Essential plasticity and redundancy of metabolism unveiled by synthetic lethality analysis

We unravel how functional plasticity and redundancy are essential mechanisms underlying the ability to survive of metabolic networks. We perform an exhaustive computational screening of synthetic lethal reaction pairs in Escherichia coli in a minimal medium and we find that synthetic lethal pairs divide in two different groups depending on whether the synthetic lethal interaction works as a backup or as a parallel use mechanism, the first corresponding to essential plasticity and the second to essential redundancy. In E. coli, the analysis of pathways entanglement through essential redundancy supports the view that synthetic lethality affects preferentially a single function or pathway. In contrast, essential plasticity, the dominant class, tends to be inter-pathway but strongly localized and unveils Cell Envelope Biosynthesis as an essential backup for Membrane Lipid Metabolism. When comparing E. coli and Mycoplasma pneumoniae, we find that the metabolic networks of the two organisms exhibit a large difference in the relative importance of plasticity and redundancy which is consistent with the conjecture that plasticity is a sophisticated mechanism that requires a complex organization. Finally, coessential reaction pairs are explored in different environmental conditions to uncover the interplay between the two mechanisms. We find that synthetic lethal interactions and their classification in plasticity and redundancy are basically insensitive to medium composition, and are highly conserved even when the environment is enriched with nonessential compounds or overconstrained to decrease maximum biomass formation.Comment: 22 pages, 4 figure

Lipid Metabolism and Comparative Genomics

Unilever asked the Study Group to focus on two problems. The first concerned dysregulated lipid metabolism which is a feature of many diseases including metabolic syndrome, obesity and coronary heart disease. The Study Group was asked to develop a model of the kinetics of lipoprotein metabolism between healthy and obese states incorporating the activities of key enzymes. The second concerned the use of comparative genomics in understanding and comparing metabolic networks in bacterium. Comparative genomics is a method to make inferences on the genome of a new organism using information of a previously charaterised organism. The first mathematical question is how one would quantify such a metabolic map in a statistical sense, in particular, where there are different levels of confidence for presense of different parts of the map. The next and most important question is how one can design a measurement strategy to maximise the confidence in the accuracy of the metabolic map

Elasticity sampling links thermodynamics to metabolic control

Metabolic networks can be turned into kinetic models in a predefined steady state by sampling the reaction elasticities in this state. Elasticities for many reversible rate laws can be computed from the reaction Gibbs free energies, which are determined by the state, and from physically unconstrained saturation values. Starting from a network structure with allosteric regulation and consistent metabolic fluxes and concentrations, one can sample the elasticities, compute the control coefficients, and reconstruct a kinetic model with consistent reversible rate laws. Some of the model variables are manually chosen, fitted to data, or optimised, while the others are computed from them. The resulting model ensemble allows for probabilistic predictions, for instance, about possible dynamic behaviour. By adding more data or tighter constraints, the predictions can be made more precise. Model variants differing in network structure, flux distributions, thermodynamic forces, regulation, or rate laws can be realised by different model ensembles and compared by significance tests. The thermodynamic forces have specific effects on flux control, on the synergisms between enzymes, and on the emergence and propagation of metabolite fluctuations. Large kinetic models could help to simulate global metabolic dynamics and to predict the effects of enzyme inhibition, differential expression, genetic modifications, and their combinations on metabolic fluxes. MATLAB code for elasticity sampling is freely available

A probabilistic model for gene content evolution with duplication, loss, and horizontal transfer

We introduce a Markov model for the evolution of a gene family along a phylogeny. The model includes parameters for the rates of horizontal gene transfer, gene duplication, and gene loss, in addition to branch lengths in the phylogeny. The likelihood for the changes in the size of a gene family across different organisms can be calculated in O(N+hM^2) time and O(N+M^2) space, where N is the number of organisms, $h$ is the height of the phylogeny, and M is the sum of family sizes. We apply the model to the evolution of gene content in Preoteobacteria using the gene families in the COG (Clusters of Orthologous Groups) database

Estimating the size of the solution space of metabolic networks

In this work we propose a novel algorithmic strategy that allows for an efficient characterization of the whole set of stable fluxes compatible with the metabolic constraints. The algorithm, based on the well-known Bethe approximation, allows the computation in polynomial time of the volume of a non full-dimensional convex polytope in high dimensions. The result of our algorithm match closely the prediction of Monte Carlo based estimations of the flux distributions of the Red Blood Cell metabolic network but in incomparably shorter time. We also analyze the statistical properties of the average fluxes of the reactions in the E-Coli metabolic network and finally to test the effect of gene knock-outs on the size of the solution space of the E-Coli central metabolism.Comment: 8 pages, 7 pdf figure

Scaling laws in bacterial genomes: A side-effect of selection of mutational robustness?

In the past few years, numerous research projects have focused on identifying and understanding scaling properties in the gene content of prokaryote genomes and the intricacy of their regulation networks. Yet, and despite the increasing amount of data available, the origins of these scalings remain an open question. The RAevol model, a digital genetics model, provides us with an insight into the mechanisms involved in an evolutionary process. The results we present here show that (i) our model reproduces qualitatively these scaling laws and that (ii) these laws are not due to differences in lifestyles but to differences in the spontaneous rates of mutations and rearrangements. We argue that this is due to an indirect selective pressure for robustness that constrains the genome size