Allometric scaling relationships pervade biological organization at
multiple scales. The protocell might be an exception to this rule,
therefore implying that one of fundamental principles of current living
things might have appeared later in evolution.
The form of allometric relationships is
Y = Y0Mb
where Y is some dependent variable, Y0 is a normalization constant, M is body mass, and b is the scaling exponent. Empirical values of b for different allometries are usually multiples of 1/4, as predicted by recently developed metabolic theory (West et al. 1997; Brown et al. 2004). According to this theory, biological rates are ultimately limited by the rates at which energy and materials are distributed between surfaces where they are exchanged and the tissues where they are used. It predicts that the distribution network will have a fractal-like architecture, and that whole-organism metabolic rate (i.e. the power required to sustain an organism) should scale as M3/4. Although some controversy exists on the universal form of the scaling of metabolism (Kozlowski & Konarzewski 2004), a recent evaluation of published empirical data strongly supports the theoretical M3/4 scaling (Savage et al. 2004).
The scaling of metabolism underpins the rest of predicted allometries, which, in most cases, are also well-supported by empirical measurements. A number of cellular processes scale with cellular size, such as membrane transport, biosynthesis, DNA replication and cell division. A major question is whether such allometries emerged at the very beggining of life on earth, or they are something that results from the fast evolution and increase of size of protocells and, eventually, of organisms. That is, we can view one or two crucial transitions in the origins of life on Earth: one, if life emerged at the same time that allometric scaling laws, or two, if first appeared life, and then, through allometric scaling relationships appeared through a process of optimization in the distribution of energy and materials across membranes. So far, metabolic theory assumes that natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. This optimization process seems to reinforce the two-transitions scenario, but it is not a definitive argument.
1. Metabolic power as a function of mass on a logarithmic scale. The
solid line is the M3/4 prediction (from West et al. 2002)
Despite the breadth of research on allometric scaling, organisms (e.g. bacteria) and mollecular complexes (e.g. mithocondrial respiratory complex) at the microscopic end of the scale have been largely ignored. An important exception is the work of West et al. (2002), including the metabolic power of unicells, an isolated mammalian cell, a single mithocondrion, a single molecular unit of the mithocondrial respiratory complex (HADH dehydrogenase plus cytochrome bc1 plus cytochrome oxidase), and a single molecule of mammalian cytochrome oxidase. They showed that metabolic power scales with M3/4, up to 10-18 g of size (or mass) (see Figure 1). If this scaling relation is extrapolated down to the proto-organism size scale, we obtain 5*10-22 W for the 4*10-20 g system, which is about two orders of magnitude below the expected metabolic power limit (Rasmussen et al. 2003). However, the protocell has about half the energy-to-biomass efficiency of an actual unicell, so that the metabolic rate of the protocell is estimated to be 12*10-22 W instead of allometric prediction of 5*10-22 W.
This difference in efficiency between the protocell and an actual
cell would imply that allometric scaling in biology appeared later in
evolution, as a process of optimization of nutrient transport. In this
sense, an important gap exists between the protocell and an actual
Brown, J.H. & West, G.B. (eds) (2000) Scaling in Biology. Oxford University Press.
Brown, J.H., et al. (2004) Toward a metabolic theory of ecology. Ecology 85, 1771-1789.
West, G.B., Brown, J.H. & Enquist, B.J. (1997) A general model for the origin of allometric scaling laws in biology. Science 276, 122-126.
West, G.B., Woodruff, W.H. & Brown, J.H. (2002) Allometric scaling of metabolic rate from molecules and mitochondria to cells and mammals. PNAS 99, 2473-2478.
Kozlowski, J. & Konarzewski, M. (2004) Is West, Brown and Enquists model of allometric scaling mathematically correct and mathematically relevant? Funct. Ecol. 18, 283-289.
Savage, V.M. et al. (2004) The predominance of quarter-power scaling in biology. Funct. Ecol. 18, 257-282.
Rasmussen, L., Chen, M., Nilsson, M. & Abe, S. (2003) Bridging nonliving and living matter. Artificial Life 9, 269-316.