Fig 1.
Three synthetic networks used to benchmark BMCA.
A) TopA, B) TopB, C) TopC, adapted from Millard et al. [18]. Cyan lines describe the allosteric regulation. For TopC, only negative allosteric regulation is shown.
Table 1.
Summaries of ground truth coefficient value ranges for all three networks and their allosteric variations.
Fig 2.
Overview of BMCA benchmarking experiments.
Synthetic models are simulated using tellurium (16) to produce datasets of fluxes and concentrations of enzymes, internal metabolites, and external metabolites. The ground truth FCC values and elasticities are also calculated from the simulation. For each model variation, five parallel BMCA runs take place: one without any omitted data and one each of omitting one data type. Each BMCA run results in a set of posterior distributions for elasticities. The HDI for each posterior distribution is computed, resulting in a single value for each elasticity. These elasticity sets are compared with ground truth elasticity values and then used to calculate control coefficient values which are subsequently compared with the ground truth control coefficients.
Table 2.
Prior distributions of the BMCA model.
Fig 3.
Comparison of BMCA predictions from the emll method and the v-based method on TopB.
(A) Elasticities, (B) CCCs, and (C) FCCs predicted by BMCA for TopB using both the emll and v-based methods. No data were omitted, and no allosteric regulation was present. Each dot represents the median of the predicted distribution means across ten different enzyme perturbation strengths. Error bars indicate the range of these predictions. (D) Elasticity predictions from the emll method for TopA with a strong allosteric regulator (ground truth elasticity = –3.61). The method was applied to ten datasets with varying enzyme perturbation strengths; colored dots indicate which dataset each prediction came from. The gray dashed line marks perfect agreement with ground truth values, and the pink dashed line marks the ground truth elasticity of the regulator.
Fig 4.
BMCA elasticity predictions compared against ground truth values for TopB.
Each dot signifies the median while the error bars represent the range of the predicted elasticity values across the different enzyme perturbation levels tested. The titles for each graph indicate which data type was omitted when running BMCA. All of the graphs are zoomed in as the ground truth elasticity.
Fig 5.
BMCA-predicted elasticities for TopC across all perturbation strengths compared against ground truth values.
A) Comparison of elasticities for ground truth values less than a magnitude of 10. B) Comparison of elasticities for all ground truth values. Each dot signifies the median while the error bars represent the range of the predicted elasticity values across the different enzyme perturbation levels tested.
Table 3.
Results of Levene’s test comparing predicted elasticities across varying perturbation levels for different network variations.
n is the Hill coefficient for the regulators. For Reg2 conditions, the two Hill coefficients are listed in order as Reg1 and Reg2.
Table 4.
Ground truth elasticity values before and after allostery was increased for TopA and B.
Ground truth elasticity values are provided for the allosteric regulators at different Hill coefficients (n).
Fig 6.
Elasticity predictions for model variations with strong allosteric regulators.
BMCA-predicted elasticities from ten different perturbation strength datasets for (A) TopA and (B) TopB, each with one or two strong allosteric regulators (Hill coefficient = 3 or 4). Each dot represents the median of the predicted distribution means across the ten enzyme perturbation strengths. The pink dashed line indicates the ground truth elasticity of the first regulator, and the green dashed line indicates that of the second regulator.
Fig 7.
BMCA CCC predictions compared against ground truth values for TopA.
Each dot signifies the median of the predicted CCC values for the different enzyme perturbation levels tested. The titles for each graph indicate which data type was omitted when running BMCA.
Fig 8.
BMCA FCC predictions compared against ground truth values for TopB.
Each dot signifies the median across the different enzyme perturbation levels tested. The titles for each graph indicate which data type was omitted when running BMCA. Corrections for FCC values for reactions whose enzymes are being perturbed have been applied.
Fig 9.
Aggregated Spearman correlation coefficients from comparisons between ground truth rankings of FCC values and FCC values predicted by the BMCA algorithm.
Fig 10.
Number of enzymes correctly predicted as having one of the top ten highest FCC values based on the various data types omitted when running BMCA.
The height of the bars represent the mean of the predictions across all the perturbation levels and allosteric regulation levels; the error bars represent the standard deviation.
Table 5.
Summary of effects on different control coefficients when different types of data types are omitted from BMCA.