20,575 research outputs found
Enzyme economy in metabolic networks
Metabolic systems are governed by a compromise between metabolic benefit and
enzyme cost. This hypothesis and its consequences can be studied by kinetic
models in which enzyme profiles are chosen by optimality principles. In
enzyme-optimal states, active enzymes must provide benefits: a higher enzyme
level must provide a metabolic benefit to justify the additional enzyme cost.
This entails general relations between metabolic fluxes, reaction elasticities,
and enzyme costs, the laws of metabolic economics. The laws can be formulated
using economic potentials and loads, state variables that quantify how
metabolites, reactions, and enzymes affect the metabolic performance in a
steady state. Economic balance equations link them to fluxes, reaction
elasticities, and enzyme levels locally in the network. Economically feasible
fluxes must be free of futile cycles and must lead from lower to higher
economic potentials, just like thermodynamics makes them lead from higher to
lower chemical potentials. Metabolic economics provides algebraic conditions
for economical fluxes, which are independent of the underlying kinetic models.
It justifies and extends the principle of minimal fluxes and shows how to
construct kinetic models in enzyme-optimal states, where all enzymes have a
positive influence on the metabolic performance
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
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
Systems approaches to modelling pathways and networks.
Peer reviewedPreprin
How enzyme economy shapes metabolic fluxes
Metabolic fluxes are governed by physical and economic principles.
Stationarity constrains them to a subspace in flux space and thermodynamics
makes them lead from higher to lower chemical potentials. At the same time,
fluxes in cells represent a compromise between metabolic performance and enzyme
cost. To capture this, some flux prediction methods penalise larger fluxes by
heuristic cost terms. Economic flux analysis, in contrast, postulates a balance
between enzyme costs and metabolic benefits as a necessary condition for fluxes
to be realised by kinetic models with optimal enzyme levels. The constraints
are formulated using economic potentials, state variables that capture the
enzyme labour embodied in metabolites. Generally, fluxes must lead from lower
to higher economic potentials. This principle, which resembles thermodynamic
constraints, can complement stationarity and thermodynamic constraints in flux
analysis. Futile modes, which would be incompatible with economic potentials,
are defined algebraically and can be systematically removed from flux
distributions. Enzymes that participate in potential futile modes are likely
targets of regulation. Economic flux analysis can predict high-yield and
low-yield strategies, and captures preemptive expression, multi-objective
optimisation, and flux distributions across several cells living in symbiosis.
Inspired by labour value theories in economics, it justifies and extends the
principle of minimal fluxes and provides an intuitive framework to model the
complex interplay of fluxes, metabolic control, and enzyme costs in cells
Gene regulatory networks elucidating huanglongbing disease mechanisms.
Next-generation sequencing was exploited to gain deeper insight into the response to infection by Candidatus liberibacter asiaticus (CaLas), especially the immune disregulation and metabolic dysfunction caused by source-sink disruption. Previous fruit transcriptome data were compared with additional RNA-Seq data in three tissues: immature fruit, and young and mature leaves. Four categories of orchard trees were studied: symptomatic, asymptomatic, apparently healthy, and healthy. Principal component analysis found distinct expression patterns between immature and mature fruits and leaf samples for all four categories of trees. A predicted protein - protein interaction network identified HLB-regulated genes for sugar transporters playing key roles in the overall plant responses. Gene set and pathway enrichment analyses highlight the role of sucrose and starch metabolism in disease symptom development in all tissues. HLB-regulated genes (glucose-phosphate-transporter, invertase, starch-related genes) would likely determine the source-sink relationship disruption. In infected leaves, transcriptomic changes were observed for light reactions genes (downregulation), sucrose metabolism (upregulation), and starch biosynthesis (upregulation). In parallel, symptomatic fruits over-expressed genes involved in photosynthesis, sucrose and raffinose metabolism, and downregulated starch biosynthesis. We visualized gene networks between tissues inducing a source-sink shift. CaLas alters the hormone crosstalk, resulting in weak and ineffective tissue-specific plant immune responses necessary for bacterial clearance. Accordingly, expression of WRKYs (including WRKY70) was higher in fruits than in leaves. Systemic acquired responses were inadequately activated in young leaves, generally considered the sites where most new infections occur
Conditions for duality between fluxes and concentrations in biochemical networks
Mathematical and computational modelling of biochemical networks is often
done in terms of either the concentrations of molecular species or the fluxes
of biochemical reactions. When is mathematical modelling from either
perspective equivalent to the other? Mathematical duality translates concepts,
theorems or mathematical structures into other concepts, theorems or
structures, in a one-to-one manner. We present a novel stoichiometric condition
that is necessary and sufficient for duality between unidirectional fluxes and
concentrations. Our numerical experiments, with computational models derived
from a range of genome-scale biochemical networks, suggest that this
flux-concentration duality is a pervasive property of biochemical networks. We
also provide a combinatorial characterisation that is sufficient to ensure
flux-concentration duality. That is, for every two disjoint sets of molecular
species, there is at least one reaction complex that involves species from only
one of the two sets. When unidirectional fluxes and molecular species
concentrations are dual vectors, this implies that the behaviour of the
corresponding biochemical network can be described entirely in terms of either
concentrations or unidirectional fluxes
Generalized power method for sparse principal component analysis
In this paper we develop a new approach to sparse principal component
analysis (sparse PCA). We propose two single-unit and two block optimization
formulations of the sparse PCA problem, aimed at extracting a single sparse
dominant principal component of a data matrix, or more components at once,
respectively. While the initial formulations involve nonconvex functions, and
are therefore computationally intractable, we rewrite them into the form of an
optimization program involving maximization of a convex function on a compact
set. The dimension of the search space is decreased enormously if the data
matrix has many more columns (variables) than rows. We then propose and analyze
a simple gradient method suited for the task. It appears that our algorithm has
best convergence properties in the case when either the objective function or
the feasible set are strongly convex, which is the case with our single-unit
formulations and can be enforced in the block case. Finally, we demonstrate
numerically on a set of random and gene expression test problems that our
approach outperforms existing algorithms both in quality of the obtained
solution and in computational speed.Comment: Submitte
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