(color online) Simulation of transition at constant loading rate and optimization method. (a) Force-dependent folding and unfolding rates (Eqs. 2 and 3) of DNA hairpin with parameters s⁻¹, pN, nm, and nm. (b) State time trace at loading rate of 0.01 pN/s. The force increases from 6 pN to 13 pN, then decreases to 6 pN. (c) Logarithm of probability converges to a maximal value in the optimization process with initial values of s⁻¹, pN, nm, and nm with optimized parameters shown in Fig. 5.