Biomedical Engineering Reference
In-Depth Information
Figure 7.25
Different adsorption and desorption kinetics depending on the kinetic constants.
When desorption follows adsorption, the kinetics of desorption depends not
only on the desorption coefficient
k
off
, but also on the values of G
0
and
k
on
. This
property in shown in Figure 7.25 where different desorption kinetics are sketched,
depending on the value of the saturation level.
7.3.4 Biological Reactions
7.3.4.1 Introduction
In the preceding sections, we have dealt with chemical and biochemical reactions,
in the sense where the reactants were chemical or biochemical. In biology, there are
slightly different types of reactions mainly because one has to take into account
the rate of birth or death of living organisms by introducing a source or sink term
in the reaction equations. However, these reactions have basically a mathematical
formulation similar to chemical and biochemical reactions.
7.3.4.2 Predator-Prey Systems and the Lotka-Volterra Equations
Volterra developed this model in 1925 to predict the evolution of populations of
animals in biology (fish population in the Adriatic Sea); nearly at the same time
Lotka derived the same model for some chemical reactions [7, 8]. In the frame of
this topic, we are mostly interested in the biochemical aspect of the model and we
present it briefly to introduce the special form of the competition terms in the sys-
tem of Lotka-Volterra equations. We will show later that competition-displacement
reactions for immunoassays present similarity with the predator-prey model and we
will use the competition terms extracted from the Lotka-Volterra model.
Biologists have developed models to predict the evolution of two interconnected
populations, especially if one population is the prey and the other is the predator.
It has been observed that the fluctuations of the two populations are closely linked
(Figure 7.26).
