CHO fed-batch feed strategies

A small, self-contained simulation of a fed-batch CHO (mammalian) cell culture, built to answer three questions clearly:

1. What are the feed strategies, and how do they differ? → model.py + compare.py
2. How do you optimize each one? → optimize.py
3. How do you select between them? → the ranked table from compare.py

The model is the usual mass balance + Monod kinetics for [Xv, Glc, Lac, P, V] (viable cells, glucose, lactate, titer, volume). Parameters are illustrative, not literature-calibrated — the point is the shape of each strategy, not exact numbers.

The one idea that matters

A feed law like if Glc < 5: pump on else off is discontinuous. Feed that straight into an adaptive ODE solver and the answer drifts with the solver tolerance — it is numerically ill-posed. Every strategy here is instead integrated so the right-hand side is smooth over each segment:

• clock-based feeds (bolus) are integrated between their known switch times;
• state-based feeds (the relay controller) are integrated up to the exact switch time, located by a root-finder, then restarted with the pump flipped.

That is the whole reason model.py exists and simple_cho_fedbatch.py (the naive starting point) does not.

The five strategies

strategy	feed law	knob
batch	no feed — starves and crashes (baseline)	—
constant	fixed slow trickle	F_const
bolus	one shot of feed per day	F_bolus
hysteresis	relay: feed below a setpoint, stop above	glc_on
smooth	the relay with a soft (tanh) switch	glc_on

Results

Comparison at default parameters (compare.py). Batch starves once glucose runs out; every feed strategy keeps glucose up so cells survive and titer keeps climbing.

strategy	titer (mg/L)	peak VCD	final lactate (mM)	pump switches
bolus	1412.5	24.8	312.9	28
smooth	1213.4	25.1	307.8	0
hysteresis	1211.1	25.0	307.1	456
constant	957.3	12.8	181.0	0
batch	342.6	4.6	42.0	0

Selection is not just "highest titer": hysteresis and smooth reach nearly the same titer, but smooth does it with zero pump chatter while the relay switches hundreds of times — so smooth is the better real-world choice at a similar result.

Optimizing each strategy (optimize.py). Sweep each strategy's one knob: too little feed starves, too much dilutes the product, and the peak in between is the optimum.

strategy	knob	best value	best titer (mg/L)
constant	F_const	0.0024	1406.8
bolus	F_bolus	0.0586	1432.1
hysteresis	glc_on	18.0	1241.5

Files

model.py                # the model + 5 strategies + metrics (import this)
compare.py              # run all strategies -> ranked table + overlay plot
optimize.py             # scan each strategy's knob -> best setting per strategy
simple_cho_fedbatch.py  # the naive Day-1 starting point (batch only)
results/                # generated figures and CSVs

Run it

pip install -r requirements.txt
python compare.py     # differences + selection
python optimize.py    # per-strategy tuning

Everything writes into results/.