Quorum Sensing: Spatial Autoinducer Diffusion Front (2D)

Population & Field

Cell density 220 cells

Diffusion coefficient D 0.60

Dilution / flushing rate δ 0.35

Receptor threshold K 1.00

Induced feedback gain 12×

Autoinducer Field

mean [AI] = 0K

Mean [AI]

0.00

Cells ON (quorate)

Field spread (max−min)

0.00

Time since >50% ON

not yet

How it works (2D model)

The 3D companion simulator treats the autoinducer as instantly and perfectly mixed — one shared number for the whole chamber. Real signal molecules don't teleport: they diffuse outward from each secreting cell through the medium. This 2D version solves that honestly as a genuine reaction-diffusion PDE on a spatial grid:

∂A/∂t = D·∇²A + S(x,y) − δ·A

S(x,y) = Σ_cells (p0 if OFF, p1 if ON) · splat(x−x_i, y−y_i)
D = diffusion coefficient,  δ = dilution / degradation rate

Each cell reads only the local concentration under itself — not the domain average — and switches ON with the same cooperative Hill-type probability as the well-mixed model:

P(ON | A_local) = A_local^n / (A_local^n + K^n),   n ≈ 3

This produces genuinely different behaviour a well-mixed model cannot show: a tight, dense pocket of cells can locally exceed K and ignite a self-reinforcing patch — visible as a bright core on the heatmap — even while the field's domain-wide average is still below threshold. If diffusion is fast enough (large D) and cells are close enough, that patch expands as a spreading activation front until the whole population is quorate; if diffusion is slow or δ washes the signal away faster than it can accumulate locally, isolated pockets can stay permanently dark even at cell densities that would trigger the well-mixed 3D model. In the fast-diffusion limit this 2D model's steady state converges back to the same well-mixed balance the 3D sim computes — diffusion homogenizes the field once D is large enough relative to the domain size.

Cell density — more cells packed into the same area raise local secretion density, the classic quorum trigger, but now unevenly across space.
Diffusion coefficient D — how fast the signal spreads from each secreting cell; low D keeps quorum sensing hyper-local (small clusters ignite independently), high D approaches the well-mixed limit.
Dilution / flushing rate δ — an open system (flowing medium) washing the signal away vs. a closed one letting it accumulate.
Receptor threshold K — how much local autoinducer the LuxR-type receptor needs to bind before triggering transcription.
Induced feedback gain — how much harder an ON cell secretes than an OFF cell (p1/p0), setting how sharp and self-reinforcing the local ignition is.

OFF cell (basal secretion) ON cell (quorum-activated) Low [AI] field High [AI] field