Nonequilibrium Work Relations in Single-Molecule Pulling Experiments

Povzetek

The Jarzynski equality and the Crooks fluctuation theorem allow equilibrium free-energy differences to be recovered
from an ensemble of nonequilibrium single-molecule pulling trajectories, but the accuracy of the recovered free
energy depends strongly on pulling speed, trajectory number, and the resulting width of the work distribution, a
dependence not always characterized quantitatively for a given molecular construct. We report dual-beam
optical-tweezer pulling experiments on a DNA hairpin construct (20-base-pair stem, 4-nucleotide loop), collecting
1,050 unfolding and 1,050 refolding trajectories across four pulling speeds from 20 to 800 nm/s. Work distributions
broadened and their means shifted upward with pulling speed, from a mean unfolding work of 68.4 ± 1.2 kT at 20
nm/s to 94.7 ± 2.8 kT at 800 nm/s (mean ± SEM, n = 250-300 per speed), while Jarzynski-equality free-energy
estimates computed from unfolding trajectories alone overestimated the equilibrium value obtained by
Crooks-theorem bidirectional analysis at the slowest speed (65.1 ± 1.4 kT vs. 63.8 ± 0.6 kT, a 2.0% bias) and this
bias grew to 12.4% at the fastest speed tested. Crooks-theorem estimates combining unfolding and refolding work
distributions recovered a free-energy difference of 63.8 ± 0.6 kT, essentially pulling-speed independent (range
63.5-64.1 kT across all four speeds, one-way ANOVA p = 0.41), and agreeing with the nearest-neighbor
thermodynamic prediction for this hairpin sequence (64.5 kT) to within 1.1%. Bootstrap resampling (2,000 replicates
per condition) showed that Jarzynski-estimator variance decreased with trajectory number approximately as
N^-0.85, slower than the N^-1 scaling expected for well-behaved estimators, reflecting the known sensitivity of the
exponential average to rare, low-work trajectories; convergence to within 2 kT of the asymptotic estimate required at
least 480 trajectories at the fastest pulling speed but only 140 at the slowest. These results provide a quantitative
benchmark for the trajectory numbers and pulling-speed ranges needed to recover accurate free energies from
single-molecule pulling experiments and reinforce the practical advantage of bidirectional Crooks-theorem analysis
over unidirectional Jarzynski averaging when fast pulling is experimentally necessary.