One shared extracellular pool exchanges with separate producer and receiver membrane and intracellular pools. Cells are stationary. A producer patch occupies the first 1 mm by default; nonproducing receivers occupy the chamber.
Mass balance
Jej = ke(K φmj C − Mj)
Jij = ki φij[Mj/(K φmj) − Cij]
Xj = kx Ij
∂E/∂t = ∂x(D φe ∂x C) − ΣJej + ΣXj − deE
∂Mj/∂t = Jej − Jij
∂Ij/∂t = Jij − Xj + Sj − diIj
E, M and I are amounts per total chamber volume. C = E/φe is extracellular nM; Cij = Ij/φij is intracellular nM. The membrane profile displays combined membrane amount per bulk volume. j denotes producing or receiving cells. Efflux redistributes signal; it does not destroy it.
Source and response
Production enters producer cytosol: S = q ρp g(t)(1 + βyp) / (6.02214076 × 10¹¹), in nM per bulk volume per hour. q is molecules per producer per hour; g is one until synthesis stops, then zero. Receivers do not produce AHL.
H = Ciⁿ / (KRⁿ + Ciⁿ)
dy/dt = (H − y)/τ
H is a phenomenological receptor activity under a nondepleting approximation. y is an abstract output. Feedback is optional and does not establish bistability. All signal pools and responses initially equal zero.
Membrane types
There is no calibrated Gram-positive or Gram-negative coefficient. An effective membrane compartment cannot resolve an outer membrane and periplasm, and peptidoglycan is not extra lipid volume. Peptide QS systems need different transport and sensing models.
Communities and reach
Receivers fill the chamber from “Receiver community starts at” to its right end. Zero places them throughout; a larger value leaves a cell-free gap between the producers and a receiver community. Inside a community, signal held in membranes and cytosol does not diffuse, so spreading slows by R = 1 + (K φm + φi)/φe when exchange is fast and nothing is exported. The effective diffusivity there is D/R. The study “Across a community” uses 10¹¹ receivers/mL, about a tenth of the volume, and lets only D and K follow chain length along the illustrative trend. Matrix binding, flow, growth, and uneven density are not included.
Two reference signals
The study “C4 and 3-oxo-C12” and the Reference signal control use one value per property for C4-HSL and 3-oxo-C12-HSL, the two Pseudomonas aeruginosa signals. Every other setting stays as entered.
| Property | C4-HSL | 3-oxo-C12-HSL | Basis |
|---|
| Diffusivity D | 2.37 mm²/h | 1.2 mm²/h | 3-oxo-C12 measured in agar (Tica et al. 2024). C4 is extrapolated from the two anchors. |
| Membrane affinity K | 12 | 7950 | K = exp(−ΔG/RT) from simulated free energies of −6.36 and −23.16 kJ/mol in a DOPC bilayer at 310 K (Jin et al. 2021). This is the depth of the free-energy minimum, not a measured partition coefficient. |
| Liquid ↔ membrane | 3300 h⁻¹ | 5 h⁻¹ | Assumption: both signals adsorb to membranes at the same rate, so release is slower in proportion to affinity. Cells then fill within about a minute for C4-HSL and within minutes for 3-oxo-C12-HSL, as in Pearson et al. 1999 (under 30 s and about 5 min). |
| Membrane ↔ cytosol | 127 h⁻¹ | 10 h⁻¹ | Ratio from the simulated translocation barriers, 28.63 and 35.18 kJ/mol (Jin et al. 2021). The absolute value is an assumption. |
| Active export | 0 | 10 h⁻¹ | Pearson et al. 1999 show efflux of 3-oxo-C12-HSL by MexAB-OprM and free diffusion of C4-HSL. The rate is an assumption. |
| Extracellular loss | 0.10 h⁻¹ | 0.03 h⁻¹ | From more than 90% and about 50% lost over 24 h in a P. aeruginosa culture at 37 °C as the pH rose to 8.5 (Yates et al. 2002). Lactone ring opening depends strongly on pH and temperature. |
“Cells : medium” is receiver-associated signal per cell volume divided by the extracellular concentration at the probe. Pearson et al. measured about 1 for C4-HSL and about 3 for 3-oxo-C12-HSL. With K = 7950 the model gives a far larger ratio for 3-oxo-C12-HSL: the simulated affinity, or the assumed membrane volume, probably overstates association with live cells. Synthase output and receptor recognition also differ between real signals and are not varied here. 3-oxo-C12-HSL aggregates above roughly 80 µM (Gahan et al. 2020); the model has no aggregated pool and stays far below that range.
Evidence and assumptions
Tica et al. 2024 provide the C6/C12 agar diffusion anchors. Other D values use a two-anchor estimate. K(C6) = 100 and K(C12) = 5000 are illustrative assumptions throughout.
Jin et al. 2021 motivate separating affinity from translocation. Pearson et al. 1999 demonstrate signal-specific transport and efflux in one organism. These studies do not calibrate the current production, membrane, entry, export, or receptor parameters.
No growth, flow, substrate limitation, receptor depletion, matrix binding, aggregation, or explicit chemical interconversion. Chemical losses are first-order. The model has five physical pools and a degradation ledger. Conservative diffusion and a local matrix exponential preserve amount and positivity.
“Not reached” means no 50% response crossing in the selected observation window. Inspect the chemical curve before interpreting output persistence. Parameter sweeps are sensitivity scenarios, not statistical confidence intervals.