Effect of vanadate, a potent alkaline phosphatase inhibitor, on 45Ca and 32Pi uptake by matrix vesicle-enriched fractions from chicken epiphyseal cartilage

Although alkaline phosphatase has been long associated with the mineralization process, its exact function remains to be elucidated. To clarify its possible role in matrix vesicle-mediated mineralization, we tested the effect of vanadate, a phosphate analogue and powerful competitive inhibitor of alkaline phosphatase activity, on calcium and phosphate uptakes by a matrix vesicle-enriched microsomal fraction. Vanadate was also tested in a hydroxyapatite-seeded ion uptake system to determine possible direct effects on mineral formation. The effect of vanadate on vesicle mineral ion uptake was complex; low dosages of vanadate (2-20 microM) were stimulatory to Ca2+ uptake, but were inhibitory to Pi. Higher dosages (greater than 67 microM) were inhibitory to both ions. The effect of vanadate on ion uptake was strongly influenced by the stage of vesicle loading; major effects were seen during the lag and early uptake phases, and minimal effects were seen in the terminal stages. Concentrations of vanadate highly inhibitory to vesicle ion uptake had minimal effects on ion accretion by a hydroxyapatite-seeded system. Inhibition of alkaline phosphatase activity by vanadate broadly paralleled inhibition of Pi and Ca2+ uptake; however, at low vanadate concentrations, inhibition of Pi uptake closely paralleled that of alkaline phosphatase. The data indicate that vanadate binds with high affinity to Pi-loading sites, blocking initial Pi uptake. Complexation between vanadate and Ca2+ may be responsible for the stimulation of Ca2+ uptake at early stages of vesicle ion loading with low levels of vanadate by enhancing binding of Ca2+ to the vesicles. It may also account for the selective inhibition of Ca2+ uptake during the rapid stage of vesicle ion loading with high levels of vanadate by reducing Ca2+ ion activity. The close parallelism between inhibition of early Pi uptake and of alkaline phosphatase activity supports the concept that alkaline phosphatase is involved in Pi transport during the early stages of matrix vesicle ion loading. However, the fact that only about half of the Pi uptake was affected by vanadate, despite the progressive inhibition of alkaline phosphatase activity, indicates that alkaline phosphatase is not solely responsible for Pi uptake by the matrix vesicle-enriched fraction.     

Inhibition of red cell Ca2+-ATPase by vanadate

1. The Mg2+- plus Ca2+-dependent ATPase (Ca2+-ATPase) in human red cell membranes is susceptible to inhibition by low concentrations of vanadate. 2. Several natural activators of Ca2+-ATPase (Mg2+, K+, Na+ and calmodulin) modify inhibition by increasing the apparent affinity of the enzyme for vanadate. 3. Among the ligands tests, K+, in combination with Mg2+, had the most pronounced effect on inhibition by vanadate. 4. Under conditions optimal for inhibition of Ca2+-ATPase, the K 1/2 for vanadate was 1.5 microM and inhibition was nearly complete at saturating vanadate concentrations. 5. There are similarities between the kinetics of inhibition of red cell Ca2+-ATPase and (Na+ + K+)-ATPase prepared from a variety of sources; however, (Na+ + K+)-ATPase is approx. 3 times more sensitive to inhibition by vanadate.     

Vanadate stimulation of insulin release in normal mouse islets.

The effects of vanadate (Na3VO4) on pancreatic B-cell function were studied in normal mouse islets. Vanadate did not affect basal insulin release but potentiated the effect of 7-30 mM glucose at concentrations of 0.1-1 mM. This effect was progressive and slowly reversible. It was abolished by omission of extracellular Ca2+ but unaffected by blockers of adrenergic or muscarinic receptors. Comparison of the changes in membrane potential, 86Rb efflux and 45Ca efflux that vanadate and ouabain produced in B-cells made it possible to exclude the hypothesis that vanadate increases insulin release by blocking the sodium pump. Vanadate was also without effect on cAMP levels. On the other hand, it markedly changed the characteristics of the Ca(2+)-dependent electrical activity and of the oscillations of cytoplasmic Ca2+ recorded in B-cells stimulated by 15 mM glucose. In the steady state, Ca2+ influx was increased by vanadate, and this resulted in a rise in cytoplasmic Ca2+. The exact mechanisms underlying these changes could not be established but a blockade of K channels was excluded. In the presence of LiCl, vanadate markedly increased inositol phosphate levels in islet cells. This effect was attenuated but not suppressed by omission of Ca2+. A small increase in inositol bisphosphate was still produced by vanadate in the absence of LiCl. These results suggest that vanadate both stimulates phosphoinositide breakdown and inhibits inositol phosphate degradation. In conclusion, vanadate does not induce insulin release, but markedly potentiates the stimulation by glucose. This property is not due to an inhibition of the sodium pump or to a rise in cAMP concentration. It results from a complex interplay between changes in B-cell membrane potential, phosphoinositide metabolism and Ca2+ handling.     

The interaction of vanadate ions with the Ca-ATPase from sarcoplasmic reticulum

The interaction of vanadate ions with the Ca-ATPase from sarcoplasmic reticulum vesicles was studied in a native and a fluorescein-labeled ATPase preparation (Pick, U., and Karlish, S. J. D. (1980) Biochim. Biophys. Acta 626, 255-261). Vanadate induced a fluorescence enhancement in a fluorescein-labeled enzyme, indicating that it shifts the equilibrium between the two conformational states of the enzyme by forming a stable E2-Mg-vanadate complex (E2 is the low affinity Ca2+ binding conformational state of the sarcoplasmic reticulum Ca-ATPase). Indications for tight binding of vanadate to the enzyme (K1/2 = 10 microM) in the absence of Ca2+ and for a slow dissociation of vanadate from the enzyme in the presence of Ca2+ are presented. The enzyme-vanadate complex was identified by the appearance of a time lag in the onset of Ca2+ uptake and by a slowing of the fluorescence quenching response to Ca2+. Ca2+ prevented the binding of vanadate to the enzyme. Pyrophosphate (Kd = 2 mM) and ATP (Kd = 25 microM) competitively inhibited the binding of vanadate, indicating that vanadate binds to the low affinity ATP binding site. Binding of vanadate inhibited the high affinity Ca2+ binding to the enzyme at 4 degrees C. Vanadate also inhibited the phosphorylation reaction by inorganic phosphate (Ki = 10 microM) but had no effect on the phosphorylation by ATP. It is suggested that vanadate binds to a special region in the low affinity ATP binding site which is exposed only in the E2 conformation of the enzyme in the absence of Ca2+ and which controls the rate of the conformation transition in the dephosphorylated enzyme. The implications of these results to the role of the low affinity ATP binding sites are discussed.     

The effect of calcium and Ca antagonists upon excitation-contraction coupling

The effect of a Ca2+-free tetraethylammonium sulfate solution on force development in short skeletal muscle fibres of the frog was investigated under voltage clamp control. Maximum force could still be reached under this condition. The removal of external Ca2+, however, caused an acceleration of force inactivation leading to a shift of the steady-state potential dependence of force inactivation to more negative potentials. With reference to the "modulated-receptor hypothesis" this result was explained by assuming a potential-dependent binding of Ca2+ to a force-controlling system in the T-tubular membrane, with a low affinity in the depolarized-inactivated state. A dissociation of Ca2+ is assumed to turn the system into a secondary inactivated state (paralysis) from which it only slowly recovers after repolarization. Ca antagonists like D600 and diltiazem accelerated the shift into paralysis, probably by an allosteric displacement of Ca2+ from its binding site. The application of 1-2 microM of the Ca antagonist nifedipine blocked the inward Ca2+ current and caused a prolongation of the transient force development following a depolarization. A similar retardation of force inactivation and a threshold shift to more negative potentials occurred when the Ca2+ chelator ethyleneglycol-bis (beta-aminoethyl ether)-N,N'-tetraacetic acid (EGTA) was injected into the fibre and when in Ca2+-free solutions sodium ions entered the cell through Ca2+ channels.     

New vanadate-induced Ca2+ pathway in human red cells

Vanadate is a commonly used Ca2+ pump blocker, exerting a substantial effect on Ca2+ extrusion at millimolar concentrations in human red cells. At such levels, vanadate also seems to open an L type-like Ca2+ channel in these cells (J Biol Chem 257 (1982) 7414; Gen Physiol Biophys 16 (1997) 359). Since neither a dose-dependence effect nor a metabolic requirement for the latter action could be found in the literature, we have addressed this matter in the present work. Accordingly, vanadate action on Ca2+ entry was systematically investigated in both young and old human red cells after metabolic depletion. Although vanadate enhanced Ca2+ entry indifferently in either cell type, a distinct over-all effect was paradoxically found depending on whether or not metabolic substrates that give rise to ATP were present. In ATP-depleted cells, unlike with ATP-containing cells, vanadate-stimulated Ca2+ entry was neither blocked by raising external K+ nor by adding voltage-dependent Ca2+ channel blockers (nifedipine, calciseptine, FTX3.3) or compounds affecting polyphosphoinositide metabolism (Li+, neomycin). Likewise, full substitution of external Na+ by other cations did not inhibit vanadate-enhanced Ca2+ entry. Regardless of the cell age, stimulation by vanadate depended strongly on internal Na+ (0-30 mM). Vanadate stimulation was significantly reduced (about 55%) by heparin (10 mg/ml) only in young cells and by ryanodine (about 35%, 250 microM) in old cells. The results suggest presence of a new vanadate-induced Ca2+ entry pathway in ATP-depleted cells.     

The digitonin-permeabilized pancreatic islet model. Effect of myo-inositol 1,4,5-trisphosphate on Ca2+ mobilization.

Glucose-induced insulin secretion is thought to be mediated by submicromolar increases in intracellular Ca2+, although the intracellular processes are not well understood. We have used the previously characterized digitonin-permeabilized insulin-secreting pancreatic islet model to study the role of myo-inositol 1,4,5-trisphosphate (IP3), a putative second messenger for mobilization of intracellular Ca2+. Ca2+ efflux from the endoplasmic reticulum was studied with or without vanadate present to inhibit Ca2+ reuptake. IP3 (10 microM), at a free Ca2+ level of 0.06 microM, increased Ca2+ release by 30% and, when vanadate was present, by 50%. Maximal and half-maximal Ca2+ release was observed at 10 microM- and 2.5 microM-IP3, respectively. IP3 provoked a rapid release that was followed by slow reuptake. Reuptake was diminished in the presence of vanadate. Inositol 1,4-bisphosphate, inositol 1-phosphate and other phosphoinositide metabolites did not have any significant effect. Because increases in Ca2+ levels in the submicromolar range have been previously shown to induce insulin release in digitonin-permeabilized islets, our results are consistent with the concept of IP3 serving as a second messenger for insulin secretion.     

High affinity Ca2+-stimulated Mg2+-dependent ATPase in rat brain synaptosomes, synaptic membranes, and microsomes

High affinity Ca2+-stimulated Mg2+-dependent ATPase activity of nerve ending particles (synaptosomes) from rat brain tissue appears to be associated primarily with isolated synaptic plasma membranes. The synaptic membrane (Ca2+ + Mg2+)-ATPase activity was found to exhibit strict dependence on Mg2+ for the presence of the activity, a high affinity for Ca2+ (K0.5 = 0.23 microM), and relatively high affinities for both Mg2+ and ATP (K0.5 = 6.0 microM for Mg2+ and KM = 18.9 microM for ATP). These kinetic constants were determined in incubation media that were buffered with the divalent cation chelator trans-cyclohexane-1,2-diamine-N,N,N',N'-tetraacetic acid. The enzyme activity was not inhibited by ouabain or oligomycin but was sensitive to low concentrations of vanadate. The microsomal membrane subfraction was the other brain subcellular fraction with a high affinity (Ca2+ + Mg2+)-ATPase activity which approximated that of the synaptic plasma membranes. The two membrane-related high affinity (Ca2+ + Mg2+)-ATPase activities could be distinguished on the basis of their differential sensitivity to vanadate at concentrations below 10 microM. Only the synaptic plasma membrane (Ca2+ + Mg2+)-ATPase was inhibited by 0.25-10 microM vanadate. The studies described here indicate the possible involvement of both the microsomal and the neuronal plasma membrane (Ca2+ + Mg2+)-ATPase in high affinity Ca2+ transport across membranes of brain neurons. In addition, they suggest a means by which the relative contributions of each transport system might be evaluated based on their differential sensitivity to inhibition by vanadate.     

Measurement of sarcoplasmic reticulum Ca2+ content in intact amphibian skeletal muscle fibres with 4-chloro-m-cresol.

Single skeletal muscle fibres were isolated from the toad (Bufo marinus) and isometric force and myoplasmic free calcium concentration ([Ca2+]i) were measured. Brief applications of 4-chloro- m-cresol (4-CmC, 0.2-5 mM) elevated [Ca2+]i reversibly in a dose-dependent manner. The lowest concentration of 4-CmC which reliably gave maximal [Ca2+]i was 2 mM and it was, therefore, used for measurement of sarcoplasmic reticulum (SR) Ca2+ content. Tetanic stimulations (100 Hz) increased [Ca2+]i from a resting level of 105 +/- 47 nM (n = 10) to 1370 +/- 220 nM (n = 6). Application of 2 mM 4-CmC produced a contracture that was 54 +/- 16% (n = 6) of the tetanic force and elevated [Ca2+]i to a peak of 3520 +/- 540 nM (n = 8). Both force and [Ca2+]i levels (resting and tetanic) were restored after 10 min of washout of 4-CmC. In skinned muscle fibres, the myofibrillar Ca(2+)-sensitivity was not changed by 4-CmC, but maximal force was reduced to 74 +/- 10% (n = 4). The magnitude of the peak of the 4-CmC-induced Ca2+ transient was not significantly changed by removal of extracellular Ca2+ nor by inhibiting the SR Ca2+ pump with 2,5-di-tert-butylhydroquinone. Treatment of intact fibres with 30 mM caffeine produced a peak Ca2+ level that was indistinguishable from 2 mM 4-CmC. These results indicate that it is possible to measure the SR Ca2+ content in the same fibre with 4-CmC without loss of normal muscle function.     

Effect of vanadate on force and myosin light chain phosphorylation in skinned aortic smooth muscle.

The effects of vanadate were examined on Ca2+-activated force and phosphorylation of 20-kDa myosin light chain in membrane-permeabilized rabbit aortic smooth muscle strips. Addition of vanadate during maximum contraction reduced the force in a dose-dependent manner, and inhibited it almost completely at 1 mM. Two-dimensional polyacrylamide gel electrophoretic analyses revealed that vanadate also reduced the phosphorylation of 20- kDa myosin light chain in a dose-dependent manner from approximately 50% in the absence of vanadate to approximately 20% in the presence of 1 mM vanadate. The effects of 1 mM vanadate on purified myosin light chain kinase and phosphatase were then examined using purified myosin as substrate, and it was found that vanadate neither inhibited myosin light chain kinase nor activated myosin light chain phosphatase. These results indicate that the reduction in the 20-kDa myosin light chain phosphorylation level by vanadate may be effected through its inhibition of the force generation in skinned smooth muscle strip, as evidenced by the finding that vanadate eliminated the enhancement of myosin light chain kinase activity brought about by the interaction between purified myosin and actin.     

Effect of vanadate on Ca++-activation in skeletal muscle

Vanadate (0.1 mM) reduces tension of glycerinated rabbit psoas muscle fibers, shifts tension--pCa curve to lower pCa, increases the rate constant of delayed tension development and changes dependence of this rate constant on the level of Ca2+-activation. Vanadate influence stops the increase of the rate constant with the rise of Ca++-activated tension. Since actin-myosin-ADP complex is dissociated by vanadate, the muscle performance at low activation levels is supposed to be conditioned largely by the cross-bridges interacting with actin of the actin blocks switched on by myosin-ADP. Kinetics of such cross-bridges differs from that of the cross bridges interacting with actin activated by Ca++ binding to troponin C.     

Reduced sensitivity of glycerinated rabbit m.psoas fibers to diprotonated vanadate during decrease in pH

Vanadate (Na3VO4) action of the isometric force of maximal Ca2(+)-activated fibre has been studied at pH from 6.3 to 7.3. Acidification was shown to decrease the force declining vanadate effect: appearance of the dissociation constant estimated from force--H2VO4--dependence increases about two-fold following the pH decreasing from 7.3 to 6.3. Therefore the well-known decline of the force at acidification is accompanied by a decrease of the sensitivity to vanadate. These both phenomena can have a common nature and reflect, for example, a decreasing complex AM.ADP+ responsible for the force and interaction with vanadate. Our findings permit to think that the changes in pH with fatigue increasing the diprotonated form of phosphate simultaneously reduce the sensitivity of the contractile system to this form.     

Effect of phallotoxins on the mechanism of Ca2+-activation of glycerinated fibers of the rabbit psoas muscle

The effect of phalloidin (Ph) and some of its derivatives on isometric tension and spectrum of mechanical relaxation times of single fibres was under investigation. It was shown that Ph had a great effect only at low levels of Ca2+-activation, evoking multi-phase changes of isometric tension and a sharp rise of the rate constant of delayed tension development up to value close to that for control fibres at high [Ca2+]. As to their efficiency to change Ca2+-sensitive parameters of the fibres, phallotoxins can be arranged as follows: Ph approximately equal to Ph-sulfone greater than Ph-sulfoxide B approximately equal to dethio-Ph greater than Ph-sulfoxide A greater than or equal to seco-Ph. There is a qualitative correlation of this sequence with the actin stabilising properties for all these substances with the exception of dethio-Ph. These findings are discussed from the viewpoint of two different "on" actin states, only one of them being Ph-sensitive.     

Pressure effects on sarcoplasmic reticulum

The irreversible effects of pressure (1-2000 atm) upon the enzymatic activity and structure of the Ca2+-ATPase of sarcoplasmic reticulum were investigated. Sarcoplasmic reticulum vesicles suspended in a medium of 0.1 M KCl, 10 mM imidazole, pH 7.0, 5 mM MgCl2, and 0.5 mM EGTA irreversibly lose their Ca2+ transport and Ca2+-stimulated ATPase activities on exposure to pressures of 800-2000 atmospheres. The pressure-induced inactivation of Ca2+-ATPase is accompanied by inhibition of the formation of phosphorylated enzyme intermediate, an increase in the passive Ca2+ permeability of the membrane, and structural changes in the Ca2+-ATPase as shown by disruption of Ca2+-ATPase membrane crystals, increased susceptibility to tryptic digestion, unmasking of SH groups, and loss of the conformational responses to Ca2+ and vanadate. The sensitivity to pressure is influenced by enzyme conformation. Ca2+ or vanadate + EGTA protect the Ca2+-ATPase against pressure-induced inactivation, implying a greater stability of the enzyme in the E1 and E2 states than in the conformational equilibrium that prevails at low [Ca2+] in the absence of vanadate. Protection against pressure inactivation was also observed in the presence of sucrose, glycerol, ethylene glycol and 1 M KCl, suggesting that water density modifying groups significantly affect the stability of Ca2+-ATPase under pressure.     

Vanadate oligomer inhibition of passive and active Ca2+ translocation by the Ca2+ pump of sarcoplasmic reticulum

'Monovanadate' containing mainly monomeric, dimeric and tetrameric vanadate species or 'decavanadate', containing mainly decameric vanadate species inhibits the passive and the active efflux of Ca2+ through the sarcoplasmic reticulum calcium pump. When the efflux of Ca2+ by sarcoplasmic reticulum vesicles is not associated with ATP synthesis both vanadate solutions inhibit the passive efflux of Ca2+. However, only 'decavanadate' exerts noticeable effects when the efflux of Ca2+ is associated with ATP synthesis being the active efflux of Ca2+ almost completely inhibited by decameric species concentration as low as 40 microM.     

An intracellular calcium store is present in Leishmania donovani glycosomes

A fourth intracellular Ca2+ pool in Leishmania donovani was identified by permeabilizing plasma membrane with digitonin. In Fura 2 loaded cells Ca2+ was released synergistically when mitochondrial function was blocked by antimycin and oligomycin. Vanadate did not have any effect if applied before incorporation of these mitochondrial poisons. However, the same inhibitor which inhibits Ca2+-ATPase activity of endoplasmic reticulum was able to release Ca2+ at a slow rate when added after antimycin and oligomycin. Alkalization of cytoplasmic pH allowed further release of Ca2+ essentially from the acidocalcisome. Purified glycosomes could mediate Ca2+ uptake mechanism in presence of vanadate whereas bafilomycin, a specific and potent inhibitor of vacuolar proton pump did not have any effect. Glycosomal Ca2+-ATPase activity was optimum at pH 7.5. The apparent Km for calciumin presence of vanadate was 12 nM. Taken together, it may be suggested that a vanadate-insensitive Ca2+-ATPase is present in the membrane of this microbody. Presence of glycosomal Ca2+ was further confirmed by imaging of Ca2+ activity in the Fura 2 loaded purified organelle using confocal laser. Results reveal that newly localized glycosomal calcium may essentially be an effective candidate to play a significant role in cellular function.     

Characteristics of Mg2+-dependent, ATP-activated Ca2+ transport in synaptic and microsomal membranes and in permeabilized synaptosomes

Synaptic plasma membranes isolated from rat brain exhibited a Ca2+ transport process that was strictly dependent on the presence of Mg2+ and activated by ATP hydrolysis. The characteristics of this ATP-activated transport process included a high affinity for Ca2+ and ATP with the Kact for these two substrates being 0.7 and 5 microM, respectively, and a lower affinity for Mg2+, Kact = 54 microM. The estimated constants for ATP-activated Ca2+ transport into synaptic membrane vesicles and the dependence of such transport on Mg2+ were indicative that such transport was related to the previously described high affinity (Ca2+ + Mg2+)-ATPase in synaptic membranes. An ATP- and Mg2+-dependent Ca2+ transport process with very similar kinetic characteristics was present also in a general microsomal membrane fraction obtained from brain tissue. The synaptic and microsomal membrane ATP-activated transport processes exhibited differences in their sensitivity to vanadate inhibition. Interaction with vanadate was fairly complex and best analyzed by a two-component model. Thus, the estimated Ki values for vanadate were 0.2 and 6.6 microM for the synaptic membranes and 0.7 and 13.8 microM for the microsomes. Since the microsomal membranes contain a substantial population of intraneuronal endoplasmic reticulum vesicles, the effects of vanadate on Ca2+ transport into intraneuronal membrane organelles, other than mitochondria, was determined in saponin-permeabilized synaptosomes. The estimated Ki values for vanadate inhibition of Ca2+ transport activity were 0.7 and 13 microM. The accumulation of Ca2+ into synaptic plasma membrane vesicles was readily reversed by activation of the Na+-Ca2+ exchange carrier, whereas the Ca2+ associated with intrasynaptosomal organelles was not affected by changes in [Na+]. Thus, there are at least two ATP-dependent Ca2+ transporting processes localized on two distinct neuronal membranes, one on the plasma membrane and the second on intraneuronal membranes.     

Different effects of verapamil and low calcium on repetitive contractile activity of frog fatigue-resistant and easily-fatigued muscle fibres.

The effects of low calcium and verapamil on contractility of two muscle fibre types (m. iliofibularis, Rana temporaria) upon different stimulation protocols were been compared. Verapamil (0.02 mmol/l) induced temporal excitation-contraction coupling failure during single tetanic stimulation and enhanced the decline of tetanic force during 30 s repetitive tetanic stimulation in both fatigue-resistant fibres and easily-fatigued fibres. In contrast to verapamil, low extracellular calcium (0.02 mmol/l) only enhanced the decline of tetanic force in fatigue-resistant during repetitive tetanic stimulation but had no effect on easily-fatigued fibres. The effect of verapamil on the decline of tetanic force in fatigue-resistant fibres was more profound in low calcium conditions. Both verapamil and low calcium eliminated twitch facilitation that appeared after prolonged contractile activity in fatigue-resistant fibres. 4mmol/l Ni+2, used as calcium channel antagonist, had effects similar to low calcium medium. It could be concluded that (i) extracellular Ca2+-requirements for excitation-contraction coupling are different in fatigue-resistant and easily-fatigued fibres; (ii) the effects of verapamil on force performance are not entirely dependent upon calcium channel blockade.     

Rate constant of muscle force redevelopment reflects cooperative activation as well as cross-bridge kinetics.

The rate of muscle force redevelopment after release-restretch protocols has previously been interpreted using a simple two-state cross-bridge cycling model with rate constants for transitions between non-force-bearing and force-bearing states, f, and between force-bearing and non-force-bearing states, g. Changes in the rate constant of force redevelopment, as with varying levels of Ca2+ activation, have traditionally been attributed to Ca(2+)-dependent f. The current work adds to this original model a state of unactivated, noncycling cross-bridges. The resulting differential equation for activated, force-bearing cross-bridges, Ncf, was Ncf = -[g+f(K/(K + 1))] Ncf+f(K/(K + 1))NT, where K is an equilibrium constant defining the distribution between cycling and noncycling cross-bridges and NT is the total number of cross-bridges. Cooperativity by which force-bearing cross-bridges participate in their own activation was introduced by making K depend on Ncf. Model results demonstrated that such cooperativity, which tends to enhance force generation at low levels of Ca2+ activation, has a counter-intuitive effect of slowing force redevelopment. These dynamic effects of cooperativity are most pronounced at low Ca2+ activation. As Ca2+ activation increases, the cooperative effects become less important to the dynamics of force redevelopment and, at the highest levels of Ca2+ activation, the dynamics of force redevelopment reflect factors other than cooperative mechanisms. These results expand on earlier interpretations of Ca2+ dependence of force redevelopment; rather than Ca(2+)-dependent f, Ca(2+)-dependent force redevelopment arises from changing expressions of cooperativity between force-bearing cross-bridges and activation.