Download 3. Optimization methods

Biological Network Analysis:
Metabolic Optimization Methods
Tomer Shlomi
Winter 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
min c T x
s.t.
l  Ax  b
 x
CBM Example (I)
CBM Example (II)
CBM Example (III)
Flux Balance Analysis
• Searches for a steady-state flux distribution v:
S∙v=0
0
 
0
0
 
• Satisfying thermodynamic and capacity constraints:
vmin≤v ≤vmax
• With maximal growth rate
Max vbiomass
Lecture Outline
1. Growth rate predictions
a.
Phenotypic Phase Plane (PPP) analysis
2. Gene knockout lethality predictions
a.
b.
c.
FBA
Minimization of Metabolic Adjustment (MOMA)
Regulatory On/Off Minimization (ROOM)
3. Predicting knockout strategy for metabolic production
a.
b.
OptKnock
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:
Max vbiomass
S∙v=0
vmin≤v ≤vmax
• 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)
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.)
•Region 3- the uptake of additional succinate has
a negative effect. Cellular resources are required to
eliminate excessive succinate.
Growth rate
Observations:
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
The experimentally
determined growth rate were
on the line of optimality of
the PPP !
Ibarra et al., Nature 2002
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
Why?
Day 1-40 – evolution toward
optimal growth
Day 40 –optimal growth
Day 60 –optimal growth (no
change)
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
Gene knockout lethality:
Resolving Discrepancies (I)
2. Gene essentiality prediction
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,
s.t
S∙v = 0,
vmin  v  vmax
vj = 0, jG
- minimize Euclidian distance
- mass balance constraints
- capacity constraints
- 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
byp
A
B
C
cof
E
cof
byp
D
Wild-type solution
Knockout solution
Regulatory On/Off
Minimization (ROOM) (II)
• 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.
Min yi
s.t
v – y ( vmax - w)  w
v – y ( vmin - w)  w
S∙v = 0,
vj = 0, jG
- minimize changes
- distance constraints
- distance constraints
- mass balance constraints
- knockout constraints
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
13
• 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
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
Vanillin
The major compound in Vanilla
Bioengineering Objective:
Produce Vanillin
Bacteria Objective:
Grow Fast
Bioengineering Objective
Produce 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 grow
Removed
reactions
have zero
flux
The max number
of reactions to
remove
Succinate Production Strains
OptStrain
• An integrated framework for redesigning
microbial production systems
Step 1: Creation of universal reactions DB
Step 2: Compute maximal theoretical
metabolite production yield
Step 3: Identifying the minimal number of
required to be added to an organism to
achieve 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 reactions
are 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 5keto-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.