The Price of Being Right: Energy per Correct Bit in Ribosomal Proofreading

The ribosome incorporates amino acids at an error rate near 1e-4 per residue, although equilibrium codon-anticodon discrimination alone gives near 1e-2. Kinetic proofreading buys the difference with GTP hydrolysis. From published inputs at 310 K (cellular GTP hydrolysis 50 kJ/mol, one proofreading step, 4 high-energy phosphate equivalents per elongation cycle), the proofreading step adds 8.3027e-20 J per amino acid on a total cycle cost of 3.3211e-19 J. One Hopfield step predicts the observed error exactly: (1e-2)^2 = 1e-4. The gain is 6.644 bits of error exponent but only 0.1214 Shannon bits per residue. Total energy per correct bit is 7.6876e-20 J, 25.91 times kT ln2 at 310 K; extra energy per exponent bit is 1.2497e-20 J (4.21 Landauer units) and per Shannon bit gained 6.8406e-19 J (230.58 units). A silicon DRAM access at 2.0e-11 J per bit costs 2.60e8 times more per bit. The trade-off is linear in the logarithm of the error improvement: half a GTP per decade at the stated discrimination. Model calculations are labelled SIMULATED, NOT MEASURED. Deposit includes paper PDF, computation script and outputs.