Dynamic Energy Budget Theory - I

Tânia Sousa with contributions from : Tjalling Jager & Bas Kooijman

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?

A Theory of Metabolism

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?

Environmental Applications

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". Victimswere diagnosed as having a degeneration of their nervous ystems.

Minimata Disaster: Mercury Poisoning

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 ...

Daphnia reproduction test OECD guideline 211

Ecotoxicology

Reproduction test

Reproduction test

Reproduction test

wait for 21 days …

Range of Concentrations

Dose-response plot

EC50

tota

l off

spri

ng

log concentration

NOEC

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?”

What does this answer tell me about other situations? (almost) nothing! EC50EC50

tota

loffs

prin

g

log concentration

Organisms are complex…

Response to stress depends on 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

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

What is DEB theory?

Growth as a function of

time

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: Von Bertalanffy growth

trb

BeLLLtL )()(

A widespread biological empirical

fact:Kleiber’s Law

Metabolism (respiration or heat production) as a function of mass

Metabolism increases with weigth raised to the power 3/4

Max Kleiber originally formulated this basic relationship back in the 1930s.

bM aW

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.

A widespread biological empirical fact:

Indirect Calorimetry

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

Basic Concepts in DEB Theory

Life spanlog10 a

Volumelog10 m3

earth

whale

bacterium

water molecule

life on earth

whalebacterium

ATP molecule

30

20

10

0

-10

-20

-30

Metabolism in a DEB

individual. The boundary of the

organism Rectangles are state

variables

A DEB organism

ME - Reserve

MV - StructureMH - Maturity

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?

DEB model: the State Variables

These gouramis are from the same nest, they have the same age and lived in the same tankSocial interaction during feeding caused the huge size differenceAge-based models for growth are bound to fail; growth depends on food intake

Why not age as a state variable?

Trichopsis vittatus

Strong homeostasis

Reserve & Structure have constant aggregated chemical composition

DEB model: Reserve and Structure

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

Metabolism at the chemical level is very complex

It is not possible to impose mass conservation without modeling all chemical reactions (which is impossible).

Why not use thousands of chemical species and chemical reactions to define

the organism?

Weak homeostasis

At constant food organisms tend to constant aggregated chemical composition

DEB model: Reserve and Structure

Empirical support: growing biomass tends to constant chemical composition at constant food

Weak homeostasis -> higher control over metabolism

Life Stages (dark blue) and transitions (light

blue)

Essential switch points for metabolic behavior Birth (start of feeding) Puberty (start of allocation to reproduction)

Switch points sometimes in reversed order (aphids)

DEB model: Maturity

embryo juvenile adult

fertilization birth puberty deathweaning

baby infant

MHb- threshold of maturity at birth

MHp- threshold of maturity at puberty

Life-stages: Metamorphosis

MH

b - Extremes in relative maturity at birth

Ommatophoca rossii (Ross Seal) ♂ 1.7-2.1 m, 129-216 kg♀ 1.3-2.2 m, 159-204 kgAt birth: 1 m, 16.5 kg; ab = 270 d

Didelphus marsupiales (Am opossum) ♂, ♀ 0.5 + 0.5 m, 6.5 kgAt birth: <2 g; ab = 8-13 d10-12 (upto 25) young/litter, 2 litters/a

Notation 1

Indices for compounds

Indices for transformations

General

Notation 2

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

A DEB organism

ME - Reserve

MV - Structure

Feeding

MH - Maturity

XAJ EAJ

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)

Feeding & Assimilation

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 area

- surface maximum assimilation rate -yield of reserve on food

If food availability is constant (or abundant)

feeding increases proportional to area or L2

(for isomorphs)

Feeding rate

Mytilus edulisData: Winter 1973

Length, cm

Filtra

tion

rate

, l/h

Intra-taxon predation: efficient conversion

yEX a high yield of reserve on food

Hemiphractus fasciatusis a frog-eating frog

Beroe spis a comb jelly-eating comb jelly

Solaster papposus is a starfish-eating starfish

Chrysaora hysoscella is a jelly fish-eating jelly fish

Euspira catena is a snail-eating snail

Coluber constrictor is a snake-eating snake

Asplanchna girodiis a rotifer-eating rotifer

Didinium nasutumis a ciliate-eating ciliate

Esox lucius is a fish-eating fish

Enallagma carunculatum is a insect-eating insect

Falco peregrinus is a bird-eating bird

Acinonyx jubatus is a mammal-eating mammal

Intra-taxon predation: efficient conversionyEX a high yield of reserve on food

K 293K; 6400

}exp{)(

1

11

TTTT

TTkTk

A

AA ln ra

te

104 T-1, K-1

Daphnia magna

Metabolic rates: the effect of temperature

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

reproductionyoung/d

ingestion106 cells/h

growth, d-1

aging, d-1

Arrhenius relationship: