Optimal uptake kinetics: 2009 ASLO Meeting

Optimal uptake kinetics: physiological acclimation explains
the pattern of nitrate uptake by phytoplankton in the ocean
S. Lan Smith, Yasuhiro Yamanaka
Ecosystem Change Research Program, FRCGC (JAMSTEC), Japan
Markus Pahlow & Andreas Oschlies
Leibniz Institute of Marine Sciences at Kiel Univ. (IFM-GEOMAR), Germany

ASLO Aquatic Science Meeting, Nice, France 29 January, 2009

Rate Expressions for Nutrient Uptake
Michaelis-Menten (MM) Equation
Vmax S U
Uptake Rate, U(S) = [ K + S ] S
s

Affinity-based Equation (Aksnes & Egge, MEPS, 1991)
1 More general
V(S) = [ (A S)−1 + (V )−1 ] Reduces to MM as a special case
s max

Optimal Uptake (OU) Equation (Pahlow, MEPS, 2005) Both are
mostly protein
Uptake Sites more sites => Greater Affinity, A (lower Ks)
& contain
Internal Enzymes more enzymes => Greater Vmax lots of N.

fA = fractional allocation
Cell
Ion Channels
= Uptake Sites
of internal N:
A = A0 fA
Nutrient Internal
Vmax= V0 (1 − fA)
Ions Enzymes

Acclimation
Low Nutrient Conc. High Nutrient Conc.
S. Lan Smith, FRCGC ECRP

Optimal Uptake Kinetics: Combining two equations
for Limiting nutrient, L with conc. SL
Pahlow's Optimal Uptake Equation came from combining these two equations:
1 1
VLim = fA =
[(1−fA)V0, L ]−1 + [fAA0, LSL]−1 1/2
A0, LSL
( ) +1
V0, L
Affinity-based uptake equation Optimal acclimation
(Aknes & Egge, MEPS, 1991), as equation (Pahlow, 2005).
modified by Pahlow (MEPS, 2005) so He assumed
that V0 and A0 vary with N allocation. instantaneous acclimation.
OU Equation for a single (limiting) nutrient
assuming instantaneous acclimation (Pahlow, MEPS, 2005):
V0 SL
VOU =
V0 V0 SL 0.5
()( )
+2 + SL
A0 A0


Short-term Approximation for Optimal Uptake Kinetics

for Limiting nutrient, L with concentration SL
Pahlow's Optimal Uptake Equation came from combining these two equations:
1 1
VLim = fA =
[(1−fA)V0, L ]−1 + [fAA0, LSL]−1 1/2
A0, LSL
( ) +1
V0, L
If phytoplankton do NOT
have time to acclimate,
The quot;Squot; in this equation
SL sample water, is NOT the instantaneous
add nutrients concentration, SL.
ship
expts. Let Sa be the concentration
to which phytoplankton
Here quot;SLquot; is the have acclimated,
Sa
concentration in the BEFORE sampling and
bottles for incubation before the expts. to
Ocean
experiments. measure uptake rate.


Short-term OU Approximation predicts changes in Ks

Ks values come from fitting the MM equation to experimental data.
Modern expts. usually last < 2-3 hours,
to minimize changes in concentration.
The OU Equation (Pahlow, MEPS, 2005)
can be re-arranged to:
This short-term approximation predicts
A0 Sa
( )
0.5
how Vmax and Ks (fit to the MM eqn.)
V0 V0 S should vary with nutrient conc., Sa
A0 Sa 0.5
( )
1+ It applies over timescales shorter
V0
VOU = than the time required to acclimate.
V0 Sa 0.5
( )
+S S is the concentration in the bottles
A0
during incubation expts.
Thus,
V0 Sa
( ) 0.5
Ks =
A0 Sa = concentration in seawater (before sampling).

S. Lan Smith, FRCGC, JAMSTEC April, 2008

Apparent Half Saturation quot;Constantsquot; Predicted by OU kinetics
Uptake Rate Equations
The New The Classic
OU Equation for a single nutrient Michaelis-Menten (MM) Equation:
(Pahlow, MEPS, 2005): Vmax S
VMM =
V0 S Κs + S
VOU =
()( )V0 VS 0.5
+2 0 +S where S is
A0 A0 nutrient concentration
Acclimated
(long-term) response
Short-term OU approximation
( )
Kapp (µmol L-1}

A0 Sa 0.5
OU
1. 5

V0 V0 S
( )
1. 0
A0 Sa 0.5
KN = 0.7 1+
V0
0. 5

VOU =
short-term OU
( )
V0 Sa 0.5
+S
0. 0

A0
0 1 2 3 4
-1
[NO3] (µmol L ]

S. Lan Smith, FRCGC, JAMSTEC 6 November, 2008

Dependence of KNO3 on Nitrate Concentration in Field Studies
Collos et al. (J. Phycol., 2005) Data (x) from marine field studies
examined the relationship between as compiled by Collos (2005)
half-saturation constant for nitrate uptake
1.5
and nitrate concentration, using data
n = 38 data pts.
complied from many field studies.
They found a linear relationship 0.5
between the log-transformed data. log KNO3

log KNO3 = a + b log [NO3] -0.5
Significant relationship
which is equivalent to: (b != 0) at level p < 10-9
r2 = 0.562
KNO3 = a [NO3] b -1.5
-2.0 -0.5 0.5
Optimal Uptake kinetics predicts:
log NO3
KNO3 = a [NO3] 0.50 Least-squares fits to the data:

b is not significantly different from 0.50 log Ks = − 0.089 + 0.62 log NO3
(ANOVA, p < 0.20) log Ks = − 0.152 + 0.50 log NO3
The data is cosistent with OU kinetics.

An Independent Test Using Data from Different Field Studies
But the data in Collos (2005) came from Data (x) compiled from 2 studies
many studies, some of which used
different methods to determine KNO3.
0
The data at right are from two studies:
Harrison et al (Limnol. Oceanogr., 1996) N. Atlantic
-1
McCarthy et al (Deep Sea Res. II, 1999) Arabian Sea
log KNO3
which used similar methods.
This provides an independent test, -2
over wide regions of the ocean,
n = 61 data pts.
and over wide ranges of concentration.
-3
-2.5 -1.0 0.0
Significant relationship (b != 0) at level p < 10-10
log NO3
r2 = 0.54 for the general equation
r2 = 0.52 for the eqn. with b = 0.50
Least-squares fits to the data:
b is not significantly different from 0.50 log Ks = − 0.17 + 0.62 log NO3
(ANOVA, p < 0.119 )
log Ks = − 0.36 + 0.50 log NO3
The data is cosistent with OU kinetics.

Field Experiments Measure the Response of Assemblages

The mix of species varies with location
& with nutrient concentrations

quot;Grey Areaquot;
= What we don't understand
Why does the nitrate uptake
response of the community of
phytoplankton agree with the OU
equation ?
Is it just luck ?
For two independent compilations?


Why should the same equation describe so many different species?
Acclimation: Each Organism changes in response to its environment.
Cell Same Cell
Ion Channels
For changing nutrient
= Uptake Sites
concentration
Nutrient Internal low high
Ions Enzymes
A trade-off:
different uses for
the same resource.
The same trade-off could apply to species evolving for different environments.
Speciation: Different Organisms evolve to dominate in different environments.
Large Species
Ion Channels Small Species
= Uptake Sites For changing nutrient
concentration
Nutrient
Ions
low high
The same trade-off.

Different Interpretations of Phytoplankton's Response to Nutrients
Traditional New
in terms of MM kinetics in terms of OU kinetics
Differences in Ks & Vmax reflect All phytoplankton acclimate
intrinsic differences between to nutrient concentrations in the
species. same way, subject to the same
physiological trade-off.
Different species have evolved
different strategies to aquire Yes, there are differences, but
nutrients and grow. the overall pattern can mostly
be explained by the similarities.
Different environments favor
different strategies. Implies high(er) predictability
e.g., high nutrients they all behave similarly
vs. low nutrients w/ pulses
Implies low predictability:
We cannot predict patterns
in these intrinsic properties.

What difference does OU kinetics make in Global Models?
Collaboration with Prof. A.Oschiles & Dr. M Pahlow (Kiel Univ., Germany)
OU kinetics (The SPONGE from Smith & Yamanaka, Limnol. Oceanogr. 52, 2007)
substituted into a marine ecosystem model:
Univ. of Victoria Earth System Climate Model
(Schmittner et al, GBC 19, 2005; Schmittner et al., GBC 22, 2008)
Two nutrients (N & P), coarse resolution OGCM (1.8 x 3.6 degrees)
Long simulations: years 1865-2000
Significant Differences: OU version vs. Original (Michaelis-Menten kinetics).
Apparent half-saturation constant, Kapp Relative Difference: Integrated P. Prod.
KN = 0.7 mmol L-1 in original MM version (OU - MM) %

S. Lan Smith, FRCGC, JAMSTEC 6 November, 2008

Differences in Zonnally Averaged Primary Production

Top: Relative (%) Difference (OU - MM)
in Annual PP for Year 2000.

more PP in subtropical gyres
less in upwelling regions

Bottom: Absolute Difference Difference:
OU − MM
(OU - MM) 2100
2000
in zonally averaged PP 1770

for selected years

difference increasing over time

S. Lan Smith, FRCGC, JAMSTEC ECRP

Optimal Uptake kinetics describes the observed variations in
quot;half-saturation constantsquot; fit to the MM equation for field expts.
The Optimality-based explanation:
All phytoplankton acclimate to the ambient nutrient concentration
by altering their physiology, subject to the same trade-off.
This implies greater predictability than MM kinetics.
This acclimation requires more time than typical incubation
experiments used to measure uptake (2-3 h).
MM parameters from short-term expts. do not accurately
represent the long-term response of phytoplankton.
In a global Earth System Climate Model, OU kinetics yields
significantly different dynamics than MM kinetics.
OU kinetics is a superior alternative to MM kinetics for modeling.
ASLO Aquatic Science Meeting, Nice, France 29 January, 2009

Vmax varies even more than Ks

Vmax varies more than predicted by
1.5
the Short-term OU approximation.
1.0
log Vmax

We expect this because of:
0.5
Inhibition of Nitrate Uptake by NH4
reducing rates at low nitrate
0.0
where [NH4] is often higher
-0.5
Possible temperature dependence
1 2 3 4 (lower rates at Nitrate,
log [NO3] where temp. should be low)
Data (x) from field expts. in the N. Atlantic
Harrison et al. (Limnol. Oceanogr. 41, 1996)

Line is the best-fit of the Short-term OU
Approximation for Vmax.


Optimal uptake kinetics: 2009 ASLO Meeting

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Optimal uptake kinetics: 2009 ASLO Meeting