J. Anim. Sci. 2004. 82:2043-2049
© 2004 American Society of Animal Science
Effects of biological type of beef steers on vitamin D, calcium, and phosphorus status1
J. L. Montgomery*,2,
J. R. Blanton, Jr.*,
R. L. Horst
,
M. L. Galyean*,
K. J. Morrow, Jr.
,3,
D. B. Wester
and
M. F. Miller*,4
* Department of Animal and Food Science and
and
Department of Range, Wildlife, and Fisheries Management, Texas Tech University, Lubbock 79409;
and
National Animal Disease Center, USDA-ARS, Ames, IA 50010; and
and
Department of Cell Biology and Biochemistry, Texas Tech University Health Science Center, Lubbock 79409
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Abstract
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Feedlot steers (n = 36) from three biological types (Bos indicus, Bos taurus-Continental, and Bos taurus-English) were used to determine the Ca, P, and vitamin D3 status of feedlot cattle. The USDA yield and quality grade traits were measured at slaughter, and the concentrations of vitamin D3 (VITD) and the metabolites 25-hydroxyvitamin D3 (25-OH D) and 1,25-dihydroxyvitamin D3 (1,25-(OH)2 D) were determined in LM, liver, kidney, and plasma. Plasma and muscle Ca and P concentrations also were determined. Biological type of cattle affected a number of carcass traits. Carcasses from Bos taurus-English cattle had more marbling, resulting in higher quality grades (P < 0.05). Carcasses from Bos taurus-Continental cattle had lower calculated yield grades (P < 0.05) than did carcasses from cattle in the other biological types. In general, differences in carcass traits resulting from biological type were consistent with other reports. Plasma and LM Ca and P concentrations were not affected (P = 0.06) by biological type of cattle, indicating that Ca and P homeostasis is a conserved trait across the different types of cattle. Plasma VITD and 25-OH D concentrations were not affected (P = 0.41) by biological type, whereas plasma 1,25-(OH)2 D concentration was lower (P < 0.05) in Bos taurus-English cattle than in Bos taurus-Continental and Bos indicus cattle. Liver VITD and 25-OH D were not affected by biological type (P = 0.76), but liver 1,25-(OH)2 D concentration was greater (P < 0.05) in Bos indicus cattle than in Bos taurus-Continental cattle. Kidney vitamin D metabolite concentrations were not affected by biological type of cattle (P = 0.21). Muscle VITD concentration was greater (P < 0.05) in Bos taurus-English cattle than in the other two biological types, and muscle 25-OH D concentrations were greater (P < 0.05) in Bos taurus-English cattle than in Bos indicus cattle. Muscle 1,25-(OH)2 D concentration was less (P < 0.05) in the Bos taurus-Continental cattle than in the other two biological types. Cooking eliminated vitamin D metabolite differences among the biological types. Our results suggest that Bos indicus cattle had greater 1,25-(OH)2 D (the biologically active form) in tissues, and greater 1,25-(OH)2 D plasma concentrations than Bos taurus cattle. Thus, the need for VITD supplementation and optimal levels of Ca and P in feedlot diets might differ between Bos indicus and Bos taurus cattle.
Key Words: Beef Breeds Calcium Phosphorus Vitamin D
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Introduction
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The vitamin D endocrine system increases dietary absorption and active transport of Ca and P, thereby maintaining Ca and P homeostasis in beef cattle. The vitamin D requirement of beef cattle is 275 IU/kg of dry diet, with an IU defined as 0.025 µg of vitamin D3 (VITD) or its equivalent, vitamin D2 (NRC, 2000
). Animals exposed to sunlight presumably do not require dietary vitamin D, whereas animals not exposed to sunlight may require dietary fortification. Sun-cured hay may provide sufficient vitamin D to prevent vitamin D deficiency (Thomas and Moore, 1951
). Hence, because vitamin D is synthesized by beef cattle exposed to sunlight and/or adequate in cattle fed sun-cured forages, vitamin D supplementation is rarely required (NRC, 2000
). However, the movement away from pasture feeding systems toward confinement feeding of stored feeds and the decrease in roughage in the diet of beef cattle might have increased the need for dietary supplementation of vitamin D.
Although a minimal concentration of VITD in the diet of beef cattle has been defined to prevent deficiency, differences in the vitamin D, Ca, and P status within different biological types of feedlot beef cattle have not been determined. Thus, our objective was to define the vitamin D, Ca, and P status of different biological types of beef cattle. Presumably, differences in vitamin D, Ca, and P status resulting from differences in biological type of beef cattle might be used as a basis to alter VITD, Ca, or P supplementation practices at the feedlot.
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Materials and Methods
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Experimental Design
The entire experimental design, treatments, and experimental animals are fully explained in our previous reports (Montgomery et al., 2004a
,b
). In total, 150 beef steers were purchased for use in this experiment. The steers were of three biological types: Bos taurus-English (n = 50), Bos taurus-Continental (n = 50), and Bos indicus (n = 50). The Bos taurus-English steers were from a single southern Texas ranch and were 87 to 100% Bos taurus-English type cattle, predominantly Angus and Hereford. The Bos taurus-Continental steers were 62 to 100% Bos taurus-Continental cattle, predominantly Charolais and Limousin, and originated from three different Texas ranches. The Bos indicus steers were 50 to 100% Bos indicus type steers, predominantly Brahman, and originated from a number of southern Texas ranches. The lightest and heaviest steers of each biological type were not used in the experiment. The remaining 144 steers were split into the three respective breed types. Within 14 d of initial processing, each steer was again individually weighed unshrunk, implanted with Ralgro (Schering-Plough Animal Health, Kenilworth, NJ), and sorted to their assigned pens. Before the dietary treatment period, two steers were removed from the experiment because of health problems (142 steers remained). The dietary treatments consisted of 0.0, 0.5, 1.0, or 5.0 x 106 IU/steer daily of VITD (Roche Vitamins Inc., Nutley, NJ) during the last 8 d of feeding. Four pens per biological type, three steers per pen, received one of the four vitamin D3 treatments for the last 8 d of feeding. Pens had partially slotted concrete floors. The total feeding period was 123 d in length. Because vitamin D3 supplementation would affect the plasma and tissue concentrations of vitamin D, Ca, and P, only data from the control animals (n = 36; 12 per biological type) were analyzed for this experiment.
Diet
After processing and sorting the cattle, the steers were all fed the same 90% concentrate diet (Montgomery et al., 2004a
). Ingredient composition of the finishing diet (DM basis) was 75.1% steam flaked corn, 10.0% sorghum silage, 4.0% cane molasses, 3.0% yellow grease, 0.9% urea, 4.5% cottonseed meal, and 2.5% supplement. Mixing procedures and the composition of the supplement were presented by Montgomery et al. (2004a)
. The diet was formulated to meet or exceed NRC (2000)
requirements for all nutrients throughout the study, and it did not contain supplemental vitamin D. Once the total diet was mixed, the amount of feed allotted to each pen was delivered using a computer-controlled belt-feeding system to each pen. Each feed bunk was evaluated visually at approximately 0700 to 0730 daily. The quantity of feed remaining in each bunk was estimated, and the daily allotment of feed for each pen was recorded. This bunk-reading process was designed to allow for little or no accumulation of unconsumed feed (0 to 0.5 kg/pen). Dietary values for DM, ash, CP, ADF, Ca, and P were presented by Montgomery et al. (2004a)
.
Slaughter and Carcass Evaluation
Blood was collected during exsanguination of each steer. The blood samples were collected into 13 x 100 mm sodium heparin (143 USP units) 10-mL Vacutainer (Becton Dickinson, Franklin Lakes, NJ) tubes. Blood samples were stored on ice for up to 3 h after sampling, and transported to the laboratory, where the tubes were centrifuged for 15 min at 500 x g. Plasma was collected from the centrifuged tubes and stored in 4-mL cryotubes at 20°C. Ionized Ca2+ concentrations were determined in duplicate by atomic absorption spectrometry (Perkin-Elmer Corp., 1965
) on a Perkin Elmer model 2380 atomic absorption spectrometer (Perkin Elmer Inc., Wellesley, MA). Plasma P concentrations were determined with a Thermomax microplate reader (Molecular Devices, Sunnyvale, CA) according to the methods of Parekh and Jung (1970)
.
Liver samples were collected from the right hepatic lobe (lobus hepatis dexter). A 30-g longissimus lumborum muscle sample was removed from each right carcass side at approximately 20 min postmortem for calpain determination according to the procedures of Koohmaraie (1990)
. Carcass pH was measured using a model 230A Orion temperature-compensated pH meter (Orion Research, Boston, MA) between the 11th and 12th ribs at 3 and 24 h postmortem. Carcass temperature also was measured at 3 and 24 h postmortem using a Hantover model TM99A-H digital thermometer (Hantover, Middlefield, CT). Hot carcass weight also was collected at slaughter. Carcasses were spray-chilled for 48 h (1°C). After chilling, carcasses were ribbed, and USDA quality and yield grade traits were recorded.
Carcasses were evaluated for percentage of kidney, pelvic, and heart fat (KPH), backfat thickness, LM area, USDA yield grade, marbling score, skeletal maturity, lean maturity, overall maturity, USDA quality grade, lean color, lean texture, lean firmness, heat ring, and the incidence of dark cutting beef (USDA, 1989
). Commission Internationale de lEclairage (CIE) L* (muscle lightness), a* (muscle redness), b* (muscle yellowness), saturation index, and hue angle values were collected from the LM of each carcass at the 12th and 13th LM planes with a Hunter Miniscan XE Plus spectrometer (Reston, VA) using illuminant D65 and a 3.5-cm aperture. Two readings were taken and averaged for each carcass. The percentage of myoglobin, oxymyoglobin, and metmyoglobin was calculated using the specific wavelength method as described by Krzywicki (1979)
. Dressing percent and yield grades were calculated from the carcass factors collected. After collection of carcass traits and color data, the carcasses were fabricated.
Chemical Analyses of Muscle
Percentage of moisture and percentage of free, bound, and immobilized water were determined on longissimus samples using the procedures of Wierbicki and Deatherage (1958)
. Muscle Ca and P concentrations were determined on longissimus samples according to AOAC (1990)
techniques. A 5-g muscle sample was placed in a crucible and dried in a vacuum drying oven at 100°C for 24 h. Samples were then ashed in a muffle furnace at 625°C for 18 h. Samples were then cooled to room temperature and dissolved in 50 mL of 3 N HCl and boiled to an approximate volume of 25 mL. Samples were then filtered through Q2 filter paper (Fisher Scientific, Houston TX) into a 100-mL flask and diluted to volume. Thereafter, 4 mL of the diluted sample was placed in a test tube with 5.5 mL of distilled water and 0.5 mL of 5% (wt/vol) solution of lanthanum chloride. Calcium concentrations were determined in duplicate by atomic absorption spectrometry (Perkin-Elmer Corp., 1965
) on a Perkin Elmer model 2380 atomic absorption spectrometer (Perkin Elmer Inc.). Muscle P concentrations also were determined colormetrically on the diluted samples (in duplicate) according to AOAC (1990)
procedures using a Beckman DU-50 Spectrophotometer (Beckman Coulter, Chaska, MN).
Vitamin D3, 25-Hydroxyvitamin D3, and 1,25-Dihydroxyvitamin D3 in Plasma, Beef, Liver, and Kidney
Vitamin D3, 25-hydroxyvitamin D3 (25-OH D), and 1,25-dihydroxyvitamin D3 (1,25-(OH)2 D) concentrations were quantified by a modification of the methods of Montgomery et al. (2000)
, as explained in Montgomery et al. (2002)
. For kidney, liver, muscle, and cooked steaks (samples were cooked to 71°C then stored at 4°C overnight), 2-g samples of tissues were homogenized in 8 mL of PBS with a Polytron (Kinematica AG, Littan-Lucerne, Switzerland) for 60 s. A 2-mL aliquot of the homogenate was transferred to a 29- x 147-mm capped glass tube. Approximately 50 ng of vitamin D2 and 1,000 cpm of 3H-25-OH D and 3H-1,25-(OH)2 D were added to the 2-mL aliquot for recovery estimates. Samples were then extracted, and the concentration of vitamin D3 was determined by HPLC with a Supelco Sil LC-5 column (0.46 x 25 cm) at 2 mL/min. Tissue (liver, kidney, and muscle) concentrations of 25-OH D and 1,25-(OH)2 D were determined by RIA after HPLC separation. Plasma VITD, 25-OH D, and 1,25-(OH)2 D concentrations were determined using similar methods.
Statistical Analyses
Data were analyzed using a completely random design with three (biological type) treatments. For all the analyses, the experimental unit was a pen of three steers, and a significance level of 5% was used. Data were analyzed according to Steel and Torrie (1980)
, and least squares means were calculated using the Proc GLM procedures of SAS (SAS Inst., Inc., Cary, NC). Differences among treatment means were determined using the PDIFF option.
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Results and Discussion
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Carcass Traits
Biological type of cattle has been shown to affect a number of carcass traits, including yield and quality grade factors. In the current study, dressing percent, hot carcass weight, percentage of KPH, carcass pH, and carcass temperature measurements were not affected by biological type (P = 0.26; Table 1
). Our results agree with those of Page et al. (2001)
, who reported that dressing percent, hot carcass weight, KPH, carcass pH, and carcass temperature did not differ between Bos taurus and Bos indicus carcasses. In the current study, the different lean color factors, lean and skeletal maturity, lean texture, and lean firmness measurements were not affected by biological type (P = 0.09; Table 1
). Shackelford et al. (1994)
reported that Bos indicus cattle were more likely to have lighter cherry red-colored lean than Bos taurus cattle; however, lean color and texture were found to have considerable genetic variation. The current study involved fewer animals than did the study of Shackelford et al. (1994)
; therefore, lack of differences in lean color among the different biological types may have been attributed to our small sample size.
As expected, a number of carcass quality and yield factors were affected by biological type in our study. Marbling scores and quality grades were greater in the carcasses from Bos taurus-English cattle than those from carcasses of the Bos indicus and Bos taurus-Continental groups (P < 0.05; Table 1
). Huffman et al. (1990)
also noted that Angus cattle had greater marbling and higher quality grades than did Brahman cattle, and Wheeler et al. (1996)
indicated that Bos taurus-English cattle tended to have more marbling and higher quality grades than did Bos taurus-Continental cattle. Conversely, Itoh et al. (1999)
reported no difference in i.m. fat between Bos taurus-English and Bos taurus-Continental breeds. Carcasses from the Bos taurus-Continental group of cattle had lower (P < 0.05) back fat thickness than Bos indicus and Bos taurus-English carcasses. Wheeler et al. (1996)
also reported that Bos taurus-English cattle tended to have carcasses with greater numerical yield grades and marbling contents than Bos taurus-Continental cattle, whereas Pringle et al. (1997
; 1999)
reported that marbling and yield grades were greater in Bos taurus-English type cattle than in Bos indicus cattle.
In the current study, carcasses from the Bos taurus-Continental group had lower (P < 0.05) adjusted back fat thickness as measured by adjusted preliminary yield grade than did carcasses from Bos taurus-English cattle, and the Bos taurus-Continental group had lower (P < 0.05) numerical yield grades than the other biological types of carcasses (Table 1
). Furthermore, carcasses from the Bos taurus-Continental group in our study had larger (P < 0.05) LM area than did Bos indicus carcasses; this finding agrees with the results reported by Huffman et al. (1990)
. In general, the effects of biological type of cattle on carcass characteristics were expected and consistent with previously published reports cited above.
Muscle and Plasma Properties
Plasma and muscle concentrations of Ca and P did not differ between the three biological types (P = 0.31; Table 2
). Because there were no differences in Ca or P homeostasis between the three biological types tested, the current study provides further evidence that Ca and P homeostasis are tightly regulated within and across biological types of cattle (Horst, 1986
). However, the Ca-activated µ-calpain enzyme activity in longissimus was greater (P < 0.05) in samples from Bos indicus cattle than in Bos taurus-Continental cattle, whereas longissimus m-calpain activity was not affected by breed type. In contrast, Johnson et al. (1990)
, Whipple et al. (1990)
, and Pringle et al. (1999)
reported no differences in µ-calpain or m-calpain activity between Bos taurus and Bos indicus cattle; however, Wheeler et al. (1990)
and Pringle et al. (1997)
reported that increasing the percentage of genetic makeup of Bos indicus cattle led to decreased µ-calpain activity compared with Bos taurus-English cattle. Similar to our results, Wheeler et al. (1990)
and Pringle et al. (1997)
) reported that m-calpain activity was not influenced by biological type. Thus, our results indicate that Bos indicus cattle had increased µ-calpain activity, whereas most other experiments have indicated the opposite. It should be noted that the inhibitor of the Ca-activated calpains, calpastatin, was not measured in the current study, but activity of this protein has been reported to be increased in Bos indicus cattle compared with Bos taurus cattle (Johnson et al., 1990
; Whipple et al., 1990
; Pringle et al., 1997
). Percentages of longissimus moisture, free water, bound water, and immobilized water did not differ among the biological types (P = 0.08) evaluated in the current study.
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Table 2. The effect of biological type of feedlot steers on basal plasma and muscle Ca and P concentrations, calpain activity, and percentage of muscle moisture, free water, bound water, and immobilized water
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Vitamin D Residues and Status
Vitamin D3 or vitamin D2 supplied by the diet is transported by a vitamin D-binding protein to the liver. The liver functions as a storehouse of vitamin D, typically preventing the circulation of high levels of vitamin D in the blood stream; the basal concentration of vitamin D in the blood of dairy cattle is 1 to 3 ng/mL of plasma (Horst and Littledike, 1982
). In the liver, VITD is processed into an intermediate, 25-OH D, which is not the active form of the vitamin, but it is typically stored in the liver until required (DeLuca, 1979
; Reichel et al., 1989
). The production of 25-OH D depends on the vitamin D content of the diet (NRC, 2001
), but plasma 25-OH D has been reported to be the best indicator of the vitamin D status of animals (Horst et al., 1994
), with basal concentrations ranging from 30 to 50 ng/mL of plasma in dairy cattle. When the active form of vitamin D (steroid) is needed, 25-OH D is transported to the kidney, where the biologically active form, 1,25-(OH)2 D, is produced. The production of the biologically active 1,25-(OH)2 D is controlled by parathyroid hormone and by the Ca and phosphate concentrations in the blood, as well as by feedback regulation from the active form of the vitamin (Norman and Henry, 1993
; Feldman et al., 1998
). In the current study, VITD and 25-OH D concentrations in the liver were not (P = 0.06) influenced by biological type of cattle (Table 3
), but 1,25-(OH)2 D liver concentrations were. Liver 1,25-(OH)2 D concentrations were greater in Bos indicus than in Bos taurus-Continental cattle (P < 0.05). Kidney VITD, 25-(OH) D, and 1,25-(OH)2 D concentrations were not affected (P = 0.21) by biological type.
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Table 3. The effect of biological type of feedlot steers on vitamin D3, 25-hydroxyvitamin D3, and 1,25-dihydroxyvitamin D3 concentrations in liver, kidney, muscle (strip loin) and plasma samplesa
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Muscle (longissimus) concentrations of VITD were greater (P < 0.05) in Bos taurus-English cattle than in Bos taurus-Continental or Bos indicus steers (Table 3
). Similarly, muscle concentrations of 25-(OH) D were greater (P < 0.05) in Bos taurus-English steers than in Bos indicus steers. Raw LM concentrations of 1,25-(OH)2 D were less (P < 0.05) in Bos taurus-Continental cattle than in Bos indicus and Bos taurus-English cattle. Cooked (71°C) longissimus steak VITD, 25-(OH) D, and 1,25-(OH)2 D concentrations were not affected by biological type of cattle; however, the different vitamin D metabolites (as-is basis) tended to be increased in concentration as a result of moisture loss within steaks.
Plasma concentrations of VITD and 25-(OH) D were not affected (P = 0.41) by biological type of the steers (Table 3
); however, plasma 1,25-(OH)2 D concentration was lower (P < 0.05) in Bos taurus-English steers than in Bos indicus and Bos taurus-Continental steers. The active form of vitamin D that affects Ca and P homeostasis is 1,25-(OH)2 D (Horst and Littledike, 1982
; Horst, 1986
). The 1,25-(OH)2 D concentrations of plasma and the different tissues tended to be greater, although not consistently so in all tissues, in the Bos indicus cattle than in the other two biological types. Tissues may function as a storehouse for the vitamin D metabolites, especially VITD and 25-(OH) D. Thus, Bos indicus cattle seem to have high concentrations of plasma 1,25-(OH)2 D, possibly as a result of the storage of the VITD and 25-(OH) D. Differences in storage were especially noticeable between Bos indicus and Bos taurus-Continental cattle. Because Bos indicus cattle originated from a hot, sunny area (India), this difference in 1,25-(OH)2 D metabolism and tissue storage may be attributable to environmental adaptation of Bos indicus cattle compared with Bos taurus cattle, which originated in England and Europe. Furthermore, plasma concentrations of 1,25-(OH)2 D were less in the Bos taurus-English cattle than the other two biological types, possibly indicating a lower baseline plasma concentration. A lower plasma concentration of 1,25-(OH)2 D in Bos taurus-English cattle might be attributable to genetic adaptation to an environment with less sunlight vs. that of the Bos taurus-Continental and Bos indicus breeds.
The quantity of dietary vitamin D required to provide adequate substrate for production of 1,25-(OH)2 D is difficult to define (NRC, 2001
). Sommerfeldt et al. (1983)
indicated that orally administered tritium-labeled vitamin D2 had one-third to half the activity of VITD, possibly because of the degradation that occurs in the rumen (Sommerfeldt et al., 1979
). However, more recent data suggest this discrimination of vitamin D2 is the result of decreased binding of vitamin D2 metabolites to vitamin D-binding proteins in the blood, leading to more rapid clearance of vitamin D2 metabolites from plasma (Horst and Littledike, 1982
; NRC, 2001
). Thus, VITD supplementation may be more effective in a feedlot diet than the vitamin D2 typically found in plant products. Results of the current study indicate that vitamin D metabolite metabolism may have been modified by adaptation over time in Bos indicus cattle compared with Bos taurus cattle. Because Bos indicus cattle have a propensity to store the active metabolite of vitamin D, 1,25-(OH)2 D, in tissues and have increased blood concentrations of the metabolite, it may be feasible to lower the VITD supplementation, and perhaps the Ca and P content, in the feedlot diet without negatively affecting Ca and P homeostasis or feedlot performance. This might provide a small economic advantage for Bos indicus cattle. Alternatively, high plasma and tissue concentration of 1,25-(OH)2 D might suggest that Bos indicus cattle have higher nutritional requirements for VITD than other biological types. Thus, additional research is needed before practical recommendations can be made.
Bos indicus steers had higher concentrations of liver and muscle 1,25-(OH)2 D compared with Bos taurus-Continental cattle, and higher concentrations of plasma 1,25-(OH)2 D compared with Bos taurus-English cattle, thereby indicating that Bos indicus cattle may have higher baseline concentrations of the active form of vitamin D. Perhaps the higher levels of 1,25-(OH)2 D within Bos indicus cattle makes them more refractory to the effects of vitamin D on Ca uptake by muscle tissue. However, muscle Ca was not affected by biological type of cattle, whereas the Ca-activated protease µ-calpain was greater in Bos indicus cattle. These differences in baseline 1,25-(OH)2 D and calpain data might lead one to conclude that Bos indicus cattle should be more tender than Bos taurus cattle, a conclusion not substantiated by the literature (Wheeler et al., 1990
, 1996
). It is important to note that a number of contributing factors, such as parathyroid hormone concentration, muscle calpastatin concentration, and implants, can affect vitamin D and Ca concentrations and, possibly, meat tenderness. Further research into these matters is needed.
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Implications
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Calcium and phosphorus homeostasis are closely regulated, resulting in minimal differences in tissue and blood Ca and P concentrations among biological types of cattle. Nonetheless, vitamin D metabolite concentrations in tissues and blood were influenced by biological type of cattle. Bos indicus cattle had a propensity for greater concentrations of the active metabolite of vitamin D, 1,25-dihydroxyvitamin D3, in tissue. Bos taurus-English cattle had decreased blood concentrations of 1,25-dihydroxyvitamin D3 compared with Bos taurus-Continental and Bos indicus cattle. Further research is needed to determine the practical consequences of these differences in vitamin D concentrations among biological types of cattle.
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Footnotes
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1 This research was funded in part by grants from the National Cattlemens Beef Association, Texas Beef Council, Roche Vitamins, Inc., and the Center for Feed Industry Research and Education at Texas Tech University. Texas Tech Univ. Publ. No. T-5-452. 
2 Current address: Intervet Inc., 29160 Intervet Lane, Millsboro, DE 19966. 
3 Current address: Meridian Bioscience, Inc., 3471 River Hills Dr., Cincinnati, OH 45244. 
4 Correspondence: Box 42162 (phone: 806-742-2804; fax: 806-742-0169; e-mail: mfmrraider{at}aol.com).
Received for publication October 7, 2003.
Accepted for publication April 5, 2004.
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