Title Go-and-Back method: effective estimation of the hidden motion of proteins from single-molecule time

We present an effective method for estimating the motion of proteins from the motion of attached probe particles in single-molecule experiments. The framework naturally incorporates Langevin dynamics to compute the most probable trajectory of the protein. By using a perturbation expansion technique, we achieve computational costs more than 3 orders of magnitude smaller than the conventional gradient descent method without loss of simplicity in the computation algorithm. We present illustrative applications of the method using simple models of single-molecule experiments and confirm that the proposed method yields reasonable and stable estimates of the hidden motion in a highly efficient manner.