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Metabolic_networks_lecture2 (1).ppt
1. Constraint-Based Modeling of Metabolic Networks
Tomer Shlomi
School of Computer Science, Tel-Aviv University, Tel-Aviv, Israel
March, 2008
2. 2
Outline
Introduction to metabolism and metabolic networks
Constraints-based modeling
Mathematical formulation and methods
Linear programming
Our research
Integrated metabolic/regulatory networks
Human tissue-specific metabolic behavior
3. 3
Metabolism
Metabolism is the totality of all the chemical
reactions that operate in a living organism.
Catabolic reactions
Breakdown and produce energy
Anabolic reactions
Use energy and build up essential
cell components
4. 4
It’s the essence of life..
Tremendous importance in Medicine:
In born errors of metabolism cause acute symptoms and even
death on early age
Metabolic diseases (obesity, diabetics) are major sources of
morbidity and mortality
Metabolic enzymes and their regulators gradually becoming viable
drug targets
Bioengineering:
Efficient production of biological products
The best understood cellular network
Why Study Metabolism?
5. 5
Metabolites and Biochemical
Reactions
Metabolite: an organic substance, e.g. glucose, oxygen
Biochemical reaction: the process in which two or more molecules
(reactants) interact, usually with the help of an enzyme, and produce
a product
Most of the reactions are catalyzed by enzymes (proteins)
Glucose + ATP
Glucokinase
Glucose-6-Phosphate + ADP
6. 6
Modeling the Network Function:
Kinetic Models
Dynamics of metabolic behavior over time
Metabolite concentrations
Enzyme concentrations
Enzyme activity rate – depends on enzyme concentrations and
metabolite concentrations
Solved using a set of differential equations
Impossible to model large-scale networks
Requires specific enzyme rates data
Too complicated
7. 7
Modeling the Network Function
Accuracy
Scale
Kinetic models
Approx. kinetics
• Dynamical systems
• Requires kinetic constants (mostly unknown)
Topological
analysis
• Graph theory
• Structural network properties: degree
distribution, centrality, clusters, etc’
Constraint-based
models
• Optimization theory
• Constrained space of possible, steady-
state network behaviors
• Probabilistic models, discrete models, etc’
Conventional
functional models
Metabolic
PPI
8. 8
Constraint Based Modeling
Provides a steady-state description of metabolic behavior
A single, constant flux rate for each reaction
Ignores metabolite concentrations
Independent of enzyme activity rates
Assume a set of constraints on reaction fluxes
Genome scale models
Flux rate:
μ-mol / (mg * h)
9. 9
Constraint Based Modeling
Under the constraints:
Mass balance: metabolite production and consumption rates are
equal
Thermodynamic: irreversibility of reactions
Enzymatic capacity: bounds on enzyme rates
Availability of nutrients
Find a steady-state flux distribution through all
biochemical reactions
10. 10
Additional Constraints
Transcriptional regulatory constraints (Covert, et. al., 2002)
Boolean representation of regulatory network
Energy balance analysis (Beard, et. al., 2002)
Loops are not feasible according to thermodynamic principles
Reaction directionality
Depending on metabolite concentrations
FBA solution space
Meaningful
solutions
14. 14
Phenotype Predictions: Flux
Predictions
Predict metabolic fluxes following gene knockouts
Search for short alternative pathways to adapt for gene knockouts
(Regulatory On/Off Minimization)
16. 16
Strain design: maximizing
metabolite production rate
Identify a set of gene whose knockout increases the production rate
of some metabolite
The knockout of reaction v3 increases the production rate of
metabolite F
18. 18
Mathematical Representation
Stoichiometric matrix – network topology with stoichiometry of
biochemical reactions
Mass balance
S·v = 0
Subspace of R
Thermodynamic
vi > 0
Convex cone
Capacity
vi < vmax
Bounded convex cone
Glucose + ATP
Glucokinase
Glucose-6-Phosphate + ADP
Glucose -1
ATP -1
G-6-P +1
ADP +1
Glucokinase
n
19. 19
Determination of Likely Physiological
States
How to identify plausible physiological states?
Optimization methods
Maximal biomass production rate
Minimal ATP production rate
Minimal nutrient uptake rate
Exploring the solution space
Extreme pathways
Elementary modes
20. 20
Biomass Production Optimization
Metabolic demands of precursors and cofactors required for 1g of
biomass of E. coli
Classes of macromolecules:
Amino Acids, Carbohydrates
Ribonucleotides, Deoxyribonucleotides
Lipids, Phospholipids
Sterol, Fatty acids
These precursors are removed from the
metabolic network in the corresponding ratios
We define a growth reaction
Z = 41.2570 VATP - 3.547VNADH+18.225VNADPH + ….
21. 21
Flux Balance Analysis (FBA)
Biomass production rate represents growth rate
Solved using Linear Programming (LP)
Max vgro, - maximize growth
s.t
S∙v = 0, - mass balance constraints
vmin v vmax - capacity constraints
Finds flux distribution with maximal growth rate
Fell, et al (1986), Varma and Palsson (1993)
30. 30
Linear Programming Algorithms
Simplex algorithm
Travels through polytope vertices in the optimization direction
Guaranteed to find an optimial solution
Exponential running time in worse case
Used in practice (takes less than a second)
Interior point
Worse case running time is polynomial
31. 31
Exploring a Convex Solution Space
Linear programming may result in multiple alternative solutions
Alternative solutions represent different possible metabolic
behaviors (through alternative pathways)
The solution space can be explored by various sampling and
optimization methods
32. 32
Topological Methods
Network based pathways:
Extreme Pathways (Schilling, et. al., 1999)
Elementary Flux Modes (Schuster, el. al., 1999)
Decomposing flux distribution into extreme pathways
Extreme pathways defining phenotypic phase planes
Uniform random sampling
Not biased by a statement of an objective
33. 33
Extreme Pathways and
Elementary Flux Modes
Unique set of vectors that spans a solution space
Consists of minimum number of reactions
Extreme Pathways are systematically independent
(convex basis vectors)
35. 35
Regulatory Constraints
FBA predicts that both Galactose and
Glucose are simultaneously
consumed when present in the
media
When Glucose is present, the
concentration of active CRP
decreases and represses the
expression of the GAL system
Boolean logic formulation:
GalK = Crp and NOT(GalR or GalS)
Glucose-6-p
Galactose Glucose
Fructose-6-p
Galactose-1-p
Glucose-1-p
galK
galT
CRP
36. 36
Integrated Metabolic/Regulatory Models
(Boolean vector)
Genome-scale integrated model for E. coli (Covert 2004)
1010 genes (104 TFs, 906 genes)
817 proteins
1083 reactions
Regulatory
state
Metabolic
state
37. 37
Research Objectives
Develop a method that finds regulatory/metabolic steady-state
solutions and characterizes the space of possible solutions in a
large-scale model
Study the expression and metabolic activity profiles of metabolic
genes in E. coli under multiple environments
Quantify the the extent to which different levels of metabolic and
transcriptional regulatory constraints determine metabolic behavior
Identify genes whose expression pattern is not optimally tuned for
cellular flux demand
38. 38
The Steady-state Regulatory FBA
Method
SR-FBA is an optimization method that finds a consistent pair of
metabolic and regulatory steady-states
Based on Mixed Integer Linear Programming
Formulate the inter-dependency between the metabolic and regulatory
state using linear equations
Regulatory
state
Metabolic
state
v
v1
v2
v3
…
g
0
1
1
…
g1 = g2 AND NOT (g3)
g3 = NOT g4
…
S·v = 0
vmin < v < vmax
Stoichiometric
matrix
39. 39
SR-FBA: Regulation → Metabolism
The activity of each reaction depends on the presence specific catalyzing
enzymes
For each reaction define a Boolean variable ri specifying whether the
reaction can be catalyzed by enzymes available from the expressed genes
Formulate the relation between the Boolean variable ri and the flux through
reaction i
Met1 Met3
Met2
Gene2
Gene1 Gene3
Protein2 Protein3
Enzyme1
Enzyme
complex2
AND
OR
i
i
i
i r
v
)
1
(
i
i
i
i r
v
)
1
(
)
0
(
i
r
i
i
i v
if then
else
0
i
v
r1
r1 = g1 OR (g2 AND g3)
g1 g2 g3
40. 40
SR-FBA: Metabolism → Regulation
The presence of certain metabolites activates/represses the activity of
specific TFs
For each such metabolite we define a Boolean variable mj specifying
whether it is actively synthesized, which is used to formulate TF regulation
equations
Me1
Met2 Met4
Met3
TF2 TF3
TF1
TF2 = NOT(TF1) AND (MET3 OR TF3)
)
0
(
i
v
if then 1
j
m
0
j
m
else
i
i
j v
m )
(
i
i
i
j v
m
)
(
mj
41. 41
Basic Concepts:
Gene Expression and Activity
Genes are characterized by:
Expression state – A gene can be expressed, not expressed.
Metabolic activity state – Enzyme coding gene can be active, not
active (i.e., carrying non-zero metabolic flux)
The expression and activity states are determined by considering the
entire space of possible steady-state solutions:
Adapt Flux Variability Analysis (Mahadevan 2003) for steady-state
metabolic/regulatory solutions
Genes may have undetermined expression or activity states –
referred to as “potentially expressed” or “potentially active” states
Activity
Expression
-
√
TF
√
√
Regulated gene
√
-
Non-regulated gene
42. 42
Results: Validation of Expression
and Flux Predictions
Prediction of expression state changes between aerobic and
anaerobic conditions are in agreement with experimental data (p-
value = 10-300)
Prediction of metabolic flux values in glucose medium are
significantly correlated with measurements via NMR spectroscopy
(spearman correlation 0.942)
43. 43
Gene Expression and Activity
across Media
SR-FBA was applied on 103 aerobic and anaerobic growth media
Inter-media variability - undetermined expression or activity state in a given
media
Intra-media variability - variable expression or activity states across media
A very small fraction of genes show intra-media variability in expression
A relatively high fraction of genes show intra-media variability in flux activity
Gene expression is likely to be more strongly coupled with environmental
condition than reaction’s flux activity
44. 44
The Functional Effects of
Regulation on Metabolism
Metabolic constraints determine the activity of 45-51% of the genes
depending of growth media (covering 57% of all genes)
The integrated model determines the activity of additional 13-20% of
the genes (covering 36% of all genes)
13-17% are directly regulated (via a TF)
2-3% are indirectly regulated
The activity of the remaining
30% of the genes is undetermined
45. 45
Redundant Expression of Metabolic
Genes
Previous works have shown only a moderate correlation between
expression and metabolic flux (Daran, 2003)
How does regulatory constraints match these flux activity states?
An active gene must be expressed
A non-active gene may “redundantly expressed”
36 genes are redundantly expressed in at least one medium
46. 46
Validating Redundantly Expressed
Genes
Several transporter affected by Crp are predicted to be redundantly
expressed in media lacking glucose
Fatty acid degradation pathway is predicted to be redundantly
expressed in many aerobic conditions without glycerol
We find that 12 genes that are predicted to be redundantly
expressed in a certain media have significantly high expression in
these media compared to media in which they are predicted to be
non-expressed
47. 47
SR-FBA Summary
We developed a method that finds regulatory/metabolic steady-state
solutions and characterizes the space of possible solutions in a large-scale
model
We quantified the extent to which different levels of constraints determined
metabolic behavior
45-51% of the genes - metabolic constraints
13-20% of the genes - regulatory constraints
We identified 36 genes that are “redundantly expressed”, i.e., expressed
even though the fluxes of their associated reactions are zero
SR-FBA enables one to address a host of new questions concerning the
interplay between regulation and metabolism
SR-FBA code is available via WEB: http://www.cs.tau.ac.il/~shlomito/SR-FBA