Across species of widely differing body size (e.g. mouse to elephant), cell size does not vary appreciably whereas cell number does. Therefore, species of larger mature size are characterized by having a greater number of cells than animals of smaller mature size. It has long been recognized that BMR varies with animal size. As animal size increases so does BMR, although not in direct proportion to the increase in size. From experimental observa- tions, it has been shown that BMR increases in proportion to body weight raised to the power 0.73. Therefore as animal size increases across species, cell number increases in direct proportion to weight but metabolic rate increases in proportion to weight to the power 0.73. Thus metabolic rate per cell decreases as animal size increases (cellular metabolic rate will change in proportion to weight raised to the power of minus 0.27). Does this mean that cells from a large animal are incapable of metabolizing at rates equivalent to those from a small animal? Studies by Wheatley and Clegg (1994) suggest that this is not the case. They compiled data from a number of sources which compared metabolic rates of isolated cells or tissue slices taken from animals varying in size from 0.012 (mouse) to 780 (horse) kg. Whilst there was some reduction in metabolic rate measured in vitro as animal size increased, the
magnitude of the differences in vitrowere relatively small when compared with the differences in metabolic rates in vivo.
Indeed, in the studies of O2 consumption and sodium pump activity referred to earlier (Gregg and Milligan, 1982; McBride and Milligan, 1984, 1985a, b), there were few if any treatment effects on total O2con- sumption of different tissues incubated in vitro. Coulson (1993) argues that the differ- ences in metabolic rates in vivo on a per cell basis are due to differences in the rate of supply of oxygen to these cells. For many metabolic pathways, the supply of oxygen is the rate-limiting step and deliv- ery of it depends primarily on blood flow (oxygen extraction rates as tissues are per- fused are remarkably similar across species). His argument, which he refers to as the ‘Flow Theory’, is based on certain physical constraints imposed on animal design (Coulson, 1993). Firstly, that blood pressure has to be maintained within cer- tain limits (high enough to ensure that red blood cells can pass through capillary beds and plasma can perfuse cells, but not so high as to cause damage to blood vessels).
Secondly, since blood volume is approxi- mately 6.5% of body weight in animals (Schmidt-Nielsen, 1984), as animals increase in size, for blood volume to remain a fixed proportion of size, the diam- eter of the major blood vessels must decrease. As the diameter of blood vessels decreases, then the rate of flow of blood through them must also decrease in order to prevent blood pressure increasing dra- matically.
Coulson uses the Flow Theory to argue that the rate of oxygen supply to tissues thus decreases as animal size increases, resulting in lower metabolic rates, expressed on a per cell basis, in larger animals. He uses this argument to explain differences between species of differing mature size and also to explain changes in the rate of growth as an animal matures. In this case, the cells within an animal’s body will have a certain requirement for energy in order to meet their basal costs. Whilst oxygen supply is sufficient to ensure rates of energy production in excess of this fixed
cost, the potential exists for the cells or tissues to grow. Therefore, as the animal grows, the diameter of major blood vessels must decrease in order to maintain blood volume at a fixed proportion of body weight. As this happens, so blood flow rates decrease, and hence the rate of oxygen supply to the tissues within the animal’s body also falls. The resting meta- bolic rate of cells and thus their potential to produce ATP will decline, reducing the rate of growth. Additionally, as cells grow, their surface area increases, causing higher rates of Na+ leakage. Therefore, as fixed costs increase and the potential metabolic rate of the cells decreases, the excess energy production over the fixed costs decreases, and hence the potential for growth reduces. Mature size is reached for a particular animal when fixed costs and potential energy supply coincide.
The potential for growth will depend on the difference between fixed costs of cells and their metabolic rate. Since fixed costs are determined in part by cell size (and this does not vary appreciably across species) and metabolic rate declines as mature size increases (as discussed above), the fractional or proportional rate of growth also declines across species as mature size increases. The fractional rate of growth is effectively the rate of growth on a per cell basis. Although this is lower in an animal of larger mature size than it is in a smaller one, the absolute rate of growth of the whole animal will be greater as larger animals contain many more cells than smaller ones do.
Conclusions
Care needs to be taken in the interpretation of measurements of Na+,K+-ATPase activity made in vitro. The incubation medium used, whether it employs CO2/HCO3 as the main buffer or not (increasing the potential for cycling of carbonic acid across the plasma membrane), whether it contains a single energy substrate or a more balanced set of nutrients, and how tightly controlled pH and osmolarity can all
influence the rate of Na+entry into the cell, and hence Na+,K+-ATPase activity. Nearly all measurements of ion transport have been made on isolated cells or pieces of tissue removed from the animal and incubated in vitro. The incubation medium used is usually devoid of hormones and contains standardized (and often high) levels of substrate. The differences observed indicate that some intrinsic property of cells has been altered and that this persists for the period of time between tissue removal and the measurements being made.
Consideration of physiological pro- cesses at the level of individual cells enables the understanding of energy use. It can be appreciated that many energetic costs are consequences of particular meta- bolic or physical processes, and thus the opportunity to manipulate them is limited.
High rates of metabolic activity equate with increased basal metabolic requirements of individual cells. For example, high rates of CO2production will increase the rate of H+ efflux from cells as part of facilitated diffusion of CO2, in turn increasing energy use by Na+,K+-ATPase. The ability of cells to divide or to grow is dependent on hormonal stimuli that increase pHi as part of the sequence of events they trigger. This increases basal energy use by increasing the rate of H+ efflux, again increasing Na+,K+-ATPase activity.
Ensuring that the balance of nutrients is optimal will ensure that the potential for wasteful cycling of acetate across the cell membrane is minimized. Acetate cycling will be greater when the concentration of
acetate in blood is high relative to the cell’s ability to metabolize it. The availability of other nutrients can influence this (Illius and Jessop, 1996).
Therefore, the ability of weak acids such as acetic and carbonic acids to act as proton ionophores is worthy of further investigation as a new concept which might offer the possibility of a unifying theory to account for previously contradic- tory observations. It may explain the changes in efficiency of use of metaboliz- able energy with differing diets, the causes of which have not yet been elucidated satisfactorily. Understanding the causes of reduced metabolic efficiency and the associated heat increment would be of tremendous advantage, for example in developing improved feeding strategies when combating heat stress. The possi- bility of metabolic energy dissipation as a result of a physical transmembrane influence of metabolites could yield a very profound new insight into the energy metabolism of many species beyond ruminants. Such information will be required in order to assess the causes of differences in energy use between animals of differing genotype. Taylor et al. (1987) reported that maintenance needs of cattle varied with breed. Such differences cannot be accounted for by changes in the propor- tions of metabolically active tissues (Taylor et al., 1991; Webster, 1993), thus indicating that differences in metabolic efficiency exist. Identification of nutrients and hormones that have a direct influence on metabolic efficiency will be necessary to understand the causes of such variation.
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