Biol. Lett. first extending the model of Gillooly et al. (2005) to doi:10.1098/rsbl.2007.0403 yield predictions on rates of protein evolution, and then Published online testing these predictions using new data compiled for Evolutionary biology diverse species from different thermal environments. Effects of metabolic rate 2. BACKGROUND The Gillooly et al. (2005) model incorporates the on protein evolution effects of body size and temperature on mass- specific metabolic rate, B (W gK1), using the following James F. Gillooly1,*, Michael W. McCoy1 equation (Gillooly et al. 2001): and Andrew P. Allen2 K1=4 KE=kT B Z b0M e ; ð2:1Þ 1 Department of Zoology, University of Florida, Gainesville, where M is size (g); T is temperature in Kelvin (K); FL 32611, USA 2National Center for Ecological Analysis and Synthesis, and b0 is a normalization constant independent of size K3/4 Santa Barbara, CA 93101, USA and temperature (W g ). The 1/4-power scaling of *Author for correspondence ([email protected]fl.edu). metabolic rate with size, and the exponential increase in metabolic rate with temperature, described by the Since the modern evolutionary synthesis was K = first proposed early in the twentieth century, Boltzmann–Arrhenius factor, e E kT ,arewellsup- attention has focused on assessing the relative ported by both theory and data (Peters 1983; contribution of mutation versus natural selec- West et al. 1997; Gillooly et al. 2001). Here E is the tion on protein evolution. Here we test a model activation energy of the respiratory complex that yields general quantitative predictions on (approx. 0.6–0.7 eV) and k is Boltzmann’s constant rates of protein evolution by combining (8.62!10K5 eV KK1). principles of individual energetics with Kimura’s Gillooly et al. (2005) formulated their model of neutral theory. The model successfully predicts much of the heterogeneity in rates of protein molecular evolution using equation (2.1) by invoking evolution for diverse eukaryotes (i.e. fishes, two simplifying assumptions. First, point mutations amphibians, reptiles, birds, mammals) from occur at a rate proportional to mass-specific metabolic different thermal environments. Data also show rate. This assumption is consistent with the that the ratio of non-synonymous to synonymous hypotheses that mutation rates are governed by nucleotide substitution is independent of body the production of oxidative free radicals, and the size, and thus presumably of effective population hypothesis that mutation rates are governed by errors size. These findings indicate that rates of protein that occur during germline replication (see Martin & evolution are largely controlled by mutation Palumbi 1993). Second, the point mutations fixed in rates, which in turn are strongly influenced by populations are selectively neutral, which is reason- individual metabolic rate. able, provided that the selection coefficient is less Keywords: metabolic theory; neutral theory; than half the reciprocal of the effective population size mutation; scaling; molecular evolution for most mutations (Kimura 1983). Given these assumptions, their model predicts that the synon- ymous substitution rate per unit absolute time, as K1 1. INTRODUCTION (substitutions per nucleotide Myr ), should be con- trolled by metabolic rate, B, through its effects on the Variation in mutation rates is often invoked to explain point mutation rate, vB (mutations per nucleotide - heterogeneity in rates of non-coding DNA evolution, K Myr 1), as follows: as predicted by Kimura’s neutral theory (Kimura 1983; Kumar 2005). While some research has pointed K1=4 KE=kT as Z fsvB Z fsvb0M e ; ð2:2Þ to a link between mutation and protein evolution (e.g. Stanley & Harrison 1999), other studies indicate that where v is the number of mutations per nucleotide protein evolution is controlled primarily by natural per unit energy flux through a gram of tissue K1 selection (Gillespie 1991; McDonald & Kreitman (mutations per nucleotide g J )andfs is the fraction 1991; Sawyer 2003). Resolution of this issue has been of synonymous mutations that are neutral. Gillooly hampered by our limited understanding of the factors et al.(2005)obtained support for equation (2.2) that control mutation rates (Bromham & Penny 2003). using extensive nuclear and mitochondrial data Recent studies have shed light on this issue by (see also Estabrook et al. 2007). As explained by showing that mutation rate is strongly influenced by Gillooly et al. (2005), since generation times have the metabolic rate and the factors that control it (Martin & same size and temperature dependence as metabolic rate, their model predicts that the mutation rate Palumbi 1993; Allen et al.2006; Wright et al. 2006). In per generation is independent of size and temperature. particular, Gillooly et al. (2005) presented evidence that variation in synonymous rates of nucleotide substitution can be predicted based on the body size 3. EXTENDING THE GILLOOLY et al. (2005) and temperature dependence of metabolic rate. MODEL TO PROTEIN EVOLUTION However, it is unclear whether interspecific differences Equation (2.2) can be extended to encompass protein in metabolic rate, due to differences in size and evolution by assuming that most changes to amino temperature, can also explain variation in rates of acid sequences are also the result of neutral protein evolution. Here we examine this question by mutations. This assumption implies that the non- Electronic supplementary material is available at http://dx.doi.org/ synonymous rate of nucleotide substitution, an, 10.1098/rsbl.2007.0403 or via http://www.journals.royalsoc.ac.uk. should be proportional to the synonymous rate, as, Received 27 July 2007 This journal is q 2007 The Royal Society Accepted 5 September 2007 2 J. F. Gillooly et al. Energetics of protein evolution c bird ( ) mammal reptile 24 amphibian fish invertebrate 20 ) 0 1/4 (a) ) E/kT e 16 –1 y = –0.18x+20.77 body mass r2 = 0.50, n = 36 Myr –1 –4 –1 Myr –1 (d) 24 y = –0.62x+20.38 2 –8 r = 0.53, n = 36 20 0 (b) 16 y = –0.14x + 20.13 r2 = 0.25, n = 48 –4 (e) 24 –8 y = –0.59x + 18.98 r2 = 0.47, n = 48 temperature-corrected substitution rate in (substitutions site body-mass-corrected substitution rate in (substitutions site 3739 41 43 20 inverse temperature (1/kT) 16 y = –0.16x+19.16 r2 = 0.32, n = 30 0 5 10 15 20 ln (body mass) (g) Figure 1. Effect of temperature on body size-corrected rates of amino acid substitution for (a) NADH and (b) cytochrome b. Effect of body size on temperature-corrected rates of amino acid substitution for these same mitochondrial proteins and the haemoglobin nuclear gene family (c,NADH;d,cytochromeb; e, haemoglobin). The temperature dependence of evolutionary rates could not be evaluated for haemoglobin because these data are only for mammals. Fitted model-I regression slopes (solid lines) and predicted slopes (dashed lines) are presented for all panels. and should therefore show the same body size and synonymous rates of DNA substitution, ‘tick’ at a temperature dependence as metabolic rate, B, constant rate per unit energy rather than per unit time. Equations (3.1) and (3.2) yield two predictions on Z ð = Þ Z Z K1=4 KE=kT ; ð : Þ an fn fs as fnvB fnvb0M e 3 1 rates of protein evolution. First, for a given gene or where fn is the fraction of non-synonymous mutations protein, equations (3.1) and (3.2) predict that the that are selectively neutral. Equation (3.1) implies logarithms of size-corrected rates of non-synonymous 1/4 that protein evolution, aa (amino acid substitutions nucleotide and amino acid substitution, ln(aM ), per amino acid MyrK1), should also be governed by should be linear functions of inverse absolute metabolic rate, temperature, 1/kT, with slopes of KEzK0.65 eV. Second, logarithms of temperature-corrected rates, Z Z K1=4 KE=kT ; : aa favaB favab0M e ð3 2Þ ln(a eE/kT), should be linear functions of the logar- K where fa is the fraction of amino acid changes that are ithm of body size, ln(M), with slopes of 1/4. neutral and va is the number of amino acid changes per We evaluated these predictions using protein unit energy flux. Given that both v and va are evolution data compiled for a diverse suite of independent of size and temperature, equations (3.1) endotherms and ectotherms that span a range of and (3.2) predict that rates of protein evolution, like body sizes (approx. 1–107 g) and temperatures Biol. Lett. Energetics of protein evolution J. F. Gillooly et al. 3 0.015 0.4 (a) (d) 0.010 0.2 bird mammal reptile amphibian 0.005 fish invertebrate 0 y = 0.14x y = –0.002x+0.10 2 2 0 r = 0.88, n = 36 r = 0.0008, n = 36 ) –0.2 –1 Myr 0.020 0.4 –1 (b) (e) 0.2 0.010 0 y = 0.11x y = 0.002x+0.04 r2 n r2 = 0.07, n = 48 = 0.73, = 48 –0.2 0 0.05 0.10 0.15 substitutions non-synonymous/synonymous protein evolution (amino acid substitutions site protein evolution 4 (c) ( f ) 0.008 2 0.004 0 y = 0.74x y = 0.027x+0.12 2 2 r = 0.94, n = 20 –2 r = 0.04, n = 20 0 0.005 0.010 0.015 0 5 10 15 20 synonymous DNA evolution ln (body mass) (g) (substitutions site–1 Myr–1) Figure 2. Predicted linear relationship between rates of amino acid and synonymous DNA evolution for (a) NADH, (b) cytochrome b and (c) haemoglobin. Fitted lines are forced through the origin using model-I regression. Ratio of non- synonymous to synonymous substitution versus the logarithm of body mass for (d ) NADH, (e) cytochrome b and ( f ) haemoglobin.