Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks

Testing mechanistic models of complex cellular processes remains a key challenge of systems biology despite the availability of high-throughput snapshot data from single-cells. That is because completely specified mechanistic models typically have to make so many assumptions that each individual assumption is only marginally tested in global model comparisons with data. We show how incompletely specified mechanistic models can be used to translate qualitative knowledge of molecular interactions into reaction rate functions from covariability data between pairs of components. In contrast to existing methods, our approach does not require perturbations, temporal information, observing all components within a complex network, or complete model knowledge. Its key ingredients are universal probability balance equations for stationary stochastic processes combined with partial knowledge of qualitative network interactions and high precision probability distributions to quantify fluctuations within biochemical reaction networks. This approach promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from snapshots of their stochastic fluctuations.