Balancing Photosynthesis and Growth
39
In an extension to the model of Burmaster (1979), Morel (1987) introduced feedback between nutrient status and uptake rate. He assumed that the
regulation of nutrient uptake is effected through the saturated uptake rate
v Ill' while the half-saturation parameter Kill can be considered constant. In
his model, v III is a linear decreasing function of cell quota with a maximal
saturated uptake rate v'", at maximal nutrient starvation ( Q = Q') and a
minimal saturated uptake rate v"", corresponding to ( Q = Q'') That is,
v =v' -(v' -v") Q-Q'
m
m
m
"'Q"-(l
(3.14)
Morel (1987) showed that under the steady-state condition [Eq. (3.6)]
this model also is equivalent to a Monod-type relationship between growth
rate and external concentration, which can be written as
"
s
-~ --"';;""""--'
)J - "
n Q'
Q K ~+s
m v~ Q"
(3.15)
If we take into consideration the definition of affinity (a' = v'm/K",) and
that the steady-state condition [Eq. (3.6)] implies that v" .. = jJ"Q" when
p = p", it is clear that Eq. (3.15) is also the equivalent of Eq. (3.10) for the
case where nutrient efflux is negligible (S' = 0).
3.4 Balancing Photosynthesis and Growth
In a particularly elegant, but for some reason rarely cited, model of
balanced phytoplankton growth, Shuter (1979) assumed that the material
in algal cells can be partitioned into four major compartments: structural,
photosynthetic, biosynthetic, and storage. The structural compartment was
assumed to be a fixed fraction of cell mass, while the other three were
allowed to vary in response to the growth conditions. Shuter (1979) showed
that if the growth rate is constrained by a given level of light or nutrient
limitation, there will be a unique, optimal allocation of photosynthate into
the three variable compartments, that will ensure balanced growth. In this
context, balanced growth means that cellular proportions between the four
compartments will remain fixed from generation to generation.
If growth is nutrient-limited, the model of Shuter (1979) predicts that the
photosynthetic compartment should increase in proportion to the growth
rate. This means that the cell should not allocate more material to the
photosynthetic apparatus than is needed to produce the amount of photosynthate required to support growth. In the limiting case where nutrient
limitation is so severe than no net growth is possible, the size of the photosynthetic compartment should only be sufficient to support maintenance.
39
In an extension to the model of Burmaster (1979), Morel (1987) introduced feedback between nutrient status and uptake rate. He assumed that the
regulation of nutrient uptake is effected through the saturated uptake rate
v Ill' while the half-saturation parameter Kill can be considered constant. In
his model, v III is a linear decreasing function of cell quota with a maximal
saturated uptake rate v'", at maximal nutrient starvation ( Q = Q') and a
minimal saturated uptake rate v"", corresponding to ( Q = Q'') That is,
v =v' -(v' -v") Q-Q'
m
m
m
"'Q"-(l
(3.14)
Morel (1987) showed that under the steady-state condition [Eq. (3.6)]
this model also is equivalent to a Monod-type relationship between growth
rate and external concentration, which can be written as
"
s
-~ --"';;""""--'
)J - "
n Q'
Q K ~+s
m v~ Q"
(3.15)
If we take into consideration the definition of affinity (a' = v'm/K",) and
that the steady-state condition [Eq. (3.6)] implies that v" .. = jJ"Q" when
p = p", it is clear that Eq. (3.15) is also the equivalent of Eq. (3.10) for the
case where nutrient efflux is negligible (S' = 0).
3.4 Balancing Photosynthesis and Growth
In a particularly elegant, but for some reason rarely cited, model of
balanced phytoplankton growth, Shuter (1979) assumed that the material
in algal cells can be partitioned into four major compartments: structural,
photosynthetic, biosynthetic, and storage. The structural compartment was
assumed to be a fixed fraction of cell mass, while the other three were
allowed to vary in response to the growth conditions. Shuter (1979) showed
that if the growth rate is constrained by a given level of light or nutrient
limitation, there will be a unique, optimal allocation of photosynthate into
the three variable compartments, that will ensure balanced growth. In this
context, balanced growth means that cellular proportions between the four
compartments will remain fixed from generation to generation.
If growth is nutrient-limited, the model of Shuter (1979) predicts that the
photosynthetic compartment should increase in proportion to the growth
rate. This means that the cell should not allocate more material to the
photosynthetic apparatus than is needed to produce the amount of photosynthate required to support growth. In the limiting case where nutrient
limitation is so severe than no net growth is possible, the size of the photosynthetic compartment should only be sufficient to support maintenance.