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Minimal protocell size and metabolism: the relevance of allometric scaling laws.


Most biological scaling relationships are manifestations of a single underlying scaling process,
which appears to be based on quarter powers and to be unique to LIVING things
                                                                                                J.H. Brown et al. 2000


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.

allometries_cellsFig. 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 unicell.


Selected references
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.


Stoichiometric imbalances at the very beggining of life?


There are limits to what combinations of chemical elements can function as a living cell. Indeed, a distinct stoichiometric signature of living systems is one tool used to separate life from non-life in ancient fossilized material (e.g. Watanabe et al. 2000). One of fundamental characteristic of life on Earth, from molecules to ecosystems, is its stoichiometric imbalances with respect to their environment. Basically, the proportion of nutrients (i.e. nitrogen, N, and phosphorous, P) is greater inside cells and organisms than that observed in the environment, leading to lower C:N, C:P, and N:P ratios. The question is therefore whether such imbalances appeared at the very beggining of life, or whether they appear later; in other words, whether stoichiometric imbalances of actual cells correspond to those observed in artificial protocells.

Figure 2 N:P ratios across different biomolecules (from Sterner & Elser 2002)

In this sense, it is crucial to know the stoichiometric composition of the protocell and that from actual cells. One of major differences between both is the stoichiometry of the genetic system involving information-bearing molecules that encode the critical molecular processes and simultaneously participates catalytically in the metabolism. In the protocell, these are PNAs (i.e. peptide nucleotid acids), whilst in actual cells these are DNA or RNA. Significant differences on C:P and N:P ratios exist between PNAs and DNA (see Figure 3), differences that are manifested on the stoichiometry of the entire cell.

Briefly, C:P and N:P ratios are much lower in DNA than in PNA, because PNA molecules simply do not contain P as DNA molecules do. Unlike nucleotids, PNAs lack pentose sugar phosphate groups; i.e. the backbone is uncharged. In current biology P is generally viewed as the limiting nutrient for fundamental processes within organisms (e.g. growth) and within cells (e.g. photosynthesis and respiration). Therefore, the acqusition of P for encoding molecules and other metabolic processes  in which P is the crucial element (e.g. accumulation of energy in ATP form) might have appeared later in life evolution, representing an important difference between current biology and the protocell.
 











References
Watanabe, Y., Martini, J.E.J., & Ohmoto, H. (2000) Geochemical evidence for terrestrial ecosystems 2.6 billion years ago. Nature 408, 574-578.
Sterner, R.W. and Elser, J.J. (2002) Ecological Stoichiometry. Princeton University Press, Princeton, New Jersey, USA.