Understanding the Nutritional Control of Metabolic Flux in S. cerevisiae
Sean R Hackett and Josh Rabinowitz
Summary
Quantifying fluxes
The space of possible fluxes through the metabolic network can
be bounded by determining the rates that molecules are takenup from the media, and the rates that the monomers that are
polymerized to create macromolecules are created. Under
steady-state conditions, the concentration of metabolites won’t
change over time so flux balance will be satisfied for each
metabolite and mass balance of nutrients and macromolecules
will exist. With these boundary fluxes constrained, pathway
degeneracies can be resolved by incorporating either kinetic
information from isotopic tracer methods or through an estimate
of flux carried related to predicted absolute flux. For each
condition, this information can be integrated using flux balance
analysis, in order to find an optimal set of fluxes that conforms
to boundary constraints and experimental data
While the information necessary to quantify flux in a metabolismwide manner is still accumulating, analysis of a limited number of
reactions is currently possible.
For these reactions, the flux will be proportional to the product of
the concentration of a macromolecule and the rate which volume
is removed from the reaction vessel.
Looking at ribonucleotide synthesis, the intracellular concentration
of RNA in faster dividing cultures implies a quadratic relationship
between dilution rate and flux into ribonucleotides.
RNA concentration
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4
Phosphorous
Carbon
Nitrogen
Leucine
Uracil
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10
p <1.75e−07
RNA abundance ug/uL cell volume per hour
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Phosphorous
Carbon
Nitrogen
Leucine
Uracil
0
0
Background
Rate of RNA synthesis
5
RNA abundance ug/uL cell volume
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Yeast must efficiently balance anabolism with nutrient availability in order to grow
optimally in diverse environments.
Previous efforts to characterize the
physiology underlying this control have focused on looking at patterns of
transcriptional and metabolite variability under 25 nutritional conditions differing
either in the nature of the limiting nutrient, or how stringent the limitation is. This
has revealed major patterns associated with nutrient invariant and nutrient
specific limitation, but given us little insight into how the relative flux through
reactions is shaped by nutrient availability and how this flux-control is
accomplished at a mechanistic level. As an attempt to address this, I will
characterize the fluxes across conditions by measuring the rate that nutrients are
absorbed and the rates that they are being polymerized to create the
macromolecules necessary for growth. From this point, the flux through all
reactions can be predicted using flux balance analysis. To compliment this direct
measurement of flux, we can use proteomics and metabolomics to evaluate
whether predicted fluxes are consistent with measured fluxes and whether
modifications of the mechanism are supported. This will allow us to determine
how flux through individual enzymes is controlled across nutrient conditions and
ultimately how flux is regulated at a systems-level.
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Dilution rate (fraction of volume turnover / hr)
The variation in flux through any reaction can be related to its
reaction mechanism, where the flux through the reaction is
described as a function of kinetic parameters, concentration of
metabolites and enzyme abundance.
Ascertaining the concentration of species is an experimental
challenge. What we will actual use is the relative concentration of
enzymes (using proteomics) and the absolute concentration of
metabolites (we currently only have relative for both) and we will
have to make assumptions about the subcellular provenance of
species, initially assuming that concentrations are uniform
regardless of compartment.
Within this framework, variation in V (found above) will be
related to variation in intracellular concentration of substrates
and other competitive species, and Vmax related changes in the
level of an enyzme or its activity.
For most reactions, published mechanisms are available, as well
as binding affinities for a fair number of metabolites, but these
affinities are inconsistent and we may be missing some molecules
(or covalent modifications) that are necessary to adequately
describe flux as a function of species and parameters. To
address these concerns we need to compare predicted to true
flux across a set of models characterized by the set of species,
the nature of their interaction and the kinetic parameters involved
in a reaction.
To describe this relationship exactly, we need precise
measurements of the intracellular concentration of all relevant
species, to know the kinetic nature of their interaction and to
know which species are sufficient to describe the mechanism.
Metabolomics
For a set of reactions where the flux is proportional to the rate of
RNA synthesis, this approach reveals that for some reactions the
established mechanisms are pretty good, while for others the
predicted flux is inconsistent with the observed flux.
Dihydroorotase (URA4) flux
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Carbon limited
Nitrogen limited
Phosphorous limited
Leucine limited
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Carbon limited
Nitrogen limited
Phosphorous limited
Leucine limited
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0.2
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0.2
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relative flux
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relative flux
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1.2
1.4
Dihydroorotate dehydrogenase (URA1) flux
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2
measured flux
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4
1
Recap
Metabolism-wide strategy
To determine whether modifications to reaction mechanisms should
be sought or whether predictions of flux from the abundance of
established metabolites and enzymes are consistent with the carried
flux, the best linear relationship between v and vpred can be sought.
This can be found by minimizing the coefficient of variation of v/vpred
over a set of parameters Θ.
Boer 2010
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Explaining flux variation
A simplified case
Brauer 2008
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Dilution rate (fraction of volume turnover / hr)
In order for microbes to have prospered, they have evolved regulatory
mechanisms that allow them to adjust their metabolic strategy under varying
conditions. On their quest for division, two of the largest challenges that they
face are how to attain a relatively invariant quantity of macromolecules from
diverse nutrient sources, where some resources may be abundant and others
scarce; and how to chemically translate increased nutrient availability into faster
production of macromolecules. Looking at nutrient conditions that differ in the
nature of the limiting nutrient and how much is available, the physiology
underlying these central regulatory questions can be investigated. This has
previously been done at the transcriptional and metabolomic level. Across these
conditions there is both nutrient independent and nutrient-specific variation in flux
associated with changes in the rate of division. This suggests that the control of
flux across these conditions could be accomplished either through hierarchical
control of flux, where variation in the flux through a reaction is related to the level
or activity of the enzyme or through metabolic regulation where flux is controlled
by substrate occupancy.
Transcriptomics
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2
measured flux
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4
Scaling the simplified case up to a metabolism-wide strategy will be
conceptually similar. Optimization will still be carried out on a perreaction basis, but the desire to evaluate different classes of reaction
mechanisms will require the use of Bayesian statistics and more
powerful optimization tools, namely genetic algorithms.
The
likelihood of each model, characterized by a set of parameters, can
be evaluated as the product of the densities of vi evaluated at a
mean vi_pred. This likelihood is then combined with the prior
probability of the values of parameters to create a bayes factor.
These bayes factors can then be viewed as the fitness of a model
and this fitness can be optimized through the process of parameter
mutation and selection.
• There are large differences in patterns
of flux across nutrient conditions.
These are primarily related to the
growth rate, but there likely limitingnutrient specific differences as well.
• These patterns are linked at the level of
reaction mechanisms to variation in
metabolites and enzymes
• Understanding the source of variation
driving flux through individual reactions
will allow us to study global regulation
and flux control.
Acknowledgements
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Josh Rabinowitz
Tomer Shlomi
John Storey
Keyur Desai
David Botstein
Pat Gibney
Sandy Silverman
Jonathan Goya
David Perlman
P50 GM071508