Fluctuation Theorems for Entropy Production in Molecular Motors

Povzetek

Molecular motors such as kinesin convert chemical free energy from ATP hydrolysis into mechanical work while
operating at length and energy scales where thermal fluctuations are comparable to the useful work extracted per
step, making individual trajectories stochastic and occasionally entropy-consuming even though the ensemble
average dissipates entropy. We tested the Crooks fluctuation theorem and the integral form of the Jarzynski
equality using single-molecule optical-trap trajectories from a stochastic model of kinesin stepping calibrated
against published stall-force and stepping-rate data, generating 22,000 forward and 22,000 reverse trajectories
across six applied load forces from 0 to 7 pN. Entropy production per step, computed from the log-ratio of forward
and reverse path probabilities, averaged 4.1 k_B at zero load and declined to 0.9 k_B near the stall force of 7.2 pN,
and the distribution of single-trajectory entropy production was negative (entropy-consuming) in 3.8% of steps at
zero load, rising to 21.4% of steps near stall force, consistent with the fluctuation theorem's prediction that
negative-entropy-production events become proportionally more frequent as the mean dissipation rate falls. The
Crooks relation P_F(+Sigma)/P_R(-Sigma) = exp(Sigma/k_B) held across the full range of applied loads with the
fitted slope of ln[P_F/P_R] versus Sigma equal to 1.00 +/- 0.03 (R^2 = 0.991, n = 6 load conditions), and the
Jarzynski equality reconstructed the equilibrium free-energy change of a single stepping cycle to within 4% of the
input model value using as few as 500 trajectories, though estimator variance grew sharply below 200 trajectories.
A bootstrap analysis (2,000 resamples per condition) showed that the fitted Crooks slope remained within its 95%
confidence interval of unity at every load tested, and a sensitivity analysis varying the assumed internal load-sharing
parameter by +/-20% shifted the fitted slope by less than 0.04, indicating the result is not an artifact of a specific
mechanochemical parameterization. These findings provide a quantitative, trajectory-resolved validation of
fluctuation-theorem predictions for a biological molecular motor operating near its stall force and establish practical
sample-size guidance for extracting reliable free-energy estimates from single-molecule stepping data using
nonequilibrium work relations.