Signatures of arithmetic simplicity in metabolic network architecture

Metabolic networks perform some of the most fundamental functions in living cells, including energy transduction and building block biosynthesis. While these are the best characterized networks in living systems, understanding their evolutionary history and complex wiring constitutes one of the most fascinating open questions in biology, intimately related to the enigma of life's origin itself. Is the evolution of metabolism subject to general principles, beyond the unpredictable accumulation of multiple historical accidents? Here we search for such principles by applying to an artificial chemical universe some of the methodologies developed for the study of genome scale models of cellular metabolism. In particular, we use metabolic flux constraint-based models to exhaustively search for artificial chemistry pathways that can optimally perform an array of elementary metabolic functions. Despite the simplicity of the model employed, we find that the ensuing pathways display a surprisingly rich set of properties, including the existence of autocatalytic cycles and hierarchical modules, the appearance of universally preferable metabolites and reactions, and a logarithmic trend of pathway length as a function of input/output molecule size. Some of these properties can be derived analytically, borrowing methods previously used in cryptography. In addition, by mapping biochemical networks onto a simplified carbon atom reaction backbone, we find that several of the properties predicted by the artificial chemistry model hold for real metabolic networks. These findings suggest that optimality principles and arithmetic simplicity might lie beneath some aspects of biochemical complexity

Minimal cut sets in a metabolic network are elementary modes in a dual network

Motivation: Elementary modes (EMs) and minimal cut sets (MCSs) provide important techniques for metabolic network modeling. Whereas EMs describe minimal subnetworks that can function in steady state, MCSs are sets of reactions whose removal will disable certain network functions. Effective algorithms were developed for EM computation while calculation of MCSs is typically addressed by indirect methods requiring the computation of EMs as initial step. Results: In this contribution, we provide a method that determines MCSs directly without calculating the EMs. We introduce a duality framework for metabolic networks where the enumeration of MCSs in the original network is reduced to identifying the EMs in a dual network. As a further extension, we propose a generalization of MCSs in metabolic networks by allowing the combination of inhomogeneous constraints on reaction rates. This framework provides a promising tool to open the concept of EMs and MCSs to a wider class of applications. Contact: [email protected]; [email protected] Supplementary information: Supplementary data are available at Bioinformatics onlin

Flux cost functions and the choice of metabolic fluxes

Metabolic fluxes in cells are governed by physical, biochemical, physiological, and economic principles. Cells may show "economical" behaviour, trading metabolic performance against the costly side-effects of high enzyme or metabolite concentrations. Some constraint-based flux prediction methods score fluxes by heuristic flux costs as proxies of enzyme investments. However, linear cost functions ignore enzyme kinetics and the tight coupling between fluxes, metabolite levels and enzyme levels. To derive more realistic cost functions, I define an apparent "enzymatic flux cost" as the minimal enzyme cost at which the fluxes can be realised in a given kinetic model, and a "kinetic flux cost", which includes metabolite cost. I discuss the mathematical properties of such flux cost functions, their usage for flux prediction, and their importance for cells' metabolic strategies. The enzymatic flux cost scales linearly with the fluxes and is a concave function on the flux polytope. The costs of two flows are usually not additive, due to an additional "compromise cost". Between flux polytopes, where fluxes change their directions, the enzymatic cost shows a jump. With strictly concave flux cost functions, cells can reduce their enzymatic cost by running different fluxes in different cell compartments or at different moments in time. The enzymactic flux cost can be translated into an approximated cell growth rate, a convex function on the flux polytope. Growth-maximising metabolic states can be predicted by Flux Cost Minimisation (FCM), a variant of FBA based on general flux cost functions. The solutions are flux distributions in corners of the flux polytope, i.e. typically elementary flux modes. Enzymatic flux costs can be linearly or nonlinearly approximated, providing model parameters for linear FBA based on kinetic parameters and extracellular concentrations, and justified by a kinetic model

Metabolic Pathway Analysis: from small to genome-scale networks

The need for mathematical modelling of biological processes has grown alongside with the achievements in the experimental field leading to the appearance and development of new fields like systems biology. Systems biology aims at generating new knowledge through modelling and integration of experimental data in order to develop a holistic understanding of organisms. In the first part of my PhD thesis, I compare two different levels of abstraction used for computing metabolic pathways, constraint-based and graph theoretical methods. I show that the current representations of metabolism as a simple graph correspond to wrong mathematical descriptions of metabolic pathways. On the other hand, the use of stoichiometric information and convex analysis as modelling framework like in elementary flux mode analysis, allows to correctly predict metabolic pathways. In the second part of the thesis, I present two of the first methods, based on elementary flux mode analysis, that can compute metabolic pathways in such large metabolic networks: the K-shortest EFMs method and the EFMEvolver method. These methods contribute to an enrichment of the mathematical tools available to model cell biology and more precisely, metabolism. The application of these new methods to biotechnological problems is also explored in this part. In the last part of my thesis, I give an overview of recent achievements in metabolic network reconstruction and constraint-based modelling as well as open issues. Moreover, I discuss possible strategies for integrating experimental data with elementary flux mode analysis. Further improvements in elementary flux mode computation on that direction are put forward