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From embryo to senescence with DEB theory for metab org Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb/ Melbourne, 2012/08/07 From embryo to senescence with DEB theory for metab org Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb/ Contents: • intro • surface/volume • selection • embryo development • ageing Melbourne, 2012/08/07 Energy Budgets Basic processes Life history events • Feeding • Digestion • Storing • Growth • Maturation • Maintenance • Reproduction • Product formation • Aging • zero: start of development • birth: start of feeding start of acceleration • metamorphosis: end of acceleration • puberty: end of maturation start of reproduction All processes interact during the life cycle Life stages embryo juvenile adult Some DEB pillars • life as coupled chemical transformations • life cycle perspective of individual as primary target • energy & mass & time balances • stoichiometric constraints via Synthesizing Units • surface area/ volume relationships • spatial structure & transport • syntrophy (basis for symbioses) • homeostasis • intensive/extensive parameters: scaling • evolutionary perspective Standard DEB scheme 2b 1 food type, 1 reserve, 1 structure, isomorph food feeding defecation faeces assimilation reserve somatic maintenance growth structure 1- maturity maintenance maturation reproduction maturity offspring time: searching & handling feeding surface area weak & strong homeostasis κ-rule for allocation to soma maintenance has priority somatic maint structure maturity maint maturity stage transition: maturation embryo: no feeding, reprod juvenile: no reproduction adult: no maturation maternal effect: reserve density at birth equals that of mother initially: zero structure, maturity Empirical special cases of DEB 11.1 year author model year author model 1780 Lavoisier multiple regression of heat against mineral fluxes 1950 Emerson cube root growth of bacterial colonies 1825 Gompertz Survival probability for aging 1951 Huggett & Widdas foetal growth 1889 Arrhenius 1891 DEB theory is axiomatic, temperature dependence of 1951 Weibull rates basedphysiological on mechanisms allometric growth of body parts Huxley 1955 Best not meant to glue empirical models survival probability for aging diffusion limitation of uptake 1902 Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration 1905 Blackman bilinear functional response 1959 Leudeking & Piret microbial product formation 1910 Hill 1973 Droop 1920 1927 Since many empirical models Cooperative binding hyperbolic functional response 1959 Holling to begrowth special cases of &DEB theory von Bertalanffy of maintenance in yields of biomass Pütterturn out 1962 Marr Pirt individuals the data behind these models support DEB theory logistic population growth reserve (cell quota) dynamics Pearl 1928 Fisher & Tippitt Weibull aging 1974 Rahn & Ar water loss in bird eggs 1932 Kleiber respiration scales with body weight3/ 4 1975 Hungate digestion 1932 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos This makes DEB theory very well tested against data length, mm Von Bert growth rate -1, d Growth at constant food time, d Von Bertalanffy growth curve: ultimate length, mm volume, m3 Bacillus = 0.2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m3 volume, m3 hyphal length, mm Mixtures of V0 & V1 morphs Escherichia = 0.28 Kubitschek 1990 time, min Streptococcus = 0.6 Mitchison 1961 time, min Dynamic mixtures of V0- & V1-morphs Respiration: assim + maint + growth Assim, maint mass Growth in diam time at constant food V0-morph V1-morph Dynamic mixtures of V0- & V1-morphs Celleporella 15 cm/yr Respiration mixture mass1/2 isomorph mass3/4 33 33 16 16 5 5 2 2 0.5 cm/yr 0.5 cm/yr White et al 2011 Am. Nat., 178: 746-754 Dynamic mixtures of V0- & V1-morphs Celleporella 33, 24 cm/yr Respiration mixture mass1/2 isomorph mass3/4 33 16 5 2 0.5 cm/yr White et al 2011 Am. Nat., 178: 746-754 Selection affects par values Gallus gallus Red jungle fowl Indian River Broiler White leghorn ml O2 d-1 ml CO2 d-1 Respiration ontogeny in birds altricial Troglodytes aëdon Data: Kendeigh 1940 age, d precocial Gallus domesticus Data: Romijn & Lokhorst 1951 age, d Observations: just prior to hatching • respiration shows a plateau in precocial, not in altricial birds • pore size and frequency in egg shell is such that O2 flux has constant resistance Conclusion: ontogeny is constrained by diffusion limitation in precocial birds (Rahn et al 1990) DEB theory: reserve dynamics controls ontogeny (same pattern in species without shells) Minimization of water loss causes observed constant flux resistance Embryonic development weight, g embryo yolk time, d O2 consumption, ml/h Zonneveld & Kooijman 1993 Bul. Math. Biol. 55: 609-635 Crocodylus johnstoni, Data: Whitehead 1987 time, d Twinning: separation of cells Kooijman 2009 J. Math. Biol. 58: 377--394 Maternal effect: reserve density at birth = reserve density of mother Kooijman 2012 J. Math. Biol. subm Parameter estimates from add_my_pet 2012/06/17, egg development only Embryo: isomorphic v constant length Acceleration of development Early juvenile: V1-morphic v, {pAm} increase with length Late juvenile/adult: isomorphic time since birth v, {pAm} constant Found in: bivalves, gastropods, copepods, amphipods, decapods, collembolas, echinoderms, lancelets, tunas, flatfish, anchovy, Danio, caecilians, marsupials Anchovy Engraulis encrasicolus length, cm embryo 0.16 cm 0.4 cm time, d 1.2 cm >4 cm Pecquerie 2008 PhD thesis VU A’dam 0.9 cm 0.22 cm Stage transitions at maturity thresholds Danio rerio 28.5°C Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 Stage transitions < birth : isomorph birth-metamorphosis: V1-morph > metamorphosis : isomorph at maturity thresholds Danio rerio 28.5°C Data: Lauwrence et al 2008 caloric restriction Data: Augustine Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 10log 10log yolkiness spec maturity at birth Acceleration 10log coelenterata lophotrochozoa ecdysozoa invert deuterostomata ectotherm vertebrata endotherm vertebrata acceleration 10log acceleration Acceleration of development acceleration no yes development Casey Muller indirect Crinia georgiana Geocrinia vitellina Crinia nimbus Nicky Mitchell Pseudophryne bibronii direct Acceleration of development birth metam birth max dry weight 500 mg Dry mass, mg hatch Crinia georgiana 1 metam Mueller et al 2012, Comp. Biochem. Physiol. A 163: 103-110 ¼ age, d 0 12 °C O2 nmol/h ½ hatch ¾ hatch birth 1 ¾ ¼ age, d 0 hatch birth ½ O2 nmol/h Dry mass, mg max dry weight 200 mg metam Pseudophryne bibronii metam age, d age, d Free radicals Aging Aging results from damage by Reactive Oxygen Species (ROS) Gerschman 1954 link with DEB model via dioxygen consumption & metabolic activity Aging is binary in unicellulars, and gradual in multicellulars age-affected cells no longer divide Typical aging only occurs in multicellulars with irreversible cell differentiation that have post-mitotic tissues Induction of damage inducing compounds dioxygen consumption contribution from assimilation is not included because of more local occurrence in organism Empirical evidence points to acceleration of aging Damage inducing compounds generate • damage inducing compounds • damage compounds; hazard rate density of damage compounds Some chemical compounds (e.g. RNS) and -radiation can stimulate aging Ageing metabolism O2 ROS damage inducing compounds continuous endotherms mitochondrional DNA damage compounds proteins effect on hazard DEB module • Weibull (1951) & Gompertz (1825) model are special cases • based on mechanisms • links with energetics body length, cm survival prob Aging: ectotherms & feeding - ad libitum - restricted 100-600 d time, d Poecilia reticulata Data: Comfort, 1963 time, d Aging: endotherms & feeding embryo weight, g body weight, g feeding level 1 0.75 0.44 survival probability time, d time, d 0.44 0.75 time, d 1 Van Leeuwen et al 2002 Biogerontology 3: 373-381 Life span • hardly depends on food in ecotherms • decreases for increasing food in endotherms Data on Mus musculus: Weindruch et al 1986, MacDowell et al 1927 body length, mm survival prob Aging: sex differentiation time, d time, d Differences in aging between sexes are caused by differences in energy investment ratio g Data on Daphnia magna: MacArthur & Baillie 1929 age after eclosion, d h(t ) he t2 ha k M a 0 3 R 2 κ R gl Data: Rose 1984 Drosophila melanogaster No growth surviving number surviving number Weibull Model =3 # of eggs/beetle, d-1 Aging in adult insects age after eclosion, d Data: Ernsting & Isaaks, 1991 Notiophilus biguttatus survival based on observed reproduction initial random mort age after eclosion, d h e t t1 t2 h(t ) ha k M a 0 3 R(t 2 ) dt2 dt1 2 κ R gl 0 0 ha e0 : High food, 20/10 °C κ R gl3 -2 0.63 a High food, 10 °C 0.547 a-2 Low food, 20/10 °C 0.374 a-2 General Weibull fits DEB Both models are fitted to the same data They fit equally well and have both 4 parameters Contrary to the Weibull model the DEB model - is based on tested assumptions - has links with energetics via hW and hG. Data from Elandt-Johnson & Johnson 1980 for white USA males in the period 1969-1971 Ageing among species Right whale slope 1/3, 1/5 Conclusion for life span • hardly depends on max body size of ectotherms • increases with length in endotherms Ricklefs & Finch 1995 DEB tele course 2013 http://www.bio.vu.nl/thb/deb/ Free of financial costs; Some 108 or 216 h effort investment Program for 2013: Feb/Mar general theory (5w) April symposium at NIOZ-Texel (NL) (8 + 3 d) Target audience: PhD students We encourage participation in groups who organize local meetings weekly Cambridge Univ Press 2009 Software package DEBtool for Octave/ Matlab freely downloadable Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/ Audience: thank you for your attention