DNA Nanorobot Lock Kinetics & Cargo Diffusion (2D)

Unlocking Trigger

Toehold length 6 nt

Trigger strand [T] 50 nM

Locks required (AND-gate) 2 / 4

Temperature 25 °C

Live Readout

Locks open

0 / 4

Reaction time

0.0 s

Cargo released

0.0%

Diffusion D

– µm²/s

How it works (2D model)

This 2D companion renders the same DNA-nanorobot chemistry as the 3D scene through two native 2D representations instead of a flattened camera view: a strand-displacement reaction-coordinate ladder diagram for the four AND-gated locks, and a real 2D finite-difference solution of the diffusion equation for the cargo concentration field, instead of animating discrete particles.

Each lock is a memoryless (pseudo-first-order) toehold-displacement process, exactly as in the 3D model:

P(lock still closed at t) = exp(−k_obs · t)
k_obs = k(b) · [T] · 2^((Temp−25)/10)
k(b) ≈ k_max · (1 − e^(−b/b0)) + k_leak

The dashed curve on the kinetics chart is this exact analytical survival curve, frozen at the k_obs in effect when the trigger was injected; the solid trace is the actual 4-lock stochastic realization, sampled every frame from the same Monte-Carlo test used in the 3D scene. The lid opens once N locks required are all displaced (AND-gate).

Once open, cargo doesn't just jitter as individual dots — it's modeled as a concentration field u(x,y) obeying the 2D diffusion (heat) equation, solved by explicit finite differences on a grid:

∂u/∂t = D·(∂²u/∂x² + ∂²u/∂y²)
u[i,j] += D·Δt·(u[i-1,j]+u[i+1,j]+u[i,j-1]+u[i,j+1]-4·u[i,j])
D = k_B·T / (6π·η·r)   (Stokes–Einstein, r ≈ 4 nm cargo radius)

The box wall is a reflective (zero-flux) boundary in the grid; once the AND-gate fires, the wall segment facing outward becomes transparent, and the field diffuses into the surrounding medium exactly as Fick's law predicts — total concentration is conserved throughout (nothing is created or destroyed, only redistributed). Raising temperature increases both k_obs and D, exactly as in the 3D model.

Closed lock Displaced lock Cargo concentration