bioreactor studies of heterologous protein production by ...

probability @), the change of plasmid-bearing cells in the biofilm cm be expressed as the
net resuit of ceii growth in the bio- piasmid loss and ceIl defachment fkom the biofilrn:
-= aY,' P ~ X ~ - P P ~ X ~ - ~ ~ X ~ = ( + ~ - P P ~ - (6.1) ~ ~ ) X ~
df
htegrating Equation (6.1) gives the foilowing:
w here
X: = x,+ exp(pi - ppi - k,)t = x,+ -(-kit) (6-2)
Li =-(pi -ppi -kdd)
Similarly. the change in plasmid-fne ce& in the biofii.cn can be described as:
A sum of Equations (6.1) and (6.4) yields:
where Xi = X: + X;, denoting the total biofilm celI mas. Assuming that at steady state
the total biofi cefl mas remains constant during continiiuous culture, Equation (6.5)
becomes:
Equation (6.6) shows that at steady state, the ceil detachment rate constant (k&) equak to
the specific growth rate of the biofilm (n). Substituthg Equation (6.6) into (6.3) gives
the following:
5 = pci (6.7)