The role played by ADP in modulating cross-bridge function has been difficult to study, because it is hard to buffer ADP concentration in skinned muscle preparations. To solve this, we used an analog of ADP, spin-labeled ADP (SL-ADP). SL-ADP binds tightly to myosin but is a very poor substrate for creatine kinase or pyruvate kinase. Thus ATP can be regenerated, allowing well-defined concentrations of both ATP and SL-ADP. We measured isometric ATPase rate and isometric tension as a function of both [SL-ADP], 0.1–2 mM, and [ATP], 0.05–0.5 mM, in skinned rabbit psoas muscle, simulating fresh or fatigued states. Saturating levels of SL-ADP increased isometric tension (by P′), the absolute value of P′ being nearly constant, ∼0.04 N/mm2, in variable ATP levels, pH 7. Tension decreased (50–60%) at pH 6, but upon addition of SL-ADP, P′ was still ∼0.04 N/mm2. The ATPase was inhibited competitively by SL-ADP with an inhibition constant,K i, of ∼240 and 280 μM at pH 7 and 6, respectively. Isometric force and ATPase activity could both be fit by a simple model of cross-bridge kinetics.
- skeletal muscle
- cross-bridge modeling
during skeletal muscle fatigue, several major mechanical and energetic changes take place. These changes include a decrease in the maximal tension (P0), a slower maximal contraction velocity (V max), a slower rate of relaxation (15,16, 24), and a higher tension economy, i.e., more tension generated per ATP hydrolyzed (9, 10). A popular hypothesis is that many of these changes may be due to the effects of increased levels of specific metabolites, including ADP, on muscle cross bridges. However, data to support this hypothesis have not been unambiguous, and many aspects of fatigue remain unexplained.
Studies of fatigue in vivo are complex because numerous metabolites change, making the correlation with the alterations of the properties of the muscle difficult to establish (for review, see Refs.12 and 20). To delineate the effects of a single metabolite, such as ADP, permeabilized isolated fibers have been studied in vitro (8, 13, 19, 23, 27, 30). Measurements made at 10–15°C suggested that the drop in tension is probably due to the lower pH and higher free inorganic phosphate concentration ([Pi]) observed during fatigue (5, 28, 31,42), but these effects are much reduced at more physiological temperatures (34, 42, 44, 41). A lower pH is also known to decrease contraction velocity; however, it does not completely account for the drop in V max seen during fatigue (34, 42).
According to the accepted model of the actomyosin cross-bridge cycle, ADP, which increases from 20 to 200 μM during fatigue (14), should compete with ATP for the ATP binding site on myosin and thereby slow down cross-bridge detachment (13, 36,38). This, in turn, should inhibit ATPase activity and contraction velocity and should enhance isometric tension. Together, these effects would increase the economy of contraction. However, to date the observed effects of increased ADP on the tension and ATPase activity, although in the right direction, have been found to be too small to make a significant contribution (4, 8, 13, 29, 30,40).
In skinned muscle studies, an ATP-regenerating system [with creatine kinase (CK) or pyruvate kinase (PK)] can be used to maintain ATP concentrations within the fiber. However, if one were to add additional ADP to a solution with an ATP-regenerating system, it would quickly be phosphorylated to ATP, leaving little time to observe the effects of increasing ADP on fiber mechanics. To circumvent this problem, investigators have used high concentrations of nucleotides in the absence of a regeneration system and have estimated intracellular concentrations by analyzing the diffusion of nucleotides (8). Photolysis of caged compounds has also been used for instantaneous generation of ADP (29). Also, higher ADP concentrations have been generated by addition of extra creatine (Cr) to the bathing solution (4).
We have recently come up with one solution that facilitates the study of the effects of ADP in skinned muscle preparations while controlling other nucleotide concentrations with a regeneration system. We have found that attachment of a spin label, to the 2′ or 3′ positions on the ribose of ATP, greatly inhibits interaction with CK or PK. This analog binds to myosin and to actomyosin with an affinity that is equal to that of ADP (11), and mechanical data presented here reconfirmed this conclusion. Thus we were able to use an ATP-regenerating system to maintain a well-defined concentration of ATP within the fiber, avoiding the buildup of ADP from hydrolysis of ATP, and we could then measure the mechanical responses of the fiber over wide ranges of ATP and spin-labeled ADP (SL-ADP) concentrations. We determined the effects of SL-ADP on ATPase activity and tension at varying concentrations of ATP, finding that SL-ADP changes ATPase activity and tension in a competitive manner. The cross-bridge interactions are also affected by lowering of pH and/or accumulation of Pi, discussed above, and under such conditions we hypothesized that the effects of SL-ADP may be different from those obtained at control conditions (i.e., high ATP, low Pi, pH 7).
The results can be explained by a simple model in which SL-ADP competes with ATP at the end of the power stroke. An adequate fit to the data required that cross bridges in force-generating states were capable of rapid exchange with pre-power stroke cross bridges. Thus the transition from pre-power stroke cross bridges to force-generating cross bridges can be reversed by binding of SL-ADP, which occurs at the end of the power stroke.
Rabbits (New Zealand White) were heavily sedated and euthanized according to the guidelines of the Institutional Animal Care and Use Committee for the University of California, San Francisco. Psoas fibers were harvested and chemically skinned as described previously (7). For mechanical experiments, single fibers were dissected from a bundle of fibers on a cold stage while still immersed in the skinning solution. A single fiber was then mounted between a solid-state force transducer and a rapid motor for changing fiber length, as previously described (7), using Duco cement (Dencon Consumer Products, Danvers, MA) diluted in acetone. The apparatus had two temperature-controlled wells, and fibers could be rapidly switched between solutions. The fiber was then lowered into a relaxing solution, and fiber length and thickness were measured. The length of the unfixed portion of the fiber between the arms varied from 3 to 6 mm, fiber diameter ranged from 50 to 80 μm, and initial sarcomere length ranged from 2.2 to 2.4 μm.
A common protocol was to first immerse the fiber in a relaxing solution (well 1) and allow complete perfusion of CK and phosphocreatine (PCr) or PK and phosphoenol pyruvate (PEP) and nucleotides (∼3 min). The fiber was then switched to an activating solution in well 2, and mechanical measurements were made. After measurements, the fiber was returned to well 1 and the solution in well 2 was replaced by the same fresh or another appropriate experimental buffer. Mechanical measurements were repeated, and the fiber was returned to the relaxing solution. The solution inwell 2 was changed again, and mechanical measurements were repeated for a last time under control conditions to determine stability of the fiber. A 10% decline in P0 was set as our performance criterion. Damaged fibers were discarded. All fiber experiments were done at 10°C in both wells, and the bathing solutions were continuously stirred.
The basic rigor buffers contained (in mM) 120 potassium acetate (KAc), 5 MgCl2, 1 EGTA, and either 50 MOPS (pH 7) or 50 MES (pH 6). Phosphate (3–54 mM) was added to this solution, keeping the ionic strength constant by changing KAc (35). A relaxing solution was achieved by adding 0.05–0.5 mM ATP and either 20 mM PCr with 1 mg/ml CK or 20 mM PEP with 1 mg/ml PK. These solutions were made fresh on each experimental day. Activating solution was achieved at pCa 4.5. A range of SL-ADP concentrations was used (0.1–2 mM) to examine the effects of the ADP analog on mechanical fiber properties. The concentration of free Mg2+ varied in our experiments from 3.8 to 4.9 mM. Variation of Mg2+ in this range had no perceptible effect on fiber function. For some experiments involving measurements of ATPase activity at very low [ATP], trace contamination of ADP in the SL-ADP, ∼0.1–0.5%, was removed by treatment of the stock solution of SL-ADP with 1 mg/ml myofibrils and 0.02 mg/ml adenylate kinase for 10 min at room temperature. This incubation hydrolyzes ADP to AMP but does not affect SL-ADP. The activity of the adenylate kinase was then inhibited by adding 100 μM diadenosine pentaphosphate, the myofibrils were removed by centrifugation, and the purified SL-ADP was used. All reagents were purchased from Sigma (St. Louis, MO).
In addition to mechanical experiments, the ATPase activities of rabbit psoas myofibrils [prepared basically as described by Etlinger et al. (18)] were measured by direct determination of NADH depletion linked to ADP production, described in more detail previously (33). Activating solutions contained 10 mM PEP, 0.25 mM β-NADH, 0.07 mg/ml lactate dehydrogenase (LDH), and 0.2 mg/ml pyruvate kinase. The activities of the enzymes used were (in μmol · min−1 · mg protein−1) 200 CK (pH 7, 37°C), 430 PK (pH 7.6, 37°C), and 940 LDH (pH 7.5, 37°C).
SL-ADP was synthesized according to Crowder and Cooke (11). Both thin-layer chromatography (TLC) and mechanical measurements revealed that SL-ADP was very slowly phosphorylated to SL-ATP by CK. Enzyme activity was tested by incubating the SL-ADP with the enzyme in rigor buffer at 10°C. At specified times an aliquot was removed and spotted on a precoated high-performance TLC aluminum plate (silica gel, 60 F254, 0.2 nm; Merck, Darmstadt, Germany) along with appropriate controls. The plate was well dried and developed in an isopropanol:NH4OH:H2O solution (6:3:1 vol/vol) at room temperature. After development, the spots corresponding to SL-ADP and SL-ATP were scraped and extracted in 600 mM KCl and 50 mM MOPS, pH 7.5, and the presence and quantity of SL-nucleotide was measured by electron paramagnetic resonance (EPR) spectroscopy (ER/200D; IBM Instruments, Danbury, CT). A 1 mM solution of SL-ADP was approximately half phosphorylated, 50 ± 12% (n = 4), in 15 min at 10°C by 1 mg/ml CK. This rate is only 0.06% of the activity of CK for ADP under similar conditions. For our mechanical experiments performed at 10°C within 90 s of adding SL-ADP, the conversion rate was slow enough that negligible SL-ATP would be generated within the fiber. In addition, during the course of the experiments we discovered that SL-ADP was not phosphorylated by the PK-PEP system, within the accuracy of our measurements (again TLC, EPR, and mechanical measurements). Thus we switched to the PK-PEP system, which gave results identical to those of the CK-PCr system but allowed SL-ADP solutions to be used for a longer time.
ATP regeneration system.
To verify the capability of 1 mg/ml PK to maintain ATP concentration and eliminate ADP, we measured force (n = 6) at three conditions: in the presence of 150 μM ATP, 3 mM Pi, and 20 mM PEP, pH 7. We compared force generated with 1 mg/ml PK vs. 2 mg/ml PK, which gave forces of 0.093 ± 0.003 and 0.092 ± 0.002 N/mm2, respectively; we also compared force generated with 1 mg/ml PK and then with the addition of 1 mM ADP, which resulted in forces of 0.096 ± 0.003 and 0.094 ± 0.005 N/mm2, respectively. In the latter comparison, a small drop in force was observed that was expected as the PK rapidly rephosphorylated the added ADP to ATP, thus making more ATP available to the fiber. We estimated internal [ADP] to be <25 μM, based on a calculation of the production, consumption, and diffusion of ADP according to the equations of Ref. 8. Thus, in the experiments described here, competition from internally generated ADP is much less than that from added SL-ADP.
Force data for each condition (in N/mm2) were averaged and are expressed as means ± SD; n represents the number of fibers used, when reported. In the case of parameters based on fits, the ±95% confidence interval is given (i.e., when reporting inhibition or dissociation constants). Mean force data were fit by assuming that the effect of SL-ADP could be expressed as a simple binding isotherm Equation 1where PSL-ADP is the tension as a function of [SL-ADP], P0 is the maximum isometric tension in the absence of SL-ADP, P′ is the increment in tension approached as SL-ADP increases to saturating levels, and K is an apparent dissociation constant that describes the strength of the binding of SL-ADP in competition with ATP.
Simple three- and four-state models of cross-bridge kinetics were analyzed using commercially available software (Berkeley Madonna, vers. 8.0.1; R. I. Macey and G. F. Oster). The kinetic rates were determined from the experimental data obtained for force and ATPase activity in our isometric fibers and myofibrils. For a four-state model, cross bridges are assumed to be in one of four states:state 1, detached from actin, or attached weakly without generating force; state 2, attached to actin in the power stroke; state 3, attached to actin in the state achieved following binding of SL-ADP at the myosin nucleotide site; orstate 4, attached to actin with no nucleotide at the myosin site. States 2, 3, and 4 all generate force. We envision the following cross-bridge cycle. Cross bridges start in state 1, having ATP or ADP Pi at the nucleotide site and do not generate force. The transition tostate 2 involves some conformational change in myosin, associated with the release of Pi that produces actin-attached force-generating cross bridges. State 2 is in reality a mixture of different states, and ADP release and binding involve one of these, which is state 3 in the model. Release of ADP from state 3 leads to the rigor state, state 4. The binding of ATP in state 4 returns the cross bridge to state 1. The force generated by the model is a function of the populations in the force-generating states,states 2, 3, and 4, and the amount of force generated by a cross bridge in each one of these states. The magnitudes of the relative forces generated by cross bridges instates 2, 3, and 4 are not known. We assume here that the transitions among states 2,3, and 4 do not change the conformation of the cross bridge so that all these states generate the same force. Release of ADP from force-generating cross bridges does not change the strain on the cross bridge, so rigor states (state 4) maintain the same tension as state 2 or 3. However, the effect of relaxing this assumption did not change the conclusions. At high levels of ATP, the population of states 3 and 4is small, and the fraction of force-generating cross bridges is given by the steady-state distributions of states 1 and2. For a three-state model, states 2 and 3were combined. As we will discuss later, a four-state model was more applicable (see Fig. 5). ATPase activity was calculated as the flux from state 4 back to state 1. The model was not sensitive to the exact values of the rate constants connectingstates 1, 2, and 3, as long as certain conditions were satisfied. In particular, the reverse transitions had to be more rapid than the flux through the states, or P′ would not be a constant. The values of the rate constants k 12,k 21, k 23, andk 32 were set so that the ATPase activity was 1 s−1 and the fraction of the non-force state, state 1, was 50% at high [ATP]. The assumption that 50% of the cross bridges generate force is arbitrary, but the exact value is not crucial, and the data could be fit equally well by assuming other values, e.g., 25%. In the simulations shown, all four rate constants were set to 3 s−1. However, the conclusions were similar if they were varied between 1 and 10, keeping the flux through them at the assumed ATPase rate of 1 s−1, by using variable ratios of forward to backward rate constants to keep the flux constant.
The rate constant involving the binding of ATP was set by a fit to the ATPase activity. The rate constant k 41 involves the binding of ATP, and thus it depends directly on [ATP]. The magnitude of this rate constant can be determined from the dependence of the ATPase activity on [ATP]. When [ATP] is equal toK m, the rate constant k 41must be such that the average time required to make the transition fromstate 4 to state 1, 1/k 41, must be equal to the cycle time at saturating [ATP], 1 s. The observed value of K m at pH 7 sets the second-order binding constant for ATP to be 3.6 × 104M−1 · s−1. Thusk 41 = 3.6 × 104 × [ATP] s−1, where [ATP] is molar. The rates of binding or release of ADP from the rigor state of active cross bridges are not known. In the model the rate of release was set at 50 s−1, and the conclusions were not changed if this value was 10 times smaller or larger. The transition involving the binding of SL-ADP,k 43, is directly proportional to [SL-ADP]. This rate constant was set by using the known affinity of SL-ADP for the rigor state, 5 × 103 M−1 [Ref.11 and more recent measurements (data not shown)]. Thusk 43 = 2.5 × 105 × [ADP] s−1, where [ADP] is molar. These rates change when the pH is decreased to 6.
SL-ADP increases isometric tension.
In analyzing the effect of SL-ADP on isometric tension, we activated a fiber and allowed it to rise to a stable peak force (P0). We then added SL-ADP and allowed the tension increase to reach a stable value. A sample data set is presented in Fig.1, showing where we added 0.5 mM of SL-ADP to a fiber activated in 50 μM ATP. The fiber could then be returned to a bath that lacked SL-ADP, and tension returned to control values, showing that the increase was reversible.
In Fig. 2, we present the effect of adding 0.1–2.0 mM SL-ADP to fibers at 50, 150, or 500 μM ATP. At low [ATP], the fiber tension was high and decreased with increasing [ATP]. Addition of SL-ADP increased tension at all values of ATP, as shown in Fig. 2 and Table 1. At lower [ATP], the same increase in tension required lower concentrations of SL-ADP. This is expected if the increase in tension is a result of SL-ADP acting as a competitive inhibitor of the binding of ATP and the subsequent dissociation of myosin heads from actin.
Also shown in Fig. 2 are fits to the data, assuming that the effect of SL-ADP could be expressed as a simple binding isotherm (see Eq. 1 in methods). This simple approach provided a good fit to the data under all conditions, providing values for the two free parameters, K and P′, shown in Table 1.K is an apparent dissociation constant that describes the strength of the binding of SL-ADP in competition with ATP. The value of K increased as [ATP] increased, as expected for competition between SL-ADP and ATP. The tension increase, P′, reached a plateau that was ∼0.04 N/mm2 greater than the P0 observed in the absence of SL-ADP for variable [ATP] and pH (Table 1). Notably, in the presence of added phosphate, the value of P′ decreased (Table 1 and Fig. 3). The near-constant value of P′ found as [ATP] varied is not expected from simple models of cross-bridge action, which predict that the tension increase should be lower at lower [ATP], where the initial tension is higher because of the presence of rigor cross bridges.
The relationship between P0 and P′ is not linear. As noted above, increasing ATP lowered P0 but not P′, with the ratio P′/P0 equal to 0.37, 0.41, and 0.62 for [ATP] of 50, 150, and 500 μM, respectively. Increasing phosphate or decreasing pH from 7 to 6 decreased isometric tension production (Table 1), as expected from previous reports. For example, reduction in pH from 7 to 6 (3 mM Pi) produced a 67.5 ± 2.3% force decline (or 0.060 ± 0.021 N/mm2, n = 3). Addition of saturating SL-ADP gave a ratio of 1.37, which is greater than that observed at 7. Addition of 54 mM Pi also decreased P0 and increased the ratio P′/P0 to 1.0.
The conditions of low pH and high Pi employed in our study were intended to simulate the conditions found in muscle fibers during severe muscle fatigue and, thus, are of interest in understanding the role of increased concentrations of SL-ADP (and thus ADP) in this state of the muscle. As shown in Table 1 and Fig. 2, SL-ADP produced the same absolute increase in tension at the lower pH as seen at pH 7 (3 mM Pi). Thus SL-ADP produces a larger relative increase in tension at the lower pH. In contrast, the addition of SL-ADP to fibers incubated in high phosphate produced a smaller P′ than seen at lower concentrations of phosphate (Table 1 and Fig. 3). Although the change in P0 was approximately the same for pH 6 (3 mM Pi) and pH 7 (54 mM Pi), the value of P′ in the latter case was less than half that in the former (see Table 1). The smaller value of P′ found in the presence of high Pi was also observed at pH 6. At both pH 7 and pH 6, the inhibition of P0 by Pi tended to be greater than the inhibition of P′. These data suggest that the inhibition in P0 caused by Pi is due to a different mechanism than inhibition in P0 caused by H+accumulation.
Comparison with previous results.
In a number of previous investigations the effect of ADP on fiber tension was measured by addition of relatively high millimolar concentrations of ADP to fibers activated in millimolar ATP (8,13, 27, 29, 30, 40). These investigations have found that tension increases by ∼10% upon addition of 1 mM ADP to fibers activated in 3–5 mM ATP. To determine whether SL-ADP would have the same effect on tension as reported in these earlier studies, we added 1 mM SL-ADP or 1 mM ADP to fully activated fibers in 3 mM ATP and 3 mM Pi, in the absence of an ATP-regenerating system (pH 7, 10°C). The average increase in tension was 12 ± 5% for SL-ADP or 10 ± 2.5% for ADP (n = 3). The value we obtained for ADP is similar to the results of previous investigations and is similar to that for SL-ADP. The equivalence of the force increase found for SL-ADP and ADP further shows that the presence of the label on the ribose does not alter the binding of the analog to myosin in active fibers, as initially reported by Crowder and Cooke (11) in an EPR spectra analysis. Moreover, mant-ADP, a fluorescent analog that is similar in structure to SL-ADP, also binds to myosin similarly to ADP (45).
SL-ADP decreases isometric ATPase activity.
The effect of SL-ADP on the ATPase activity was determined by using myofibrils from psoas muscle. The myofibrils were first cross-linked lightly with glutaraldehyde to prevent shortening so that they were a reasonable model of an isometric muscle fiber (22). The ATPase activity was determined as a function of concentration for both ATP and SL-ADP. Our data show that SL-ADP acted as a competitive inhibitor of the binding of the substrate ATP (Fig.4). Competitive inhibition is described by the equation Equation 2where V max is the activity at infinite [ATP], K m is the Michaelis constant describing the binding of the substrate ATP, and K i is the inhibition constant describing the strength of the binding of the inhibitor SL-ADP. In the presence of a concentration of SL-ADP equal toK i, the ATPase follows Michaelis-Menten kinetics with an apparent K m that is twice theK m in the absence of SL-ADP. At pH 7 (Fig.4 A), our results defined a K m for the ATPase activity of 29 ± 8 μM and a K ifor the inhibition of the ATPase activity by SL-ADP of 240 ± 20 μM. Similar experiments performed at pH 6 (Fig. 4 B) revealed a decrease in the value of K m to 4.8 ± 2 μM; however, the value of K iremained approximately the same at 280 ± 50 μM, indicating that ATP bound more tightly to myosin at the lower pH, whereas SL-ADP bound about the same. This conclusion is also supported by the observation that the ratio of K (the concentration of SL-ADP required to half saturate the tension response) to [ATP] is greater at the lower pH (see discussion).
The main findings of the present study are that SL-ADP increased isometric tension and decreased ATPase rate in skinned rabbit psoas muscle fibers. In current models of cross-bridge interaction, ATP is thought to dissociate the rigor state cross bridges (nucleotide-free myosin heads), which occur upon release of ADP from force-generating states in the cross-bridge cycle (17, 21, 36). The binding of ADP, preventing cross-bridge dissociation in vivo, would be expected to increase tension and decrease ATP utilization rate. In general, as discussed in the Introduction, experimental studies have confirmed these predictions, as do the results presented here. The measurements described here explore the effects of the competition of ATP with an ADP analog over a wider range of concentrations of both nucleotides, allowing us to show that the ADP analog is a pure competitor with ATP and to determine how this competition changes with changing conditions. In particular, we address the question of the role of ADP in muscle fatigue. Finally, we present a model that describes nucleotide competition in isometric fibers.
Muscle properties at pH 7.
The current results support and extend the results of a number of previous investigations, all of which showed that increased [ADP] potentiates isometric tension (8, 13, 27, 29, 30, 40, 23). In most of these investigations high concentrations of ADP competed against high concentrations of ATP in the absence of an ATP-regenerating system. We have advanced these observations by showing that this effect is also seen over a wider range of nucleotide concentrations, including more physiological (lower) concentrations of ADP. The potentiation of tension measured here at these lower ADP concentrations is in rough agreement with that seen earlier when the concentrations are extrapolated to the higher values previously used. We are in agreement with one study that showed that at high levels of ATP, low levels of ADP have little or no effect (4). We also agree with a study where addition of 0.7 mM ADP resulted in ∼7% force increase (23). In the present study, the ATPase activity of isometric myofibrils was inhibited by SL-ADP. The values for K m for ATP and forK i, 29 and 240 μM at pH 7, respectively, are both slightly higher than those observed by Sleep and Glyn (22,39) using ADP instead of SL-ADP (K m= 17 μM and K i = 170 μM).
Effects of lower pH and/or increased Pi.
At pH 6, a pH that is approached during severe fatigue, there was a decrement in tension relative to that found at pH 7 of ∼50%, as has previously been shown (5, 16, 23, 28, 31, 32). The addition of SL-ADP produced the same absolute increase in fiber tension as was found at pH 7 (Table 1 or Fig. 2), which a simple model, described below, could explain. K was about two- to threefold higher, showing that SL-ADP competed more weakly with ATP than at pH 7. We found that the weaker competition arises from tighter binding of ATP. At pH 6, we found a decrease in the value of K m to 4.8 ± 2 μM; however, the value of K i remained the same (280 ± 50 μM), indicating that ATP bound more tightly to myosin at the lower pH, whereas SL-ADP bound about the same. No previous study has explored the effects of pH on nucleotide binding in fibers, and the tighter binding of ATP at the lower pH could have important implications for fatigue.
An increase in Pi at pH 7 lowered tension to about the same level as achieved at pH 6, but Pi also decreased the absolute increment in tension, P′, produced by SL-ADP. Addition of Pi increased the value of K , indicating that SL-ADP competed more weakly with ATP at the higher Pi. This could be due to a direct competition between SL-ADP and Pi for the active site of myosin. Previous work has shown a weak competition between ATP and Pi(35).
In general, during fatigue in vivo, average [ADP] is observed to rise to ∼200 μM and average [ATP] to not fall below 2–3 mM (see Ref. 20 for review). The effects of ADP seen in vitro in skinned fibers and myofibrils under similar conditions have been too small to produce a significant effect on the physiological properties of fatigued fibers in vivo. Our results generally agree with this conclusion. Our data using SL-ADP predict that if the ADP concentration were raised from 20 μM to 500 μM and the ATP level was decreased from 5 mM to 2 mM, the effect of ADP would be a 4% increase in force at pH 7. At pH 6, the relative effect of SL-ADP is greater, but it is a weaker competitor with ATP, so the relative effect on tension would be about the same as at pH 7. Thus the rise in ADP seen during fatigue can only play a significant role if the actual changes in the concentrations of the nucleotides are greater in the interior of the myofibrils than what has been inferred from measurements averaged over whole muscles. Is this possible? The ATP and ADP concentrations have been mostly measured in whole muscle using NMR or biopsy homogenates (14, 20). Both of these methods produce an average value of each nucleotide distributed throughout the fiber and in many different fibers that may not be equally activated or equally fatigued. Recent analyses by one of us (C. Karatzaferi) of single human muscle fibers using maximal intensity exercise (25, 26) have shown a large variability in nucleotide content of the different fiber types at rest and postexercise, with much lower levels of ATP and near depletion of PCr in some postexercise fast fiber fragments. Moreover, it has been calculated that ADP could rise to as high as 3.0 mM during contraction, when the PCr store is depleted (43). Our measurements show that if myofibrillar ADP reached 1 mM with 3 mM ATP, the effect would be an approximately further twofold increase in force to ∼8% at either pH 7 or pH 6. Although an increase in the [ADP] may increase the tension economy by potentiating tension and inhibiting the ATPase activity, the effect on the tension, described above, will still be modest, and the effect on ATPase activity will be even smaller. Thus another mechanism must also operate to produce the twofold increase in tension economy seen in fatigue (9,10).
Modeling cross-bridge kinetics.
Force and ATPase activity in isometric fibers as a function of ATP and SL-ADP were analyzed by using a simple model to determine values for the relevant kinetic parameters governing the binding of nucleotides in the fiber (Fig. 5). Cross bridges are assumed to be in one of four states, described in Fig. 5. The effect of SL-ADP is to increase the rate of the transition from the rigor state,state 4, back into state 3. As the concentration of SL-ADP increases, the proportion of cross bridges in state 4 decreases, effectively decreasing the rate of ATP binding by decreasing the concentration of state 4. The effect of increasing the rate of this transition will be to increase force and inhibit the ATPase activity, as observed. The model allows us to quantify these phenomena and to draw connections between force and ATPase activity.
The goal of the model was to explain both the isometric force and the ATPase activity with the same set of rate constants and with the measured affinity of SL-ADP for the rigor state. This goal was not easily obtained, and a number of models were investigated that were not able to fit the data. The fit to the data was much worse in the absence of state 3, i.e., with the binding of SL-ADP leading directly back to the power stroke. Models in which the transitions from the non-force-generating state 1 to the force-generatingstates 2 and 3 were effectively irreversible all had a common problem. At saturating concentrations of SL-ADP, all cross bridges accumulated in state 3. Thus the force increase was greater when starting from conditions with lower force, modeled by a lower population of state 2, and the final force approached a maximum regardless of the initial conditions, in contrast to the data shown in Figs. 2 and 3. A variety of models in which additional states with bound SL-ADP had a different force per cross bridge than that of active cross bridges all suffered from a similar problem. This problem could be fixed by assuming that reverse transitions connect state 3 to state 2 to state 1, allowing the force-generating states to exchange significantly with the pre-force state. Thus, in the model, cross bridges that bind SL-ADP can back up all the way to the pre-force state, which precedes the power stroke. This is a dramatic conclusion with a quasi-equilibrium that spans the entire power stroke. In the model there is only one irreversible transition, that from state 4 back to state 1, a transition involving the binding of ATP. Measurements of the relative affinities of actin and ATP for myosin suggest that this transition should be irreversible (see Ref. 6 for review).
The model simulation of the ATPase activity as a function of [ATP] can be used to determine the rate constant for the binding of ATP tostate 4, as described in methods. The observed value of K m at pH 7 sets the second-order binding constant for ATP to 3.6 × 104M−1 · s−1. Thusk 41 = 3.6 × 104 × [ATP] s−1. The observed affinity of SL-ADP for myosin in rigor muscle, K d = 200 μM, measured using EPR spectroscopy, was used to set the ratio ofk 34 to k 43 (Ref.11 and recent unpublished observations). Taking the value of k 34 to be 50 s−1,k 43 = 2.5 × 105 × [ADP] s−1. At pH 6, the lower value ofK m, 4.8 μM, leads to a faster rate for the binding of ATP, 8.7 × 104M−1 · s−1. EPR spectroscopy showed that the dissociation constant for SL-ADP binding to rigor fibers was not greatly changed by lowering the pH to 6, so the value of k 43 remained as set at pH 7. The value for the second-order binding constant for ATP, 3.6 × 104M−1 · s−1 at pH 7, is ∼10-fold slower than that measured for binding to rigor fibers following photorelease of ATP from caged ATP (13). This may indicate that ATP binds more slowly to nucleotide free myosin heads in active fibers than in rigor fibers. The rate of binding of ADP or SL-ADP to either active or rigor cross bridges has not been measured directly.
One test of the model is whether the second-order rate constants, for the binding of nucleotides, discussed above, can accurately simulate the general properties of the effect of ATP and SL-ADP on isometric tension. We first consider the effect of ATP on fiber tension. As observed previously, as [ATP] is raised from 50 μM to 1 mM, the isometric tension decreases by ∼30–40%. The most obvious explanation for the higher tension seen at the lower [ATP] is that it is due to the buildup of force-generating cross bridges in rigor states. However, the K m for the ATPase activity observed here or previously (22), 15–30 μM, suggested that rigor states would only be populated at [ATP] below 50 μM, leading some investigators to question this explanation (22). The model proposed here provides an excellent fit to the tension as a function of ATP by using the observed value ofK m for the ATPase activity. The apparent discrepancy between the low value for K m and the range of [ATP] over which tension falls is resolved, because the fraction of detached cross bridges is large at all [ATP], allowing modest changes in k 41 × [ATP] to provide significant changes in tension.
The model also explains the major features of the effect of SL-ADP on fiber tension. As [ATP] increases, the concentration of SL-ADP required to achieve half the force potentiation,K , also increases (Table 1). As shown in Fig. 6, the simulated values ofK match the observed values very well. A stringent test of the model is that the greater value ofK seen at pH 6 is quantitatively explained by the changes observed in the values ofK m and K i at this pH. The sixfold change in K m, coupled with a twofold decrease in the maximum ATPase activity and the almost unchanged value of K d for binding of SL-ADP, shows that the strength of the competition of SL-ADP with ATP will decrease by about a factor of 3, which is close to what was observed in the tension measurements.
The model also predicts that the potentiation of tension achieved at saturating SL-ADP, P′, is approximately a constant for different initial values of [ATP] and pH. When the pH is decreased from 7 to 6, tension decreases by more than half. This could be due to a decrease in the force generated per cross bridge, or it could be due to a decrease in the population of force-generating cross bridges. Measurements of fiber stiffness, which also decreases, suggest the latter possibility. This can be simulated in the model by decreasing the rate of the transition from detached to force-generating cross bridges,k 12, resulting in a buildup of cross bridges instate 1, with a decrease in force-generating cross bridges. The model now predicts that the addition of saturating SL-ADP produces approximately the same absolute increase in tension. The model predicts an approximately constant value of P′ as [ATP] is varied above 50 μM, but it underestimates the value at 50 μM. The model predicts that the ATPase activity will be inhibited by SL-ADP following approximately competitive behavior, with a K i of 140 μM at pH 7. This is lower than that observed here for SL-ADP (240 μM) but is not far from that previously observed for ADP (170 μM) by Sleep and Glyn (39).
Addition of phosphate (Pi) also decreases force production, but in contrast to a change in pH, the value of P′ is also decreased. Higher Pi concentrations lower the free energy available from the hydrolysis of ATP and thus lower the free energy available to generate isometric force (see Ref. 35 for review). The decrease in fiber force in our model is thus attributed to a lower force generated in states 2 and 3. With this assumption, the values of P′ are decreased by the same relative amount as P0, which is more than was observed (see Fig. 3). The difference between model and data shows that the effect of Pi is more complex than can be explained with this simple model.
The assumption in our model that cross bridges can back up from the end to the beginning of the power stroke has not been considered in most previous models, but there is some evidence supporting it (2,3). In general, strongly bound cross bridges require binding of ATP to be dissociated from actin. Transitions in the forward direction through the power stroke are much faster than the reverse transitions, or the reverse transitions occur only upon stretching the cross bridges into strained positions. Thus the progression through the power stroke is effectively irreversible. Our model does not include strain dependence, raising the question of how cross bridges can make transitions from state 3, at the end of the power stroke, back to state 1, at the beginning of the power stroke. Reversal back to state 1 would require resynthesis of ATP from ADP and Pi. The input of energy required would come from fluctuations in the relative positions of actin and myosin, which occur on a time scale that is rapid compared with the cross-bridge cycle (37). Moreover, rapid transitions between strongly attached and detached cross bridges have been observed by measurements of stiffness in rapid length changes (3). Furthermore, incorporation of Pi from the medium into ATP in active muscle fibers shows that the transition from state 2 tostate 1 can occur (2). Our conclusions can also help provide a molecular explanation for one recent model of cross-bridge function in which force was treated as a macroscopic thermodynamic variable (1).
In conclusion, the present data define the strength of the competition between ATP and an analog of ADP, SL-ADP, which binds to myosin similarly to ADP. SL-ADP is a weak competitive inhibitor of ATP binding. Although it has a greater relative effect at a lower pH, ATP binds more tightly at the lower pH so that the competition occurs at even greater concentrations of SL-ADP. Thus, although an increase in the ADP concentration may increase the tension economy by potentiating tension and inhibiting the ATPase activity, the effect on the tension will be modest and the effect on ATPase activity will be even smaller in fatigue. The simple model presented in Fig. 5 correctly predicts many of the major features of the effect of addition of SL-ADP on the properties of active isometric fibers. A major conclusion is that the effects of SL-ADP on both tension and ATPase activity can be explained with the same kinetic constants in a simple four-state model. Agreement between the model and the data requires that cross bridges can make reverse transitions from the states at the end of the force generation back to non-force-generating states, which is a novel proposition.
We thank Marija Matuska for synthesizing SL-ADP.
This work was supported by National Heart, Lung, and Blood Institute Grant HL-32145 (R. Cooke). C. Karatzaferi is a recipient of an American Heart Association Fellowship.
Address for reprint requests and other correspondence: R. Cooke, Box 0448, Dept. of Biochemistry & Biophysics, Univ. of California, San Francisco, CA 94143-0448 (E-mail:).
The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
First published November 27, 2002;10.1152/ajpcell.00291.2002
- Copyright © 2003 the American Physiological Society