Regulatory On/Off Minimization Of Metabolic Flux Changes Following Genetic Perturbations

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Regulatory On/Off Minimization Of Metabolic Flux
Changes Following Genetic Perturbations
Tomer Shlomi School of Computer Science, Tel-Aviv
University, Tel-Aviv, Israel Omer Berkman Dept.
of Computer Science, The Academic College of
Tel-Aviv Yaffo, Tel-Aviv, Israel. The research
of this author was done while on sabbatical at
Tel Aviv University Eytan Ruppin School of
Computer Science and School of Medicine, Tel-Aviv
University, Tel-Aviv, Israel March, 2005
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Outline

• Cellular adaptation to gene knockouts
• Flux Balance Analysis (FBA)
• Minimization Of Metabolic Adjustment (MOMA)
• Regulatory On/Off Minimization (ROOM)
• Implementation issues
• Knockout phenotype predictions
• Intracellular fluxes in E. coli
• Linearity of flow
• Growth rates
• Lethality in S. cerevisiae
• Summary

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Cellular Adaptation to Genetic and Environmental
Perturbations

• Transient changes in expression levels in
  hundreds of genes (Gasch 2000, Ideker 2001)
• Convergence to expression steady-state close to
  the wild-type (Gasch 2000, Daran 2004, Braun
  2004)
• Drop in growth rates followed by a gradual
  increase (Fong 2004)

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Flux Balance Analysis (FBA)

• Finds flux distribution with maximal growth
  rate, irrespectively of the wild-types flux
  distribution

• Multiple optimal solutions exist
• Solved using Linear Programming (LP)

Max vgro, - maximize growth s.t Sv
0, - mass balance constraints vmin ? v ?
vmax - capacity constraints
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Minimization Of Metabolic Adjustment (MOMA)

• Segre, D., Vitkup, D. Church, G. (2002)
• Improves FBA flux predictions for knocked-out
  organisms
• Solved using Quadratic Programming (QP)

• Finds flux distribution with minimal Euclidian
  distance from the wild-type

Min (v-w)², - minimize Euclidian
distance s.t Sv 0, - mass balance
constraints vmin ? v ? vmax - capacity
constraints vj 0, j?G - knockout
constraints
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Regulatory On/Off Minimization (ROOM)

• Predicts the metabolic steady-state following the
  adaptation to the knockout
• Assumes the organism adapts by minimizing the set
  of regulatory changes

Boolean Regulatory Change
Boolean Flux Change

• Finds flux distribution with minimal number of
  Boolean flux changes

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ROOM Implementation

• Solved using Mixed Integer Linear Programming
  (MILP)
• Boolean variable yi

yi 1
Flux vi change from wild-type

• Min ?yi - minimize changes
• s.t
• v y ( vmax - w) ? w - distance constraints
• v y ( vmin - w) ? w - distance constraints
• Sv 0, - mass balance constraints
• vj 0, j?G - knockout constraints

• MILP is NP-Hard
• Relax Boolean constraints - solve using LP
• Relax strict constraint of proximity to
  wild-type

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Example Network
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ROOMs Implicit Growth Rate Maximization

• ROOM implicitly attempts to maintain the maximal
  possible growth rate of the wild-type organism
• A change in growth requires numerous changes in
  fluxes

M1
M2
Growth Reaction
. .
Biomass
Mn
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Intracellular Flux Measurements

• Intracellular fluxes measurements in E. coli
  central carbon metabolism
• Obtained using NMR spectroscopy in C labelling
  experiments
• 5 knockouts pyk, pgi, zwf, gnd, ppc in
  Glycolysis and Pentose Phosphate pathways
• Glucose limited and Ammonia limited medias
• FBA wild-type predictions above 90 accuracy

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• Emmerling, M. et al. (2002), Hua, Q. et al.
  (2003), Jiao, Z et al. (2003), Peng, et. al
  (2004)

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Knockout Flux Predictions

• ROOM flux predictions are significantly more
  accurate than MOMA and FBA in 5 out of 9
  experiments

• ROOM steady-state growth rate predictions are
  significantly more accurate than MOMA

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Significant Flux Changes

• ROOM flux predictions have less significant flux
  changes than MOMA

• ROOM correctly identifies short alternative
  pathways for knocked out reactions

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Linearity of Flow

• Flow is biased in one direction in metabolic
  branch-points (Ihmels, et al, 2004)

• Quantitative score The percentage of
  branch-points that preserve linearity of flow

• ROOM and FBA achieve significantly higher
  linearity of flow scores than MOMA

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Final Growth Rates Predictions

• Growth rate measurements during adaptation to
  gene knockouts (Fong, et. al., 2004)
• ROOM and FBA provide better predictions the final
  growth rates (correlation of 0.73 vs. 0.66 for
  MOMA)
• MOMA provides better predictions for transient
  post-perturbation growth rates (correlation of
  0.83 vs. 0.77 for ROOM and FBA)

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Knockout Lethality Predictions

• FBA gene knockout predictions for S. cerevisiae
  (Famili,I. et al, 2003)
• MOMA fails to identify short alternative pathways

• ROOM and FBA lethality predictions are
  significantly more accurate than MOMA predictions

ROOM
MOMA
FBA
29
31
26
Lethal
96
72
96
Non-Lethal
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Summary

• ROOM predicts metabolic steady-state after
  adaptation
• Provides accurate flux predictions
• Preserved flux linearity
• Finds alternative pathways
• Predicts steady-state growth rates

• MOMA predicts transient metabolic states
  following the knockout
• Provides more accurate transient growth rates

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Possible Extensions

• Uniform cost for changes in flux through all
  reactions in associated with a gene
• Uniform cost for change through all genes in the
  same operon
• Incorporate ROOM in a combined regulatory/metaboli
  c model (Covert el. al., 2004).
• Explore alternative metrics

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• Thank you for listening
• Questions