7,122 research outputs found
Including metabolite concentrations into flux balance analysis: thermodynamic realizability as a constraint on flux distributions in metabolic networks
<p>Abstract</p> <p>Background</p> <p>In recent years, constrained optimization – usually referred to as flux balance analysis (FBA) – has become a widely applied method for the computation of stationary fluxes in large-scale metabolic networks. The striking advantage of FBA as compared to kinetic modeling is that it basically requires only knowledge of the stoichiometry of the network. On the other hand, results of FBA are to a large degree hypothetical because the method relies on plausible but hardly provable optimality principles that are thought to govern metabolic flux distributions.</p> <p>Results</p> <p>To augment the reliability of FBA-based flux calculations we propose an additional side constraint which assures thermodynamic realizability, i.e. that the flux directions are consistent with the corresponding changes of Gibb's free energies. The latter depend on metabolite levels for which plausible ranges can be inferred from experimental data. Computationally, our method results in the solution of a mixed integer linear optimization problem with quadratic scoring function. An optimal flux distribution together with a metabolite profile is determined which assures thermodynamic realizability with minimal deviations of metabolite levels from their expected values. We applied our novel approach to two exemplary metabolic networks of different complexity, the metabolic core network of erythrocytes (30 reactions) and the metabolic network iJR904 of <it>Escherichia coli </it>(931 reactions). Our calculations show that increasing network complexity entails increasing sensitivity of predicted flux distributions to variations of standard Gibb's free energy changes and metabolite concentration ranges. We demonstrate the usefulness of our method for assessing critical concentrations of external metabolites preventing attainment of a metabolic steady state.</p> <p>Conclusion</p> <p>Our method incorporates the thermodynamic link between flux directions and metabolite concentrations into a practical computational algorithm. The weakness of conventional FBA to rely on intuitive assumptions about the reversibility of biochemical reactions is overcome. This enables the computation of reliable flux distributions even under extreme conditions of the network (e.g. enzyme inhibition, depletion of substrates or accumulation of end products) where metabolite concentrations may be drastically altered.</p
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
An analytic approximation of the feasible space of metabolic networks
Assuming a steady-state condition within a cell, metabolic fluxes satisfy an
under-determined linear system of stoichiometric equations. Characterizing the
space of fluxes that satisfy such equations along with given bounds (and
possibly additional relevant constraints) is considered of utmost importance
for the understanding of cellular metabolism. Extreme values for each
individual flux can be computed with Linear Programming (as Flux Balance
Analysis), and their marginal distributions can be approximately computed with
Monte-Carlo sampling. Here we present an approximate analytic method for the
latter task based on Expectation Propagation equations that does not involve
sampling and can achieve much better predictions than other existing analytic
methods. The method is iterative, and its computation time is dominated by one
matrix inversion per iteration. With respect to sampling, we show through
extensive simulation that it has some advantages including computation time,
and the ability to efficiently fix empirically estimated distributions of
fluxes
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
Uniform sampling of steady states in metabolic networks: heterogeneous scales and rounding
The uniform sampling of convex polytopes is an interesting computational
problem with many applications in inference from linear constraints, but the
performances of sampling algorithms can be affected by ill-conditioning. This
is the case of inferring the feasible steady states in models of metabolic
networks, since they can show heterogeneous time scales . In this work we focus
on rounding procedures based on building an ellipsoid that closely matches the
sampling space, that can be used to define an efficient hit-and-run (HR) Markov
Chain Monte Carlo. In this way the uniformity of the sampling of the convex
space of interest is rigorously guaranteed, at odds with non markovian methods.
We analyze and compare three rounding methods in order to sample the feasible
steady states of metabolic networks of three models of growing size up to
genomic scale. The first is based on principal component analysis (PCA), the
second on linear programming (LP) and finally we employ the lovasz ellipsoid
method (LEM). Our results show that a rounding procedure is mandatory for the
application of the HR in these inference problem and suggest that a combination
of LEM or LP with a subsequent PCA perform the best. We finally compare the
distributions of the HR with that of two heuristics based on the Artificially
Centered hit-and-run (ACHR), gpSampler and optGpSampler. They show a good
agreement with the results of the HR for the small network, while on genome
scale models present inconsistencies.Comment: Replacement with major revision
Volume of the steady-state space of financial flows in a monetary stock-flow-consistent model
We show that a steady-state stock-flow consistent macro-economic model can be
represented as a Constraint Satisfaction Problem (CSP).The set of solutions is
a polytope, which volume depends on the constraintsapplied and reveals the
potential fragility of the economic circuit,with no need to study the dynamics.
Several methods to compute the volume are compared, inspired by operations
research methods and theanalysis of metabolic networks, both exact and
approximate.We also introduce a random transaction matrix, and study the
particularcase of linear flows with respect to money stocks
- …