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Metabolism & Allometry

Metabolism & Allometry. log metabolic rate. log body mass. Jan 11 th , 2007. Physics Model of an Animal. · Mass & Energy are conserved. Δ M in. Δ H in. In = Out. All loses accounted for. h. Δ W out. · Is the model testable?. Δ M stored. Δ H stored. Measurements to test theory.

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Metabolism & Allometry

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  1. Metabolism & Allometry log metabolic rate log body mass Jan 11th, 2007

  2. Physics Model of an Animal ·Mass & Energy are conserved ΔMin ΔHin In = Out All loses accounted for h ΔWout ·Is the model testable? ΔMstored ΔHstored Measurements to test theory ΔHout ΔMout ΔQout ·Unifying principles can describe phenomena

  3. Zoologist’s Model of an Animal Fuel + O2 = ΔH + waste Heat of reaction, ΔH = Δm h Δm = mass of food [kg] Fuel + O2 h = enthalpy[J/kg] ‘in’ ‘heat’ ΔH ΔH = energy Waste i.e. flight

  4. How do we measure metabolic rate? Fuel + O2 = ΔH + waste ΔH/Δt= metabolic rate or power Г Mass specific metabolic rate Г/M Hummingbird muscle: mass specific power Г/M ≈ 100 W/kg (highest among vertebrates) Measure O2 , and fuel, intake to estimate energy (ΔH)) required to hover (ΔW) (Chai & Dudley, 1995, Nature)

  5. Measuring Г in other animals (usually at rest) ΔHin

  6. Allometry:how things scale with mass Г M

  7. Range of body sizes: 1021 Blue whale: >108 g Mycoplasma: <10-13 g (Giant sequoias excluded for now)

  8. How big is a blue whale? Brachiosaur Blue whale

  9. How much of a difference is 1021? 1021 Blue whale The sun

  10. Does size matter? Blue whale: >108 g Mycoplasma: <10-13 g

  11. "You can drop a mouse down a thousand-yard mine shaft; and,on arriving at the bottom, it gets a slight shock and walksaway, provided that the ground is fairly soft. A rat is killed,a man is broken, a horse splashes." `On being the right size', by J. B. S. Haldane (1928).

  12. How to study the consequences of size: Scaling slope = α Y log(Y) intercept = a mass log(mass) Y = aMα Length of leg, Y

  13. Allometric equations: Y = aMα Isometric, α = 1(i.e. blood volume) log(Y) log(mass)

  14. Allometric equations: Y = aMα Isometric, α = 1(i.e. blood volume) log(Y) Allometric, α ≠ 1(i.e. metabolic rate) log(mass)

  15. Allometric equations: Y = aMα Allometric, α ≠ 1(i.e. skeletal mass, mammals) Isometric, α = 1(i.e. blood volume) log(Y) Allometric, α ≠ 1(i.e. metabolic rate) log(mass)

  16. Size matters, but why? Sleep scales too, but with brain size, not body size: 14 hrs/day 4 hrs/day

  17. Scaling transcends biology: F/M Fruit fly thorax Diesel engine (Marden, J. H. 2005. J. Exp. Biol.)

  18. What determines the allometry of metabolic rate? • Energy demand of all cells • But is it supply limited? (see West et al., 2005) Гo = M0.75 Y o = M-0.25(mass specific met. rate) M

  19. Smaller animals live fast, but die young • A gram of tissue, on average, expends the same amount of energy before it dies in any animal. Y Life span = M1/4 o= M-1/4 M

  20. Metabolic rates (in W) of mammalian cells • Energy requirements of cells are situation dependent West, G. B. et al. 2005

  21. Resting or basal metabolic rate (BMR) scales: 4M3/4

  22. Metabolic rate is dynamic

  23. Metabolic rate is dynamic Aerobic scope ‘metabolic activity factor’ b Гmax=bГo b b Гmax=b4M0.75 In this example, b ≈ 10

  24. Keep this in mind for the staircase olympics Гrun=bГo b= ? b b Гrun=b4M0.75

  25. Consequences of scaling of Г, an example Blood vol. = M1 Г = 4M3/4 log(Y) o = M-1/4 log(mass) Diving capacity = 1000 m deep, 1 hr long

  26. Allometry of diving capacity O2 storage = M1 Γ = M3/4 Dive duration = M1/4 M1/4 (Schreer and Kovacs, 1997; Croll et al., 2001, Halsey et al., 2006)

  27. Other consequences: migration ΔH = Δm h Г = ΔH/Δt Ruby throated hummingbird Humpback whale Г/M high low Migration Alaska - Mexico Alaska - Mexico Fasting capacity low high

  28. Advice for assignments • State your assumptions and justify them with first principles if possible Lift Lift = Mg M Surface area = 4πr2 Mg

  29. Advice for assignments • Look up data from published resources to include in your physical model or to compare your calculated results. Include a copy of the article with your assignment (no monographs please). Hummingbird muscle: mass specific power Г/M ≈ 100 W/kg (Chai & Dudley, 1995, Nature) • Compare your results and conclusions with other animals, or even man-made machines.

  30. Advice for building physical models • Build a model or theory to predict, then test with data • Start simple, add complexity slowly • Model after machines that we know more about Alexander, R. M. (2005). Models and the scaling of energy costs for locomotion. J. Exp. Biol.208,1645 -1652.

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