Now in the name of all the gods at once,
Upon what meat doth this our Caesar feed,
That he is grown so great?

William Shakespeare

The sigmoid curve

If animal height or weight are measured from conception to senescence, the data usually follow a flattened "S" shape called the sigmoid curve. But the growth curves of meat animals raised under commercial conditions may appear as relatively flat slopes (the middle segment of the flat "S"), and the sigmoid shape may only become apparent if the data include very young animals or animal beyond a typical market weight. In other words, growth velocity is approximately constant during the commercial growing period.

Acceleration and deceleration

At first, the fertilized ovum divides mitotically with little or no growth in mass. However, as soon as it develops the means of assimilating energy, the growth of the embryo accelerates. At birth and weaning there may be a temporary deceleration of growth as an animal switches from one source of nutrients to another. Except for a slight acceleration at puberty, subsequent growth maintains a steady average velocity until the terminal deceleration that occurs as animals reach their mature size. However, although the average velocity may be smooth, there may be an underlying circadian (daily) periodicity in growth rate or even erratic spurts of growth.

Anabolism versus catabolism

Anabolism is the building up of body components, while catabolism is their destruction.

Protein turnover

Protein turnover is the time between anabolism and catabolism of an individual protein. If protein turnover rates are measured in growing meat animals, the half-life for protein synthesis is shorter than the half-life for protein catabolism. The half-life is used, as in studies of radioactivity, because it may take an impossibly long time for 100% to turnover, so we only wait for 50%. For meat animals, the half-lives of the important meat proteins are around several days in length, with muscle proteins being much faster than connective tissue proteins. In the muscles of young animals, both the rates of protein synthesis and degradation are faster than in older animals. In the muscle tissue of growing animals, insulin is the most important factor that inhibits the degradation of myofibrillar proteins when anabolism exceeds catabolism. Epinephrine and serotonin have similar but minor effects. In fasting animals, where catabolism exceeds anabolism, proteolysis is promoted by glucocorticoids.

von Bertalanffy's equation

This is based on the concept that each increment to body weight (W) represents the triumph of anabolism over catabolism,

dW/dt = a.Wb - c.Wd

body weight increment = anabolic increment - catabolic loss

This yields values for parameters b and d that are between 2/3 and 1, much like the power relationships of body mass or volume to body surface area. Heat loss tends to be proportional to skin area, while gut areas may be rate limiting for nutrient uptake. Both heat generation and anabolic systems tend to be related to body volume. The von Bertalanffy growth equation requires some integration over time since the rates of anabolism and catabolism may have short-term fluctuations.

The occurrence of muscle growth in a meat animal provides clear evidence that the average rate of protein synthesis excedes the average rate of protein degradation. It must be remembered, however, that the inbalance in favor of anabolism may not be very large or very stable. With in vitro measurements of protein metabolism in excised muscle samples there is a serious risk that the muscle may have been released from its normal physiological duties and from endocrine and neural control mechanisms responsible for its long-term metabolic control. For example, isolated fast and slow growing muscles from broiler and layer-type poultry may exhibit similar rates of protein anabolism and catabolism when maintained in vitro, despite the occurrence of extreme differences in muscle growth in vivo. However, when myoblasts from embryos of broiler and layer-type chickens are compared in vitro, the greater capacity of cells from broilers to accumulate protein may be attributable to a lower rate of protein degradation. Another subtlety that complicates the picture is that animals with a rapid rate of protein accumulation also may have an elevated rate of muscle protein degradation and it has been proposed that selection for meat yield in poultry should be based on decreasing the rates of degeneration, rather than attempting to increase the rate of synthesis. However, in beef, one would not want to jeopardize post mortem proteolysis because it makes an important contribution to taste and tenderness.

Energy content

Body weight is partitioned between several commercially important compartments. Less energy is required to form a kilogram of lean meat than to form a kilogram of dissectable fat. Thus, a progressive diversion of feed energy away from protein accumulation and towards fat deposition may contribute to the decelerating curve of body weight growth in meat animals, although in consistently fat animals such as pigs this effect may be only slight. The decrease in feed efficiency that occurs with increased live weight in pigs is primarily caused by increased maintenance cost and not increased fat deposition. The time at which the diversion to fat deposition occurs may depend on the breed of animal, and is late in animals with a large adult size. The relative amount of water in the lean tissues of the body decreases with age. The rate of decrease in water content may be altered at weaning and at the onset of sexual maturity.

Body area versus mass

In attempting to give a biological meaning to the terms b and d in von Bertalanffy's equation, one cannot simply assume that the proportional growth of the surface areas of the body keeps pace with the growth of the whole body. In pigs, for example, the small intestine grows rapidly after birth but reaches its mature length between 5 and 6 months of age. A similar early growth attainment of final size is found in the alimentary tract of cattle. Similarly, with heat loss from the body surface, the increased insulation provided by subcutaneous fat must be taken into account. Various regions of the body may differ in their depth of subcutaneous adipose insulation, and there are considerable differences between breeds in the contribution of each body region to the total body area.

Robertson's autocatalytic equation

There is a resemblence between sigmoid growth curves and those of autocatalytic or self-accelerating chemical reactions in which the product of a simple reaction acts as a catalyst to accelerate further reaction. In a first order chemical reaction, the reaction rate is proportional to only one concentration. For example, in a decomposition reaction the disappearance of the decomposing substance is given by,

-dc/dt = k.c

disappearance rate = reaction constant x substance concentration

The initial concentration of the substance (a) is reduced by the amount lost (x) so that its concentration becomes a-x and the equation soon changes to,

- d(a-x)/dt = k(a-x)

Since da/dt, the derivative of a constant is zero,

dx/dt = k(a-x)

Robertson took the case of an autocatalytic reaction where the reaction constant (k) was multiplied by the mass or concentration of the catalyst that was the reaction product itself (x),

dx/dt = kx(a-x)

The curve of this reaction was sigmoid and resembled growth curves for body weight (W),

dW/dt = kW(a-W)

Its initial acceleration results from the increase of the catalytic reaction product, and its later deceleration results from a depletion of the raw material or starting substance. Robertson was aware of the fact that overall body growth was the sum of a very large number of individual reactions rather than a single reaction, but he forced himself to chose between two alternatives: either the similarity of autocatalytic reaction curves and animal growth curves was a mere superficial resemblence or, alternatively, it was a meaningful indication of an underlying "master-reaction" working on autocatalytic principles. Robertson chose the latter alternative on an intuitive basis. It is usually considered that there is little or no evidence in support of Robertson's choice, and that his logistic equation survives today only as a means of fitting a curve to growth data. It might be wise, however, to refrain from passing judgement on Robertson's intuition until we actually find out how growth is regulated.

Robertson's initial chemical reaction catalysed itself: animals initially add new cells that form further new cells, and for a while the system may behave like a population of microorganisms proliferating in an abundant nutrient medium. Even under these conditions, however, mitotic rates usually show some deceleration. For example, in chick embryos at the 17-somite stage, the number of cells is doubled in 4 hours, but to double the numbers again then takes about 13 hours. As young farm animals grow larger, they consume more feed and store increasing amounts of fat. After a certain point, however, the capacity for energy storage becomes limited by the increasing demands of cellular maintenance and repair, and by the diversion of energy towards reproduction. These self-accelerating and limiting factors work in the same way as those in von Bertalanffy's equation. If the postnatal body tissues of birds and mammals were composed solely of undifferentiated cells like those of the embryo, self-acceleration by cell proliferation might be taken seriously. In meat animals, however, this is not the case.

In the skeletal muscles, massive amounts of protein are assembled into myofibrils. Myofibrils grow in length by forming new sarcomeres at their ends, and they grow radially before they subdivide by longitudinal splitting. New proteins for the myofibril are formed by the activity of ribosomes. Thus, myofibrillar growth per se is not self-accelerating, except in an indirect manner - stronger animals might get more to eat. The growth of adipose tissue is dominated by triglyceride accumulation. Triglyceride accumulation is not self-accelerating, and it provides an even smaller indirect advantage to the animal's growth. Thus, the accelerating phase of growth in meat animals becomes all the more remarkable when we realize that much of the newly added biological material is not self-replicating.

Age-based equations

In the equations considered so far, the final deceleration necessary to create a sigmoid curve has originated from, or has been proportional to the enlarged body mass itself. Another way of thinking about the control of deceleration is to envisage it a function of time, so that the growth rate decreases in simple inverse proportion to animal age

1/W . dW/dt = k/t

specific growth rate = species constant / age

Growth curves constructed in this manner, with animal age as the controlling factor in deceleration, never reach a point of zero growth in older animals. Although perpetual growth may occur in lower vertebrates, until cut short by accidental death, there is a finite upper limit to the size of mammals and birds. In agriculture, age-based growth curves may provide a reasonable fit to growth data since the commercial growing period is in the first half of the sigmoid curve.

Instead of growth rate declining in simple inverse proportion to age, it may decline in logarithmic proportion, as in the equation proposed by Gompertz way back in 1825 to calculate financial returns on monetary investments! Thus, in a Gompertz relationship, the logarithm of specific growth rate plotted against time yields a negative linear slope. The Gompertz curve is asymmetric about its inflection point, which occurs early in the curve while the logistic curve is symmetrical.

Linear growth - the flat part of the "S"

During the commercial growth of meat animals to market weight, growth may appear almost linear with a constant velocity. During this time, myofibrils, triglyceride and bone matrix accumulate passively by accretionary growth, and the constraints to growth have no measurable impact that may be isolated from sampling error and experimental error. This biologically distinct period of linear growth may be isolated from its sigmoid context to improve the fit of predicted curves to actual data.

Chronological versus physiological age

In the comparison of breeds that differ in their rate of physiological development, it is difficult to justify the use of chronological age rather than physiological age to predict the decline in the logarithm of the specific growth rate. Another problem with time as the regulatory parameter of growth is that it makes no allowance for periods when an animal may cease growing because of restricted nutrient intake or stress. This problem does not arise with body weight as the regulatory parameter, and it could also be avoided by using physiological age rather than chronological age. There are, however, no simple units with which to measure physiological age.

The concept of physiological age has been used to create a physiological time scale called metabolic age, based on the relationship between mature size and the chronological time taken to reach it. The chronological time taken to reach mature weight is made proportional to the mature weight raised to the 0.27th power so that the units of metabolic age are those of chronological age divided by the 0.27th power of mature weight. Another approach to the problem of measuring physiological age is to evaluate animals on the basis of a set of criteria that change as animals grow older. Some of the criteria that have been suggested are: physical and chemical tests of the degree of cross linking in collagen, elasticity of the aorta, accumulation of lipofuscin brain cell pigment, and the mitotic potential of cultured cells.

Genetic selection for leaness in pigs may have delayed their physiological maturation. Thus, genetic selection might be more effective if animals are given a high plane of nutrition and suitable environmental conditions for optimal growth. In model systems, however, the responses to selection appear to be more complex, and genetic advances made under optimal conditions may not automatically be expressed if the animals are switched from optimal to suboptimal environmental growth restraints. One aspect of this problem is that physiological maturation may be delayed in a population whose growth is environmentally restrained.

Growth rhythms

Intrinsic seasonal rhythms in muscle growth are difficult to identify in farm animals that reach market weight in less than a year since intrinsic rhythms are difficult to isolate from seasonal reproductive cycles and seasonal cycles in the nutrient quality of animal feed. In laboratory animal experiments, intrinsic seasonal changes in rates of growth and cellular regeneration have been found to persist even in animals kept under constant conditions of temperature and day length. Seasonal rhythms occur in milk and egg production. In Scottish free-grazing sheep, the average empty body weight of ewes peaks in November and reaches a minimum at the end of April, with subcutaneous fat providing the primary energy reserve depleted during gestation.

Effect of light

In poultry, light has a profound effect on aspects of animal behavior such as feeding and roosting that then secondarily affect growth rate. For example, poultry may be reared at a low intensity of light so that they expend less energy on muscular activity, but then they may start to use other clues, such as temperature or sounds of activity to adjust or entrain their circadian rhythm of activity. Chickens exhibit maximum growth if they area fed late in the evening, because then they have all night to work through the feed stored in their crop. But to do this, the chickens must learn how to anticipate the start of the period of darkness, and they may do this more readily if the light intensity is slowly decreased to simulate dusk. The more rapid growth of chickens under these conditions originates from increased feed intake and increased feed efficiency. Chickens also show enhanced growth if kept at a continuously low light intensity, but in this case there is no increase in feed efficiency. The effects of illumination may be found in the levels of thyroxine production in baby chicks.

Supplemental illumination also stimulates growth in lambs and cattle, possibly acting via the gonads since stimulation of growth may occur in heifers but not in steers. In lambs, prolactin concentration is increased by long day-length but thyroxine, STH, and insulin concentrations are not. In heifers, prolactin concentrations also are increased by a long photoperiod that has no effect on STH levels, but prolactin may not be the major mediating factor in the effect of photoperiod on growth rate.