Download Type II functional response: Key parameterization for marine

Type II functional response:
Key parameterization for marine
ecosystem models
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Encounter-handling processes
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Predation
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Light harvesting
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Nutrient uptake
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Analogy with enzyme kinetics
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Monod kinetics
Production rate
Enzymatic reaction
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Substrate concentration
Takenaga et al. (1999)
Drug Metabolism and
Disposition, 27, 213
Enzyme kinetics of
conversion of NB-506 to
ED-501 in rat plasma
Michaelis-Menten relationship
Vmax = maximum production rate
Ksat = half-saturation
Phosphate uptake by phytoplankton
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Phosphate uptake by a
laboratory culture of
phytoplankton
Redrawn from Yamamoto and
Taruntani (1999)
Solid line:
PO4
V =V max
PO4 + k sat
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Vmax = 1.1 pmol cell-1 hr-1
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Ksat = 1.5 μmol l-1
Photosynthesis and irradiance
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Falkowski et al. (1985)
Isochrysis galbana in
laboratory culture
P O2=P
max
O2
I
I k I
PO2max = 19.5 μmol O2 cell-1 min-1 x1010
KI = 110.0 μmol quanta m-2 s-1
Predation and prey density
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Berge et al. Aquatic
Microbial Ecology,
50, 279, (2008)
Ingestion of
phytoplankton
Rhodomonas salina
by dinoflagellate
Karlodinium armiger
in laboratory setting
Predation and prey density
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Prey concentration
Berge et al. Aquatic
Microbial Ecology, 50,
289 (2008)
Ingestion rate of
phytoplankton
Rhodomonas salina by
dinoflagellate Karlodinium
armiger in laboratory
setting
Why can all be described by the same function?
Enzymatic reaction
Microbial nutrient uptake
Photosynthesis-irradiance
Predator-prey
Prey concentration
Michaelis-Menten: Enzyme kinetics
Leonor Michaelis and Maud Menten (1913)
Described succinctly by Caperon (1967)
schematically
Menten and Michaelis
Simplest model of enzymatic reaction
Simplest model of enzymatic reaction
substrate
free enzyme
Substrate-enzyme
complex
free enzyme
product
Simplest model of enzymatic reaction
substrate
Substrate-enzyme
complex
free enzyme
[A] = concentration of A
(mol m-3)
free enzyme
product
Rate equations
conservation of enzyme
Total
free
(1)
complexed
complex
(2)
Substrate
(3)
product
(4)
“ENCOUNTER” “HANDLING”
Production rate, PC , = - “Handling”
Describe production rate in terms of
substrate concentration
Assuming complex is in “equilibrium”
(1) (2) combine to give
So production rate is
Maximum production rate
● Rate of production if enzyme always fully occupied
● Encounter not limiting
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Ksat harder to interpret
α
Differentiate with respect to [A]
α = Vmax/Ksat
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α is the “affinity” or “clearance rate”.
The rate at which substrate molecules are captured if all of the
enzymes are always free.
● i.e. extreme encounter limited situation
Enzymatic reaction
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Takenaga et al. (1999)
Drug Metabolism and
Disposition, 27, 213
Enzyme kinetics of
conversion of NB-506 to
ED-501 in rat plasma
Predation and prey density
●
●
Prey concentration
Berge et al. Aquatic
Microbial Ecology, 50,
289 (2008)
Ingestion rate of
phytoplankton
Rhodomonas salina by
dinoflagellate Karlodinium
armiger in laboratory
setting
Predator-Prey Interactions
predator + prey → occupied predator → predator
ZT = total predator density
P=prey density
Holling type II;
Type II Functional Response
C.S. Holling (1959)
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Holling type II function
Photosynthesis-irradiance
Photosynthesis-irradiance
photons
PSU
PSU*
Corg
Inorganic
C
Photosynthesis - irradiance
Max rate of
photosynthesis = KH PSUT
Proportional to amount of
pigment and “handling time”
Acclimation by changing
pigment concentration or
downstream efficiency of
utilizing captured energy
Acclimation of pigments in nature
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Data from Anna Hickman
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Atlantic Meridional Transect 15, 2.5oN, 24.5oW
Phosphate uptake by phytoplankton
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Phosphate uptake by a
laboratory culture of
phytoplankton
Redrawn from Yamamoto and
Taruntani (1999)
Solid line:
PO4
V =V max
PO4 k sat
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Vmax = 1.1 pmol cell-1 hr-1
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Ksat = 1.5 μmol l-1
Nutrient acquisition
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Transporter mediated
uptake at cell wall
Down-gradient diffusion
towards cell through
molecular boundary layer
Munk and Riley, J. Marine Res.
(1952); Pasciak and Gavis,
Limnology and Oceanogr. (1984); R.
Armstrong, Deep-Sea Res. (2008)
= nutrient concentration just outside cell wall
= ambient nutrient concentration in medium
= interior concentration of nutrient
Treat transfer across cell
wall by transporter: model
as enzymatic reaction
Relating near-cell and ambient
substrate concentrations
A = cell surface area,
{ET} = area density of transporters
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A
Vmax proportional to area density of transporters, {ET}
But this expression in terms of near-cell substrate
concentration [Ao]
–
ambient concentration measured in laboratory, [A∞]
Molecular diffusion towards cell
Down-gradient molecular diffusion
(mol A m-2 s-1)
V is flux towards cell through any
sphere radius, r: (mol A cell-1 s-1)
Molecular diffusion towards cell
Integrate
With boundary conditions
Assuming uptake at cell surface matches diffusive arrival we
find a second expression for uptake, V (mol A cell -1 s-1)
Equate the two expressions for V to
eliminate [Ao] and solve ...
Enzyme-like
transporters
Molecular diffusion
towards cell
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See Armstrong, Deep-Sea Res. I, 55, 1311-1317 (2008)
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Alternatively examine two simple limits, ...
Limit 1. Transporter limited, diffusion fast
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~
Transport across cell wall limiting
Maximum uptake proportional to cell
surface area; radius2
Maximum uptake depends on total
density of transporters {ET}
...acclimation: Cell can adjust number
density of transporters
Limit 2. Diffusion limited
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<<
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Transport towards cell limiting
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Uptake proportional to cell radius
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...acclimation: Cell can adjust number
density of transporters
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Vmax transporter limited
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Affinity and Ksat diffusion limited
Why can all be described by the same function?
Enzymatic reaction
Microbial nutrient uptake
Photosynthesis-irradiance
Predator-prey
Prey concentration
“Encounter-handling” processes
lead to Type II functional response
Enzyme kinetics analogy
Empirically relate microbial growth to
external nutrient concentration
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Empirical evidence for Michaelis-Menten form
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Monod – 1942
Monod (1949)
Relationship to nutrient uptake
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Growth rate = uptake / cell quota
–μ
=V/Q
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(s-1) = (moles cell-1 s-1)/(moles cell-1)
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For fixed elemental quota, Q (moles cell -1)
–
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μ~V
Hence, growth rate also follows Type II form
Key Points
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Common functional form between “production
rate” and “substrate concentration:
–
enzymatic reactions
–
resource acquisition by individuals
All represented by Type II functional response
Provides basic ingredients for a model of
phytoplankton population
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Resource limited growth, predation