Dietary fiber cannot be broken down by human enzymes, so it is fermented by gut bacteria. This is a two-step syntrophic cross-feeding chain: primary fermenters degrade fiber into lactate and acetate, and a distinct group of cross-feeding bacteria (many butyrate producers, e.g. Faecalibacterium, Roseburia) cannot use fiber directly but consume those intermediates to make butyrate — the metabolite the colon epithelium prefers as fuel. Neither species could reach this yield alone; it is genuine metabolic crosstalk.
Each population and pool follows Monod (Michaelis–Menten-form) kinetics, integrated every frame with a clamped time step:
dS/dt = supply − k₁·A·S/(Ks+S)
dA/dt = μ₁·A·S/(Ks+S) − dA·A
dM/dt = y₁·k₁·A·S/(Ks+S) − k₂·B·M/(Km+M) − decay·M
dB/dt = μ₂·B·M/(Km+M) − dB·B
dP/dt = y₂·k₂·B·M/(Km+M) − absorption·P
pH ≈ 7.2 − s·(M + P)
- Fiber supply — how much fermentable substrate S enters the reactor per unit time.
- Primary fermenter growth (μ₁) — how fast species A grows on fiber and produces the lactate/acetate pool M (the amber spheres and yellow-green flow).
- Cross-feeder efficiency (μ₂, y₂) — how effectively species B (teal) turns M into butyrate P (pink flow to the wall).
- Epithelial absorption — how fast the colon wall clears butyrate; colonocytes use it as their preferred energy source, which is why low absorption lets P — and therefore acidity — build up in the lumen.
More SCFA in the lumen drives pH down (acidification), which in turn suppresses pH-sensitive pathobionts — a real, measured mechanism by which cross-feeding shapes the whole community, not just the two species directly exchanging metabolites.