Adapting a bioprocess model to a new strain

BIOMEDANA WORKED EXAMPLE

Model adaptation: fit on early observations, check later ones

A simplified demonstration of parameter reuse and adaptation. A source growth curve is adapted to deterministic synthetic target observations; later observations are held out of fitting.

Calculated live in your browser from the equations below. These are BioMedAna illustrative outputs, not experimental observations or published study results.

Model structure

X(t; r) = 12 / [1 + 23 · exp(−rt)]
Source rate: r = 0.50 day⁻¹
Synthetic target: X(t; 0.72) · [1 + 0.025 sin(1.7t)]
Adapted rate: argminᵣ Σtraining [X(t; r) − Xobserved(t)]²
Held-out RMSE = √mean[(Xpredicted − Xobserved)²]

Parameters and initial conditions

All values below are assumptions for this worked example, not parameters attributed to the paper.

Interpret the example

The adapted model is evaluated against observations excluded from fitting. Its smaller error in this constructed example illustrates why adaptation should be checked separately from calibration.

Assumptions and limits

The target is generated from the same model family, making this an easy adaptation task. This is a one-parameter educational example, not the paper's microalgal hybrid-transfer architecture, experimental dataset or uncertainty analysis.

The culture examples use fourth-order Runge–Kutta integration with 0.02-day steps and non-negative state bounds. They simulate glucose addition at constant volume. No uncertainty band is shown because this example has no validated error model.

// Synthetic observations are generated independently of the fitted rate.
// Only the first n days enter the fitting objective.
for (let rate = 0.3; rate <= 1.0; rate += 0.001) {
  const error = training.reduce((sum, row) =>
    sum + (logistic(row.day, rate) - row.observed) ** 2, 0);
  // Keep the candidate with minimum training error.
}
// Evaluate source and adapted models on the remaining days.