Kinetic Proofreading — Hopfield Mechanism

Without proofreading, error rate = e^{−ΔΔG/kT}. Kinetic proofreading (Hopfield 1974) allows the system to discriminate beyond thermodynamic equilibrium by consuming ATP — error rate ∝ e^{−n·ΔΔG/kT} after n proofreading steps.

ΔΔG/kT 2.00 Proofreading steps n 2 ATP cost factor 3.0×

Error Rates

Michaelis-Menten:
ε₀ = ?
After proofreading:
ε_n = ?
Improvement: ?×

Energy Cost

Each proofreading step
consumes ~1 ATP (~25 kT)
Total cost: ? ATP
Speed penalty: ?×

Biological Context

tRNA selection (ribosome):
n≈2, ΔΔG≈3kT
ε_obs ≈ 10⁻⁴ to 10⁻⁵
DNA polymerase: n≈3