1. Links between aging & energetics Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb Rostock, 2004/10/28

2. Contents Rostock, 2004/10/28 DEB theory introduction metabolic rate Effects of toxicants sublethal effects lethal effects Effects of free radicals sleep tumour induction & growth Aging dilution by growth damage amplification effects of caloric restriction

3. Dynamic Energy Budget theory for metabolic organisation Uptake of substrates (nutrients, light, food) by organisms and their use (maintenance, growth, development, reproduction) First principles, quantitative, axiomatic set up Aim: Biological equivalent of Theoretical Physics Primary target: the individual with consequences for sub-organismal organization supra-organismal organization Relationships between levels of organisation Many popular empirical models are special cases of DEB

4. molecule cell individual population ecosystem system earth time space Space-time scales When changing the space-time scale, new processes will become important other will become less important Individuals are special because of straightforward energy/mass balances Each process has its characteristic domain of space-time scales

5. Empirical special cases of DEB yearauthormodelyearauthormodel 1780Lavoisier multiple regression of heat against mineral fluxes 1950Emerson cube root growth of bacterial colonies 1825Gompertz Survival probability for aging 1951Huggett & Widdas foetal growth 1889Arrhenius temperature dependence of physiological rates 1951Weibull survival probability for aging 1891Huxley allometric growth of body parts 1955Best diffusion limitation of uptake 1902Henri Michaelis--Menten kinetics 1957Smith embryonic respiration 1905Blackman bilinear functional response 1959Leudeking & Piret microbial product formation 1910Hill Cooperative binding 1959Holling hyperbolic functional response 1920Pütter von Bertalanffy growth of individuals 1962Marr & Pirt maintenance in yields of biomass 1927Pearl logistic population growth 1973Droop reserve (cell quota) dynamics 1928Fisher & Tippitt Weibull aging 1974Rahn & Ar water loss in bird eggs 1932Kleiber respiration scales with body weight 3/ 4 1975Hungate digestion 1932Mayneord cube root growth of tumours 1977Beer & Anderson development of salmonid embryos DEB theory is axiomatic, based on mechanisms not meant to glue empirical models Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory This makes DEB theory very well tested against data

6. These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake : These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake Not age, but size: Trichopsis vittatus

7. Some DEB pillars life cycle perspective of individual as primary target embryo, juvenile, adult (levels in metabolic organization) life as coupled chemical transformations (reserve & structure) time, energy & mass balances surface area/ volume relationships (spatial structure & transport) homeostasis (stoichiometric constraints via Synthesizing Units) syntrophy (basis for symbioses, evolutionary perspective) intensive/extensive parameters: body size scaling

8. Biomass: reserve(s) + structure(s) Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition Compounds in reserve(s): equal turnover times, no maintenance costs structure: unequal turnover times, maintenance costs Reasons to delineate reserve, distinct from structure metabolic memory explanation of respiration patterns (freshly laid eggs don’t respire) biomass composition depends on growth rate fluxes are linear sums of assimilation, dissipation and growth basis of method of indirect calorimetry explanation of inter-species body size scaling relationships

9. 1-  maturity maintenance maturity offspring maturation reproduction Basic DEB scheme foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth 

10. Usually quantified in three different ways consumption of dioxygen production of carbon dioxide dissipation of heat DEB theory: These fluxes are weighted sums of assimilation maintenance growth Weight coefficients might differ Not constant, depends on size & feeding conditions Metabolic rate

11. Log weight, g Log metabolic rate, w endotherms ectotherms unicellulars slope = 1 slope = 2/3 Length, cm O 2 consumption,  l/h Inter-species Intra-species 0.0226 L 2 + 0.0185 L 3 0.0516 L 2.44 2 curves fitted: (Daphnia pulex)

12. Scaling of metabolic rate comparisonintra-speciesinter-species maintenance growth Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms

13. 1-  maturity maintenance maturity offspring maturation reproduction Modes of action of toxicants foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth  Lethal effects: hazard rate Mode of action affects translation to pop level   assimilation   maintenance costs   growth costs   reproduction costs   hazard to embryo

14. Toxic effect on survival Effect of Dieldrin on survival of Poecilia One-compartment kinetics Hazard rate is linear in internal concentration killing rate 0.038 l  g -1 d -1 elimination rate 0.712 d -1 NEC 4.49  g l -1

15. Many factors contribute to hazard genetic factors (apoptosis) starvation (diet deficiencies, type II diabetes) environmental factors (physical, chemical, toxicants) pathogens (disease) accidents (predation) aging

16. Free radicals  Sleep elephant man dog cat ferret opossum 10 log body weight, kg 10 log REM sleep, h/d Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesis Science 294: 1058-1063 Amount of sleep No thermo-regulation during REM sleep Dolphins: no REM sleep

17. Free radicals  Tumour induction Tumour induction is linear in conc free radicals & other tumour inducing compounds It can occur via genotoxic effect (damage of genome) non-genotic effects (effects on cell-to-cell signalling) No Effect Concentration might be positive

18. 1-  1-  u Competitive tumour growth foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth maturity maintenance maturity offspring maturation reproduction tumour  uu Allocation to tumour  relative maint workload Isomorphy: is constant Tumour tissue: low spec growth costs low spec maint costs Van Leeuwen et al., 2003 The embedded tumour: host physiology is important for the evaluation of tumour growth. British J Cancer 89, 2254-2268 maint

19. Tumor growth  DEB theory The shape of the tumor growth curve is not assumed a priori, and is very flexible, depending on parameter values The model predicts that, in general, tumors develop faster in young than in old hosts According to the model, tumors grow slower in calorically restricted animals than in ad libitum fed animals. The effect of CR on tumor growth fades away during long-term CR The model explains why tumor-mediated body-weight loss is often more dramatic than expected

20. Free radicals  Aging Aging results from damage by Reactive Oxygen Species (ROS) Gerschman 1954 link with DEB model via dioxygen consumption & metabolic activity Dioxygen use in association with assimilation is not included because of more local occurrence in organism Its affects are 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 Empirical evidence points to an acceleration mechanism damage inducing compounds amplification of existing damage Some chemical compounds (e.g. RNS) and  -radiation can stimulate aging

21. Hazard rate due to aging  damage density: Damage forms  damage inducing compounds: Damage inducing compounds form  catabolic rate: i.e. dioxygen consumption excluding contributions from assimilation Result for If mean life span >> growth period : Weibull’s model Problems: bad fit with endotherm data, but good fit with ectotherm data effect of increase in food uptake balanced by dilution by growth Aging: Damage induction ageing acceleration maintenance rate coeff structural volume time hazard rate survival prob

22. Aging & Growth age, d length, mm survival probability DEB aging model: k M = 0.073 d -1 ; h a = 2.53 10 -6 d -2 Weibull model: shape par = 3.1 Data: Slob & Janse 1988 Von Bertalanffy model: r B = 0.015 d -1 L  = 35 mm Lymnaea stagnalis

23. Aging in adult insects age after eclosion, d surviving number # of eggs/beetle, d -1 Drosophila melanogaster Notiophilus biguttatus Data: Rose 1984 Data: Ernsting & Isaaks, 1991 High food, 20/10 °C 0.63 a -2 High food, 10 °C 0.547 a -2 Low food, 20/10 °C 0.374 a -2 survival based on observed reproduction No growth initial random mort Weibull model

24. Aging & Sex age, d length, mm Hazard rate, d -1 Common aging acceleration 2.587 10 -5 d -2 Data: MacArthur & Baillie 1929 Conclusion: differences in aging are due to differences in energetics Daphnia magnafemale male

25. RNS  Aging age, d Hazard rate, d -1 Food levels: 20, 30, 60, 120, 240 paramecia d -1 rotifer -1 Aging acceleration linear in food level Data: Robertson & Salt 1981 Suggestion: Paramecia are rich in NO 3 2- & NO 2 2- from lettuce, which enhances aging Asplanchna girodi Ultimate volume 10 -12 m 3 Aging acceleration, 0.001 d -2

26. One cell from a tetrad Deinococcus radiodurans (Deinobacteria, Hadobacteria) Very resistant against  -radiation by accumulation of Mn 2+ which neutralizes ROS that is formed  -Radiation  ROS  Aging

27. Stringent response  Aging k M /r m h a /r m 0.050.10 0.01 0.050.01 Fraction of dead cells Scaled throughput rate of chemostat r m : max spec growth rate k M : maintenance rate coefficient h a : aging rate e: scaled reserve density g: investment ratio Stringent response occurs in bacteria at low substrate concentration Substantial change in physiology (e.g. accumulation of ppGpp) Suggestion: Result of aging in bacteria Low substrate  low growth  long division intervals

28. Aging in humans age, d Surviving fraction Data from Elandt-Johnson & Johnson 1980 q = 0.988 h = 0.0013 a -1 h W = 0.01275 a -1  = 6.8 Aging accelerates in endotherms Not captured by damage induction model

29. Lung cancer in mice Weibull model fitted: High adult incidence rate Following low rate in juveniles Female mice 200ppm butadiene (KM-adjusted data) Toxicology and carcinogenesis studies of 1,3-butadiene in B6C3F 1 mice National Toxicology Program (USA) 1993 lung cancer free probability

30. Amplification mechanisms Weindruch R 1996 Caloric restriction and aging. Scientific American 231, 46-52. Kowald A 2001 The mitochondrial theory of aging, Biological Signals & Receptors 10, 162-175. Kowald A & Kirkwood TBL 2000 Accumulation of defective mitochondria through delayed degradation of damaged organelles and its possible role in the aging of post-mitotic cells. J ournal of Theoretical Biology 202, 145-160. 1) Affected mitochondria produce more ROS 2) Affected mitochondria grow and degrade at different rates

31. Aging: Damage amplification Hazard rate due to aging  damage density Damage forms  catabolic rate + amplification rate Specific amplification rate is linear in catabolic rate Result for If mean life span >> growth period: Gompertz’s model Van Leeuwen et al 2002 A mathematical model that accounts for the caloric restriction on body weight and longivety Biogerontology 3: 373-381 ROS import spec rate damaged mitoch growth r ROS feedback vol

32. Food intake  Surface area Data from Kluyver 1961 & Grundel 1987 weight 1/3, g 1/3 age, d feeding rate, g/d Parus atricapillus males females This assumption in DEB theory is usually realistic

33. Carcinogenicity study with B[a]P in rats Kroese et al., (2001) RIVM technical report nr. 658603 010 males females males Food intake is constant in laboratory rodents Probably as a result of experimental conditions

34. Aging: Damage amplification Van Leeuwen et al 2002 A mathematical model that accounts for the caloric restriction on body weight and longivety Biogerontology 3: 373-381 Data: Weindruch et al, 1986 Feeding level: 1, 0.75, 0.44 times ad libitum Caloric restriction extends life span time, d weight, g srvivors, % time, d specific metabolic rate

35. Aging  DEB theory The aging process can be modelled within the DEB framework as a result of internally produced ROS that affects the hazard rate no max life span exists; consistency with lethal effects of toxicants The model is able to predict differences in life expectancy on the basis of differences in food intake The model predicts CR-induced decrease in mass-adjusted energy expenditure to disappear with long-term CR The model provides a physiologically-based interpretation of the Gompertz parameters The model suggests that two essential feed-back processes take place

36. Aging: Function Observation: Aging related hazard rate remains low during embryonic and juvenile stages becomes high at start of reproduction Suggestion: Organisms decrease protection level in adult stage use ROS to create genetic diversity among gametes use genetic diversity for adaptation to changing environment efficient defence (peroxidase dismutase) or repair systems or reduced ROS production can increase life span, but reduce genome diversity

37. Aging: Open questions Damage Induction (DI)  Damage Amplification (DA) model Should 1-par DI-model always be replaced by 3-par DA model? Can DI-model approximate DA-model under certain conditions? How important is dilution by growth? Is it possible to improve the models, while preserving simplicity & generality workload model for synthesis of mitochondria Is dioxygen consumption that is linked to assimilation of importance? Should/can cause of death by aging be specified more explicitly? tumours, weakening of defense systems (immune system)

38. DEB tele-course 2005 Feb – April 2005, 10 weeks, 200 h no financial costs http://www.bio.vu.nl/thb/deb/course/ Download slides of Rostock lecture by Bas Kooijman http://www.bio.vu.nl/thb/users/bas/lectures/