In a companion paper (Gerrits et al., in press), a mechanistic growth simulation model is described, developed for preruminant calves between 80 and 240 kg live weight (Lw).⁴ The objectives of this 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 ingested nutrients through intermediary metabolism to growth, consisting of accretions of protein, fat, ash and water. The model can also be used to predict amino acid requirements. It is based largely on data derived from two experiments with preruminant calves, especially designed for its construction (Gerrits et al. 1996). The objectives of the research reported in this paper are to evaluate model behavior, to test the sensitivity of model predictions to changes in model parameters, and to test the predictive quality of the model. To achieve this objective, several simulations were performed. First, driving variables (intake of nutrients) were varied. Second, model parameters were varied. Third, two published experiments, not used for the development of the model, were simulated and the results compared with the experimental observations. Finally, the behavior, sensitivity and predictive quality of the simulation of amino acid requirements were tested. Throughout this paper, results of the simulations performed are presented directly following the description of the simulation.

A reference simulation is chosen as the starting point for many of the simulations performed throughout this paper. It was decided to simulate a fast growing calf in the middle of the weight range for which the model was developed. The results of the reference simulation are obtained at 160 kg Lw, starting the simulation at 120 kg Lw. The nutrient intakes at 160 kg Lw are as follows: milk proteins (N × 5.92; Gerrits et al., in press), 556 g/d; fat, 428 g/d; lactose, 924 g/d; (pregelatinized) starch, 86 g/d.

BEHAVIORAL AND SENSITIVITY ANALYSIS

Changing driving variables

As shown in Figure 1, increasing the dietary carbohydrate:fat ratio at equal protein and gross energy intakes leads to an interesting shift in model predictions from fat to protein deposition. The simulated protein deposition rate increases from 178 to 217 g/d when the carbohydrate:fat ratio increases from 0.5 to 1.8. Fat deposition decreases from 285 to 224 g/d. Consequently, the rate of live weight gain increases from 1286 to 1430 g/d. In the model, the decreased availability of dietary fatty acids (244 g/d) with an increasing carbohydrate:fat ratio is only partly compensated for by an increased rate of de novo fatty acid synthesis (44 g/d) and a reduced fatty acid oxidation rate (144 g/d). The input into the acetyl-CoA pool from glycolysis increases with an increasing carbohydrate:fat ratio. This increase is larger than the increased net output to the fatty acid pool. Therefore, the acetyl-CoA concentration rises, causing the increased protein synthesis rates (see Gerrits et al., in press).

Unfortunately, the results of this modeling exercise could not be compared with experimental data in the live weight range 80-240 kg. The simulations, however, partly confirm the results of Donnelly (1983), who found similar effects with preruminant calves of 40-70 kg at a low dietary protein to energy ratio. At the high dietary protein to energy ratio, these effects were not observed, which was partly attributed to a narrower range in dietary carbohydrate:fat ratio tested with the high protein low energy diets. Model behavior, however, is similar when the carbohydrate:fat ratio is varied at different protein intakes (results not shown). It is known that a shift in energy intake from lipogenic to glycogenic sources increases the insulin production, which stimulates protein deposition (Reeds and Davis 1992). This is in line with the simulated shift in partitioning of nutrients, described above.

Changing major model assumptions

The sensitivity of model predictions to variation in the daily expenditure on protein for maintenance is tested by separately varying the three maintenance components, represented by the model: 1) endogenous urinary losses are varied from 50 to 350 mg N/(kg^0.75·d) (default is 180); 2) metabolic fecal losses are varied from zero to 7 g N/(kg dry matter intake) (default is 2.46); 3) protein losses from skin and hair are varied from 3 to 47 mg N/(kg^0.75·d) (default is 18). Increased N losses via all three pathways do not exert detrimental effects on rate of gain of protein, fat and live weight. The effects were all in a similar direction, which is illustrated in Figure 2 for increased metabolic fecal losses. In all three cases, the effect on protein deposition rate is less than expected on the basis of the increased N losses. Increased N losses lead to a decrease in the concentration of amino acids, which in turn decreases the rate of amino acid oxidation, provided that the increased losses do not cause an amino acid imbalance. By this mechanism, a large part of the increased N losses is compensated for. Seventy-nine percent of increased net fecal N losses, for example, is compensated for in this way. The small decrease in the fat deposition rate with increased N losses is caused by a lower energy yield from amino acid oxidation and increased energy expenditure on protein synthesis (in the second and third pathways). It is realized that the increased costs of protein synthesis are probably underestimated because only the net fecal endogenous losses, i.e., the difference between synthesis and reabsorption,.are modeled.

As an example, the effect of increasing the FDR of hide protein from 2 to 20%/d on tissue deposition rates is shown in Figure 2. Increasing the FDR of hide protein slightly decreases the total protein deposition rate. The increased FDR leads to an increased amino acid concentration. This, in turn, leads to an increased amino acid oxidation rate, leaving less amino acid to be deposited. The decrease in protein deposition rate, however, is small, indicating that hide protein synthesis is increased to an almost similar extent as degradation. Increasing the FDR of hide protein from 2 to 20%/d increases the protein degradation rate with 662 g/d and increases the protein synthesis rate with 650 g/d, leaving a difference of 12 g/d. As expected, increasing the FDR of hide protein negatively affects the fat deposition rate. The response of fat deposition rate is larger than that of protein deposition rate and is caused by the increased energy expenditure on protein turnover. Furthermore, by increasing the amino acid fluxes, increased protein turnover will affect the amino acid requirements. This effect will be discussed later in this paper.

Table 1. The effect of changing stoichiometric assumptions in the model simulating metabolism of preruminant calves on the energy costs of protein turnover, synthesis of dispensable amino acids (DAA), fat synthesis and incorporation of Ca and P into bone ash, in the reference simulation1 [View Table]

Sensitivity to changes in kinetic parameters

Table 3. Sensitivity of rates of gain of protein, fat and live weight and of rate of principal transactions, predicted by the model simulating metabolism of preruminant calves, to 25% changes in all kinetic parameters involved in energy metabolism, compared with the reference simulation1 [View Table]

Table 2. Sensitivity of rates of gain of protein, fat and live weight and of rate of principal transactions, predicted by the model simulating metabolism of preruminant calves, to 25% changes in all kinetic parameters involved in protein metabolism, compared with the reference simulation1 [View Table]

As expected, the model is sensitive to changes in the parameters describing the amino acid oxidation transaction. Increasing the affinity constant by 25% decreases the amino acid oxidation rate by 115 mmol/d (about 12 g protein/d), which is consequently used for protein deposition. Changes in the steepness parameter for amino acid oxidation are hardly reflected in the amino acid oxidation rate. This may be specific, however, for the reference simulation. The rate of amino acid oxidation in the reference simulation is near 50% of its maximum velocity (V_max), a rate at which the transaction is not sensitive to changes in steepness parameters (Thornley and Johnson 1990). At both lower and higher amino acid concentrations, caused by lower and higher protein intakes, respectively, the model is more sensitive to changes in this steepness parameter. The model is highly sensitive to changes in all parameters in the muscle protein synthesis transaction, especially the V_max . This is a consequence of relating the deposition rate of the other protein tissues to muscle protein deposition rate, as discussed earlier in this paper.

Model predictions are moderately sensitive to changes in the V_max for fatty acid oxidation, fat synthesis and the additional energy costs for growth (Table 3). Maximum velocities in this model are scaled with tissue size in which the transaction considered is expected to take place (Gerrits et al., in press). Therefore, in general, the model is more sensitive to changes in V_max than to similar changes in other model parameters.

COMPARISON WITH PUBLISHED EXPERIMENTS

Van Es and Van Weerden (1970)

The results of the simulation of weight gain and N retention are presented in Figure 3. The root MSPE of live weight gain was 15.4% of the observed mean. Fifty-two per cent of MSPE was attributed to the overall bias and 48% to the disturbance proportion. The deviation of the regression slope from 1 did not contribute to the MSPE, indicating that the wide variation in growth rates caused by the feeding strategies was quantitatively predicted by the model. The consistent overestimation of growth rate was about 100 g/d. It is thought that the actual live weight gain was less than would have occurred in an optimal situation. In these experiments, the calves were transported each period to climate respiration chambers in which energy balances were measured during a 24-h period.

The predicted N retention is in general agreement with the observed values (Fig. 3). The root MSPE was 11.6% of the observed mean. Although the overall mean was well predicted (2% of the MSPE was attributed to overall bias), the observed variation in N retention, caused by the experimental treatments was less well predicted than the observed growth rates (deviation of regression slope from 1 contributed 35 and 0% to the MSPE, respectively). This may be due to the short period of collection in the N balance (6 d), whereas growth rates were determined over a longer period (28-33 d). A large part of the variation in the observed N retention was due to health problems during the collection period, rather than to the experimental treatments (Van Weerden 1968).

Meulenbroeks et al. (1986)

The results are presented in Table 4. Generally, results of the simulations corresponded well with the observed rates of gain. Especially the predicted contrasts between the two feeding levels were predicted accurately. The deviation of the regression slope from 1 contributed only 6, 10 and 0% to the MSPE of live weight gain, N retention and fat deposition rates, respectively. Consistent with the observations, predicted rate of gain of weight, protein and fat decreased slightly with time. Simulated rates of weight gain were only slightly higher than the average observed rates. The simulated N retention agrees with the observed values. The predicted fat deposition rates are about 50 g/d higher than the observed values, whereas the observed contrast was predicted accurately. The overall bias proportion contributed 94% of the MSPE for fat deposition. The overestimation would be about twice the standard error of fat deposition, measured in slaughter experiments (Gerrits et al. 1996). The overestimation could be caused by inadequate representation of the fat metabolism in the model. Considering the close agreement between the predicted and observed contrasts in fat deposition rate between the two feeding levels, this is unlikely. Alternatively, the overestimation could be caused by a difference in the way the fat deposition is determined, i.e., calculated from the measured heat production and nitrogen balance vs. direct measurement in the slaughter experiments on which the model is based. According to Van Es and Boekholt (1987), however, this could explain only a small part of the overestimation. More likely, the difference between the observed and predicted values represents a real difference in fat deposition rates between our experiments and that of Meulenbroeks et al. (1986). Housing calves in metabolism crates in a respiration chamber could lead to increased maintenance energy requirements, which would be reflected in the fat deposition rate (Van Es and Boekholt 1987). An increase in maintenance requirement from 460 to 500 kJ/(kg^0.75·d), for example, could account for a difference of about 40 g/d in fat deposition in a calf of 200 kg Lw, assuming an energetic efficiency for fat deposition of 0.8. Additionally, the different genetic background of the calves used by Meulenbroeks (40% HF ) and the calves used in our experiments (70% HF ) could explain part of the difference (<20%) between observed and simulated fat deposition rates.

Table 4. Comparison of experimental observations with model predictions of daily nitrogen retention, rate of fat deposition and live weight gain at two levels of intake in the live weight range 180-230 kg1 [View Table]

SIMULATION OF AMINO ACID REQUIREMENTS

Model behavior

In the model, amino acids are expressed as amino acyl residues. To allow comparison of the simulated requirements with literature values, the results, presented in Table 5, are already converted into grams amino acid per day. When compared at similar protein deposition rates (e.g., high protein intake in the range 80-100 kg Lw vs. low protein intake in the range 220-240 kg Lw, Table 5), the simulated requirement for all indispensable amino acids (in g/d) increases with increasing Lw. This is caused by 1) increased endogenous amino acid losses, due to higher dry matter intakes at higher live weights; 2) increased scurf losses from the hide protein pool at higher live weights; and 3) higher inevitable oxidative losses (in g/d). Inevitable oxidative losses of a specific amino acid depend on protein pool sizes and therefore also on live weight (Gerrits et al., in press). The relative contribution of these components to the increased requirements is not equal for individual amino acids. However, for all amino acids, the increased endogenous fecal losses are the most important factor, followed by the increased inevitable oxidative losses and the increased scurf losses.

Table 5. The amount of each indispensable amino acid needed to simulate maximum protein (N × 5.48) deposition rate of preruminant calves in three live weight ranges at two protein (N × 5.92) intake levels [View Table]

Obviously, higher protein deposition rates lead to increased amino acid requirements because more substrate is needed for protein deposition (Table 5). However, when expressed per gram protein deposited, requirements decrease with an increasing deposition rate, caused by the same mechanisms as the increased amino acid requirements with increasing live weight, discussed above.

Changes in the requirements with changes in live weight or protein deposition rate are not always equal for all amino acids (Table 5). This is caused by changes in the composition of protein deposition. Muscle protein deposition, for example, becomes relatively more important with increasing protein deposition rates, causing a slight shift in the requirements for individual amino acids. Analogously, with higher dry matter intakes, the amino acid pattern of endogenous protein losses becomes more important.

Sensitivity of model predictions to the major assumptions

The simulated requirement for methionine + cystine in the reference simulation was 11.1 g/d. Increasing the methionine + cystine content of muscle protein by 25% increased the simulated requirement by 10%. Increasing the inevitable oxidative losses for methionine + cystine to 5 or 10% of the methionine + cystine flux increased the simulated requirement by 15 and 42%, respectively. Increasing visceral protein turnover by increasing its FDR to 35%/d increased the simulated requirement by 10%. The last is in agreement with the suggestion of Simon (1989) that visceral protein may be more important in defining amino acid requirements than can be expected on the grounds of its contribution to body protein. Increasing the methionine + cystine content of muscle protein (the largest protein pool) has an important effect on the requirement. It directly increases the need for deposition, but also increases the methionine + cystine flux, and thus the inevitable oxidative losses.

Comparison with experimentally derived amino acid requirements

The simulated methionine + cystine and the lysine requirement for calves between 220 and 240 kg at the high protein intake level in Table 5 can be compared with unpublished experiments of Tolman et al. (1991, internal report). They varied methionine + cystine and lysine intake from 13 to 21 and from 27 to 45 g/d, respectively, measuring N retention of 48 preruminant calves in the weight range 220-250 kg. They found little response of N retention to the increased amino acid intakes. The measured N retention varied around 36 g/d. The simulated requirements, 13 and 27 g/d for methionine + cystine and lysine, respectively, are just outside the measured range of Tolman et al. (1991). This may provide an explanation for the lack of response in these experiments.

DISCUSSION

The model is quite sensitive to changes in maintenance energy requirements, indicating their quantitative importance. The simulated effects are generally in line with our expectations. The observation, however, that increased maintenance energy requirements can be partly compensated for by decreasing the additional energy costs for growth is not very likely. Reconsidering the representation of this flux therefore seems appropriate. For example, part of the additional energy costs for growth could be coupled to tissue deposition rate rather than to the concentration of acetyl-CoA. Before doing so, it would be important to decompose this flux into energy spent on defined physiological processes.

The model is marginally sensitive to changes in the protein requirements for maintenance. Increased maintenance protein losses are compensated for roughly 70-80% in simulations by reducing the amino acid oxidation rate. Although not likely to be so large, it is possible that a compensation mechanism of this kind exists. There are, for example, some indications that the efficiency of utilization of absorbed protein for replacing endogenous urinary and endogenous fecal nitrogen losses in ruminants is higher than that for growth. The estimated efficiencies vary between 0.5 and 1 (Owens 1987), whereas the gross efficiency of utilization of absorbed protein varies between 0.35 and 0.60 in fast growing, preruminant calves (Gerrits et al. 1996). The representation of protein requirements for maintenance in the model may be a crude approximation (Millward et al. 1990). Considering its quantitative importance, however, the simple approach used seems appropriate for growing calves.

The deposition rate of visceral, hide and bone protein is directly related to the muscle protein deposition rate. This approach provides a simple solution to a complex problem. It has the additional advantage that turnover of hide, bone and visceral protein can be varied by simply changing the FDR of these tissues. The direction of the predicted effects of changes in protein turnover is according to our expectations. However, quantitatively, the effects may be underestimated. About 20% of the increased expenditure on protein synthesis and degradation is compensated for by a decrease in the additional energy expenditure for growth. On the other hand, there are indications that the energy costs of growth do not increase proportionally with protein turnover rate. Summers et al. (1986) questioned whether the stoichiometry of peptide bond formation is fixed. Additionally, Lobley (1990) stated that increased protein turnover rates do not always lead to higher rates of oxygen consumption. A disadvantage of relating the deposition rate of the three protein pools to the rate of muscle protein deposition is that it makes the model highly sensitive to changes in the parameters determining muscle protein synthesis. Furthermore, variation in muscle protein turnover cannot be simulated by varying its FDR. This is also the case for body fat turnover (results not presented).

Protein synthesis is quantitatively the largest energy-consuming process defined in the model. Increasing the ATP requirement for protein synthesis from 3 to 5 mol ATP/mol peptide bond synthesis reduced the fat deposition rate by 40 g/d. In the reference simulation, 21% of the total energy expenditure is spent on protein turnover. Similar results were obtained by Gill et al. (1989), who simulated 19% for growing lambs. Also, the simulated increase in the ATP expenditure with increasing ATP requirement for protein synthesis and degradation corresponded well with their simulations.

The model provides a useful tool for estimating amino acid requirements. Simulated requirements depend strongly on nutritional circumstances and respond to changes in the amino acid profiles of the tissues, body weight, protein turnover rate and inevitable oxidative losses. More attention must be paid to these inevitable oxidative losses for individual amino acids. Also, recent data on the amino acid profiles of the tissues would improve the reliability of estimations of amino acid requirements. Obviously, the relative importance of an amino acid profile of a tissue depends on the contribution of that tissue to whole-body protein and on the protein turnover rate of that tissue.

It can be concluded that the model is a useful tool for the development of feeding strategies. The model responds well to changes in the quantity and the quality of the feed offered and provides a means for estimation of amino acid requirements. Apart from the use of the metabolic model in research, there is, in our opinion, considerable scope for using this type of model to replace feeding tables, currently the basis for most feeding strategies.