J. Anim. Sci. 2002. 80:2452-2460
© 2002 American Society of Animal Science
Protein and fat utilization in lactating sows: II. Challenging behavior of a model of metabolism1
J. P. McNamara*,2 and
J. E. Pettigrew
* Department of Animal Sciences, Washington State University, Pullman 99164-6351 and
and
Department of Animal Sciences, University of Illinois, Urbana 61801
2 Correspondence:
233 Clark Hall, P.O. Box 646351, Washington State University, Pullman 99164-6351 (phone: 509-335-4113; fax: 509-335-4246; E-mail:
mcnamara{at}wsu.edu).
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Abstract
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The objective was to challenge the behavior of an existing mechanistic model of sow metabolism using data from a study that determined effects of fat and amino acid intakes on milk production, body and mammary composition in sows nursing 10 to 12 pigs. Sows were second through fourth parity; litter size was standardized at 12 pigs within 3 d of farrowing, and lactation was for 20 d. Diets were formulated and fed to provide three different amounts of protein intake and two different amounts of fat intake. Data were used to challenge the behavior of an existing mechanistic, deterministic, dynamic model for describing variation in milk production and changes in body composition. Nutrient intake and initial body weights and compositions were used as direct inputs into the model. The model could describe milk production within 1 SD of the mean on all rations. The model described body fat within 1 SD of observed values, but overestimated final body protein by approximately 30% (or between 1 and 2 SD). The model described the change in body fat and protein in response to 5% additional fat in the ration within 1 SD of observed (simulated - observed = -1.1 kg for protein and -0.7 for fat). The simulated response to dietary protein was within 1 SD (2.6 kg): simulated response from medium to high protein was 1.0 kg, observed 1.2; simulated response from medium to low was -0.7 kg, observed 0.3 kg. Thus, the model was not as accurate in describing the body protein response to a low-protein diet and overall, overestimated the retention of body protein. This model has utility for setting specific research hypotheses and may be amenable to use by nutritionists in a variety of applications. Further improvement in the ability of the model to describe metabolism and production of lactating sows is limited by a severe lack of data on metabolic interactions. Data on rates of muscle protein synthesis and proteolysis and interactions between amino acids, fatty acids, and glucose are needed to improve this and other models of sow production.
Key Words: Amino Acids • Fats • Lactation • Metabolism • Simulation Models • Sow
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Introduction
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The use of mechanistic, biomathematical models in predicting nutrient requirements and describing animal performance and resultant incorporation of mechanistic elements into practical models is a major research focus (Black et al., 1986; Pettigrew et al., 1992a; Baldwin, 1995). A lack of data often limits these efforts (McNamara and Boyd, 1998) though progress continues (Bastianelli et al., 1996; Knabe et al., 1996; Dourmad et al., 1998). The Nutrient Requirements of Dairy Cattle incorporated mechanistic elements into a practical decision support tool (NRC, 2001). The Nutrient Requirements of Swine (NRC, 1998) also incorporated extensive model equations utilizing some mechanistic elements as well.
Mechanism-based models bring order to descriptions of complex systems (Pettigrew et al., 1992a,b; Baldwin, 1995). Refinement requires identification and estimation of parameters describing subcellular pathways and integration to describe nutrient use in the whole animal. To obtain valid independent estimation of parameters requires experiments over a range of responses and measurement of several parameters simultaneously (Pettigrew et al., 1992a, b; Baldwin, 1995). If the new data set suggests that a change in elements or parameters is warranted, then the model is revised and performance again tested. This process of model challenge is accepted in mathematics, physics, chemistry, and much of biochemistry and biology, yet it is still a relatively new process in the animal sciences (Baldwin, 1995; McNamara and Boyd, 1998; Boston et al., 2000). Our objective was to challenge behavior and sensitivity of an existing mechanistic, dynamic model of metabolism in the lactating sow (Pettigrew et al., 1992a, HREF="#PETTIGREW-ETAL-1992B">b) for describing use of body protein and fat under a range of protein and fat intakes, specifically in sows nursing large litters (11 to 12 pigs).
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Materials and Methods
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Experimental Procedures
Sows were Landrace x Yorkshire crossbreds and blocked into two parity groups: parity 2 or parity 3 and 4. Details of pregnancy and gestation rations are given in companion paper (McNamara and Pettigrew, 2002). Treatments were high and low fat (HF, LF) -5% added fat or not, with Low, Medium, or High Protein (LP, MP, HP): 11.6% CP, 0.8% lysine; 13.1% CP, 0.9% lysine; and 14.7% CP, 1.0% lysine. All other measures and procedures can be found in the companion paper (McNamara and Pettigrew, 2002).
Brief Model Description
A summary table of pertinent terms and equations is provided (Table 1
). In brief, the model has as inputs the actual nutrient intake on a daily basis of total amino acids other than lysine (FAa), lysine (FLy), fat (FLli), starch (FSt), fiber (cellulose: FCe, hemicellulose: FHc, and lignin: FLg), and ash (FAs). These inputs can either be simulated via equations in the model or, as in this case for research purposes, measured directly along with daily feed intake and included as inputs into the model. Starting empty body weight (QEW) and body composition (fat (iTs) and protein (iPb)) can be input if known, as they were for these simulations. The expected yield of milk is set with a parameter named milk yield factor (MYF), which is used in an equation that drives the initial amount of lactose synthesis, and milk yield is calculated assuming a constant concentration of milk lactose (Pettigrew et al., 1992a). Lactose synthesis can then be altered by changes in glucose or amino acid availability. The curve and parameter values were derived from compilations of published studies available at the time the model was constructed but are variable and can be changed from simulation to simulation if warranted by new data. Milk protein and fat yield are driven by the lactation curve and are also responsive to substrate concentrations of lysine (for milk protein) and fatty acids and glucose (for milk fat). If milk yield is known, in this case when simulating research data, then the MYF can be set to match observations, for example, in a control group to determine whether the model can match the observed milk yield given the dietary inputs, as well as to determine the ability of the model to respond to dietary inputs in the other body pools. The model integrates the flux into and out of, and the size of body pools for glucose, acetate, lysine, other amino acids, fatty acids, body fat, body protein, and visceral protein over time, based on parameters set at the initiation of a simulation (for example: initial pool sizes, maximal velocities, and substrate sensitivities) and substrate availability. The entire text of the model can be found in Pettigrew et al. (1992a), and a disk copy is available upon request. The model requires Advanced Continuous Simulation Language (ACSL, AEgis Simulation, Inc., Huntsville, AL).
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Table 1. Pertinent abbreviations, parameters and equations of a mechanistic, dynamic model of metabolism in the lactating sowa
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Modifications to Published Model Used in the Present Study
The model with modifications used in these challenges has been used in previously published works (McNamara, 1998; McNamara and Boyd, 1998); however, all the modifications from the original equations have never been fully published. The model takes absorbed nutrients and describes chemical interconversions, aggregated among tissues, for the major pathways of protein and fatty acid synthesis, oxidation of amino acids, fatty acids and glucose, and mammary synthesis of milk fat, protein, and lactose. The model keeps track of energy demand (ATP) as a direct function of the summation of energy utilizing and generating reactions. A brief description of the modifications with a few sample equations is given here. The full text of the original and revised model code will be made available by the corresponding author upon request.
The original equations as put forth in Pettigrew et al. (1992a) still comprise the basic workings of the model. The major modifications made were 1) removing ATP as a state variable involved as a substrate and a product in several metabolic reactions and incorporating it as a "zero pool" that was "zeroed out" in each time iteration based on supply and demand (summation of all ATP utilizing reactions), and 2) removal of acetyl CoA as a state variable and substrate or product in various equations, followed by aggregation of these equations into the pertinent metabolic process (for example, lipogenesis from glucose or oxidation of amino acids to carbon dioxide). In the original model, ATP and acetyl CoA were described as a "total body pool" or state variables, aggregated over all tissues and functions. The reasons for these modifications were made to follow some basic modeling principles. The two major principles are to model as close to reality as is known and reasonable (given limitations on simplicity, technical methods and the like), and to model only what can be observed or readily extrapolated from observations. In no animal do ATP or acetyl CoA comprise one "body pool," but rather exist in compartments, such as cells or tissues; therefore, one major principle of modeling cannot be met: no direct experimental observation can support or refute the description in the model. These compounds are substrates and products in many reactions in many different cell types. Thus, the concentration and magnitude and direction of flux (catabolic vs anabolic) are widely varied among tissues and often in the opposite direction. For example, in the negative glucose balance of lactation, carbon is flowing from fatty acid to acetyl CoA in adipose tissue and generating ATP, while in the mammary tissue the flow is from acetate (from glucose) through acetyl CoA to fatty acids and requiring ATP. Therefore it is important to retain the level of pathway aggregation in such a model at a consistent level of organization. The other major reason is that the model becomes more simplified and defensible (also arising from the reasons above). A corollary reason is that the new modifications make this model similar in function and construction to the older, more thoroughly evaluated model of metabolism in the lactating dairy cow (Baldwin, 1995), which allows direct comparisons of their utility for their primary objective of setting and testing research hypotheses.
The following equations exemplify the modifications. The first is the inclusion of ATP as a zero pool such that production of ATP (PAt) is (please see Table 1
for definitions):
and the utilization of ATP is the sum of ATP utilization (UAt) in all such reactions:
Once these are calculated, the net requirement for ATP (utilization, driven by actual demand in metabolic reactions) minus that produced (from known oxidative and interconversion reactions) is zeroed out by demand oxidation of a mix of fatty acids and glucose, which varies with availability (as in the animal):
(Requirement for (additional) ATP = Utilization of ATP — Production of ATP); and
(Production of ATP for required oxygen (Ox) consumption = production from fatty acid oxidation to carbon dioxide and glucose oxidation to carbon dioxide). Through these and corollary equations, the energy, oxygen, and carbon dioxide balances are calculated. For a more in-depth description of this approach, see Baldwin (1995, Chapter 16).
The second example of modification is given by the equations describing glucose oxidation and conversion to fatty acids in total nonmammary tissues (body fat synthesis):
where UGlAy is glucose oxidation to acetyl CoA, v indicates maximal velocity, M represents the Michaelis constant for glucose in this reaction (also commonly referred to as sensitivity constant); thGlAy is an exponent (steepness factor), which can alter the sensitivity of a reaction to a concentration or other parameter; and J is an inhibition factor (Pettigrew et al., 1992a). Thus, this reaction calculates, on a total body basis (in moles/day), the oxidation of glucose to acetyl CoA as a function of the maximal velocity and Michealis constant for glucose, and inhibition by acetyl CoA concentration. Similar equations are used for oxidation of amino and fatty acids.
The acetyl CoA generated can then be used for fatty acid synthesis in the body or in the mammary gland, acetate synthesis (total body) or oxidized to CO2 to form ATP. The following equation describes acetyl CoA conversion to fatty acids (Fa) as a function of maximal velocity, Michaelis constants and acetyl CoA, glucose, and ATP concentrations and inhibition by fatty acid concentration:
Although from principles at a biochemical pathway level, these variables have an effect on fatty acid synthesis, as noted above, there is no one "acetyl CoA pool," and, in fact, the flux of these reactions can vary from tissue to tissue (liver vs adipose, for example). Following the aggregation at the pathway level as used by Baldwin (1995), we revised these equations, for example, conversion of glucose to body fat (Ts):
Thus, body fat synthesis from glucose is a function of glucose availability, the maximal velocity, and the Michaelis constant. This is a more simplified form and can be measured and, thus, challenged more directly (see Parmley and McNamara (1996) and McNamara (1998) for examples of measurements, which can be made and used in model challenges).
Modeling Simulations
The modeling simulations were conducted using this existing modified version of a model of metabolism in lactating sows (Pettigrew et al., 1992a) running on Advanced Continuous Simulation Language Software (AEgis Simulation, Inc., Huntsville, AL; see Baldwin, 1995 for language details). We used the actual starting BW measured for all animals at beginning of lactation (d 1) and the protein and fat composition as a percentage of BW measured in the initial slaughter group to calculate initial body compositions. For purposes of these model challenges, the control group was designated as the medium protein, low fat fed group (LFMP).
The challenge was conducted setting the MYF to describe the milk yield of all individual sows for which we had body composition (n = 37) to determine how the model behaved in describing changes in body protein and fat. A reminder is needed that this and other similarly based research models (Baldwin, 1995) do not have a primary objective of predicting milk production from feed intake or calculating requirements from expected production rates. Rather, they have the objective of describing the biochemical transactions taking place in animals in various situations and to identify where the critical gaps in our knowledge exist. Such models may also have good predictive value in the field if sufficient information is known about the genetic potential (milk production, litter size) as well as nutritional inputs of the animals. Thus, in one study one might determine how well the model describes milk yield when nutrient intake is varied, and in another study one might ask how well the model may describe milk production under various litter sizes; while in this study we asked how well the model described body protein and fat use under varied protein and fat intakes at a similar milk demand.
Simulations were conducted for each treatment group using the treatment mean for inputs (dietary intake at the given nutrient composition, initial starting body weight, initial body protein and fat composition). In this model, body fat includes both carcass and visceral fat, but not, for example, lipid in the skin or head. Body protein is actually allotted to two pools, body and viscera. Body protein is actually muscle protein and does not include protein in the head, skin, and fat, though the model parameters could be changed to do this. Visceral protein is that in intestinal organs, liver, kidney, heart, spleen, and mammary gland. Simulations were run, and simulated outputs of milk and components and change in body composition were compared with observed values for determination of how well the model behaved. The dynamic model can output the values of its variables at any unit of time desired, since this research output was gathered on a daily basis (the time step was one day) and summed as necessary for weekly or total lactation comparisons.
Design and Statistical Analyses
The design and experimental analysis of the observations were described in (McNamara and Pettigrew, 2002). The simulated data for milk production, body protein, and body fat were subjected to statistical reduction (means, SD), and the first level conclusion for these challenges was made that the model behaved adequately if the simulated mean is within 1 observed SD of the observed mean. Second, the simulated values for milk production, empty body weight, body fat, and body protein (including final body fat, final body weight, protein and change in body weight, fat, and body protein) were subjected to the same model analysis as for the observed data. Statistical significance was compared to ask if the model data set resulted in any different inferences than the observed data set.
In addition, regressions of simulated vs observed data for milk production and ending body compositions were done, and residuals calculated (Steel and Torrie, 1980). The mean square prediction error and its components: mean bias [(O - S)2] (O = observed; S = simulated); line bias [Sp2(1 - b)2] (Sp = standard deviation of the prediction, b = slope of predicted vs observed) and random error [SO2(1 - r2)] (SO = standard deviation of the observations and r2 = regression coefficient) were determined (Roseler et al., 1997) to describe basic causes of variation in the model.
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Results and Discussion
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Detailed results on observed animal performance and composition are given in the preceding paper (McNamara and Pettigrew, 2002). Pertinent experimental data will be reported in this paper as the modeling simulations are compared to the observed data.
Model Simulation Results
The observed and simulated total lactation milk production data demonstrate that the model can describe milk production from dietary inputs and mechanistic parameters describing chemical interconversions (Figure 1). Thus, the model is robust, and when knowledge of nutrient inputs and sow phenotype (starting body fat, body protein) is available, milk production can be described. In this study, the simulated milk yield was set to match the observations, so it sets the obvious question of "So what is learned?" What is learned is that it is only because the internal mechanistic equations and parameters are robust that the model can in fact work. This demonstrates that for describing milk production from observed nutrient intakes and known biochemical interconversions, the model accounts for most of the known variation, leaving random error in measurements as the remaining major source of variation.
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Figure 1. Observed and simulated milk production of sows fed varying dietary fat and protein. Observed milk production was calculated from piglet growth by [milk (kg) = (2.50 x ADG) + (80.2 x piglet BW) + 7] (Noblet and Etienne, 1989). The solid line indicates the regression from the data, and the dashed line is the result of forcing the intercept to zero, basically demonstrated that the intercept was close to zero with little mean or line bias.
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A more important point is that in both reality and in the model, varying fat from 2 to 7% of the ration and protein from below 700 to more than 900 g/d, even in high producing sows, did not have an effect on overall milk production. Feed intake was set in the experiment to remove this variable and specifically test only the effects of protein and fat input. The model simulated this experimental reality well and did simulate a lower milk production in the low-protein, low-fat group, based on the observed nutrient intakes. The majority of the depression in litter growth on the low-protein diet was accounted for by diminished growth in the third week of lactation (data not shown). However, the model simulated the depression in milk yield over the entire lactation, not only in the third week. This indicates a need for further precision in the dynamic relation between flux rates and time. No other model, and certainly no empirical model, is sufficient to even test this question.
The model described accumulation of body fat compared to observed within 1 SD of the measurements for all main and interaction effects (Table 2 (main effects) and Table 3 (interactions)). The model simulated 2.4 kg more body fat on the HF than the LF treatments while the observed effect was 3.1 kg. However, the model simulated too much body fat on the low-protein rations. The observed effect of moving from medium to low protein on change in body fat was a loss of another 3.9 kg, while the model predicted an increased gain of 0.2 kg. This was also seen on the interaction means (Table 3) where the observed change in body fat on LFLP and HFLP was -4.1 and -1.3 kg, while the model predicted a gain of 1.4 and 2.9 kg. Even so, these values are within 1 SD of the mean.
The line bias in describing body fat at the end of lactation is evident in Figure 2, in which the model generally behaves in the proper direction, but displays a mean bias of 7.0, a line bias of 9.17 and random error of 38.1, or 12.8, 17.5, and 69.7% of the total mean square prediction error. A bias in the mean indicates errors in parameters (maximal lipid synthesis or lipolysis) that are systematic, but can easily be changed up or down and reevaluated. A bias in the linear relationships indicates underlying misunderstanding of how body fat accumulation changes with changing nutrient intake and milk outflow. For example, the equation forms could be more sensitive to availability of fatty acids or glucose. This would be done through resetting of kinetic substrate sensitivity parameters for lipogenesis, esterification, or lipolysis. It was suggested earlier that such systematic errors existed compared to actual observations of these parameters in lactating sows (McNamara, 1998; Parmley and McNamara, 1996). This independent evaluation data set corroborates the findings at the tissue level with animal level data. The next step would be to calculate new potential parameter values for reevaluation.
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Figure 2. Observed and simulated body fat at 20 d of lactation in sows fed varying protein and fat. Data were collected and simulations run on individual animals as described in methods. The linear relationship was Simulated Body Fat, kg = 23.2 + 0.27 x Observed Body Fat; r2 = 0.19; SEyx = 3.9 kg. The mean bias was 7.0; line bias was 9.17; random error was 38.1; or 12.8, 17.5, and 69.7% of mean square prediction error.
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The model description of the change in body protein during lactation was that the effect of high protein minus medium protein was 1.0 kg more lost on medium protein compared to 1.2 kg for observed. For the effect of medium minus low protein, the simulated effect was a gain of 0.7 kg (low gained more than medium) compared to -0.4 for observed (observed low protein lost 0.4 kg less than medium protein). For interaction effects, in the observed data set there was a greater loss of body protein as protein intake decreased on either high- or low-fat diets, and this was described by the model, though the mean positive bias in body protein remained.
The model is partitioning too much of the observed amino acid intake into body protein by the end of a 21-d lactation. Figure 3 demonstrates the mean bias of 7.6, line bias of 0.33 and random error of 16.8, or 86.0, 2.0, and 12.0% of total variation. Thus, in this case, the primary problem (mean bias) is in the balance of parameters describing protein synthesis and proteolysis; such parameters can easily be tested for a better value. The lower line bias coupled with the ability to describe less body protein on the low-protein intakes (Tables 2 and 3), indicates that the model is sensitive to the effect of amino acid availability but not sufficiently so. As for body fat, this would be remedied with a recalculation of the kinetic sensitivity parameters in the appropriate equations.
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Figure 3. Observed and simulated body protein at 20 d of lactation in sows fed varying protein and fat. Data were collected and simulations run on individual animals as described in methods. The linear relationship was Simulated Body Protein, kg = 7.63 + 0.72 x Observed Body Protein; r2 = 0.51; SEyx = 1.4 kg. The mean bias was 14.5; line bias = 0.33; random error 16.8; or 86.0, 2.0, and 12.0% of mean square prediction error.
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A primary finding from this analysis is that the equation forms describing fat and amino acid metabolism are most likely adequate in form, and the existing parameter values are valid estimates from the knowledge base available when this model was constructed. Another primary finding was that the description of amino acid partitioning to body protein resulted in approximately a 30% error in overprediction of amino acid use for body protein.
This preliminary analysis would suggest two hypotheses: 1) that the sensitivities for body fat and body protein synthesis in the model are set too low, so that they are running at near maximal rates and insensitive to realistic changes in substrate supply and 2) that parameters describing the basic energetic and amino acid needs for maintenance are too low in the model. The latter hypothesis has been identified as being the most likely major problem with the analogous model of dairy cattle metabolism (McNamara and Baldwin, 2000). Data collected recently from sows would suggest that the costs of increased protein turnover are significantly increased in the sow (Yang et al., 2000), and these would not be accounted for fully in the present model. In addition, data collected from growing pigs would also suggest that the estimates for protein turnover rates used in the present model are too low (Knap 1996; Knap and Schrama, 1996). These hypotheses will be amenable to testing when sufficient data are available from lactating sows.
As an example of the types of potential errors involved in modeling biochemical transactions, we should consider the use of glucose. Glucose is a major driving function of many reactions in the body, and, in this model and similar mechanistic models of metabolism in the cow (Baldwin, 1995), glucose concentration is a major driving function of several pathways. During lactation, body protein is a source of amino acids for milk protein synthesis and also for gluconeogenic amino acids when glucose is in deficit. We have already described the error in amino acids use as primarily a mean bias and not a line (or response) bias. In this study, lowering the dietary protein concentration increased the starch intake, resulting in a deficit of amino acids for protein synthesis and adequacy of glucose. These two events would have opposing effects on rates of gluconeogenesis. The respectable ability of this model to capture those interactions is described in Figure 4. Simulated blood glucose concentrations decreased during lactation as milk production increased (Figure 4a), as is well known (Pettigrew et al., 1992a). The model described the greatest concentrations of glucose on the two low-protein diets that were greatest in starch. The model also described an increase in gluconeogenesis from amino acids as milk production increased over time, as one would expect (Figure 4b). Also, gluconeogenesis was lowest on the two diets with more starch and greatest on the diet with the least starch (high fat, high protein). Thus, the model is behaving in a robust and realistic fashion regarding glucose availability.
However, it is clear the sensitivity of the reactions describing the interactions of amino acid supply, glucose use, gluconeogenesis, and replacement by fat of glucose for oxidative energy needs is not sufficient. This is a matter of degree, not concept. Overall, the simulation results indicate we still need specific research into muscle protein turnover in lactation if we are to quantitatively describe lactational metabolism. This result makes sense, as information available when the model parameters were originally set were from literature values of lower-producing sows, of genetic lines with less body lean, and nursing pigs with smaller litters. The model provides the framework for future research to identify the specific key reactions and control mechanisms which to study and incorporate into future models.
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Implications
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The modeling approach has been used with success in swine research and production. The model in this study has a research objective to demonstrate where knowledge is inadequate to determine the focus for future research efforts. The model, nevertheless, demonstrates a fair robustness. The present equations are sufficient to predict output responses to dietary protein. The model behavior is in the right direction for body fat and protein use; however, sensitivity with present parameter values is inadequate. The present experiment suggests the following: 1) current knowledge provides an adequate basis for relating milk outputs with dietary inputs, 2) knowledge on rates of proteolysis, protein synthesis, lipolysis, lipogenesis, and gluconeogenesis during lactation is inadequate to predict changes in body protein and fat pools, and 3) equations, which incorporate further regulatory elements describing proteolysis and lipolysis, are needed.
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Footnotes
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1 College of Agriculture and Home Economics Research Center, Washington State University, Pullman. Project Numbers 0107, 0249 and 3407. Supported in part by the National Institutes of Health (RD24529) and the National Pork Producers Council (1598). 
Received for publication June 1, 2001.
Accepted for publication May 14, 2002.
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Abstract
Introduction
—; 13.1% CP —
—; or 14.7% CP —
—; or 7% fat with 11.6% CP –•–; 13.1% CP –
– for a 20-d lactation. The simulations with the least starch intake (high protein) had the lowest blood glucose, and those with the greatest starch intake (low protein) had the highest simulated blood glucose concentrations. b. Simulated rates of gluconeogenesis from amino acids in sows fed varying protein and fat intakes during lactation. Data are simulated rates of amino acid conversion to glucose in moles per day from the six treatments. The simulations with the least starch intake and high protein intake had the greatest conversion of amino acids to glucose, and those with the greatest starch intake and low protein intake had the least conversion of amino acids to glucose.
