Biological Network Analysis:Metabolic Optimization

Methods

Tomer ShlomiWinter 2008

Linear Programming• c, l, A, b, α, β are parameters• Problem may be either feasible or infeasible• If the problem has an unique optimal value:

– It may either have a single optimal solution– Or a space of optimal solutions

• Alternatively, the problem may be unbounded

x

bAxl

ts

xcT

..

min

CBM Example (I)

CBM Example (II)

CBM Example (III)

Flux Balance Analysis

0

0

0

• Searches for a steady-state flux distribution v:

• Satisfying thermodynamic and capacity constraints:

S∙v=0

vmin≤v ≤vmax

• With maximal growth rate

Max vbiomass

Lecture Outline1. Growth rate predictions

a. Phenotypic Phase Plane (PPP) analysis

2. Gene knockout lethality predictionsa. FBAb. Minimization of Metabolic Adjustment (MOMA)c. Regulatory On/Off Minimization (ROOM)

3. Predicting knockout strategy for metabolic productiona. OptKnockb. OptStrain

4. Gene function prediction

1. Growth rate predictions

Flux Balance Analysis (reminder)

• Searches for a steady-state flux distribution v with maximal growth rate:

S∙v=0vmin≤v ≤vmax

Max vbiomass

• Requires bounds on metabolite uptake rates (b1)

Phenotype Phase Planes (PPP) (I)X axis – Succinate uptake rate

Y axis – Oxygene uptake rate

Z axis - Growth rate (maximal value of the objective function as function of succinate and oxygen uptake)

Line of optimality

Phenotype Phase Planes (PPP) (II)Observations:

Schilling 2001

•Metabolic network is unable to utilize succinate as sole carbon source in anaerobic conditinos.

•Region 1: oxygen excess – this region is wasteful – (less carbon is available for biomass production since it is oxidized to eliminate the excess oxygen.)

Succinate

Oxygene

Gro

wth

rate

•Region 3- the uptake of additional succinate has a negative effect. Cellular resources are required to eliminate excessive succinate.

Does E. coli behave according to Phenotype

Phase Planes? (I)

• E. coli was grown with malate as sole carbon source.

• A range of substrate concentrations and temperatures were used in order to vary the malate uptake rate (MUR).

• Oxygen uptake rate (OUR) and growth rate were measured

Does E. coli behave according to Phenotype

Phase Planes? (II)Malate/oxygen PPP

Ibarra et al., Nature 2002

The experimentally determined growth rate

were on the line of optimality of the PPP !

Does E. coli behave according to Phenotype Phase Planes?

(III)Same experiments were made using glycerol as sole carbon source

Day 0 – Sub optimal growth

Day 1-40 – evolution toward optimal growth

Day 40 –optimal growth

Day 60 –optimal growth (no change)

Why?

2. Gene Knockout Lethality

Predicting Knockout Lethality (I)

• A gene knockout is simulated by setting the flux through the corresponding reaction to zero

• The corresponding reactions are identified by evaluating the Boolean gene-to-reaction mapping in the model

Predicting Knockout Lethality (II)

• A gene is predicted essential if it’s knockout yields a significant drop in the maximal possible growth rate

• v1 is essential for growth • v6 is not essential for growth

Gene knockout lethality:E. coli in glycerol minimal

media

• In total, 819 out of the 896 mutants (91%) showed growth behaviors in glycerol minimal medium in agreement with computational predictions

• 69% correct prediction out of the experimental essential genes

2. Gene essentiality prediction

Gene knockout lethality:Resolving Discrepancies (I)

Gene knockout lethality:Resolving Discrepancies (II)

Gene knockout lethality:Resolving Discrepancies (II)

3. MOMA and ROOM

Minimization of Metabolic Adjustment (MOMA) (I)

• FBA assumes optimality of growth for wild type – evolution drives the growth rate towards optimality

• This assumption is not necessarily correct following a gene knockout!

• What other objective can capture the • biological essence of these mutations?

(hint – the title of this slide)

Minimization of Metabolic Adjustment (MOMA) (II)

• Assumption: following the knockout, the mutant remains as close as possible to the wild-type strain

• The flux distribution of mutant should also satisfy all constraints as in FBA

Minimization of Metabolic Adjustment (MOMA) (III)

Formally:w – the wild-type optimal growth vector (obtained via FBA).v – a vector in mutant flux space.Find Vm which minimizes the Euclidian distance to Vwt :

Min (w -v)², - minimize Euclidian distance

s.t

S∙v = 0, - mass balance constraints

vmin v vmax - capacity constraints

vj = 0, jG - knockout constraints

Solved using Quadratic Programming (QP)

w

v

Validating MOMA: Gene essentiality prediction

Validating MOMA: Experimental fluxes

Regulatory On/Off Minimization (ROOM) (I)

• Assumption: The organism adapts by minimizing the set of flux changes (via the regulatory system)

• Search for a feasible flux distribution with minimal number of changes from the wild-type

A B C

D

E

byp

cof

byp

cof

Wild-type solution

Knockout solution

Regulatory On/Off Minimization (ROOM) (II)

Min yi - minimize changes

s.t

v – y ( vmax - w) w - distance constraints

v – y ( vmin - w) w - distance constraints

S∙v = 0, - mass balance constraints

vj = 0, jG - knockout constraints

• Integer variables are required to track the ‘number of changes in flux’ from the wild-type

• Use Boolean auxiliary variables y to reflect changes in flux between the wild-type and mutant

• yi=0 if and only if vi = wi

• Formulate a MILP problem to find a pair of v and y with a minimal sum of yi’s.

Validating ROOM: Alternative pathways

• ROOM identifies short alternative pathways to re-route metabolic flux following a gene knockout, in accordance with experimental data

Validating ROOM: Experimental fluxes (I)

• Intracellular fluxes measurements in E. coli central carbon metabolism

• Obtained using NMR spectroscopy in C labelling experiments

• Knockouts: pyk, pgi, zwf, and gnd in Glycolysis and Pentose Phosphate pathways

• Glucose limited and Ammonia limited medias

• FBA wild-type predictions above 90% accuracy

13

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

(*) Based on a figure from Jiao, Z., et al.

Validating ROOM: Experimental fluxes (II)

• ROOM flux predictions are significantly more accurate than MOMA and FBA in 4 out of 8 experiments• ROOM growth rate predictions are significantly more accurate than MOMA

4. Metabolite Production

Constraint-based Modeling:Biotechnological Applications• Design bacteria that produces chemicals of interest

Bacteria Objective: Grow Fast

VanillinThe major compound in Vanilla

Bioengineering Objective:Produce Vanillin

Bioengineering ObjectiveProduce Vanillin

OptKnock• Designing microbial organisms for efficient

production of metabolites• Finds reactions whose removal increases the

production of metabolite of interest

OptKnock: Optimization problem (I)

• A nested (bi-level) optimization problem is needed

OptKnock: Optimization problem (I)

• A nested (bi-level) optimization problem is needed

Reactions to

remove

Cells have to

growRemove

d reactions have

zero fluxThe max

number of reactions to

remove

Succinate Production Strains

OptStrain• An integrated framework for redesigning microbial production systemsStep 1: Creation of universal reactions DBStep 2: Compute maximal theoretical metabolite production yield Step 3: Identifying the minimal number of required to be added to an organism toachieve the maximal production yield.Step 4: Adding the identified reactions and finding gene deletions that ensure metabolite secretion (OptKnock)

OptStrain: Step 1

• Creation of universal reactions DB• Download set of known reactions from KEGG

(Kyoto Encyclopedia of Genes and Genomes)• Validate reaction data consistency – remove

unbalanced reaction• Define a universal stoichiometric matrix S.

OptStrain: Step 2

• Determination of maximal theoretical yield of a metabolite of interest

• Yield – metabolite production rate per unit of substrate uptake

• Use LP to find the maximal yield for different substrates, denoted R

OptStrain: Step 3• Identification of minimum number of non-

native reactions for a host organism

• MILP formulation – yi represented whether reaction i should be added to the organism

OptStrain: Step 4

• Incorporating the non-native reactions into the host organism’s stoichiometric model

• Eliminate genes such that biomass production is coupled with the production of the metabolite of interest

• OptKnock

Case study: Hydrogen production

• The highest hydrogen yield (0.126 g/g substrate consumed) is obtained for methanol

Case study: Hydrogen production (I)

• Testing E. coli on glucose media• Step 3 reveals that new reactionsare needed for E. coli on glucose

Case study: Hydrogen production (II)

• C. acetobutylicum - the "Weizmann Organism", after Chaim Weizmann, who in 1916 helped discover how C. acetobutylicum culture could be used to produce acetone, butanol, and ethanol from starch

• The knockout of 2 reactions tightly couple biomass production and metabolite hydrogen secretion

Case study: Vanillin production (I)

• Vanillin is an important flavor and aroma molecule (found in vanilla pods)

• Maximal theoretical production rate: 0.63 (g/g glucose)• E. coli needs 3 new reactions to achieve this vanillin

yield• Previous bioengineering experiments have already

involved the extraction of these 3 reactions from Neurospora crassa and their addition to E. coli

• However, the resulting vanillin production rate was only 0.15

Case study: Vanillin production (II)

• OptStrain predicts knockout sets that provide a vanillin yield of 0.57 (g vanillin/g glucose) in E. coli

• This is close to the maximal theoretical production rate

4. Gene function prediction

Refining Genome Annotation

• A substantial fraction of the genes have unknown function• An integrated computational/experimental approach for

predicting gene function:– Identify discrepancies between model predictions and

growth phenotyping in E. coli– An algorithm then identifies missing reactions whose

addition could reconcile model predictions and experimental observations

– Search for ORFs that might be responsible for these missing activities based on literature searches, sequence-homology, etc

– experimental verification of the algorithm’s predictions via growth phenotypes of single-deletion strains

Refining Genome Annotation

Refining E.coli’s Annotation

• Identify 50 minimal medium conditions in which the model cannot explain the observed (experimental) growth

• Identify reactions whose addition enables growth for 26 of the environemnts

• 6 cases are investigated in depth

New Transporter Genes (I)

• Growth on propionate and 5-keto-D-gluconate require the addition of relevant transporters

• Currently, such transporters are unknown• 8 potential transporters are identified via

literature searches, sequence-homology, etc• Only putP deletion showed reduced growth in

propionate• Only idnT deletion showed reduced growth in 5-

keto-D-gluconate• Both genes show increased expression level on

these media

New Transporter Genes (II)

• The algorithm found a missing reaction that secretes a byproduct in thymidine metabolism – thymine

• Experimental inspection of the growth media support this finding

• The identity of the transporter gene remained unclear

Growth on D-Malate• The algorithm finds two missing reactions:

– D-Malate transporter– Decarboxilation of D-Malate to Pyruvate

References:• Edwards JS, Ramakrishna R, Palsson BO. 2002. Characterizing the metabolic

phenotype: a phenotype phase plane analysis. Biotechnol Bioeng 77(1):27-36.• Ibarra RU, Edwards JS, Palsson BO. 2002. Escherichia coli K-12 undergoes

adaptive evolution to achieve in silico predicted optimal growth. Nature 420(6912):186-9.

• Segre D, Vitkup D, Church GM. 2002. Analysis of optimality in natural and perturbed metabolic networks. Proc Natl Acad Sci U S A 99(23):15112-7.

• Shlomi T, Berkman O, Ruppin E. 2005. Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proc Natl Acad Sci U S A 102(21):7695-700.

• Burgard AP, Pharkya P, Maranas CD. 2003. Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol Bioeng 84(6):647-57.

• Pharkya P, Burgard AP, Maranas CD. 2004. OptStrain: a computational framework for redesign of microbial production systems. Genome Res 14(11):2367-76.

• Reed JL, Patel TR, Chen KH, Joyce AR, Applebee MK, Herring CD, Bui OT, Knight EM, Fong SS, Palsson BO. 2006. Systems approach to refining genome annotation. Proc Natl Acad Sci U S A 103(46):17480-4.