Fig 1.
Overview of the modeling framework.
(A) The stoichiometry of the reaction network is used to determine prior distributions for the elasticity parameters. (B) The elasticity parameters represented in matrix form, where the column outlined in orange corresponds to m1 in (A). (C) For a metabolite m1, the prior distribution has predominately negative support for reactions in which the metabolite is a product (rA), positive support for reactions in which the metabolite is a reactant (rB), and a zero-centered, sparsity inducing prior for reactions in which the metabolite does not participate (rC).
Fig 2.
(A) Schematic of the considered pathway. Inferred allosteric interactions are shown in gray, in which arrows indicate an activation, while bar-headed lines indicate inhibition. (B) Traces for values as estimated by NUTS. Samples come from four parallel chains stacked together as indicated by the shaded regions. Resulting posterior densities are indicated by the inset on the right. (C) Posterior predictive distributions of steady-state flux and metabolite concentrations. Points represent medians of the posterior predictive distributions, with lines extending to cover the 95% highest posterior density. Slight jitter was added to differentiate the distributions as estimated by NUTS and ADVI. (D) Pairplot of the posterior distributions of elasticity variables as estimated via NUTS. Strong correlations can exist between fitted parameters, which are missed by the mean-field ADVI approximation. (E) Violin plot of distributions in FCCs as estimated by the two inference methods. Median and inner quartile range are indicated by the inner box plots, overlaid on a kernel density plot of each distribution.
Fig 3.
Inference on a medium-scale metabolic network with limited data.
(A) Schematic of a portion of the considered metabolic network corresponding to lysine biosynthesis. Reactions shown in green were experimentally determined to improve lysine yields. The allosteric regulation of lysC by SDAP (N-succinyl-L,L-2,6-diaminopimelate) inferred by the model is shown in gray. (B) Experimental vs posterior predictive distributions for lysine flux. Error lines extend to cover the 95% highest posterior density (HPD) interval. (C) Distributions of elasticities informed by the experimental results. Prior distributions for these elasticities are shown in light gray. The one allosteric elasticity confidently inferred is shown as the last entry. (D) Flux control coefficients for each reaction in the model. Prior distributions (light gray) are mostly centered around zero. Posterior distributions (dark gray) are highlighted in green if their 95% HPD does not overlap zero. All lines indicate 95% HPD ranges, dots indicate median.
Fig 4.
Parameterizing a genome-scale kinetic model with multiomics data.
(A) Distributions in log-transformed (unitless) experimental data after normalizing with respect to the phosphate-limited reference state. (B) Posterior predictive distributions after fitting with ADVI. Higher weight was given to experimental datapoints close to the reference state (±1.5) as indicated by the gray boxes. (C) Heat map of correlation coefficient between experimental enzyme measurements (x-axis) and experimental boundary flux measurements. Boundary fluxes and enzymes are sorted with hierarchical clustering. (D) Heat map of FCC as estimated from posterior parameter distributions. Boundary flux and enzyme ordering match those determined in (C). Colors represent medians of the posterior predictive distributions, FCCs with a direction that could not be confidently determined are colored white.
Table 1.
Largest significant correlations between measured enzymes and measured boundary fluxes.
Table 2.
Largest FCCs for the modulation of measured enzymes on measured boundary fluxes.
FCC ranges represent upper and lower bounds of the 95% highest posterior density. Enzyme-boundary pairs that also appear as confident predictions prior to including experimental data are omitted.