Two Point Monod Parameters

Solve the exact two-point Monod model for mu-max and Ks, rejecting observations that imply nonpositive saturation parameters.

Description

The Monod model describes a saturating relationship between substrate concentration and specific growth rate.

The Monod model describes a saturating relationship between substrate concentration and specific growth rate. Two observations can determine its two parameters exactly when their relationship implies positive saturation parameters.^[1]

Solve the exact two-point Monod model for mu-max and Ks, rejecting observations that imply nonpositive saturation parameters.

When to use Two Point Monod Parameters

Use this tool to solve the exact two-point Monod model for mu-max and Ks, rejecting observations that imply nonpositive saturation parameters.

Prepare the sample, count, growth or assay measurements requested by this tool. Confirm units, sampling periods and reporting bases; supply independently established comparison criteria where requested.

How to use Two Point Monod Parameters and understand its results

Prepare the sample, count, growth or assay measurements requested by this tool. Confirm units, sampling periods and reporting bases; supply independently established comparison criteria where requested.
Enter substrateConcentrations, specificGrowthRates using the field table and calculation rules, then run the tool.
Read maximumGrowthRatePerHour, halfSaturationConcentration. The explanation below defines the units, signs, ordering and any flags or placeholder values.
If the tool reports an input issue, correct the values and run it again. Apply the stated assumptions when interpreting a successfully returned result.

Input field	Meaning	Value type; see rules below	Requirement
substrateConcentrations	Substrate concentrations	list of number	Required
specificGrowthRates	Specific growth rates	list of number	Required

Enter exactly two positive substrate concentrations in increasing order and their two positive growth rates per hour. The denominator and solved Ks must be positive. The tool returns μmax per hour and half-saturation concentration in the substrate unit, rejecting incompatible observations.

Sequences checked for increasing order must be nonempty and strictly increasing; additional calculation rules may require more samples.

Ks = S1 S2(μ2−μ1)/(μ1 S2−μ2 S1); μmax = μ1(Ks+S1)/S1

Units, indexing, boundary conditions and exceptional cases are defined in the calculation rules above.

Output field	Meaning	Value type
maximumGrowthRatePerHour	Maximum growth rate per hour	number
halfSaturationConcentration	Half saturation concentration	number

json

{
  "input": {
    "substrateConcentrations": [
      1,
      3
    ],
    "specificGrowthRates": [
      0.2,
      0.3
    ]
  },
  "output": {
    "maximumGrowthRatePerHour": 0.3999999999999999,
    "halfSaturationConcentration": 0.9999999999999994
  }
}

Limitations and assumptions

This is an exact two-point solution rather than a regression with uncertainty or a goodness-of-fit test. Extra observations, noisy data and inhibition need a different model.

Numeric inputs must be finite. Follow the calculation-specific rules for overflow, underflow and exceptional cases. Lists are limited to 100,000 entries; the rules above may require smaller limits. Missing required fields, extra fields, wrong value types and violations of the calculation rules are input errors.

Alternative or Complementary methods

Use Feed Limited Chemostat Washout: Screen the feed-limited Monod chemostat washout boundary from flow, volume, and feed substrate; equality is the zero-biomass boundary. For a complementary task, use Chemostat Residual Substrate: Solve the non-washout Monod chemostat branch and check whether the feed can sustain its residual substrate concentration.

References

Two Point Monod Parameters — tool.io

Similar or alternative tools

Feed Limited Chemostat Washout
Screen the feed-limited Monod chemostat washout boundary from flow, volume, and feed substrate; equality is the zero-biomass boundary.
Chemostat Residual Substrate
Solve the non-washout Monod chemostat branch and check whether the feed can sustain its residual substrate concentration.