Specific Growth Rate (μ) - Substrate Inhibition

Maximum theoretical growth rate under ideal conditions. Units: inverse hours (h⁻¹).
Substrate concentration at which μ = μmax / 2 (in the absence of inhibition). Units: g/L (or consistent concentration units).
Current concentration of the limiting substrate. Units: g/L (must match Ks units).
Constant characterizing the strength of substrate inhibition. Units: g/L (must match S and Ks units).

Calculation Explanation

This calculator estimates the specific growth rate (μ) using the Monod model modified to account for substrate inhibition. High concentrations of some substrates can inhibit growth.

Formula:
μ = (μmax ⋅ S) / (Ks + S + (S² / Ki))

Where:

Ensure consistent units for S, Ks, and Ki.
The model assumes substrate concentration (S) is the primary limiting factor, modified by inhibition at high S.

Reference: Typical Ks Values

Microorganism Substrate Ks (mg/L)
Aerobacter aerogenesGlucose0.26
Aerobacter aerogenesGlycerol4.1
Aspergillus nigerGlucose5.0
Aspergillus nigerSucrose0.16
Azotobacter vinelandiiGlucose4.0
Candida utilisEthanol0.0013
Escherichia coliGlucose0.02
Escherichia coliLactose0.2
Lactobacillus caseiLactose1.2
Penicillium chrysogenumGlucose0.04
Penicillium chrysogenumLactose0.02
Pseudomonas sp.Methanol0.7
Saccharomyces cerevisiaeGlucose25
Saccharomyces cerevisiaeEthanol0.05-0.1
Source: Adapted from various biochemical engineering texts.