Enzyme allocation problems in kinetic metabolic networks: optimal solutions are elementary flux modes.

The survival and proliferation of cells and organisms require a highly coordinated allocation of cellular resources to ensure the efficient synthesis of cellular components. In particular, the total enzymatic capacity for cellular metabolism is limited by finite resources that are shared between all enzymes, such as cytosolic space, energy expenditure for amino-acid synthesis, or micro-nutrients. While extensive work has been done to study constrained optimization problems based only on stoichiometric information, mathematical results that characterize the optimal flux in kinetic metabolic networks are still scarce. Here, we study constrained enzyme allocation problems with general kinetics, using the theory of oriented matroids. We give a rigorous proof for the fact that optimal solutions of the non-linear optimization problem are elementary flux modes. This finding has significant consequences for our understanding of optimality in metabolic networks as well as for the identification of metabolic switches and the computation of optimal flux distributions in kinetic metabolic networks.

[1]  B. Teusink,et al.  Shifts in growth strategies reflect tradeoffs in cellular economics , 2009, Molecular systems biology.

[2]  R. Milo,et al.  Glycolytic strategy as a tradeoff between energy yield and protein cost , 2013, Proceedings of the National Academy of Sciences.

[3]  R. Rockafellar.  The Elementary Vectors of a Subspace of RiY , 2022 .

[4]  Nathan E. Lewis,et al.  A proof for loop-law constraints in stoichiometric metabolic networks , 2012, BMC Systems Biology.

[5]  Jason A. Papin,et al.  Applications of genome-scale metabolic reconstructions , 2009, Molecular systems biology.

[6]  Yi Zhou,et al.  Catabolic efficiency of aerobic glycolysis: The Warburg effect revisited , 2010, BMC Systems Biology.

[7]  Bas Teusink,et al.  Metabolic shifts: a fitness perspective for microbial cell factories , 2012, Biotechnology Letters.

[8]  G. Ziegler.  Lectures on Polytopes , 1994 .

[9]  E. Negelein,et al.  THE METABOLISM OF CARCINOMA CELLS , 2011 .

[10]  Steffen Klamt,et al.  Two approaches for metabolic pathway analysis? , 2003, Trends in biotechnology.

[11]  Z. Oltvai,et al.  Molecular Crowding Defines a Common Origin for the Warburg Effect in Proliferating Cells and the Lactate Threshold in Muscle Physiology , 2011, PloS one.

[12]  D. Fell,et al.  Is maximization of molar yield in metabolic networks favoured by evolution? , 2008, Journal of theoretical biology.

[13]  Walter Kern,et al.  Linear Programming Duality , 1992 .

[14]  S. Schuster,et al.  ON ELEMENTARY FLUX MODES IN BIOCHEMICAL REACTION SYSTEMS AT STEADY STATE , 1994 .

[15]  F. Doyle,et al.  Dynamic flux balance analysis of diauxic growth in Escherichia coli. , 2002, Biophysical journal.

[16]  Björn H. Junker,et al.  Computational Models of Metabolism: Stability and Regulation in Metabolic Networks , 2008 .

[17]  H G Crabtree,et al.  The carbohydrate metabolism of certain pathological overgrowths. , 1928, The Biochemical journal.

[18]  Jeffrey D Orth,et al.  What is flux balance analysis? , 2010, Nature Biotechnology.

[19]  D. Fell,et al.  Reaction routes in biochemical reaction systems: Algebraic properties, validated calculation procedure and example from nucleotide metabolism , 2002, Journal of mathematical biology.

[20]  Radhakrishnan Mahadevan,et al.  Economics of membrane occupancy and respiro-fermentation , 2011, Molecular systems biology.

[21]  Alexander Bockmayr,et al.  Fast thermodynamically constrained flux variability analysis , 2013, Bioinform..

[22]  Robert Urbanczik,et al.  The geometry of the flux cone of a metabolic network. , 2005, Biophysical journal.

[23]  U. Sauer,et al.  Multidimensional Optimality of Microbial Metabolism , 2012, Science.

[24]  R. Heinrich,et al.  The Regulation of Cellular Systems , 1996, Springer US.

[25]  Frank J. Bruggeman,et al.  Optimality Principles in the Regulation of Metabolic Networks , 2012, Metabolites.

[26]  Steffen Klamt,et al.  Computation of elementary modes: a unifying framework and the new binary approach , 2004, BMC Bioinformatics.

[27]  H. Qian,et al.  Thermodynamic constraints for biochemical networks. , 2004, Journal of theoretical biology.

[28]  Günter M. Ziegler,et al.  Oriented Matroids , 2017, Handbook of Discrete and Computational Geometry, 2nd Ed..

[29]  M. Antoniewicz.  Dynamic metabolic flux analysis--tools for probing transient states of metabolic networks. , 2013, Current opinion in biotechnology.

[30]  Janet B. Jones-Oliveira,et al.  An algebraic-combinatorial model for the identification and mapping of biochemical pathways , 2001, Bulletin of mathematical biology.

[31]  Christoph Kaleta,et al.  Combining Metabolic Pathway Analysis with Evolutionary Game Theory. Explaining the occurrence of low-yield pathways by an analytic optimization approach , 2011, Biosyst..

[32]  Georg Regensburger,et al.  Generalized Mass Action Systems: Complex Balancing Equilibria and Sign Vectors of the Stoichiometric and Kinetic-Order Subspaces , 2012, SIAM J. Appl. Math..

[33]  Josephus Hulshof,et al.  Metabolic states with maximal specific rate carry flux through an elementary flux mode , 2014, The FEBS journal.

[34]  Alexander Bockmayr,et al.  Thermodynamic Constraints for Metabolic Networks , 2012 .

[35]  M. A. de Menezes,et al.  Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity , 2007, Proceedings of the National Academy of Sciences.

[36]  W. Kern,et al.  Linear Programming Duality: An Introduction to Oriented Matroids , 1992 .

[37]  O. Warburg,et al.  The Metabolism of Carcinoma Cells , 1925 .

[38]  Ziv Bar-Joseph,et al.  Impact of the solvent capacity constraint on E. coli metabolism , 2008, BMC Systems Biology.

[39]  D. Sabatini,et al.  Cancer Cell Metabolism: Warburg and Beyond , 2008, Cell.

[40]  Emma Saavedra,et al.  Energy metabolism in tumor cells , 2007, The FEBS journal.

[41]  Vincent Fromion,et al.  Cell design in bacteria as a convex optimization problem , 2011, Autom..

[42]  Roded Sharan,et al.  Genome-Scale Metabolic Modeling Elucidates the Role of Proliferative Adaptation in Causing the Warburg Effect , 2011, PLoS Comput. Biol..

[43]  L. Cantley,et al.  Cancer Cell Metabolism , 2012 .

[44]  Alexander Bockmayr,et al.  A new constraint-based description of the steady-state flux cone of metabolic networks , 2009, Discret. Appl. Math..