Colonic SCFA Uptake: 2D Diffusion-Reaction Profile

Colonic Conditions

Luminal pH 6.5

SCFA supply concentration 40 mM

MCT1 transporter density 10

Simulation speed 1.0×

Live Readouts

Protonated (HA)

–

Deprotonated (A⁻)

–

Passive flux

– mM/s

MCT1 flux

– mM/s

Transporter saturation

–

Total uptake

– mM/s

Legend

Protonated HA field — passive diffusion Deprotonated A⁻ field — needs MCT1 carrier Absorbed pool (epithelium → blood)

How it works

This is a 1D finite-difference reaction-diffusion model, not a particle scene: total SCFA concentration C(x,t) diffuses along a spatial axis x from the lumen toward the epithelial membrane, obeying the discretized diffusion equation ∂C/∂t = D·∂²C/∂x². At every point, the local pool splits instantaneously into protonated (HA) and deprotonated (A⁻) fractions via the Henderson–Hasselbalch equation:

pH = pKa + log10( [A⁻] / [HA] )
fraction protonated (HA)   = 1 / (1 + 10^(pH − pKa))
fraction deprotonated (A⁻) = 10^(pH − pKa) / (1 + 10^(pH − pKa))

Butyrate's pKa is about 4.8, well below the physiological colonic range (5.5–7.5), so most luminal SCFA is the charged anion A⁻. Only mass at the membrane node crosses, via two independent sink terms subtracted from the diffusing field and re-injected on the epithelial side (mass-conserving):

Passive flux = k·[HA at membrane] — linear in concentration, so this pathway never saturates.
MCT1 flux = Vmax·[A⁻ at membrane] / (Km + [A⁻ at membrane]) — Michaelis–Menten kinetics; Vmax scales with transporter density, so raising it lifts the ceiling of the ionized pathway but never touches the passive one.

The concentration-profile chart shows the diffusing HA/A⁻ fields as filled curves across the lumen, the membrane as a narrow band whose two flow bars show the instantaneous split between the two crossing routes, and the absorbed pool building up on the epithelial/blood side. The strip chart below plots both fluxes over time, so saturation of the MCT1 route becomes directly visible as the transporter-flux trace flattens while its bar keeps climbing.

Colonic lumen (diffusing field) Epithelial membrane (crossing) Epithelium → bloodstream

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Colonic SCFA Uptake: 2D Diffusion-Reaction Concentration Profile