Proteins and Amino Acids
use of a Four-Parameter Logistic Equation to Evaluate the Response of Growing Rats to Ten Levels of Each Indispensable Amino Acid1»2 MARK J. GAHL,* MARK D. FINKE,3 THOMAS D. CRENSHAW* AND N. J. BENEVENGA*' Departments of *Meat and Animal Science and ^Nutritional Sciences, University of Wisconsin, Madison, WI 53706 is attained. A continuous decline in the response per unit of intake, as the intake approaches the re quirement for maximum gain, has been referred to as diminishing returns (3, 4). The slope-ratio assay (5, 6), a linear method, does not take the diminishing returns response into consideration when evaluating protein quality. Doubling the intake of a protein with a value of 50% (relative nutritive value) compared with the control protein will not necessarily result in an equivalent performance because the diminishing returns response to each protein may be different. This difference in response may be due to variation in the efficiency of use of different first limiting amino acids (LAA)4or to variation in efficiency of use of different amounts of the LAA (7). Finke et al. (8-10) evaluated the use of a logistic equation to estimate protein quality by describing the entire dose response range (zero intake to ma-rimnm gain) of animals, which included diminishing returns. By evaluating protein quality with nonlinear methodology, the rel ative value of proteins can be compared at any per-
ABSTRACT Over a 21-d period, 400 [four rats/level, 10 levels/a mino acid, 10 indispensable amino acids (IAA)] male weanling rats (65.9 ±0.3 g; mean ±SEM) were fed diets with one of 10 levels of each of the 10 IAA. In addition, four rats were fed an amino acid-free diet and 16 rats were killed on d 0 for individual body composition. With the exception of the limiting amino acid (LAA), an increment (35% of the requirement) of each IAA was added to the mixture to insure that the LAA remained first limiting. A four-parameter logistic equation was used to describe the nitrogen and weight gain responses of rats to each IAA. Conservation of nitrogen, defined as a predicted ¿/-intercept value greater than the value observed for rats fed an amino acid-free diet (-0.304 + 0.023 g N/21 d), was seen when diets devoid of total aromatic amino acids or lysine (-0.062 ± 0.013 g N/21 d) or histidine, leucine, tryptophan or valine (-0.115 ±0.011 g N/21 d) were fed. When total sulfur amino acids were first limiting, diminishing returns (a decrease in the first derivative) was evident from zero intake to Rmtx (estimated asymptotic response maxi mum). In contrast, when other IAA were limiting, diminishing returns were apparent after approximately the first third of the full response. Based on the first derivative of the response curves, the efficiency of ni trogen gain depends on the LAA.The dietary LAAwould be expected to influence the shape of the response curve and therefore influence the quantitative aspects of diminishing returns. J. Nutr. 121: 1720-1729, 1991. INDEXING KEY WORDS:
'Supported
•Indispensable amino adds •logistic equation •parameter sharing •diminishing returns •rats
$3.00 ©1991 American
Institute
of Nutrition.
and Life Sciences,
Society of Animal Science, Lexington, KY, August 1989. [Gahl, M. I-, Finke, M. D., Benevenga, N. J. &. Crenshaw, T. D. (1989) Use of a four parameter logistic model (LM) to evaluate the response of growing rats to ten levels of each indispensable amino acid (IAA). J. Anim. Sci. 67(Suppl. 1): 240). 'Current address: ALPO Pet Foods, Inc., P.O. Box 2187, Rt. 309 & Pope Road, Allentown, PA 18001. 'Abbreviations used: IAA, indispensable amino acid; LAA, lim iting amino acid; R^^ estimated asymptotic response ma-gim^m. K^, Michaelis-Menton constant; S-TDH, serine-threonine dehydratase; TAA, total aromatic amino acids; TSA, total sulfur amino acids.
The growth response of rats to graded levels of amino acids is described better by a curvilinear analysis than by a break-point analysis (1, 2). There fore, the instantaneous efficiency [di/dl, derivative of the response (r) with respect to intake (/)] of amino acid utilization will approach zero as mayimiiTn gain 0022-3166/91
by the College of Agricultural
University of Wisconsin, Madison, WI 53706 and Purina Mills, St. Louis, MO. 'Presented in part at the 81st Annual Meeting of the American
Received 26 November
1720 Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
1990. Accepted
14 May 1991.
GROWTH RESPONSE TO EACH INDISPENSABLE AMINO ACID
formance level rather than comparisons being made at a fixed level of intake (7), as is the case when the protein efficiency ratio (11) is used. The efficiency of amino acid utilization for ni trogen deposition is dependent on the dietary level of the LAA fed (12, 13). Of the indispensable amino acids (IAA), the first LAA is expected to be used with the highest efficiency (14). Rats fed diets calculated to be limiting in threonine consistently gained more crude protein per day than did rats fed diets with an equal percentage of the National Research Council requirement for lysine, indicating a greater efficiency of threonine utilization for crude protein gain (15). The difference in efficiency is based on the as sumption that the requirement is known. Heger and Frydrych (2) compared the relative efficiencies of each IAA from zero intake to intake supporting a growth rate of 4.2 g/d. The maximum cumulative efficiency (0.65 to 0.85), which is a ratio of total amino acid retained to total amino acid consumed, was observed at intakes between 30 and 60% of the requirement for all of the IAA except for the total sulfur amino acids (TSA) and for histidine. The maximum efficiency ob served for TSA was 0.55 and that for histidine was >1.0 at low intakes. An efficiency for histidine >1.0 was ascribed to the nitrogen balance technique used (2). Because the amino acids are used with different efficiencies, the LAA in a protein would be expected to impact on the response of animals to graded levels of that protein. However, the design of the ex periment by Heger and Frydrych (2)was such that the IAA other than the LAA were fixed at 100% of the requirement for maximum growth (see inset in Fig. 1) and that the LAA was graded from 0 to 120% of the requirement. As a result of this design, another amino acid may have become first limiting or co-limiting as the concentration of the first limiting amino acid in the diet approached the requirement level. In addition to the concern that the first limiting amino acid remain first limiting, the effect of excess amino acids on the efficiency of utilization of the LAA should also be considered. The response of rats fed a diet first limiting in lysine was not significantly affected by a 25 or 50% excess of the other amino acids (16). However, excess amino acids significantly decreased body weight, dry matter, crude protein and lipid gain when rats were fed diets first limiting in threonine (17). These results suggest that rats differ in response to excess amino acids, depending upon which amino acid is first limiting. In an attempt to minimize the negative effect of excess amino acids and to assure that the first limiting amino acid re mains first limiting, a 35% excess of the other amino acids was selected in the current experiment. The present investigation was conducted to compare the efficiency of utilization of each IAA when limiting. A nonlinear equation was used to describe the entire dose-response relationship, and the calculated Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
200
1721
Graded LAA - fixed other AA
10
FIGURE 1 Amino acid (AA) formulation of diets fed to rats. The relationship of the level of the limiting amino acid (LAA)is shown relative to the level of the other amino acids provided by the amino acid mixture (see Table 1). The other amino acids were provided at 35% above the relative level of the LAA rather than simply incrementing the LAA with the other amino acids provided at a constant level ¡inset).
derivative of the response function was then used to compare the efficiency of use of each LAA from zero intake to levels of intake supporting maximum gain.
MATERIALS AND METHODS A 21-d growth trial was conducted with individ ually caged male weanling Sprague-Dawley (SpragueDawley, Madison, WI) rats in a room maintained at 24*C with a 12-h light:dark cycle. Rats had free access to food and water and were treated according to campus laboratory animal guidelines. Rats and indi vidual food cups were weighed on d 0, 4, 7, 11, 14, 18 and 21 for calculation of cumulative body weight change and cumulative food intake. Each diet was formulated to contain one of 10 levels of each of the 10 IAA. All purified diets contained (g/100 g) 1.0 vitamin mix (AIN-76); 3.5 mineral mix (AIN-76); 0.4 choline-Cl; 3.0 cellulose and 5.0 com oil (Archer Daniels Midland, Decatur, DL).All ingredients were from U.S. Biochemical (Cleveland, OH) unless stated otherwise. Amino acid requirements (18) for gain
1722
GAHL ET AL.
(Table 1) were used in the formulation of the diets. The concentrations of dispensable amino acids con sidered to be 100% of the "requirement" for the rats used in these studies are also Usted in Table 1. When an IAA was made the first LAA, it was omitted from the amino acid mix and incorporated into the diets at levels to provide 0, 15, 30, 45, 60, 75, 90, 105, 125 or 150% of the requirement, with the amino acid mix being scaled to provide 35, 50, 65, 80, 95, 110, 125, 140, 160 or 185% of their respective requirements (Fig. 1). A 4 to 1 ratio of com starch (Staley, Decatur, IL) and sucrose (Teklad Test Diets, Madison, WI) was added to bring each diet to 100%. Intake of the LAA (mmol/21 d) was calculated from the composition of the diet and total 21-d cumulative food intake. After adaptation to the environment and a purified diet, 420 rats (65.9 ±0.3 g; mean ±SEM)were divided into 105 groups of four rats each. Four randomly assigned groups (n - 16) were killed to determine initial body composition. One group was fed an amino acid-free diet as a control. The remaining 100 groups were fed one of the 100 diets. Rats were killed by chloroform inhalation, gastro intestinal contents were removed and the entire empty body was frozen and then chopped into six to eight pieces. The chopped empty body was dried by lyophilization and ground in liquid nitrogen using a Waring blender. Duplicate subsamples were used for nitrogen determination following a 100-min digestion in a hydrogen peroxide-sulfuric acid solution at 375"C. Nitrogen was determined using a phenolhypochlorite colorimetrie determination of ammonia (19). Recovery of nitrogen from the digestion of a tyrosine standard using this procedure ranged from 94 to 104%. Changes in body nitrogen were determined by the comparative slaughter technique. The predicted body nitrogen on d 0 for each rat was estimated using a linear regression equation relating live weight on d 0 to the amount of nitrogen determined in the four groups [n = 16) of rats killed on d 0. The change in body nitrogen was determined as the difference be tween analyzed nitrogen on d 21 and estimated body nitrogen on d 0. Weight gain and nitrogen gain were described by a four-parameter logistic equation. This equation was chosen because of its ability to provide the best fit (based on the pattern of residuals and the lowest residual sum of squares) to a wide variety of doseresponse curves (20, 21). The logistic equation used previously (8) was modified (Steve C. Denham, Center for Veterinary Medicine, Food and Drug Administra tion, Rockville, MD, personal communication,- see also réf.10) to provide a more correct mathematical expression. The modification involved the intake var iable, /, which had units (mmol of LAA intake) in the exponent and gave the variable, d, units [exp (1/mmol of amino acid intake)] so that if was unitless. The term d1must be unitless if r is to have the appropriate Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
TABLE
1
Composition of the amino acid miliare at levels considered be 100% of the National Research Council requirement (réf.18) for maximum gain' Amino acid
to
Amount g/100 g
Indispensable Arginine Histidine Isoleucine Leucine Lysine2 Methionine Cystine Phenylalamne Tyrosine Threonine Tryptophan Valine Dispensable
0.60 0.30 0.50 0.75 0.70 0.40 0.20 0.53 0.27 0.50 0.15 0.60
Alanine
0.40 0.40 4.00 0.60 0.40 0.40 0.40
Aspartic acid Glutamic acid Glycine Proline Serine Asparagine
'Diets were formulated to contain one of the 10 levels selected for each of the separate indispensable amino acids studied. 2Lysine was added as the monohydrochloride salt. All other amino acids were supplemented in the free form.
units [Rna and b have units analogous to r and c is unitless). To simplify d1,the following transformation was made: where d1- e$h d', let -k - In d, and then d1 - e~tÃ-. Thus, k has reciprocal units of I, so the units cancel to simplify the expression. The resulting equation is: r -
+ c) - RaJ l + c-e-
The parameters are defined as follows: The r variable (dependent variable) is the response (nitrogen or weight gain, g/21 d). The variable I (predictor variable) is the intake of the LAA, expressed as mmol/21 d or as relative mmol/21 d (Rmmol/21 d). Rmmol is the ratio of mmol of LAA intake to the mmol of LAA required to achieve 95% R^^. The parameter !?„,„ is the asymptotic maximum gain (g/21 d). The variable b represents the y-intercept (g/21 d), which is the response to zero intake of the LAA. The parameter k is a scaling parameter that scales I. The parameter c is a shaping parameter that locates the inflection point. The transformation of the logistic equation described above does not change the results reported by Finke et al. (8-10). The d oik parameter estimates
GROWTH
RESPONSE TO EACH INDISPENSABLE
AMINO ACID
1723
TABLE 2 Parameter
estimates
(logistic equation) for nitrogen
gain (g/21 d) vs. Snnaol intake/21
d1
Parameter1 LAA ArgHisHeLeuLysTSA3TAA"ThrTrpVal0.635 0.065-0.115 ± 0.011-0.308 ± 0.013-0.115 ± 0.011-0.062 ± 0.013-0.308 ± 0.013-0.062 ± 0.013-0.308 ± 0.013-0.115 ± 0.011-0.115 ± ±0.0112.03
0.233.30 ± 0.362.03 ± 0.232.03 ± 0.233.30 ± 0.361.08 ± 0.192.03 ± 0.233.30 ± 0.363.30 ± 0.362.03 ± ±0.230.446
0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± ±0.0253.910
0.0633.910 ± 0.0634.257 ± 0.0754.257 ± 0.0754.257 ± 0.0754.257 ± 0.0754.257 ± 0.0754.257 ±
0.0754.257 ± 0.0754.257 ± ±0.075 'See text for definition of parameters in the logistic equation. Parameter estimates are based on 10 groups of four rats fed one of the 10 levels for each amino acid. The nitrogen gain response of four rats fed an amino acid-free diet was -0.304 ±0.023 g/21 a, which corresponds to the h parameter estimate. Rmmol intake/21 d was multiplied by 10 as discussed in the text. Rmmol is the mmol of limiting amino acid (LAA) intake divided by the mmol of LAA required for 95% of Rnal (asymptotic response maximum). 2£stimate±asymptotic SE. 'Total sulfur amino acids. "Total aromatic amino acids.
can be interconverted using -k - In d. One problem is that the SE are not so easily transformed. To obtain the SE for k, the previous data can be re-analyzed using the new equation. The new fit will give the k parameter estimates and the associated SE;the other three parameter estimates and the corresponding SE will remain essentially unchanged. The dose-response relationships (weight gain or ni trogen gain vs. mmol of LAA intake/21 d) were fit simultaneously with and without parameter sharing to detect differences due to LAA (8). The data were analyzed utilizing the nonlinear least squares pro cedure with the Marquardt option (22). The effect of the constraints on the fit was tested using the extra sum of squares principle and examination of residuals (23). Weighted regression (inverse of the variance) was used to control heteroscedasticity. A f statistic was calculated for each pair of parameter estimates (each pair of b estimates or each pair of c estimates, etc.). The pair of parameter estimates with the least signif icant t statistic was forced to share a common value, which was estimated in the following fit. This pro cedure was repeated until the extra sum of squares test was significant. The previous fit was then con sidered the final set of parameter estimates. The final set of parameter estimates was used to predict the requirement (mmol of LAA/21 d required to support 95% of £„«) for each IAA (24). The Rmmol was calculated for each rat. The curves were fit again using weight gain or nitrogen gain vs. Rmmol. The purpose of the second fit was to scale the amino acids so comparisons could be made, taking into consider ation relative differences in the magnitude of each IAA requirement. Rmmol was multiplied by 10 to Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
facilitate convergence. However, Rmmol has been multiplied by 100 to express intake as a percentage of the predicted requirement in the figures. RESULTS The parameter estimates determined by fitting the logistic equation to nitrogen gain (g/21 d) or weight gain (g/21 d) data are shown in Tables 2 and 3. Based on these results the amino acids can be divided into four groups in regard to the predicted responses at zero intake of the LAA (b parameter). The shared b parameter estimates were compared with the average response of rats fed the respective 0% LAA diet (Diet 1, Fig. 2). Although differences appear between the predicted and observed values (threonine, tryptophan, valine), the predicted value was estimated utilizing the entire data set, whereas the observed value is based on four rats. Therefore, the error terms may not be directly comparable and the differences may not be real. In order to obtain the best estimate of the b parameter, as well as the other three parameters, data for all rats (with the exception of those fed the amino acid-free diet) were used. The data for rats fed the histidine-devoid diet (Diet 1)were not included due to an error in the diets offered this treatment group. Diet 1 was devoid of the LAA, and the other IAA were provided at 35% of the requirement. The food intakes of rats fed the arginine-devoid and lysine-devoid diets were different (P < 0.05) from the food intake of rats fed the amino acid-free diet. The nitrogen retentions of rats fed the diets devoid of isoleucine, TSA or threonine were similar to the nitrogen retention of
GAHL ET AL.
1724
0.8 i
b (y intercept) i Observed
0.6CN
en
0.4 -
'5c 0.2-
c CD OÃ0.0
-0.2
-
< p -o.-< Arg
His
Ile
Leu
Lys TSA TAA Thr
Deficient
Trp
Val -AA
IAA
FIGURE 2 Conservation of indispensable amino acids (IAA) when the diet was devoid of the limiting amino acid but provided 35% of the requirement for all other amino acids. Both the observed [mean ±SEM for rats fed Diet I (n 4), Fig. 1] and the predicted (b parameter from the logistic equation) responses are shown. Only the predicted response to a histidine-devoid diet is shown. The observed value was omitted because of apparent errors. The response of rats (n 4) to an amino acid-free diet is represented by -AA. TSA total sulfur amino acids; TAA - total aromatic amino acids.
rats fed the amino acid-free diet (Fig. 2). Conservation of endogenous amino acids was observed in rats fed diets devoid of histidine, leucine, tryptophan or valine, such that the predicted nitrogen loss was only 37% as much as in rats fed the amino acid-free diet. Conservation of endogenous amino acids was also observed in rats fed diets devoid of either lysine or total aromatic amino acids (TAA), such that the pre dicted nitrogen loss was only 20% as much as in rats fed the amino acid-free diet. The arginine-devoid diet supported a positive nitrogen gain (0.72 g/21 d). Similar patterns of conservation were observed with weight gain (data not shown). Using nitrogen gain as the dependent variable, all four parameters were shared (Table 2) when either leucine or valine was limiting, such that the responses for rats fed diets limiting in these two amino acids were identical. When weight gain was the dependent variable, the response curves for tryp tophan and valine were identical (Table 3). Other Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
curves were significantly different in at least one parameter estimate (P < 0.05). The effect of the c parameter estimate on the shape of the curve can be compared in Figure 3 for the curves in which TSA or threonine were limiting. When the R^^ k and b parameter estimates are shared, a smaller c parameter estimate results in a curve with a greater slope (8). By using Rmmol amino acid intake as the predictor variable, the data were scaled relative to 100% of the predicted requirement, and therefore, the k parameter estimate was shared for all 10 dose response relation ships (Tables 2 and 3). To evaluate the Himini »hingreturns response, the first derivative of the logistic equation was calculated using the parameter estimates for each amino acid (Fig. 4). Plotting the derivative of each curve illus trates that instantaneous efficiency asymptotically approaches zero. In other words, the efficiency of amino acid utilization for nitrogen gain when adding an additional increment of the LAA to the diet near gain approaches zero. The instantaneous efficiency was the greatest at 20 to 30% of the pre dicted requirement (Rmmol) for nitrogen gain. An exception to this pattern was observed for TSA. Maximum efficiency of TSA occurred near zero intake and declined thereafter, indicating a large diminishing returns response. For the other LAA, diminishing returns responses began at apparently less than half the requirement for maximum nitrogen gain. At intake levels >50% of the requirement for maximum nitrogen gain, threonine was utilized with the highest numerical instantaneous efficiency, as re ported earlier (15). The requirement for each IAA was predicted again using the parameter estimates for nitrogen gain or weight gain relative to the respective Rmmol. The requirement for maximum gain was defined (24) as the intake predicted to support 95% of JR^, (95% of the asymptotic plateau). The requirement was ex pressed as the millimoles of amino acid required for maximum nitrogen gain or weight gain in 21 d for a rat with an initial weight of 65 g (Table 4). Compared with National Research Council requirements, the amino acid requirements of the rats used in this experiment were overestimated to the largest degree for the TSA, whereas the requirement for arginine was underestimated to the largest degree. To express the requirements as a percentage of the diet, food intake was estimated at the predicted re quirement using a polynomial equation. Food intake increased to a maximum and then declined. The maximum food intake occurred at a LAA level less than the requirement for maximum gain. The poly nomial equation (footnote 1, Table 4) allowed the flexibility to fit a response curve of this shape where an asymptotic equation such as the logistic equation would not fit the observed responses.
GROWTH
RESPONSE TO EACH INDISPENSABLE
AMINO ACID
1725
TABLE 3 Parameter estimates (logistic equation) for weight gain (g/21 d) vs. Rmmol intake/21 d' Parameter2 LAA Arg HisHeLeuLys
TSA3TAA4ThrTrp
Val20.54
±0.95 0.41-20.41 -14.54 ± 0.54-14.54 ± 0.42-11.76 ± ±0.59 -20.41 ± 0.54-11.76 0.59-20.41 ± 0.54-14.54 ± ±0.42 -14.54 ±0.421.95
±0.24 2.67 0.331.95 ± 0.241.57 ± 0.201.95 ± ±0.24 0.74 0.151.57 ± 0.202.67 ± 0.331.95 ± ±0.24 1.95 ±0.240.414
±0.022 0.414 0.0220.414 ± 0.0220.414 ± 0.0220.414 ± ±0.022 0.414 ± 0.0220.414 0.0220.414 ± 0.0220.414 ± ±0.022 0.414 ±0.022113.0
±1.6 1.6125.1 113.0 ± ±1.9125.1 1.9125.1 ± ±1.9 125.1 ± 1.9125.1 1.9125.1 ± 1.9125.1 ± ±1.9 125.1 ±1.9
'See text for definition of parameters in the logistic equation. Parameter estimates are based on 10 groups of four rats fed one of the 10 levels for each amino acid. The weight gain response of four rats fed an amino acid-free diet was -20.25 ±2.87 g/21 d, which corresponds to the b parameter estimate. Rmmol intake/21 d was multiplied by 10 as discussed in the text. Rmmol is the mmol of limiting amino acid (LAA) intake divided by the mmol of LAA required for 95% of £„,„ (asymptotic response Estimate ±asymptotic SE. 3Total sulfur amino acids. "Total aromatic amino acids.
DISCUSSION The requirements for 95% of RM in Table 4 reflect the increased requirement of the IAA for nitrogen gain as compared with weight gain. Nitrogen gain would be the response variable of choice because it reflects directly the response of the rat to the LAA. Weight gain may be influenced by changes in body composition (e.g., increased lipid gain rather than en hanced protein synthesis). However, weight gain offers an alternative to nitrogen gain, yet is less ac curate for evaluating protein quality. There is less work and expense involved in measuring weight gain; at the same time the diminishing returns response can be described, which offers the advantage of com paring relative protein quality at equal performance levels rather than at equal intakes. As shown in Tables 2 and 3, £„,« was not shared when the results for arginine and histidine were com pared with the other eight IAA. The parameter R^ would be expected to be shared over all LAA. Finke et al. (8-10) observed that Rma[was shared for the weight gain or nitrogen gain of rats fed several protein mix tures that differed in protein quality. The response with arginine and histidine was unexpected and no explanation is offered for the 10% lower !?„,„ esti mate. The response of rats to graded levels of a LAA was curvilinear, especially at responses near ma^in-nim. These responses are consistent with findings of Heger and Frydrych (2) and Yoshida and Ashida (1). The efficiency of amino acid utilization is possibly related to the oxidation rate of the LAA. If so, the oxidation rate would be expected to increase curvilinearly with Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
incremental increases of dietary amino acids. Curvi linear analysis is not typically utilized with amino acid oxidation experiments. A break-point analysis of responses was reported for lysine (25), histidine (26), tryptophan (27), threonine (28) and leucine (29). Oxi dation of the LAA remained low (5 to 10%) at levels of intake less than the requirement for maximum growth, but at levels above the requirement, oxi dation tended to be proportional to the concentration in the diet. Although the break-point analysis of the previous experiments seems appropriate for the ob served responses, the diets were formulated such that the LAA was fed at graded levels from below to above levels required to support maximum gain, whereas the levels of the other amino acids were constant. A concern with this approach is that as the apparent maximum gain is approached, the supposedly LAA actually becomes co-limiting or another amino acid becomes first limiting. A different LAA would be expected to impact on the response relationship of the animal and perhaps create a break-point response, rather than the curvilinear response expected from incremental levels of a LAA that remains clearly first limiting. Rats fed a diet devoid of any one of the IAA would be expected to respond the same as rats fed an amino acid-free diet. Conservation of the IAA is not ex pected because the chemical score of the diet is zero and the net protein utilization is expected to be zero (30). Only rats fed diets devoid of isoleucine, TSA or threonine elicited the expected response. Rats fed amino acid mixtures devoid of histidine, leucine, TAA, tryptophan or valine lost about two-thirds as much weight as rats fed the amino acid-free diet,
GAHL ET AL.
1726
-0.4 O
T
1
1
20
40
60
1
1
1
80 100120140
1
T
20
1
1
40
60
Intake,
1
1
1
T
80 100 120140
i
1
1
20
40
60
1
1
1
80 100120
r 140
Rmmol
FIGURE 3 Nitrogen gain response curves generated using the parameter estimates for the logistic equation for rats fed diets limiting in one indispensable amino acid: lysine, TSA (total sulfur amino acids), threonine or tryptophan; isoleucine, leucine or valine,- arginine, histidine or TAA (total aromatic amino acids). The mean ±SEMfor each group of four rats was plotted for each dietary amino acid level. Rmmol as presented on the graph was calculated as the mmole of limiting amino acid (LAA) divided by the mmole of LAA required for 95% of RmaLtimes 100. The intercept values (b parameter) are shown in detail in Figure 2. The response curves for leucine and valine were not different as a result of sharing all four parameters of the logistic equation. R^^ (asymptotic response maximum) was shared for the arginine and histidine curves, whereas the RO^ for the TAA curve was shared with the data sets for the other seven amino acids.
whereas rats fed a lysine-devoid amino acid mixture lost only one-third as much weight (31-33). The current results (Fig. 2) show similar observations except that the TAA seemed to be conserved to the same degree as lysine. Because arginine is condi tionally indispensable at low levels of growth, rats gained weight. The positive gain of rats fed an arginine-devoid amino acid mixture is consistent with observations of Mercer et al. (34). The maximum efficiency observed by Heger and Frydrych (2) was in rats fed diets providing 30 to 60% of the requirement of the LAA. This range for maximum efficiency was similar to that observed by Bunce and King (12, 13). Maximum instantaneous efficiency (slope of the response curve) was observed at 20 to 30% of the predicted requirement (Rmmol) for nitrogen gain (current results). At
use of a Four-Parameter Logistic Equation to Evaluate the Response of Growing Rats to Ten Levels of Each Indispensable Amino Acid1»2 MARK J. GAHL,* MARK D. FINKE,3 THOMAS D. CRENSHAW* AND N. J. BENEVENGA*' Departments of *Meat and Animal Science and ^Nutritional Sciences, University of Wisconsin, Madison, WI 53706 is attained. A continuous decline in the response per unit of intake, as the intake approaches the re quirement for maximum gain, has been referred to as diminishing returns (3, 4). The slope-ratio assay (5, 6), a linear method, does not take the diminishing returns response into consideration when evaluating protein quality. Doubling the intake of a protein with a value of 50% (relative nutritive value) compared with the control protein will not necessarily result in an equivalent performance because the diminishing returns response to each protein may be different. This difference in response may be due to variation in the efficiency of use of different first limiting amino acids (LAA)4or to variation in efficiency of use of different amounts of the LAA (7). Finke et al. (8-10) evaluated the use of a logistic equation to estimate protein quality by describing the entire dose response range (zero intake to ma-rimnm gain) of animals, which included diminishing returns. By evaluating protein quality with nonlinear methodology, the rel ative value of proteins can be compared at any per-
ABSTRACT Over a 21-d period, 400 [four rats/level, 10 levels/a mino acid, 10 indispensable amino acids (IAA)] male weanling rats (65.9 ±0.3 g; mean ±SEM) were fed diets with one of 10 levels of each of the 10 IAA. In addition, four rats were fed an amino acid-free diet and 16 rats were killed on d 0 for individual body composition. With the exception of the limiting amino acid (LAA), an increment (35% of the requirement) of each IAA was added to the mixture to insure that the LAA remained first limiting. A four-parameter logistic equation was used to describe the nitrogen and weight gain responses of rats to each IAA. Conservation of nitrogen, defined as a predicted ¿/-intercept value greater than the value observed for rats fed an amino acid-free diet (-0.304 + 0.023 g N/21 d), was seen when diets devoid of total aromatic amino acids or lysine (-0.062 ± 0.013 g N/21 d) or histidine, leucine, tryptophan or valine (-0.115 ±0.011 g N/21 d) were fed. When total sulfur amino acids were first limiting, diminishing returns (a decrease in the first derivative) was evident from zero intake to Rmtx (estimated asymptotic response maxi mum). In contrast, when other IAA were limiting, diminishing returns were apparent after approximately the first third of the full response. Based on the first derivative of the response curves, the efficiency of ni trogen gain depends on the LAA.The dietary LAAwould be expected to influence the shape of the response curve and therefore influence the quantitative aspects of diminishing returns. J. Nutr. 121: 1720-1729, 1991. INDEXING KEY WORDS:
'Supported
•Indispensable amino adds •logistic equation •parameter sharing •diminishing returns •rats
$3.00 ©1991 American
Institute
of Nutrition.
and Life Sciences,
Society of Animal Science, Lexington, KY, August 1989. [Gahl, M. I-, Finke, M. D., Benevenga, N. J. &. Crenshaw, T. D. (1989) Use of a four parameter logistic model (LM) to evaluate the response of growing rats to ten levels of each indispensable amino acid (IAA). J. Anim. Sci. 67(Suppl. 1): 240). 'Current address: ALPO Pet Foods, Inc., P.O. Box 2187, Rt. 309 & Pope Road, Allentown, PA 18001. 'Abbreviations used: IAA, indispensable amino acid; LAA, lim iting amino acid; R^^ estimated asymptotic response ma-gim^m. K^, Michaelis-Menton constant; S-TDH, serine-threonine dehydratase; TAA, total aromatic amino acids; TSA, total sulfur amino acids.
The growth response of rats to graded levels of amino acids is described better by a curvilinear analysis than by a break-point analysis (1, 2). There fore, the instantaneous efficiency [di/dl, derivative of the response (r) with respect to intake (/)] of amino acid utilization will approach zero as mayimiiTn gain 0022-3166/91
by the College of Agricultural
University of Wisconsin, Madison, WI 53706 and Purina Mills, St. Louis, MO. 'Presented in part at the 81st Annual Meeting of the American
Received 26 November
1720 Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
1990. Accepted
14 May 1991.
GROWTH RESPONSE TO EACH INDISPENSABLE AMINO ACID
formance level rather than comparisons being made at a fixed level of intake (7), as is the case when the protein efficiency ratio (11) is used. The efficiency of amino acid utilization for ni trogen deposition is dependent on the dietary level of the LAA fed (12, 13). Of the indispensable amino acids (IAA), the first LAA is expected to be used with the highest efficiency (14). Rats fed diets calculated to be limiting in threonine consistently gained more crude protein per day than did rats fed diets with an equal percentage of the National Research Council requirement for lysine, indicating a greater efficiency of threonine utilization for crude protein gain (15). The difference in efficiency is based on the as sumption that the requirement is known. Heger and Frydrych (2) compared the relative efficiencies of each IAA from zero intake to intake supporting a growth rate of 4.2 g/d. The maximum cumulative efficiency (0.65 to 0.85), which is a ratio of total amino acid retained to total amino acid consumed, was observed at intakes between 30 and 60% of the requirement for all of the IAA except for the total sulfur amino acids (TSA) and for histidine. The maximum efficiency ob served for TSA was 0.55 and that for histidine was >1.0 at low intakes. An efficiency for histidine >1.0 was ascribed to the nitrogen balance technique used (2). Because the amino acids are used with different efficiencies, the LAA in a protein would be expected to impact on the response of animals to graded levels of that protein. However, the design of the ex periment by Heger and Frydrych (2)was such that the IAA other than the LAA were fixed at 100% of the requirement for maximum growth (see inset in Fig. 1) and that the LAA was graded from 0 to 120% of the requirement. As a result of this design, another amino acid may have become first limiting or co-limiting as the concentration of the first limiting amino acid in the diet approached the requirement level. In addition to the concern that the first limiting amino acid remain first limiting, the effect of excess amino acids on the efficiency of utilization of the LAA should also be considered. The response of rats fed a diet first limiting in lysine was not significantly affected by a 25 or 50% excess of the other amino acids (16). However, excess amino acids significantly decreased body weight, dry matter, crude protein and lipid gain when rats were fed diets first limiting in threonine (17). These results suggest that rats differ in response to excess amino acids, depending upon which amino acid is first limiting. In an attempt to minimize the negative effect of excess amino acids and to assure that the first limiting amino acid re mains first limiting, a 35% excess of the other amino acids was selected in the current experiment. The present investigation was conducted to compare the efficiency of utilization of each IAA when limiting. A nonlinear equation was used to describe the entire dose-response relationship, and the calculated Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
200
1721
Graded LAA - fixed other AA
10
FIGURE 1 Amino acid (AA) formulation of diets fed to rats. The relationship of the level of the limiting amino acid (LAA)is shown relative to the level of the other amino acids provided by the amino acid mixture (see Table 1). The other amino acids were provided at 35% above the relative level of the LAA rather than simply incrementing the LAA with the other amino acids provided at a constant level ¡inset).
derivative of the response function was then used to compare the efficiency of use of each LAA from zero intake to levels of intake supporting maximum gain.
MATERIALS AND METHODS A 21-d growth trial was conducted with individ ually caged male weanling Sprague-Dawley (SpragueDawley, Madison, WI) rats in a room maintained at 24*C with a 12-h light:dark cycle. Rats had free access to food and water and were treated according to campus laboratory animal guidelines. Rats and indi vidual food cups were weighed on d 0, 4, 7, 11, 14, 18 and 21 for calculation of cumulative body weight change and cumulative food intake. Each diet was formulated to contain one of 10 levels of each of the 10 IAA. All purified diets contained (g/100 g) 1.0 vitamin mix (AIN-76); 3.5 mineral mix (AIN-76); 0.4 choline-Cl; 3.0 cellulose and 5.0 com oil (Archer Daniels Midland, Decatur, DL).All ingredients were from U.S. Biochemical (Cleveland, OH) unless stated otherwise. Amino acid requirements (18) for gain
1722
GAHL ET AL.
(Table 1) were used in the formulation of the diets. The concentrations of dispensable amino acids con sidered to be 100% of the "requirement" for the rats used in these studies are also Usted in Table 1. When an IAA was made the first LAA, it was omitted from the amino acid mix and incorporated into the diets at levels to provide 0, 15, 30, 45, 60, 75, 90, 105, 125 or 150% of the requirement, with the amino acid mix being scaled to provide 35, 50, 65, 80, 95, 110, 125, 140, 160 or 185% of their respective requirements (Fig. 1). A 4 to 1 ratio of com starch (Staley, Decatur, IL) and sucrose (Teklad Test Diets, Madison, WI) was added to bring each diet to 100%. Intake of the LAA (mmol/21 d) was calculated from the composition of the diet and total 21-d cumulative food intake. After adaptation to the environment and a purified diet, 420 rats (65.9 ±0.3 g; mean ±SEM)were divided into 105 groups of four rats each. Four randomly assigned groups (n - 16) were killed to determine initial body composition. One group was fed an amino acid-free diet as a control. The remaining 100 groups were fed one of the 100 diets. Rats were killed by chloroform inhalation, gastro intestinal contents were removed and the entire empty body was frozen and then chopped into six to eight pieces. The chopped empty body was dried by lyophilization and ground in liquid nitrogen using a Waring blender. Duplicate subsamples were used for nitrogen determination following a 100-min digestion in a hydrogen peroxide-sulfuric acid solution at 375"C. Nitrogen was determined using a phenolhypochlorite colorimetrie determination of ammonia (19). Recovery of nitrogen from the digestion of a tyrosine standard using this procedure ranged from 94 to 104%. Changes in body nitrogen were determined by the comparative slaughter technique. The predicted body nitrogen on d 0 for each rat was estimated using a linear regression equation relating live weight on d 0 to the amount of nitrogen determined in the four groups [n = 16) of rats killed on d 0. The change in body nitrogen was determined as the difference be tween analyzed nitrogen on d 21 and estimated body nitrogen on d 0. Weight gain and nitrogen gain were described by a four-parameter logistic equation. This equation was chosen because of its ability to provide the best fit (based on the pattern of residuals and the lowest residual sum of squares) to a wide variety of doseresponse curves (20, 21). The logistic equation used previously (8) was modified (Steve C. Denham, Center for Veterinary Medicine, Food and Drug Administra tion, Rockville, MD, personal communication,- see also réf.10) to provide a more correct mathematical expression. The modification involved the intake var iable, /, which had units (mmol of LAA intake) in the exponent and gave the variable, d, units [exp (1/mmol of amino acid intake)] so that if was unitless. The term d1must be unitless if r is to have the appropriate Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
TABLE
1
Composition of the amino acid miliare at levels considered be 100% of the National Research Council requirement (réf.18) for maximum gain' Amino acid
to
Amount g/100 g
Indispensable Arginine Histidine Isoleucine Leucine Lysine2 Methionine Cystine Phenylalamne Tyrosine Threonine Tryptophan Valine Dispensable
0.60 0.30 0.50 0.75 0.70 0.40 0.20 0.53 0.27 0.50 0.15 0.60
Alanine
0.40 0.40 4.00 0.60 0.40 0.40 0.40
Aspartic acid Glutamic acid Glycine Proline Serine Asparagine
'Diets were formulated to contain one of the 10 levels selected for each of the separate indispensable amino acids studied. 2Lysine was added as the monohydrochloride salt. All other amino acids were supplemented in the free form.
units [Rna and b have units analogous to r and c is unitless). To simplify d1,the following transformation was made: where d1- e$h d', let -k - In d, and then d1 - e~tÃ-. Thus, k has reciprocal units of I, so the units cancel to simplify the expression. The resulting equation is: r -
+ c) - RaJ l + c-e-
The parameters are defined as follows: The r variable (dependent variable) is the response (nitrogen or weight gain, g/21 d). The variable I (predictor variable) is the intake of the LAA, expressed as mmol/21 d or as relative mmol/21 d (Rmmol/21 d). Rmmol is the ratio of mmol of LAA intake to the mmol of LAA required to achieve 95% R^^. The parameter !?„,„ is the asymptotic maximum gain (g/21 d). The variable b represents the y-intercept (g/21 d), which is the response to zero intake of the LAA. The parameter k is a scaling parameter that scales I. The parameter c is a shaping parameter that locates the inflection point. The transformation of the logistic equation described above does not change the results reported by Finke et al. (8-10). The d oik parameter estimates
GROWTH
RESPONSE TO EACH INDISPENSABLE
AMINO ACID
1723
TABLE 2 Parameter
estimates
(logistic equation) for nitrogen
gain (g/21 d) vs. Snnaol intake/21
d1
Parameter1 LAA ArgHisHeLeuLysTSA3TAA"ThrTrpVal0.635 0.065-0.115 ± 0.011-0.308 ± 0.013-0.115 ± 0.011-0.062 ± 0.013-0.308 ± 0.013-0.062 ± 0.013-0.308 ± 0.013-0.115 ± 0.011-0.115 ± ±0.0112.03
0.233.30 ± 0.362.03 ± 0.232.03 ± 0.233.30 ± 0.361.08 ± 0.192.03 ± 0.233.30 ± 0.363.30 ± 0.362.03 ± ±0.230.446
0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± 0.0250.446 ± ±0.0253.910
0.0633.910 ± 0.0634.257 ± 0.0754.257 ± 0.0754.257 ± 0.0754.257 ± 0.0754.257 ± 0.0754.257 ±
0.0754.257 ± 0.0754.257 ± ±0.075 'See text for definition of parameters in the logistic equation. Parameter estimates are based on 10 groups of four rats fed one of the 10 levels for each amino acid. The nitrogen gain response of four rats fed an amino acid-free diet was -0.304 ±0.023 g/21 a, which corresponds to the h parameter estimate. Rmmol intake/21 d was multiplied by 10 as discussed in the text. Rmmol is the mmol of limiting amino acid (LAA) intake divided by the mmol of LAA required for 95% of Rnal (asymptotic response maximum). 2£stimate±asymptotic SE. 'Total sulfur amino acids. "Total aromatic amino acids.
can be interconverted using -k - In d. One problem is that the SE are not so easily transformed. To obtain the SE for k, the previous data can be re-analyzed using the new equation. The new fit will give the k parameter estimates and the associated SE;the other three parameter estimates and the corresponding SE will remain essentially unchanged. The dose-response relationships (weight gain or ni trogen gain vs. mmol of LAA intake/21 d) were fit simultaneously with and without parameter sharing to detect differences due to LAA (8). The data were analyzed utilizing the nonlinear least squares pro cedure with the Marquardt option (22). The effect of the constraints on the fit was tested using the extra sum of squares principle and examination of residuals (23). Weighted regression (inverse of the variance) was used to control heteroscedasticity. A f statistic was calculated for each pair of parameter estimates (each pair of b estimates or each pair of c estimates, etc.). The pair of parameter estimates with the least signif icant t statistic was forced to share a common value, which was estimated in the following fit. This pro cedure was repeated until the extra sum of squares test was significant. The previous fit was then con sidered the final set of parameter estimates. The final set of parameter estimates was used to predict the requirement (mmol of LAA/21 d required to support 95% of £„«) for each IAA (24). The Rmmol was calculated for each rat. The curves were fit again using weight gain or nitrogen gain vs. Rmmol. The purpose of the second fit was to scale the amino acids so comparisons could be made, taking into consider ation relative differences in the magnitude of each IAA requirement. Rmmol was multiplied by 10 to Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
facilitate convergence. However, Rmmol has been multiplied by 100 to express intake as a percentage of the predicted requirement in the figures. RESULTS The parameter estimates determined by fitting the logistic equation to nitrogen gain (g/21 d) or weight gain (g/21 d) data are shown in Tables 2 and 3. Based on these results the amino acids can be divided into four groups in regard to the predicted responses at zero intake of the LAA (b parameter). The shared b parameter estimates were compared with the average response of rats fed the respective 0% LAA diet (Diet 1, Fig. 2). Although differences appear between the predicted and observed values (threonine, tryptophan, valine), the predicted value was estimated utilizing the entire data set, whereas the observed value is based on four rats. Therefore, the error terms may not be directly comparable and the differences may not be real. In order to obtain the best estimate of the b parameter, as well as the other three parameters, data for all rats (with the exception of those fed the amino acid-free diet) were used. The data for rats fed the histidine-devoid diet (Diet 1)were not included due to an error in the diets offered this treatment group. Diet 1 was devoid of the LAA, and the other IAA were provided at 35% of the requirement. The food intakes of rats fed the arginine-devoid and lysine-devoid diets were different (P < 0.05) from the food intake of rats fed the amino acid-free diet. The nitrogen retentions of rats fed the diets devoid of isoleucine, TSA or threonine were similar to the nitrogen retention of
GAHL ET AL.
1724
0.8 i
b (y intercept) i Observed
0.6CN
en
0.4 -
'5c 0.2-
c CD OÃ0.0
-0.2
-
< p -o.-< Arg
His
Ile
Leu
Lys TSA TAA Thr
Deficient
Trp
Val -AA
IAA
FIGURE 2 Conservation of indispensable amino acids (IAA) when the diet was devoid of the limiting amino acid but provided 35% of the requirement for all other amino acids. Both the observed [mean ±SEM for rats fed Diet I (n 4), Fig. 1] and the predicted (b parameter from the logistic equation) responses are shown. Only the predicted response to a histidine-devoid diet is shown. The observed value was omitted because of apparent errors. The response of rats (n 4) to an amino acid-free diet is represented by -AA. TSA total sulfur amino acids; TAA - total aromatic amino acids.
rats fed the amino acid-free diet (Fig. 2). Conservation of endogenous amino acids was observed in rats fed diets devoid of histidine, leucine, tryptophan or valine, such that the predicted nitrogen loss was only 37% as much as in rats fed the amino acid-free diet. Conservation of endogenous amino acids was also observed in rats fed diets devoid of either lysine or total aromatic amino acids (TAA), such that the pre dicted nitrogen loss was only 20% as much as in rats fed the amino acid-free diet. The arginine-devoid diet supported a positive nitrogen gain (0.72 g/21 d). Similar patterns of conservation were observed with weight gain (data not shown). Using nitrogen gain as the dependent variable, all four parameters were shared (Table 2) when either leucine or valine was limiting, such that the responses for rats fed diets limiting in these two amino acids were identical. When weight gain was the dependent variable, the response curves for tryp tophan and valine were identical (Table 3). Other Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
curves were significantly different in at least one parameter estimate (P < 0.05). The effect of the c parameter estimate on the shape of the curve can be compared in Figure 3 for the curves in which TSA or threonine were limiting. When the R^^ k and b parameter estimates are shared, a smaller c parameter estimate results in a curve with a greater slope (8). By using Rmmol amino acid intake as the predictor variable, the data were scaled relative to 100% of the predicted requirement, and therefore, the k parameter estimate was shared for all 10 dose response relation ships (Tables 2 and 3). To evaluate the Himini »hingreturns response, the first derivative of the logistic equation was calculated using the parameter estimates for each amino acid (Fig. 4). Plotting the derivative of each curve illus trates that instantaneous efficiency asymptotically approaches zero. In other words, the efficiency of amino acid utilization for nitrogen gain when adding an additional increment of the LAA to the diet near gain approaches zero. The instantaneous efficiency was the greatest at 20 to 30% of the pre dicted requirement (Rmmol) for nitrogen gain. An exception to this pattern was observed for TSA. Maximum efficiency of TSA occurred near zero intake and declined thereafter, indicating a large diminishing returns response. For the other LAA, diminishing returns responses began at apparently less than half the requirement for maximum nitrogen gain. At intake levels >50% of the requirement for maximum nitrogen gain, threonine was utilized with the highest numerical instantaneous efficiency, as re ported earlier (15). The requirement for each IAA was predicted again using the parameter estimates for nitrogen gain or weight gain relative to the respective Rmmol. The requirement for maximum gain was defined (24) as the intake predicted to support 95% of JR^, (95% of the asymptotic plateau). The requirement was ex pressed as the millimoles of amino acid required for maximum nitrogen gain or weight gain in 21 d for a rat with an initial weight of 65 g (Table 4). Compared with National Research Council requirements, the amino acid requirements of the rats used in this experiment were overestimated to the largest degree for the TSA, whereas the requirement for arginine was underestimated to the largest degree. To express the requirements as a percentage of the diet, food intake was estimated at the predicted re quirement using a polynomial equation. Food intake increased to a maximum and then declined. The maximum food intake occurred at a LAA level less than the requirement for maximum gain. The poly nomial equation (footnote 1, Table 4) allowed the flexibility to fit a response curve of this shape where an asymptotic equation such as the logistic equation would not fit the observed responses.
GROWTH
RESPONSE TO EACH INDISPENSABLE
AMINO ACID
1725
TABLE 3 Parameter estimates (logistic equation) for weight gain (g/21 d) vs. Rmmol intake/21 d' Parameter2 LAA Arg HisHeLeuLys
TSA3TAA4ThrTrp
Val20.54
±0.95 0.41-20.41 -14.54 ± 0.54-14.54 ± 0.42-11.76 ± ±0.59 -20.41 ± 0.54-11.76 0.59-20.41 ± 0.54-14.54 ± ±0.42 -14.54 ±0.421.95
±0.24 2.67 0.331.95 ± 0.241.57 ± 0.201.95 ± ±0.24 0.74 0.151.57 ± 0.202.67 ± 0.331.95 ± ±0.24 1.95 ±0.240.414
±0.022 0.414 0.0220.414 ± 0.0220.414 ± 0.0220.414 ± ±0.022 0.414 ± 0.0220.414 0.0220.414 ± 0.0220.414 ± ±0.022 0.414 ±0.022113.0
±1.6 1.6125.1 113.0 ± ±1.9125.1 1.9125.1 ± ±1.9 125.1 ± 1.9125.1 1.9125.1 ± 1.9125.1 ± ±1.9 125.1 ±1.9
'See text for definition of parameters in the logistic equation. Parameter estimates are based on 10 groups of four rats fed one of the 10 levels for each amino acid. The weight gain response of four rats fed an amino acid-free diet was -20.25 ±2.87 g/21 d, which corresponds to the b parameter estimate. Rmmol intake/21 d was multiplied by 10 as discussed in the text. Rmmol is the mmol of limiting amino acid (LAA) intake divided by the mmol of LAA required for 95% of £„,„ (asymptotic response Estimate ±asymptotic SE. 3Total sulfur amino acids. "Total aromatic amino acids.
DISCUSSION The requirements for 95% of RM in Table 4 reflect the increased requirement of the IAA for nitrogen gain as compared with weight gain. Nitrogen gain would be the response variable of choice because it reflects directly the response of the rat to the LAA. Weight gain may be influenced by changes in body composition (e.g., increased lipid gain rather than en hanced protein synthesis). However, weight gain offers an alternative to nitrogen gain, yet is less ac curate for evaluating protein quality. There is less work and expense involved in measuring weight gain; at the same time the diminishing returns response can be described, which offers the advantage of com paring relative protein quality at equal performance levels rather than at equal intakes. As shown in Tables 2 and 3, £„,« was not shared when the results for arginine and histidine were com pared with the other eight IAA. The parameter R^ would be expected to be shared over all LAA. Finke et al. (8-10) observed that Rma[was shared for the weight gain or nitrogen gain of rats fed several protein mix tures that differed in protein quality. The response with arginine and histidine was unexpected and no explanation is offered for the 10% lower !?„,„ esti mate. The response of rats to graded levels of a LAA was curvilinear, especially at responses near ma^in-nim. These responses are consistent with findings of Heger and Frydrych (2) and Yoshida and Ashida (1). The efficiency of amino acid utilization is possibly related to the oxidation rate of the LAA. If so, the oxidation rate would be expected to increase curvilinearly with Downloaded from https://academic.oup.com/jn/article-abstract/121/11/1720/4744078 by guest on 23 August 2018
incremental increases of dietary amino acids. Curvi linear analysis is not typically utilized with amino acid oxidation experiments. A break-point analysis of responses was reported for lysine (25), histidine (26), tryptophan (27), threonine (28) and leucine (29). Oxi dation of the LAA remained low (5 to 10%) at levels of intake less than the requirement for maximum growth, but at levels above the requirement, oxi dation tended to be proportional to the concentration in the diet. Although the break-point analysis of the previous experiments seems appropriate for the ob served responses, the diets were formulated such that the LAA was fed at graded levels from below to above levels required to support maximum gain, whereas the levels of the other amino acids were constant. A concern with this approach is that as the apparent maximum gain is approached, the supposedly LAA actually becomes co-limiting or another amino acid becomes first limiting. A different LAA would be expected to impact on the response relationship of the animal and perhaps create a break-point response, rather than the curvilinear response expected from incremental levels of a LAA that remains clearly first limiting. Rats fed a diet devoid of any one of the IAA would be expected to respond the same as rats fed an amino acid-free diet. Conservation of the IAA is not ex pected because the chemical score of the diet is zero and the net protein utilization is expected to be zero (30). Only rats fed diets devoid of isoleucine, TSA or threonine elicited the expected response. Rats fed amino acid mixtures devoid of histidine, leucine, TAA, tryptophan or valine lost about two-thirds as much weight as rats fed the amino acid-free diet,
GAHL ET AL.
1726
-0.4 O
T
1
1
20
40
60
1
1
1
80 100120140
1
T
20
1
1
40
60
Intake,
1
1
1
T
80 100 120140
i
1
1
20
40
60
1
1
1
80 100120
r 140
Rmmol
FIGURE 3 Nitrogen gain response curves generated using the parameter estimates for the logistic equation for rats fed diets limiting in one indispensable amino acid: lysine, TSA (total sulfur amino acids), threonine or tryptophan; isoleucine, leucine or valine,- arginine, histidine or TAA (total aromatic amino acids). The mean ±SEMfor each group of four rats was plotted for each dietary amino acid level. Rmmol as presented on the graph was calculated as the mmole of limiting amino acid (LAA) divided by the mmole of LAA required for 95% of RmaLtimes 100. The intercept values (b parameter) are shown in detail in Figure 2. The response curves for leucine and valine were not different as a result of sharing all four parameters of the logistic equation. R^^ (asymptotic response maximum) was shared for the arginine and histidine curves, whereas the RO^ for the TAA curve was shared with the data sets for the other seven amino acids.
whereas rats fed a lysine-devoid amino acid mixture lost only one-third as much weight (31-33). The current results (Fig. 2) show similar observations except that the TAA seemed to be conserved to the same degree as lysine. Because arginine is condi tionally indispensable at low levels of growth, rats gained weight. The positive gain of rats fed an arginine-devoid amino acid mixture is consistent with observations of Mercer et al. (34). The maximum efficiency observed by Heger and Frydrych (2) was in rats fed diets providing 30 to 60% of the requirement of the LAA. This range for maximum efficiency was similar to that observed by Bunce and King (12, 13). Maximum instantaneous efficiency (slope of the response curve) was observed at 20 to 30% of the predicted requirement (Rmmol) for nitrogen gain (current results). At
