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 EvaluationEvaluation

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. B 365:

Empirical special cases of DEB 11.1 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/ Hungate 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

Empirical patterns: stylised facts 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 Bertalanffy For different constant food levels the inverse von Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time Reproduction Reproduction increases with size intra-specifically, but decreases with size inter-specifically Respiration Animal eggs and plant seeds initially hardly use O 2 The use of O 2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O 2 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: CO 2, O 2 and N-waste From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B 363:

Empirical patterns a From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B 363:

Empirical patterns b From Sousa et al 2008 Phil. Trans. R. Soc. Lond. B 363:

Topological alternatives 11.1c From Lika & Kooijman 2011 J. Sea Res 66:

Test of properties 11.1d From Lika & Kooijman 2011 J. Sea Res, 66:

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 Fundamental knowledge of metabolic organisation has many practical applications

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

DEB theory reveals unexpected links 11.1g Length, mm O 2 consumption, μl/h 1/yield, mmol glucose/ mg cells 1/spec growth rate, 1/h Daphnia Streptococcus 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

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

Diffusion cannot occur in cells 11.2b

Self- ionization of water in cells 11.2c A cell of volume 0.25 mm 3 and pH 7 at 25°C has m = 14 protons N = water molecules confidence intervals of pH 95, 90, 80, 60 % pH cell volume,  m 3 modified Bessel function 7

Crowding affects transport 11.2d cytoskeletal polymers ribosomes nucleic acids proteins

ATP generation & use 11.2e 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

Classic energetics 11.3 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 From: Mader, S. S Biology, WCB This decomposition occurs at several places in DEBs

Classic energetics 11.3a From: Duve, C. de 1984 A guided tour of the living cell, Sci. Am. Lib., New York heterotroph autotroph The classic concept on metabolic regulation focusses on ATP generation and use. The application of this concept in DEB theory is problematic.

Static Energy Budgets 11.3 b From: Brafield, A. E. and Llewellyn, M. J Animal energetics, Blackie, Glasgow C energy from food P production (growth) F energy in faeces U energy in urine R heat 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

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

Static Energy Budgets (SEBs) 11.4a Differences with DEBs overheads interpretation of respiration interpretation of urination metabolic memory life cycle perspective change in states gross ingested faeces urine apparent assimilated gross metabolised net metabolised spec dynamic action workmaintenance somatic maintenance activity thermo regulation production growth products reproduction

Production model 11.4c foodfaeces assimilation feeding defecation maintenance offspring reproduction reserve structure growth

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)

Dynamic Energy Budget theory 1 Basic ConceptsBasic Concepts 2 Standard DEB modelStandard DEB model 3 MetabolismMetabolism 4 Univariate DEB modelsUnivariate DEB models 5 Multivariate DEB modelsMultivariate DEB models 6 Effects of compoundsEffects of compounds 7 Extensions of DEB modelsExtensions of DEB models 8 Co-variation of par valuesCo-variation of par values 9 Living togetherLiving together 10 EvolutionEvolution 11 EvaluationEvaluation