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The objective of this thesis was to characterize the growth stoichiometry, the specific recombinant protein productivity and the regulation of the alcohol oxidase (AOX) enzyme of a Pichia pastoris Mut+ strain, performing conventional chemostat cultures and transient changes of culture parameters in continuous cultures. A P. pastoris strain secreting avidin was chosen as case study. The investigation focused on an analysis of the influence of specific growth rate, culture temperature and on use of mixed substrates. First, a chemically defined medium was designed for the production of recombinant biotin-free avidin in continuous cultures. Indeed, one problem with heterologous expression systems secreting avidin is that biotin, which is an essential vitamin for most microorganisms, binds strongly to the produced recombinant avidin. The addition of low amounts of biotin (20 µg L-1 biotin for a cell density of 8 g L-1) resulted in stable chemostat cultures on methanol with the concomitant production of biotin-free avidin. The influence of the specific growth rate on growth stoichiometry, recombinant avidin productivity and specific alcohol oxidase activity was studied with chemostat cultures on glycerol and on methanol. Results showed that the substrate consumption rate for maintenance purposes was low: 0.007 and 0.011 C-mol C-mol-1 h-1 for growth on glycerol and methanol, respectively. No recombinant avidin was detected in cultures growing on glycerol, but a partial derepression of the synthesis of AOX was observed. During chemostat cultures on methanol, the specific AOX activity was 20 to 100-fold higher than in chemostat cultures on glycerol and the specific avidin production rate was growth-associated, increasing linearly with dilution rate. No relationship between the specific avidin production rate and the specific AOX activity could be established, although avidin was expressed under the control of the AOX1 promoter. The applicability of a new and dynamic cultivation method, which consists in increasing linearly the temperature during continuous culture, was investigated. Comparison of culture characteristics determined during pseudo-steady state continuous cultures with linear increase of temperature at a rate of 0.1°C h-1 and during chemostat cultures showed that this technique can be used as a fast and accurate tool for the characterization of host cells according to cultivation temperature. Results showed that cultivation at a lower temperature than the optimal growth temperature of 30°C did not influence significantly the recombinant avidin productivity. The regulation of the AOX enzyme was investigated in continuous cultures on glycerol, methanol or mixed substrate cultures on glycerol and methanol with sudden changes of nutrient supply or pulses of methanol. Results showed that use of mixed feeds of glycerol and methanol allowed faster adaptation of cellular metabolism after growth on glycerol due to faster synthesis of methanol dissimilating enzymes. Pulse experiments showed that during cultures on methanol or during mixed substrate cultures, a sudden increase in the consumption rate of methanol after a transient increase in methanol led to the excretion of toxic intermediates (formaldehyde, formic acid) and to wash-out of the culture. This sudden increase in methanol consumption rate is due to the high amount of AOX synthesized during growth at low residual methanol concentrations. The use of mixed feeds of glycerol and methanol or sorbitol and methanol during the induction phase in place of methanol as sole carbon source was investigated by performing pseudo-steady state continuous cultures with linear changes in the methanol fraction of the feed medium. This technique was validated with comparisons with results obtained during high cell density fed-batch cultures. The volumetric avidin production rate could be increased by up to 30% with mixed feeds due to higher biomass yields during mixed substrate growth (10% increase with a feed of 60% methanol - 40% C-mol C-mol-1 glycerol at 0.06 h-1, 30% increase with a feed of 43% methanol - 57% C-mol C-mol-1 sorbitol at 0.03 h-1 ). Moreover, heat production and oxygen consumption rates could be significantly reduced using mixed substrate growth (reduction of 28% with 60% methanol - 40% C-mol C-mol-1 glycerol at 0.06 h-1; reduction of 38% with 43% methanol - 57% C-mol C-mol-1 sorbitol at 0.03 h-1), which is very useful for the performance of high cell density cultures. By contrast with glycerol, control of residual sorbitol concentration is not a critical point because sorbitol is a non-repressive carbon source with respect to AOX expression. Indeed, accumulation of sorbitol in the culture medium did not affect the specific avidin production rate. Finally, based on the results obtained during steady-state and transient continuous cultures, an optimal high cell density fed-batch strategy was proposed at a 2 L scale for the production of recombinant avidin with the studied strain. A performance of 1.06 mg h-1 avidin could be achieved with an exponential mixed feed of 43% methanol and 57% C-mol C-mol-1 sorbitol at 0.03 h-1 during the induction phase.