Chapter 8
Two-Stage Nutrient Uptake
In the nutrient-rich waters of the Thames type, a burst of algal
growth may sometimes cease before any serious depletion of the
mineral nutrient in the water has apparently taken place.
(Nature, 21 Sept. 1946)
8.1 Two-Stage Nutrient Uptake Model
In the previous model we have investigated a chemical reaction that may take place
within a cell. In this chapter, we model in more detail the activities of an entire cell
that receives nutrients from its environment, uses these nutrients for growth and
maintenance, and then excretes waste products back into its environment.
Assume a cell with an internal nutrient concentration Q is immersed in a media
with a nutrient concentration N. The growth of the cell biomass X is directly
dependent on the internal rather than the external nutrient concentration. Nutrient
uptake is proportional to the cell biomass. The proportionality factor is MU. An
outline of the structure of this system is given in Fig. 8.1. The model is called the
Caperon–Droop model. For a reference on the origins of this model see Spain [1].
Through respiration and mortality, the nutrient is passed back into solution
outside the cell. The rate of return from the cell is proportional to the biomass of
the cell. The proportionality factor is R. There is a minimum level of the internal
nutrient concentration, Q 0 , which is needed before the cell will grow at all. Thus,
the change in cell biomass, ΔX, is
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_8,
© Springer International Publishing Switzerland 2014
75
Two-Stage Nutrient Uptake
In the nutrient-rich waters of the Thames type, a burst of algal
growth may sometimes cease before any serious depletion of the
mineral nutrient in the water has apparently taken place.
(Nature, 21 Sept. 1946)
8.1 Two-Stage Nutrient Uptake Model
In the previous model we have investigated a chemical reaction that may take place
within a cell. In this chapter, we model in more detail the activities of an entire cell
that receives nutrients from its environment, uses these nutrients for growth and
maintenance, and then excretes waste products back into its environment.
Assume a cell with an internal nutrient concentration Q is immersed in a media
with a nutrient concentration N. The growth of the cell biomass X is directly
dependent on the internal rather than the external nutrient concentration. Nutrient
uptake is proportional to the cell biomass. The proportionality factor is MU. An
outline of the structure of this system is given in Fig. 8.1. The model is called the
Caperon–Droop model. For a reference on the origins of this model see Spain [1].
Through respiration and mortality, the nutrient is passed back into solution
outside the cell. The rate of return from the cell is proportional to the biomass of
the cell. The proportionality factor is R. There is a minimum level of the internal
nutrient concentration, Q 0 , which is needed before the cell will grow at all. Thus,
the change in cell biomass, ΔX, is
A save-disabled version of STELLA and the computer models of this book are available at
www.iseesystems.com/modelingdynamicbiologicalsystems.
B. Hannon and M. Ruth, Modeling Dynamic Biological Systems,
Modeling Dynamic Systems, DOI 10.1007/978-3-319-05615-9_8,
© Springer International Publishing Switzerland 2014
75