nr. 477 - 2011 - Institut for Natur, Systemer og Modeller (NSM)

5.7 Discussion of Marée et al. (2006)’s Model Assumptions 35
phenomenon called cooperativity occurs. Cooperativity describes the phenomenon that
an enzyme can become more (or less) prone to bind with substrates after binding with
one substrate (Murray, 2002, p.197). If the enzyme becomes more prone to bind, then
we speak of positive cooperativity, if the enzyme remains as prone to bind as before
binding to the substrate, then it is neutral cooperativity (Michaelis-Menten), and finally
if it becomes less prone to bind we call it negative cooperativity (Murray, 2002,
p.201). The Hill-coefficient reveals if we are dealing with negative, neutral or positive
cooperativity.
Marée et al. (2006) do no want to model cooperativity, they just want the cytokine
induced apoptosis to be saturated, therefore we find that the use of a Michaelis-Menten
function is a sound assumption.
Implication of secretion of cytokines upon Ba phagocytosis
In Stoffels et al. (2004) they find that NOD macrophages produce cytotoxic cytokines
upon encountering necrotic as well as apoptotic cells, while Brouckaert et al. (2004)
holds that phagocytosis of neither apoptotic nor necrotic cells generates proinflammatory
cytokines (Brouckaert et al., 2004, p.1089). The results of Brouckaert et al. (2004)
indicates that phagocytosis of necrotic cells is less efficient than phagocytosis of apoptotic
cells – it may be so because the macrophages are better “tuned in” to the apoptotic
cells (Pociot (2009)). This is at variance with the assumption of Marée et al. (2006).
Brouckaert et al. (2004) does not dispute the fact that cytokines are observed together
with necrotic cells, but speculates that it is the necrotic cells themselves, rather than
the macrophages, that release cytokines, and speculates further that the inflammatory
effect is enhanced because the macrophages spend too much time engulfing the necrotic
cells, leaving more apoptotic cells to enter secondary necrosis (Brouckaert et al., 2004,
p.1099) thus proliferating the cytokines. Of course one could adjust the model to fit
these different result, but we must note that the macrophages studied in Brouckaert
et al. (2004) are of the so-called L929sA-type. The L929sA-type macrophage is associated
with cancer cells (Pociot (2009)), which obfuscates our ability to draw direct
parallels to NOD-macrophages.
Turning back to the results of Stoffels et al. (2004) and assuming that they are correct in
their findings, and further more assuming that the rate of secretion of cytokines based
on engulfment of apoptotic β-cells is equal to that from phagocytosis of necrotic cells,
then equation 5.10 is transformed to
dC
dt = αBnMa + αBaMa − δC (5.25)
This seemingly minor adjustment (remember that the secretion rate, α was a mere
5 × 10 −9 nM cell −2 d −1 ) has a dramatic effect on the dynamics of the Balb/c mice, for
now the concentrations Ma, Ba, Bn, C do not go to zero, rendering the Balb/c mouse in
the same dire state as the NOD-mouse; see figure 5.8. This is of course at variance with
experimental observations. Thus if Stoffels et al. (2004) are correct, then the hypothesis
of Marée et al. (2006), that the onset of T1D in NOD, but not in Balb/c, mice is a
consequence of phagocytosis rate cannot hold. Something else must be involved. One
possibility is that the NOD-macrophages themselves have a predisposition for secreting