Rate exponentially sensitive to toehold length — DNA computing foundation
Toehold-mediated strand displacement (Zhang & Winfree 2009): An invader strand binds to an exposed toehold domain (τ nt), then displaces the incumbent strand via branch migration. The second-order rate constant k₂ increases exponentially with toehold length:
k₂(τ) ≈ k₀ · exp(α·τ) where α ≈ 0.1–0.2 per nt per ΔG contribution.
Enables cascaded DNA circuits (AND/OR gates, amplifiers) without enzymes, operating at ~nM concentrations.