176
Chapter 5
Specific growth rate (tv1)
Fig. 5.14 The specific glucose and oxygen uptake rates and the specific rates of formation of acetate,
formate, and ethanol as functions of the specific growth rate calculated by maximizing the specific
growth rate of the
E. coli
metabolic model using linear programming.
where
r,
is the net specific rate of consumption of the ith compound,
e.g.,
oxygen, acetate, or an amino
acid. Thus, the shadow price reflects the effects that changes in individual metabolic rates have on the
specific growth rate. Table 5.4 gives some of the shadow prices calculated by the metabolic model for
different specific oxygen uptake rates (r0). At low
r„
the shadow price for oxygen is positive,
i.e.,
by
increasing
ra
the specific growth rate can be increased. When r
0
is at its maximum, the specific growth
rate cannot be increased further by increasing
r0
and the shadow price is therefore zero. At anaerobic
conditions
(r0
= 0), the shadow price for NADH is negative due to the inability of the cell to oxidize this
cofactor,
i.e.,
if NADH production increases the specific growth rate will decrease. This indicates that
cofactor regeneration can limit growth at anaerobic conditions. For ATP it is observed that the shadow
price is high at anaerobic conditions and decreases with increasing
r0.
Thus, supply of ATP for growth
becomes less limiting for cells growing aerobically compared with anaerobic growth. The positive
shadow price for ATP supports the above statement, that the cells are ATP limited and when respiration
reaches its upper limit the cells will start to seek other routes for ATP formation - namely by formation
of acetate. The shadow price for acetate is zero when the specific oxygen uptake rate is below 20 mmoles
(g DW h)'1. The likely reason is that the ATP yield in connection with acetate formation is much less
than the ATP yield in respiration, and the cells will therefore prefer to increase respiration. It is
interesting to notice that the shadow price for ethanol is positive even when the specific oxygen uptake
rate is below 20 mmoles (g DW h )'. This could be a consequence of oxidation of NADH being a
problem for the cell since formation of ethanol involves a route from acetyl-CoA where NADH is
oxidized. However, the energy metabolism is likely to dominate at these conditions, and the cell will
therefore prefer to oxidize NADH in the oxidative respiration, without activating the route to ethanol.
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