Download Research paradigms behind amino acid requirements of the

Research paradigms behind amino acid requirements of the lactating sow:
Theory and future application'
N. L. Trottie9 and X. F. Guan
Department of Animal Science, Michigan State University, East Lansing 48824
ABSTRACT: Significant progress has been made in
nized. It will become essential to identify what pools
are significant contributors of amino acid provision to
the mammary system, and whether milk or the mammary system itself should be the protein accretion pool
to derive the amino acid profile. Third, the single nutrient input approach and simple regression does not completely take into account the basic knowledge behind
nutrition. By moving from simple regression to surface
response models, new experimental designs will emerge
to address multiple amino acid interactions. The empirical and factorial approach to define amino acid requirements will still be useful in the future, only if more
sophisticated biological and statistical models are used
to study and fit the complex nutrient-biological interactions taking place during lactation.
establishing amino acid requirements for the lactating
sow through prediction models. Further understanding
of amino acid nutrition is essential to maximize genetic
potential for litter weight gain and milk production of
the sow. Three research paradigms behind sow amino
acid nutrition are discussed. These paradigms may be
recognized as limiting factors that could impede further
progress in amino acid nutrition of the sow. First, the
approaches to estimate amino acid requirements, such
as the factorial and empirical approach, will only be
optimized by switching to a different focus (e.g., the
efficiency of amino acid utilization for milk synthesis).
Second, the significance of a practical application for
an ideal protein for the lactating sow should be recog-
Key Words: Sow, Lactation, Amino Acid, Response Surface Model, Ideal Protein, Requirement
02000 American Society of Animal Science. ALL rights reserved.
Introduction
J. h i m . Sci. 2000. 78(Suppl. 3):48-58
better reflection of individual biological variation.
There is no doubt, however, that further progress in
amino acid nutrition of the sow is necessary to optimize
lactation, and current limitations must be recognized.
Defining amino acid requirements of the lactating
sow is confined to three main research paradigms. The
first paradigm is the approach used in defining amino
acid requirements. The empirical and factorial approaches both have limitations mainly as pertains t o
the response criteria used and the biological assumptions made behind each approach. The second paradigm
is the ideal dietary protein for the lactating sow. Milk
is currently the protein accretion pool on which the
amino acid profile is based. Evidence for other pools
exists, and thus knowledge beyond nutrient intake and
lactation performance will become increasingly important. The third paradigm is the type of experimental
design used in determining amino acid requirements.
Most designs focus on the use of simple regressions
and single amino acid titration studies. Information
relating amino acid interactions and lactational performance is scarce and may be oversimplified due to limitations of factorial designs. With the notion of the
biological system complexity, other designs, such as
response surface models, should be investigated. The
objective of this paper is to discuss these paradigms
Defining the amino acid requirements of the lactating
sow is essential to optimize dietary formulation for ensuring maximum milk production and litter weight
gain. However, the quest for establishment of amino
acid requirements for the lactating sow during the past
20 yr, particularly in regard to lysine, has given rise
to a wide variety of estimates (Pettigrew, 1993). This
variability has nonetheless permitted development of
models that allow prediction of any amino acid requirement to be made based on litter weight gain or production level, feed intake, and body weight loss of sows
during lactation (NRC, 1998). This has significantly
contributed to the progress of amino acid nutrition of
the lactating sow. For example, recommendations for
amino acid requirements are now based on predicted
feed intake and production levels, and therefore are a
'The authors gratefully acknowledge the critical review of Tom D.
Crenshaw (Univ. of Wisconsin) and Rob Tempelman (Michigan State
Univ.) on the RSM section. Authors also acknowledge Allen Tucker
(Michigan State Univ.) for critical review of the manuscript.
'To whom correspondence should be addressed (phone: (517) 4325140; fax: (517) 432-0190; E-mail: [email protected]).
48
Amino acid requirements of the lactating sow
and raise questions regarding their limitations to the
progress of amino acid nutrition research for the lactating sow.
Approaches to Defining Amino Acid
Requirements
Despite the availability of lactation models to predict
amino acid requirements, the amino acid requirement
of the lactating sow is a controversial issue. This is
largely due both to the lack of information and t o the
variability of estimates of essential amino acid requirements. For instance, requirements of a few essential
amino acids (other than lysine) such as valine (Richert
et al., 1996,1997b1,methionine (Schneider et al., 19921,
and tryptophan (Libal et al., 1997) have only recently
been determined through empirical studies. Lysine requirements, however, have been extensively researched
for the past 20 yr (NRC, 19981, and estimates of dietary
requirements vary significantly. The paucity of data
regarding empirically derived requirements of most
amino acids and the inconsistency in lactational performance responses to graded levels of dietary lysine is
partly inherent in the response criteria and approaches
used to estimate requirements.
Respoizse Criteria
A substantial challenge behind designing nutritional
studies with lactating sows has been selecting the response criteria that would most accurately reflect lactational performance. Average daily litter gain has been
the response criterion of choice for measurement of lactational performance in sows because litter size is the
highest determining factor in influencing milk production level (Hartmann et al., 1997).Its variability within
an experimental treatment is high, however, because
it is an indirect measure of milk production, and because milk yield is the product of both sow lactation
potential and pig growth potential. Other response criteria, such as blood urea nitrogen (BUN) (Coma et al.,
1996) and nitrogen balance (Dourmad et al., 1998),have
been used to a limited extent to estimate lysine requirements. The BUN approach assumes that the requirement of the limiting amino acid in question is met at
the nadir where utilization of all amino acids for protein
synthesis is maximized and body protein degradation
is minimized. Blood urea nitrogen represents catabolism of amino acids arising from basal protein turnover
as well as from excess amino acids arising from intestinal absorption and not incorporated into protein. Unless the balance is optimal or ideal, the BUN value may
not indicate minimal protein tissue catabolism.
Using the BUN approach, Coma et al. (1996) found
that the lysine requirement for a sow nursing a litter
with a daily growth rate of 2.2 kg was 57 g/d. The linear
increase in lysine intake corresponded to a quadratic
decrease in BUN. Increasing dietary level of that single
amino acid above the nadir would increase BUN due
49
to deamination and oxidation, which implies that the
amino acid is in excess of the requirement. Use of BUN
as a response criterion may not be applicable to nonlimiting amino acids. It has been suggested that branchedchain amino acids may be needed at higher levels than
at the requirement value estimated using BUN (R.
Goodband, unpublished data). For example, increasing
the dietary valine level increases litter weight gain and
simultaneously increases BUN (Richert et al., 1996).
This suggests that valine may be oxidized rather than
incorporated into milk protein and be utilized for nonprotein synthesis functions essential for milk production.
Tremendous effort and years of work have been dedicated to determining lysine requirements of the lactating sow using litter weight gain as the response
criterion. The variability in litter weight gain in response to varying levels of dietary lysine allowed development of a useful model to predict lysine requirements
(Pettigrew, 1993; NRC, 1998). The prediction model is
based on a simple regression approach. By combining
selected empirical studies performed over the past 20
yr, it has been established that 26 g of lysine is required
for each kilogram oflitter weight gain. Are further studies essential to determine lysine requirements for milk
production? The increase in litter weight gain in response to increasing dietary lysine observed over the
last 20 yr is a combination of increase in number of
pigs, resulting from improved managerial techniques,
and pig growth. The current national average is 8.8
pigs per litter (USDA, 1999). If litter size will be maximized to 14 or 16,which would occupy all the functional
glands of a sow’s mammary system, it is difficult to
predict whether 26 g lysine will still be required for
each kilogram of litter growth. It is most likely that as
long as the increase in litter weight gain represents the
product of pig number and pig growth, the prediction
will remain similar. It is possible, however, with development of new genetics, that sow efficiency for milk
protein synthesis will change, modifying the slope of
the regression line, such that 26 g of lysine may be in
excess of or below the requirement.
Empirical and Factorial A p p r o a c h
The empirical and factorial approaches have both
been used, but the empirical approach has been preferentially employed. The empirical approach involves the
addition of graded concentrations of the test amino acid
in its crystalline form to a diet deficient in that amino
acid (D’Mello, 1982). The response curve is then used
to determine the optimal dose for given levels of the
response criteria chosen, such as milk production or
litter weight gain. In the factorial approach, amino acid
requirements are determined from the sum of the functional components (Fuller, 1994). Milk amino acid composition and production level are the main components
used for estimating amino acid requirements for the
lactating sow.
50
Trottier and Guan
Both methods have several flaws that should be addressed in the context of future amino acid nutrition
research in lactating sows. The biggest obstacle in using
the empirical approach for the lactating sow is the limited feed intake capacity of the sow and, to some extent,
the accuracy of feed intake measurement. Accurate
measurement of feed intake represents an essential
prerequisite for satisfactory interpretation of the data
in dose-response experiments (D’Mello, 1994). Sows
typically lose body weight during lactation to buffer
nutrient demand imposed by the nursing litter (Weldon
et al., 1994). Hence, amino acids that are made available from body protein pools are not part of the estimated amino acid intake needed to maximize milk
protein deposition. This has contributed t o the wide
variation in dietary lysine requirement estimates
among studies. The NRC (1998) model now predicts
dietary amino acid requirements of sows taking into
consideration expected daily feed intake and body protein loss. Hence, “dietary” amino acid requirements are
determined by the empirical approach, whereas amino
acid requirements for milk production per se are estimated by the factorial approach.
Empirical studies thus far have been based on titration of single amino acids and simple regression modeling of the response. Consequently, two concerns are
now surfacing. First, what will be the design of choice
to address multiple amino acid interactions, and what
is the ideal protein for the lactating sow? Second, with
the advent of molecular biology techniques and new
livestock genetics, the question ofwhether conventional
empirical studies will keep pace with the need for new
nutritional requirements should be considered. The latter concern has also been raised by Buttery and D’Mello
(1994), in particular regarding the time commitment
and economics of repeating studies to re-evaluate amino
acid responses.
Using a factorial approach, if we calculate the lysine
requirement for milk production in a sow nursing a
litter gaining 2 kg/d we achieve estimates similar to
those found when we use the regression approach (Table l). Both approaches reveal key factors that should
be addressed in the future to ensure progress in amino
acid nutrition of the sow. First, in the case of the regression approach, efficiency of lysine utilization is unknown but assumed to be constant across milk
production levels, litter sizes, stages of lactation, and
feed intake levels. Because all other indispensable
amino acids are based on lysine concentration in milk,
the efficiency of utilization of these amino acids is also
assumed to be constant. Evidence suggesting that milk
is perhaps not the sole protein pool to derive all indispensable amino acids requirements will be discussed
later. In the case of the factorial approach, accuracy of
requirement estimates is primarily dependent on
knowledge of utilization efficiency for each amino acid.
Because these coefficients are unknown, a single value
derived from the efficiency of digestible nitrogen utilization (.7) is used for all amino acids (see Table 1footnote).
Table 1. Calculated amino acid requirements for a
lactating sow weighing 160 kg postfarrowing and
expected to produce a litter growth rate of 2 kg per
day, based on a factorial or regression approach
Amino acid
Arginine
Histidine
Isoleucine
Leucine
Lysine
Methionine
Total sulfur
Phenylalanine
Total aromatic
Threonine
Tryptophan
Valine
Factorial approach,
g/aa
Regression approach,
g/db
34.16
20.93
29.34
60.82
54.05
13.92
25.91
29.51
60.32
32.11
9.74
39.18
34.16
20.92
28.51
59.68
54.09
13.96
26.25
28.59
58.44
32.12
9.76
39.22
“Amino acid requirements were calculated the following way: 1)
2,000 g litter weight gain corresponds t o 388 g milk protein output
per day; 388 g x g M 1 6 g N in milk = g AA in milk/day. 2) ( g AA
in milWdayY.7 (efficiencyof N utilization into milk protein synthesis)
= digestible AA required for milk. 3) (Digestible AA required for milk/
.8) + total AA for maintenance = total AA dietary requirement.
bAmino acid requirements were calculated the following way
(adapted from Pettigrew, 1993): 1)26 g lysinenig litter growth (see
text) x 2 kg (expected daily litter growth rate) = 52 g. 2 ) 52 g x
AA:lysine ratio in milk protein + maintenance = total amino acid
requirement.
Second, the potential contribution of amino acids from
body protein pool to milk protein synthesis can be derived using either the empirical or factorial approaches.
However, de novo amino acid contribution estimates are
unlikely to be useful in predicting dietary requirements
unless the efficiency of amino acid utilization coming
from the whole-body protein pool is known. Third, it is
assumed that amino acids arising from the body protein
pool are all utilized for milk protein synthesis, although
other physiological needs should be identified. The latter highlights the need of developing approaches to focus on the biological processes between amino acid
intake and lactation performance. Amino acid requirement estimates derived from either the factorial and
regression approaches are similar. This indicates that
further titration studies with lysine alone are most
likely not going to contribute substantially to the current body of knowledge. Estimates of the efficiency of
lysine and other indispensable amino acid utilization
for milk production in the lactating sow should be the
highest priority in the next decade.
Ideal Amino Acid Profile
Limits to an Ideal Protein for the Lactating Sow
A second research paradigm is concerned with defining the ideal dietary amino acid profile for lactating
sows. The ideal protein concept was originally formulated for growing animals (Cole, 1978; Fuller et al.,
1979). By definition, the ideal protein yields an opti-
Amino acid requirements of the lactating sow
40
51
sents non-milk protein synthesis requirements, as suggested earlier for valine based on the BUN response.
1
30 -
Variation in the Ideal Dietary Amino Acid Profile for
Lactat ion
20 -
?
l n r ;
rn
10 -
0
Arg
-10
Lys
Val
Ile
Thr
Phe
His
Met
1
Figure 1. Daily mammary amino acid uptake, output
in milk, and mammary retention (adapted from Trottier et
al., 1997). Black bars indicate uptake, shaded bars indicate
output, and open bars indicate the difference between
uptake and output.
mum dietary balance of indispensable amino acids, supplied with sufficient nitrogen for the synthesis of
dispensable amino acids, that matches the animal’s requirements for growth and minimizes nitrogen loss
(Cole and Van Lunen, 1994). Whereas carcass protein
accretion represents the main pool from which the dietary amino acid profile is derived in the growing pig,
milk represents the main protein accretion pool in the
lactating sow. As shown in Table 1,amino acid requirements for lactation are estimated from an empirically
derived lysine requirement and the milk profile for
other amino acids relative to lysine. In theory, the ideal
protein concept could be applied to the lactating sow,
although two limitations should be recognized.
The first limitation is the metabolic status of sows
during lactation. Most sows are catabolic throughout
lactation, because feed intake is a major limiting factor
for meeting dietary requirements. As body protein contributes to the pool of circulating amino acids during
catabolism, the amino acid profile derived from the diet
is modified, thus rendering the practical significance of
an ideal dietary amino acid profile questionable. Second, if milk only is used as the basis for setting the
ideal amino acid profile, there is no consideration for
the amino acid metabolism associated with mammary
gland functions. Hence, regression and factorial approaches have similar amino acid requirement estimates for milk production when feed intake is not
limiting (Table 1). For instance, amino acids such as
leucine, isoleucine, valine, and arginine are taken up
by the mammary gland of the sow in excess of their
appearance in milk (Figure 1) (Trottier et al., 1997;
Guan et al., 1998). Similar results were found in other
species, such as the goat (Bequette et a]., 1997) and
dairy cow (Guinard and Rulquin, 1994). This “excess
uptake” could be associated with specific metabolic
functions for the process of milk production and repre-
Proposed amino acid profile ratios relative to lysine
have varied significantly. Table 2 represents a summary of amino acid ratios for the lactating sow from
1981 to 1998. Ratios from the Agricultural Research
Council (ARC, 1981) and Pettigrew (1993) are similar
because they are based on milk amino acid profile. The
amino acid ratios from the NRC (1988) were calculated
based on amino acid requirement values relative to
lysine. The basis of NRC (1988) amino acid requirements other than lysine are mostly factorially derived.
The ratios in NRC (1998) are based on Pettigrew’s
(1993) ratios, except for valine, for which the ratio has
been increased from .73 to .85. This increase in valine:lysine ratio deviates from the amino acid profile
found in milk. The increase was based on the studies
of Richert et al. (19961, in which dietary valine supplementation in diets for high-producing sows increased
litter weight gain. This is further supported by other
studies (Nielsen et al., 1996; Trottier et al., 1997; Guan
et al., 1998) in which va1ine:lysine ratios across the
porcine mammary gland varied from .88 to 1.06, as
shown in Table 2. The discrepancy of amino acid ratios
relative to lysine among different sources indicates that
the ideal protein for the lactating sow remains undefined. The milk amino acid profile may not accurately
reflect the dietary profile required for maximum milk
synthesis and production.
The complexity behind the biological control of milk
production may not allow the application of an ideal
amino acid concept for the sow. We are now testing a
method to facilitate the study of multiple amino acid
interactions and identify limiting amino acids. A criterion of amino acid requirements based on arteriovenous
differences of amino acids across the mammary gland
was investigated (Trottier et al., 1997; Guan et al.,
1998). Preliminary findings indicate that the mathematical relationship between lysine uptake by the porcine mammary gland and arterial and(or) dietary
supply is quadratic (Trottier, 1997). Recent findings
(Figure 2) (Guan et al., 1998) indicate that this relationship exists for all limiting amino acids, and the point
of maximal response may correspond to amino acid requirements. In contrast to other response criteria and
approaches, the arteriovenous difference method potentially estimates multiple limiting amino acids concurrently, rather than estimating the requirement for a
single amino acid. Defining the ideal protein for the
lactating sow will require adaptation of new biological
methods by which multiple amino acids metabolism can
be concurrently studied. In addition, a transition into
more sophisticated statistical design, as proposed in
the following section, is essential.
52
Trottier and Guan
Table 2. Suggested dietary amino acid (AA) ratios relative to lysine for lactating sows
Based on milk AA
profile
Amino acid
~~
ARC"
11981)
NRC~
(1988)
Pettigrew
(1993)
( 1998)
.67
.39
.70
1.15
1.00
.66
.42
.65
.80
1.00
-
-
.66
.40
.55
1.15
1.00
.26
.45
.55
1.12
.58
.18
.73
.49-.53
.39
.55
1.05-1.09
1.00
.25
.49
.53
1.09-1.11
.65-.63
.18
.84-.86
NRC'
Based on mammary AA uptake
Trottier et a1
( 1997)
Nielsen et al.
(1996)
Guan et a1
(1998)
1.25
.30
.76
1.50
1.00
.28
.65
1.09
.79
1.48
1.00
.26
1.16
.30
.79
1.23
1.00
.33
-
-
.61
-
-
.61
.61
~
Arginine
Histidine
Isoleucine
Leucine
Lysine
Methionine
Total sulfur"
Phenylalanine
Total aromaticd
Threonine
Tryptophan
Valine
.55
.60
-
-
1.15
.70
.19
.70
1.17
.72
.20
1.00
28
.68
.64
-
__
.88
.89
.18
1.06
"Agricultural Research Council (ARC. 1981).
"National Research Council (NRC, 1988) ratios are calculated from M requirements.
'National Research Council (NRC, 1998)ratios are based on study by Pettigrew (1993),except for valine. Ranges indicate ratios corresponding
to different milk production level and sow body weight change combinations.
dTotal sulfur contains methionine and cystine and total aromatic contains phenylalanine and tyrosine. Because cystine and tyrosine are
probably synthesized in the mammary gland, the total sulfur and aromatic AA uptake by the mammary gland cannot be estimated accurately.
Using Response Surface Methodology to
Establish Dietary Amino Acid Ratios
Respoizse Surface Model Methodology
Although the response in performance of the lactating sow has been successfully modeled using one independent variable, dietary lysine intake (Pettigrew et
al., 1992; Pettigrew, 1993, 1997; Kerr, 1997; Guan et
al., 1998; NRC, 19981, the models remain incomplete.
A difficult task for modeling is establishment of appropriate ratios between dietary amino acids to maximize
6.0
1
' 1
aJ
aJ
Max. log Lysine A-V difference
I
I
I
Y
'
Lysine intake = -bl2c
I
= a + bX
+ cX*(c< 0)
v
0.0
0
10
20
30
40
50
60
70
80
90
.
100
Dietary lysine intake, g/d
Figure 2. Relationship between the log lysine arteriovenous (A-V) difference across the porcine mammary gland
and the daily dietary lysine intake (Guan et al., 1998).
Lysine A-V difference reaches a plateau at a certain dietary intake of lysine that corresponds to dietary lysine requirement.
performance in the lactating sow. Optimal dietary ratios of amino acids for the lactating sow discussed above
(Table 2) have yet to be successfully modeled.
Traditional factorial experimental designs can be
used to test interactions among multiple experimental
factors. However, factorial designs cannot efficiently
identify curvature among multiple independent variables, at least within a reasonable number of treatment
groups that can be economically and practically handled. Optimal experimental designs should be employed
to model these curvatures to define a combination of
amino acids to describe the most desirable response in
growth rate. Response surface methodology (RSM) is
one technique that addresses optimization issues. The
RSM includes three major procedures, as follows: 1)
the experimental strategy for exploring the space of
multiple input independent variables; 2) empirical statistical modeling to develop an acceptable approximating relationship between the response and those
variables; and 3) optimization methods for finding a
combination of levels of variables that produces the
most desirable response. The RSM has been used extensively in engineering, physical, chemical, medical, biological, and agricultural sciences. However, the RSM
has been employed only to a limited extent in swine
nutrition. Golz and Crenshaw (19901 used a response
surface design to examine the interrelationships of dietary sodium, potassium, and chloride on growth rate
in young pigs. During the last decade, no other studies
in swine nutrition have been performed using response
surface design. The RSM may provide a method to optimize quantitative relationships of dietary nutrients for
lactating sows, such as dietary intake of metabolic energy, ideal amino acid patterns, or multiple limiting
amino acids. The response criteria may include milk
protein output, milk yield, daily litter weight gain,
Amino acid requiremenIts of the lactating sow
i
(0, 1.414)
9
(0, -1.414)
Figure 3. Graphical depiction of the central composite
design for fitting the second-order response surface
model.
BUN, and(or) mammary arteriovenous differences in
plasma free amino acids.
Whereas a common procedure is to vary one factor
while holding other factors constant, RSM techniques
allow simultaneous variation of several factors to find
a combination of quantitative levels that leads to an
optimum response. The response y of a given system to
multiple input independent variables XI,x2, . . . xk, can
be described by the following empirical model:
For example, y can be daily milk yield of the lactating
sow, and x can be dietary intakes of several limiting
amino acids. The form of the true response function f is
unknown and perhaps very complicated, and the error
term (e) represents other sources of variability not accounted for in f . Usually, the function f is a first- or
second-order polynomial (Myers and Montgomery,
1995). In an appropriate experimental regression design, representative combinations of different levels of
independent variables should be symmetrically distributed across the whole response surface in order to model
the nature of the response. A second-order regression
model is usually employed to fit the response surface.
Box and Wilson (1951) developed a central composite
design specifically for fitting the second-order response
surface. For two independent factors, a graphical depiction of this design is shown in Figure 3. The treatments
are indicated by the dots. There are five levels of each
independent variable that involve three components
(Neter et al., 1996). 1) Corner points have four coded
coordinates ( f l , f l ) ,which is a two-level, full factorial
design to provide for the estimation of linear main ef-
53
fects and all two-factor interaction effects. 2) Axial
points have 4 coded coordinates (f1.414, 0) or (0,
f1.4141, which enhance estimates of quadratic effects.
3) Central points have four replicates of coded coordinates (0, 01, which estimate pure error in a lack of fit
test. Note that the design essentially consists of eight
equally spaced points on a circle of radius 22 with four
treatments in the design center. The second-order response surface model (SORSM) is fitted to the data
generated from the central composite design. The
SORSM is expressed as follows:
The geometric nature of this second-order response
function can be of three graphical types: maximum,
minimum, or saddle point. In the same experiment,
the geometric nature of a second-order response may
change as a function of the response criteria. For example, in a RSM of amino acid ratios for lactating sows,
we expect a maximum litter weight gain (or milk yield)
but a minimum fecal and(or) urinary nitrogen excretion
if dietary ratios of amino acids are the most appropriate
for the lactating sow. Analysis of response surface design has been discussed in detail elsewhere (Myers and
Montgomery, 1995; Neter et al., 1996). The RSM is a
collection of statistical and mathematical techniques
useful for developing, improving, and optimizing processes. Fitting data with a SORSM is one example when
central composite designs are used. Any response surface model can be fit to a data set, but the difficulty
arises in determining which fit is the best fit in terms
of both statistical and biological principles. Indiscriminate use of response surface models to fit available data
may be misleading from the true nature of the response.
Thus, careful attention to experimental designs for exploring the response surface are essential. First, central
composite or optimal response surface experimental designs should be employed to generate a whole data set;
second, data must be fit using appropriate response
surface models; third, the response surface models
should be formally analyzed to obtain a recombination
of levels that leads to an optimal response; fourth, biological interpretation of the response is essential.
Modeling Lysine and Valine Requirements
and Ratios in the Lactating Sow Using RSM
Response surface designs have not been used to estimate optimal ratios among dietary limiting amino acids
for the lactating sow. To explain the current variation
in requirement estimates and in dietary ratios of valine
to lysine for a given litter growth rate, we attempted
to define the response surface of lysine and valine in
the lactating sow and to identify which step, in terms
of experimental strategy, should be taken next. Daily
litter weight gain (kg/d), adjusted to a 21-d lactation
period, was chosen as the response, based on the most
54
Trottier and Guan
recent available data (Johnston et al., 1993; King et al.,
1993; Knabe et al., 1996; Richert et al., 1996, 1997a,b;
Libal et al., 1997; Dourmad et al., 1998; Guan et al.,
1998; Sauber et al., 1998; Touchette et al., 1998a,b).
Both dietary lysine and valine levels (%, as-fed basis)
were adopted either directly from reported papers when
available or calculated based on the composition of the
diet provided in the papers. Figure 4 represents a threedimensional (3-D) mesh plot of the response surface of
daily litter weight gain against dietary lysine and valine levels in the lactating sow. Three distinct peaks
are present in the 3-D mesh plot. The response surface
shown may be confounded by genetic, environmental,
management, litter size, and(or) other nutritional factors besides dietary lysine and valine levels. The three
peaks from the 3-D mesh plots, however, offer insight
into the range of lysine and valine levels on which future
experiments may need to focus. Investigation of this
range, which corresponds to the area between the peaks
of 1to 1.5% dietary lysine and 1to 1.25%valine, would
allow one to obtain the real nature of the whole response
surface. This should constitute the central point of a
central composite design employed in designing future
experiments with lysine and valine.
Corresponding to the 3-D mesh plot, a 2-D contour
plot, generated from the same data set above, is shown
in Figure 5. The contour lines display a set of constant
responses. Again, as seen in the 3-D mesh plot, three
sets of contour lines indicate better response of litter
weight gain around 2.3 and 2.4 kg/d. Figure 5 shows
that the dietary ratio of lysine to valine in most studies
was concentrated around 1:l.However, this ratio may
not be the most appropriate because of uncertainty
about the shape of the response surface outside this
ratio. More data should be generated simultaneously
from representative ratios in an optimization design.
Table 3 shows our suggested combinations of dietary
lysine and valine levels, needed to fit a RSM as in Figure
3. The dietary ratio of valine to lysine is set at 1 : l as
a central point (i.e., treatments 9 to 12), on the basis
of both the NRC (1988) recommended ratio and the
above preliminary analysis of the response surface. The
middle level of dietary lysine was set at 1.0% (i.e., the
uncoded level at the central point). Treatments 1 t o 4
and 5 t o 8 represent corner points and axial points,
respectively. Both the highest level and the lowest level
of dietary lysine or valine are feasible for performing
this experiment. Although the lack of data produced
Figure 4. Three-dimensional mesh plot of litter weight gain against dietary lysine and valine levels in the lactating
sow. Data were obtained from Johnston et al., 1993; King et al., 1993; Knabe et al., 1996; Richert et al., 1996, 1997a,b;
Libal et al., 1997; Dourmad et al., 1998; Guan et a)., 1998; Sauber et al., 1998; and Touchette et al., 1998a,b.
55
Amino acid requirements of the lactating sow
1.75
1s o
1.25
s
a?
n
.I
CI
2
1.00
a
c)
a,
.CI
n
0.75
0.50
‘ 1
-\
0.25
0.25
0.50
1.00
0.75
1.25
1.50
1.75
Dietary lysine, %
Figure 5. Two-dimensional contour plot of litter weight gain against dietary lysine and valine levels in the lactating
~ Data
7
.
were obtained from Johnston et al., 1993; King et al., 1993; Knabe et al., 1996; Richert et al., 1996, 1997a,b;
Libal et al., 1997; Dourmad et al., 1998; Guan et al., 1998; Sauber et al., 1998; and Touchette et al., 1998a,b. Line and
numbers (1.9, 2.0, 2.1, 2.2, 2.3, and 2.4 kg/d) represent litter weight gain (kg/d).
~
0
Table 3. A suggested two-factor rotatable central
composite design with four replications
at central point
Dietary lysine, %
Treatment
Coded
Dietary valine, %
Uncoded
Coded
Uncoded
.47
.47
1.53
1.53
.25
1.75
1
1
1
1
1
1
-1
1
-1
1
0
0
-1.414
1.414
0
0
0
0
.47
1.53
.47
1.53
1
1
.25
1.75
1
1
1
1
~
1
2
3
4
5
6
7
a
9
10
11
12
-1
-1
1
1
-1.414
1.414
0
0
0
0
0
0
from appropriate experimental designs does not allow
an accurate analysis of the response surface, the
SORSM was employed to fit the data set above. The
SORSM was performed using the RSREG Procedure of
SAS (1996).
Figure 6 shows the 3-D fit of the response surface of
litter weight gain against dietary lysine and valine levels in the lactating sow. The estimated stationary point
is a saddle point, but the model was not significant ( P
< .15).The second-order response surface obtained does
not have a unique optimum, that is, a single maximum
response point that could not be achieved a t a particular
combination of levels of dietary lysine and valine based
on this data set. However, when we search for the region
of optimum response using the ridge analysis (Myers
and Montgomery, 1995), a speculative predicted maximum response (daily litter weight gain) results from
increasing the ratio of dietary valine to lysine (Table
4). For example, when the dietary ratio of valine to
lysine increases from .93 to 1.2 (i.e., dietary valine in-
56
Trottier and Guan
Figure 6. Three-dimensional fitted response surface of litter weight gain against dietary lysine and valine concentrations in the lactating sow (based on the second-order model litter weight gain = 3" + lysine + & valine + ;j3 lysine'
+ /j4 valine2 + J5 lysine x valine + e). Data were obtained from Johnston et al., 1993; King et al., 1993; Knabe et al.,
1996; Richert et a]., 1996, 1997a,b; Libal et al., 1997; Dourmad et al., 1998; Guan et al., 1998; Sauber et al., 1998; and
Touchette et al., 1998a,b. Dots represent published experimental response points. Shaded area represents the fitted
second-order response surface.
creasing from .90 to 1.01% and lysine decreasing from
.97 to .84%), the predicted daily litter weight gain increases from 2.15 to 2.39 kg/d. Keep in mind that the
above fitted SORSM might not reflect the true nature
Table 4. Estimated ridge of maximum response for
daily litter weight gaina
Estimated
response,
kg/d
Dietary lysine.
Dietary valine,
SE
5%
%
Dietary ratio of
valineAysine
2.14
2.20
2.28
2.39
2.52
.06
.06
.06
.09
.16
.97
.93
.a9
.84
.a0
.90
.94
.98
1.01
1.05
.93
1.01
1.10
1.20
1.30
aThe estimated response was calculated using the following equation jr = 1.6317 - .7368X1 + 1.8907X~+ 2.3297XI2 + 1.7816X2' 4.7091X1X2(P= .1410), where j r , XI, and XZ denote predicted litter
weight gain (kg/d), dietary lysine (%), and dietary valine (%I, respectively.
of the whole response because of lack of data generated
from optimal experimental designs. We could predict
more accurately the response surface of the sow's milk
production to diet manipulation with the aid of optimal
experimental designs. In turn, this could generate more
precise estimates of optimal dietary amino acid ratios.
Implications
Determination of amino acid requirement estimates
has been the focus of sow lactation research for the past
two decades. Although significant progress has been
made recently through biomathematical models, further understanding of amino acid nutrition is essential
to maximize genetic potential for litter weight gain and
milk production of the sow. Therefore, it is proposed
that the future of amino acid nutrition research should
depend on a critical evaluation of the past and current
research approaches, and recognition of the limiting
factors that could impede further progress. Three re-
Amino acid requirements of the lactating sow
search paradigms behind sow amino acid nutrition have
been identified and discussed. First, the approaches to
estimate amino acid requirements, such as the factorial
and regression (derived form empirical work) approach,
are equally valid within our current understanding of
amino acid nutrition of the sow. Both approaches, however, will only be optimized by switching to a different
focus: the efficiency of amino acid utilization for milk
synthesis. Second, with the negative nitrogen balance
usually taking place during lactation due t o limited
feed intake capacity of the sow, the significance of a
practical application for an ideal protein should be recognized. It will become essential to identify what pools
are significant contributors of amino acid provision to
the mammary system, and whether milk or the mammary system itself should be the protein accretion pool
to derive the amino acid profile. In addition, information on requirement estimates for other limiting amino
acids through empirical work using novel biological and
statistical methods will be important to validate proposed ideal amino acid profiles. Third, the single nutrient input approach and simple regression does not
completely take into account the basic knowledge behind nutrition (i.e., nutrients work interactively to produce a n optimum response). Novel approaches to
modeling responses for more rapid and efficient determination of amino acid requirements will be necessary.
This is becoming critical as new genetics are emerging.
The empirical approach to defining amino acid requirements will be useful only if more sophisticated statistical models are used to fit the complex nutrientbiological interactions taking place during lactation.
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