The origin of allometric scaling laws in biology from genomes to ecosystems: towards a quantitative unifying theory of biological structure and organization

Abstract

Life is almost certainly the most complex and diverse physical system in the universe, covering more than 27 orders of magnitude in mass, from the molecules of the genetic code and metabolic process up to whales and sequoias. Organisms themselves span a mass range of over 21 orders of magnitude, ranging from the smallest microbes (10 -13 ·g) to the largest mammals and plants (10 8 ·g). This vast range exceeds that of the Earth's mass relative to that of the galaxy (which is 'only' 18 orders of magnitude) and is comparable to the mass of an electron relative to that of a cat. Similarly, the metabolic power required to support life over this immense range spans more than 21 orders of magnitude. Despite this amazing diversity and complexity, many of the most fundamental biological processes manifest an extraordinary simplicity when viewed as a function of size, regardless of the class or taxonomic group being considered. Indeed, we shall argue that mass, and to a lesser extent temperature, is the prime determinant of variation in physiological behaviour when different organisms are compared over many orders of magnitude.Scaling with size typically follows a simple power law behaviour of the form:where Y is some observable biological quantity, Y 0 is a normalization constant, and M b is the mass of the organism (Calder, 1984;McMahon and Bonner, 1983;Niklas, 1994;Peters, 1986;Schmidt-Nielsen, 1984). An additional simplification is that the exponent, b, takes on a limited set of values, which are typically simple multiples of 1/4. Among the many variables that obey these simple quarter-power allometric scaling laws are nearly all biological rates, times, and dimensions; they include metabolic rate (bഠ3/4), lifespan (bഠ1/4), growth rate (bഠ-1/4), heart rate (bഠ-1/4), DNA nucleotide substitution rate (bഠ-1/4), lengths of aortas and heights of trees (bഠ1/4), radii of aortas and tree trunks Life is the most complex physical phenomenon in the Universe, manifesting an extraordinary diversity of form and function over an enormous scale from the largest animals and plants to the smallest microbes and subcellular units. Despite this many of its most fundamental and complex phenomena scale with size in a surprisingly simple fashion. For example, metabolic rate scales as the 3/4-power of mass over 27 orders of magnitude, from molecular and intracellular levels up to the largest organisms. Similarly, time-scales (such as lifespans and growth rates) and sizes (such as bacterial genome lengths, tree heights and mitochondrial densities) scale with exponents that are typically simple powers of 1/4. The universality and simplicity of these relationships suggest that fundamental universal principles underly much of the coarse-grained generic structure and organisation of living systems. We have proposed a set of principles based on the observation that almost all life is sustained by hierarchical branching networks, which we assume have invariant terminal units, are space-filling and are optimised by the process of natural selection. W...

The relationship between social status, behaviour, growth and steroids in male helpers and breeders of a cooperatively breeding cichlid

“…It is standard practice to allometrically correct physiological measurements related to the overall metabolism of the focal animal, correcting for the overall body size of the individual (West and Brown, 2005). Therefore, hormones released into the water have been scaled to body mass in previous studies, dividing the excreted levels by body mass (Oliveira et al, 2003;Hirschenhauser et al, 2004).…”

Flies evolved small bodies and cells at high or fluctuating temperatures

“…Arguably, variation in cell volume has been understudied as a potential driver of physiological performance. A provocative theory of metabolism even makes a bold and erroneous assumption that cells are of the same size in all organisms (West & Brown, 2005). Quite the opposite, cell size has varied among tissues, individuals, or species whenever biologists have focused their lenses on this subject (Arendt, 2007; Czarnoleski, Cooper, Kierat, & Angilletta, 2013; Kozłowski, Czarnołęski, François‐Krassowska, Maciak, & Pis, 2010; Stevenson, Hill, & Bryant, 1995).…”

Connections between Warburg’s and Szentgyorgyi’s Approach about the Causes of Cancer

“…Moreover, the scaling of the metabolic activity is different in mitochondrial or non-mitochondrial metabolism. The normal mitochondrial metabolism performs the Krebs cycle, and its scaling exponent is well distributed around p=¾, [77,137], while the scaling exponent of fermentative respiration is near to ⅔ [144]. Remarkably, the healthy mammalian cells and the mitochondria that are 5 orders of magnitude lighter, as the respiratory complexes (having further 5 orders of magnitude less mass than mitochondria) are fit well on the allometric scaling with ¾, [145].…”