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The relationship between ATP and R-values in postmortem bovine Longissimus dorsi muscle
Meat Science 33 (1993) 253-263
The Relationship Between A T P and R-Values in Postmortem Bovine Longissimus dorsi Muscle* K. C. Koh~, T. D. Bidner§, K. W. McMillin & M. B. Kim:~ Louisiana Agricultural Experiment Station, Louisiana State University Agricultural Center, Baton Rouge, Louisiana 70803, USA {Received 9 December 1991; revised version received 21 January 1992; accepted 1 February 1992)
ABSTRACT To study the relationship between A TP and each of three R-values (R248, R250 and R258) in beef longissimus dorsi muscle data, appropriate mathematical functional forms were estimated by the B o x - C o x transformation and then tested for linearity. Two separate tests for linearity indicated that the relationships between A TP and the three R-values were nonlinear. A shifting parameter restriction on the B o x - C o x model was used to produce a curve that was more parallel to the y axis in the lower range of x axis, but the restriction lowered the R 2 compared with the Box-Cox model. A TP (1 pmol) could be estimated by R248 of 0.925, R250 of 0.967 and R258 of 1"038 with standard errors o f 0"033, 0"034 and 0"032, respectively. There were no significant differences among the three R-values for the prediction of A TP, but there was a suggestion that R258 was the preferred R-value for predicting A TP in beef muscle. INTRODUCTION D u r i n g the c o n t r a c t i o n - r e l a x a t i o n cycle in p r e r i g o r muscle, a d e n o s i n e 5't r i p h o s p h a t e (ATP) is n e e d e d for muscle relaxation, b u t in the absence o f * Approved for publication by the Director of the Louisiana Agricultural Experiment Station as manuscript number 90-11-4531. **Present address: Division of Animal Nutrition & Products Livestock Experiment Station, Suwon 440-350, Republic of Korea. § To whom correspondence should be addressed. $ Present address: SAS Institute, Gary, NC, USA. 253 Meat Science 0309-1740/92/$05.00 © 1992 Elsevier Science Publishers Ltd, England. Printed in Great Britain
254
K. C. Koh, T. D. Bidner, K. W. McMillin, M. B. Kim
ATP in postmortem muscle after rigor onset, actin and myosin remain tightly bound and extensibility is lost (Bate-Smith & Bendall, 1947; Bendall, 1951; Greaser, 1976). Both Bate-Smith & Bendall (1947) and Marsh (1981) have reported a relationship between decreased extensibility in postmortem muscle and decreased ATP content. Rigor development can be estimated through measurements of ATP depletion (De Fremery & Pool, 1960). During rigor development, ATP is progressively dephosphorylated to adenosine 5'-diphosphate (ADP), adenosine 5'-monophosphate (AMP) and then deaminated to inosine monophosphate (IMP), which is further metabolized to inosine and finally to hypoxanthine (Bendall, 1973). The maximum absorbance of adenine nucleotides (ATP, ADP and AMP) are measured at 258-260 nm, IMP and inosine at 248-259 nm, and hypoxanthine at 250 nm (Bendall & Davey, 1957; Newbold & Scopes, 1967; Khan & Frey, 1971; Honikel & Fischer, 1977). Using these metabolic pathways and the maximum absorbances of these high-energy phosphate compounds, simple methods of estimating ATP and thus rigor development have been sought by measuring the extent of dephosphorylation and deamination of adenine nucleotides into inosinic acid; for example, A 265/A 25o by Bendall & Davey (1957), A25o/A26 o and A28o/A26 o by Dannert & Pearson (1967), A258/A25 o by Khan & Frey (1971), and A248/A26 o by Davidek & Velisek (1973). Honikel & Fischer (1977) proposed that 'R-value', a ratio of A25o/A26o, could be used as a simple and rapid method for detection of the ATP to IMP deamination and for segregation of pale, soft, exudative and dark, firm, dry pork from normal pork. These authors compared this method with the direct measurement of ATP. However, there are only limited reports in the literature that compared the statistical relationships between ATP and R-values. Honikel & Fischer (1977) presented a figure which indicated that the two variables had a nonlinear relationship, and Honikel et al. (1981) made the assumption that 1 #mol ATP/g muscle corresponded to a R250 of 1.10 based upon their earlier work (Honikel & Fischer, 1977). Since the original work, several authors have measured the extent of ATP breakdown using R250 (Honikel & Hamm, 1978; Fischer & Harem, 1980; Honikel et al., 1983). Recently, R250 has also been used to follow the development of rigor in poultry (Lyon et al., 1989; McGinnis et al., 1989; Papa & Fletcher, 1988; Papa et al., 1989; Sams et al., 1988) and to estimate the rate of postmortem metabolism in poultry (Sams et aL, 1988) and in beef (Coon et aL, 1983; Bernthal et al., 1989). Both R248 and R258 are similar to R250, and any of these three Rvalues could have been utilized to predict ATP and to determine rigor development. Calkins et aL (1982, 1983) compared these three R-values for predicting meat tenderness. The objectives of this research were to study the mathematical functional
A TP and R-values in postmortem bovine longissimus dorsi muscle
255
relationships between ATP concentration and each of three R-values (R248, R250 and R258) for beef muscle, to obtain prediction equations for ATP using each R-value, and to determine the most useful R-value in predicting ATP concentration.
MATERIAL AND METHODS
Source of data The first dataset (DATA1) utilized the data reported by Koh et al. (1987) with 109 observations. All cattle were slaughtered at the Louisiana State University Agricultural Center Meat Laboratory. The second dataset was obtained from a second experiment consisting of 12 Brahman-AngusHereford steers that had been fed a high concentrate diet for 210 days. After slaughter, the carcasses were held at two different temperatures (4°C or 16C) for 3 h and the subcutaneous fat over the shortloin (the twelfth thoracic to the sixth lumbar vertebrae) was removed from each of the right sides. The samples for ATP and R-values were obtained in the same manner as Koh et al. (1987), except that the sampling intervals for the second experiment were 1, 4, 8, 12 and 24 h p o s t m o r t e m for a total of 120 observations (DATA2). The combined data set consisted of 229 observations (Combined DATA).
ATP and R-values The tissue samples were stored in liquid nitrogen until deproteination by the procedure of Lamprecht & Trautschold (1974). After deproteination, two 5-ml aliquots of supernatant were used to determine ATP and R-values (Fig. 1). The ATP concentration was measured following the procedure of Koh et al. (1987). R-values (R248, R250 and R258) were measured using a calibrated Beckman DB Spectrophotometer following the procedure of Calkins et al. (1983). In the present study, the absorbances at 248, 250, 258, 260, 265 and 280 nm were designated A248, A250, A258, A260, A265 and A28o, respectively, and the ratios of A248/A260, A2so/A260 and A258/A250 were named R248, R250 and R258, respectively.
Statistical analysis To determine the best mathematical functional form for the relationship between ATP and each of three R-values (R248, R250 and R258), the Box-Cox transformation method (Box & Cox, 1964) was used with a Shazam nonlinear program (White, 1984). Two different mathematical
256
K. C. Koh, T. D. Bidner, K. W. McMillin, M. B. Kim
Grind 4g of tissue with liquid nitrogen (LN2)
Add 13 ml of 6% HC104, grind to powder with LN z added, and thaw at 4°C
Homogenise for 90 s
Centrifuge at 3000g for 10min at 2°C
2/ Neutralise 5 ml of the supernatant to pH 7.4 Adjust 5 ml of the supernatant to pH 6.0-6"5 using 2M KOH with 5M K2CO 3
Ice-bath for 10min
Ice-bath for 60min
Filter (Whatman No. 1)
Filter (Whatman No. 1)
od.
od.
Enzymatic assay with glucose 6-phosphate dehydrogenase and hexokinase using 50mM triethanolamine buffer (pH 7'5)
Spectrophotometry at 248, 250, 258 and 260nm using 0'5M Na-phosphate buffer (pH 6-5)
Fig. 1. Procedure for tissue deproteination.
models (linear and nonlinear) with coefficients were obtained based upon the Box-Cox method. The equations given under the nonlinearity assumption were chosen for the relationship between ATP and each of three R-values as a result of two separate tests for linearity, the maximum likelihood ratio test (Hogg & Craig, 1978) and Ramsey's (1974) specification test, both tests indicated that the relationships between ATP and each of the R-values were nonlinear. In an effort to produce curves similar to Honikel & Fischer (1977), additional equations were obtained. Their assumption that the relationship between ATP and R250 would be hyperbolic (Honikel, 1984, personal communication) was reasonable. As the ATP content approached zero, R250 would become infinite because the numerator (the content of IMP)
A TP and R-values in postmortem bovine longissimus dorsi muscle
257
increased as the denominator (the content of ATP) decreased. Therefore, a restriction of shift parameters was added to the B o x - C o x model based upon the data of the present study in which R248 and R250 were always greater than 0.65 and 0.75, respectively, whereas R258 was always smaller than 1-45. N o n n e s t e d regression analysis with the artificial regression model (Davidson & MacKinnon, 1981) was utilized to determine which of the three R-values (R248, R250 and R258) was the most accurate predictor of ATP.
RESULTS Estimation of mathematical functional forms All the likelihood ratio tests for each data set (DATA1, DATA2, Combined D A T A ) strongly rejected (p < 0-000 1) the null hypothesis that there was a linear relationship between A T P and each of the three R-values (Table 1). Ramsey's specification test showed no evidence (p < 0.0001) of accepting the linearity hypothesis, H 0 : b 2 = b 3 = b 4 = 0 (Table 2). Both of these tests indicated that all the relationships between A T P and each of the R-values (R248, R250 and R258) were nonlinear. The coefficients o f e q n (1) for the nonlinear relationship obtained from the general B o x - C o x model are presented in Table 3, which 'best' fit the Combined D A T A . The curves representing estimated A T P values using the nonlinear coefficients o f e q n (1) were generated and superimposed over individual data points of the scatter plot of Combined Data (Fig. 2, eqn (1)). However, the curve for R250 generated by this process was not parallel to the y axis (ordinate) in the lower range of the x axis (abscissa). The earlier work of Honikel & Fischer (1977) indicated a slightly different shape in the lower range of the curve. Therefore, one restriction of shift parameters was used in TABLE 1 Maximum Likelihood Ratio Statistics for the Test of Linearity of the Mathematical Functional Forms of R248, R250 and R258a'b Data set
R248
R250
R258
DATA1 DATA2 Combined DATA
139.874 92-618 262.218
141'732 93.714 263.968
! 16.172 70"856 233-714
a All test statistics are asymptotically distributed as Z{2j-Z~2~= 2(Lt - Lo) where L 1 = L=ax of H 1 (nonlinear) and Lo = Lmaxof H o (linear). b All test statistics are indicative of the strong rejection of the linearity hypothesis at p < 0.000 1.
258
K. C. Koh, T. D. Bidner, K. W. M c M i l l i n , M. B. K i m
TABLE 2 Ramsey's specification test values for the linearity of the mathematical functional forms of R248, R250 a n d R258 a'b D a t a set
R248
R250
R258
DATA 1 DATA2 Combined DATA
17.445 18"755 21.447
29' 197 20'556 26.457
4'259 6-731 7.171
a All F test statistics are distributed as: F(3, 104) for D A T A 1 F(3, 115) for D A T A 2 F(3, 224) for C o m b i n e d D A T A h All test statistics are indicative o f the strong rejection o f the linearity hypothesis at p < 0.0001.
TABLE 3 Coefficients of the Prediction E q u a t i o n for A T P by R248, R250 and R 2 5 8 in the General B o x - C o x Model a Dataset
R-value
ao
Combined DATA
R248
-0.349 ( - 11"77) d - 0"065 ( - 2.27) -0.235 (-8.16)
R250 R258
aI
-5.645 ( - 37-02) - 6.049 ( - 38-24) 7'852 (38.18)
ATPI )~' = ao + a l RI a2~ + ei h Zmax: M a x i m u m likelihood function. c R2: adjusted R-square. aThe n u m b e r s in parenthesis are t statistics.
2z
22
L,,,~
R 2c
0.410
0.362
-50.239
0.857
0.428
- 0.052
- 44-93
0-865
0.394
- 1.14
-43.222
0'865
(1)
order to change the slope of the curve in the lower range of the x axis. The equations obtained with the shift parameters (eqn (2) for R248 and R250 and eqn (3) for R258) were used to draw a curve over the scatter plots of Combined Data (Fig. 2, eqn (2)). The restrictions slightly lowered the R 2 value. The adjusted R 2 decreased to 0"822, 0"819 and 0"831 (Table 4, eqns (2) and (3)) from 0"857, 0.865 and 0.865 (Table 3, eqn (1)) for R248, R250 and R258, respectively. ATP estimation
The range in standard errors (SE) of predicted ATP values by R248, R250 and R258 using eqns (2) and (3) were 0-033-0.079, 0.033-0-109 and
A TP and R-values in postmortem bovine longissimus dorsi muscle
--:
ATP(0410)
:
---
ATP
= - 0 . 3 4 9 - 5.645"R248 (0362)
(Eq 1)
- - : ATp(0 428) = -0.065 - 0.049"R250 (-0052) (Eq 1)
= -1.576 + 1 . 3 5 0 / ~
(Eq 2)
---:
(Eq 2)
":.
E 0.o
i~.'"
~,..~ t . 5
;e
~ 0.0 "~ Z.5 .,,,
t.0
E~t,t. 5
0
.. ,,
,
t.0
'
"~"
E:~- 1.5
I:1. t,,- 1.5
11. 1.0 I'-"
. ",,
"
..
' ' '': '
0.5
0.5 0.0
= -1.154 + 1 . 0 0 3 / ~
4.oi .
4.0
<
ATP
4.5
4.5
O
259
"-
. .....,;~
0.01
. . . . . . . . • ", , , , 1.15 0.T5 0.05 0.05 1.05 1.15 1.7'0 1.35 1.45
, ,
0.T5 0.05 l . f l
L 1 5 1.15
I,,25 1.|5
1.45 1.55
R250
R248
(a)
(b) __ : ATp(O 394) = - 0 235 - 7 852'R258 ('1 14o) (Eq 1) .. :
ATP
= - 3 978 + 3 ] 9 4 / ' v ~
(Eq 3)
4,5 4.0
•::2
~1 3.5 a}
,
E s.o
'..../
"~
2,5
'
.,.. : ,,
.';-
E
1.0~
, ",,.
•
11,. 1.0 I'-" '<
0.5
oo 0,65 0.75 0.05 0.05 1.05 1.15 1.25 1.35 1.45
R258
(c) Fig. 2.
Prediction equations of ATP estimated by Box-Cox transformation using three R-values: (a) R248; (b) R250; (c) R258.
0"032-0"076, respectively. From these equations, 1/~mol ATP was equivalent to R248 of 0.925, R250 of 0.967 and R258 of 1.038 with SE of 0.033, 0-034 and 0"032, respectively. Evaluation of R-values
The nonnested regression analysis strongly (p < 0.0001) rejected the null hypotheses that R248 was superior to the other two R-values in predicting ATP and that R250 was superior to the other two R-values. However, the
260
K. C. Koh, T. D. Bidner, K. W. M c M i l l i n , M. B. K i m
TABLE 4 Coefficients o f t h e P r e d i c t i o n E q u a t i o n s for A T P by R248, R 2 5 0 a n d R258 in t h e shifted B o x - C o x M o d e l w i t h t h e R e s t r i c t e d P o w e r P a r a m e t e r s " Dataset
R-value
Combined DATA
R248 R250 R258
bo - 1.576 ( - 17.14) d - 1.154 ( - 14.30) - 3.978 (-25.15)
b1
Lma bx
1.350 (32.44) 1'003 (32.12) 3"194 (33.51)
- 162.351
0.822
- 164"281
0.819
- 156.266
0.831
aATPi=bo+bl(Ri_0.65 )- 0.5 + e i for R248 = b o + b~(R i - 0 " 7 5 ) -0.5 + e i for R250. = b o + bl( 1 4 5 - R i } - 0.5 + g"i for R258 h L .... : M a x i m u m l i k e l i h o o d f u n c t i o n . ' R2: a d j u s t e d R - s q u a r e . J T h e n u m b e r s in p a r e n t h e s e s a r e t statistics.
R 2C
(2) (3) (3)
null hypothesis that R258 was superior to the other two R-values was not rejected strongly (p = 0.0361). Thus, there was a suggestion that R258 could be superior to R248 and R250 in predicting ATP.
DISCUSSION Estimation of mathematical functional forms Linearity tests for the mathematical functional forms obtained in this study for the relationships between ATP and each of three R-values (R248, R250 and R258) indicated the relationships were nonlinear. Both equations obtained by the general Box-Cox model without and with shift parameters (eqns (1) and (2), respectively) were satisfactory for the purpose of predicting ATP using R248, R250 or R258. Although having a lower R 2, the latter equation had a simpler mathematical functional form and would be more convenient in data analysis since least squares rather than nonlinear regression could be used. Our results for R250 confirmed the earlier work of Honikel & Fischer (1977) that the relationship between ATP and R250 was nonlinear. The curve of ATP versus R250 for beef muscle (Fig. 2(b), eqn (2)) was similar to the original curve of Honikel & Fischer (1977) for pork muscle. Khan & Frey (1971) reported a linear relationship (12 observations) between A T P and R258 in chicken muscle although their data indicated a
A TP and R-values in postmortem bovine longissimus dorsi muscle
261
nonlinear relationship between R258 versus percentage of total soluble phosphates. Davidek & Velisek (1973) calculated R248 values but did not report the type of the relationship between R248 and ATP. ATP estimation
Since the original work of Honikel & Fischer (1977), only a limited number of studies have been conducted on the mathematical functional relationship between R250 and ATP. Calkins et al. (1982) reported that for nonstimulated steer carcasses, R250 of 1-12 was equivalent to 1.0~mol ATP. Honikel et al. (1981) indicated that 1/~mol ATP was equivalent to 1"10 of R250 from the work of Honikel & Fischer (1977). Later, Honikel et al. (1983) showed that 1/~mol ATP was estimated by R250 of 1-075. In the work of Roncales et al. (1989), 1/~mol of ATP could be estimated to be equivalent to R250 of approximately 1.2 for lamb muscle. The variation in R250 values reported in the literature for the equivalency to 1/~mol ATP may be partially accounted for by the variation in the initial content of ATP in the prerigor state (2-5#mol by Honikel & Fischer, 1977; 2.52/~mol by Jolley et al., 1980-1; >3/~mol by Calkins et al., 1982; 4#mol by Honikel et al., 1983; 2-4/~mol by Koh et al., 1987; 4-6/~mol by Roncales et al., 1989). Initial ATP values may be influenced by storage conditions of the samples prior to ATP measurement. Factors such as the length of time and storage conditions under liquid nitrogen, the sampling time p o s t m o r t e m , incorporation of iodoacetate, or a combination of these and other factors could affect initial ATP values. In the present study, R250 of 0-967 would be equivalent to 1.0/~mol ATP. It would be more reliable to determine changes in R-values over the course of time p o s t m o r t e m rather than determining a single R-value to predict ATP. The standard errors in predicted ATP values by R-values are large, and there has been considerable variation in reported R250 values that were equivalent to 1 #mol ATP/g muscle. Evaluation of R-values
There was a trend for R258 to be superior to R248 and R250 in the predictability of ATP, but the scatter plots of all three R-values had similar patterns when an inverse form of R258 was compared with R248 and R250. The R248 and R250 were similar to each other. Since the peaks of IMP (at 250 nm) and of mixtures of IMP, inosine and hypoxanthine (at 248 nm) in muscle extracts overlap, the changes in absorbances at 248 nm and 250 nm should be similar.
262
K. C. Koh, T. D. Bidner, K. W. McMillin, M. B. Kim
Summary Our results indicated a nonlinear relationship between A T P and R-values. There were no significant differences for the prediction of A T P by the three R-values, but there was a suggestion that R258 was the preferred R-value. Since an R-value is a dynamic measure of the ratio in postmortem muscle of the amounts of adenine nucleotides (ATP, ADP, A M P ) and of I M P and/or its degradation derivatives such as inosine and hypoxanthine, the R-value should indicate the status of energy charge in postmortem muscle better than a single measure of A T P content.
REFERENCES Bate-Smith, E. C. & Bendall, J. R. (1947). J. Physiol., 106, 177. Bendall, J. R. (1951). J. Physiol., 114, 71. Bendall, J. R. (1973). In The Structure and Function of Muscle, 2nd edn, ed. G. H. Bourne. Academic Press, New York, p. 244. Bendall, J. R. & Davey, C. L. (1957). Biochim. Biophys. Acta, 26, 93. Bernthal, P. H., Booren, A. M. & Gray, J. I. (1989). Meat Sci., 25, 143. Box, G. E. P. & Cox, D. R. (1964). J. R. Star. Soc. Ser. B, 26, 211. Calkins, C. R., Branecky, L. J., Dutson, T. R., Smith, G. C. & Carpenter, Z. L. (1983). J. Food Sci., 48, 23. Calkins, C. R., Dutson, T. R., Smith, G. C. & Carpenter, Z. L. (1982). J. FoodSci., 47, 1350. Coon, F. P., Calkins, C. R. & Mandigo, R. W. (1983). J. Food Sci., 48, 1731. Dannert, R. D. & Pearson, A. M. (1967). J. Food Sci., 32, 49. Davidek, J. & Velisek, J. (1973). Fleischwirtschqft, 9, 1285. Davidson, R. & MacKinnon, J. G. (1981). Econometrica, 49, 781. De Fremery, D. & Pool, M. F. (1960). Food Res., 25, 73. Fischer, C. & Hamm, R. (1980). Meat Sci., 4, 41. Greaser, M. L. (1976). Proc. Recip. Meat Conf., 29, 395. Hogg, R. V. & Craig, A. T. (1978). Introduction to Mathematical Statistics, 4th edn. Macmillan Publishing Co., New York, p. 258. Honikel, K. O. & Fischer, C. (1977). J. Food Sci., 42, 1633. Honikel, K. O. & Hamm, R. (1978). Meat Sci., 2, 181. Honikel, K. O., Fischer, C., Hamid, A. & Hamm, R. (1981). J. Food Sci., 46, 1. Honikel, K. O., Roncales, P. & Hamm, R. (1983). Meat Sci., 8, 221. Jolley, P. D., Honikel, K. O. & Hamm, R. (1980 81). Meat Sci., 5, 99. Khan, A. W. & Frey, A. R. (1971). Can. Inst. Food Tech. J., 4, 139. Koh, K. C., Bidner, T. D., McMillin, K. W. & Hill, G. M. (1987). Meat Sci., 21, 189. Lamprecht, W. & Trautschold, I. (1974). In Methods of Enzymatic Analysis, 2nd edn, ed. H. U. Bergmeyer. Academic Press, New York, p. 2101. Lyon, C. E., Davis, C. E., Dickens, J. A. & Papa, C. M. (1989). Poultry Sci., 68, 249. Marsh, B. B. (1981). Proc. Recip. Meat Conf., 34, 75. McGinnis, J. P., Fletcher, D. L., Papa, C. M. & Buhr, R. J. (1989). Poultry Sei., 68, 386.
A TP and R-values in postmortem bovine longissimus dorsi muscle
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Newbold, R. P. & Scopes, R. K. (1967). Biochem. J., 105, 127. Papa, C. M. & Fletcher, D. L. (1988). Poultry Sci., 67, 635. Papa, C. M., Lyon, C. E. & Fletcher, D. L. (1989). Poultry Sci., 68, 238. Ramsey, J. B. (1974). In Frontiers in Econometrics, ed. P. Zarembka. Academic Press, New York, p. 13. Roncales, P., Beltran, J. A., Jaime, I. & Lopez-Lorenzo, P. (1989). J. Food Sci., 54, 1365. Sams, A. R., Janky, D. M. & Woodward, S. A. (1988). Poultry Sci., 67 (Suppl. 1), 150. White, K. J. (1984). SHAZAM. An Econometrics Computer Program (Version 4.6). University of British Columbia, Vancouver, BC.
The Relationship Between A T P and R-Values in Postmortem Bovine Longissimus dorsi Muscle* K. C. Koh~, T. D. Bidner§, K. W. McMillin & M. B. Kim:~ Louisiana Agricultural Experiment Station, Louisiana State University Agricultural Center, Baton Rouge, Louisiana 70803, USA {Received 9 December 1991; revised version received 21 January 1992; accepted 1 February 1992)
ABSTRACT To study the relationship between A TP and each of three R-values (R248, R250 and R258) in beef longissimus dorsi muscle data, appropriate mathematical functional forms were estimated by the B o x - C o x transformation and then tested for linearity. Two separate tests for linearity indicated that the relationships between A TP and the three R-values were nonlinear. A shifting parameter restriction on the B o x - C o x model was used to produce a curve that was more parallel to the y axis in the lower range of x axis, but the restriction lowered the R 2 compared with the Box-Cox model. A TP (1 pmol) could be estimated by R248 of 0.925, R250 of 0.967 and R258 of 1"038 with standard errors o f 0"033, 0"034 and 0"032, respectively. There were no significant differences among the three R-values for the prediction of A TP, but there was a suggestion that R258 was the preferred R-value for predicting A TP in beef muscle. INTRODUCTION D u r i n g the c o n t r a c t i o n - r e l a x a t i o n cycle in p r e r i g o r muscle, a d e n o s i n e 5't r i p h o s p h a t e (ATP) is n e e d e d for muscle relaxation, b u t in the absence o f * Approved for publication by the Director of the Louisiana Agricultural Experiment Station as manuscript number 90-11-4531. **Present address: Division of Animal Nutrition & Products Livestock Experiment Station, Suwon 440-350, Republic of Korea. § To whom correspondence should be addressed. $ Present address: SAS Institute, Gary, NC, USA. 253 Meat Science 0309-1740/92/$05.00 © 1992 Elsevier Science Publishers Ltd, England. Printed in Great Britain
254
K. C. Koh, T. D. Bidner, K. W. McMillin, M. B. Kim
ATP in postmortem muscle after rigor onset, actin and myosin remain tightly bound and extensibility is lost (Bate-Smith & Bendall, 1947; Bendall, 1951; Greaser, 1976). Both Bate-Smith & Bendall (1947) and Marsh (1981) have reported a relationship between decreased extensibility in postmortem muscle and decreased ATP content. Rigor development can be estimated through measurements of ATP depletion (De Fremery & Pool, 1960). During rigor development, ATP is progressively dephosphorylated to adenosine 5'-diphosphate (ADP), adenosine 5'-monophosphate (AMP) and then deaminated to inosine monophosphate (IMP), which is further metabolized to inosine and finally to hypoxanthine (Bendall, 1973). The maximum absorbance of adenine nucleotides (ATP, ADP and AMP) are measured at 258-260 nm, IMP and inosine at 248-259 nm, and hypoxanthine at 250 nm (Bendall & Davey, 1957; Newbold & Scopes, 1967; Khan & Frey, 1971; Honikel & Fischer, 1977). Using these metabolic pathways and the maximum absorbances of these high-energy phosphate compounds, simple methods of estimating ATP and thus rigor development have been sought by measuring the extent of dephosphorylation and deamination of adenine nucleotides into inosinic acid; for example, A 265/A 25o by Bendall & Davey (1957), A25o/A26 o and A28o/A26 o by Dannert & Pearson (1967), A258/A25 o by Khan & Frey (1971), and A248/A26 o by Davidek & Velisek (1973). Honikel & Fischer (1977) proposed that 'R-value', a ratio of A25o/A26o, could be used as a simple and rapid method for detection of the ATP to IMP deamination and for segregation of pale, soft, exudative and dark, firm, dry pork from normal pork. These authors compared this method with the direct measurement of ATP. However, there are only limited reports in the literature that compared the statistical relationships between ATP and R-values. Honikel & Fischer (1977) presented a figure which indicated that the two variables had a nonlinear relationship, and Honikel et al. (1981) made the assumption that 1 #mol ATP/g muscle corresponded to a R250 of 1.10 based upon their earlier work (Honikel & Fischer, 1977). Since the original work, several authors have measured the extent of ATP breakdown using R250 (Honikel & Hamm, 1978; Fischer & Harem, 1980; Honikel et al., 1983). Recently, R250 has also been used to follow the development of rigor in poultry (Lyon et al., 1989; McGinnis et al., 1989; Papa & Fletcher, 1988; Papa et al., 1989; Sams et al., 1988) and to estimate the rate of postmortem metabolism in poultry (Sams et aL, 1988) and in beef (Coon et aL, 1983; Bernthal et al., 1989). Both R248 and R258 are similar to R250, and any of these three Rvalues could have been utilized to predict ATP and to determine rigor development. Calkins et aL (1982, 1983) compared these three R-values for predicting meat tenderness. The objectives of this research were to study the mathematical functional
A TP and R-values in postmortem bovine longissimus dorsi muscle
255
relationships between ATP concentration and each of three R-values (R248, R250 and R258) for beef muscle, to obtain prediction equations for ATP using each R-value, and to determine the most useful R-value in predicting ATP concentration.
MATERIAL AND METHODS
Source of data The first dataset (DATA1) utilized the data reported by Koh et al. (1987) with 109 observations. All cattle were slaughtered at the Louisiana State University Agricultural Center Meat Laboratory. The second dataset was obtained from a second experiment consisting of 12 Brahman-AngusHereford steers that had been fed a high concentrate diet for 210 days. After slaughter, the carcasses were held at two different temperatures (4°C or 16C) for 3 h and the subcutaneous fat over the shortloin (the twelfth thoracic to the sixth lumbar vertebrae) was removed from each of the right sides. The samples for ATP and R-values were obtained in the same manner as Koh et al. (1987), except that the sampling intervals for the second experiment were 1, 4, 8, 12 and 24 h p o s t m o r t e m for a total of 120 observations (DATA2). The combined data set consisted of 229 observations (Combined DATA).
ATP and R-values The tissue samples were stored in liquid nitrogen until deproteination by the procedure of Lamprecht & Trautschold (1974). After deproteination, two 5-ml aliquots of supernatant were used to determine ATP and R-values (Fig. 1). The ATP concentration was measured following the procedure of Koh et al. (1987). R-values (R248, R250 and R258) were measured using a calibrated Beckman DB Spectrophotometer following the procedure of Calkins et al. (1983). In the present study, the absorbances at 248, 250, 258, 260, 265 and 280 nm were designated A248, A250, A258, A260, A265 and A28o, respectively, and the ratios of A248/A260, A2so/A260 and A258/A250 were named R248, R250 and R258, respectively.
Statistical analysis To determine the best mathematical functional form for the relationship between ATP and each of three R-values (R248, R250 and R258), the Box-Cox transformation method (Box & Cox, 1964) was used with a Shazam nonlinear program (White, 1984). Two different mathematical
256
K. C. Koh, T. D. Bidner, K. W. McMillin, M. B. Kim
Grind 4g of tissue with liquid nitrogen (LN2)
Add 13 ml of 6% HC104, grind to powder with LN z added, and thaw at 4°C
Homogenise for 90 s
Centrifuge at 3000g for 10min at 2°C
2/ Neutralise 5 ml of the supernatant to pH 7.4 Adjust 5 ml of the supernatant to pH 6.0-6"5 using 2M KOH with 5M K2CO 3
Ice-bath for 10min
Ice-bath for 60min
Filter (Whatman No. 1)
Filter (Whatman No. 1)
od.
od.
Enzymatic assay with glucose 6-phosphate dehydrogenase and hexokinase using 50mM triethanolamine buffer (pH 7'5)
Spectrophotometry at 248, 250, 258 and 260nm using 0'5M Na-phosphate buffer (pH 6-5)
Fig. 1. Procedure for tissue deproteination.
models (linear and nonlinear) with coefficients were obtained based upon the Box-Cox method. The equations given under the nonlinearity assumption were chosen for the relationship between ATP and each of three R-values as a result of two separate tests for linearity, the maximum likelihood ratio test (Hogg & Craig, 1978) and Ramsey's (1974) specification test, both tests indicated that the relationships between ATP and each of the R-values were nonlinear. In an effort to produce curves similar to Honikel & Fischer (1977), additional equations were obtained. Their assumption that the relationship between ATP and R250 would be hyperbolic (Honikel, 1984, personal communication) was reasonable. As the ATP content approached zero, R250 would become infinite because the numerator (the content of IMP)
A TP and R-values in postmortem bovine longissimus dorsi muscle
257
increased as the denominator (the content of ATP) decreased. Therefore, a restriction of shift parameters was added to the B o x - C o x model based upon the data of the present study in which R248 and R250 were always greater than 0.65 and 0.75, respectively, whereas R258 was always smaller than 1-45. N o n n e s t e d regression analysis with the artificial regression model (Davidson & MacKinnon, 1981) was utilized to determine which of the three R-values (R248, R250 and R258) was the most accurate predictor of ATP.
RESULTS Estimation of mathematical functional forms All the likelihood ratio tests for each data set (DATA1, DATA2, Combined D A T A ) strongly rejected (p < 0-000 1) the null hypothesis that there was a linear relationship between A T P and each of the three R-values (Table 1). Ramsey's specification test showed no evidence (p < 0.0001) of accepting the linearity hypothesis, H 0 : b 2 = b 3 = b 4 = 0 (Table 2). Both of these tests indicated that all the relationships between A T P and each of the R-values (R248, R250 and R258) were nonlinear. The coefficients o f e q n (1) for the nonlinear relationship obtained from the general B o x - C o x model are presented in Table 3, which 'best' fit the Combined D A T A . The curves representing estimated A T P values using the nonlinear coefficients o f e q n (1) were generated and superimposed over individual data points of the scatter plot of Combined Data (Fig. 2, eqn (1)). However, the curve for R250 generated by this process was not parallel to the y axis (ordinate) in the lower range of the x axis (abscissa). The earlier work of Honikel & Fischer (1977) indicated a slightly different shape in the lower range of the curve. Therefore, one restriction of shift parameters was used in TABLE 1 Maximum Likelihood Ratio Statistics for the Test of Linearity of the Mathematical Functional Forms of R248, R250 and R258a'b Data set
R248
R250
R258
DATA1 DATA2 Combined DATA
139.874 92-618 262.218
141'732 93.714 263.968
! 16.172 70"856 233-714
a All test statistics are asymptotically distributed as Z{2j-Z~2~= 2(Lt - Lo) where L 1 = L=ax of H 1 (nonlinear) and Lo = Lmaxof H o (linear). b All test statistics are indicative of the strong rejection of the linearity hypothesis at p < 0.000 1.
258
K. C. Koh, T. D. Bidner, K. W. M c M i l l i n , M. B. K i m
TABLE 2 Ramsey's specification test values for the linearity of the mathematical functional forms of R248, R250 a n d R258 a'b D a t a set
R248
R250
R258
DATA 1 DATA2 Combined DATA
17.445 18"755 21.447
29' 197 20'556 26.457
4'259 6-731 7.171
a All F test statistics are distributed as: F(3, 104) for D A T A 1 F(3, 115) for D A T A 2 F(3, 224) for C o m b i n e d D A T A h All test statistics are indicative o f the strong rejection o f the linearity hypothesis at p < 0.0001.
TABLE 3 Coefficients of the Prediction E q u a t i o n for A T P by R248, R250 and R 2 5 8 in the General B o x - C o x Model a Dataset
R-value
ao
Combined DATA
R248
-0.349 ( - 11"77) d - 0"065 ( - 2.27) -0.235 (-8.16)
R250 R258
aI
-5.645 ( - 37-02) - 6.049 ( - 38-24) 7'852 (38.18)
ATPI )~' = ao + a l RI a2~ + ei h Zmax: M a x i m u m likelihood function. c R2: adjusted R-square. aThe n u m b e r s in parenthesis are t statistics.
2z
22
L,,,~
R 2c
0.410
0.362
-50.239
0.857
0.428
- 0.052
- 44-93
0-865
0.394
- 1.14
-43.222
0'865
(1)
order to change the slope of the curve in the lower range of the x axis. The equations obtained with the shift parameters (eqn (2) for R248 and R250 and eqn (3) for R258) were used to draw a curve over the scatter plots of Combined Data (Fig. 2, eqn (2)). The restrictions slightly lowered the R 2 value. The adjusted R 2 decreased to 0"822, 0"819 and 0"831 (Table 4, eqns (2) and (3)) from 0"857, 0.865 and 0.865 (Table 3, eqn (1)) for R248, R250 and R258, respectively. ATP estimation
The range in standard errors (SE) of predicted ATP values by R248, R250 and R258 using eqns (2) and (3) were 0-033-0.079, 0.033-0-109 and
A TP and R-values in postmortem bovine longissimus dorsi muscle
--:
ATP(0410)
:
---
ATP
= - 0 . 3 4 9 - 5.645"R248 (0362)
(Eq 1)
- - : ATp(0 428) = -0.065 - 0.049"R250 (-0052) (Eq 1)
= -1.576 + 1 . 3 5 0 / ~
(Eq 2)
---:
(Eq 2)
":.
E 0.o
i~.'"
~,..~ t . 5
;e
~ 0.0 "~ Z.5 .,,,
t.0
E~t,t. 5
0
.. ,,
,
t.0
'
"~"
E:~- 1.5
I:1. t,,- 1.5
11. 1.0 I'-"
. ",,
"
..
' ' '': '
0.5
0.5 0.0
= -1.154 + 1 . 0 0 3 / ~
4.oi .
4.0
<
ATP
4.5
4.5
O
259
"-
. .....,;~
0.01
. . . . . . . . • ", , , , 1.15 0.T5 0.05 0.05 1.05 1.15 1.7'0 1.35 1.45
, ,
0.T5 0.05 l . f l
L 1 5 1.15
I,,25 1.|5
1.45 1.55
R250
R248
(a)
(b) __ : ATp(O 394) = - 0 235 - 7 852'R258 ('1 14o) (Eq 1) .. :
ATP
= - 3 978 + 3 ] 9 4 / ' v ~
(Eq 3)
4,5 4.0
•::2
~1 3.5 a}
,
E s.o
'..../
"~
2,5
'
.,.. : ,,
.';-
E
1.0~
, ",,.
•
11,. 1.0 I'-" '<
0.5
oo 0,65 0.75 0.05 0.05 1.05 1.15 1.25 1.35 1.45
R258
(c) Fig. 2.
Prediction equations of ATP estimated by Box-Cox transformation using three R-values: (a) R248; (b) R250; (c) R258.
0"032-0"076, respectively. From these equations, 1/~mol ATP was equivalent to R248 of 0.925, R250 of 0.967 and R258 of 1.038 with SE of 0.033, 0-034 and 0"032, respectively. Evaluation of R-values
The nonnested regression analysis strongly (p < 0.0001) rejected the null hypotheses that R248 was superior to the other two R-values in predicting ATP and that R250 was superior to the other two R-values. However, the
260
K. C. Koh, T. D. Bidner, K. W. M c M i l l i n , M. B. K i m
TABLE 4 Coefficients o f t h e P r e d i c t i o n E q u a t i o n s for A T P by R248, R 2 5 0 a n d R258 in t h e shifted B o x - C o x M o d e l w i t h t h e R e s t r i c t e d P o w e r P a r a m e t e r s " Dataset
R-value
Combined DATA
R248 R250 R258
bo - 1.576 ( - 17.14) d - 1.154 ( - 14.30) - 3.978 (-25.15)
b1
Lma bx
1.350 (32.44) 1'003 (32.12) 3"194 (33.51)
- 162.351
0.822
- 164"281
0.819
- 156.266
0.831
aATPi=bo+bl(Ri_0.65 )- 0.5 + e i for R248 = b o + b~(R i - 0 " 7 5 ) -0.5 + e i for R250. = b o + bl( 1 4 5 - R i } - 0.5 + g"i for R258 h L .... : M a x i m u m l i k e l i h o o d f u n c t i o n . ' R2: a d j u s t e d R - s q u a r e . J T h e n u m b e r s in p a r e n t h e s e s a r e t statistics.
R 2C
(2) (3) (3)
null hypothesis that R258 was superior to the other two R-values was not rejected strongly (p = 0.0361). Thus, there was a suggestion that R258 could be superior to R248 and R250 in predicting ATP.
DISCUSSION Estimation of mathematical functional forms Linearity tests for the mathematical functional forms obtained in this study for the relationships between ATP and each of three R-values (R248, R250 and R258) indicated the relationships were nonlinear. Both equations obtained by the general Box-Cox model without and with shift parameters (eqns (1) and (2), respectively) were satisfactory for the purpose of predicting ATP using R248, R250 or R258. Although having a lower R 2, the latter equation had a simpler mathematical functional form and would be more convenient in data analysis since least squares rather than nonlinear regression could be used. Our results for R250 confirmed the earlier work of Honikel & Fischer (1977) that the relationship between ATP and R250 was nonlinear. The curve of ATP versus R250 for beef muscle (Fig. 2(b), eqn (2)) was similar to the original curve of Honikel & Fischer (1977) for pork muscle. Khan & Frey (1971) reported a linear relationship (12 observations) between A T P and R258 in chicken muscle although their data indicated a
A TP and R-values in postmortem bovine longissimus dorsi muscle
261
nonlinear relationship between R258 versus percentage of total soluble phosphates. Davidek & Velisek (1973) calculated R248 values but did not report the type of the relationship between R248 and ATP. ATP estimation
Since the original work of Honikel & Fischer (1977), only a limited number of studies have been conducted on the mathematical functional relationship between R250 and ATP. Calkins et al. (1982) reported that for nonstimulated steer carcasses, R250 of 1-12 was equivalent to 1.0~mol ATP. Honikel et al. (1981) indicated that 1/~mol ATP was equivalent to 1"10 of R250 from the work of Honikel & Fischer (1977). Later, Honikel et al. (1983) showed that 1/~mol ATP was estimated by R250 of 1-075. In the work of Roncales et al. (1989), 1/~mol of ATP could be estimated to be equivalent to R250 of approximately 1.2 for lamb muscle. The variation in R250 values reported in the literature for the equivalency to 1/~mol ATP may be partially accounted for by the variation in the initial content of ATP in the prerigor state (2-5#mol by Honikel & Fischer, 1977; 2.52/~mol by Jolley et al., 1980-1; >3/~mol by Calkins et al., 1982; 4#mol by Honikel et al., 1983; 2-4/~mol by Koh et al., 1987; 4-6/~mol by Roncales et al., 1989). Initial ATP values may be influenced by storage conditions of the samples prior to ATP measurement. Factors such as the length of time and storage conditions under liquid nitrogen, the sampling time p o s t m o r t e m , incorporation of iodoacetate, or a combination of these and other factors could affect initial ATP values. In the present study, R250 of 0-967 would be equivalent to 1.0/~mol ATP. It would be more reliable to determine changes in R-values over the course of time p o s t m o r t e m rather than determining a single R-value to predict ATP. The standard errors in predicted ATP values by R-values are large, and there has been considerable variation in reported R250 values that were equivalent to 1 #mol ATP/g muscle. Evaluation of R-values
There was a trend for R258 to be superior to R248 and R250 in the predictability of ATP, but the scatter plots of all three R-values had similar patterns when an inverse form of R258 was compared with R248 and R250. The R248 and R250 were similar to each other. Since the peaks of IMP (at 250 nm) and of mixtures of IMP, inosine and hypoxanthine (at 248 nm) in muscle extracts overlap, the changes in absorbances at 248 nm and 250 nm should be similar.
262
K. C. Koh, T. D. Bidner, K. W. McMillin, M. B. Kim
Summary Our results indicated a nonlinear relationship between A T P and R-values. There were no significant differences for the prediction of A T P by the three R-values, but there was a suggestion that R258 was the preferred R-value. Since an R-value is a dynamic measure of the ratio in postmortem muscle of the amounts of adenine nucleotides (ATP, ADP, A M P ) and of I M P and/or its degradation derivatives such as inosine and hypoxanthine, the R-value should indicate the status of energy charge in postmortem muscle better than a single measure of A T P content.
REFERENCES Bate-Smith, E. C. & Bendall, J. R. (1947). J. Physiol., 106, 177. Bendall, J. R. (1951). J. Physiol., 114, 71. Bendall, J. R. (1973). In The Structure and Function of Muscle, 2nd edn, ed. G. H. Bourne. Academic Press, New York, p. 244. Bendall, J. R. & Davey, C. L. (1957). Biochim. Biophys. Acta, 26, 93. Bernthal, P. H., Booren, A. M. & Gray, J. I. (1989). Meat Sci., 25, 143. Box, G. E. P. & Cox, D. R. (1964). J. R. Star. Soc. Ser. B, 26, 211. Calkins, C. R., Branecky, L. J., Dutson, T. R., Smith, G. C. & Carpenter, Z. L. (1983). J. Food Sci., 48, 23. Calkins, C. R., Dutson, T. R., Smith, G. C. & Carpenter, Z. L. (1982). J. FoodSci., 47, 1350. Coon, F. P., Calkins, C. R. & Mandigo, R. W. (1983). J. Food Sci., 48, 1731. Dannert, R. D. & Pearson, A. M. (1967). J. Food Sci., 32, 49. Davidek, J. & Velisek, J. (1973). Fleischwirtschqft, 9, 1285. Davidson, R. & MacKinnon, J. G. (1981). Econometrica, 49, 781. De Fremery, D. & Pool, M. F. (1960). Food Res., 25, 73. Fischer, C. & Hamm, R. (1980). Meat Sci., 4, 41. Greaser, M. L. (1976). Proc. Recip. Meat Conf., 29, 395. Hogg, R. V. & Craig, A. T. (1978). Introduction to Mathematical Statistics, 4th edn. Macmillan Publishing Co., New York, p. 258. Honikel, K. O. & Fischer, C. (1977). J. Food Sci., 42, 1633. Honikel, K. O. & Hamm, R. (1978). Meat Sci., 2, 181. Honikel, K. O., Fischer, C., Hamid, A. & Hamm, R. (1981). J. Food Sci., 46, 1. Honikel, K. O., Roncales, P. & Hamm, R. (1983). Meat Sci., 8, 221. Jolley, P. D., Honikel, K. O. & Hamm, R. (1980 81). Meat Sci., 5, 99. Khan, A. W. & Frey, A. R. (1971). Can. Inst. Food Tech. J., 4, 139. Koh, K. C., Bidner, T. D., McMillin, K. W. & Hill, G. M. (1987). Meat Sci., 21, 189. Lamprecht, W. & Trautschold, I. (1974). In Methods of Enzymatic Analysis, 2nd edn, ed. H. U. Bergmeyer. Academic Press, New York, p. 2101. Lyon, C. E., Davis, C. E., Dickens, J. A. & Papa, C. M. (1989). Poultry Sci., 68, 249. Marsh, B. B. (1981). Proc. Recip. Meat Conf., 34, 75. McGinnis, J. P., Fletcher, D. L., Papa, C. M. & Buhr, R. J. (1989). Poultry Sei., 68, 386.
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Newbold, R. P. & Scopes, R. K. (1967). Biochem. J., 105, 127. Papa, C. M. & Fletcher, D. L. (1988). Poultry Sci., 67, 635. Papa, C. M., Lyon, C. E. & Fletcher, D. L. (1989). Poultry Sci., 68, 238. Ramsey, J. B. (1974). In Frontiers in Econometrics, ed. P. Zarembka. Academic Press, New York, p. 13. Roncales, P., Beltran, J. A., Jaime, I. & Lopez-Lorenzo, P. (1989). J. Food Sci., 54, 1365. Sams, A. R., Janky, D. M. & Woodward, S. A. (1988). Poultry Sci., 67 (Suppl. 1), 150. White, K. J. (1984). SHAZAM. An Econometrics Computer Program (Version 4.6). University of British Columbia, Vancouver, BC.