Biomedical Engineering Reference
In-Depth Information
Reaction rate ( R S )
R max
R max /2
0
k M
Substrate concentration ( C S )
FIGURE 3.2
The Michaelis-Menten law displaying a nonlinear relation between the nutri-
ent or oxygen consumption rate, R S , by unit area of cell layer versus the local
concentration of the nutrient or oxygen solute molecule.
reaction rate of the cell uptake is of first-order type in concentration, whereas
at increasing concentration, this rate asymptotically approaches a constant
value, V max . Then, the rate R S of oxygen consumption by unit area of cell
layer with a surface density σ cel takes the following expression (Figure 3.2):
C
C + K M
C
C + K M
R S =
σ cel ×
V max ×
=
R max ×
(3.1)
where the minus sign indicates that the presence of a cell layer has a sink
effect on the nutrient molecules concentration C.
Note that the oxygen consumption by unit volume within such porous
substrates is then
R V = S V ×
R S
(3.2)
Owing to the complexity of the biological and biochemical phenomena tak-
ing place in nutrient uptake by cells, simplified models are often used for the
description of these enzymatic processes. As a result, and by extension, this
law is also used for the description of other biological phenomena such as cell
population growth, absorption of biochemical molecules within kidneys, or
consumption of drugs by tumoral cells. On the basis of experimental studies,
it has been shown that the maximal oxygen consumption rate, V max , depends
on the cell type and may vary by several orders of magnitude. This vari-
ability could partially be explained by the variety of the experimental setups
(culture protocol, scaffold type, cell concentration, state of the cells, etc.) as
well as by the diversity of the measurement methods (oxygen electrode or
measurement by fluorescence, for example). However, regarding the Michaelis
constant K M , literature values are close to each other for a given type of given
nutrient.
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