Efficient Two-Dimensional Control of Barrier Crossing

Modern advances in single-molecule biophysics make possible the precise spatial and temporal control of biological systems. Despite the relative freedom of control, experiments and simulations rarely exploit the possibility of optimized control protocols, and the ones that do are generally limited to optimization of a single control parameter. We design minimum-dissipation protocols for harmonic trapping potentials under two-dimensional control (of both trap center and stiffness), for driven barrier crossing. This greater control allows specification of both the time-dependent mean and variance of the position distribution, and results in qualitatively distinct designed protocols. For any duration, the designed protocols significantly improve performance in terms of both dissipation and flux compared to naive and one-dimensional control.