DEB theory - past and futureMPDE 2013

Bas KooijmanDept theoretical biology

Vrije Universiteit AmsterdamBas@bio.vu.nl

http://www.bio.vu.nl/thb

Osnabrück, 2013/08/27/09:00-09:45

Energy Budgets

Processes

• feeding• digestion• storing• growth• maturation• maintenance• reproduction• product formation• aging

Life history events

• zero: start of development• birth: start of feeding start of acceleration• metamorphosis: end of acceleration• puberty: end of maturation start of reproduction

Life stages

embryo

juvenile

adult

molecule organ individual ecosystem system earth

Fluxes

• organics food, faeces, biomass

• minerals CO2, H2O, O2, NH3

• products wood, shells, moults

• heat• entropy• isotopes

Empirical patternsFeeding 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

Food chains n=2

time, h time, h

glucose

Escherichia coli

Dictyostelium

mg/

ml

mm

3 /m

lm

m3 /

ml

cell

vol,

m3

cell

vol,

m3

X0(0) 0.433 mg. ml-1

X1(0) 0.361 X2(0) 0.084 mm3.ml-1

e1(0) 1 e2(0) 1 -

XK1 0.40 XK2 0.18

g1 0.86 g2 4.43 -

kM1 0.008 kM2 0.16 h-1

kE1 0.67 kE2 2.05 h-1

jXm1 0.65 jXm2 0.26

ml

mm,

ml

g 3μ

13

h,hmm

mg

Data from Dent et al 1976h = 0.064 h-1, Xr = 1mg ml-1, 25 °C

Kooijman & Kooi,1996 Nonlin. World 3: 77 - 83

Growth on reserve

Opt

ical

Den

sity

at 5

40 n

m

Con

c. p

otas

sium

, mM

Potassium limited growth of E. coli at 30 °CData Mulder 1988; DEB model fitted

OD increases by factor 4 during nutrient starvationinternal reserve fuels 9 hours of growth

time, h

Yield vs growth

1/spec growth rate, 1/h

1/yi

eld,

mm

ol g

luco

se/

mg

cells

Streptococcus bovis, Russell & Baldwin (1979)

Marr-Pirt (no reserve)DEB

spec growth rate

yield

Russell & Cook (1995): this is evidence for down-regulation of maintenance at high growth ratesDEB theory: high reserve density gives high growth rates structure requires maintenance, reserves do not

Cell quota

Droop 1968J Mar Biol Assoc UK 48: 689-733

Vitamin B12 limited growth of Monochrysis lutheri

Droop’s model

subsistence quota540 molecules/cell

Droop → DEB• quota → structure + reserve• static → dynamic• include maintenance• population → individual• V1- → iso-morph

Migration: metabolic memory

Some populations of humpback whale Megaptera novaeangliae (36 Mg) migrate 26 Mm anually without feeding, A 15 m mother gets a 6 m calf in tropical waters, gives it 600 l milk/d for 6 months and together return to cold waters to resume feeding in summer

Product Formation

throughput rate, h-1

glyc

erol

, eth

anol

, g/l

pyru

vate

, mg/

l

glycerol

ethanol

pyru

vate

Glucose-limited growth of SaccharomycesData from Schatzmann, 1975

According to Dynamic Energy Budget theory:

Product formation rate = wA . Assimilation rate + wM . Maintenance rate + wG . Growth rate

For pyruvate: wG<0

Method of indirect calorimetry

Empirical origin (multiple regression): Lavoisier 1780

Heat production = wC CO2-production + wO O2-consumption + wN N-waste production

DEB-explanation:Mass and heat fluxes = wA assimilation + wD dissipation + wG growthApplies to CO2, O2, N-waste, heat, food, faeces, …

For V1-morphs: dissipation maintenance

Metabolic rate

Log weight, g

Log metabolic rate,

w

endotherms

ectotherms

unicellulars

slope = 1

slope = 2/3

Length, cm

O2 consum

ption,

l/h

Inter-speciesIntra-species

0.0226 L2 + 0.0185 L3

0.0516 L2.44

2 curves fitted:

(Daphnia pulex)

Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

Homeostasisstrong constant composition of pools (reserves/structures) generalized compounds, stoichiometric contraints on synthesis

weak constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis)

structural

constant relative proportions during growth in constant environments isomorphy .work load allocation

thermal ectothermy homeothermy endothermy

acquisition supply demand systems; development of sensors, behavioural adaptations

Topological alternatives

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

Test of properties

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

Surface area/volume interactions• biosphere: thin skin wrapping the earth light from outside, nutrient exchange from inside is across surfaces production (nutrient concentration) volume of environment

• food availability for cows: amount of grass per surface area environment food availability for daphnids: amount of algae per volume environment

• feeding rate surface area; maintenance rate volume (Wallace, 1865)

• many enzymes are only active if linked to membranes (surfaces) substrate and product concentrations linked to volumes change in their concentrations gives local info about cell size ratio of volume and surface area gives a length

Change in body shapeIsomorph: surface area volume2/3

volumetric length = volume1/3

V0-morph: surface area volume0

V1-morph: surface area volume1

Ceratium

Mucor

Merismopedia

Isomorphic growth

diam

eter

, m

Wei

ght1/

3 , g

1/3

leng

th, m

m

time, h time, h

time, dtime, d

Amoeba proteusPrescott 1957

Saccharomyces carlsbergensisBerg & Ljunggren 1922

Pleurobrachia pileusGreve 1971

Toxostoma recurvirostreRicklefs 1968

Wei

ght1/

3 , g

1/3

Mixtures of V0 & V1 morphs 4.2.3a

volu

me,

m

3vo

lum

e,

m3

volu

me,

m

3

hyph

al le

ngth

, mm

time, h time, min

time, mintime, min

Fusarium = 0Trinci 1990

Bacillus = 0.2Collins & Richmond 1962

Escherichia = 0.28Kubitschek 1990

Streptococcus = 0.6Mitchison 1961

Mixtures of changes in shape

Dynamic mixtures between morphs

Lichen Rhizocarpon

V1- V0-morph

V1- iso- V0-morph

outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases time

Synthesizing units

Are enzymes that follow classic enzyme kinetics E + S ES EP E + PWith two modifications: back flux is negligibly small E + S ES EP E + P specification of transformation is on the basis of arrival fluxes of substrates rather than concentrations

The concept concentration is problematic in spatially heterogeneous environments, such as inside cellsIn spatially homogeneous environments, arrival fluxes are proportional to concentrations

Evolution of DEB systemsvariable structure

composition

strong homeostasisfor structure

delay of use ofinternal substrates

increase ofmaintenance costs

inernalization of maintenance

installation ofmaturation program

strong homeostasisfor reserve

reproductionjuvenile embryo + adult

Kooijman & Troost 2007 Biol Rev, 82, 1-30

54321

specialization of structure

7

8

an

ima

ls

6

pro

ka

ryo

tes

9plants

Add_my_pet

2013/08/28:

303 species

15 phyla

all 13 chordate classes

surv

ivor

fun

ctio

n

surv

ivor

fun

ctio

n

Allocation to somapo

p gr

owth

rat

e, d

-1

max

rep

rod

rate

, #d-1

Frequency distribution of κ among species in the add_my_pet collection:

Mean κ = 0.81, but optimum is κ = 0.5

Lika et al 2011 , Kooijman & Lika 2013J. Sea Res, 22: 278-288, Biol Rev, subm

Selection for reproduction

White Leghorn

Red Jungle fowl

Indian River broiler

Kooijman & Lika 2013Am Nat subm

Waste to hurryExploiting blooming resources requires blooming yourself

• high numerical response• short life cycle• small body size• fast reproduction• fast growth• high feeding rate• resting stages between blooms

-rule explains why [pM] needs to be high

Ecosystem significance:flux through basis food pyramid

Kooijman 2013Oikos 122: 348-357

Standard DEB model: growth

Rhizoprionodon acutusmilk shark

Embryonic development

time, d

wei

ght,

g

O2 c

onsu

mpt

ion,

ml/h

Crocodylus johnstoni,Data: Whitehead 1987

yolk

embryo

time, d

Metabolic accelerationDef: long-term increase of respiration relative to standard DEB expectation

Types• acceleration of maturation (allocation)• type X acceleration: food• type A acceleration: assimilation• type M acceleration: morph• type T acceleration: temperature

Short-term increase in respiration (no metabolic acceleration)• heat increment of feeding• boosts of activity• migration• pregnancy/ lactation

Ctenophora

Cnidaria

Tunicata

Leptocardii

Echinodermata

Mixini

Cephalaspidorphi

Chondrichthyes Actinopterygii

Amphibia

ReptiliaAves

Mammalia

Chaetognatha

Rotifera

Gastrotricha

Platyhelminthes

AnnelidaMollusca

Tardigrada

NematodaCrustacea

Arachnida

Enthognatha

Insecta

1 2 5 10

Sarcopterygii

Deuterostomia

Ecdysozoa

Lophotrochozoa

Platy

zoa

Radiata

Anthocephala

Bryozoa

Type M acceleration

acceleration factor Kooijman 2013Biol. Rev. subm

Hemimetabolic insect ontogeny

Acyrthosiphon pisumpea aphid

Locusta migratoriamigratory locust

Embryo: isomorphJuvenile: V1-morphAdult: no growth

30 27 24 21 18 °C

Maturity thresholds

RadiataBilateriaPlatyzoaLophotrochozoaEcdyspzoaInvert deuterostomesEctothermic vertEndothermic vert

birth metam

puberty

Open symbols:acceleration

Growth ratesRadiataBilateriaPlatyzoaLophotrochozoaEcdyspzoaInvert deuterostomesEctothermic vertEndothermic vert

Kooijman & Lika 2013Proc R Soc B subm

birth metam

puberty

Open symbols:acceleration

Bijection data - parameter space

Assumptions• abundant food• temperature constant• water content of E = that of V• zero surface linked som maint• zero Gompertz stress

Known• mol-weights of E & V• chem potentials of E & V• maturity maint rate coeff • growth efficiency • reproduction efficiency

Supply-demand spectrumcontrols of energetics: environmental → internal

Supply-demand spectrum

Supply-demand spectrum

Future DEB research

• Add_my_pet: taxon-specific patterns application in evolution, ecology, conservation, technology

• More-reserve/structure systems: nutrition, plants, behavioural ecology

• Molecular level interaction biochemical modules on basis of mutual syntrophy

• Ecosystem level canonical community, body size spectra

DEB tele course 2015

http://www.bio.vu.nl/thb/deb/

Free of financial costs; Some 108 or 216 h effort investment

Program for 2015: Feb/Mar general theory (5w: 02/19-03/26) April symposium in Marseille (F) (8d +3 d: 04/13-24) Target audience: PhD students

We encourage participation in groups who organize local meetings weekly

Software package DEBtool for Octave/ Matlab freely downloadable

Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/

Cambridge Univ Press 2009

Audience: thank you for your attention