Antibody-Drug Conjugate 2D: Reaction-Diffusion Bystander Model

Linker Chemistry

Antigen density (target cells) 70%

Drug-antibody ratio (DAR) 4

Payload diffusion radius 1.3 cell-widths

Live Readouts

Free ADC (extracellular)

Internalized

Antigen⁺ killed

0 / 0

Bystander killed

0 / 0

Sim time

0.0 h

Payload field peak

0.00

How it works

This is the 2D counterpart to the 3D ADC pharmacology model — not a flattened version of it. Free ADC molecules here undergo genuine isotropic 2D Brownian diffusion, ⟨r²⟩ = 4·D·t, instead of the 3D version's gravity-settling particles. Binding an antigen-positive cell still follows first-order kinetics per contact:

P(bind) = 1 − exp(−k·θ·Δt)

The real difference is how released payload spreads. Instead of an instant analytic sum over cell pairs, cleaved payload is injected as a point source into a continuous concentration field C(x,y,t) and evolved every frame by explicitly solving the 2D reaction-diffusion PDE with finite differences:

∂C/∂t = D·∇²C − C/τ
D = R_diff² / τ   (so the steady screened-diffusion
                    decay length equals the slider's R_diff)

The steady-state solution of this equation around a continuous point source is the modified Bessel function K₀(r/R_diff), which falls off almost exactly like exp(−r/R_diff) once r is a few R_diff — the same screening profile the 3D model assumes analytically, but here it emerges from actually solving the diffusion equation rather than assuming its answer. Cells accumulate cytotoxic exposure by locally sampling this field each frame (dL/dt = k·C), and die once the integral crosses a fixed threshold.

Cleavable linker — released payload is small and membrane-permeable, so it is injected into the diffusing field and can reach and kill antigen-negative bystander cells within roughly one R_diff of a cleaving cell.
Non-cleavable linker — the cytotoxic adduct cannot cross membranes, so it accumulates directly inside the internalizing cell only; the diffusion field is never touched.

Toggle the linker, and watch the purple field (visualised directly from the PDE's own concentration grid) spread — or fail to spread — from each cleaving cell exactly as the equation dictates.

Antigen⁺ tumor cell Antigen⁻ bystander cell Free ADC (Brownian) Diffusion field C(x,y) Dead cell