Dynamic Energy
Budget Theory - I

with contributions from :
Tânia Sousa
Tjalling Jager & Bas Kooijman
A Theory of Metabolism
 What is metabolism?

A Theory of Metabolism
 What is metabolism?

 “Using resources (energy and materials) to make new
cells, to repair old ones, and to get rid of wastes
requires the assemblage of biochemical pathways that
we call metabolism. Metabolism is a universal feature
of life that links organisms with their environment,
and with each other.”
A Theory of Metabolism
 What is metabolism?

 “Using resources (energy and materials) to make new
cells, to repair old ones, and to get rid of wastes
requires the assemblage of biochemical pathways that
we call metabolism. Metabolism is a universal feature
of life that links organisms with their environment,
and with each other.”
 What should a theory of metabolism look like?
A Theory of Metabolism

 What is metabolism?
 What should a theory of metabolism look like?
 It should be a qualitative and quantitative description
of how organisms use mass and energy to do the
things they need to do to stay alive
A Theory of Metabolism

 What is metabolism?
 What should a theory of metabolism look like?
 It should be a qualitative and quantitative description
of how organisms use mass and energy to do the
things they need to do to stay alive
 Which type of questions can a theory of metabolism
help you with?
A Theory of Metabolism

 What is metabolism?
 What should a theory of metabolism look like?
 Which type of questions can a theory of metabolism
help you with?
 What is the minimum amount of food (and habitat) a
panda needs to survive?
 If the temperature of ocean increases by 0.5ºC what
will happen to the survival of the sardine larvae?
Environmental Applications
 Toxicology

 Which is the toxicity of the environmental
concentration of a compound?
 Which are the toxic effects of a compound?
 Climate Change
 Will an increase in 1ºC have a drastic impact
on the distribution range of a species?
 Waste water treatment plant
 What are the necessary conditions to
mantain an healthy microbian comunity in
the biological reactors?
 Fisheries Management
 What is the sustainable fishing quota?
Minimata Disaster: Mercury Poisoning

 Minamata is a small factory town dominated by the
Chisso Corporation. The town faces the Shiranui Sea,
and Minamata Bay is part of this sea.
 Chisso Corporation started developing plastics,
drugs, and perfumes through the use of a chemical
called acetaldehyde in 1932. Acetaldehyde is
produced using mercury as a compound, and was
key component in the production of their products.
 In the mid-1950's people begin to
notice a "strange disease". Victims
were diagnosed as having a
degeneration of their nervous
ystems.
Human-made toxicants
 Wide variety of uses

 paints, detergents, solvents, pesticides,
pharmaceuticals, polymers, …
 probably some 100.000 compounds
 Chemical industry is BIG business!
 production value 2009: 3.4 trillion dollar
(3.400.000.000.000 $)
 equals the GDP of Germany
 All are toxic, some are intended to kill
 fungicides, insecticides, herbicides,
nematicides, molluscicides, …
Human-made & natural toxicant
Dioxins

 e.g., 2,3,7,8-TCDD
 human: paper and fiber bleaching, incineration of
waste, metal smelting, cigarette smoke
 natural: incomplete combustion of chlorine-containing
things
Natural toxicants: defense
Oleandrin

 oleander (Nerium oleander)
 gastrointestinal and cardiac effects, skin irritation,
CNS effects (coma), death
Human-made vs. natural
What is the difference?
 Time scale

 major increase after second world war
 rapid development of new types of molecules
 Spatial scale
 amounts emitted
 landscape and even global instead of local
 Since 1970’s, most countries have programmes for
environmental protection ...
Ecotoxicology

 Daphnia reproduction test OECD guideline 211
Reproduction test

Reproduction test

Reproduction test

wait for 21 days …
Range of Concentrations

Dose-response plot

total offspring
NOEC
EC50
log concentration
If EC50 is the answer …

… what was the question?
“What is the concentration of chemical X that leads to
50% effect on the total number of offspring of
Daphnia magna (Straus) after 21-day constant
exposure under standardised laboratory
conditions?”
 (almost) nothing!
total offspring
 What does this answer tell me about other
situations?
EC50
log concentration
Organisms are complex…

 Response to stress depends on
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


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
organism (species, life stage, sex, …)
endpoint (size, reproduction, development, …)
type of stressor (toxicant, radiation, parasites, …)
exposure scenario (pulsed, multiple stress, …)
environmental conditions (temperature, food, …)
etc., etc.
E.g., effect on reproduction

E.g., effect on reproduction

E.g., effect on reproduction

E.g., effect on reproduction

E.g., effect on reproduction

To understand an effect on reproduction …
• need to know how food is used to make offspring
• and how chemicals interfere with this process
Why is DEB important for toxicity?

 The use of DEB theory allows extrapolation of
toxicity test results to other situations and other
species
 To study the effects of toxicity on life-history traits,
DEB follows naturally




food is used to fuel all traits over the life cycle
toxicants affect DEB parameters
should allow extrapolation to untested conditions
it is valuable for environmental risk assessment
What is DEB theory?

 It captures the quantitative aspects of metabolism at
the individual level for all species
 Why the hope for generality?
 universality of physics and evolution
 Entropy production is >=0
 widespread biological empirical patterns
A widespread biological empirical fact:
Von Bertalanffy growth

 Growth as a function of time
L(t )  L  ( L  Lb ) e  rB t
 Depends on length at birth,
maximum length and
growth rate
 It was proposed in 1929 by
Putter and in 1938 by Von
Bertalanffy
A widespread biological empirical fact:
Kleiber’s Law

 Metabolism (respiration or
heat production) as a
function of mass
M  aW b
 Metabolism increases with
weigth raised to the power
3/4
 Max Kleiber originally
formulated this basic
relationship back in the
1930s.
A widespread biological empirical fact:
Indirect Calorimetry

 Indirect calorimetry calculates heat that living
organisms produce from their production of carbon
dioxide and nitrogen waste and from their
consumption of oxygen.
 Lavoisier noted in 1780 that heat
production can be predicted from
oxygen consumption this way,
using multiple regression.
Basic concepts in DEB Theory

 Consistency with other scientific knowledge
(thermodynamics, evolution, etc)
 Consistency with empirical data
 Life-cycle approach: embryo, juvenile and adult
 Occam’s razor: the general model should be as
simple as possible (and not more)
Basic Concepts in DEB Theory

 The individual: time and spatial scales
Volume
30
log10 m3
Life span
earth
log10 a
20
life on earth
whale
10
0
bacterium
ATP molecule
whale
-10
-20
-30
bacterium
water molecule
A DEB organism

ME - Reserve
 Metabolism in a DEB
individual.
 The boundary of the
organism
 Rectangles are state
variables
MH - Maturity
MV - Structure
DEB model: the State Variables

 What defines a DEB organism?
 Biomass
 Mv - Mass of Structure
 ME - Mass of Reserve
 Life-Cycle approach: different life stages
 MH - Level of Maturity (it represents neither mass nor
energy)
 What about other possibles state variables such as
age?
Why not age as a state variable?

Trichopsis vittatus
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
DEB model: Reserve and Structure
 Strong homeostasis

 Reserve & Structure have constant aggregated
chemical composition
 Why more than 1 state variable to define the biomass?
 The aggregated chemical composition of organisms is not constant –
it changes with the growth rate
 Why not more than 2 state variables to define biomass?
 Two are sufficient (in animals and bacteria) to capture the change in
aggregated chemical composition with the growth rate
 Strong homeostasis -> higher control over metabolism
Why not use thousands of chemical species
and chemical reactions to define the organism?

 Metabolism at the chemical level is very complex
 It is not possible to impose mass conservation without
modeling all chemical reactions (which is impossible).
DEB model: Reserve and Structure
 Weak homeostasis

 At constant food organisms tend to constant
aggregated chemical composition
 Empirical support: growing biomass tends to constant
chemical composition at constant food
 Weak homeostasis -> higher control over metabolism
DEB model: Maturity

 Life Stages (dark blue) and transitions (light blue)
embryo
fertilization
baby
birth
juvenile
adult
infant
weaning
puberty
death
 Essential switch points for metabolic behavior
 Birth (start of feeding)
 Puberty (start of allocation to reproduction)
 Switch points sometimes in reversed order (aphids)
MHb- threshold of maturity at birth
MHp- threshold of maturity at puberty
Life-stages: Metamorphosis

MHb - Extremes in relative maturity at birth

Didelphus marsupiales (Am opossum)
♂, ♀ 0.5 + 0.5 m, 6.5 kg
At birth: <2 g; ab = 8-13 d
10-12 (upto 25) young/litter, 2 litters/a
Ommatophoca rossii (Ross Seal)
♂ 1.7-2.1 m, 129-216 kg
♀ 1.3-2.2 m, 159-204 kg
At birth: 1 m, 16.5 kg; ab = 270 d
Notation 1

Notation 2
General
Indices for compounds
Indices for transformations

A DEB organism

Feeding
J XA
J EA
ME - Reserve
Assimilation
MH - Maturity
MV - Structure
 Metabolism in a DEB
individual.
 Rectangles are state
variables
 Arrows are flows of food
JXA, reserve JEA, JEC, JEM, JET ,
JEG, JER, JEJ or structure JVG.
 Circles are processes
Feeding & Assimilation

 Feeding: the uptake of food
 Assimilation: conversion of substrate (food,
nutrients, light) into reserve(s)
 Depends on substrate availability & structural
surface area (e.g. surface area of the gut)
𝐽𝐸𝐴 = 𝑦𝐸𝑋 𝐽𝑋𝐴 = 𝑓(𝑋) 𝐽𝐸𝐴𝑚 𝑉 2/3
𝐽𝐸𝐴𝑚 - surface maximum assimilation rate
𝑦𝐸𝑋 -yield of reserve on food
 Empirical pattern: the heat increment of feeding suggests that
there are processes only associated with food processing
 Strong homeostasis imposes a fixed conversion efficiency
 Consistency with other fields: mass transfer (needed for
acquisition, digestion and food processing) is proportional to
Feeding rate

Filtration rate, l/h
 If food availability is constant (or abundant) feeding
increases proportional to area or L2 (for isomorphs)
Mytilus edulis
Data: Winter 1973
Length, cm
Intra-taxon predation: efficient conversion
yEX a high yield of reserve on food

Hemiphractus fasciatus
is a frog-eating frog
Beroe sp
is a comb jelly-eating comb jelly
Euspira catena
is a snail-eating snail
Coluber constrictor
is a snake-eating snake
Solaster papposus
is a starfish-eating starfish
Chrysaora hysoscella
is a jelly fish-eating jelly fish
Intra-taxon predation: efficient conversion
yEX a high yield of reserve on food

Asplanchna girodi
is a rotifer-eating rotifer
Falco peregrinus
is a bird-eating bird
Didinium nasutum
is a ciliate-eating ciliate
Acinonyx jubatus
is a mammal-eating mammal
Esox lucius
is a fish-eating fish
Enallagma carunculatum
is a insect-eating insect
Metabolic rates: the effect of temperature
 Arrhenius relationship:
T T
k (T )  k1 exp{ A  A }
T1 T
TA  6400 K; T1  293 K
Daphnia magna
ln rate

reproduction
young/d
ingestion
106 cells/h
growth, d-1
aging, d-1
104 T-1, K-1
 The Arrhenius relationship has good empirical support
 The Arrhenius temperature is given by minus the slope: the
higher the Arrhenius temperature the more sensitive
organisms are to changes in temperature