Understanding body composition and efficiency in ruminants : a non-linear approach.

Abstract

Understanding body composition and efficiency in ruminants: a non-linear approach V.H. Oddy , A.J. Ball and A.B. Pleasants 1 2 3 l NSW Agriculture, Cattle and Beef Industry CRC, University of New England, Armidale NSW 2351 Australia * Department of Animal Science, Cattle and Beef Industry CRC, University of New England, Armidale NSW 2351 Australia 3 AgResearch, Whatawhata Research Station, Whatawhata, New Zealand Summary We present the ideas behind an approach we are working with to develop a system to understand and describe variation in body composition, growth and efficiency of nutrient use in ruminants. The mathematics and philosophy of non-linear dynamic systems are briefly presented and our rationale for using this approach are outlined. The following simplifying assumptions are employed. Protein mass is used as an index of cellularity, the dynamics of which arise from interaction between an unfolding of genetic message and the environment. Protein turnover is used as a proxy for tissue energy expenditure. Heat production arises from separate pools (viscera and muscle) with respectively high and low protein turnover per unit mass, but low and high protein mass. Fat deposition occurs from energy not used for protein turnover and deposition or lost as heat. Feed intake is regulated as a balance between energy intake, expenditure, and environmental losses and inputs. All the above interact. In this system, growth and efficiency of nutrient use arise from interactions between structural (inherited) and environmental (energy and amino acid supply) elements, rather than implicit mechanisms. Several novel representations are incorporated. Rate of protein deposition behaves as if it is first order with respect to protein mass in unperturbed (normal or continuously grown) animals. In perturbed systems, the future trajectory of potential protein deposition is altered to target a potential protein mass which may differ from the original depending on timing and extent of deviation. Differences in feed composition alter efficiency of energy retention in ruminants through the effect of the feed on visceral mass and energy expenditure. Through this approach, the need to invoke variation in efficiency of energy use for maintenance and growth due to differences in substrate use is not required. Both the short term variation and long term stability seen in ad libitum feed intake of individual animals arises from the time scale of the dynamics of the interactions, rather than specific causes. The work is unfiiished, and is presented in this early form to promote discussion. Introduction Important challenges that confront applied animal scientists are: l to reduce cost of production through improvement in efficiency of nutrient use; to increase precision of estimation of the output of saleable product and the quality of that product; and reduce environmental impact of production through: - reduction in overall energy use l a - minimisation of waste products, for example, excreta and fat, and - minimise adverse consequences of production processes in, for example, food safety, animal welfare and environmental degradation. Quantitative understanding of the factors which affect efficiency either in terms of monetary or nutrient use, and improvement in achieving market goals, is a prerequisite to meeting these challenges. The efficiency of nutrient use for growth of individual animals is affected . bY . 0 stage of maturity-less mature animals have a higher gross efficiency because their voluntary feed intake, as a multiple of maintenance, decreases with age; composition of gain-leaner animals are more efficient when expressed as g gain/MJ eaten (but perhaps not when expressed as MJ gain/MJ eaten); heat production due to: - activity-less activity less heat production; - relative size of visceral organs-visceral organs have a disproportionately high rate of energy utilisation compared to carcass tissues 0 l Recent Advances in Animal Nutrition in Australia 7997 University of New England, Armidale NSW 2357, Australia 210 Oddy et al. (Ferrell, 1988) so animals with proportionately less visceral mass are more efficient, - turnover of protein and ion transport processes-lower turnover relative to mass should be associated with reduced energy expenditure (Webster, 1984; Milligan and McBride, 1985; Knapp and Schrama, 1996); and l pattern and amount of nutrients supplied by a feed (Webster, 1989). These are influenced by both genetic and environmental factors (e.g. nutrition, disease, temperature, growth promotants). Our challenge is to draw these aspects together at the individual animal level to predict growth of body components in response to feed and environmental factors in animals of diverse genotype. This paper describes our thinking about how growth and body composition, and in turn the efficiency of individual animals, can be predicted from simple assumptions using non-linear mathematical techniques. Our thinking is not complete, and this paper should be viewed as a statement of progress rather than a definitive document. The nature of the problem Previous growth rate (usually arising from nutritional treatment) affects finishing growth rate, retail meat yield, fat depth and intrainuscular fat content of beef cattle (Carstens, 1995; Oddy et al. 1997; Table 1) and lambs (Hegarty et al. 1994). Low growth rate of weaned ruminants pre-finishing may be accompanied by enhanced growth during finishing, and a greater proportion of lean and less fat in the finished carcass. On the other hand, low growth rate before weaning, or early in life may reduce subsequent growth, and increase fat deposition (Carstens, 1995; Oddy et al. 1997). Thus, prior nutrient restriction may affect body composition either by increasing or decreasing fat content at a given weight, depending on the age of the animal at the time of feed restriction and the extent of feed restriction at that time. The practical implication of these observations is that previous nutrition can alter subsequent body composition, but the magnitude and direction of change is dependent on the stage of growth at which alteration of nutritional input occurs. This is not predictable by our present feeding systems. There is a need for a feeding system for ruminants which predicts not only the weight gain of an animal, but also describes outputs of marketable body components and some meat quality attributes. Immediate inputs to such a system ideally should remain much the same as in present feeding systems and represent animal genotype, gender, feed quality and amount, and some elements of the thermal and disease environment. An additional input will be some description of the nature of prior growth, both with respect to time relative to developmental pattern, and extent relative to potential (for more details, see the companion paper, Ball et al. 1997). , Current feeding systems do not allow body composition to be adequately predicted. Only one, SCA (1990), attempts to do so by providing empirical relationships between rate of gain, current and potential weight, and composition. NRC (1996) use body condition score to adjust for previous nutrition. However, it is acknowledged that this does not adequately describe potential changes in body composition. The basic premise of current feeding systems for ruminants is to use a single term for efficiency of feed for weight gain which encompasses deposition of energy in both fat and protein. In the California net energy (NE) system and its derivatives (NRC, 1996) variation in efficiency of feed utilisation is seen as a property of the feed which is given an estimate of feed value for maintenance and another value for growth or yet another for lactation. In the metabolisable energy (ME) system, feed is described by a single energy value, and variation in efficiency of use is derived fi=om a function describing the interaction between feed and animal. In both, there is no adjustment in efficiency of feed use for age, or composition of body gain. Present systems assume the current state of the animal is the major determinant of the animal component which responds to feed intake. Accordingly they cannot satisfactorily incorporate previous nutritional effects. Although SCA (1990) and NRC (1996) attempt to account for prior nutrition, they do so by linear adjustments to intake, rather than account for the changes in body composition which emerge in response to variation in feed regime. Inclusion of genotype, Understanding body compostion and efficiency in ruminants 211 gender and growth promotant induced differences between animals in feeding systems are confounded within a size term (used as a proxy for both mature size and hence body composition) and are reflected in estimates of maintenance requirements, rather than in a description of body composition and hence as a contributor to variation in efficiency of gain. These and other shortcomings of current ruminant feeding systems are described by Ferrell(1995). To be fair to the current feeding systems, they are limited by the realities of data collection and analysis, and the corresponding error structures which are implicit in the data, and the linear methods used for analysis. Moreover, they evolved fiom a time when feeding for liveweight and liveweight gain and milk production were the required production goals. Product description and meat quality was less well accepted as an important attribute of output from ruminants. With the success of the products of the intensive livestock industries in the marketplace, which arose predominantly from consistency of supply of relatively cheap high quality meat products, the technical needs of the ruminant production industries have to change to compete. Our way of looking at the problem Animals are self organising, structurally stable, systems, both `open' or `dissipative ' with regard to energy and matter (nutrient) flow, and `closed' or `conservative' with regard to information flow (in particular the expression of potential as contained within the genome). They operate far from equilibrium conditions. Indeed., in living systems, equilibrium is death. The mathematics required for dealing with such systems is that of non-linear rather than linear systems. This requires quite a different approach to that traditionally used in development of feeding systems. In particular it requires consideration of animals as `selfmaking' (autopoietic) entities, in which reinforcing interactions (feed back and feed forward) couple the internal and external environments of an animal. With this view, we see variation in body composition as a result of interactions between internal information (genotype) and external inputs (the dissipative system) which arise from the environment, of which matter and energy (nutrition) are the major components. Those variations in growth and efficiency which are essentially expressed in the open domain arise, we believe, from the dynamics of the interaction between feed (energy and amino acid) intake, deposition of protein and fat (which give rise to changes in body composition) and heat production (Figure 1). Combining components of both internal and external control directly confronts the research paradigm of the experimental animal scientist. In our experiments we generally observe states at a point in time, and not the evolution of the states through time. We experiment by attempting to hold factors other than the experimental variable constant, but in animal studies we know this is rarely true. Although the experimental and statistical techniques available to remove unwanted influences have become increasingly sophisticated (i.e. reduce variation to either random effects or include them in the error term) they constrain our capacity to appropriately incorporate variation arising from several sources simultaneously. Non-linear models do not obey superposition rules, so extracting effects assuming additivity is questionable. New mathematical techniques which can simultaneously consider non-linear interactions are emerging. This mathematics of nonlinear dynamic systems requires us to think differently about the biology, but at the same time offers opportunities to deal with the complex problems of animal growth and efficiency in, perhaps, a more realistic way. We outline here an initial attempt to develop the guidelines for a non-linear dynamic system to interpret and analyse factors which influence efficiency and body composition in animals. Although it is intended only to outline our ideas in a general sense, we have attempted to draw together the key components to illustrate the implications in the special case of compensatory gain. The ideas presented here comprise the major components that will be integrated in a framework which uses non-linear dynamics to predict body composition and efficiency of gain of sheep and cattle. We believe that a high degree of simplification is sufficient to capture most of the observed behaviour of animal growth, body composition and efficiency. Figure 1 Schema for a minimal model describing the interactions between body protein and fat energy (and hence weight and body composition) and feed intake. Note that this is not meant to represent a compartmental model. The important elements are the arrows denoting matter and energy flow and interactions, and the boxes represent both capacity for pattern emergence and mass storage. 212 Oddy et al. Past representations of the problem Growth is a change in weight of the organism. It is a summation of a number of components which are developing at different rates, and which interact within themselves and externally with the environment. Current models of animal growth work from either one of two premises. Growth is either pulled through time by some notion of maturity (e.g. weight (Brody, 1945), DNA (Baldwin and Black, 1979), ash (as a proxy for bone growth, France et aZ. 1987), protein (Whittemore, 1986)), or is pushed through time by ingestion of nutrients (e.g. food intake (Parkes, 1982); energy intake (Blaxter and Boyne, 1976); energy intake and amino acid supply (Graham et al. 1976)). The approach which we believe has come closest to prediction of body composition (and through that carcass yield) is that of Keele et al. (1992) and Williams et al. (1992). These workers have constructed a model of cattle growth and body composition based on the assumption that faster rates of growth contain more fat, and that the allometric relationship between body components holds. Using these simple assumptions the model they have developed is able to predict the direction of changes in body composition associated with changes in growth rate, but not where the composition of the diet induces changes in body composition. Unfortunately, it does not adequately predict where previous nutritional effects are substantial, such as seem to occur with nutrient restriction in pastoral conditions in Australia. In these circumstances, we have found that faster growth during compensatory growth is associated with higher rates of protein (and water) deposition, but that rate of fat deposition may not increase (Oddy et al. 1994 and Table 1). The nutritional inputs used in the model of Keele et al. (1992) preclude use of the model to predict effects of diet on body composition. Although other attempts have been made to incorporate interactions between growth `potential ' and feed intake (for example, Oltjen et al. 1986; Baldwin, 1995; Schinckel and de Lange, 1996), these are usually constrained by the number and functional form of the equations used, and the manner in which they interact. In particular the form, and number, of the equations chosen constrains the dynamics of the system, yet there is little recognition of this mathematical impasse. appropriate environmental constraints. The first task is to construct a minimal model that can describe the behaviour of the system. Our current attempt is shown in Figure 1. The choice of level of abstraction to represent the system as simply and as completely as possible is not arbitrary. The rigorous process of system development will both require and provide fundamental information about the constructs incorporated. The minimal components we wish to describe are temporal development of I mass of protein in the carcass, and non-carcass (viscera); II mass of fat; and III their summation to body weight and liveweight. The units used for the model are energy (MJ). Transformations to mass are made on the basis of 24, and 39 MJ/kg for protein and fat respectively. The assumptions included in our simple model are: I the animal mass; 1s attracted to some future protein * Our approach We are trying to distil from our understanding of biochemistry and physiology simple mechanisms that capture the main elements of the animals `emergent properties `, and evaluate the mathematical consequences of the simplifications. The problem we are trying to resolve is how to represent an animal, as a simplified or model system, realistically in terms of growth of the major components of the body given genetic and nutritional inputs and II heat production is a function of feed intake and protein mass of the animal; III the animal is homeothermic, i.e. regulates its body temperature within narrow limits IV feed intake is simultaneously attracted to an amino acid and energy `target ' consistent with assumption i) above, and constrained by heat production (body temperature, assumption iii) and overall level of body fat; Understanding body compostion and efficiency in ruminants 213 V fat deposition is the difference between energy intake, energy deposited in protein and heat production; VI other body components (water, ash) can be predicted from their relationship with protein. The key elements of our approach are to bring together relationships between feed intake and heat production through protein mass and gain in viscera (viscera being a high turnover, low mass component) and in the carcass (low turnover, high mass). The purpose of including protein rather than animal weight as the attractor is to capture some image of the growth of cell number and size (and hence phenotype) in animals. This thinking is a simplification of the DNA size concept introduced by Baldwin and Black (1979), but overcomes the confounding introduced by between tissue variation in protein/DNA, particularly in muscle (Di Marco et al, 1987). This approach is consistent with both measurement capabilities and the level of abstraction of the model. The approach to estimation of efficiency differs to previous feeding systems. Traditional feeding systems utilise empirically derived linear (additive) relationships between feed, weight (and through weight, body composition) and heat production. Our approach uses empirically derived dynamic relationships which encompass simultaneous interactions between feed intake, body components (protein and fat and hence weight), and heat production. In this construction, efficiency of energy use for maintenance and is an outcome rather than an input. The system we are working with can be described by the following five coupled non-linear differential equations written here in general form: Each equation contains functions of terms from other coupled equations. Unlike models derived directly Corn experimental data, the equations are built from behavioural analysis of the system of equations to ensure that they have properties that include and mimic the observed (experimental) behaviours of the system. This is an iterative process between the mathematicians and biologists and takes place before any numerical solutions are derived. Our simple notions of cause and effect have come under close scrutiny during this process, including the idea that complex behaviours can arise tiom simple laws. The first step in the model building process is to look at the behaviour of the components of the system that the model will ultimately capture. The difference in approach to that used in development of previous feeding systems is that a qualitative analysis of the system's behaviour is conducted before numerical solutions are sought. This is to ensure that the equations will generate realistic solutions. Some of the qualitative and quantitative characteristics that influence our thinking about the form of the separate equations for protein (muscle and viscera), fat, heat production and feed intake are shown below. Protein deposition We have recently shown that rate of protein deposition in well (continuously) grown animals can be described by a simple first order relationship between fractional accretion rate of protein and protein mass. This seems to hold in different genotypes of sheep and cattle (Dobos and Oddy, 1994) and pigs (data Tom Thompson et al. 1997). The intercept at zero protein mass is the same for animals of different potential protein mass, and in continuously grown animals only one parameter is required to define different genotypes. However, when protein deposition has been perturbed from the pattern of the well grown animal, the behaviour of protein gain during return to normal protein mass is complex and appears to follow a pattern resembling a damped oscillation (Figure 2). The pattern of return to normal growth state seems to be symmetrical. Perturbations in rate of protein gain to less than expected for protein mass result in subsequent higher rate of protein gain when conditions allow. Return Corn higher than expected rates of protein gain for protein mass (such as occur during nutrient infusion) results in less than expected rates of protein gain (0rskov et al. 1976; Oddy, unpublished). The kinetics of protein gain in muscle with respect to feed intake appear to follow an exponentially 214 Oddy et al. Figure 3 Relationship between metabolisable energy intake and net protein deposition, and protein synthesis and degradation in hind limb muscle of wether lambs of similar weight and age. From data presented in Oddy, 1993. decreasing form (Oddy, 1993; Figure 3). In viscera the kinetics of protein gain with respect to intake are less clearly described, but limited data for small intestine (Neutze et al. 1997) suggest a similar form of relationship between intake and protein gain as in muscle, although the parameters would be expected to differ. Protein depositon is the balance between two energy requiring (heat producing) processes, protein synthesis and degradation. The form of the relationship between rate of protein deposition, rate of protein synthesis and degradation is shown in Figure 3. This general form applies at least in muscle (Oddy, 1986) and small intestine (Neutze et al. 1997). The form of the relationship between protein synthesis and degradation differs between tissues only by the amount of synthesis relative to deposition. In muscle, where synthesis exceeds deposition by perhaps 5 to 1, the relationship between feed intake and protein degradation is as shown in Figure 3, but, in viscera, where protein synthesis exceeds deposition by perhaps 20 to 1, lprotein degradation and synthesis have almost the same form. This arises from the equality, protein deposition = synthesis-degradation (which also means that only two components need be described to specify the relationship). The relationships between protein deposition, synthesis and degradation are confounded not only because of the equality above, but also because variation in these parameters is induced by variation in feed energy (and amino acid) intake and between animal variation from both genotype and previous growth history. It is notable that the form of the relationship between feed intake and protein synthesis is the same as that between feed intake and heat production (Figure 8). We have shown that, at least in muscle, genotype affects the form of the relationship between protein deposition and feed energy intake through alteration in the rate of protein degradation (and hence protein synthesis) with respect to feed intake (Figure 4). Thus genetic and history effects do not change the form, but alter the position of the relationships between energy (and amino acid) intake and protein synthesis, degradation and deposition as shown in Figure 4. The information contained in these diagrams is drawn not from a single experiment but an overview of many. The diagrams tell us about the form of the equations needed to describe protein deposition generally in muscle and viscera, the manner in which they change relative to each other, immediate and past feed intake and in genetically different animals. Figure 3 indicates that the relationships between feed intake and protein deposition are cubic in form for muscle. It is important to determine if protein deposition in muscle and viscera follow the same trajectory with respect to feed intake during periods of increased and decreased intake. Figure 5 suggests that viscera at least does not follow the same relationship during periods of reduced feed intake as during increased intake. This suggests that there is a bifurcation in the viscera, and Understanding body compostion and efficiency in ruminants 215 possibly muscle, response to feed intake. The form of equations used to describe protein gain in both muscle and viscera was set to correspond to the implications of Figure 3 and Figure 5 (i.e. cubic in form with a single bifurcation node). The equations are : where m' = dm./dt, v' = dv/dt, and I = dI/dt are rate of energy gain in muscle, viscera and feed intake (MJ/d) respectively; a, b, c, d, a, p, y, 6 are parameters (which may be either constants or functions). By equating b =, andc=, a potential (a Lyapunov function) is derived such that df, / dm = d4 / dv defmes an attractor in m,v space. The field approaching this attractor is the potential. The potential formulation is dynamically identical with the dynamic system (gradient) equations but can be resolved with approximately 2/3 the number of parameters. The bifurcation diagram for muscle, viscera and intake is shown in Figure 6. The actual state (growth trajectory) tracks between two stable basins of attraction, such that as intake increases above a certain value the preferred attractor is high protein gain, and as intake falls below a particular value the preferred attractor is is low protein gain (or loss). The distance between the attractors (the cusp distance) may vary, and at times be quite small. That is as far as we have progressed to date with development of the equations. There are several areas in which we plan to incorporate genotype into the protein system. The most obvious is in the rate of approach to a `mature or potential' protein pool to capture the simplicity shown in Figure 2. The others are in the area of variation in feed intake with regard to protein mass and heat production (derived from protein synthesis as proxy) which will be discussed next. 30 276 Oddy et al. Heat production Lean body mass is more closely related to heat production than is total body mass (Graham, 1967; Waterlow et al. 1976; Webster, 1980; Baker et al. 199 1). Viscera has a substantially higher specific rate of heat production (i.e. heat production per unit mass) than does muscle, as measured by oxygen consumption (Eisemann et al. 1996). Muscle has a higher rate of heat production than fat. This suggests that the proportion of the highly metabolically active visceral tissues relative to muscle weight will affect the heat production of the animal. Two mechanisms link lean body (protein) mass to heat production: turnover of protein, of which protein synthesis is the major energy utilising process; and ion transport--i. e. maintenance of intracellular integritywhich in itself seems to be related to protein synthesis (Milligan and McBride, 1985; Webster, 1980). Protein synthesis per unit of protein mass generally declines with age (growth) as does utilisation of energy for maintenance relative to protein mass. An approach which deals with the contribution of protein synthesis to heat production, and hence maintenance requirements, has recently been suggested by Knapp and Schrama (1996). These authors propose that a dynamic maintenance requirement can be calculated from different energy costs for synthesis of newly deposited protein and existing protein in different body pools. Although sound theoretically, such an approach is difficult to quantify because current methods for measurement of protein synthesis in animals are unable to distinguish between peptide bonds formed in `new ' or `old ' proteins. The contribution of protein synthesis to heat production (calculated on the basis that 1 g protein synthesised requires a minimum of 4.5 kJ for peptide bond formation) suggests that whole body protein synthesis may contribute from 15 to 30% of heat production. The close relationship between protein synthesis and heat production summarised by Webster (1980) suggests that protein synthesis is quantitatively entrained with other energy utilising processes, and provides at least a convenient proxy by which dynamics of heat production can be estimated and investigated. As shown in Table 2, the relative contribution of protein synthesis to oxygen utilisation varies between tissues. The highest rate of protein synthesis and oxygen utilisation is in visceral organs. It is for this reason, and their higher specific energy utilisation, (Ortigues and Doreau, 1995), that we have chosen to describe the viscera separately Corn the more slowly turning over, and hence less energy demanding, carcass proteins in our description of protein deposition and heat production. We are accustomed to comparing energy retention with respect to intake. Such ideas are the basis of the metabolisable (ME) and net energy (NE) feeding systems. In general the relationship is of the form shown in Figure 7. This implies that the relationship between ME intake (MET) and heat production has a curvilinear form (Figure 8) which is the same shape as the relationship between protein synthesis and ME1 (Figure 3). We Figure 7 An example of the relationship between metabolisable energy intake and energy retention in sheep (data from Corbett et al. 1966). Figure 8 Relationship between heat production and ME intake. The different lines show the general effect of change in energy density of the feed. Table 2 Oxygen uptake in tissues and the minimal proportion of tissue and whole body oxygen consumption due to protein synthesis. Understanding body compostion and efficiency in ruminants 277 propose that variation in slope of the relationship between ME1 and heat production, and by definition, energy retention, arises from variation in heat production in muscle and viscera because of changes in protein turnover and mass of protein in these different pools (Knapp and Schrama, 1996). The effect of feeds of different energy density (MJ ME / kg feed dry matter, M/D) on heat production has been both a cornerstone and a source of controversy in the field of ruminant nutrition. Our view is that these effects are mediated through affects on visceral mass (Ferrell et al. 1986) and protein turnover and hence energy expenditure (Neutze et al. 1997), and to a lesser extent on muscular energy expenditure (Ortigues and Doreau, 1995). This proposal is consistent with the suggestion of Sainz (199 1) that heat production in lambs eating different diets was better related to visceral mass and an undefined function of energy intake, than visceral mass alone. Sainz speculated that the undefined function of energy intake co