Transcript Dynamic Energy Budget theory

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 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 2010
Phil. Trans. R. Soc. Lond. B 365: 3413-3428
Empirical special cases of DEB
11.1
year author
model
year
author
model
1780
Lavoisier
multiple regression of heat
against mineral fluxes
1950
Emerson
cube root growth of bacterial
colonies
1825
Gompertz
1891
Survival probability for aging
DEB theory
is axiomatic, 1951 Huggett & Widdas
temperature dependence of
Arrhenius
1951
Weibull
based
on
mechanisms
physiological rates
allometric growth
of body parts
Huxleynot meant
1955
Best
to glue
empirical
models
1902
Henri
1905
Blackman
1889
1910
1920
Michaelis--Menten kinetics
1957
Smith
foetal growth
survival probability for aging
diffusion limitation of uptake
embryonic respiration
bilinear functional response
1959
Leudeking & Piret microbial product formation
Since many
empirical models
Cooperative binding
hyperbolic functional response
Hill
1959
Holling
turn out
to be special cases
of DEB theory
von Bertalanffy growth of
maintenance in yields of biomass
Pütter
1962
Marr & Pirt
individuals
the data
behind these models support DEB theory
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
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
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)
Many species continue to grow after
reproduction has started
Growth of isomorphic organisms at abundant
food is well described by the von Bertalanffy
The chemical composition of organisms depends on
For different constant food levels the inverse von
Bertalanffy growth rate increases linearly with
the nutritional status (starved vs well-fed)
ultimate length
The chemical composition of organisms growing
The von Bertalanffy growth rate of different species at constant food density becomes constant
decreases almost linearly with the maximum
body length
Fetuses increase in weight approximately
Dissipating heat is a weighted sum of 3 mass flows:
proportional to cubed time
CO2, O2 and N-waste
Stoichiometry
Energy
Reproduction
Reproduction increases with size intra-specifically,
but decreases with size inter-specifically
From Sousa et al 2008
Phil. Trans. R. Soc. Lond. B 363:2453 -2464
Empirical patterns 1 11.1a
From Sousa et al 2008
Phil. Trans. R. Soc. Lond. B 363:2453 -2464
Empirical patterns 2 11.1b
From Sousa et al 2008
Phil. Trans. R. Soc. Lond. B 363:2453 -2464
Topological alternatives 11.1c
From Lika & Kooijman 2011
J. Sea Res 66: 381-391
Test of properties 11.1d
From Lika & Kooijman 2011
J. 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
Daphnia
Length, mm
1/yield, mmol glucose/ mg cells
O2 consumption, μl/h
11.1g
Streptococcus
1/spec growth rate, 1/h
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
modified Bessel function
pH
confidence intervals of pH
95, 90, 80, 60 %
A cell of volume 0.25 mm3
and pH 7 at 25°C has
m = 14 protons
N = 8 109 water molecules
7
cell volume, m3
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
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
If ADP/ATP ratio varies, then
rates of generation & use varies, but not
necessarily the rates of transformations they drive
Classic energetics 11.3
This decomposition occurs
at several places in DEBs
From: Mader, S. S.
1993 Biology, WCB
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
Classic energetics 11.3a
heterotroph
autotroph
The classic concept on metabolic regulation
focusses on ATP generation and use.
The application of this concept in DEB theory is problematic.
From: Duve, C. de 1984 A guided tour of the living cell, Sci. Am. Lib., New York
Static Energy Budgets 11.3b
Numbers: kJ in 28 d
Basic difference with dynamic budgets:
C energy from food
P production (growth) Production is quantified as energy fixed
F energy in faeces
in new tissue, not as energy allocated to
U energy in urine
growth: excludes overheads
R heat
Heat includes overheads of growth,
reproduction and other processes, it does not
quantify maintenance costs
From: Brafield, A. E. and Llewellyn, M. J. 1982 Animal energetics, Blackie, Glasgow
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
gross ingested
Differences with DEBs
• overheads
interpretation of respiration
interpretation of urination
• metabolic memory
• life cycle perspective
change in states
faeces
apparent assimilated
urine
gross metabolised
spec dynamic action
net metabolised
maintenance
work
production
somatic
activity
maintenance
growth
products
thermo
reproduction
regulation
Production model 11.4c
food
feeding
defecation
faeces
assimilation
maintenance
growth
structure
reserve
reproduction
offspring
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 together
10 Evolution
11 Evaluation