Scientists have been measuring organisms metabolic rate per gram as a way of

Transcription

1 1 Mechanism of Power Laws in Allometric Scaling in Biology Thursday 3/22/12: Scientists have been measuring organisms metabolic rate per gram as a way of comparing various species metabolic efficiency. Geoffrey West and others have shown that larger animals tend to be more metabolically efficient, where the size of the animal correlates with its metabolic rate according to a 3/4 th exponent. 1 The accepted explanation is that this is due to the fractal structure of their branching circulatory systems. However, this explanation does not explain the various allometric scaling laws of bacteria, single-celled eukaryotes, sponges, and other organisms that lack circulatory systems. These simpler organisms metabolic rates scale according to different power laws. Single-celled eukaryotes have been observed to follow a scaling law with an exponent of one, while even simpler bacteria scale at an exponent greater than one, meaning they get less efficient as their mass increases. 2 Although substantial amounts of empirical data support these power laws, very few mechanisms have been proposed to explain them. 3 Here, we propose a plausible explanation for metabolic scaling trends across all species, by using a bottom-up approach. At every level of complexity, life is organized into networks. Every living organism is an open system that exchanges information with its environment in the form of chemicals and energy. All cells use the information they obtain from the environment to maintain homeostasis and reproduce. When chemical reactions come together in an organism, these reactions become dependent on one another and interact, i.e. the reactions become entrained. By chemical coupling together in a chain of reactions, the energy from one chemical reaction is caught and used in the next step of a metabolic process, harnessing the energy that may have otherwise dissipated into the environment as heat.

2 2 Over evolutionary time, network motifs have become more robust and interconnected. For example, in simpler organisms, such as bacteria, the proteins that the organism uses to interpret signals from the environment and exchange information are simple, but in eukaryotes they are much more complex. Likewise, prokaryotic transcription is simple. One enzyme binds to DNA, followed by several subunits that transcribe DNA into RNA by working down the line. 4 In eukaryotes, transcription is much more complicated. Introns must be removed, and the machinery involved in translation requires the movement of histones for proper gene regulation. 5 In prokaryotes, glycosylation is less complex and works by different mechanisms than in eukaryotes. In prokaryotes there are many different forms of these proteins, because there has been no selective pressure for energy efficiency, and less entrainment with as many systems as you see in eukaryotes. 6 Complex information network carry adaptive benefits, allowing organisms to process information faster and more efficiently. This is known as the network effect. A random network, where interacting elements called nodes are connected to one another along edges at random, is seven times slower and far less robust than a real network (produced by natural selection) with the same number of nodes and edges. 7 Whenever a new node is created, via mutation, that is inefficient, the organism is put at a selective disadvantage when energy (food) is less available in the environment. When a node adds to energy efficiency, however, it will be selected for during times of low energy in the environment (i.e. starvation). Complex networks allow for energy efficiency through robustness and fidelity. By becoming more intricate, cellular processes trap a larger portion of the information and energy brought into the cell. For example, bacteria ferment and eukaryotes respire. A fermenting bacterium may produce only two moles ATP per mole glucose. 8 Yeast, a single-celled eukaryote, with its more complex, robust

3 3 information network, made up of many entrained systems working together, can produce 32 moles ATP per mole glucose. The response of the eukaryotic network allows the increased ATP production: glucose availability in the cell and a threshold concentration of ATP and ADP together trigger ATP synthesis. 9 Increased copying fidelity is another adaptive benefit of the complex eukaryotic information network. Different transcription enzymes have different rates of fidelity; the mutation rate in bacteria is a ten times greater than in single celled eukaryotes, which is ten times greater than in invertebrates, which is ten times greater than in vertebrates. This fidelity allows for better information transfer, which decreases the amount of energy needed to fix mistakes. 10 Large multicellular organisms tend to have the most complex information networks, and thus, have a lower metabolic rate per gram because they use, rather than dissipate, a larger fraction of the chemical energy they take in. For example, lets look at insulin production in humans. In multicellular organisms, the mechanisms that begin ATP synthesis are entrained with other chemical processes, allowing for storage of excess glucose before immediate use through insulin. With different specializations, a body is able to use glucose more efficiently through selective storage and use. 11 The more that cellular mechanisms entrain, the more efficient the organism becomes. Naturally, then, an organism with entire organ systems entrained together in a complex network will be more energy efficient than a simple, single-celled eukaryote or bacterium. By keeping in mind what environment these organisms evolved in, we can explain why certain animals, like camels, have a lower metabolic rate than, for example, kangaroo rats, which, in the same environment, have lower BMR/g. The answer does not depend on body size; rather, in the complexity of the organisms entrained biochemical networks. By considering network effect produced by entrained chemical reactions, we gain insight into an evolutionary pattern of

4 4 complexity and energy efficiency going hand in hand. Complex biological networks create energy efficiency. This fact explains the various allometric scaling laws. By connecting the principles of information theory, complexity theory, and thermodynamics in an evolutionary context, we achieve a plausible explanation for this observed phenomenon. Using these principles in the context of evolution could also help explain other interesting emergent phenomena across the progression of evolution, from molecule to man Brown, West. (1997) Scaling in Biology. Oxford University press, Inc. 2 John P. DeLonga,, Jordan G. Okiea, Melanie E. Mosesa, Richard M. Siblyd, and James H. Brown (2010) Shifts in metabolic scaling, production, and efficiency across major evolutionary transitions in life. PNAS vol. 107 (29) page (Check). 3 Stumpf, Porter (2012) The Critical Truth about power Laws Science. Vol. 335, page

5 5 4 Raven, Peter H. (2011). Biology: ninth edition. New York: McGraw-Hill. pp Mohamed Ouhammouch, Robert E. Dewhurst, Winfried Hausner, Michael Thomm, and E. Peter Geiduschek (2003). "Activation of archaeal transcription by recruitment of the TATAbinding protein". PNAS Col. 100 (9): page Sara Moens and J. Vanderleyden. (1997) Glycoproteins in prokaryotes. Archives of Microbiology. Volume 168(3), page Alon. (2007) An Introduction to systems Biology: Design Principles of Biological Circuits. Taylor and Francis group, LLC. Page 34 8 Thomas Pfeiffer, Stefan Schuster, Sebastian Bonhoeffe. (2001) Cooperation and Competition in the Evolution of ATP-Producing Pathway. Science. Vol. 292, page Alan E. Senior,, Sashi Nadanaciva, Joachim Weber. (2002) The molecular mechanism of ATP synthesis by F1F0-ATP synthase. Bioenergetics.Vol 1553(3), Pages Michael Lynch and John S. Conery ( 2003) The Origins of Genome Complexity Science Vol. 302, page A. K. Saha, T. G. Kurowski, and N. B. Ruderman (1995) A malonyl-coa fuel-sensing mechanism in muscle: effects of insulin, glucose, and denervation. AJP - Endo vol. 269(2) page E283-E Behzad Mohit, Thermoinfocomplexity: A Comprehensive Theory of Evolution, 2012.