This journal is The Royal Society of Chemistry 3 A Design Automation Framework for Computational Bioenergetics in Biological Networks Claudio Angione, a Jole Costanza, b Giovanni Carapezza, a Pietro Lió a and Giuseppe Nicosia b Received Xth XXXXXXXXXX XX, Accepted Xth XXXXXXXXX XX First published on the web Xth XXXXXXXXXX X DOI:.39/bx The bioenergetic activity of mitochondria can be thoroughly investigated by using computational methods. In particular, in our work we focus on ATP and NADH, namely the metabolites representing the production of energy in the cell. We develop a computational framework to perform an exhaustive investigation at the level of species, reactions, genes and metabolic pathways. The framework integrates several methods implementing the state-of-the-art algorithms for many-objective optimization, sensitivity, and identifiability analysis applied to biological systems. We use this computational framework to analyze three case studies related to the human mitochondria and the algal metabolism Chlamydomonas reinhardtii, formally described with algebraic differential equations or flux balance analysis. Integrating the results of our framework applied to interacting organelles would provide a general-purpose method for assessing the production of energy in a biological network. Supplementary Information. dominated points NADH mmolh - gdw - ] -. -. -.3 -. -.5 -. -.7 35 5 5 55 5 7 75 5 9 ATP mmolh - gdw - ] Electronic Supplementary Information (ESI) available: details of any supplementary information available should be included here]. See DOI:.39/bx/ a Computer Laboratory, University of Cambridge, William Gates Building, 5 JJ Thomson Avenue, Cambridge, UK. b Department of Mathematics & Computer Science, University of Catania, Viale Andrea Doria, 955, Catania, Italy. Fig. S Effect of the genetic algorithm on the Pareto front when optimizing ATP and NADH in the FBA mitochondrial model. This evolution has been carried out with individual and halted at the th generation. ATP production and NADH production maximization in the FBA framework for mitochondria. The figure represents the evolution of the multi-objective optimization results, reporting all the feasible and Pareto points until the generation. We optimized a limited set of the uptake rate fluxes (only twelve exchange fluxes) in order to increase the energy state of the cellular organelle. We optimized only the twelve fluxes that have a fixed value reported in the work by Smith et al..
This journal is The Royal Society of Chemistry 3 uptake rate] opt - uptake rate] initial 5 9 75 5 3 5 Urea Thiamin diphosphate Orthophosphate Fe+ L--Aminoadipate L-Alanine Hexadecanoic acid CO -Oxoadipate Phosphatidylserine Sulfate Octanoic acid CoA CDP Thiosulfate (S)-Lactate L-Glutamine UDP GDP Glutathione HO NAD+ dcdp dctp ADP L-Asparagine Putrescine dgdp FAD dadp dgtp dttp Phosphatidylcholine Glycerol datp Phosphatidylethanolamine Sulfite dtdp Fumarate L-Threonine L-Phenylalanine L-Serine Acetaldehyde L-Methionine L-Lysine L-Proline HCO3- Butanoic acid L-Cysteine Propanoate L-Valine H+ Biomass Succinate 5-Aminolevulinate ATP H+ L-Tyrosine -Oxoglutarate L-Leucine Glycine L-Arginine L-Tryptophan L-Aspartate Oxaloacetate L-Glutamate (S)-Malate L-Isoleucine (R)-3-Hydroxybutanoate Isocitrate alpha-d-glucose Citrate Oxygen Fig. S The histogram highlights the difference between the optimal values and the initial values of the uptake rates in the mitochondrial metabolism modeled through FBA for maximizing the ATP and NADH production. The values are related to the maximum ATP production point obtained from the Pareto front in blue of Figure.
This journal is The Royal Society of Chemistry 3 Metabolite] opt /Metabolite] initial Metabolite] opt /Metabolite] initial (a) GP c (b) GP c Metabolite] opt /Metabolite] initial Metabolite] opt /Metabolite] initial.5.5 (c) GP c (d) GP c Metabolite] opt /Metabolite] initial.5.5 (e) GP c Fig. S3 The plots represent the ratio between the 55 optimal metabolite concentrations and the metabolite concentration before the optimization (overproduction and underproduction states) in DAEs mitochondrial model by Bazil et al.. For each plot, we report the results for the solution (in red) that reaches the maximum ATP and the minimum NADH and the solution (in green) that reaches the minimum ATP and maximum NADH when the concentration of calcium in the matrix is (a) 5, (b), (c), (d).5 5 and (e) 5 /.5. 3
This journal is The Royal Society of Chemistry 3 Ca + ] =.5 5 Ca + ] = 5 /.5 Ca + ] = Ca + ] = Variable Metabolite Groups r cv Groups r cv Groups r cv Groups r cv x x,x 37.9.5 x,x.979. x,x.977.5 x,x 53.99.95 x K m x,x 7.99.9 x,x 37.9.7 x,x 3.9. x.9.5 x 3 x 3,x 5,x 7.9.5 x 3,x.9.79 x 3,x 39.95.33 x 3,x.957.3 x x,x 3.95. x,x.99.7 x,x 39.9.53 x,x.97.9 x 5 x 5,x 3.9.7 x 3,x 5.9.3 x 5,x.93.5 x 5,x 9,x 37,x 39.97. x x,x 3.9.3 x,x,x 5.9.55 x,x 3,x.9. x,x,x.9.35 x 7 x 7,x.977. x 7,x 5.95.9 x 7.99.7 x 7,x 3.97.95 x x,x 5.95.5 x,x.9.57 x,x 5.933.5 x,x 35,x 3.99.3 x 9 x 9,x,x 3.97.35 x 9,x,x 37.99.5 x 5,x,x 9.93.37 x 9,x 9.97.39 x x,x 3.9.5 x,x 5.9. x,x,x.99.37 x.995.5 x x,x 5.99.73 x,x 3,x.99.79 x,x 5.9.9 x,x 5.9.9 x x,x 9.97.3 x,x 9,x.9.7 x,x.95.3 x,x 39.97. x 3 x 3.9. x 3.99.5 x 3.99.39 x 3,x 3.9.3 x x 7,x.977. x,x 9.99.3 x,x,x.9.397 x,x.97.3 x 5 x 5,x.99.5 x 5,x 5.959. x 5,x.99.7 x 5,x.99.5 x PY R m x,x 3,x 37.9.579 x,x 3.95.399 x,x,x 7.9.55 x,x 5.95.3 x 7 x 7,x.9.95 x 5,x 7.97.9 x,x 7.935.53 x 7,x.9.55 x x,x 35,x 7.9.3 x,x 9,x.99.9 x 5,x.99.5 x,x,x 3.9.3 x 9 H im n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. x K im n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. x Na im n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. x Mg im n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. x 3 Ca im n.a. n.a. n.a. n.a. n.a. n.a. n.a. n.a. x AT P im x,x.99.53 x,x.93.55 x,x,x 5.97.3 x,x,x 5.9. x 5 x 5,x 3,x 5.977.99 x 5,x 3.95.7 x 5,x 3.93. x,x 5.939.739 x x,x 3.9.7 x.993.33 x,x,x.97.5 x,x.9.39 x 7 x 7,x 35,x 5.9.5 x 7,x.99.5 x,x 7.97.7 x 7,x 33,x 3.97. x PY R im x,x.99.5 x,x 37,x.99.9 x,x.979.3 x,x 3,x.99.57 x 9 x,x 9.9.3 x 7,x 9.97.5 x 9,x 3.95.39 x 9,x 9.97.3 x 3 x,x 3,x 37.99.575 x,x 3,x 5.977.5 x 3,x 3.9.7 x 7,x 7,x 3.97.7 x 3 x 3,x 3.99.5 x 9,x 3.9.97 x,x 3,x 7.9.37 x 3,x 55.9.37 x 3 x 9,x 3,x 5.9.9 x 3,x 37.9.77 x,x 3.9.9 x,x 3,x 5.9.57 x 33 x 33.97.39 x,x 33,x 3.993.75 x 33,x,x 55.9. x 33,x 5.97.35 x 3 x 3.99.53 x 3,x 9.9.773 x 3.9. x,x 3.9.9 x 35 x,x 5,x 35.9. x,x 35.939. x 5,x 35.955. x,x 35,x 5.9.5 x 3 x,x 3.9.5 x 5,x 3,x 53.97.355 x 3,x.95.5 x 3,x 5.997.997 x 37 K c x 37,x.935.3 x 9,x 37.99. x 9,x,x 3,x 37.9.59 x 37,x,x 5.99.3 x 3 x,x,x 3.9.393 x 9,x 7,x 3.9.3 x 3,x 5.979.37 x 3,x.97.373 x 39 x,x 39.99.5 x,x 39.99.5 x 39.97.7 x,x 5,x 39,x 5.993.53 x x 5,x 3,x.97. x,x.99. x,x.97.3 x 3,x.975.9 x AT P c x.99. x 9,x 5,x.995. x 5,x.95. x 5,x,x,x.99.5 x x,x,x 5.9.37 x,x.9.3 x,x.95.375 x,x,x 5.95. x 3 x 3.9.3 x 35,x 3.97.7 x 5,x 3.93.97 x 3,x 9.97.53 x x 5,x 3,x.9.375 x 5,x,x.9.33 x,x,x 5.9.395 x,x,x.99.35 x 5 x,x 5.99. x,x 5.9.3 x 5,x 5.97.5 x 5,x 5.93.7 x x 7,x.9.57 x,x.93.77 x,x.93. x,x,x.9.55 x 7 x,x 7.93.59 x,x 33,x 7,x.99.5 x 3,x 3,x 7.9. x 7.99. x x 7,x,x 9.99.5 x,x.9. x 35,x,x 5.95.9 x,x.959.93 x 9 x 9.993. x 3,x 9,x 5.9.7 x 9,x 5.95.5 x 9.995.9 x 5 x 7,x 5.99.37 x 5,x 5.9.97 x,x 5.95.5 x,x,x,x 5.995.3 x 5 x 5,x 5.97.53 x,x 5.9. x 5.9.5 x,x 5.95. x 5 x 5,x 5.97.79 x,x 35,x 5.979. x 3,x 3,x 5.9. x 3,x 5.997.95 x 53 PY R c x,x 53.95.3 x 9,x 5,x 53.97.3 x,x 53.99.7 x,x 53,x 55.99.3 x 5 x,x 5.97.9 x 37,x 5.973.7 x 3,x 5.9.37 x 5,x,x 5.99.7 x 55 Ca m x 55.99.3 x 37,x 55.99.7 x 55.9.55 x 3,x 55.9.577 Table S Identifiability analysis applied on the non dominated points of the ATP-NADH Pareto front with four different amount of calcium concentration nmol/mg] in the matrix. The variables, i.e. initial concentrations of the 55 metabolites, are grouped according to functional relations. The value of r is an indicator of the amount of variance of the response explained by the predictors. A large ratio cv(x) = std(x)/mean(x) indicates that the data are scattered, thus suggesting practical non-identifiability. n.a. stands for not available, when metabolites do not play any role in the two-objective maximization of ATP and NADH. An asterisk is added when r >.9 and cv >.. Two asterisks indicate a strong interdependence between variables, i.e. the same functional group has been detected even if the role of response and predictors is switched. For instance, for a low increase in the calcium concentration Ca +] =.5 5, ATP shows a strong functional relation with Pyruvate.
This journal is The Royal Society of Chemistry 3 min ATP, min NADH max ATP, max NADH Metabolite] opt /Metabolite] initial.5 x GP c.5 x 3.5 Pim.5.5.5 x Fig. S Ratio between the 55 optimal metabolite concentrations and the metabolite concentration before the optimization in DAEs mitochondrial model of Bazil et al.. We report the results (in red) of the trade-off found when the algorithm minimizes ATP and NADH in cancer conditions, and the results (in green) of the trade-off found when algorithm maximizes ATP and NADH in cancer conditions. Fig. S Functional relation among the three decision variables Na, Pi and AcCoA nmol/mg] in the matrix, thus highlighting the structural non-identifiability of these variables. This group has been detected for the etabolite with Ca +] =.5 5 nmol/mg. σ* e+.. e- e- e-. e+5 e+ µ* Free potassium Free magnesium Aspartate CoA Pi Citrate Free sodium Oxaloacetate Extra-mit ADP Free proton Extra-mit pyruvate Extra-mit succinate Extra-mit malate Glutamate Extra-mit Free calcium Extra-mit aspartate Extra-mit ATP Extra-mit Pi Extra-mit isocitrate Extra-mit citrate Fumarate Isocitrate a-ketoglutarate Malate Succinyl-CoA Pyruvate Extra-mit Free potassium Succinate Innermembrane ADP Extra-mit Free magnesium Innermembrane ATP Extra-mit AMP Innermembrane pyruvate Innermembrane Pi Extra-mit glutamate Total Extra-mit free sodium Innermembrane succinate Innermembrane malate Innermembrane glutamate Total acetyl-coa Innermembrane isocitrate Innermembrane a-ketoglutarate Extra-mit a-ketoglutarate Extra-mit glucose Extra-mit glcphosphate Extra-mit funarate Innermembrane aspartate Innermembrane citrate Innermembrane AMP Innermembrane fumarate.5.5 x 5.5.5 x 3.5.5 x Fig. S5 Sensitivity analysis on the DAEs mitochondrial model by Bazil et al.. In this experiment, we evaluate the sensitivity of the metabolite concentrations of the metabolic network. The plot shows the mean and the standard deviation of the elementary effects computed through the Morris method 3. The labels on the key are sorted according to the sensitivity ranking. Fig. S7 Optimal transformations (y axis) found for the three decision variables Na, Pi and AcCoA (x axis) nmol/mg] with Ca + ] =.5 5 nmol/mg. Although AcCoA has been assigned to the same functional group, it shows a different behavior for low concentrations, while Na and Pi exhibit a similar behavior. 5
This journal is The Royal Society of Chemistry 3 3 5 x 5.5 5.3..5..7..9..5 x.5 Pyrm.5 x 5 Fig. S Functional relation among the two decision variables Mg and CoASH nmol/mg] in the matrix, thus highlighting the structural non-identifiability of these variables. This group has been detected for Mg with an increased concentration of calcium Ca + ] = nmol/mg. Fig. S Functional relation among the three decision variables H, Pyr and AcCoA nmol/mg] in the matrix, thus highlighting the structural non-identifiability of these variables. This group has been detected for Mg when the matrix calcium concentration is 5 /.5 nmol/mg..3..5..7..9. 5 7 9 x 5.5.5 Pyr m x 5.5.5 x 5 5 5 3 Fig. S9 The transformations (y axis) found for the two decision variables Mg and CoASH (x axis) nmol/mg] when Ca +] = nmol/mg. Fig. S Optimal transformations (y axis) found for the three decision variables H, Pyr and AcCoA (x axis) nmol/mg] when calcium is reduced to 5 /.5 nmol/mg. Although H has been assigned to the same functional group, it shows a different behavior for low concentrations, while Pyr and AcCoA exhibit a similar behavior.
This journal is The Royal Society of Chemistry 3 x.9 3.5..7 3.5..5..3...5 Asp m.... Na x 5 m Fig. S Functional relation among the two decision variables Asp and CoASH nmol/mg] in the matrix. These two metabolites have a strong structural non-identifiability. This group has been detected both for Asp and for CoASH when the matrix calcium concentration is 5 /.5 nmol/mg. Fig. S Functional relation among the two decision variables Na and GLU nmol/mg] in the matrix. This group has been detected with a reduced concentration of calcium in the matrix, i.e. Ca + ] = nmol/mg. Asp m.... Na x 5 m.5.5 3 3.5.... GLU x m Fig. S3 Optimal transformations (y axis) found for the two decision variables Asp and CoASH nmol/mg] (x axis) when calcium is reduced to 5 /.5 nmol/mg. Fig. S5 Optimal transformations (y axis) found for the two decision variables Na and GLU (x axis) nmol/mg], with Ca + ] = nmol/mg. 7
This journal is The Royal Society of Chemistry 3 x.9..7..5..3....5.7.75..5.9.95 Fig. S Functional relation among the two decision variables Mg and MAL nmol/mg] in the matrix, highlighting the strong structural non-identifiability of these variables. This group has been detected for both the components of the pair when maximizing simultaneously ATP and NADH in the DAEs model of the mitochondrion when simulating the cancer condition. References A. Smith and A. Robinson, BMC systems biology,, 5,. J. Bazil, G. Buzzard and A. Rundell, PLoS computational biology,,, e3. 3 M. Morris, Technometrics, 99, 33, 7..9..7..5..3.. x.5.5.5 Fig. S7 Functional relation among Mg and SCoA in the matrix, highlighting the strong structural non-identifiability of these variables. This group has been detected for both the components of the pair when minimizing ATP and NADH in the DAEs model of the mitochondrion simulating the cancer condition. This indicates strong interdependence between Mg and SCoA in the cancer condition of the mitochondrion.