Empirical models of nutrient uptake

Many of the well-established paradigms relating to the uptake and deployment of nutrients and the ways in which these impinge upon the growth and dynamics of phytoplankton are founded on a welter of experimental observations. However, it is a small number of classic studies that have provided much of the insight and understanding, into which the majority of observations can be interpolated. For instance, the model of Dugdale (1967) recognised the saturable transport capacity (corresponding to the fully 'open' condition of the receptors) and the simultaneous dependence of the rate of uptake upon resource availability in the adjacent medium. Dugdale showed that the relationship between the rate of uptake of nutrients in starved cells and the concentrations in which the nutrient is proffered conforms to Michaelis-Menten enzyme kinetics, as expressed by the Monod equation. Dugdale's (1967) general equation stated:

Figure 4.4

Uptake rates of molybdate-reactive phosphorus by cells of Chlorella sp., pre-starved of phosphorus, as a function of concentration, according to data of Nyholm (1977). Redrawn with permission from Reynolds (1997a).

Figure 4.4

Uptake rates of molybdate-reactive phosphorus by cells of Chlorella sp., pre-starved of phosphorus, as a function of concentration, according to data of Nyholm (1977). Redrawn with permission from Reynolds (1997a).

The equation recognises that the rate of uptake of a nutrient by fully receptive cells is a function of the resource concentration, S, up to a saturable limit of VUmax. Ku is the constant of half saturation (i.e. the concentration of nutrient satisfies half the maximum uptake capacity). There is no way to predict these values accurately save by experimental determination. Many measurements show close conformity to the predicted behaviour and, hence, to the generalised plot in Fig. 4.4, showing the uptake of phosphorus by Chlorella, as described by Nyholm (1977). Because the uptake rates and affinities are, however, very variable among individual phytoplank-ton species, they are most conveniently intercom-pared by reference to the magnitudes of alga-and nutrient-specific values of VUmax and Ku. For instance, a relatively high VUmax capacity combined with a low Ku is indicative of high uptake affinity for a given nutrient.

The Monod model has been widely applied and found to describe adequately the uptake by algae of essential micronutrients, under the starvation conditions described. It has been found to be less satisfactory for the description of nutrient-limited growth rates. This may be attributed, in part, to inappropriate application and a misplaced assumption - analogous to the one about photosynthesis and growth - that growth rates are as rapid as the relevant materials can be assembled. In fact, growing cells may take up nutrients when they are abundant much more rapidly than they can deploy them, just as they can sustain growth at the expense of internal stores at times when the rate of uptake may be constrained by low external concentrations. Droop (1973, 1974) cleverly adapted the Dugdale model to include a variable internal store in order to represent the impact of the cell quota on the rate of growth. The impacts of nutrient deficiencies on cell replication are considered in Chapter 5 (see Sections 5.4.4, 5.4.5). However, it is useful to introduce here the concept of an internal store in the context of its influence on uptake and, indeed, its relevance to how we judge 'limitation' and its role in interspecific competition for resources.

It is, firstly, quite plain that the intracellular content of the cell starved of a given particular resource will not just be low (leaving the cell very responsive to new resource) but it will probably be close to the absolute minimum for the cell to stay alive. This is Droop's 'minimum cell quota' (q0) and it is too small to be able to sustain any growth. Secondly, raising the actual internal content (q) above the minimal threshold (essentially through uptake) makes resource available to deployment and growth. At low but steady rates of supply, some proportionality between the rates of growth (r ) and resource is expected to be evident. Interpolating (q - q0) for S, r' for Vu and rmax for VUmax in Eq. (4.11), the Droop equation states:

the literature. In the following considerations, the usage is necessarily precise, adhering to the definitions shown in Box 4.1.

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