Inferring metabolic phenotypes from the exometabolome through a thermodynamic variational principle

Abstract

Networks of biochemical reactions, like cellular metabolic networks, are kept in non-equilibrium steady states by the exchange fluxes connecting them to the environment. In most cases, feasible flux configurations can be derived from minimal mass-balance assumptions upon prescribing in-and outtake fluxes.Here we consider the problem of inferring intracellular flux patterns from extracellular metabolite levels. Resorting to a thermodynamic out of equilibrium variational principle to describe the network at steady state, we show that the switch from fermentative to oxidative phenotypes in cells can be characterized in terms of the glucose, lactate, oxygen and carbon dioxide concentrations. Results obtained for an exactly solvable toy model are fully recovered for a large scale reconstruction of human catabolism. Finally we argue that, in spite of the many approximations involved in the theory, available data for several human cell types are well described by the predicted phenotypic map of the problem.

Focus on the emerging new fields of network physiology and network medicine

“…Investigating the chromatin interaction network, Boulos et al [45] took advantage of a graphical theoretical approach to uncover 'master' replication initiation zones organized at the N/U-domain borders that play key role in the 3D organization of the human DNA. Utilizing a thermodynamic out-of-equilibrium variational principle approach to cellular metabolic networks, De Martino et al [46] identify intracellular flux patterns from extracellular metabolic interactions and the role of non-equilibrium steady states for the function of metabolic networks. Lin et al [47] develop a Boolean network framework to investigate the dynamics and function of the p53 regulatory network and the role of this network in tumor suppression, identifying two-phase dynamics in response to DNA damage and oncogene activation.…”

Microenvironmental cooperation promotes early spread and bistability of a Warburg-like phenotype

“…The first terms on the right-hand-sides of (8,9) represent the local concentration smoothing due to diffusion, with D S and D W the diffusion coefficients, d the number of neighbors of cell i (d = 4 in our case) and the sum runs over the set i ( )  of neighbors of cell i. The second terms describe the changes due to import or export of compounds by cells, with u i and v i depending on concentrations as discussed in (2), ( 3), ( 4) and (5).…”

“…A similar scenario has been observed in immune cells 5 . Many studies have addressed the functional role 6 as well as the origin of this kind of metabolic re-programming at different levels, focusing most recently on the constraints on cellular energy metabolism imposed by different metabolic demands [7][8][9] , macromolecular crowding 10 , costs associated to gene expression [11][12][13] , membrane occupancy 14 or intrinsic limits to mitochondrial oxidative phosphorylation 15 , as well as on hypoxia 16 and dynamical mechanisms like flux sensors 17 (see refs 18, 19 for recent reviews of different models and possible mechanisms).…”

The free lunch of a scale-free metabolism

“…From the positive side, such an energy balance analysis can be rewarding from several aspects, since, apart from assessing metabolites concentrations [29], free energies [30], potentially regulated sites [31], it reveals that the metabolic space has a more complex multimodal structure. The additional layer of complexity provided by thermodynamics could enrich the possibility of biophysical modelling especially in presence of heterogeneity, cell-to-cell interactions and/or metabolic shuttling, and from a theroretical viewpoint could potentially lead to new variational principles [32]. A simple toy model has been provided to illustrate a possible mechanism of symmetry breaking while maximizing for an objective function.…”