MgADP on the Ca²⁺ sensitivity, test solutions containing 4 mm MgADP and 1 mm MgATP were chosen because P_-Ca was relatively small (3 ± 1 % of the control P_o at pCa 10) at these nucleotide concentrations. Moreover, a number of reports (Allen et al. 1985; Kingsley et al. 1991) have suggested that ischaemic contracture might develop at intracellular MgATP concentrations of ≈1 mm. The isometric force values expressed relative to the control (Fig. 3A) illustrate that MgADP partly restored the isometric force not only at saturating (to 49 ± 2 % of the control) but also at intermediate Ca²⁺ concentrations. Partial recovery of the Ca²⁺ sensitivity is illustrated in Fig. 3B, which shows force values normalized to the maximal isometric force levels and the curves obtained by fitting the data to the Hill equation. Under the control conditions, pCa₅₀ was 5.62 ± 0.03. It decreased to 4.10 ± 0.07 during simulated ischaemia and recovered to 4.74 ± 0.05 when the 4 mm MgATP was replaced by 4 mm MgADP (these changes were highly significant, P < 0.0001). The Hill coefficient (n_H) decreased from the control value of 3.1 ± 0.2 to 1.9 ± 0.3 (P < 0.01) due to simulated ischaemia, and did not change significantly when 4 mm MgADP (and 1 mm MgATP) was applied (n_H = 2.0 ± 0.2).

Figure 3. The relations between force and pCa indicate the partial recovery of the Ca²⁺ sensitivity of isometric force production under ischaemic conditions in the presence of MgADP.

Averaged force vs. pCa relations were obtained by fitting means of force values to the Hill equation under control conditions (○) or simulated ischaemic conditions in the presence of 5 mm MgATP + 0 mm MgADP (▪) and in the presence of 1 mm MgATP + 4 mm MgADP (▪). A, means of force values are expressed relative to the control P_o (relative force vs. pCa relation). B, means are normalized to the reconstructed P_o values resulting from curve fittings on A (normalized force vs. pCa relation). Symbols depict means ± s.e.m. (n = 8-13) in A; error bars are omitted from B.

Increasing MgADP concentration decreases V_o and k_tr under ischaemic conditions

The effects of the different [MgADP] and [MgATP] combinations on ischaemic V_o and k_tr were studied at saturating Ca²⁺ concentrations. The V_o was determined from the force signals obtained when the amplitude of shortening during slack tests was varied. Figure 4A demonstrates that the same increases in the amplitude of the length changes resulted in more pronounced elongations in slack time when [MgADP] was increased from 2.5 to 4 mm ([MgATP] decreased from 2.5 to 1 mm). V_o decreased from 0.38 to 0.13 L_o s⁻¹ as a result of this change in adenine nucleotide composition. The magnitude of k_tr was obtained by fitting an exponential to the force transients after restretching of the myocytes to L_o. These measurements were also performed under control conditions (5 mm MgATP). The example in Fig. 4B illustrates that the time course of force recovery was greatly slowed in an ischaemic solution containing 4 mm MgADP and 1 mm MgATP (k_tr = 0.71 s⁻¹) in comparison with the control (nonischaemic) value (k_tr = 9.78 s⁻¹). The means of the measured V_o and k_tr values, together with an estimate of 2 L_o s⁻¹ for V_o under the control conditions (Ricciardi et al. 1994; McDonald et al. 1998), are shown in Fig. 4C. The marked and gradual reduction in k_tr on elevation of the [MgADP] (and decrease of the [MgATP]), together with the similar concentration dependence of V_o, suggests that a reduction in the cross-bridge cycling rate is involved in the observed [MgADP]-dependent increase in force under the simulated ischaemic conditions.

The measurements of V_o at different MgADP and MgATP concentrations were also used to estimate the inhibition constant for MgADP (K_i) under ischaemic conditions. K_i was obtained from the curve fit shown in Fig. 4C, with the assumption of the competitive inhibition of MgADP and MgATP for the same myosin binding site (Cooke & Pate, 1985):

(3)

where V_o,max denotes the velocity of unloaded shortening at 5 mm MgATP and K_m (10 μM) is the Michaelis-Menten constant for MgATP binding (Ebus et al. 2001). The curve fit resulted in a V_o,max (± s.d.) of 0.66 ± 0.10 L_o s⁻¹ (which is similar to the value obtained by Ricciardi et al. (1994) at pH 6.2) and a K_i of 0.012 ± 0.003 mm.

In some experiments (n = 5 myocytes) P¹,P⁵-di(adenosine-5′) pentaphosphate (0.2 mm) was included in the test solutions in order to determine the potential effect of the myokinase activity on the intracellular [MgADP] and the subsequent force production during ischaemic conditions. Previous experimental efforts that followed the same approach led to controversial results (Ventura-Clapier & Veksler, 1994; Veksler et al. 1997; Stapleton & Allshire, 1998). In our experiments no effect of the myokinase inhibitor P¹,P⁵-di(adenosine-5′) pentaphosphate on the mechanical data was observed under the simulated ischaemic conditions (data not shown).

Reconstruction of intra- and extracellular MgATP and MgADP concentration gradients for myocytes

Cooke & Pate (1985) calculated the intracellular concentration gradients of adenine nucleotides in skinned skeletal muscle fibres activated in the absence of CP. We performed similar calculations for preparations of myocytes with significantly smaller diameters (20 μm in our calculations; Fig. 5). During our experiments, we did not routinely stir the solutions, so extracellular diffusion and an unstirred layer were therefore taken into account. The extracellular adenine nucleotide diffusion constant (270 μm² s⁻¹) was derived in accordance with Yoshizaki et al. (1987). The ratio of this value for the extracellular diffusion (270 μm² s⁻¹) and that used by Cooke & Pate (1985) for the intracellular diffusion (20 μm s⁻¹) is significantly higher than the ratio found by Kushmerick & Podolsky (1969). Therefore, model calculations were also performed for cases in which the intracellular adenine nucleotide diffusion constant was raised to 110 μm² s⁻¹ in accordance to this latter study (○, •). Figure 5 reveals that the intracellular MgATP concentrations are significantly reduced compared to the nominal ones only in the event of no stirring, with the lower diffusion constant. This might imply that our experimentally obtained relationship between the nominal MgATP (and MgADP) concentrations and force could have been distorted by the combination of MgATP hydrolysis and limited diffusion. In three myocytes, however, where vigorous stirring was switched on and off in a repetitive fashion, no appreciable difference in force could be discerned at various MgATP and MgADP levels, suggesting that the model calculations illustrated by ○, • or ▪ (Fig. 5B) reflect our experimental conditions more faithfully. This indicates that small vibrations in the set-up provide adequate stirring of the solution and/or that the rate of intracellular diffusion of the adenine nucleotides is greater than 20 μm² s⁻¹. Furthermore, it may be noted that a reduction in the K_i for MgADP of ATPase activity from 0.2 mm (Cooke & Pate, 1985) to the K_i value obtained in this study on the basis of V_o measurements, 0.012 mm, would reduce the deviation between the mean and nominal MgATP concentrations to less than 25 %.

Figure 5. The extent of possible intracellular MgADP concentration changes due to an interplay between actomyosin ATPase and adenine nucleotide diffusion in the absence of CP.

A, calculations of MgATP concentration profiles inside and outside the preparations under ischaemic conditions according to Eqn (1). The initial [MgATP] and [MgADP] were 1 and 4 mm, respectively. Concentration profiles illustrate results of calculations with low intracellular adenine nucleotide diffusion (20 μm² s⁻¹). B, log-log plot of averaged [MgATP] for a myocyte cross-section with a diameter of 20 μm as a function of the nominal [MgATP] in the bathing solution. Symbols illustrate the calculated mean [MgATP] for different intracellular diffusion constants and the presence or absence of stirring (•, 110 μm² s⁻¹, stirred; ○, 110 μm² s⁻¹, unstirred; ▪, 20 μm² s⁻¹, stirred; ▪, 20 μm² s⁻¹, unstirred). Calculations involving low intracellular adenine nucleotide diffusion (20 μm² s⁻¹) in the absence of stirring resulted in a significant deviation from the nominal [MgATP]. Data points illustrate results of calculations with K_i = 0.2 mm. Model calculations with a lower inhibitory constant (K_i = 0.012 mm) resulted in smaller (< 25 %) concentration differences.

Discussion

This paper characterizes the influence of MgADP on Ca²⁺-dependent and Ca²⁺-independent force in the presence of P_i and at low pH in isolated myocyte preparations. Kinetic data and model calculations of cross-bridge cycling demonstrate the key role of MgADP in promoting force generation during advanced stages of cardiac ischaemia.

MgADP increases isometric force under ischaemic conditions

MgADP promoted both the active and the Ca²⁺-independent force under simulated ischaemic conditions (Fig. 2). Between MgADP concentrations of 2.5 and 4.5 mm, the increase in the active, Ca²⁺-activated force was chiefly responsible for the gradual recovery in isometric force. Above 4.5 mm MgADP, however, the Ca²⁺-independent component became dominant. In the presence of 1 mm MgATP and 4 mm MgADP the isometric force recovered to almost 50 % of the nonischaemic control value. Quantification of the active component at this force level is complicated because of the cooperative interaction between the MgADP-bound cross-bridges and the Ca²⁺ activation process (Lu et al. 2001). However, the low force value in the absence of Ca²⁺ (3 % of the control) implies that this cooperative interaction plays a minor role in the presence of 1 mm MgATP and 4 mm MgADP under the ischaemic conditions.

In our experiments, 4 mm MgADP partly restored the Ca²⁺ sensitivity of isometric force production (from pCa₅₀ 4.1 to 4.74, ΔpCa₅₀ = 0.64, which corresponds to a 61.2 μM difference in free [Ca²⁺]) in the presence of 1 mm MgATP. Godt & Nosek (1989), using 0.7 mm MgADP, could not prevent the reduction in isometric force and in its Ca²⁺ sensitivity when 17.38 mm P_i was added and pH was reduced from 7.0 to 6.65, either in skeletal or in cardiac muscle preparations from the rabbit. Hence, our findings indicate that higher MgADP concentrations than applied by Godt & Nosek (1989) are required to effectively oppose the depressant effects of P_i and low pH on the maximal Ca²⁺-activated force and its Ca²⁺ sensitivity in cardiac muscle.

MgADP modulates overall cross-bridge kinetics under ischaemic conditions

It is generally accepted that the rate of cross-bridge detachment limits the unloaded shortening velocity (e.g. Ferenczi et al. 1984) and that MgADP dissociation from actomyosin is sufficiently slow to control this process (Siemankowski et al. 1985; Martin & Barsotti, 1994). Increase of the level of MgADP in competitive inhibition with the declining MgATP level (Pate & Cooke, 1989) would then conserve cross-bridges in strongly bound force-generating states, resulting in an apparent reduction in overall cross-bridge cycling rate and an increase in isometric force. P_i accumulation, however, inhibits the transition leading to force generation (Hibberd et al. 1985; Kentish, 1991; Palmer & Kentish, 1994) and may accelerate transitions between cross-bridge states. In the presence of ischaemic metabolites (30 mm P_i and pH 6.2), a decrease in the MgATP concentration reduced the rate of cross-bridge cycling, but major alterations became apparent only below 1 mm MgATP (Ebus et al. 2001).

Our V_o and k_tr data show that application of MgADP (with decreasing [MgATP]) in combination with the ischaemic metabolites resulted in a large and concentration-dependent reduction in overall cross-bridge cycling rate even at relatively high [MgATP] (>1 mm). On the basis of these observations and data in the literature (Ricciardi et al. 1994; McDonald et al. 1998), we postulate that V_o and k_tr report similar relative changes in overall cross-bridge kinetics between [MgADP] of 2.5 and 4.9 mm. The value of 0.35 L_o s⁻¹ for V_o in the presence of 2.5 mm MgADP (and 2.5 mm MgATP) is considerably less than expected on the basis of acidosis (Ricciardi et al. 1994), and cannot readily be explained by the combination of acidosis and P_i either (Cooke et al. 1988). Thus, the reduction in V_o and k_tr, together with the profound effects on isometric force production and its Ca²⁺ sensitivity, strongly suggest that the overall cross-bridge kinetics and the distribution between weakly and strongly bound cross-bridges are effectively influenced by MgADP in the presence of P_i, low pH and low [MgATP].

Values of the inhibition constant (K_i) of MgADP for myofibrillar ATPase in skeletal muscle fibres range between 0.1 and 0.2 mm (cf. Sleep & Glyn, 1986). The results of Cooke & Pate (1985) suggest that the inhibition constants for shortening velocity and ATPase are similar. Our measurements of V_o at different MgADP concentrations suggest that K_i might be considerably less (0.012 ± 0.003 mm) in rat cardiac myocytes. This reduction by an order of magnitude is surprising but it is consistent with the previous qualitative observation that cardiac contractile proteins are more sensitive than skeletal muscle proteins to [MgADP] (Tian et al. 1997).

It appeared that the [MgATP] dependences of the ischaemic force with and without Ca²⁺ diverged more in the presence of MgADP than in its absence (Fig. 2). The most likely explanation for this observation is that alterations in the distribution of cross-bridges due to the combination of MgADP and low MgATP enhanced the cooperative process of Ca²⁺ activation more effectively than did low MgATP concentration alone. Alternatively, in the absence of CP, diffusion limitations might have resulted in higher intracellular MgADP and lower MgATP concentrations during the mimicked ischaemic conditions. Our model calculations and experiments with stirring, however, argue against this latter possibility. The apparent lack of an appreciable intracellular adenine nucleotide concentration gradient can be explained by the smaller diameter of the myocytes compared to skinned skeletal muscle fibres, a faster intracellular nucleotide diffusion than used by Cooke & Pate (1985), the low K_i value of MgADP for myofibrillar ATPase in cardiac tissue, or by a combination of these factors.

The simulations of the cross-bridge model for cardiac tissue (described in the Appendix) clearly indicate that the alterations in metabolite concentrations and their impact on the free energy change of ATP hydrolysis under ischaemic conditions are sufficient to explain the change observed in the MgATP dependence of force development (Fig. 2). Therefore, it appears that the enhancement of the force-promoting role of MgADP under ischaemic conditions is a natural consequence of the thermodynamic changes in the free energy profiles of the different cross-bridge states.

MgADP accumulation during ischaemia

Extrapolation of our results to the intact ischaemic myocardium is complicated by differences between the applied experimental and in vivo conditions. While the force-P_i relationship was independent of temperature in skeletal myofibrils of the rabbit (Tesi et al. 2002), intracellular acidification decreased the contractile force (Pate et al. 1995) much less at 30 than at 10 °C. The effect of temperature on the P_i, pH and MgADP dependences of myocardial force has not yet been extensively investigated. However, based on a postulated decreased myocardial effect of acidosis at 37 °C, restoration of the contractile force by MgADP is expected in the presence of lower MgADP concentrations than shown in this study.

In contrast to the applied isometric conditions, length changes occur during the physiological cardiac cycle. Therefore, one may speculate that MgADP may affect cross-bridges differently during shortenings (i.e. during isotonic conditions). The resemblance of the [MgADP] dependences of k_tr (measured at a constant 2.2 μm sarcomere length) and of V_o (measured at 79–83 % of L_o), however, argues against this possibility.

The physiological myoplasmic MgADP level ([MgADP]_i) is kept low by ATP resynthesis, a process depending chiefly on the creatine kinase reaction. However, during myocardial ischaemia the exact [MgADP]_i, and more precisely [MgADP]_i in the myofibrillar compartment, is unknown. Following the cessation of blood flow, the intracellular CP pool rapidly declines, leading ultimately to a decrease in [MgATP]_i and to the accumulation of its breakdown products (Allen & Orchard, 1987), possibly in a spatially inhomogeneous manner. MgADP might be degraded further (Allen et al. 1985) by the myokinase reaction. The calculation of [MgADP]_i during ischaemia is not straightforward (Ingwall, 1987) because creatine kinase (Ventura-Clapier & Veksler, 1994), myokinase (Golding et al. 1995) and other enzymes involved in the catabolic processes (Gustafson et al. 1999) are all sensitive to ischaemic metabolites. Recent data on intact skeletal muscle fibres suggest that [MgADP]_i may reach levels high enough to induce marked alterations in cross-bridge kinetics (Westerblad et al. 1998).

Results of this study indicate that MgADP stabilizes the force-generating cross-bridge state in the presence of ischaemic metabolites, causes an increase in Ca²⁺ sensitivity, facilitates the process of Ca²⁺ activation and shifts the MgATP threshold concentration of Ca²⁺-independent force development to higher levels. All of these mechanisms may contribute to the development of myocardial ischaemic contracture at relatively high [MgATP]_i, provided that MgADP reaches sufficient intracellular levels during ischaemia.

APPENDIX

Cross-bridge model for cardiac muscle

To simulate the MgATP dependences of isometric force under the mimicked ischaemic conditions given in the text (Fig. 2), we used the Pate & Cooke (1989) model with modifications in the free energy profiles and rate constants, as described in Tables A1 and A2. The key features of this five-state cross-bridge model are illustrated in Fig. A1. It is based on the biochemical scheme for ATP hydrolysis shown in Fig. A1A. The transitions between the states depend on the spatial variable x (cross-bridge distortion). The fractional occupancy of the cross-bridges in each state (i) is denoted by the function n_i(x). For the definitions of the rate constants governing the transitions between states, see the legend to Table A2. The modified free energy profiles under the control and ischaemic conditions, shown in Fig. A1B, were obtained by adapting the free energy profiles for fast skeletal muscle (Getz et al. 1998) according to the difference in association constants between cardiac and fast skeletal muscle (Kawai et al. 1993). Numerical integration of the set of differential equations describing the cross-bridge cycle described in Fig. A1A was performed by using Mathematica (version 4.0) and a personal computer (G3, Apple), with a range of cross-bridge distortions (x) from −4 to +10 nm.

Figure A1. A five-state model for cross-bridge action in cardiac muscle.

A, biochemical scheme of the cross-bridge cycle (M, myosin; A, actin; AM, actomyosin complex; D, ADP; P, inorganic phosphate; T, ATP). The free energy profiles, forward rate constants and cross-bridge distributions under control conditions (pH 7, P_i 0.1 mm, MgADP 30 μM, MgATP 5 mm) and mimicked ischaemic conditions (pH 6.2, P_i 30 mm, MgADP 4 mm, MgATP 1 mm) are plotted as a function of the cross-bridge distortion (x) in B, C and D, respectively. The subscripts refer to the states defined in Table A1. n_i(x) denotes the fractional occupancy of cross-bridges in state i at distortion x. The occupancy of n₅ is very small and is not visible in D.

Table A1.

Free energy in units of kT as a function of cross-bridge distortion (x)

G1(x) = 0

G2(x) =−2.3

G3(x) =−1.9 + (κ/2)(x – h)2

G4(x) =−11.5 + (κ/2)x2+ ln[Pi]

G5(x) =G4(x) + 8.4 + ln[ADP]

ΔGATP =−13.1 + ln([ATP]/([ADP][Pi]))

Subscripts correspond to states in Fig. A1A as follows: 1, M.T; 2, M.D.P; 3, AM.D.P; 4, AM.D; 5, AM. κ = 1.8 κT nm⁻², where κ is the elastic force constant, κ is the Boltzmann constant and T is the absolute temperature; h = 6 nm.

Table A2.

Rate constants (s⁻¹) as a function of distortion (nm)

Control conditions	Ischaemic conditions (pH 6.2)
k1,2 = 50	k1,2 = 50
k2,3 = 150 exp{-(x – h)/1.1)2}	k2,3 = 150 exp{-(x – h)/1.1)2}
k3,4 = 50/{1 + exp(hκ(x – h))}	k3,4 = 25/{1 + exp[hκ(x – h)]}
k4,5 = 250	k4,5 = 450
k1,5 = 5 exp{-(x/1.08)2}	k1,5 = 20 exp{-(x/1.08)2}

Subscripts correspond to states in Fig. A1A as indicated in Table A1. Values for κ and h as in Table A1. The rate constants from state i to state j are indicated by k_i,j. Reverse rates result from the Gibbs equation k_i,j =k_j,i exp(G_j–G_i)/kT, using the free energies listed in Table A1. At pH 6.2, P_i release (k_3,4) was assumed to be decreased 2-fold (cf. Chase & Kushmerick, 1988), and ADP release (k_4,5) was assumed to be increased almost 2-fold in order to account for the reduction in the maximum force and the increase in tension cost (Potma et al. 1995; Ebus et al. 2001). The 4-fold increase in rate k_1,5 at pH 6.2 resulted in the correspondence between the data and the simulated curves shown in Fig. 2A and B.

In our simulations, the size of the power stroke (h) was increased from 4 to 6 nm. This change proved necessary in order to simulate the larger changes of isometric force produced by P_i and MgADP in cardiac muscle compared to fast skeletal muscle. In addition, use was made of the distortion dependence suggested by Slawnych et al. (1994) for the rate constants governing the power stroke and cross-bridge detachment. This latter modification reduced the number of parameters in the model.

Finally, relatively minor changes in the rate constants were made by trial and error so as to improve the correspondence between the data in Fig. 2 and the computer simulations.

It can be concluded from Fig. 2 that this model provides an adequate description of the reduction in force under mimicked ischaemic conditions at 5 mm MgATP, and of the rise in force when [MgATP] is reduced both in the absence and in the presence of CP. This model unifies a robust collection of recent theoretical advances on cross-bridge action and experimental data in both cardiac and skeletal muscle but it is certainly not unique.