Free-energy reconstruction from experiments performed under different biasing programs

Recently developed nonequilibrium statistical physics relationships, including Jarzynski’s equality and the Crooks fluctuation theorem, have been used to calculate equilibrium thermodynamic properties using data from both laboratory and computational experiments. Although Jarzynski’s derivation does not include an explicit time dependency, prior work utilizing the relationship to reconstruct free-energy surfaces has combined data from experiments performed under identical conditions. Here, a formalism is developed for combining data from a variety of biasing protocols, as in dynamic force spectroscopy experiments. The method is then demonstrated on data from simulations conducted under a wide range of pulling velocities and with a random biasing protocol.

Figure 1

(Color online) Average free-energy surfaces reconstructed from 200 trajectories loaded at $10\mathrm{pN}∕\mathrm{s}$, using mean work $⟨W⟩$, fluctuation-dissipation theorem $F_{FD}$, and Jarzynski equality $F_{JE}$ metrics. Standard deviations are indicated by error bars and the original potential $F_o$ by the thick dashed line.

Figure 2

(Color online) Smoothed force-extension profiles from trajectories at 20 evenly spaced velocities.

Figure 3

(Color online) Average free-energy surfaces reconstructed from ten blocks of trajectories loaded at 20 different velocities, annotated as in Fig. 1.

Figure 4

(Color online) Twenty representative bias program from random force loading simulations.

Figure 5

(Color online) Average free-energy surfaces reconstructed from 10 blocks of 20 trajectories simulated with random force loading rates, annotated as in Fig. 1.