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ANIMAL NUTRITION |
Department of Animal and Poultry Science, University of Guelph, Guelph, ON, Canada N1G 2W1
| Abstract |
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Key Words: casein growing pig lysine nonstarch polysaccharide postabsorptive efficiency wheat shorts
| INTRODUCTION |
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| MATERIALS AND METHODS |
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Two separate N-balance studies were conducted with diets limiting in either Lys (Lys study) or Thr (Thr study). For each N-balance study, 8 Yorkshire barrows with initial BW of 28 ± 1 kg for the Lys study and 24 ± 2 kg for the Thr study were obtained from the University of Guelph swine herd. The pigs were allowed to adjust to their new environment for 1 wk, weighed, and randomly assigned to 1 of 2 groups (CS or WS). Within groups, the 4 pigs were randomly assigned to 4 of the 6 experimental treatments during 4 subsequent experimental periods based on a 4 x 4 Latin Square design.
The 4 treatments were a basal diet (basal; AA level 1), 2 dietary levels of additional AA (AA levels 2 and 3) derived from CS (CS group; CS2 and CS3) or WS (WS group; WS2 and WS3) and a diet containing pectin and CS at AA level 3 (pectin). Two out of 4 treatments were identical across the 2 groups (basal and pectin).
The pigs were housed individually in floor pens during the 7-d adaptation period and transferred to metabolic crates before the N-balance period. Room temperatures were kept at thermoneutral zones for growing pigs (20 to 22°C). At the completion of the experiment, BW of the pigs was 55 ± 2 kg (Lys study) and 52 ± 4 kg (Thr study). The animal use protocol for this study was approved, and pigs were cared for according to the guidelines set by the Animal Care Committee of the University of Guelph.
Diets and Feeding
For the Lys study, the basal diet (L-basal) was formulated to contain 0.24 g of standardized ileal digestible (SID) Lys per MJ of DE, to which extra 0.095 or 0.19 g of SID Lys per MJ of DE was added from CS (L-CS2 or L-CS3, respectively) or WS (L-WS2 or L-WS3, respectively; Table 1
). A sixth diet was included that contained the same level and source of Lys as L-CS3 but to which 6% pectin (CPKelco, Wilmington, DE; Zhu et al., 2005
) was added at the expense of cornstarch (L-pectin). For the Thr study, the basal diet (T-basal) contained 0.14 g of SID Thr per MJ of DE, to which extra 0.055 or 00.11 g of SID Thr per MJ of DE was added from CS (T-CS2 or T-CS3, respectively) or from WS (T-WS2 or T-WS3, respectively; Table 2
). A sixth diet containing the same Thr level and source as CS3 but with 6% pectin was also evaluated (T-pectin). Diets were formulated based on the published nutrient content of ingredients according to NRC (1998)
. Diets were formulated in this manner to provide the animals the same daily intake of DE, and Lys or Thr within a given dietary AA level, and to ensure that daily energy intake did not limit PD (Möhn et al., 2000
; de Lange et al., 2001
).
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The L-CS2 and L-WS2 diets were prepared by blending equal portions of the L-basal and L-CS3 diets, and the L-basal and L-WS3 diets, respectively; the same approach was used in the Thr study. Feeding levels, based on 2.6 times maintenance energy requirement (NRC, 1998
), were adjusted for each experimental period based on the projected average BW of the pigs. The pigs were fed twice daily at 0830 and 1630. Water was added to the diet at a ratio of 2:1. Additional water was provided in the feeder after the pigs consumed the meal.
Nitrogen Balance
The pigs were allowed to adapt to the diets for 1 wk and were transferred from floor pens to adjustable metabolic crates on d 7 of each 14-d experimental period. Immediately before the collection period, urine collection trays were placed beneath the metabolic crates (Möhn et al., 2000
). Feces and urine were collected quantitatively from d 9 to 14.
To lower the pH to below 3, urine was collected in tared bottles containing 15 mL of 18 M sulfuric acid (Möhn et al., 2000
). Urine was collected for 24-h periods and was weighed, before 5% of the successful daily collections were taken and pooled for each animal and 5-d N-balance period. At the end of each N-balance period, 2 aliquots were taken from the pooled urine samples; one was for N analysis and another was frozen as a reserve sample.
Feces were collected using plastic bags placed around the anus of the pigs according to Zhu et al. (2005)
. Bags were replaced approximately every 3 h and were immediately frozen at 20°C. At the end of each N-balance period, feces were pooled for each pig, weighed, and homogenized using a Hobart mixer. Two sets of fecal samples were taken; one was stored at 20°C for N analysis, and another was freeze-dried for analysis of DM and titanium dioxide contents. Wasted feed, which was less than 5% of the allowance for all pigs, was pooled for each pig and N-balance period, oven-dried, weighed, and used to calculate the actual daily feed intake.
Chemical Analysis
Samples of urine, diets, and feces were analyzed for N content using standard macro-Kjeldahl analysis (AOAC, 1997
). Freeze-dried feces and diet samples were analyzed for DM and titanium dioxide contents using standard AOAC procedures (AOAC, 1997
), and fiber components (NDF and ADF) were analyzed using the Ankom filter bag technique (Ankom Technology Corporation, Fairport, NY). Total NSP contents of diets, as well as total and soluble NSP contents of WS, were determined at Massey University (Palmerston North, New Zealand) following the Englyst method (Englyst et al., 1994
). Neutral sugars were quantified using gas chromatography, and uronic acid was analyzed based on a color reaction after acid hydrolysis of the polysaccharides.
Total NSP was then calculated as the sum of the neutral sugars and uronic acid content (Englyst et al., 1994
). Soluble NSP contents of the diets were calculated based on the analyzed soluble NSP content of WS (19.25% of the total NSP) and the analyzed total NSP content of the diets. Pectin content of diet samples was determined using a colorimetric procedure according to Taylor (1993)
. Gross energy contents of diets and feces were determined using an oxygen bomb calorimeter according to standard AOAC procedures (AOAC, 1997
). Amino acid contents were determined using HPLC in the laboratory of Degussa AG (Hanau, Germany), according to Llames and Fontaine (1994)
. Reactive Lys contents of CS and WS were determined at Massey University, according to Moughan and Rutherfurd (1996)
, where reactive Lys is determined after reaction with o-methylisourea under controlled conditions, with subsequent analyses of homo-arginine.
Calculations
Total tract DM and energy digestibility, as well as fecal N excretion, were calculated using titanium dioxide as an indigestible marker (de Lange et al., 1989
; Zhu et al., 2005
). The N-balance technique was used to indirectly determine the efficiency of utilizing ileal digestible Lys and Thr intake for PD, as outlined by Zhu et al. (2005)
. Apparent ileal digestible (AID), SID, and true ileal digestible (TID) Lys and Thr contents in the diets were calculated from analyzed diet AA contents (Tables 3
and 4
) and previously determined AID, SID, and TID (Libao-Mercado et al., 2006
). Previously determined ileal Lys and Thr digestibility values were adjusted for the removal of synthetic AA from the diets, assuming 100% digestibility of synthetic AA (NRC, 1998
).
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The daily absolute disappearance of Lys and Thr (DIS, g/d), an estimate of inevitable and minimum AA catabolism in pigs fed CS-based diets (Möhn et al., 2000
; de Lange et al., 2001
), was calculated for either Lys or Thr as AID intake minus AA retention in PD minus physical AA losses with skin and hair. It was assumed that Lys and Thr losses with skin and hair were 4.04 mg/kg of BW0.75 and 3.01 mg/kg of BW0.75 per day (Moughan, 1999
), respectively.
Fractional disappearance (%DIS) of TID Lys and Thr intake was calculated as DIS (g/d) divided by daily TID intake (Zhu et al., 2005
). Efficiency of utilizing TID Lys or Thr for PD (kLys or kThr) was then calculated as 100% minus %DIS. Efficiency of utilizing SID Lys or Thr intake above maintenance AA requirements (kSID-Lys or kSIDThr) was calculated to be consistent with NRC (1998)
and was daily Lys or Thr retention in PD divided by [(SID Lys or Thr intake maintenance Lys or Thr requirements) x 100]. Maintenance requirement for Lys (36 mg/kg of BW0.75) and Thr (54 mg/kg of BW0.75) were taken from NRC (1998)
. The marginal efficiency of utilizing SID Lys or Thr intake was estimated from the slopes generated by regressing Lys or Thr retention (g/d) vs. SID Lys or SID Thr intake (g/d), respectively (Möhn et al., 2000
; de Lange et al., 2001
).
Statistical Analysis
Data were subjected to analysis of variance using the GLM procedure of SAS, v.8 (SAS Inst. Inc., Cary, NC). The statistical model was
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where
i, ßj,
ißj,
k, and
l(i) represent the effect due to group (CS vs. WS; dietary protein source), diet AA level (1 to 3) plus pectin, the interaction between group and diet AA level plus pectin, experimental period, and pig within group, respectively. Metabolic BW (BW0.75) was used as a covariate and was represented by
(Xijkl(i) X....). The various effects and contrasts were tested against the residual error (
ijkl(i)). Treatment means represented least square means.
The following contrasts were evaluated: interaction between source and diet AA level (except pectin; linear and quadratic); CS3 vs. pectin; WS3 vs. pectin; linear and quadratic contrasts for CS (basal, CS2, and CS3) and WS (basal, WS2, and WS3). Contrasts were evaluated by using the Bonferroni procedure, with the type I error rate for individual comparisons set at P < 0.006.
Total NSP intake and actual endogenous ileal AA losses, established in a previous study (Libao-Mercado et al., 2006
), were correlated with %DIS of Thr using the Corr procedure of SAS, v.8. The REG procedure of SAS was used to estimate the marginal efficiency of utilizing AA intake for retention by PD (SID Lys or Thr intake vs. Lys or Thr retention, respectively).
| RESULTS |
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All animals seemed to be in good health and consumed their feed allowances throughout the trial. During the second experimental period, however, the pig assigned the T-WS3 diet had an extremely low urine output for the first 2 d of the 5-d N balance period, resulting in 1 missing observation for this treatment.
Dietary Nutrient Composition
Actual CP contents of the Lys-limiting and Thr-limiting diets were within 4% of the anticipated dietary CP content (Tables 1
to 4![]()
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), confirming accuracy of diet preparation. In the Lys study, the analyzed total dietary Lys contents were within 4% of anticipated values (Table 1
and 3
). As a result, the actual daily Lys intakes (g/d) were close to targeted values (Table 5
). In the Thr study, the analyzed total dietary Thr contents were within 6% of anticipated values (Tables 2
and 4
). Across treatments, the actual daily Thr intakes (g/d) were generally close to targeted levels. However, for the T-WS2 treatment the determined SID Thr intake was 8% lower than for the T-CS2 treatment (Table 6
). The CS-based diets (basal, CS2, CS3), in both the Lys and Thr studies, contained 1 to 2% total NSP, which most likely reflects resistant starch present in cornstarch (Englyst et al., 1994
). Analyzed NSP content in diets containing WS (WS2, WS3) were within 7 to 8% from calculated values, based on total NSP content of WS and dietary inclusion level of WS. The L-pectin diet contained 27% more NSP than anticipated, which might be related to resistant starch in cornstarch as well.
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Efficiency of Utilizing Ileal Digestible Lysine for Body Protein Deposition
Aspects of N use, daily Lys DIS (g/d), kLys, and kSID- Lys are presented in Table 5
. There were interactive effects of dietary Lys source and Lys level (linear; P = 0.009) on PD, indicating that changes in PD with changes in Lys intakes differed between pigs fed CS and WS. A linear response in PD was observed for both CS and WS (P < 0.001), but for each gram of additional SID Lys intake, PD was 2.2 g/d greater for CS than WS. In pigs fed either CS or WS, increases in PD were associated with linear increases in urinary N excretion (P < 0.001), whereas fecal N excretion was increased only in pigs fed WS (P < 0.001).
Even though kLys and kSIDLys were calculated in different ways, these response criteria had similar values for each of the treatments. The relative treatment effects on these 2 response criteria were similar as well. In general, there was a clear interactive effect of Lys source and diet Lys level (linear; P < 0.001) on kLys, similar to what was observed for PD. Increasing diet Lys level from CS (L-basal, L-CS2, L-CS3) tended to increase daily Lys DIS (P = 0.075) but had no effect (P > 0.20) on kLys. In contrast, increasing diet Lys intake from WS (L-basal, L-WS2, L-WS3) increased daily Lys DIS and reduced kLys by more than 8 percentage units (P < 0.005). Inclusion of 6% pectin in the diet did not influence daily Lys DIS and kLys (P
0.40).
The estimated marginal efficiency of utilizing SID Lys intake for Lys retention with PD in pigs fed CS was 87% (SE 4), whereas the marginal efficiency of utilizing SID Lys intake in pigs fed WS was 72% (SE 5; Figure 1
).
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An interactive effect of dietary Thr source and Thr level (linear; P = 0.001; Table 6
) on PD was observed, similar to that for Lys. There was also a tendency toward an interaction between the effect of Thr source and the quadratic effect of Thr intake level (P = 0.059). A linear increase (P < 0.001) and no quadratic response (P > 0.10) in PD were observed for both protein sources with increasing level of Thr intake. The rate of change in PD for each gram of additional Thr intake, however, was greater for CS than for WS by about 5 g/d. In pigs fed either CS or WS, increases in PD were associated with linear increases in urinary N excretion (P < 0.001), whereas fecal N excretion was increased linearly and quadratically only in pigs fed WS (P < 0.001).
There were interactive effects of diet Thr source and Thr intake level (both linear and quadratic; P < 0.001; Table 6
) on Thr DIS, kThr, and kSIDThr, which indicates that the impact of increasing diet Thr level on Thr use differed between the 2 dietary Thr sources. In pigs fed CS-based diets, Thr DIS increased linearly with increasing Thr intake level (P < 0.01), whereas in pigs fed WS-based diets Thr DIS increased both linearly and quadratically with Thr intake level (P < 0.001). Similar to what was observed for Lys, values for kThr and kSIDThr were quite similar for each of the treatments, except for the CS diets where kSIDThr was somewhat larger than kThr. The relative treatment effects, however, were similar for both parameters. In general, increasing diet Thr levels from CS (T-basal, T-CS2, T-CS3) had no effect on kThr (P
0.10). In contrast, the inclusion of WS in the diet reduced kThr (P < 0.001) by more than 14 percentage units but only at the greatest WS inclusion level. Inclusion of 6% pectin in the diet did not influence daily Thr disappearance and kThr (P
0.10).
The marginal efficiency of utilizing SID Thr intake from CS for Thr retention with PD was 84% (SE 5), whereas the marginal efficiency was 64% (SE 5) for pigs fed WS (Figure 2
).
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| DISCUSSION |
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Observed values for kLys, kSIDLys, and the marginal efficiency of utilizing SID Lys intake for Lys retention with PD in pigs fed CS-based diets are similar to values obtained by Batterham et al. (1990)
and Mnilk et al. (1996)
but are 4 to 16 percentage units greater than the value derived by Möhn et al. (2000
; 75%) from serial slaughter data. Similarly, the observed use values for Thr in pigs fed CS-based diets are greater than those observed by de Lange et al. (2001
; 74%), who used the serial slaughter method as well. The observed systematic difference across studies can be attributed to a systematic overestimation of PD in N-balance studies, resulting largely from incomplete collection of urinary and fecal N losses (Möhn et al., 2000
). However, relative treatment effects on PD and AA use are consistent between N-balance and serial slaughter studies (Möhn et al., 2000
; de Lange et al., 2001
).
As discussed previously by Möhn et al. (2000)
, various approaches can be used to represent the main aspects of utilizing the dietary first limiting AA for PD when AA intake limits PD in growing pigs. The preferred approach is to consider TID AA intake, the chemical form in which AA are absorbed, physical AA losses for various body functions (skin and hair losses, total endogenous gut protein losses), minimum and inevitable AA catabolism, and AA retention in PD (Moughan, 1999
). Unfortunately, TID of AA, endogenous gut AA losses, and the chemical form in which AA are absorbed are not routinely evaluated in pigs fed different feed ingredients. In this study, Lys and Thr intakes are therefore expressed as SID as well as TID intake, where SID represents AID corrected for basal ileal endogenous AA losses only (Libao-Mercado et al., 2006
). Our preferred means to express AA use efficiency (k) is to relate the amounts of AA in physical body protein losses (skin and hair, endogenous gut losses) plus AA retained in body protein to TID AA intake. In this context, the inefficiency of AA use represents minimum and inevitable AA catabolism, use of AA for nonprotein compounds, and absorption of AA in a chemical form that renders them unavailable for metabolism by the pig. This approach may be further refined by representing explicitly the absorption of AA, and Lys in particular, in a chemical form that renders them unavailable for metabolism by the pig (Moughan, 1999
). As mentioned earlier, kSID- Lys and kSIDThr were consistent with estimates of AA use efficiency according to NRC (1998)
. The observed discrepancy between kThr and kSIDThr (Table 6
) can be attributed to the differing estimates of Thr requirements for body maintenance functions (de Lange et al., 2001
). According to NRC (1998)
, maintenance Thr requirements are related directly to metabolic BW, which is reflected in kSIDThr, whereas Thr losses with skin and hair and total ileal endogenous Thr losses are considered for the calculation of kThr. According to de Lange et al. (2001)
, the discrepancy between these 2 approaches to estimate Thr requirements for maintenance increases with BW. These findings highlight the need to better understand the animal and feed factors that contribute to Thr requirements for body maintenance functions. It is unlikely that an error in the estimation of endogenous ileal Thr losses (Libao-Mercado et al., 2006
) is reflected in the difference between kThr and kSIDThr; this error would be reflected in both TID of Thr and endogenous ileal Thr losses, resulting in little impact on kThr. In the current study, the slopes of the linear regression of AA retention vs. ileal digestible AA intake provide a direct estimate of the marginal use of ileal digestible Lys and Thr intake for retention with PD (Figures 1
and 2
). However, such regression analysis requires that pigs are fed multiple AA intake levels and is often prone to substantial experimental error associated with estimates of marginal use efficiency (Batterham et al., 1990
). In the current study, the errors associated with estimates of linear regression coefficients that are presented in Figures 1
and 2
(SE 0.04 to 0.05) are much larger than errors associated with estimates of kThr and kSIDThr (SE < 1.5 percentage units; at 4 observations per mean). The large error associated with estimates of the intercepts in the regression analyses illustrate some of the problems that are associated with the traditional linear regression approach that is used to quantify maintenance AA requirements (NRC, 1998
). The positive intercept for the linear relationship between Thr intake and Thr retention with PD implies Thr retention in pigs fed a Thr-free diet and is not even realistic.
In this study and in pigs fed the CS-based diets, kLys was not affected by dietary Lys level or the inclusion of 6% pectin in the diet. This is in agreement with the results reported by Möhn et al. (2000)
and Zhu et al. (2005)
, respectively. The linear reduction in kLys observed in this study with increasing dietary Lys supply from WS can be attributed to nonreactive Lys (Rutherfurd et al., 1997
) and seems not to be related to the total or soluble NSP content of WS. Based on the chemical conversion of Lys to homo-arginine under closely controlled conditions (Moughan and Rutherfurd, 1996
), 19% of the total Lys content in WS that was used in the current study was found to be nonreactive Lys (0.68% total Lys vs. 0.55% reactive Lys). This amount of nonreactive Lys is equivalent to 4.5 and 9.0% of total Lys content of diets L-WS2 and L-WS3 (Table 3
), and accounts fully for the absolute difference in kLys values between diets containing CS and WS at AA intake level 2 (4 percentage units) and level 3 (10 percentage units; Table 5
). The relative use of SID Lys in WS for PD as compared with Thr in CS (83%; Figure 1
) is consistent with reactive Lys content in WS as well. The presence of nonreactive Lys in feed ingredients can be attributed to processing or extended storage (Rutherfurd et al., 1997
). Under these conditions AA, particularly Lys, can form chemical complexes with sugars or other diet components rendering them chemically unavailable for metabolism. The current observation supports the need for a routine evaluation of reactive Lys contents in feed ingredients that are processed or stored for extended periods.
In the current study, increasing dietary Thr intake in pigs fed the CS-based diets had no impact on kThr. This observation is consistent with the findings reported by de Lange et al. (2001)
. In contrast to Zhu et al. (2005)
, the inclusion of pectin in the diet did not reduce kThr. However, in the study by Zhu et al. (2005)
, the dietary pectin + NDF contents varied between 59 and 205 g of DM/kg, whereas it was increased from 3 to 58 g of DM/kg in the current study. The kThr value based on SID Thr intake and for pigs fed T-pectin in the current study (90%) is still consistent with values observed by Zhu et al. (2005
; 89% for control diet and 80% for diets with 12% added pectin). Insoluble fiber did not influence Thr use in the study by Zhu et al. (2005)
. Possibly, soluble dietary fiber levels must exceed a threshold level before Thr use is reduced.
The impact of the dietary WS inclusion level on Thr use for PD was nonlinear and may be attributed to the relatively high PD and kThr in pigs fed the intermediate level of WS (Table 6
). Further experimentation is required, in which multiple dietary WS levels are evaluated, to establish whether a threshold inclusion level exists above which WS reduces Thr use in growing pigs. At the greatest diet Thr level, kThr in pigs fed the diet containing WS (77%) was 13 to 17 percentage units lower than values in pigs fed the diet containing CS. The kThr value of 77% may be compared with the value of 82% observed by Zhu et al. (2005)
at a comparable dietary pectin + NDF content of approximately 160 g of DM/kg. This implies that the impact of dietary fiber level on Thr use as observed by Zhu et al. (2005)
explains a substantial part, but not all, of the effect of including WS in the diet on Thr use in growing pigs.
The observed reduction in kThr at the greatest dietary WS inclusion level (T-WS3) supports earlier work (Beech and Batterham, 1991
) and indicates considerable diet effects on the efficiency of utilizing ileal digestible Thr intake for PD. Based on marginal efficiency of utilizing Thr for PD across the 3 dietary Thr intake levels (Figure 2
), the use of SID Thr in WS is 76%, relative to Thr in CS; this value is reduced to 55% if only the 2 extreme dietary Thr levels are considered. The reduction in kThr cannot be attributed to the endogenous ileal Thr losses; these are captured in the measurement of AID of Thr, which was used to calculate Thr DIS. Grala et al. (1997)
and Nyachoti et al. (1997)
suggested that part of the inefficiency of utilizing AA for PD can be attributed to metabolic costs, in the form of AA catabolism, associated with synthesis and recycling of endogenous proteins that are secreted into the digestive tract. However, in the current study diet effects on endogenous protein losses at the terminal ileum (Libao-Mercado et al., 2006
) did not explain observed difference in Thr use among the 3 diets at the greatest Thr intake level (T-CS3, T-pectin, T-WS3): both diet T-pectin and diet T-WS3 increased endogenous protein losses at the terminal ileum as compared with diet T-CS3, but only the T-WS3 diet showed a reduced Thr use efficiency. Across these 3 treatments endogenous ileal protein losses were not related to %DIS of Thr (n = 15; r = 0.11; P = 0.69). Possibly at similar endogenous ileal protein losses, dietary antinutritional factors may increase synthesis and recycling of endogenous proteins that are secreted into the gut and increase Thr catabolism (Nyachoti et al., 1997
). It is also possible that feeding diet WS3, owing to its abrasive property (de Lange et al., 1989
) or its stimulatory effect on microbial fermentation (Sakata, 1987
), increased endogenous protein losses into the hindgut. Amino acids of endogenous origin that are secreted into the hindgut, for example in Thr-rich mucin proteins, cannot be reabsorbed and represent a direct metabolic cost to the animal (de Lange et al., 1989
). The negative impact of stimulating hindgut fermentation on Thr use was recently demonstrated by Zhu et al. (2003)
. In that study the infusion of pectin into the hindgut reduced PD in pigs fed a Thr-limiting diet. The impact of microbial fermentation in the hindgut likely contributes to the high correlation across all 3 treatments (T-CS3, T-pectin, T-WS3) between total NSP intake and %DIS of Thr (n = 15; r = 0.88; P < 0.001) observed in the current study. Alternatively, NSP intake may alter the distribution of whole body protein mass, by increasing visceral organ mass, and as such influence protein turnover and AA catabolism in the pigs body (Reeds et al., 1999
) or the AA composition of retained body protein (Moughan, 1999
). The potential mechanisms by which feeding high dietary levels of WS to pigs reduces Thr use efficiency should be explored further.
| CONCLUSIONS |
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| Footnotes |
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2 Presented in part at the 2003 Conference on Digestive Physiology of Pigs held at Banff, Alberta, Canada. ![]()
3 Cargill Animal Nutrition Philippines Inc., Dampol 1st, Pulilan, Bulacan, Philippines. ![]()
4 Former address: Agribrands Purina Canada Inc., Woodstock, Ontario, Canada. Current address: Egli-Muehlen AG, Schuermatte, 6244 Nebikon, Switzerland. ![]()
5 Corresponding author: cdelange{at}uoguelph.ca
Received for publication June 7, 2005. Accepted for publication January 24, 2006.
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