Connecting cell metabolism to feeding decisions

BIOMEDANA WORKED EXAMPLE

Feed decisions: fixed addition versus model-based feedback

A reduced reactor example compares fixed glucose addition with a controller that chooses an addition rate using a one-day prediction, then repeats the decision at the next day.

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

Model structure

State: z = [X, G, P]
Candidate glucose addition: u ∈ {0, 0.5, …, 6} g/L/day
Forecast: z(t + 1) = integrate[z(t), u]
Choose u to minimize [G(t + 1) − 3]² + 0.02u²
Apply for one day; observe model state; repeat

Parameters and initial conditions

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

Interpret the example

The controller optimizes glucose tracking with a feed penalty, not product titer directly. Compare both glucose trajectory and cumulative glucose addition before judging the scenario's product output.

Assumptions and limits

The controller observes the simulated state perfectly. It has no metabolic flux network, sensor noise, actuator dynamics or qualified control system. This is a reduced teaching example, not the paper's multiscale MPC implementation.

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.

// Recompute the feed decision at each daily control interval.
for (let feed = 0; feed <= 6; feed += 0.5) {
  const next = advance(state, temperature, feed, 1, 0.02);
  const cost = (next[1] - 3) ** 2 + 0.02 * feed ** 2;
  // Keep the feed with the lowest forecast cost.
}
// Apply chosen feed for one day, then repeat.