Links between aging energetics Bas Kooijman Dept theoretical
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
Contents • DEB theory introduction metabolic rate • Effects of toxicants sublethal effects • Effects of free radicals sleep tumour induction & growth • Aging dilution by growth damage amplification effects of caloric restriction Rostock, 2004/10/28
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
Space-time scales Each process has its characteristic domain of space-time scales space system earth ecosystem population individual cell molecule 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 time
Empirical special cases of DEB 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, 1951 Weibull temperature dependence of physiological rates based on mechanisms allometric growth of body parts Huxley 1955 Best not meant to glue empirical models survival probability for aging diffusion limitation of uptake Henri Michaelis--Menten kinetics 1957 Smith embryonic respiration 1905 Blackman bilinear functional response 1959 Leudeking & Piret microbial product formation 1910 Hill 1902 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 Pütter turn out 1962 Marr Pirt individuals the data behind these 1973 models support DEB theory logistic population growth reserve (cell quota) dynamics Pearl Droop 1928 Fisher & Tippitt Weibull aging 1974 Rahn & Ar water loss in bird eggs 1932 Kleiber respiration scales with body weight 3/ 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
Not: age, but size: 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 Trichopsis vittatus
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
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
Basic DEB scheme food feeding defecation faeces assimilation somatic maintenance growth structure reserve 1 - maturity maintenance maturation reproduction maturity offspring
Metabolic rate 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 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
Scaling of metabolic rate Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms comparison maintenance growth intra-species inter-species
Modes of action of toxicants assimilation food defecation feeding somatic maintenance structure faeces growth costs assimilation reproduction costs reserve hazard to embryo maturity maintenance 1 - growth maintenance costs maturation reproduction Lethal effects: hazard rate maturity offspring Mode of action affects translation to pop level
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
Many factors contribute to hazard • genetic factors (apoptosis) • starvation (diet deficiencies, type II diabetes) • environmental factors (physical, chemical, toxicants) • pathogens (disease) • accidents (predation) • aging
Free radicals Sleep opossum ferret cat dog 10 log REM sleep, h/d Amount of sleep man elephant 10 log body weight, kg Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesis Science 294: 1058 -1063 No thermo-regulation during REM sleep Dolphins: no REM sleep
Free radicals 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
Competitive tumour growth Allocation to tumour relative maint workload food defecation feeding faeces assimilation somatic maintenance growth structure reserve maint 1 - u 1 - u tumour maturity maintenance Isomorphy: is constant Tumour tissue: low spec growth costs low spec maint costs maturation reproduction maturity offspring Van Leeuwen et al. , 2003 The embedded tumour: host physiology is important for the evaluation of tumour growth. British J Cancer 89, 2254 -2268
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
Free radicals 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
Aging: Damage induction 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 ageing acceleration maintenance rate coeff structural volume time hazard rate survival prob
length, mm survival probability Aging & Growth Lymnaea stagnalis age, d DEB aging model: k. M = 0. 073 d-1; ha = 2. 53 10 -6 d-2 Weibull model: shape par = 3. 1 Data: Slob & Janse 1988 age, d Von Bertalanffy model: r. B = 0. 015 d-1 L = 35 mm
age after eclosion, d Weibull model Data: Rose 1984 Drosophila melanogaster No growth surviving number # of eggs/beetle, d-1 Aging in adult insects age after eclosion, d survival based on observed reproduction initial random mort age after eclosion, d Data: Ernsting & Isaaks, 1991 Notiophilus biguttatus 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
Aging & Sex female length, mm Hazard rate, d-1 Daphnia magna male age, d Common aging acceleration 2. 587 10 -5 d-2 Data: Mac. Arthur & Baillie 1929 age, d Conclusion: differences in aging are due to differences in energetics
RNS Aging Food levels: 20, 30, 60, 120, 240 paramecia d-1 rotifer-1 Aging acceleration linear in food level Data: Robertson & Salt 1981 age, d Aging acceleration, 0. 001 d-2 age, d Ultimate volume 10 -12 m 3 Hazard rate, d-1 Asplanchna girodi Suggestion: Paramecia are rich in NO 32 - & NO 22 - from lettuce, which enhances aging
-Radiation ROS Aging Deinococcus radiodurans (Deinobacteria, Hadobacteria) Very resistant against -radiation by accumulation of Mn 2+ which neutralizes ROS that is formed One cell from a tetrad
Fraction of dead cells Stringent response Aging k. M/rm ha/rm 0. 05 0. 10 0. 01 0. 05 0. 01 rm: max spec growth rate k. M: maintenance rate coefficient ha: 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 pp. Gpp) Scaled throughput rate of chemostat Suggestion: Result of aging in bacteria Low substrate low growth long division intervals
Surviving fraction Aging in humans 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 age, d Data from Elandt-Johnson & Johnson 1980
lung cancer free probability Lung cancer in mice Weibull model fitted: High adult incidence rate Following low rate in juveniles Female mice 200 ppm butadiene (KM-adjusted data) Toxicology and carcinogenesis studies of 1, 3 -butadiene in B 6 C 3 F 1 mice National Toxicology Program (USA) 1993
Amplification mechanisms 1) Affected mitochondria produce more ROS Weindruch R 1996 Caloric restriction and aging. Scientific American 231, 46 -52. 2) Affected mitochondria grow and degrade at different rates • 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. Journal of Theoretical Biology 202, 145 -160.
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
Food intake Surface area weight 1/3, g 1/3 feeding rate, g/d This assumption in DEB theory is usually realistic males females age, d Parus atricapillus Data from Kluyver 1961 & Grundel 1987 age, d
Food intake is constant in laboratory rodents males females Probably as a result of experimental conditions males Carcinogenicity study with B[a]P in rats Kroese et al. , (2001) RIVM technical report nr. 658603 010 females
Aging: Damage amplification Caloric restriction extends life span srvivors, % weight, g Feeding level: 1, 0. 75, 0. 44 times ad libitum Data: Weindruch et al, 1986 Van Leeuwen et al 2002 A mathematical model that accounts for the caloric restriction on body weight and longivety Biogerontology 3: 373 -381 specific metabolic rate time, d
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
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
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)
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/
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