Dynamic Energy Budget theory

1. Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together 10 Evolution 11 Evaluation

2. Criteria for general energy models • Quantitative Based on explicit assumptions that together specify all quantitative aspects to allow for mass and energy balancing • Consistency Assumptions should be consistent in terms of internal logic, with physics and chemistry, as well as with empirical patterns • Simplicity Implied model(s) should be simple (numbers of variables and parameters) enough to allow testing against data • Generality The conditions species should fulfill to be captured by the model(s) must be explicit and make evolutionary sense • Explanatory The more empirical patterns are explained, the better the model From Sousa et al 2010 Phil. Trans. R. Soc. Lond. B365: 3413-3428

3. 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 Empirical special cases of DEB 11.1

4. Empirical patterns Feeding During starvation, organisms are able to reproduce, grow and survive for some time At abundant food, the feeding rate is at some maximum, independent of food density Growth Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalany For diffent constant food levels the inverse von Bertalany growth rate increases linearly with ultimate length The von Bertalany growth rate of dffierent species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time Reproduction Reproduction increases with size intra-specically, but decreases with size inter-specically Respiration Animal eggs and plant seeds initially hardly use dioxygen The use of dioxygen increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of dioxygen scales approximately with body weight raised to a power close to 0.75 Animals show a transient increase in metabolic rate after ingesting food (heat increment of feeding) Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant Energy Dissipating heat is a weighted sum of 3 mass flows: carbon dioxide, dioxygen and nitrogenous waste From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B363: 2453-2463

5. Empirical patterns 1 11.1a From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B363:2453 -2464

6. Empirical patterns 2 11.1b From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B363:2453 -2464

7. Topological alternatives 11.1c From Lika & Kooijman 2011 J. Sea Res, to appear

8. Test of properties 11.1d From Lika & Kooijman 2011 J. Sea Res, to appear

9. Fundamental knowledge of metabolic organisation has many practical applications Applications of DEB theory 11.1e • bioproduction: agronomy, aquaculture, fisheries • pest control • biotechnology, sewage treatment, biodegradation • (eco)toxicology, pharmacology • medicine: cancer biology, obesity, nutrition biology • global change: biogeochemical climate modeling • conservation biology; biodiversity • economy; sustainable development

10. Innovations by DEB theory 11.1f • Unifies all life on earth (bacteria, protoctists, fungi/animals, plants) • Links levels of organisation • Explains body size scaling relationships • Deals with energetic and stoichiometric constraints • Individuals that follow DEB rules can merge smoothly into a symbiosis that again follows DEB rules • Method for determining entropy of living biomass • Biomass composition depends on growth rate • Product formation has 3 degrees of freedom • Explains indirect calorimetry • Explains how yield of biomass depends on growth rate • Quantitative predictions have many practical applications

11. DEB theory reveals unexpected links 11.1g Streptococcus O2 consumption, μl/h 1/yield, mmol glucose/ mg cells Daphnia Length, mm 1/spec growth rate, 1/h respiration  length in individual animals & yield  growth in pop of prokaryotes have a lot in common, as revealed by DEB theory Reserve plays an important role in both relationships, but you need DEB theory to see why and how

12. Weird world at small scale 11.2a • Almost all transformations in cells are enzyme mediated • Classic enzyme kinetics: based on chemical kinetics (industrial enzymes) • diffusion/convection • law of mass action: transformation rate  product of conc. of substrates • larger number of molecules • constant reactor volume • Problematic application in cellular metabolism: • definition of concentration (compartments, moving organelles) • transport mechanisms (proteins with address labels, targetting, allocation) • crowding (presence of many macro-molecules that do not partake in transformation) • intrinsic stochasticity due to small numbers of molecules • liquid crystalline properties • surface area - volume relationships: membrane-cytoplasm; polymer-liquid • connectivity (many metabolites are energy substrate & building block; dilution by growth) • Alternative approach: reconstruction of transformation kinetics • on the basis of cellular input/output kinetics

13. Diffusion cannot occur in cells 11.2b

14. Self-ionization of water in cells 11.2c modified Bessel function pH confidence intervals of pH 95, 90, 80, 60 % A cell of volume 0.25 mm3 and pH 7 at 25°C has m = 14 protons N = 8 109 water molecules 7 cell volume, m3

15. Crowding affects transport 11.2d cytoskeletal polymers ribosomes nucleic acids proteins

16. ATP generation & use 11.2e 5 106 ATP molecules in bacterial cell enough for 2 s of biosynthetic work Only used if energy generating & energy demanding transformations are at different site/time If ADP/ATP ratio varies, then rates of generation & use varies, but not necessarily the rates of transformations they drive Processes that are not much faster than cell cycle, should be linked to large slow pools of metabolites, not to small fast pools DEB theory uses reserve as large slow pool for driving metabolism

17. Classic energetics11.3 This decomposition occurs at several places in DEBs From: Mader, S. S. 1993 Biology, WCB Anabolism: synthetic pathways Catabolism: degradation pathways Duality: compounds as source for energy and building blocks In DEB: from food to reserve; from reserve to structure

18. Classic energetics11.3a autotroph heterotroph The classic concept on metabolic regulation focusses on ATP generation and use. The application of this concept in DEB theory is problematic. From: Duve, C. de 1984 A guided tour of the living cell, Sci. Am. Lib., New York

19. Static Energy Budgets 11.3b Numbers: kJ in 28 d Basic difference with dynamic budgets: Production is quantified as energy fixed in new tissue, not as energy allocated to growth: excludes overheads Heat includes overheads of growth, reproduction and other processes, it does not quantify maintenance costs C energy from food P production (growth) F energy in faeces U energy in urine R heat From: Brafield, A. E. and Llewellyn, M. J. 1982 Animal energetics, Blackie, Glasgow

20. Static vs Dynamic Budgets 11.4 • Assimilation models • dynamics by nature • reserve damps food fluctuations • Net production models • time-dependent static models • no demping by reserve

21. maintenance reserve growth reproduction structure offspring Production model 11.4c defecation feeding food faeces assimilation

22. Production models 11.4d • no accommodation for embryonic stage; require additional state variables • (no food intake, still maintenance costs and growth) • no metabolic memory, no growth during starvation • require switches in case of food shortage • (reserves allocated to reproduction used for maintenance) • no natural dynamics for reserve; descriptive rules for growth vs reprod. • no explanation for body size scaling of metabolic rates, • changes in composition of biomass, metabolic memory • require complex regulation modelling for fate of metabolites • (ATP vs building blocks; consistency problem with lower levels of org.) • dividing organisms (with reserve) cannot be included • typically have descriptive set points for allocation, no mechanisms • (weight-for-age rules quantify allocation to reproduction)

23. Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together 10 Evolution 11 Evaluation