Extracting dynamical laws from targeted biological processes

Time dependent biological processes progressing towards irreversible target points, such as the dynamics of cytokinetic ring constriction, can often be characterized with one or a small set of phenomenological relevant dynamical variables. While the onset of these dynamics is typically affected by strong uncertainties, e.g., due to overlapping consecutive dynamical laws, we expect the dynamics close to completion to show its purest and most informative form. This observation motivates to align measured sample paths of such a stochastic dynamic to their irreversible target point. The resulting set of aligned sample paths can then be treated as a realization of an ensemble evolving in reverse time. Interestingly, this seemingly harmless data analysis operation of terminal alignment creates an ensemble which can not be analyzed with conventional notions of stochastic differential equations. We expose the origin of this problem and derive a general formalism which allows to recover a phenomenological description of the forward process based on the analysis of the time reversed and terminal aligned ensemble. We demonstrate the applicability of this approach on mock data of cytokinetic ring constriction.