(^) Culture methods make possible the detailed study of the responses of phytoplankton
species to environmental factors. Comparisons are made of rates of photosynthesis or
cell division under various conditions. Reproduction rates are measured by counting
cells before and after a period of growth and multiplication. Healthy, well-supplied
algal cultures will increase exponentially for a considerable period, and responses are
usually expressed as the exponential rate of increase,
(Eqn. 3.7)
(^) usually with units of d−1, or as the number of cell divisions (doublings) per day,
(Eqn. 3.8)
(^) It is useful to memorize that if μ
2 = 1, then μ = 0.69.
(^) If cells are growing under constant conditions, then the daily increase of any
cellular component (e.g. carbon or nitrogen) can be measured and used to calculate a
growth rate. Such conditions can be achieved in steady-state continuous cultures, but
are not common for incubation times less than the generation period (doubling time)
for phytoplankton. Growth rates can be determined as a function of nutrient
concentration, using the Monod relationship (which is analogous to the more familiar
Michaelis–Menten enzyme kinetic equation, see Chapter 1, pp. xx and Box 3.2):
(Eqn. 3.9)
(^)
Box 3.2 Kinetics of nutrient uptake and growth
(^) The Michaelis–Menten equation is the function most frequently used to represent cell growth as a
function of the external nutrient concentration. We introduced it in Chapter 1. Here we present it with
the symbols and parameters most often used for nutrient uptake kinetics, termed the Monod equation:
(^) where ρ is the uptake rate normalized to biomass per unit time, ρmax is the maximum uptake rate, Kρ
is the half-saturation constant and [S] is the nutrient concentration. The Monod equation is used for
short-term uptake rates (often in minutes or 1 hour). Phytoplankton can adapt to limiting nutrient
concentrations by increasing ρmax (increasing transport sites) or by reducing cellular needs for the
nutrient in question. As a substrate (e.g. nutrient) affinity measure, Kρ must be used with care,
because it is affected by ρmax. If their ρmax values are different, two hyperbolae with the same initial
slope will have different Kρ values. Larger ρmax forces a larger Kρ. Kristiansen et al. (2000) give a
nice example of this effect.
(^) For steady-state conditions, the Monod equation can be used to describe growth rate as a function of
substrate concentration:
(^) Another approach to examining kinetics of nutrient uptake is to grow cultures with a continuous
nutrient supply and then assess cell growth rates as a function of the cellular nutrient content (Q).
Under these conditions, the growth rate is calculated from the Droop equation (Droop 1968):