J. Anim. Sci. 2003. 81:683-696
© 2003 American Society of Animal Science
Modeling homeorhetic and homeostatic controls of pig growth1
P. A. Lovatto*,
and
D. Sauvant*,2
* UMR INRA-INAPG Physiologie de la Nutrition et Alimentation 75231, Paris, France and
and
Universidade Federal de Santa Maria/Bolsista CNPq, Santa Maria, RS 97119-900 Brazil
2 Correspondence:
Département des Sciences Animales, 16, rue Claude Bernard (phone: (33) 1 44 08 17 55; fax: (33) 1 44 08 18 53; E-mail:
sauvant{at}inapg.inra.fr).
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Abstract
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A dynamic mechanistic model of homeorhetic and homeostatic controls of pig growth was developed. The homeorhetic principles were based on changes in time of fractional rates of anabolism and catabolism of tissues. A minimum number of homeostatic principles integrated current data on plasma kinetics and the partitioning of nutrients between anabolism and catabolism of body tissues, and endogenous losses with integument and into the gut. The major features of the model are two levels of organization (tissue and plasma) and three body tissues (carcass proteins, visceral proteins, and body lipids). The protein tissues and plasma amino acids were subdivided into lysine, methionine and cystine, threonine, tryptophan, other essential AA, and nonessential AA compartments. Plasma glucose and fatty acids were also considered. Adenosine triphosphate and adenosine diphosphate were used to represent energy transformations, although these energy transformations were not included in the homeostatic control of pig growth. The mass variations within each of the 23 basic compartments were described with a specific deterministic, dynamic differential equation. The simulated metabolic rates of the protein and lipid tissues were similar to published data. The principal outputs from the model (protein and lipid gain, body weight, chemical body constituents, plasma parameters) showed that the proposed homeorhetic and homeostatic controls provide a mechanistic approach to modeling growth.
Key Words: Growth • Homeostasis • Models • Pigs
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Introduction
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During the last decades, animal growth has been investigated at both cellular and molecular levels and has increased our knowledge of the underlying mechanisms of growth. However, the integration of these mechanisms into metabolic models of pig growth has remained a challenge (Emmans and Kyriazakis, 1997). One of the major limitations to progress has been the difficulty in representing the systems which control nutrients flows within a model. The concept of "multiple responses to the diet" (Sauvant, 1992), which integrates the roles of both homeorhesis and homeostasis, appeared to be an adequate theoretical concept with which to model metabolism. Homeorhesis is a long-term control that expresses the genetic make-up of the animal and(or) the animal’s potential. Homeostasis is a short-term control representing the mechanisms that enable the animal to function under a range of environmental conditions. The integration of both homeorhetic and homeostatic controls of protein and body lipid turnover into a mathematical model allows for a more mechanistic representation of nutrient partitioning. This concept was used previously in a simple model of the control of amino acid metabolism in pig growth (Lovatto and Sauvant, 1999). The current paper aims to expand this concept by representing more specifically homeorhetic and some essential homeostatic controls into a mechanistic and dynamic model of pig growth.
Description of the Model
The model used a compartmental structure (Figure 1
) with organization both at the tissue and molecular level. Eighteen state variables were linked with protein metabolism: lysine, methionine and cystine, threonine, tryptophan, other essential amino acids (EAA) and nonessential amino acids (NEA) in carcass proteins, visceral proteins, and plasma. Body proteins were assumed to be the sum of AA state variables in both carcass and visceral protein tissues. Three other state variables were associated with lipid metabolism: glucose and fatty acids (FA) only represented in plasma, and body lipids (BLI) at a tissue level. As proposed in the sow model of Pettigrew et al. (1992), the FA pool comprised both nonesterified and esterified FA. Two other state variables were used to represent energy transfer within in the model: ATP and ADP. Mass balances for each state variable and the mass transfer between them are represented using specific deterministic dynamic differential equations. The basic structure of these equations is shown in Table 1 and Appendix 1.
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Figure 1. Diagram of the model. Body tissues (BT, proteins, BP; lipids, BLI), and plasma (Pa). The protein tissues are divided into carcass (ca) and viscera (vi). Biochemical subcompartments: lysine (LYS); methionine + cystine (MEC), threonine (THR), tryptophan (TRY), other essential amino acids (EAA), nonessential amino acids (NEA), glucose (Gl), nonesterified fatty acids (FA), ATP, and ADP. The end flows: endogenous digestive losses (En), integument (In), urea (UR), and respiratory chain (CO2, H2O). Solid lines show the material flows and broken lines the energy flows.
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Modeling Controls
Homeorhetic Control.
The major assumptions concerning homeorhetic controls in the model were based on principles proposed for pregnant and lactating ruminants (Bauman and Currie, 1980) and growing pigs (Danfaer, 1991). The representation of these controls assumed that growth was the difference between anabolic and catabolic flows, as was suggested in the general growth model of von Berthalanffy (1973). The nutrients flows were assumed to be proportional to the size of the respective compartments (i.e., proteins or lipids):
where BT = body tissue, Aks,BT = fractional rate of anabolism for BT tissue, Cks,BT = fractional rate of catabolism for BT tissue, and dt = time step.
As proposed by Danfaer (1991), the fractional rates of anabolism and catabolism of tissues followed exponential decays with time. For example, for anabolism, the basic expression was:
where Aks,BT = fractional rate of anabolism for BT tissue, ksb,BT = fractional rate of anabolism for BT tissue in the adult, Ai,BT = difference in the fractional rate of anabolism for BT tissue between the initial state (t = 0) and the adult, Ae,BT = fractional rate of change in the fractional rate for anabolism of BT tissue per unit time, and t = time.
The same equations were used to represent catabolism, where A values were replaced by the corresponding C values. Thus, the Aks,BT and Cks,BT decrease from an initial value toward a common value ksb,BT, for adults, according to a first-order process. In growing animals, values for Aks,BT have to be greater than those for Cks,BT. The numerical integration of these differential equations determined the anabolic and catabolic flows, protein gain (PG), lipid gain (LG) and corresponding ADG. These values were taken into account to calculate the "homeorhetic" requirements for maintenance and tissue gains. Empty body weight (eBW) was assumed to be the sum of main chemical constituents: proteins, lipids, water, and ash. Body water was calculated from body proteins as suggested Moughan et al. (1987):
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Body ash was assumed to be 20% of body protein, as proposed by Karege (1991). Body weight was assumed to be the sum of eBW and gut content, and the latter was estimated as 5% of eBW (Whittemore, 1983). The ADG was obtained by differences in BW between simulation steps of 1 day.
Homeostatic Control.
Homeostatic controls were applied so as to maintain the plasma concentrations of circulating nutrients (lysine, methionine and cystine, threonine, tryptophan, EAA, NEA, glucose, and FA) around their target values (Coik,Pa). Therefore, for a given nutrient, the difference between the actual concentration (Coi,Pa) and the Coik,Pa was used as a driving force (Table 2) influencing anabolism and catabolism. Each AA compartment was considered independently without including interactions between them. For visceral proteins (Figure 2), anabolic flows were considered a positive exponential function of standardized plasma nutrient concentration [z] = (Coi,Pa - Coik,Pa)/Coik,Pa. The intercept, when the [z] value was 0, corresponded to anabolic flow driven by homeorhesis (as described in previous section). A similar approach was adopted for the catabolic flow; however, it was an exponentially declining function of [z]. For [z] = 0, the intercept value of catabolic flows was only driven by homeorhesis. Consequently, the flows were determined by a homeorhetic process (driving by age) and a homeostatic process (driving by the plasma nutrient concentration). For example, when the concentration of a plasma nutrient falls below its target value, the nutrient is made available through decreased anabolism and increased catabolism. For carcass proteins, another homeostatic mechanism, based on the data of Reeds et al. (1978), Reeds and Lobley (1980), and Wray-Cahen et al. (1998), was used to relate anabolism and catabolism to plasma AA concentrations, and thus, directly to AA intake. They observed that both anabolism and catabolism of protein decreased following reductions in AA intake. Therefore if [z] decreased, both anabolic and catabolic turnover were assumed to decrease linearly (Figure 3). The use of exponential functions permits excess AA be more easily stored/mobilized from visceral compared to carcass proteins. Another principle of homeostatic control was applied to modulate the oxidative flow of free AA. It was assumed that this flow depended, as has been observed experimentally in growing pigs (Sève and Ballèvre, 1991), on the concentrations of free plasma AA, according to mass-action kinetics following the function:
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Table 2. Amino acid concentrations in the protein tissues, plasma, endogenous, integument, and nitrogen content of amino acids used in the model
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Figure 2. Homeostatic regulation principle applied to AA of the visceral proteins, glucose, and nonesterified fatty acids.
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where Ox1AA1–6 = kAA,ox x QAA1–6,Pa, VeAA,ox = exponential value of AA flow towards oxidation, CoAA1–6,Pa = concentration of AA1–6 in plasma, CoAA1–6k,Pa = balance concentration of AA1–6 in plasma, kAA,ox = oxidation constant for AA, and QAA1–6,Pa = quantity of AA1–6 in plasma.
Plasma Kinetics.
Plasma is a key component in terms of controlling and representing nutrient flows. Plasma volume was assumed to be 55% of blood volume, which was calculated from the data of Susenbeth and Keitel (1988) (Eq. 2.1.21, Appendix 1
). The entrance flows into plasma originate from absorbed nutrients (AA, glucose, and FA), AA derived from the catabolism of protein stores and glucose and FA from the catabolism of body lipid stores. The outflows from plasma were divided into nutrients of tissue anabolism (AA, glucose, and FA) and endogenous AA losses. The latter represents losses with integument, and endogenous gut protein, and minimum AA oxidation rates. Minimum AA oxidation contributes to minimum urinary N losses. Integument losses of AA (hair and skin epithelial desquamation) were assumed to be 105 mg•kg-0.75•d-1 according to Moughan (1999). Digestive losses of AA were assumed to be 7.087 g•kg-1 DMI, according to Hess and Sève (1999). The DMI was calculated from equations of NRC (1998). Based on biochemistry, all carbon chains derived from AA oxidation yielded glucose. The target values of plasma AA concentrations and the composition of the endogenous digestive and integument losses are shown in Table 2. The target plasma concentrations were assumed to be 900 mg•L-1 for glucose (Michel and Rérat, 1998) and 750 mg•L-1 for NEFA (Danfaer, 1999).
Quantitative Description of Tissue Metabolism
Proteins.
To accommodate two different mechanisms of homeostatic control and to account for the large differences in fractional synthesis and degradation rates (Sève et al., 1986; Andersen, 1991), body proteins were split into carcass and viscera. Carcass proteins, which are characterized by a low turnover fractional rate, were mainly skeletal muscle. The initial fractional rate for synthesis and degradation of carcass proteins was assumed to be 0.065 and 0.038•d-1, respectively, which decreased asymptotically to a common value (0.015•d-1) in the adult pig. Carcass proteins in a 25-kg pig were assumed to be 2.8 kg. Visceral proteins, which are characterized by a higher turnover fractional rate, included proteins of viscera, blood, and skin. Blood and skin proteins were included in this group because of their high turnover rates. Initial values of fractional rates of synthesis and degradation of visceral proteins were assumed to be 0.35•d-1 and 0.323•d-1, respectively, which decreased asymptotically to a common value (0.30•d-1) in the adult pig. It was assumed that the mass of visceral proteins in a 25-kg pig was 560 g. The AA composition of each tissue protein is given in Table 2.
Lipid.
Initial fractional rates of synthesis and degradation of lipids were assumed, as suggested by the results of Dunshea et al. (1992), to be 0.04 and 0.02•d-1, respectively. These fractional rates decreased asymptotically to the same value (0.01•d-1) in the adult (Danfaer, 1999). The model considered that synthesis of lipids used 90% glucose and 10% FA (Dunshea et al., 1992). In addition, the partitioning of catabolites from the degradation of lipids was assumed to yield 10% glucose (from glycerol in triglycerides) and 90% FA. The glucose and FA partitioning, for both anabolism and catabolism of lipids was constant, because the model remained in the homeorhetic state during the simulation period.
Energy Metabolism.
Energy metabolism was pooled in the ATP and ADP compartments. The main objective of the integration of ATP and ADP was to evaluate the relative energy balance of the whole model when under homeorhetic and homeostatic controls. Although specified and quantified by the model, ATP and ADP did not interact with the metabolic processes in this version of the model. The current model used total oxidation of glucose and fatty acids to synthesize ATP. The ATP dephosphorylation flows were due to the synthesis and degradation of proteins and lipids and the synthesis of urea and glycolysis. The energy costs of the phosphorylation and dephosphorylation processes were provided by Nemmann-Sorensen and Tribe (1983) and Kinney and Tucker (1992) and are indicated in Appendix 1.
Model Evaluation.
The model was evaluated by both internal and external analysis. The internal evaluation consisted of a sensitivity analysis for ADG changing key parameter values of metabolism: fractional rates of change in the fractional rate of protein metabolism (Ae,Bp, Ce,Bp) and body lipids (Ae,BLI, Ce,BLI) and the difference in the fractional rate of tissue metabolism between initial and adult state for proteins (Ai,Bp, Ci,Bp) and body lipids (Ai,BLI, Ci,BLI). In order to better quantify the impact of the two most influential parameters, a more refined sensitivity analysis (±10 and ±20%) was performed on protein gain. The external evaluation, carried out according to Bastianelli et al. (1996), compared graphically the simulated protein and lipid gains with several published data sets which had not been used in the development of the model. Model simulations were initiated from a starting body weight of 25 kg for a period of 130 d. Model development and numerical integration were performed with Dynamo Plus (Professional Dynamo Plus, 1986) using Euler’s method. The time step chosen for numerical integration was 0.001•d-1 because the amounts of free AA in the blood is only sufficient to support whole body protein synthesis for a few minutes (Schreurs et al., 1997).
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Results
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Internal Evaluation
Anabolic and Catabolic Flows.
The nutrients flows of proteins and lipids are shown in Figure 4. Between 25 to 125 kg BW, anabolic and catabolic flows of proteins increased from 380 to 1,337 g•d-1 and from 288 to 1,255 g•d-1, respectively. The simulated patterns were different for each protein tissue. Anabolic flows for carcass proteins ranged from 184 to 324 g•d-1 reaching a plateau at 119 kg BW. On the other hand, the anabolic flow of visceral proteins increased almost linearly from 196 to 1013 g•d-1. Catabolic flows of proteins increased from 107 to 256 g•d-1 and from 181 to 999 g•d-1 for carcass and viscera, respectively. The relative contribution of the two protein tissues to nutrients flows changed during the simulation period. The relative contribution of carcass to protein synthesis decreased from 48 to 24% between 25 and 125 kg BW, whereas for protein catabolism it decreased from 37 to 20%. The anabolic flow of lipids increased linearly from 120 to 534 g•d-1 between 25 and 125 kg BW, whereas the catabolic flow of lipids increased from 60 to 260 g•d-1 over the same weight interval.
Sensitivity Analysis.
The results of the sensitivity analysis for ADG are shown in Table 3. The ADG was most sensitive to parameters associated with protein anabolism (Ae,BP and Ai,BP). For both an increase and a decrease in Ae,BP values, the initial PG value at 25 kg up to a maximum for each parameter value was simulated (Figure 5). The Ae,BP changes mainly modified the BW range at which there was a maximum rate of PG. When sensitivity analysis was evaluated by altering the Ai,BP values, PG was more sensitive to the positive values (Figure 6). The differences in PG between all Ai,BP values were lowest at 25 kg, but they increased linearly until maximum PG, and thereafter, the differences decreased regularly up to 125 kg BW.
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Table 3 Sensitivity analysis on the simulated ADG between 60 to 90 kg BW by using variations of ± 20% of the main homeorhetic parameters
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Figure 5. Sensitivity analysis on protein gain by variation of fractional rate of change in the fractional rate for protein anabolism (Ae,Bp).
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Figure 6. Sensitivity analysis on protein gain by variation of difference in the fractional rate for protein anabolism between the initial state and the adult (Ai,Bp).
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Protein Gain.
The simulated and observed PG are shown in Figure 7. The daily PG increased in a quadratic manner from 91 g•d-1 at 25 kg, to 157 g•d-1 at 64 kg, and then decreased to 82 g•d-1 at 125 kg BW. Reported values of PG often form a similar pattern, but with considerable variability among experiments. The simulated PG were fairly close to the mean gain calculated from published data.
Lipid Gain.
The simulated and observed LG are shown in Figure 8. Lipid gain increased almost linearly from 60 g•d-1 at 25 kg to 274 g•d-1 at 125 kg BW. Measured LG varied greatly between experiments, and this variability increased with BW. The experimental LG were separated into two distinct groups according to the slope of the trend. Group A, mainly concerning data before 1990, was characterized by a higher rate of LG. Group B, including data from more recent experiments, had a lower rate of LG. The simulated values were closer to the latter group’s values, which represent lean genotypes.
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Discussion
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Several models of pig growth have already been published (Whittemore and Fawcett, 1976; Danfaer, 1991; de Lange, 1995). The purpose of the current model was to represent a more mechanistic description of circulating nutrients, tissue turnover, and homeorhetic and homeostatic controls of nutrients flows. The main aspect of the model presented in this paper, which was based on the intrinsic potential of anabolism and catabolism of body proteins and body lipids, was that it did not include a mathematical function to represent growth patterns. In contrast, previous models of growth in various species of animals included mathematical functions on growth and body components (PG) or capacity for growth (cell numbers and/or quantity of DNA) (Black et al., 1986; Whittemore et al., 1988). When comparing ruminant models (Schmidely, 1996), it appears that the basic control of growth, which can be considered as homeorhetic, was accomplished by using cell number and/or DNA synthesis, which were calculated from a logistic growth equation (Oltjen et al., 1986; di Marco et al., 1987; 1989). Homeostatic influences have not appeared per se in previous pig growth models; however, the process of hypertrophy (cell size and protein accretion) proposed by Oltjen et al. (1985) goes some way to representing homeostatic adaptation. In the current model, the homeostatic control was more mechanistically and realistically represented. The model was aimed at representing main principles of homeostasis and homeorhesis. The generated framework may be expanded further, for example, by representing growth responses to changes in nutrient intake and utilization of energy-yielding nutrients. This has been performed in previous models of growth either in the pig (Moughan et al., 1987) or the ruminant (di Marco et al., 1989).
Sensitivity Analysis.
Sensitivity analysis allows the identification and ranking of the major parameters controlling growth, as well as the determination of their upper and lower limits. The ADG predicted by the model was most sensitive to parameters associated with protein metabolism, particularly those associated with protein anabolism in both carcass and visceral protein. The greater sensitivity of ADG to metabolic parameters related to protein corroborates the importance of protein metabolism assumed in many growth models (Danfaer, 1991; Pomar et al., 1991; de Lange, 1995). Data from sensitivity analysis are important for growth models, because they help define parameters, which could be subsequently adapted to cover various genotypes and to link genotype and hypothetical homeorhetic control.
Protein Gain.
In growing pigs, PG is dependent on animal and environmental factors, which may explain a large part of the variations observed between published data. The increase in PG observed over the years is due to the selection programs that have been carried out (Monin et al., 1998). The agreement between observed and simulated PG was slightly better during the initial period (25 to 35 kg) than later. According to the data of Campbell et al. (1988), Hansen and Lewis (1993b), and Quiniou et al. (1996), well-fed modern pigs reach their maximal PG between 65 and 85 kg. This is consistent with PG patterns generated by the model. Moreover, the maximal PG estimated by the model was on the same order of magnitude as those published by the aforementioned authors. The sensitivity analysis of growth rate showed that Ai,BP was the parameter most closely associated with animal precocity, and Ae,BP was best associated with that of PG and growth rates. From a practical point of view, the parameters of the homeorrhetic program for protein metabolism could be adapted by fitting data from different genotypes.
Protein Anabolism.
Experimental values of protein synthesis reported in the literature increase according to a linear function of BW up until approximately 95 kg BW. The anabolic and catabolic flow reported in the literature illustrated that the model’s predictions were within the range of published values (Figure 9). Nevertheless, the variability among experimental values is large and increases with BW. In rats, this rate decreased from 29% at 23 d of age to 5% at 330 d (Millward et al., 1975), and from 30% at 25 d to 7% at 90 d (Siebrits and Barnes, 1989). In suckling piglets, it decreased from 58% at 7 d of age to 30% at 26 d (Wray-Cahen et al., 1998). Similarly, for growing pigs, it decreased from 8% for a 25-kg pig (Edmunds and Buttery, 1978) to 6% for a 43-kg pig (Simon et al., 1982). For latter BW values, simulated rates decreased from 11 to 9%. Although higher in the rat than the pig, the rates exhibit the same exponential trend in both species. When considering the partitioning of protein anabolism between viscera and carcass, van der Meulen and Jansman (1997) observed that in growing pigs, over 20% of synthesis was due to visceral proteins. This contributed to 35% for a 25-kg pig (Edmunds and Buttery, 1978) and reached 48% for a 44-kg pig (Simon, 1988) for total protein anabolism. For these BW, simulated anabolic rates of visceral proteins were higher than published values and increased from 51 to 59%. This overestimation of visceral protein synthesis highlights the problem of set growth models when trying to integrate at the tissue metabolism level because the data set available for protein metabolism is limited and variable. It is probably caused, according to Fuller et al. (1995), by differences in the experimental methodologies used to measure synthesis and degradation. However, even with the same technique large errors in calculating protein synthesis due to differences in the specific radioactivities of labeled AA in visceral organs can occur (Simon et al., 1978). A useful approach to the simultaneous and dynamic measurement of both protein synthesis and degradation is the transorgan tracer balance method, particularly if combined with the measurement of tissue amino acid labeling (Reeds and Davis, 1999). The overestimation of visceral protein synthesis may be associated with errors in fractional rates and/or mass of visceral proteins. However, more studies on protein synthesis need to be performed to confirm this hypothesis. In practice, the protein synthesis approach could be adjusted to include a selected data set from the literature.
Protein Catabolism.
Both simulated and observed catabolic protein flow increased with BW. Less data are available for measured catabolic flows of visceral and carcass proteins compared to those measured for anabolic flows. However, extrapolation of the results from Simon (1988) and van der Meulen and Jansman (1997) suggests that visceral proteins represent 20 to 40% of total protein degradation up to 50 kg BW. For the same period, the simulated contribution of these proteins to the total catabolic flow was greater than 50%. This overestimation of simulated catabolism of visceral proteins was associated with the same parameters of anabolism for visceral proteins. As both anabolism and catabolism of protein are correlated, the accurate estimation of the anabolic process could adequately predict the catabolic flow of proteins.
Lipid Gain and Lipid Metabolism.
As typically observed, simulated LG increased linearly with BW. A closer agreement with published LG was obtained using recent rather than less selected genotypes. In recent studies, Fuller et al. (1995) and Quiniou et al. (1995) have observed LG rates similar to those predicted by the model. In the proposed model, the description of lipid metabolism was less detailed than that for protein. Although the metabolic diversity of the different fat deposits is known (Mersmann et al., 1981), lack of data prevented the use of this fact in a realistic way. The same situation was observed for the major features of fatty acid metabolism. Nevertheless, the agreement between observed and simulated LG suggested that the homeorhetic control of lipid metabolism was sufficient to represent the major variations between and within animals. In general, the simulated metabolic flow of lipids agreed with the vivo data of Dunshea et al. (1992), although the simulated catabolic flow was lower than that previously observed. However, the aforementioned authors calculated the flow by an indirect approach, assuming a constant fractional rate of degradation (1%•d-1), which contrasts with the idea that this rate decreases with age.
Energy Status Evaluation.
When looking at the energy status, the proposed model took the flows of anabolism and catabolism of body proteins and body lipids as the key components of energy metabolism. These results indicate that the reactions of dephosphorylation (such as ionic exchanges, muscular activity) were not integrated into the model. Several authors have already tried to model energy metabolism in animals by including the major biochemical pathways and ATP yields and utilization (Schulz, 1978). Recently, Chudy (2000) proposed a model built on the "ATP concept," in which all metabolic processes consume or produce ATP-bound energy. This model shows that in order to obtain balanced body ATP, it is necessary to represent metabolic processes at a sufficiently detailed biochemical level, which can be accommodated within the framework of the current model.
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Implications
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The integration of homeorhetic and homeostatic controls in a mechanistic model can be used to predict anabolic and catabolic flows of protein and lipid in pig growth. Compared to more conventional models of pig growth, the present paper allows further understanding of pig growth at an integrated level in both the short- and the long-term. In its current state, the model serves more as a mechanistic and theoretical framework of nutrient partitioning than as a practical tool for predicting growth in pigs. Further development of this model will focus on the consequences of having an excess and shortage of nutrients on plasma and tissue metabolism in pig growth.
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Footnotes
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1 The authors wish to thank J. van Milgen for his suggestions concerning the form of the text and critical evaluation of the model. 
Received for publication March 22, 2001.
Accepted for publication July 10, 2002.
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Abstract
Introduction
= viscera proteins, 
= carcass proteins, and 
= lipids.
