Reconstruction of complex bond potentials from multiple rupturing time distributions

We explore the numerical reconstruction of the potential energy profile of a molecular bond from distributions of bond rupture times. For a single measured first passage time (FPT) distribution the inverse problem is highly ill-conditioned and only a few attributes (such as the height and width of an energy barrier) can usually be reconstructed. Upon more careful analysis, we find optimal temperatures (described by the effective diffusivity of the stochastic process) and initial bond configurations that yield the most efficient numerical reconstruction of simple potentials. Moreover, we show that reconstruction of more complex potentials containing multiple minima can be achieved by simultaneously using two or more measured FPT distributions, obtained under different physical conditions. For example, by changing the effective potential energy surface by known amounts, the additional FPT distributions render the inverse problem less ill-posed. We demonstrate the feasibility of reconstructing potentials with multiple minima, motivate heuristic rules-of-thumb for optimizing the reconstruction, and discuss further applications and extensions.