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
Multivariate extensions 5a
animal
symbiosis
heterotroph
phototroph
plant
Photosynthesis 5.1.3
2 H2O + 4 h  O2 + 4 H+ + 4 eCO2 + 4 H+ + 4 e-  CH2O + H2O
CO2 + H2O + light  CH2O + O2
yCH E CH 2O  yNO E NO3 
CH nHE OnOE N nNE  yCE CO 2  yHE H 2O  yOE O2  yN H E NH3
Photorespiration 5.1.3a
(C5 + C  2 C3)
(C5  C3 + C2 )
RuP2 ribulose 1,5-biphosphate
Transformations are catalized
by Rubisco, which evolved in
anaerobic environments
O2 competes with CO2
which gives an oxidation,
rather than a reduction
in Calvin (= inverse pentose
phosphate cyle)
no synthesis of
hydrocarbons at
compensation point
Calcification 5.1.4
Calcification 5.1.4a
Original hypothesis:
E.huxleyi uses bicarbonate as
supplementary DIC source;
CO2 might be growth limiting
However:
non-calcifying strains have
similar max growth rate
New hypothesis:
carbonate is used for protection
against grazing
Emiliania huxleyi
DEBtool/alga/sgr 5.2.1
sgr1, sgr2, sgr3, sgr4
The functions obtain the specific growth rate, the reserve and structure fluxes for maintenance and
the rejected reserve fluxes for 1, 2, 3 and 4 reserve systems.
All reserves are supplementary for maintenance as well as for growth,
while each reserve and structure are substitutable for maintenance.
The preference for the use of structure relative to that of reserve for maintenance can be set
with a (non-negative) preference parameter.
The value zero gives absolute priority to reserve, which gives a switch at specific growth rate 0.
All functions sgr have the same structure,
and the input/output is presented for sgri where i takes values 1, 2, 3 of 4.
Inputs:
(i,1)-matrix with reserve density mE
(i,1)-matrix with reserve turnover rate kE
(i,1)-matrix with specific maintenance costs from reserve jEM
(i,1)-matrix with costs for structure yEV
optional (i,1)-matrix with specific maintenance costs from structure jVM; default is jEM/ yEV
optional scalar or (i,1)-matrix with preference parameter alpha; default is 0
Outputs:
scalar with specific growth rate r
(i,1)-matrix with reserve flux for maintenance jEM
(i,1)-matrix with structure flux for maintenance jVMM
(i,1)-matrix with rejected reserve flux jER
scalar with info on failure (0) or success (1) of numerical procedure
An example of use is given in mydata_sgr
1 Reserve – 1 Structure
5.2
2 Reserves – 1 Structure
5.2a
Reserve Capacity & Growth
5.2b
low turnover rate: large reserve capacity
high turnover rate: small reserve capacity
Multiple reserves imply excretion 5.2.2
Excreted reserve(s) might be modified to toxicants
Simultaneous nutrient limitation 5.2.3
Specific growth rate of Pavlova lutheri as function
of intracellular phosphorus and vitamine B12 at 20 ºC
Data from Droop 1974
Note the absence of high contents for both compounds
due to damming up of reserves, and
low contents in structure (at zero growth)
Vitamin B12
kE
1.19
1.22 d-1
yXV
0.39 10-
2.35 mol.cell-1
jEAm
4.91 10-
76.6 10-15 mol.cell-1. d-1
κE
0.69
0.96
kM
0.0079
0.135 d-1
K
0.017
0.12 pM, μM
Spec growth rate, d-1
15
21
B12(pM)
1.44
68
14.4
6.8
1.44
20.4
1.44
6.8
B12-conc, pM
P
B12-cont., 10-21.mol.cell-1
Data from Droop 1974 on Pavlova lutheri
106.cells ml-1
P-conc, μM
P-content, fmol.cell-1
Reserve interactions 5.2.3a
P(μM)
Spec growth rate, d-1
Spec growth rate, d-
C,N,P-limitation
N,P reductions
5.2.4
P reductions
N reductions
Nannochloropsis gaditana
(Eugstimatophyta) in sea water
Data from Carmen Garrido Perez
Reductions by factor 1/3
starting from
24.7 mM NO3,
1.99 mM PO4
C,N,P-limitation
5.2.4a
Nannochloropsis gaditana in sea water
d
C  (k E  r )mC  nCV r  jC X  J C  kC C
DIC
dt
d
N  (k E  r )mN  nNV r  j N X
nitrate
dt
d
phosphate dt P  (k E  r )mP  nPV r  jP X
d
res. dens. dt mi  ji  k E mi
d
X  rX
structure
dt
For i  C , N , P
uptake rate
jim
ji 
1 Ki / i
spec growth rate
kE  r
ri  i mi
yEV
1
spec growth 1  1  1  1  1  1  1 
r rC rN rP rC  rN rC  rP rN  rP rC  rN  rP
C,N,P-limitation
5.2.4b
Nannochloropsis gaditana in sea water
half-saturation parameters
KC = 1.810 mM for uptake of CO2
KN = 3.186 mM for uptake of NO3
KP = 0.905 mM for uptake of PO4
max. specific uptake rate parameters
jCm = 0.046 mM/OD.h, spec uptake of CO2
jNm = 0.080 mM/OD.h, spec uptake of NO3
jPm = 0.025 mM/OD.h, spec uptake of PO4
reserve turnover rate
kE = 0.034 h-1
yield coefficients
yCV = 0.218 mM/OD, from C-res. to structure
yNV = 2.261 mM/OD, from N-res. to structure
yPV = 0.159 mM/OD, from P-res. to structure
carbon species exchange rate (fixed)
kBC = 0.729 h-1 from HCO3- to CO2
kCB = 79.5 h-1 from CO2 to HCO3-
initial conditions (fixed)
HCO3- (0) = 1.89534 mM, initial HCO3- concentratio
CO2(0) = 0.02038 mM, initial CO2 concentration
mC(0) = jCm/ kE mM/OD, initial C-reserve density
mN(0) = jNm/ kE mM/OD, initial N-reserve density
mP(0) = jPm/ kE mM/OD, initial P-reserve density
OD(0) = 0.210 initial biomass (free)
Static generalisation of κ-rule
whole body
heart
whole body
time, d
time, d
time, d
5.3.1
heart
time, d
Data: Gille & Salomon 1994
Modelling: Ingeborg van Leeuwen
Muscovy duck & mallard
Organ size & function
5.3.1a
Kidney removes N-waste from body
At constant food availability JN = aL2 + bL3
Strict isomorphy: kidney size  L3
If kidney function  kidney size: work load reduces with size
If kidney function  L2 + cL3 for length L of kidney or body
work load can be constant for appropriate weight coefficients
This translates into a morphological design constraint for kidneys
Human kidney 5.3.1b
From: Mader, S. S. 1993 Biology, WCB;
Wolpert, L. 1998 Principles of development, Oxford
Tumour growth 5.3.2
Dynamic generalization of -rule
Allocation to tumour  relative workload
food
defecation
feeding
faeces
assimilation
somatic
maintenance
growth
structure
reserve

maint
1-
1-u u
tumour
maturity
maintenance
maturation
reproduction
maturity
offspring
Isomorphy: [pMU] = [pM]
Tumour tissue:
low spec growth & maint costs
Growth curve of tumour depends on pars
no maximum size is assumed a priori
Model explains dramatic
tumour-mediated weight loss
If tumour induction occurs late,
tumours grow slower
Caloric restriction reduces tumour growth
but the effect fades
Van Leeuwen et al., 2003
British J Cancer 89, 2254-2268
Tumour Growth: workload allocation 5.3.2a
Growth curve of tumour depends on pars If tumour induction occurs late,
no maximum size is assumed a priori
tumours grows slower
Van Leeuwen et al 2003
Brit. J. Cancer 89: 2254-2263
Tumor growth  DEB theory
5.3.2b
• The shape of the tumor growth curve is not assumed a priori,
and is very flexible, depending on parameter values
• The model predicts that, in general,
tumors develop faster in young than in old hosts
• According to the model, tumors grow slower in
calorically restricted hosts than in ad libitum fed hosts.
• The effect of CR on tumor growth fades away during long-term CR
• The model explains why tumor-mediated body-weight loss
is often more dramatic than expected
Organ growth 5.3.2c
Allocation to velum vs gut
 relative workload
κvelum (t )  κ κ assim (1  f (t ))
κ gut (t )  κ κ assim f (t )
fraction of
mobilisation flux
κu
Macoma
low food
Relative organ size is weakly homeostatic
Macoma
high food
Development poaceae (angiospermae) 5.3.3
From: Mader, s. S. 1993
Biology, WCB, Dubuque
Development dicotyledonae (angiospermae) 5.3.3a
From: Mader, s. S. 1993
Biology, WCB, Dubuque
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