Studies on the interaction between rabbit liver pyruvate kinase and its allosteric effector fructose 1,6-diphosphate

Preparation of the L form of rabbit liver pyruvate kinase (EC 2.7.1.40) in the presence of fructose 1,6-diphosphate yielded an enzyme which was kinetically identical with the M or muscle-type form of pyruvate kinase found in liver. Chromatographic and dialysis studies of this complex showed that most of the fructose 1,6-diphosphate molecules were loosely bound to the enzyme, but dilution-dissociation studies and binding experiments established that there was a high initial affinity between the enzyme and fructose 1,6-diphosphate (K(assoc.)=2.3x10(9)), and that binding of the loosely bound fructose 1,6-diphosphate was concentration-dependent and a necessary condition to overcome the co-operative interaction observed with the homotropic effector phosphoenolpyruvate. Preparation of the liver enzyme in the absence of EDTA did not yield a predominantly M form of the enzyme, and incubation of the M form in the presence of EDTA did not convert it into the L form, but resulted in inhibition of enzyme activity. Immunological studies confirmed that the L and M forms in liver were distinct, and that preparation of the L form in the presence of fructose 1,6-diphosphate did not produce an enzyme antigenically different from the L form prepared in the absence of this heterotropic effector.     

Regulation of rat liver pyruvate kinase. The effect of preincubation, pH, copper ions, fructose 1,6-diphosphate and dietary changes on enzyme activity

1. Preincubation of partially purified rat liver L-type pyruvate kinase at 25 degrees for 10min. causes a marked increase in co-operativity with respect to both the substrate, phosphoenolpyruvate, and the allosteric activator, fructose 1,6-diphosphate. 2. The results are consistent with the existence of two forms of liver L-type pyruvate kinase, designated forms L(A) and L(B). It is postulated that form L(A) has a low K(m) for phosphoenolpyruvate (about 0.1mm) and is not allosterically activated, whereas form L(B) is allosterically activated by fructose 1,6-diphosphate, exhibiting in the absence of the activator sigmoidal kinetics with half-maximal activity at about 1mm-phosphoenolpyruvate. In the presence of fructose 1,6-diphosphate, form L(B) gives Michaelis-Menten kinetics with K(m) less than 0.1mm. It is further postulated that preincubation converts form L(A) into form L(B). 3. The influence of pH on the preincubation effect was studied. 4. The inhibition of pyruvate kinase by Cu(2+) was studied in detail. Though phosphoenolpyruvate and fructose 1,6-diphosphate readily protect the enzyme against Cu(2+) inhibition, little evidence of significant reversal of the inhibition by these compounds could be found. 5. The effects of starvation, fructose feeding and preincubation on the pyruvate kinase activity of crude homogenates of various tissues of the rat were also studied.     

Kinetic studies on the regulation of rabbit liver pyruvate kinase

Two kinetically distinct forms of pyruvate kinase (EC 2.7.1.40) were isolated from rabbit liver by using differential ammonium sulphate fractionation. The L or liver form, which is allosterically activated by fructose 1,6-diphosphate, was partially purified by DEAE-cellulose chromatography to give a maximum specific activity of 20 units/mg. The L form was allosterically activated by K(+) and optimum activity was recorded with 30mm-K(+), 4mm-MgADP(-), with a MgADP(-)/ADP(2-) ratio of 50:1, but inhibition occurred with K(+) concentrations in excess of 60mm. No inhibition occurred with either ATP or GTP when excess of Mg(2+) was added to counteract chelation by these ligands. Alanine (2.5mm) caused 50% inhibition at low concentrations of phosphoenolpyruvate (0.15mm). The homotropic effector, phosphoenolpyruvate, exhibited a complex allosteric pattern (n(H)=2.5), and negative co-operative interactions were observed in the presence of low concentrations of this substrate. The degree of this co-operative interaction was pH-dependent, with the Hill coefficient increasing from 1.1 to 3.2 as the pH was raised from 6.5 to 8.0. Fructose 1,6-diphosphate interfered with the activation by univalent ions, markedly decreased the apparent K(m) for phosphoenolpyruvate from 1.2mm to 0.2mm, and transformed the phosphoenolpyruvate saturation curve into a hyperbola. Concentrations of fructose 1,6-diphosphate in excess of 0.5mm inhibited this stimulated reaction. The M or muscle-type form of the enzyme was not activated by fructose 1,6-diphosphate and gave a maximum specific activity of 0.3 unit/mg. A Michaelis-Menten response was obtained when phosphoenolpyruvate was the variable substrate (K(m)=0.125mm), and this form was inhibited by ATP, as well as alanine, even in the presence of excess of Mg(2+).     

Adipose-tissue pyruvate kinase. Properties and interconversion of two active forms

1. Extraction of rat epididymal adipose tissue with buffer containing EDTA yields a pyruvate kinase, provisionally called PyK-A, the properties of which resemble in several respects those of the allosteric pyruvate kinase of liver. These properties include co-operative interactions with phosphoenolpyruvate, Mg(2+), K(+), NH(4) (+) and ATP, and sensitivity to activation by fructose 1,6-diphosphate. 2. Extraction in the absence of EDTA yields predominantly a form, PyK-B, that shows both normal Michaelis-Menten kinetics with phosphoenolpyruvate, Mg(2+) and ATP, and co-operative interactions with K(+) and NH(4) (+); this form is insensitive towards fructose 1,6-diphosphate. 3. Both forms yield simple kinetics with ADP, though K(m) values differ in the two systems. In all cases where co-operativity has been demonstrated, Hill-plot n values are between 1.4 and 2.0. 4. The conversion of PyK-A into PyK-B is mediated specifically by fructose 1,6-diphosphate; the reverse reaction is occasioned by EDTA, ATP or citrate. It is thought that a bivalent cation may be involved in this interconversion. 5. Attempts at partial purification have revealed that the enzyme resembles the pyruvate kinase of skeletal muscle, rather than that of liver, in its solubility in ammonium sulphate and elution from DEAE-cellulose. 6. The relevance of these properties in the regulation of pyruvate kinase activity in vivo in adipose tissue is discussed.     

Kinetic properties of rat liver pyruvate kinase at cellular concentrations of enzyme, substrates and modifiers

Kinetic properties of rat liver pyruvate kinase type I at pH7.5 and 6.5 were studied with physiological ranges of substrates, modifiers and Mg(2+) concentrations at increasing enzyme concentrations, including the estimated cellular concentrations (approx. 0.1mg/ml). Enzyme properties appear unaffected by increased enzyme concentration if phosphoenolpyruvate, fructose 1,6-diphosphate and inhibitors are incubated with enzyme before starting the reaction with ADP. Our data suggest that minimum cellular concentrations of MgATP and l-alanine provide virtually complete inhibition of pyruvate kinase I at pH7.5. The most likely cellular control of existing pyruvate kinase I results from the strong restoration of enzyme activity by the small physiological amounts of fructose 1,6-diphosphate. Decreasing the pH to 6.5 also restores pyruvate kinase activity, but to only about one-third of its activity in the presence of fructose 1,6-diphosphate. Neither pyruvate nor 2-phosphoglycerate at cellular concentrations inhibit the enzyme significantly.     

Comparative kinetic studies on the L-type pyruvate kinase from rat liver and the enzyme phosphorylated by cyclic 3', 5'-AMP-stimulated protein kinase.

The kinetics of rat liver L-type pyruvate kinase (EC 2.7.1.40), phosphorylated with cyclic AMP-stimulated protein kinase from the same source, and the unphosphorylated enzyme have been compared. The effects of pH and various concentrations of substrates, Mg2+, K+ and modifiers were studied. In the absence of fructose 1, 6-diphosphate at pH 7.3, the phosphorylated pyruvate kinase appeared to have a lower affinity for phosphoenolpyruvate (K0.5=0.8 mM) than the unphosphorylated enzyme (K0.5=0.3 mM). The enzyme activity vs. phosphoenolpyruvate concentration curve was more sigmoidal for the phosphorylated enzyme with a Hill coefficient of 2.6 compared to 1.6 for the unphosphorylated enzyme. Fructose 1, 6-diphosphate increased the apparent affinity of both enzyme forms for phosphoenolpyruvate. At saturating concentrations of this activator, the kinetics of both enzyme forms were transformed to approximately the same hyperbolic curve, with a Hill coefficient of 1.0 and K0.5 of about 0.04 mM for phosphoenolpyruvate. The apparent affinity of the enzyme for fructose 1, 6-diphosphate was high at 0.2 mM phosphoenolpyruvate with a K0.5=0.06 muM for the unphosphorylated pyruvate kinase and 0.13 muM for the phosphorylated enzyme. However, in the presence of 0.5 mM alanine plus 1.5 mM ATP, a higher fructose 1, 6-diphosphate concentration was needed for activation, with K0.5 of 0.4 muM for the unphosphorylated enzyme and of 1.4 muM for the phosphorylated enzyme. The results obtained strongly indicate that phosphorylation of pyruvate kinase may also inhibit the enzyme in vivo. Such an inhibition should be important during gluconeogenesis.     

Functional changes associated with the sequential transformation of L'4 into L4 pyruvate kinase.

The functional changes, associated with the sequential transformation of L'4 into L4 pyruvate kinase (ATP:pyruvate 2-O-phosphotransferase, EC 2.7.1.40) were studied. L'4 enzyme from human erythrocytes shows strong hysteretic behaviour: the initial rate of the enzyme preincubated with an unsaturating concentration of phosphoenolpyruvate is much higher than of the enzyme preincubated with ADP, at the same phosphoenolpyruvate concentration, although the "final activity" (the activity of the linear part of the reaction progress curve) was the same in both cases. This phenomenon was observed both in the presence and absence of fructose 1,6-diphosphate. High concentrations of both Mg2+free and MgATP2- diminish the difference in initial rate, between the ADP and phosphoenolpyruvate preincubated enzymes: Mg2+free by stabilizing the phosphoenolpyruvate-induced form; ATPMg2- by stabilizing the ADP-induced form. The magnitude of the difference in initial rates of the ADP-or phosphoenolpyruvate-preincubated enzyme is a function of both substrates. L4 pyruvate kinase (either from human liver or trypsin treated L'4 enzyme) does not, or to a very slight extent, show such behaviour. L'2L2 pyruvate kinase shows behaviour intermediate between L'4 and L4 enzymes. A model is proposed to describe the kinetic behaviour of L'4 and L4 enzymes.     

Kinetic properties of pyruvate kinase hybrids formed with native type L and inactivated type M subunits.

Bovine type M pyruvate kinase, which normally has hyperbolic kinetics with its substrates, was inactivated by treatment with trinitrobenzenesulfonic acid. The inactivation probably occurs through trinitrophenylation of the epsilon-amino group of a lysine residue in or near the ADP binding site. Although 90 to 95% of the enzymatic activity is lost by this treatment, the molecular weight and sedimentation coefficient of the trinitrophenylated enzyme are quite similar to values obtained with the native enzyme. The inactivated, trinitrophenylated type M pyruvate kinase was hybridized in vitro with the native bovine type L enzyme, which has sigmoidal kinetics with phosphoenolpyruvate but can be activated by fructose 1,6-diphosphate to give hyperbolic kinetics. Four enzymatically active species were produced, designated L4, L3M, L2M2, and LM3, according to their subunit composition. L4 and L3M have sigmoidal kinetics with phosphoenolpyruvate and are activated by fructose diphosphate. Little or no sigmoidicity was seen for L2M2, although this species is activated to a moderate degree by fructose diphosphate. LM3 appears to have hyperbolic kinetics and is activated only slightly by fructose diphosphate. The kinetic results obtained with hybrids containing trinitrophenylated type M subunits are quite similar to the results previously reported by Dyson and Cardenas ((1973) J. Biol. Chem. 248, 8482-8488) using native type M and type L subunits, indicating that the properties of a type L subunit are profoundly affected by the nature of the other subunits present in the tetramer. In fact, type L and type M subunits in a given hybrid seem to have similar kinetic responses toward phosphoenolpyruvate and fructose diphosphate.     

The effect of pH on the interaction of substrates and effector to yeast and rabbit muscle pyruvate kinase

The interaction of fructose 1,6-bisphosphate, phosphoenolpyruvate and ADP with pyruvate kinase (ATP: pyruvate 2-O-phosphotransferase, EC 2.7.1.40) from yeast and rabbit muscle has been studied as a function of pH utilizing the quenching of protein fluorescence at 330 nm by these ligands. Both the muscle and the yeast pyruvate kinase interact with either ADP or phosphoenolpyruvate with similar affinity, indicating that the substrate-binding sites for these two isozymes are similar. The major difference between the yeast and muscle isozymes is their affinity with fructose 1,6-bisphosphate. Fructose 1,6-bisphosphate interacts with the yeast isozyme in orders of magnitude more strongly than with the muscle isozyme. Moreover, the affinity of fructose 1,6-bisphosphate to the yeast isozyme is strongly pH-dependent, while the interaction of fructose 1,6-bisphosphate with the muscle isozyme is independent of pH. The data indicate that yeast pyruvate kinase undergoes a conformational change as the pH is increased from 6.0 to 8.5.     

Modification of human erythrocyte pyruvate kinase by an active site-directed reagent: bromopyruvate

Human erythrocyte pyruvate kinase was modified with bromopyruvate and the kinetic behavior of the modified enzyme was investigated. When the enzyme was modified with bromopyruvate in the absence of adenosine-5'-diphosphate, phosphoenolpyruvate or fructose-1,6-diphosphate the inactivation followed a pseudo first-order kinetics. The inactivation rate constant, ks, was 1.84 +/- 0.15 min(-1). Kd of the bromopyruvate-enzyme complex was 0.14 +/- 0.03 mM. The presence of adenosine-5'-diphosphate, phosphoenolpyruvate or fructose-1,6-diphosphate in the modification medium or the presence of fructose-1,6-diphosphate in the assay medium resulted in deviation of the inactivation kinetics from pseudo first-order. Phosphoenolpyruvate was better than adenosine-5'-diphosphate for protection against bromopyruvate modification whereas fructose-1,6-diphosphate was ineffective. The modified enzyme showed negative cooperativity in the presence of fructose-1,6-diphosphate whereas in the absence of it no activity was detected.     

Kinetics of the activation of rat liver pyruvate kinase by fructose 1,6-disphosphate and methods for characterizing hysteretic transitions

1. Kinetics of fructose 1,6-diphosphate activation of liver pyruvate kinase type I inhibited with MgATP and l-alanine are described as a function of enzyme and fructose 1,6-diphosphate concentrations. These results can be explained by a single pseudo-first-order transition of the enzyme into an active form, independent of the enzyme concentration. This rate constant, k(app.)=0.24s(-1) with 0.02mm-fructose 1,6-diphosphate (t(0.9) approximately 10s where t(0.9) is the time for 90% conversion), is an increasing function of fructose 1,6-diphosphate concentration far beyond that needed to maximally activate enzyme equilibrated with fructose 1,6-diphosphate (about 20mum). 2. The model equations are best analysed with numerical techniques which are described. These techniques are useful in studying similar slow transients frequently observed in stopped-flow studies of enzymes. 3. Shorter transients (t(0.9)=0.5-1.5s) were observed in the kinetic response of the enzyme to the addition of MgATP or phosphoenolpyruvate, but were not further characterized.     

Long-term effect of glucagon administration on rat liver L-type pyruvate kinase.

After 5 h of treatment with glucagon, liver L-type pyruvate kinase (ATP: pyruvate 2-0-phosphotransferase; EC 2.7.1.40) showed a significant decrease of K0.5 and the Hill coefficient (nH) in the absence of fructose 1,6-diphosphate. However, in the presence of fructose 1,6-diphosphate, liver enzymes from treated rats showed a slight decrease of K0.5 but nH remained unchanged. In both circumstances, no changes of Vmax were observed after treatment. These changes in the kinetic properties of liver L-type pyruvate kinase are consistent with the dephosphorylation of the enzyme caused by insulin release in response to treatment with glucagon.     

Pyruvate Kinase of Streptococcus lactis

The kinetic properties of pyruvate kinase (ATP:pyruvate-phosphotransferase, EC 2.7.1.40) from Streptococcus lactis have been investigated. Positive homotropic kinetics were observed with phosphoenolpyruvate and adenosine 5′-diphosphate, resulting in a sigmoid relationship between reaction velocity and substrate concentrations. This relationship was abolished with an excess of the heterotropic effector fructose-1,6-diphosphate, giving a typical Michaelis-Menten relationship. Increasing the concentration of fructose-1,6-diphosphate increased the apparent V_max values and decreased the K_m values for both substrates. Catalysis by pyruvate kinase proceeded optimally at pH 6.9 to 7.5 and was markedly inhibited by inorganic phosphate and sulfate ions. Under certain conditions adenosine 5′-triphosphate also caused inhibition. The K_m values for phosphoenolpyruvate and adenosine 5′-diphosphate in the presence of 2 mM fructose-1,6-diphosphate were 0.17 mM and 1 mM, respectively. The concentration of fructose-1,6-diphosphate giving one-half maximal velocity with 2 mM phosphoenolpyruvate and 5 mM adenosine 5′-diphosphate was 0.07 mM. The intracellular concentrations of these metabolites (0.8 mM phosphoenolpyruvate, 2.4 mM adenosine 5′-diphosphate, and 18 mM fructose-1,6-diphosphate) suggest that the pyruvate kinase in S. lactis approaches maximal activity in exponentially growing cells. The role of pyruvate kinase in the regulation of the glycolytic pathway in lactic streptococci is discussed.     

Modification of Human Erythrocyte Pyruvate Kinase by an Active Site-directed Reagent: Bromopyruvate

Human erythrocyte pyruvate kinase was modified with bromopyruvate and the kinetic behavior of the modified enzyme was investigated. When the enzyme was modified with bromopyruvate in the absence of adenosine-5′s-diphosphate, phospho-enolpyruvate or fructose-1,6-diphosphate the inactivation followed a pseudo first-order kinetics. The inactivation rate constant, k_s, was 1.84 × 0.15 min^?1. K_d of the bromopyruvate-enzyme complex was 0.14 × 0.03 mM.

The presence of adenosine-5′-diphosphate, phosphoenolpyruvate or fructose-1,6-diphosphate in the modification medium or the presence of fructose-1,6-diphosphate in the assay medium resulted in deviation of the inactivation kinetics from pseudo first-order. Phosphoenolpyruvate was better than adenosine-5′-diphosphate for protection against bromopyruvate modification whereas fructose-1,6-diphosphate was ineffective. The modified enzyme showed negative cooperativity in the presence of fructose-1,6-diphosphate whereas in the absence of it no activity was detected.     

Regulation of M2-type pyruvate kinase from human meningioma by allosteric effectors fructose 1,6 diphosphate and L-alanine.

In the present study the mechanism of action of M2-type pyruvate kinase from human meningioma in the simultaneous presence of fructose 1,6 diphosphate and L-alanine was investigated. Purified pyruvate kinase from human meningioma was allosterically inhibited by L-alanine with respect to substrates phosphoenolpyruvate and ADP. The inhibitory effects of L-alanine was partially removed by fructose 1,6 diphosphate. The purified enzyme was slightly susceptible to ATP inhibition.     

Reversal of glycolysis in yeast.

When a buffered, aerobic suspension of ethanol-grown cells of Saccharomyces cerevisiae is treated with ethanol, a rapid flux of metabolism is observed from endogenous phosphoenolpyruvate to hexose monophosphates. Intracellular concentrations of phosphoenolpyruvate, 2-phosphoglycerate, and 3-phosphoglycerate record a monotonic drop, while those of triose phosphates and fructose 1,6-diphosphate fall after an early rise; fructose 6-phosphate, mannose 6-phosphate, and glucose 6-phosphate levels rise to a plateau. Prior growth on glucose extinguishes fructose 1,6-diphosphatase activity and completely arrests the rise of the hexose monophosphates. By using mutants blocked at a number of glycolytic steps it has been concluded that the metabolic flow takes place along the Embden-Meyerhof pathway in the reverse direction bypassing pyruvate kinase and fructose 6-phosphate kinase. Ethanol acts as a trigger by supplying NADH at the glyceraldehyde 3-phosphate dehydrogenase step. The rate of the reversal in the span phosphoenolpyruvate to fructose 1,6-diphosphate approaches 40 μ mol of 3-carbon units per minute per gram of wet cells. The in vivo activity of fructose 1,6-diphosphatase is nearly a quarter of this rate.     

Electrofocusing and kinetic studies of adult and embryonic chicken pyruvate kinases.

Chicken embryos less than 15 days old contain only the K isozyme of pyruvate kinase, which appears to exist in vivo as an R,T conformational set with pI values of 7.2 and 6.6, respectively. Sets of lower pI and higher pI K-isozyme variants also are obtained. Whole embryos of 15 days or more of development show progressively increasing amounts of higher pI, lower K0.5S enzymatic variants. Tissue distribution and kinetic properties suggest that the highest pI form (pH 8.8-9.0) is an M-isozyme analogue. The intermediate forms are postulated to be hybrids. Adult liver extracts contain only the embryonic K isozyme; no evidence for an L-isozyme analogue was obtained. All major forms of the enzymes are compared with respect to saturation by phosphoenolpyruvate in the absence of effector and in the presence of fructose 1,6-diphosphate, alanine, serine, phenylalanine, tryptophan, and/or Mg-ATP.     

A comparison of the properties of the pyruvate kinases of the fat body and flight muscle of the adult male desert locust

1. The pyruvate kinases of the desert locust fat body and flight muscle were partially purified by ammonium sulphate fractionation. 2. The fat-body enzyme is allosterically activated by very low (1mum) concentrations of fructose 1,6-diphosphate, whereas the flight-muscle enzyme is unaffected by this metabolite at physiological pH. 3. Flight-muscle pyruvate kinase is activated by preincubation at 25 degrees for 5min., whereas the fat-body enzyme is unaffected by such treatment. 4. Both enzymes require 1-2mm-ADP for maximal activity and are inhibited at higher concentrations. With the fat-body enzyme inhibition by ADP is prevented by the presence of fructose 1,6-diphosphate. 5. Both enzymes are inhibited by ATP, half-maximal inhibition occurring at about 5mm-ATP. With the fat-body enzyme ATP inhibition can be reversed by fructose 1,6-diphosphate. 6. The fat-body enzyme exhibits maximal activity at about pH7.2 and the activity decreases rapidly above this pH. This inactivation at high pH is not observed in the presence of fructose 1,6-diphosphate, i.e. maximum stimulating effects of fructose 1,6-diphosphate are observed at high pH. The flight-muscle enzyme exhibits two optima, one at about pH7.2 as with the fat-body enzyme and the other at about pH8.5. Stimulation of the enzyme activity by fructose 1,6-diphosphate was observed at pH8.5 and above.     

Regulation of glycerol kinase by enzyme IIIGlc of the phosphoenolpyruvate:carbohydrate phosphotransferase system.

Wild-type glycerol kinase of Escherichia coli is inhibited by both nonphosphorylated enzyme IIIGlc of the phosphoenolpyruvate:carbohydrate phosphotransferase system and fructose 1,6-diphosphate. Mutant glycerol kinase, resistant to inhibition by fructose 1,6-diphosphate, was much less sensitive to inhibition by enzyme IIIGlc. The difference between the wild-type and mutant enzymes was even greater when inhibition was measured in the presence of both enzyme IIIGlc and fructose 1,6-diphosphate. The binding of enzyme IIIGlc to glycerol kinase required the presence of the substrate glycerol.     

Post-mortem glycolysis in ox skeletal muscle. Effect of pre-rigor freezing and thawing on the intermediary metabolism

1. Ox sternomandibularis muscle was ;slow-frozen' by placing it in air at -22 degrees or ;fast-frozen' by immersion in liquid air or acetone-solid carbon dioxide. In all cases muscles were frozen pre-rigor. Changes in length, pH and the concentrations of P(i), creatine phosphate, hexose monophosphate (glucose 1-phosphate+glucose 6-phosphate+fructose 6-phosphate), fructose diphosphate (fructose 1,6-diphosphate+(1/2) triose phosphate), lactate, ATP, ADP, AMP and NAD(+) during freezing and during subsequent thawing were determined. In addition some measurements were made of the changes in alpha-glycerophosphate, 3-phosphoglycerate, 2-phosphoglycerate, phosphoenolpyruvate and pyruvate concentrations during slow freezing. 2. Appreciable shortening and marked changes in chemical composition took place during slow freezing but not during fast freezing. 3. During slow freezing the hexose monophosphate concentration fell and fructose 1,6-diphosphate and triose phosphate increased substantially. Increases also took place in 3-phosphoglycerate, 2-phosphoglycerate and phosphoenolpyruvate, but not in pyruvate. 4. On thawing, most of the chemical changes were similar to those in unfrozen muscle post mortem, but took place much more rapidly; loss of NAD(+) was particularly rapid. Fast-frozen muscle metabolized at a faster rate on thawing than did slow-frozen muscle. 5. The overall changes in length during freezing and thawing were about the same in slow-frozen as in fast-frozen muscle.