Clara Lage

An important challenge in DNA replication analysis is to recover a so-called timing profile, that contains important information about the replication dynamics, from nonlinear observations. We show that this can be expressed as a nonlinear inverse problem where the unknown timing profile can be assumed to be piecewise affine. As this problem cannot be directly addressed with techniques for linear inverse problems, we propose a novel formalism and computational approach to harness it. In the noiseless case, we establish sufficient identifiability conditions for the timing profile, and prove that it is the solution of a non-convex optimization problem. These problems are specially challenging because of their multiple local minima. We propose the DNA-Inverse optimization method that is capable of finding their global solution in the noiseless case and proved to be effective in numerical experiments for noisy signals. Comparative analysis against state-of-the-art optimization methods highlights the superior computational efficiency of our approach. The method enables the automatic recovery of all configurations of the replication dynamics, crucial for DNA replication analysis, which was not possible with previous methods.