FIG. 3.

Molecular free energy profile from committor inversion. (a) Full two-dimensional committor $\varphi \left(q,x\right)$ for the free energy surface G(q, x) and D_q/D_x = 1. Isolines of the free energy surface are shown as black solid lines separated by 1 k_BT. Isolines of the committor are shown as red solid lines. (b) The observed committor ϕ(q) is obtained in two independent ways: from a numerical solution of Onsager’s equation (exact, red solid line) and from Brownian dynamics trajectories (blue diamonds). The analytic prediction from Eq. (9) is shown as a dark red dashed line. (c) The free energy barrier extracted by committor inversion, G_CI(q), from the exact and trajectory-estimated committor (red solid line and blue diamonds, respectively). Both barriers are compared to the hidden molecular profile G_o (gray solid line), to the analytic prediction from Eq. (11) (dark red dashed line), and to the Boltzmann-inverted free energy profile G(q) (orange solid line). The free energy surface G(q, x) has parameters similar to those obtained for the 20TS06/T4 DNA hairpin,¹⁹ $\mathrm{\Delta }{G}_0^{‡}=8.1k_{\mathrm{B}}T$, Δx^‡ = 1.5 [x], and κ_l = 2.6 k_BT/[q]², where [q] = [x] denotes units of length for the extension.