Stationary-phase antibiotic — A Bacillus species makes an antibiotic only in stationary phase in batch culture. If the same strain is grown in a 5 L continuous culture at steady state, the antibiotic productivity will...

Introduction:
Some antibiotics are strictly stationary-phase products. Continuous chemostat operation maintains cells in exponential growth at steady state. This question asks you to infer the resulting steady-state productivity for a product that requires stationary-phase physiology.

Given Data / Assumptions:

• The strain produces antibiotic only during stationary phase.
• Chemostat steady state maintains exponential growth (mu = D > 0).
• No special two-stage or cell-recycle configuration is used.

Concept / Approach:
At steady state in a single-stage chemostat, cells neither enter nor remain in stationary phase; they divide at mu = D continuously. If the biosynthetic pathway is strictly turned on only in stationary phase, the specific production rate q_p is zero in exponential phase, so volumetric productivity P_v = q_p * X is also zero under steady conditions.

Step-by-Step Solution:
Recognize physiological requirement: stationary phase is essential for expression.Recall chemostat state: exponential growth persists; stationary phase is absent.Conclude q_p = 0 at steady state, hence productivity is zero.

Verification / Alternative check:
Two-stage chemostats (growth then production) or cell-recycle/perfusion can create high-density, low-growth zones to enable production; a single-stage chemostat at steady state does not, validating the zero-productivity conclusion.

Why Other Options Are Wrong:

• (a) and (b) incorrectly suggest production during steady exponential growth.
• (d) Violates mass balance; productivity is finite and here zero.
• (e) Oscillation is not intrinsic to steady chemostat operation without feedback instabilities.

Common Pitfalls:
Confusing steady state with high cell density; assuming any continuous operation supports stationary-phase pathways without special design.

Final Answer:
be zero at steady state.