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 together10 Evolution11 Evaluation

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 2010Phil. Trans. R. Soc. Lond. B 365: 3413-3428

Empirical special cases of DEB 11.1

year author model year author model1780 Lavoisier multiple regression of heat

against mineral fluxes1950 Emerson cube root growth of bacterial

colonies

1825 Gompertz Survival probability for aging 1951 Huggett & Widdas foetal growth

1889 Arrhenius temperature dependence of physiological rates

1951 Weibull survival probability for aging

1891 Huxley allometric growth of body parts 1955 Best 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 Cooperative binding 1959 Holling hyperbolic functional response

1920 Pütter von Bertalanffy growth of individuals

1962 Marr & Pirt maintenance in yields of biomass

1927 Pearl logistic population growth 1973 Droop reserve (cell quota) dynamics

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

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 O2

The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 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: CO2, O2 and N-waste

From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363:2453 -2464

Empirical patterns 1 11.1a

From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363:2453 -2464

Empirical patterns 2 11.1b

From Sousa et al 2008Phil. Trans. R. Soc. Lond. B 363:2453 -2464

Topological alternatives 11.1c

From Lika & Kooijman 2011J. Sea Res 66: 381-391

Test of properties 11.1d

From Lika & Kooijman 2011J. Sea Res, 66: 381-391

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

O2

cons

umpt

ion,

μl/h

1/yi

eld,

mm

ol g

luco

se/

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 mediatedClassic 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 mm3

and pH 7 at 25°C hasm = 14 protons N = 8 109 water molecules

confidence intervals of pH 95, 90, 80, 60 %

pH

cell volume, m3

modified Bessel function

7

Crowding affects transport 11.2d

cytoskeletal polymers

ribosomes

nucleic acids

proteins

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

Classic energetics 11.3

Anabolism: synthetic pathwaysCatabolism: degradation pathwaysDuality: compounds as source for energy and building blocksIn DEB: from food to reserve; from reserve to structure

From: Mader, S. S. 1993 Biology, WCB

This decomposition occursat 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 11.3b

From: Brafield, A. E. and Llewellyn, M. J. 1982 Animal energetics, Blackie, Glasgow

C energy from foodP production (growth)F energy in faecesU energy in urineR 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 overheadsHeat 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

somaticmaintenance

activity

thermo regulation

production

growth productsreproduction

Production model 11.4c

food faecesassimilation

feeding defecation

maintenance

offspring

reproductionreserve

structurestructure

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 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 together10 Evolution11 Evaluation