The Optimal Metabolic Network Identification

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The Optimal Metabolic Network Identification

• Paula Jouhten
• Seminar on Computational Systems Biology
• 21.02.2007

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Introduction

• The capability to perform biochemical conversions
  is encoded in the genome
• Genome-scale metabolic network models
• Gene annotation information often incomplete
• Cell function is regulated on different levels
• What is the active set of reactions in an
  organism under specific conditions?

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Constraint-based models

• Genome-scale metabolic network models for
  micro-organisms (Escherichia coli, Saccharomyces
  cerevisiae,...)
• Enzyme-metabolite connectivities
• Stoichiometric models
• Reaction stoichiometry specifies the reactants
  and their molar ratiosametabolite1
  bmetabolite2 -gt cmetabolite3 dmetabolite4

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Feasible flux distributions

• Metabolic flux a rate at which material is
  processed through a reaction (mol/h), reaction
  rate
• Fluxome, flux distribution
• Stoichiometries define a feasible flux
  distribution solution space

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Additional constraints

• Additional constraints are included as linear
  equations or inequalities
• Steady state the metabolite pool sizes and the
  fluxes are constant
• Reaction capacity upper bound for a reaction
• Reaction reversibility
• Measurements

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Metabolic flux analysis

• Determination of the metabolic flux distribution
• Intracellular fluxes cannot be measured directly
• Stoichiometric model N q x m
• Input data -gt extracellular fluxes
• Steady-state assumption -gt a homogenous system of
  linear mass balance equations
• Additional constraints vi lt vmax

1 0 0 0 -1 -1 -1 0 0 00 1 0 0 1 0 0
-1 -1 00 0 0 0 0 1 0 1 0 -10 0 0 0
0 0 1 0 0 -1 N0 0 0 -1 0 0 0 0 0
10 0 -1 0 0 0 0 0 1 1
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Example network
REV v2, v8 IRR v1, v3, v4, v5, v6, v7, v9,
v10
1 0 0 0 -1 -1 -1 0 0 00 1 0 0 1 0 0
-1 -1 00 0 0 0 0 1 0 1 0 -10 0 0 0
0 0 1 0 0 -1 N0 0 0 -1 0 0 0 0 0
10 0 -1 0 0 0 0 0 1 1
Steady state Nv 0
Flux constraints Capacity Reversibility Measureme
nts
Steady state mass balance equations A v1 -v5
-v6 -v7 0B v2f - v2b v5 -v8f v8b -v9 0C
v6 v8f -v8b -v10 0...
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Underdetermined systems

• Determined system? redundant system?
• Metabolism contains cycles etc -gt the system is
  usually underdetermined
• Additional experimental constraints from
  isotopic-tracer experiments (carbon-13 labelling)
• Analysis of the feasible solution space
• Optimal solution

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Flux balance analysis (FBA)

• Solely based on a constraint-based model and
  linear optimisation
• Objective function maximising growth, ATP
  production,...
• Stoichiometry of growth macromolecular
  composition of cell biomass
• Not all organisms optimise for growth

subject to
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Stoichiometry of growth

• Macromolecular composition of a cell can be
  determined experimentally
• Macromolecular composition is dependent on the
  growth conditions
• Macromolecule compositions?
• Constituent synthesis routes dependent on the
  conditions?

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Optimal Metabolic Network Identification

• Model predictions and experimental data do not
  always agree (growth rate, fluxes)
• Errors in the model structure gaps,
  conditionally inactive or down-regulated
  reactions, incorrect reaction mechanisms
• What is the active set of reactions (the best
  agreement between the model predictions and the
  experimental data) in an organism under specific
  conditions?

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Bilevel-optimisation approach

• Inner problem solves the FBA for the particular
  networks structure
• Outer problem searches for an optimal network
  structure

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Bilevel formulation
minimisation of a weighted distance between the
observed and predicted flux distributions
Subject to
optimal flux distribution
Subject to
given the constraints and y (the set of active
reactions)
y is a binary variable
K allowed reaction deletions
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Formulation as a MILP

• Linear inner problem -gt duality theory
• Inner problem is converted to a set of equalities
  and inequalities
• Alternative optimal flux vectors
• Searching for all the different active sets of
  reactions resulting in the same prediction

where
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Application to evolved E. coli knock-out strains

• Knock-out strains with lower than optimal growth
  rates
• Transcriptional profiling
• 2-4 reaction deletions required for significant
  improvement of model predictions
• Regulation?