A computational approach that estimates the probability density of the initial conditions for a population of dynamical systems is presented. Its scope extends to a family of problems which includes the described protein degradation example. It permits the formulation of hypotheses that can justify the discrepancy between single-cell and population dynamics. The approach is based on a preprocessing regression that permits the incorporation of domain knowledge. This knowledge is given under the form of prior information about the trajectory of a single cell and about the dynamical behavior of the noisy observations. In similar problems, additional knowledge can be available as a prior over functions. This advantage is not possible with purely data-driven approaches and, when existing, it must be exploited. In systems biology, the chemical reactions are often understood quite well, but complex systems or networks are still under investigation. However, integration of prior knowledge comes with an high cost and, in general, feasible approaches to compute inference must be approximated.