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Prof. Yechiam Yemini (YY)

Computer Science DepartmentColumbia University

Chapter 9: Metabolic Networks

9.2 Analysis & Applications

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Overview

Extreme pathways analysisPerturbations of metabolic networksRe-engineering metabolic networks

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Summary Of Theory A state of a metabolic net is described by a flux vector

Flux vectors constitute a convex cone of feasible states F={v| Sv=0, α≤v≤β} This cone F describes the feasible modes available to the network

The flux cone is spanned by its extreme pathways (fluxes) Extreme pathways are subnets corresponding to extreme rays of F A flux vector is a weighted sum of extreme fluxes

Metabolic nets select fluxes to optimize linear objectives Objective = weighted flux (e.g., biomass growth) Optimal fluxes constitute a face of the cone F W

Z=WTV

Z = distance

Extreme pathway

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Extreme PathwaysAnalysis

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Example

system boundary1 10

87

5 9

211

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1-100-10000-1100R5P

-10-200000-11020GAP

-200-101-1002001F6P

00100-110000-10FP2

210000010-2-100Ru5P

13121110987654321

biochemical species

reactionreaction I/O

Legend

Based on M. Imielinski 2007; www.seas.upenn.edu/~agung/ese680files/imielinski.ppt

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Example

system boundary1 10

87

5 9

211

123

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1-100-10000-1100R5P

-10-200000-11020GAP

-200-101-1002001F6P

00100-110000-10FP2

210000010-2-100Ru5P

13121110987654321

Extreme pathway 4

Extreme pathway 3

Extreme pathway 2

Extreme pathway 1

0015010602200

0100000000100

0000100100100

0000001020011

13121110987654321

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Example

system boundary1 10

87

5 9

211

123

4

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1-100-10000-1100R5P

-10-200000-11020GAP

-200-101-1002001F6P

00100-110000-10FP2

210000010-2-100Ru5P

13121110987654321

Extreme pathway 4

Extreme pathway 3

Extreme pathway 2

Extreme pathway 1

0015010602200

0100000000100

0000100100100

0000001020011

13121110987654321

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Example

system boundary1 10

87

5 9

211

123

4

13

6

1-100-10000-1100R5P

-10-200000-11020GAP

-200-101-1002001F6P

00100-110000-10FP2

210000010-2-100Ru5P

13121110987654321

Extreme pathway 4

Extreme pathway 3

Extreme pathway 2

Extreme pathway 1

0015010602200

0100000000100

0000100100100

0000001020011

13121110987654321

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Example

system boundary1 10

87

5 9

211

123

4

13

6

1-100-10000-1100R5P

-10-200000-11020GAP

-200-101-1002001F6P

00100-110000-10FP2

210000010-2-100Ru5P

13121110987654321

Extreme pathway 4

Extreme pathway 3

Extreme pathway 2

Extreme pathway 1

0015010602200

0100000000100

0000100100100

0000001020011

13121110987654321

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Input Control With Extreme Pathways

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Input Control of Flux Distribution

Case 1:Only A available

Case 2:Only A availablev6 not functional

Case 3:Only C available

A B C

D

E0.75 0.50

0.25

0.25A B C

D

E0.17

0.33

0.17

A B C

D

E

0.25

0.25 0.50

0

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p1 p2 p3 p4 p5 p60

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p1 p2 p3 p4 p5 p60

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p1 p2 p3 p4 p5 p6

Objective Z=0.25 Objective Z=0.17 Objective Z=0.25

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Extreme Modes Describe Operational Phases

Recall the E.coli FBA Consider the projections of extreme pathways onto the input space The regions bounded by EPs represent operational phases

A phase represents a subnet selected to process given inputs (optimally?) E.g., diauxic shift Subnet = weighted sum of respective EPs A “phase” is defined by enzymes activating subnets (EPs) The regulatory network selects a phase based on environmental input

Oxy

gen

upta

ke ra

te

Succinate uptake rate

Phase

II

Phase III

Phase IV

Phas

e I

Infeasible

Infe

asib

le

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Input Control of Yeast Metabolism

Challenge: genome-scale analysis

Use phenotypical phases to simplifyanalysis

Consider lines of optimality (LO) Growth, ethanol production…

Duare et al. BMC Genomics 2004 5:63

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Growth Control Through Oxygen Supply

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Input Control of Growth Modes

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Perturbations of MetabolicNetworks

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In Silico Perturbations of Network Key idea: investigate impact of change on flux

Metabolic network can adapt to changesChanges: availability of nutrients and enzymes

Can in-silico models explain adaptation?Change in inputs: limit the nutrients provided by mediumChange in network: delete reactions (genes)

minutes

grow

th

generations

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system boundary1 10

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Extreme pathway 4

Extreme pathway 3

Extreme pathway 2

Extreme pathway 1

0015010602200

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In-Silico Gene Knock-Out

Knock out the enzyme (gene) of reaction 4 Gene enzyme reaction

EPs using reaction 4 are lost (e.g., EP 4) Resulting in loss of dependent subnets and fluxes (e.g., reaction 10)

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Analysis of E.Coli

Phase analysis of E.coli metabolismConsider impact of deleting genes on optimal growth

Edwards et al. BMC Bioinformatics 2000 1:1 doi:10.1186/1471-2105-1-1

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In-Silico Gene Knock-Out

Impact of gene deletions on growth is computed

The Escherichia coli MG1655 in silico metabolic genotype..J. S. Edwards, and B. O. Palsson PNAS 2000;97;5528-5533

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In Silico Gene Knock-Out

86% predictions What is the source of errors?

FBA ignores regulatory changes

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Covert & Palsson J. Bio Chem 2002Incorporating Regulatory Interactions Model

Key idea: consider quasi-static Boolean regulationCompute flux distribution for a regulatory state

Covert & Palsson. J. of Bio Chem, vol 277 (31) 2002

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Metabolic/Regulatory Interactions in E.Coli

Extend FBA with regulatory model of gene expressionUse simulation to study quasi-static dynamics

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Mutants Analysis

gene

Input metabolite (glucose, glycerol, succinate…)

Growth predictions:In-vivo/FBA/rFBA

FBA has some errorsBut rFBA gets 100% hits

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Quasi-Static Dynamic Interactions

Diauxic Shift

Regulatory state

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Minimization of Metabolic Adjustment (MOMA)

FBA models result of genedeletion as re-optimizingNetwork handles deletion by

computing new optimal flux

MOMA considers an alternatemodel for handling deletionsNetwork tries to operate “close” to

the wild-type flux “Close” = minimize Euclidian

distance from wild-type flux

Leads to a quadratic optimization

Segre et al PNAS 2002

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Regulatory On-Off Minimization (ROOM) An alternate model

Assume post-deletion flux is trying toapproximate wild-type flux

Measure of “closeness” is # ofregulatory changes

Shlomi et al PNAS 2005

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ROOM MILP ROOM Optimization

Mixed Integer Linear Programming (MILP) This is NP HardRelax constraints solve LP to approximate solution

yi = 1 Flux vi change from wild-type

Min ∑yi - minimize changess.tv – y ( vmax - w) ≤ w - distance constraintsv – y ( vmin - w) ≥ w - distance constraintsS·v = 0, - mass balance constraintsvj = 0, j∈G - knockout constraints

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Example: FBA/MOMA/ROOM

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ROOM>FBA≥MOMA Intracellular fluxes measured by tracing 13CKnock outs: pyk, pgi, zwf, ppcFBA gets over 90% wild-type predictions

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Metabolic NetworksRe-Engineered

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Optimizing Lactate ProductionKey idea: knock-out genes to optimize lactate flux

Compute optimal genes to max lactate flux (Optknock)

Evolve mutants in media with inputs to optimize production

Fong, S.S. et al, Biotechnology and Bioengineering, 91(5):643-648 (2005).

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Lactate Production

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Adaptation Effects

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Regulatory Adaptation

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Concluding Notes

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ConclusionsMetabolic net analysis can be reduced to convex analysis

Genome scale analysis can be simplified throughBy representing problems in terms of extreme pathwaysBy considering input-modes in terms of phenotypical phase plan

Metabolic network can be controlledBy controlling input supply and using adaptive evolution of netBy knocking-out selective genes to optimize flux of interest

Theoretical predictions provide good approximations

Grand challenge: integrate with regulatory & signaling nets