On Seeing the World as an Elephant or a Mycoplasma

Lower Limits and Upper Limits on Cell and Organism Size.Physical and chemical laws ultimately set the lower and upper constraints on life. At the low end, the metabolizing, self-reproducing, unicellular prokaryote has to be large enough to accommodate operational genetic and metabolic equipment, including the genome, catalytic enzymes, and ribosomes, etc., as well as for molecular traffic. Polymerases need to have access to the genome.

Ribosomes must have space to produce proteins. In reality, for free-living cells in fluctuating environments, this minimum increases somewhat because of additional machinery to contend with catastrophes (Koch 1996). Prokaryotes vary in diameter from 0.2 µm (certain mycoplasmas) to more than 700 µm (Thiomargarita, a sulfur chemolitho- troph; shown earlier in Fig. 4.1). The typical bacterium in laboratory culture, for example Escherichia coli, is about 1 x 2 µm, but under natural conditions where nutrient stress is prevalent, cell sizes frequently are smaller.

The average bacterial size in soils and lake water is 0.1 xm³ and they are even smaller in oligotrophic environments such as the open oceans (Schulz and Jorgensen 2001), close to the estimated minimum theoretically possible of a sphere of about 300 nm diameter (Young 2006). Transport of substrate to the cells is by diffusion and by advection (movement of liquid or of the cell by swimming). The implications of small scale and the non-bounded compartmentation of prokaryotic cells to diffusion and other aspects of cell physiology are fascinating (see, e.g., Koch 1996; Schulz and Jorgensen 2001; Young 2006). Depending on external substrate concentration, bacteria may be uptakelimited or diffusion-limited. Generally speaking, motile cells must be larger than 10 xm before they can gain more substrate by swimming (for upper limits and cell scaling issues, see below). Due to typically rapid diffusion at scales of about 1 xm, bacteria are surrounded by a substrate-depleted microenvironment from which they cannot escape: a ‘depletion halo’ follows them to some extent as fast as they can swim. Movement serves only to get them into somewhat more favorable nutrient or redox patches (Schulz and Jorgensen 2001; Barbara and Mitchell 2003).

At the other extreme, why are there not any really large cells? Almost all have volumes in the range of 1-1000 µm³. Apparent exceptions to this size spectrum generally can be explained by unusual internal structure or specialized function. For example, large water-containing vacuoles may occupy much of the volume of certain plant cells and the cytoplasm in the huge cells of the prokaryote Thiomargarita occupies only a very thin peripheral layer. The extraordinary size of Thiomargarita may have evolved to store nitrate, which serves the bacterium as an electron acceptor and is only sporadically available in its habitat (Schulz and Jorgensen 2001). Various plant and animal cells are inert at maturity, serving for transport or structural support, or they may contain inclusions or food as in the case of the ostrich egg, which reaches 10¹⁵ µm³.

The upper limit to a unicellular body plan appears to be set mainly by the declining surface area-to-volume relationship with increasing size expressed as the '2/3 power law', also known as the Principle (or Law) of Similitude (Thompson 1961), where S α V⁰-⁶⁷ (Niklas 2000; see later comments on scaling). This relationship is illustrated perhaps most graphically by Vogel (2003; see his Chap. 3) who says that the main difference between a bacterium and a whale is that the bacterium has 10⁸ times as much surface area, relative to its volume, as does the whale, with the amusing quip that the former has a lot outside with not much inside and the latter a lot inside and little outside. The S/V relationship inevitably takes a toll on exchange processes of nutrients and waste products.

The operative diffusion rate limit is expressed quantitatively in Fick’s Law (Koch 1971, 1990, 1996), and is relevant to both microorganisms and macroorganisms, though the latter augment diffusion in various ways by transport mechanisms, tissue systems, and cell design (see scaling issues, below). Transportation of materials up to or within the cell, specific metabolic rate, and removal of wastes, all decrease with increasing cell size. For example, Koch (1996) shows mathematically for the single, spherical prokaryotic cell that, subject to certain simplifying assumptions, the efficiency (E) of clearance (measured by the cell volumes of medium cleared per second) is expressed as E = 3D/r², where D is the diffusion constant of an exogenous small molecule and r is the radius of the cell. So, halving the size of a cell quadruples its efficiency.

In terms of evolutionary design, the foregoing implies that the size of unicellular microbes cannot increase very much from being truly ‘micro’ without incurring a severe penalty in diminished diffusion rate sufficient to supply nutrients fast enough to sustain rapid (competitive) growth. Niklas (2000) argues that maximal body (cell) size in the unicellular algae is set by size-dependent variations in surface area, intracellular metabolites and metabolic machinery, and reproductive rates. Such limits likely pertain more broadly to all unicellular organisms, though cell shape can vary, as discussed later. An alternative avenue open to natural selection to increase size would then have been through independent experiments on aggregating moderately sized cells into a multicellular body plan, as discussed above.

With respect to constraints on multicellular organism size as opposed to cell size, the upper bound seems less rigorously demarcated than is the lower limit. While there are advantages to being larger (discussed later), mechanical and physiological problems ensue if an animal or plant becomes too big. Huxley famously said long ago (1958, p. 24) “It is impossible to construct an efficient terrestrial animal much larger than an elephant”. However, the size of what can be constructed really hinges on growth form, that is, whether the organism is of unitary or modular design (Chap. 5). Modular life forms such as plants are able to add components indefinitely. In effect they use geometry to defeat some of the constraints of gravity. Organizing a soma in this fashion allows an organism to increase biomass up to a point without transgressing critical morphological limits (Hughes and Cancino 1985; see also Chap. 5). Nevertheless, there remain ultimate limits: very tall trees, for instance, eventually encounter hydraulics problems (Koch et al. 2004) and will buckle under their own weight if they exceed certain critical heights (see following section on scaling relationships and Niklas 1994a, pp. 164-186).