Question

Consider a continuous culture of Bacillus subtilis bacteria, which are used to produce the enzyme amylase during the growth phase. The relevant parameters for growth of this bacteria are μ_MAX = 0.88 hr^-1, Y_X/S = 0.5 gdw/gr substrate, S₀ = 4.0 gr substrate/L, and the Monod constant K_S = 0.3 gr/L, while the protein yield during growth phase is Y_P/X (aka product parameter α) = 0.12 g protein/gdw. The chemostat is operated at a dilution rate that is 60% of the maximum growth rate. Using this information, what is the steady state rate of product formation in the chemostat culture, in units of grams protein/L-hour?

Answer 1

Answer:

A chemostat is a bio-reactor to which fresh medium is continuously added, while culture liquid containing left over nutrients, metabolic end products and microorganisms are continuously removed at the same rate to keep the culture volume constant. The following equation is used to calculate product formation at steady state.

---------------------- (1)

  

where (dx) is the change in the cell density along with the time (dt).

x - is the cell density.

D=F/ V----------------- (2)

D is the dilution factor

F is the Flow rate of culture medium

V is the cultue volume

Calculation:

At steady state:   µ =D,

                                    x= Yx/s ([S0]-[S])

                                     x= 0.5 ([4.0-0.3])

                                        x= 0.2478.

According to the equation-1

dx/dt = 0.88* 4.0/0.3*4.0 * 0.2478 – 60(0.2478)

= 2.93*14.6202

dx/dt =42.88 grams protein/L-hour.

At the steady state, change in cell density over time forms product is 42.88 grams protein/L-hour.

Note: As per my knowledge i had written answer it may be 100% accurate, but definifely it is relevant to your question thank you so much.