BactoBox®

Normalized Growth Rate (NGR) Calculator

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Disclaimer: Using the NGR calculator is entirely at your own risk!

Theory

In a batch process, exponential growth appears as a straight line on a semi-log plot because the specific growth rate (µ) is constant, meaning the relative increase in cell density per unit time remains the same.

In a fed-batch process, the absolute growth rate can vary over time depending on the feeding strategy. If the substrate supply does not scale proportionally with biomass, growth may become substrate-limited, leading to a gradual decline in the relative increase in cell density per unit time. Conversely, if feeding is adjusted dynamically to match growth demands, microbial proliferation can be sustained at a controlled rate.

The normalized growth rate is computed as a fractional change per unit time in the total number of cells. In the calculator, each data point includes a measurement of cell concentration (X) and fermentation volume (V). The total cell count (M) is calculated as:

  M = X × V

For any two consecutive measurements taken at times T₁ and T₂ with total counts M₁ and M₂ respectively, the normalized growth rate (µ) is given by:

  µ = (M₂ − M₁) / (M₁ × (T₂ − T₁))

Tracking the normalized growth rate (NGR), which accounts for both fermentation volume and total cell density, can serve as an early warning system for process stability:

• Stable NGR → Consistent Growth
  • Indicates that the microbial culture is in a steady state, with balanced substrate uptake and biomass production.
    
  • Often observed in well-controlled fed-batch processes, where feeding is adjusted to maintain a set growth rate.
    
• Decreasing NGR → Slower Growth or Stress Response
  • May indicate substrate limitation, accumulation of inhibitory byproducts, or oxygen depletion.
  • If intentional (e.g., controlled substrate feeding to regulate productivity), it reflects a planned transition to a lower specific growth rate.
    
  • If unintended, it suggests that a limiting factor (nutrients, pH, dissolved oxygen) is restricting microbial proliferation.
    
• Increasing NGR → Accelerated Growth or System Instability
  • A controlled increase (e.g., adjusting feed rates in response to metabolic demand) can be intentional.
    
  • A sharp, unexpected rise might suggest overfeeding, metabolic shifts, or microbial contamination.
    
• Sudden Drop in NGR → Major Process Disruption
  • Likely causes: Oxygen limitation, metabolic arrest, toxic byproducts, culture contamination, or equipment failure.
  • Requires immediate investigation to identify and address the root cause.

Normalized Growth Rate (NGR) Calculator

Use this calculator to easily investigate your NGR for your fed-batch process. Make sure all inputs are in the correct units as specified.

Please note that the use of the NGR calculator is at your own risk. If you notice any unexpected behavior, let us know!

Enter up to 8 data points below. You do not need to fill in all columns, but at least two data points are required.

Concentrations can be entered in scientific notation (e.g., 5e6). Example data points are shown in grey text if you want to explore how the calculator processes data.