Biomedical Engineering Reference
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Figure 4 . Universal growth curve. A plot of the dimensionless mass ratio, r = 1 - R ( m / M ) 1/4 ,
versus the dimensionless time variable, U= ( at /4 M 1/4 ) - ln[1 - ( m 0 / M ) 1/4 ], where a = B 0 m c / E c and
m 0 is the mass at birth. Data are for a wide variety of species with determinate and indetermi-
nate growth. When plotted in this way, our model predicts that growth curves for all organisms
should fall on the same universal parameterless curve 1 - e - U (shown as a solid line). The model
identifies r as the proportion of total lifetime metabolic power used for maintenance and other
activities. This figure is reproduced with permission from West et al. (2001) (50).
for ontogenetic growth leads to scaling laws for other growth characteristics,
such as doubling times and the relative energy devoted to maintenance.
3.2. Nucleotide Substitution Rates, Cellular Energetics, and Genome Size
One of the most interesting consequences of these ideas is that nucleotide
substitution rates in DNA and rates of molecular evolution (52,53) can be char-
acterized by combining the theory of biological scaling with Kimura's classic
neutral theory of molecular evolution (54). It is assumed that point mutations,
and therefore substitutions, occur at a rate proportional to metabolic rate. This is
because most mutations are due to processes such as free radical production or
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