Model

Metabolic model in SBML forma

Additional file 3 of Making life difficult for Clostridium difficile: augmenting the pathogen’s metabolic model with transcriptomic and codon usage data for better therapeutic target characterization

Gene essentiality analysis of icdf834 and iMLTC806cdf. (PDF 49 kb

Maximization of ATP and biomass in the mitochondrial FBA model when taking into account the protein abundances as real-valued variables.

<p>The red points constitute the Pareto frontier, while the others represent all the feasible points. The points are color coded according to the generation to which they belong. Points from the early generations of the genetic algorithm are colored light grey, while points from the last ones are colored black.</p

Optimization of the FBA mitochondrial model.

<p>(Left) Maximization of ATP and NADH production in the FBA mitochondrial model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133825#pone.0133825.ref017" target="_blank">17</a>], carried out with 1000 individuals and halted at the 1500^<i>th</i> generation. We optimized the uptake rate fluxes (73 exchange fluxes) to analyze the energy state of the mitochondrion. In blue the dominated feasible points, in black the wild type conditions, i.e., before optimization and in red the non-dominated Pareto points. Negative flux values represent an uptake rate, while positive values represent a production rate. (Right) Maximization of ATP production and minimization of NADH production.</p

optBioCAD Pseudo-code.

<p>optBioCAD Pseudo-code.</p

Optimal transformations <i>β</i> (<i>y</i> axis) found for the two fluxes R01361MM (top) and R01978MM (bottom) (<i>x</i> axis) [<i>μ</i>mol min⁻¹ gDW⁻¹] in the mitochondrial FBA model [17].

<p>This plot proves that there is a strong relation between these two fluxes, with slightly different and noisier behavior in the neighborhood of 0 and 0.7.</p

Sensitivity analysis on the mitochondrial FBA model.

<p>The plot shows the mean and the standard deviation of the elementary effects computed through the Morris’ method applied on the upper bounds of the exchange reaction fluxes. The uptake rates are ranked according to their relative influence on the ATP production. The mitochondrial ATP production is highly sensitive to changes in the uptake rate of oxygen, HCO₃, L-serine, and L-aspartate.</p

Succinate dehydrogenase deficiency—inflammation stage.

<p>Optimal transformations <i>β</i> (<i>y</i> axis) found for the five fluxes R00004MM, R01280MM, R01706MM, R04544MM, and R04968MM (<i>x</i> axis) [<i>μ</i>mol min⁻¹ gDW⁻¹] in the mitochondrial FBA model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133825#pone.0133825.ref017" target="_blank">17</a>].</p

Fumarase deficiency (left) and succinate dehydrogenase deficiency (right) in the healthy stage.

<p>Functional relation found for the two fluxes R00713MM and R01648MM (<i>x</i> axis) [<i>μ</i>mol min⁻¹ gDW⁻¹] in the mitochondrial FBA model [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133825#pone.0133825.ref017" target="_blank">17</a>]. Reaction stoichiometry is reported in Table L in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0133825#pone.0133825.s001" target="_blank">S1 File</a>. In the same stage of disease, the IA can be used to detect the type of monogenic disorder through the shape of the functional relation.</p

The BioCAD framework is able to perform multi-objective optimization on gene sets and protein abundances.

<p>The optimization can be applied to the Boolean arrays of gene sets (simulating an on/off condition), to the real-valued fluxes, or to the real-valued arrays representing protein abundances. In both cases, we seek for the Pareto-optimal arrays to simultaneously optimize two or more objective functions. The optimization is augmented with sensitivity, identifiability, robustness and <i>ϵ</i>-dominance analysis. The sensitivity analysis quantifies the importance of the input variables in the model, the identifiability analysis infers functional relations between them, the robustness is used in combination with the sensitivity and quantifies if a solution is reachable even if small perturbations are applied to the system, while the <i>ϵ</i>-dominance analysis identifies sub-optimal points.</p