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

Quantifying biochemical reaction rates within complex cellular processes remains a key challenge of systems biology even as high-throughput single-cell data have become available to characterize snapshots of population variability. That is because complex systems with stochastic and non-linear interactions are difficult to analyze when not all components can be observed simultaneously and systems cannot be followed over time. Instead of using descriptive statistical models, we show that incompletely specified mechanistic models can be used to translate qualitative knowledge of interactions into reaction rate functions from covariability data between pairs of components. This promises to turn a globally intractable problem into a sequence of solvable inference problems to quantify complex interaction networks from incomplete snapshots of their stochastic fluctuations.Author summary: Statistical models are the dominant tool to interpret co-variability of molecular components in cellular processes because they can be formulated for a subset of components while leaving the full complexity of the processes unspecified. Their drawback lies in the difficulty of translating statistical associations into causal interactions. In contrast, complete mechanistic models of biochemical reaction networks are a powerful tool to describe physical interactions, but often necessitate making a large number of assumptions such that each individual assumption is only marginally tested in global model comparisons with data. We introduce a novel inference method that combines the power of both approaches by exploiting testable predictions for only partially specified mechanistic models. We present numerical proof-of-principle examples in which we reconstruct biochemical reaction rates from partial observations of variability within simulated biochemical reaction networks in the absence of cell division. In contrast to existing approaches, our algorithm does not require perturbations, temporal information, observing all components within a complex network, or complete model knowledge. Its key ingredients are partial knowledge of qualitative network interactions paired with high precision probability distributions to quantify stochastic fluctuations within biochemical reaction networks.