Scaling of number, size, and metabolic rate of cells with body size in mammals

Abstract

The size and metabolic rate of cells affect processes from the molecular to the organismal level. We present a quantitative, theoretical framework for studying relationships among cell volume, cellular metabolic rate, body size, and whole-organism metabolic rate that helps reveal the feedback between these levels of organization. We use this framework to show that average cell volume and average cellular metabolic rate cannot both remain constant with changes in body size because of the well known body-size dependence of whole-organism metabolic rate. Based on empirical data compiled for 18 cell types in mammals, we find that many cell types, including erythrocytes, hepatocytes, fibroblasts, and epithelial cells, follow a strategy in which cellular metabolic rate is body size dependent and cell volume is body size invariant. We suggest that this scaling holds for all quickly dividing cells, and conversely, that slowly dividing cells are expected to follow a strategy in which cell volume is body size dependent and cellular metabolic rate is roughly invariant with body size. Data for slowly dividing neurons and adipocytes show that cell volume does indeed scale with body size. From these results, we argue that the particular strategy followed depends on the structural and functional properties of the cell type. We also discuss consequences of these two strategies for cell number and capillary densities. Our results and conceptual framework emphasize fundamental constraints that link the structure and function of cells to that of whole organisms.

Fig. 1.

Plot of the logarithm of the mass-specific metabolic rate, B̄, versus the logarithm of body mass, M, for mammals. The data set is from Savage et al. (25), which contains a total of 626 species data points. The numerous small diamonds are the raw data. The data were binned to account for the bias toward species with small body masses, and the squares represent the average of the logarithms for every 0.1 log unit interval of mass (25). The regression line is fitted to the binned data (squares). Note that the mass-specific metabolic rate can be thought of as either the ratio of whole-organism metabolic rate to body mass, B/M (Eq. 1) or the ratio of the average cellular metabolic rate to the average cell mass, B_c/m_c (Eq. 2). It is clear that the mass-specific metabolic rate decreases with body mass with an exponent close to −1/4 [for the binned data the slope is −0.26 (P < 0.0001, n = 52, 95% C.I.: −0.29, −0.24)]. This relationship demands a tradeoff between cellular metabolic rate and cell mass as body mass varies.

Fig. 2.

Plots of the logarithm of cell volume versus the logarithm of body mass for 14 cell types that most closely follow strategy i (invariant cell mass and scaling cellular metabolic rate). Except for alveolar macrophages, the 95% CI of the slopes all include the value of 0 that is expected for strategy i (Table 1).

Fig. 3.

Plots of the logarithm of cell volume versus the logarithm of body mass for four cell types that most closely follow strategy ii (scaling cell mass and invariant cellular metabolic rate). The 95% CIs of the slopes are all >0 and near the values expected for strategy ii (Table 1).

Fig. 4.

Plots of the logarithm of cell number versus the logarithm of body mass for two cell types that most closely follow strategy ii (scaling cell mass and invariant cellular metabolic rate). The 95% CIs of the slopes all include the value of 0.75 corresponding to strategy ii (Table 1).