The Digital Twin: Predicting Growth with Droop and Steele

MAIN never runs a blind experiment on a living culture. Before any action reaches the hardware, it is simulated in a digital twin — a compact set of equations that predict how the culture will respond, resting on two classical pieces of phytoplankton ecology plus environmental modifiers.

The first is Droop’s cell-quota model: growth depends not on how much nutrient is dissolved in the water but on how much a cell has already stored internally — its quota Q. Growth follows µ = µmax·(1 − Q0/Q). This decouples uptake from growth, so a culture can bank nitrogen and keep dividing after external nutrient runs low — exactly what makes real cultures resilient. The second is Steele’s light function, which captures that photosynthesis is not monotonic in light: growth rises to an optimum, then falls as excess light inhibits the machinery.

Crucially, the twin does not use the lamp’s brightness directly. It passes light through a Beer–Lambert attenuation term — light decays exponentially with depth as the culture absorbs it — so a dense culture shades its own interior. On top of these, bell-shaped response curves for temperature and pH and a dissolved-oxygen inhibition term multiply into an effective growth rate. The result is a forward simulation: given the current state and a proposed setpoint, the twin returns a biomass trajectory, letting MAIN answer “what happens if I raise the light?” numerically instead of guessing.