Life in the shelf seas - Introduction to the Physical and Biological Oceanography of Shelf Seas - page 149

u max s NO 3
k NO 3 þ

u NO 3 ¼ ð 5 : 8 Þ

s NO 3

with u NO 3 the nitrate uptake rate, u max the maximum nitrate uptake rate and s NO 3 the
nitrate concentration. The parameter k NO 3 is the half-saturation concentration for
nitrate uptake. The shape of the curve in Fig. 5.8 looks similar to the growth-PAR
curves of Fig. 5.5 , with u max playing a similar role to P b max , and k NO 3 analogous to I k .
As with photosynthesis Equation (5.8) is an empirical description of a complex set of
biochemical processes associated with uptake (see Chapter 5 of Williams and
Follows, 2011 for a detailed analysis of why the curve has this form).

The role of cell size in nutrient uptake
The uptake of nutrients through the cell wall from the ambient dissolved pool
surrounding the cell is dependent on the size of the cell. Uptake results in a depleted
zone of nutrients close to the cell wall, with molecular diffusion of the nutrient
molecules transporting nutrients down the concentration gradient towards the cell.
A simple analysis of this situation leads to the following dependence of the maximum
cell volume-specific nutrient uptake rate, u v max

in mmol m 3 s 1 (see Chapter 2 of

Kiørboe, 2008 for a derivation):

3k m s 1
a p

u v max ¼ ð 5 : 9 Þ

where k m is the molecular diffusivity, a p is the phytoplankton cell radius and s 1 is the
concentration of the dissolved nutrient well away from the influence of the cell.
Equation (5.9) immediately tells us that small cells are better adapted than larger cells
at acquiring nutrients, and explains the dominance of small phytoplankton throughout
the open ocean oligotrophic gyres where nutrients are in very low concentrations.
Uptake by larger cells is limited by the rate at which molecular diffusion can resupply
the cell wall with nutrients. Indeed, with the inverse squared dependence on cell radius
we might reasonably ask why large cells are ever able to compete successfully; we will
return to this question when we discuss grazing and phytoplankton communities.

Phytoplankton growth: incorporating light and nutrient limitation
We now have two possible descriptions of phytoplankton growth rate. Growth in
response to light is formulated as:

a q I PAR
P b max

P p ¼ P b max tanh ð 5 : 10 Þ

Using the cell nutrient quota Q N P Nut /P C , with P Nut the amount of nutrient in the

cell and P C the amount of cell carbon, growth rate in response to the internal nutrient
supply, m N , can be written as:

¼

" #

Q min = Q N 1

N N

max

¼ ð 5 : 11 Þ

Q min = 1 Q max