Mass aspects scaling Contents mass aspects indirect calorimetry

Mass aspects & scaling Contents • mass aspects • indirect calorimetry • Synthesizing Units • covariation Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb Melbourne 2012/08/06

Macrochemical reaction eq 3. 5

Three basic fluxes 4. 3. 1 • assimilation: substrate reserve + products linked to surface area • dissipation: reserve products somatic maintenance: linked to surface area & structural volume maturity maintenance: linked to maturity maturation or reproduction overheads • growth: reserve structure + products Product formation = A assimilation + B dissipation + C growth Examples: heat, CO 2, H 2 O, O 2, NH 3 Indirect calorimetry: heat = D O 2 -flux + E CO 2 -flux + F NH 3 -flux

Synthesizing units 3. 7 b Generalized enzymes that process generalized substrates and follow classic enzyme kinetics E + S EP E + P with two modifications: • back flux is negligibly small E + S EP E + P • specification of transformation is on the basis of arrival fluxes of substrates rather than concentrations In spatially homogeneous environments: arrival fluxes concentrations

Transformation A → B Classification of behavioural modes: free & bound Michealis-Menten (Henri 1902) Holling type II (Holling 1957)

Simultaneous Substrate Processing 3. 7 c production Chemical reaction: 1 A + 1 B 1 C Poisson arrival events for molecules A and B blocked time intervals • acceptation event ¤ rejection event Kooijman, 1998 Biophys Chem 73: 179 -188

Interactions of substrates 3. 7. 3 b Kooijman, 2001 Phil Trans R Soc B 356: 331 -349

Competition & inhibition

Social inhibition of x e 3. 7. 4 b parallel biomass conc. x substrate Implications: e reserve stable co-existence of y species 1 competing species z species 2 “survival of the fittest”? absence of paradox of enrichment No socialization substrate conc. sequential dilution rate

Co-metabolism 3. 7. 5 Consider coupled transformations A C and B D Binding probability of B to free SU differs from that to SU-A complex

Photo synthesis, respiration, inhibition

Scales of life 8 a 30 Life span 10 log a earth 20 Volume 3 10 log m 10 life on earth whale 0 bacterium ATP molecule whale -10 -20 -30 bacterium water molecule

Bergmann 1847

Cebidae Dwarfing in Platyrrhini 8. 1. 2 180 g 130 g 200 -400 g 400 -535 g 480 -700 g 400 -450 g Saimiri Saguinus 780 -1250 g 700 -1000 g 3500 g Callitrix Callimico Cebuella MYA Leontopithecus Mico Aotus 20. 2 24. 8 Perelman et al 2011 Plos Genetics 7, 3, e 1001342 Cebus

Inter-species body size scaling • parameter values tend to co-vary across species • parameters are either intensive or extensive • ratios of extensive parameters are intensive • maximum body length is allocation fraction to growth + maint. (intensive) volume-specific maintenance power (intensive) surface area-specific assimilation power (extensive) • conclusion : • write physiological property as function of parameters (including maximum body weight) • evaluate this property as function of max body weight Kooijman 1986 Energy budgets can explain body size scaling relations J. Theor. Biol. 121: 269 -282

Body weight has contributions from structure and reserve If reserve allocated to reproduction hardly contributes:

Scaling of metabolic rate

Metabolic rate slope = 1 0. 0226 L 2 + 0. 0185 L 3 0. 0516 L 2. 44 Log metabolic rate, w O 2 consumption, l/h 2 curves fitted: endotherms ectotherms slope = 2/3 unicellulars Length, cm Intra-species (Daphnia pulex) Log weight, g Inter-species

Incubation time: intra-species Eudyptes first lays a small egg, then a large one, which hatches earlier if fertile It can rise one chick only If all parameters are the same, maturity at birth is reached earlier with big initial reserve

Incubation time: inter-species 10 log egg weight, g Data from Harrison 1975 incubation time, d slope = 0. 25 10 log tube noses 10 log incubation time, d European birds lb equal ° tube noses 10 log egg weight, g

slope = 0. 33 10 log gestation time, d Gestation time 8. 2. 2 l 10 log Mammals * Insectivora + Primates Edentata Lagomorpha Rodentia Carnivora � Proboscidea Hyracoidea Perissodactyla Artiodactyla adult weight, g Data from Millar 1981 Kooijman 1986 J Theor Biol 121: 269 -282

Lp, cm Length at puberty Clupoid fishes Clupea • Brevoortia ° Sprattus � Sardinops Sardina Sardinella + Engraulis * Centengraulis Stolephorus Data from Blaxter & Hunter 1982 L , cm Length at first reproduction Lp ultimate length L

Feeding rate Filtration rate, l/h slope = 1 Mytilus edulis Data: Winter 1973 Length, cm poikilothermic tetrapods Data: Farlow 1976

von Bert growth rate, a-1 Von Bertalanffy growth rate 10 log 25 °C TA = 7 k. K 10 log ultimate length, mm At 25 °C : maint rate coeff k. M = 400 a-1 energy conductance v = 0. 3 m a-1 ↑ 0

Primary parameters standard DEB model