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* Wageningen Institute of Animal Sciences, Wageningen Agricultural University, 6700 AH, Wageningen, The Netherlands and Institute of Grassland and Environmental Research, North Wyke, Okehampton, EX20 2SB, UK
ABSTRACT
INTRODUCTION
EXPERIMENTAL DATA
MODEL DESCRIPTION
RESULTS AND DISCUSSION
FOOTNOTES
LITERATURE CITED
ABSTRACT 
This paper describes the development of a mechanistic model integrating protein and energy metabolism in preruminant calves of 80-240 kg live weight. The objectives of the model are to gain insight into the partitioning of nutrients in the body of growing calves and to provide a tool for the development of feeding strategies for calves in this weight range. The model simulates the partitioning of nutrients from ingestion through intermediary metabolism to growth, consisting of accretions of protein, fat, ash and water. The model contains 10 state variables, comprising fatty acids, glucose, acetyl-CoA and amino acids as metabolite pools, and fat, ash and protein in muscle, hide, bone and viscera as body constituent pools. Turnover of protein and fat is represented. The model also includes a routine to check possible dietary amino acid imbalance and can be used to predict amino acid requirements on a theoretical basis. The model is based on two experiments, specifically designed for this purpose. Simulations of protein and fat accretion rates over a wide range of nutrient input suggest that the model is sound. It can be used as a research tool and for the development of feeding strategies for preruminant calves.
KEY WORDS: veal calves · computer simulation · mathematical model · protein metabolism · energy metabolismINTRODUCTION
During the last decade, the interest of meat producers has shifted from obtaining maximum growth of the animal to production of lean meat and an increase in the efficiency of nitrogen utilization. Simultaneously, interest in growth simulation models has increased because they provide a tool for better understanding of complex growth processes. Besides being of interest as a research tool, such models can be used in the development and evaluation of feeding strategies. For preruminant calves, no such models are available. Furthermore, the distribution of nutrients within the body of preruminant calves differs considerably from that of true monogastric animals (Gerrits et al. 1996
) so that the same principles cannot be automatically applied. The objectives of the model described in this paper are to gain insight into the partitioning of nutrients in the body of preruminant calves and to provide a tool for the development of feeding strategies for calves between 80 and 240 kg live weight (Lw).6
This paper describes a dynamic, mechanistic model that simulates the partitioning of ingested nutrients through intermediary metabolism to growth, consisting of accretion of protein, fat, ash and water. The model is based on literature data and specifically designed experiments with Holstein-Friesian × Dutch-Friesian calves (Gerrits et al. 1996). Protein metabolism of muscle, visceral, hide and bone is explicitly considered, and a calculation routine for dietary amino acid imbalance is developed. The model is designed for evaluation of long-term feeding strategies for growing preruminant dairy calves and does not consider diurnal or postprandial metabolic events. In preruminants, feed completely bypasses the rumen. Therefore, the model may also provide a valuable tool for evaluating utilization of absorbed protein and, to a lesser extent, energy in ruminating calves.
EXPERIMENTAL DATA
). The experiments were similar in design and conducted in two weight ranges: 80-160 kg and 160-40 kg Lw (Gerrits et al. 1996). Briefly, in each experiment, 36 calves were assigned in a 6 × 2 factorial arrangement to one of six protein intake levels at one of two protein-free energy intake levels. Milk proteins were used as the only feed protein source. Calves were slaughtered at the beginning and end of each experiment and analyzed for nitrogen, fat, dry matter and ash content. At 120 and 200 kg Lw, total collections of feces and urine were obtained from all animals for 5 d. Feces were analyzed for dry matter, nitrogen, fat and ash content, and urine for nitrogen, energy and creatinine content. In designing the experiments, the attempt was made to establish relationships over a wide range of nutrient input. Depending on dietary treatment, average daily gain of the empty body varied between 640 and 1340 g/d and 420 and 1370 g/d for the growth ranges of 80-160 and 160-240 kg Lw, respectively.
MODEL DESCRIPTION
General
Choice of pools and representation of fluxes. A schematic representation of the model (principal pools and transactions) is shown in Figure 1. The model traces nutrients from ingestion through intermediary metabolism into body stores. The body storage pools comprise chemical fat, ash and four protein pools. Body protein is split up into protein pools from several anatomical tissues. The following types of protein were considered: muscle, viscera (including blood), bone and hide. Muscle protein is defined as non-bone, non-hide protein in carcass, head and tail and therefore includes small amounts of other tissues (brain, connective and adipose tissue). The metabolite pools, driving the transactions between pools, were selected to represent the major effects found in the experiments (Gerrits et al. 1996) and, additionally, to allow for distinguishing glucose from fat metabolism. The following metabolite pools are considered: amino acids, fatty acids, glucose and acetyl-CoA equivalents.
Table 1.
Two-letter abbreviations for entities used in the model simulating metabolism of growing preruminant calves
Table 2.
General notation used in the model simulating metabolism of growing preruminant calves1
Table 3.
Parameter values of the model simulating metabolism of growing preruminant calves1
. This type of mathematical representation has been used before in aggregated models of metabolism (e.g., France et al. 1987, Pettigrew et al. 1992). Transactions between pools are characterized by substrate concentrations, a maximum velocity, affinity and inhibition constants and steepness parameters, as illustrated by Pettigrew et al. (1992). Two-letter symbols used in the model are listed in Table 1, the notation is summarized in Table 2, and parameter values are presented in Table 3. Simulations started at 80 kg Lw because that is the beginning weight in the experimental work.
, Toullec and Guilloteau 1989). To account for the energy yield from fermentation in the hindgut, lactose digestibility is set to an intermediate value of 95%. Starch digestibility has been shown to depend on age of the calves, source, pretreatment and level of inclusion in the diet (Toullec 1989, Van der Honing et al. 1974). For simulations in this paper, starting at 80 kg Lw, starch is assumed to be pregelatinized, it is included at a level of <5% in the diet and its digestibility is assumed to be 95%. Fecal digestibility of dietary fat varies between 94 and 97%, depending on, for example, dietary fat source (Hof 1980, Tolman and Demeersman 1991) and does not significantly differ from values obtained at the terminal ileum (Hof 1980). A value of 95% is adopted. The true digestibility of milk proteins has been shown to be close to 100% (ARC 1980, Tolman and Beelen 1996). Consistent with this observation, apparent digestibility of milk proteins varies with protein intake, as observed in the experiments and discussed by Gerrits et al. (1996). In the model, the true digestibility of milk proteins is set to 100%, and, as described later, net endogenous protein losses are modeled as a drain from the visceral protein pool.
Absorption and transport of nutrients.
In the context of this model, absorption is the transfer of nutrients from the intestinal lumen into the portal blood or lymph. Energy costs of nutrient absorption are represented in the model. Dietary fat (triglycerides) is assumed to be absorbed as mono-acylglycerol and two fatty acids (Brindley 1984). Laplaud et al. (1990) have shown that 80% of fat in intestinal lymph is present in the form of triglycerides. Therefore, energy costs are introduced for re-esterification of the fatty acids in the mucosal cell, set at 1.33 mol ATP per fatty acid equivalent (Stryer 1981). Re-esterification causes the absorption of fat to have no net effect on membrane potential. Therefore, no extra absorption costs were calculated.
). The energy costs involved are set to 0.33 mol ATP/mol monosaccharide, which is the amount of ATP needed to pump 1 mole Na+ through a membrane (Mandel and Balaban 1981).
). Therefore, energy costs for absorption from the intestinal lumen are difficult to estimate. In analogy to absorption of monosaccharides, absorption costs are set to 0.33 mol ATP/mol amino acid, considering both lower costs for diffusion, Na+-independent transport and peptide absorption, and higher costs if reabsorption of endogenous secreted protein is accounted for, as discussed by Gill et al. (1989b).
, Lobley 1990, McBride and Kelly 1990). According to reviews by Lobley (1990), McBride and Kelly (1990) and Simon (1989), ATP cost of proteolysis varies, depending on the mechanism involved (e.g., lysosomal vs. non-lysosomal). Energy costs are assumed to be 1 mol ATP/peptide bond cleaved, based on the energy yield of inhibiting intracellular proteolysis in reticulocytes described by Rapoport et al. (1985). Energy costs of urea synthesis are 4 mol ATP/mol urea synthesized and are included in the energy yield of amino acid oxidation.
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Table 4. Stoichiometry of principal transactions in the model simulating metabolism of growing preruminant calves1,2 |
and Schulz et al. (1974). Describing the relationships between water and protein, allometric relationships are adopted because of the good fit of the data and sensible behavior of allometry close to zero and infinity. Empty body weight is approached by sum of the body fat, body ash and body protein pools, and the water attached to the protein pools. In the experiments, protein, ash, fat and water did not account for 100% of the fresh material analyzed in the body composition analysis. From the experiments, a multiplication factor of 1.03 was estimated for the conversion of the sum of the body pools and water into QEw (Equation 11.1, see Table 7 for numbered equations). Live weight is assumed to be closely related to QEw . From the experiments, a multiplication factor of 1.11 was estimated (Equation 11.2).
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Table 7. Mathematical statement of the model simulating metabolism of preruminant calves1 |
). Therefore, for transactions that take place only in adipose tissue (FaFb, AyFa), the size of the reaction site is considered to be QFb0.67 (Equations 8.9 and 6.8, respectively).
Protein metabolism
General. For simplicity, all amino acids, available for synthesis or oxidation, are combined into one metabolite pool. Four body protein pools are represented, shown in the composite box in Figure 1. In the context of the present model, (crude) protein is defined as the sum of aminoacyl residues plus non-protein nitrogenous components. The amino acid composition of the protein pools and of the dietary protein, and the protein factors for the conversion of nitrogen into protein are discussed later in this paper. The fractional degradation rate (FDR) is assumed fixed for each protein pool. It was decided to make the development of the muscle protein pool dependent on substrate concentration and to relate the development of the other protein pools to muscle protein. For that purpose, relationships between accretion rates of protein in muscle and protein in bone, hide and viscera were estimated from the experiments (Fig. 2). In the model, the protein synthesis rate in bone, hide and viscera is calculated by summation of net accretion and degradation rates. Protein accretion in bone and hide appears to have some priority at low muscle protein accretion rates (Fig. 2). It may be argued that muscle growth follows rather than precedes skeletal development, and thus bone protein accretion should drive muscle protein accretion rather than the reverse. Relating muscle protein to bone protein, however, would mean a considerable enlargement of the errors made in the determination of the bone protein pool size. The approach used has the advantage of minimizing the error made because muscle protein is by far the largest of the protein pools.
.
Body protein pools. Estimation of synthesis, degradation and net accretion rates of the four body protein pools is discussed below.
found an FDR of muscle protein of 1.9%/d in milk-fed calves weighing 120 kg, using urinary 3-methylhistidine excretion as a measure for myofibrillar protein degradation. Using the same method, Jones et al. (1990) found an FDR of 3.8%/d in freely fed steers of 320 kg Lw. The FDR is set at 2.0%/d, accounting for a slight overestimate of FDR due to the 3-methylhistidine method (Simon 1989).
). It is realized, however, that concentrations of amino acids and acetyl-CoA themselves are unlikely to drive muscle protein synthesis. It is, however, the simplest way of representing the effects of changed nutrient input and is considered appropriate for the level of aggregation applied in the present model (see also discussion). The Vmax of muscle protein synthesis is expressed as a function of muscle protein mass (Equation 1.16). As discussed by Moughan (1994), maximum protein deposition capacity remains relatively constant over a large range of body weights for grower/finisher pigs and decreases to zero at maturity. However, for dairy calves, little is known about maximum (muscle) protein deposition capacity. Therefore, a simple function of muscle protein mass is used, which was calculated to result, in combination with the fixed FDR, in a slight increase in muscle protein deposition capacity with increasing muscle protein mass.
for nonsomatotropin-treated steers of about 370 kg Lw, by Lobley et al. (1980) for two heifers of 250 kg Lw and pigs of about 75 kg Lw (reviewed by Simon 1989), a value of 25%/d is chosen for FSR. This FSR was used in combination with the visceral protein retention rates, measured in the experiments, to estimate a value for the FDR, which is used in the model. From these data, FDR was computed at 24.5%/d.
), and that the flow of endogenous protein depends on the dry matter intake. The equation used (Equation 5.2) is based on data obtained with 115 milk-protein-fed calves ranging in body weight from 60 to 270 kg and dry matter intakes varying from 1 to 3 kg/d (Gerrits et al. 1996; G. H. Tolman, T.N.O. Nutritional Food Research Institute, Wageningen, The Netherlands, unpublished). The value obtained is slightly higher than the value adopted by ARC (1980), i.e., 2.46 (R2 = 0.59) vs. 1.90 g N/(kg dry matter intake·d). The relationship between visceral protein and muscle protein accretion was estimated from the experiments (Fig. 2). Protein synthesis (in g/d) is calculated as the sum of net accretion, degradation and endogenous losses (Equation 5.1).
). From this value and hide protein retention from the experiments, a corresponding FDR of 4.0%/d was calculated. Daily losses from this pool (hair and skin) are set at 0.11 Lw0.75 (in g/d; ARC 1980). Protein degradation rate is calculated from pool size and FDR; synthesis rate is calculated as the sum of degraded protein, net protein accretion and hair and skin losses (Equation 3.1). The relationship between hide protein accretion and muscle protein accretion was estimated from the experiments (Fig. 2).
). From this value and bone protein retention from our own experiments, a corresponding FDR of 6.1%/d was calculated, three times the chosen FDR for muscle protein. This value is chosen for the model. Bone protein synthesis is calculated as the sum of net accretion and degradation rate (Equation 2.1). Bone protein accretion rate is related to muscle protein accretion rate (Fig. 2).
. The profiles for muscle and hide protein are estimated from the profiles of carcass and hide, head, feet and tail samples, analyzed by Williams (1978). This estimation involved separation of the bone parts of these fractions, based on the difference in ash content of these fractions. Considering the definition of muscle protein within the model, the amino acid profile as obtained via this estimation is preferred over the amino acid profile of veal, which does not include much collagen protein. The amino acid profile of muscle protein therefore contains fewer essential amino acids than reported for veal by Vervack et al. (1977). The amino acid composition of hair and skin losses is assumed equal to the amino acid composition of the hide. The amino acid profile of the net endogenous secreted protein is assumed to be identical to the amino acid profile of ileal digesta of milk-fed calves (averaged from Lallès et al. 1990 and Tolman and Beelen 1996). The dietary protein used for the simulations in this paper was based on milk proteins, as used in the experiments (Gerrits et al. 1996).
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Table 5. Amino acid composition of bone, hide, muscle, viscera and endogenous losses in preruminant calves and of a typical milk replacer diet |
and Karman and van Boekel (1986). It is assumed that in all proteins, half of the aspartate and glutamate is in the amide form, which has been shown for casein by Walstra and Jenness (1984) and is often assumed for other proteins as well (e.g., Livesey 1984). The protein factors, presented in Table 5, are quite a bit lower than the factor 6.25, which is commonly applied. This factor, however, has been shown to be erroneous for many types of protein, mainly as a result of neglect of the amides glutamine and asparagine (Rafecas et al. 1994). The body protein pools and the amino acid pool are based on crude protein, as defined above. For the calculation of amino acid imbalance, the true protein factors are used.
Amino acid pool, Aa.
Inputs to this pool are from absorption (Equation 1.2) and from degradation of body protein (Equations 1.4-1.7). Outputs are to body protein synthesis (Equation 1.9-1.12), to oxidation (Equation 1.8) and as endogenous urinary N losses (Equation 1.13). Stoichiometry of these transactions is based on equilibrium of nitrogen and expressed per mole average amino acid residue. This average amino acid residue was based on the weighted mean of the amino acid residues of the body protein pools. Synthesis of dispensable amino acids (DAA) is modeled as input and output of the amino acid pool (Equation 1.3). Therefore, energy consumption is the only effect of this flux. The flux is calculated in the imbalance routine described below and represents the difference between ingested and deposited DAA. Synthesis of DAA requires both a carbon and a nitrogen source. Although Kreb's cycle intermediates such as 
-ketoglutarate, pyruvate and oxaloacetate usually provide the carbon, the nitrogen is provided by NH3 from other amino acids. In the model, both carbon and nitrogen are assumed to be provided by nonlimiting amino acids. To correct for the difference in carbon source (Kreb's cycle intermediates vs. amino acids), energy costs were introduced. These energy costs were calculated as the difference between the energy costs for synthesis of DAA from glucose and NH3 , and the energy yield from oxidation of these amino acids. Stoichiometry of synthesis of DAA from glucose and NH3 , as well as energy yield from oxidation, was adopted from Schulz (1978), and average energy costs were estimated at 3 mol ATP/mol DAA synthesized. Transport and transamination costs are ignored.
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Table 6. A comparison between the inevitable amino acid oxidation rates from the model for preruminant calves (resulting from the application of different oxidation proportions), and minimum oxidation rates and amino acid requirements for maintenance in growing pigs |
], because amino acid oxidation may well be increased in such situations. Endogenous urinary N excretion is assumed to be 52, 22, 13, 10 and 3% by origin from urea, creatinine, allantoin, amino acids and uric acid, respectively. Calculating this composition, literature values were adopted for excretion of allantoin and uric acid (Chen et al. 1990), amino acids (Lynch et al. 1978) and creatinine (Lindberg 1985 and our experiments). Urea was calculated to make EUN add up to 180 mg/(kg0.75·d). To correct for the difference in energy content per gram nitrogen between amino acids and EUN, an energy yield of 60 kJ/g N excreted is introduced, assumed to be released as ATP.
). Amino acid oxidation is assumed to occur in the liver. The maximum velocity (VAa,AaAy), therefore, is expressed as a function of liver weight. Liver weight (in kg) was estimated from the experiments as a function of visceral protein mass (QPv ; Equation 11.3). The Vmax was calculated from the N balance data of Robinson et al. (1996), who infused extremely large amounts of casein in the abomasum of Holstein steers (highest N input 231 g/d, steers of 200 kg Lw; 142 g N/d excreted with urine). Despite the extreme treatment of Robinson et al. (1996), the Vmax derived from these data is most certainly an underestimate of the theoretical Vmax because in in vivo experiments, conditions will never be optimal (Gill et al. 1989a). To approach a realistic Vmax , the value obtained was increased by 33%. The effect of increasing the Vmax on the rate of a transaction is discussed by Black and Reis (1979). Energy cost of urea excretion by the kidney is assumed to be 0.1 mol ATP/mol urea (Martin and Blaxter 1965).
, the presence of degradive enzymes in tissues is presumably responsible for the inevitable loss of a fraction of amino acids, even at low levels of intake. Consequently, potential reutilization of degraded protein for protein synthesis is always <100%. Furthermore, potential reutilization decreases with protein intake and depends on the amino acid considered (Moughan 1994, Simon 1989). Unfortunately, information on the magnitude of the inevitable oxidative losses of specific amino acids in preruminants is scarce. It seems sensible, however, to make these losses for a specific amino acid dependent on the amount of that amino acid passing the site of oxidation. In the model, the proportion of each amino acid inevitably oxidized is set to 0.02 times the daily amount of that amino acid entering the amino acid pool. This represents a 2% chance of each amino acid being oxidized when passing the site of oxidation. This way, both increased protein turnover and increased protein intake lead to increased oxidative losses. To place this assumption in perspective, Table 6 presents the effect of applying an inevitable oxidation proportion of either 2 or 5% on daily amounts of amino acids inevitably oxidized, compared with minimal rates of oxidation in pigs (reviewed by Fuller 1994) and with the maintenance requirements of growing pigs (Fuller et al. 1989). Maintenance requirements, estimated as the amount needed to maintain N equilibrium, would include these minimal oxidative losses (Fuller 1994). From Table 6, it appears that, for the amino acids reported by Fuller (1994), minimal oxidation is lower than the amount oxidized, caused by application of the 2%. Compared with the amino acid requirements for maintenance, which also includes other amino acid losses (e.g., endogenous fecal losses and scurf losses), application of 2% results in higher losses for most amino acids. The effect of changing this percentage on amino acid imbalance is discussed in a companion paper (Gerrits et al., in press).
Table 8.
Calculation of imbalance of dietary amino acids, synthesis of dispensable amino acids and requirements for indispensable amino acids in the model simulating metabolism of preruminant calves1,2
) and ruminants (Davenport et al. 1990). Therefore, it is assumed that a minimum of 40% of the arginine deposited has to be supplied through the diet, as suggested by Fuller (1994). This has been included in the identification of the limiting indispensable amino acid.
Energy metabolism
Body fat pool, Fb. Inputs to the body fat pool are from the fatty acid and glucose pool (Equations 9.1 and 7.7). Outputs are to the fatty acid and glucose pool (Equations 9.2 and 7.5). The body fat pool represents chemically determined fat, assumed to comprise only triacylglycerol. The molecular weight is set at 884 g/mol. Data on body fat turnover in growing calves are scarce. Vernon and Clegg (1985) state that basal lipolytic rates measured in vitro are close to lipolysis in vivo. This may be true for well-fed animals, but is likely to underestimate lipolysis in underfed animals (Mersmann 1986). Basal and maximal lipolytic rates of well-fed heifers in vitro were shown to be 6 and 60 g fatty acid/(kg adipose tissue·d), respectively (Smith et al. 1992). Assuming that there is no need for preferential lipid degradation to provide energy, a fixed fractional degradation rate of 1%/d is adopted, close to the basal lipolytic rate reported by Smith et al. (1992).
and is stimulated by acetyl-CoA concentration, allowing excess energy to be deposited as fat (Equation 6.5).
). Glucose is used as the energy source (catabolism to acetyl-CoA, Equation 7.8), as a source of glycerol in the esterification of fatty acids during fat synthesis (Equation 7.7) and as the major source of reduced NADPH in fatty acid synthesis (Equation 7.6, Wijayasinghe et al. 1986). The Vmax of glucose oxidation is set to be sufficient to cope with a high input of glucose equivalents, based on the highest feeding level in the experiments. As discussed previously, the value obtained is increased by 33% to approach a realistic Vmax . Glucose oxidation is dependent on the concentration of glucose. The affinity constant is set to prevent accumulation of glucose in the glucose pool (Equation 7.7).
Acetyl coenzyme A pool, Ay.
In the interest of simplicity, acetyl-CoA is considered to be the energy supplier in the body (see also the discussion section). Stoichiometric factors for transactions yielding and requiring energy are calculated assuming 1 mol Ay equivalent to 12 mol ATP (Stryer 1981). Inputs are from oxidation of amino acids (Equation 6.2) and fatty acids (Equation 6.3) and from glycolysis (Equation 6.4).
, Millward 1989), ion pumping (Milligan and McBride 1985, Reeds 1991) and synthesis of endogenous protein (only net endogenous protein losses are represented in the model). In addition, several substrate cycles, not represented in the model, may be part of this transaction (see Katz and Rognstad 1976). The transaction is named "additional energy costs for growth" (Ag, see Table 1) and is represented as a Michaelis-Menten function, dependent on acetyl-CoA concentration (Equation 6.16). The Vmax , affinity constant and steepness parameter are set to cover the discrepancy between the energy costs accounted for in the model and the energy balance measured in the experiments.
used empirical relationships to estimate basal energy expenditure of lean body mass, body fat and viscera, based on data for lactating cows and estimated originally by Smith (1970). Lean body mass, body fat and viscera are calculated from pool sizes (see Equations 11.4 and 11.5). For a calf of 162 kg Lw comprising 103 kg lean body mass, 21 kg viscera and 19 kg body fat, basal energy expenditure would be 0.456 MJ/kg0.75 . This is in good agreement with the estimates of metabolizable energy requirements for maintenance for preruminants by ARC (1980) and Van Es (1970) of 0.428 and 0.452 MJ/kg0.75 , respectively. This calculation of basal energy expenditure assumes a mean energy cost of ATP synthesis of 79 kJ/mol. Maintenance energy requirements are first met by all ATP-yielding transactions (see Fig. 1). The remaining part is met by oxidation of acetyl-CoA (Equations 6.6 and 6.9). During test simulations, it was verified that the sum of ATP-yielding transactions is indeed always lower than the maintenance energy requirements.
). However, no data are available to quantify the contribution of protein degradation to basal metabolic rate. Considering the ATP costs for protein synthesis and protein degradation, and assuming no net protein deposition at maintenance, protein degradation may amount to 20% of the costs of protein synthesis. Furthermore, fat turnover and absorption costs of nutrients at the maintenance energy intake level were calculated to amount to ~1% of maintenance energy expenditure. In total, 25% of the maintenance energy requirements is assumed double counted and is thus subtracted from the maintenance requirements (Equation 6.9).
Body ash pool, As
The body ash pool represents chemically determined body ash. Supply of minerals and other nutrients required for body ash deposition is considered nonlimiting. Ash accretion is considered to consist of two components: 1) ash in nonskeletal tissues: an amount depending on the pool sizes of protein in viscera, hide and muscle, and 2) ash in skeletal tissue (Equation 10.1). The ratio between ash and protein in muscle is assumed constant and is adopted from Schulz et al. (1974). The relationship between ash and protein in hide is estimated from the same data. They analyzed 12 German Friesian beef calves of either 150 or 270 kg Lw for body composition. The relationship between ash and protein in viscera is estimated from the experiments. The accretion rate of ash in skeletal tissue is made dependent on the rate of muscle protein accretion, allowing for a higher priority in skeletal development in slower growing calves.
, a cost of 2 mol ATP/mol Ca or P incorporated into bone ash, calculating the Ca and P content of bone ash from Schulz et al. (1974). The sensitivity of the model to this assumption is described in Gerrits et al. (in press).
Model calibration and summary
The affinity and inhibition constants and steepness parameters were adjusted to obtain good fit of the experimental data, i.e., the observed average muscle protein and fat deposition rates, for each weight range.) and run on a VAX computer. The differential equations for the 10 state variables are solved numerically for a given set of initial conditions and parameter values. The integration interval used is 0.01 d, with a fourth-order, fixed-step-length Runge-Kutta method. The results presented are not sensitive to small changes in initial concentrations and smaller integration intervals.
RESULTS AND DISCUSSION
Fig. 3.
Simulated (lines) and observed (symbols) response of rate of muscle protein and body fat deposition in preruminant calves to protein intake at two protein-free energy intake levels in two live weight (Lw) ranges. Low and high protein-free energy intake levels were 663, 851, 564 and 752 kJ/(kg0.75·d) for the weight ranges 80-160 and 160-240 kg Lw, respectively. Values are means ± SEM.
[View Larger Version of this Image (27K GIF file)]
Fig. 4.
Simulation of the effect of a stepwise reduction of methionine intake on average protein gain of preruminant calves in the weight range of 80-160 kg live weight, at two protein intake levels. Protein free energy intake was 820 kJ/(kg0.75·d).
[View Larger Version of this Image (22K GIF file)]
), whole-body concentrations are unlikely to vary with nutrient input, at least not within a measurable range. Inclusion of an ATP pool would be an improvement in the respect that regulatory effects have been attributed to ATP (Gill et al. 1989a). It suffers the similar limitation, however, of having a high turnover rate. Moreover, it cannot replace acetyl-CoA because it is not a substrate for fatty acid synthesis. The choice of representation of regulatory effects of energy metabolites therefore remains a concern for future models of metabolism. Alternative structures such as transferring the regulatory effects to glucose and fatty acids in combination with a simple representation of the hormonal regulation of nutrient partitioning (see Baldwin et al. 1987) may be future options. To improve the link with experimental work and to stimulate meaningful research, attention should be focused on measurable entities.
) and beef cattle (e.g., Di Marco et al. 1989, France et al. 1987, Oltjen et al. 1986), little attention has been paid to modeling growth responses to nutrient intake in preruminant calves. Clark et al. (1978) developed a simulation model for preruminant calves. This model, however, was developed to optimize the net returns to specialized veal resources. The response of protein and fat deposition rates to nutrient intake in this model was based on empirical growth equations, developed by Van Es (1970).
). The experimental work, however, revealed that these principles do not apply to preruminant calves of 80-240 kg Lw (Gerrits et al. 1996) and therefore cannot be the basis for growth simulation in preruminants.
FOOTNOTES
Manuscript received 30 April 1996. Initial reviews completed 18 June 1996. Revision accepted 21 January 1997.
LITERATURE CITED
Recommended Allowances and Feed Tables (Jarrige, R., ed.), pp. 109-119. John Libbey, London, UK.
-agonist (clenbuterol) on growth, carcass composition, protein and energy metabolism of veal calves.
Br. J. Nutr.
1987;
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