Quantifying biochemical reaction rates from static population variability within incompletely observed complex networks
Fig 2
Probability flux balances can determine biochemical rates regardless of global network dynamics.
Fixing how the production rate f(x2) of X3 depends on X2-levels, we considered four different global network topologies within the class defined by Eq (3), that exhibit diverse system dynamics and variability in X3 (left column). The insets of the right column depict numerically observed joint distributions P(x2, x3) corresponding to 100,000 independent snapshots. Although probability distributions differed greatly between the four systems, Eq (4) could identify the functional dependence of the production rate of X3 based on the numerical convex optimization algorithm detailed in the Materials & Methods. We find near perfect agreement between the inferred rate (orange crosses) and the true rate function (dashed blue line) regardless of a system’s global dynamics. This inference of f(x2) does not utilize any temporal information, its only input is the stationary joint probability distribution between the two components of interest. It relies on observing fluctuations across a wide range of X2-states as illustrated by the shaded probability distribution P(x2) with deviations occurring where X2 was rarely or never observed. While the degradation rate of X3 was assumed to be known, no information about how its production rate depends on X2, or the dynamics of X1, X2 was used.