Question

The Monod equation describes the relationship between

• A. Substrate concentration and product formation rate
• B. Specific growth rate and substrate concentration
• C. Biomass concentration and time
• D. Product formation rate and biomass concentration

Hint:

• Monod Equation: \( \mu = \mu_{max} \frac{S}{K_s + S} \).
• \(\mu\): Specific growth rate.
• \(\mu_{max}\): Maximum specific growth rate.
• \(S\): Limiting substrate concentration.
• \(K_s\): Half-saturation constant (substrate concentration at \(\mu = \mu_{max}/2\)).
• Describes how growth rate depends on a single limiting nutrient.

Answer 1

The Correct Option is B

The Monod equation is an empirical model that describes the relationship between the specific growth rate (\(\mu\)) of a microorganism and the concentration of a single limiting substrate (\(S\)). The equation is given by: \[ \mu = \mu_{max} \frac{S}{K_s + S} \] where:

• \(\mu\) is the specific growth rate (time\(^{-1}\)).
• \(\mu_{max}\) is the maximum specific growth rate (time\(^{-1}\)), achieved when substrate is not limiting (\(S \gg K_s\)).
• \(S\) is the concentration of the limiting substrate.
• \(K_s\) is the Monod constant or half-saturation constant, which is the substrate concentration at which \(\mu = \mu_{max}/2\). It is a measure of the organism's affinity for the substrate.

The Monod equation is analogous in form to the Michaelis-Menten equation for enzyme kinetics. It describes how the specific growth rate depends on the availability of a limiting nutrient. Let's analyze the options: (a) Substrate concentration and product formation rate: While related (product formation is often linked to growth or substrate consumption), the Monod equation directly relates to growth rate. (b) Specific growth rate and substrate concentration: This is precisely what the Monod equation describes. (c) Biomass concentration and time: This describes the overall growth curve, not directly the Monod relationship for specific growth rate. (d) Product formation rate and biomass concentration: This relates to specific productivity, often modeled by Luedeking-Piret or similar equations, not the Monod equation. Therefore, the Monod equation describes the relationship between specific growth rate and substrate concentration. \[ \boxed{\text{Specific growth rate and substrate concentration}} \]