Identifying a piecewise affine signal from its nonlinear observation -- application to DNA replication analysis

DNA replication stands as one of the fundamental biological processes crucial for cellular functioning. Recent experimental developments enable the study of replication dynamics at the single-molecule level for complete genomes, facilitating a deeper understanding of its main parameters. In these new data, replication dynamics is reported by the incorporation of an exogenous chemical, whose intra-cellular concentration follows a nonlinear function. The analysis of replication traces thus gives rise to a nonlinear inverse problem, presenting a nonconvex optimization challenge. We demonstrate that under noiseless conditions, the replication dynamics can be uniquely identified by the proposed model. Computing a global solution to this optimization problem is specially challenging because of its multiple local minima. We present the DNA-inverse optimization method that is capable of finding this global solution even in the presence of noise. Comparative analysis against state-of-the-art optimization methods highlights the superior computational efficiency of our approach. DNA-inverse enables the automatic recovery of all configurations of the replication dynamics, which was not possible with previous methods.