Transcript Modeling and Analysis of Metabolic Networks

Constraint-Based Modeling of Metabolic Networks
based on:
“Genome-scale models of microbial cells:
Evaluating the consequences of constraints”, Price, et. al (2004)
Tomer Shlomi
School of Computer Science, Tel-Aviv University, Tel-Aviv, Israel
January, 2006
Outline
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Metabolism and metabolic networks
Kinetic models vs. constraints-based modeling
Flux Balance Analysis
Exploring the solution space
Altering phenotypic potential: gene knockouts
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Cellular Metabolism
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The essence of life..
Catabolism and anabolism
The metabolic core – production of energy – anaerobic and aerobic
metabolism
Probably the best understood of all cellular networks: metabolic,
PPI, regulatory, signaling
Tremendous importance in Medicine; antibiotics, metabolic
disorders, liver disorders, heart disorders
Bioengineering; efficient production of biological products.
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Metabolites and Biochemical
Reactions
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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
Glucose + ATP
Glucokinase
Glucose-6-Phosphate + ADP
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Kinetic Models
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Dynamics of metabolic behavior over time
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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
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Requires specific enzyme rates data
Too complicated
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Constraint Based Modeling
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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)
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Constraint Based Modeling
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Find a steady-state flux distribution through all
biochemical reactions
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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
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Metabolic Networks
Genome
Annotation
Biochemistry
Cell
Physiology
Inferred
Reactions
Network Reconstruction
Metabolic Network
Analytical Methods
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Mathematical Representation
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Stoichiometric matrix – network topology with stoichiometry of
biochemical reactions
Glucokinase
Glucose + ATP
Glucokinase
Glucose-6-Phosphate + ADP
Mass balance
S·v = 0
n
Subspace of R
Glucose
ATP
-1
-1
G-6-P
ADP
+1
+1
Thermodynamic
vi > 0
Convex cone
Capacity
vi < vmax
Bounded convex cone
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Growth Medium Constraints
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Exchange reactions enable the uptake of nutrients from the media
and the secretion of waste products
Glucose
Oxygen
Lower bound
0
0
Upper bound
2.5
Inf
-Inf
0
CO2
G-Ex O-Ex Co2-Ex
Glucose
Oxygen
CO2
1
1
1
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Determination of Likely Physiological
States
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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
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Outline: Optimization Methods
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Predicting the metabolic state of a wild-type strain
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Flux Balance Analysis (FBA)
Predicting the metabolic state after a gene knockout
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Minimization Of Metabolic Adjustment
Regulatory On/Off Minimization
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Biomass Production Optimization
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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 + ….
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Biomass Composition Issues
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Varies across different organisms
Depends on the growth medium
Depends on the growth rate
The optimum does not change much with changes in composition
within a class of macromolecules
The optimum does change if the relative composition of the major
macromolecules changes
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Flux Balance Analysis (FBA)
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Finds flux distribution with maximal growth rate
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Successfully predicts:
 Growth rates
 Nutrient uptake rates
 Byproduct secretion rates
Solved using Linear Programming (LP)
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Max vgro,
s.t
S∙v = 0,
vmin  v  vmax
- maximize growth
- mass balance constraints
- capacity constraints
Fell, et al (1986), Varma and Palsson (1993)
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FBA Example (1)
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FBA Example (2)
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FBA Example (2)
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Linear Programming Basics (1)
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Linear Programming Basics (2)
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Linear Programming Basics (3)
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Linear Programming: Types of
Solutions (1)
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Linear Programming: Types of
Solutions (2)
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Linear Programming Algorithms
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Simplex
 Used in practice
 Does not guarantee polynomial running time
Interior point
 Worse case running time is polynomial
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Phenotype Predictions: Evolving
Growth Rate
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Exploring the Convex Solution
Space
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Alternative Optima
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The optimal FBA solution is not unique
One solution
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Optimal solutions
Near-optimal solutions
Basic solutions enumeration – MILP (Lee, et. al, 2000)
Flux variability analysis (Mahadevan, et. al. 2003)
Hit and run sampling (Almaas, et. al, 2004)
Uniform random sampling (Wiback, et. al, 2004)
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What Do Multiple Solutions
Represent ?
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Some of the solutions probably do not represent biologically
meaningful metabolic behaviors as there are missing constraints
Previous studies tackled this problem by:
 Incorporating additional constraints: regulatory constraints
(Covert, et. al., 2004)
 Looking for reactions for which new constraints may significantly
reduce the solution space (Wiback, et. al., 2004)
FBA solution space
Meaningful
solutions
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Interpretations of Metabolic Space
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Effect of exogenous factors – the metabolic space corresponds to
growth in a medium under various external conditions that are
beyond the model’s scope such as stress or temperature
Heterogeneity within a population - the metabolic space represents
heterogenous metabolic behaviors by individuals within a cell
population (Mahadevan, et. al., 2003, Price, et. al., 2004)
Alternative evolutionary paths – the metabolic space represents
different metabolic states attainable through different evolutionary
paths (Mahadevan, et. al., 2003, Fong, et. al., 2004)
The three interpretations are obviously not mutually exclusive
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Alternative Optima: Basic Solutions
Enumeration
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Lee, et. al, 2000
Basic solutions – metabolic states with minimal number
of non-zero fluxes
Different solutions differ in at least a single zero flux
Use Mixed Integer Linear Programming
Formulate optimization as to identify new solutions that
are different from the previous ones
Applicable only to small scale models
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Alternative Optima: Flux Variability
Analysis
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Mahadevan, et. al. 2003
Find metabolic states with extreme values of fluxes
Use linear programming to minimize and maximize the
flux through each reaction while satisfying all constraints
Max / Min vi,
s.t
S∙v = 0,
vmin  v  vmax
Vgro = Vopt
- maximize growth
- mass balance constraints
- capacity constraints
- set maximal growth rate
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Alternative Optima: Hit and Run
Sampling
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Almaas, et. al, 2004
Based on a random walk inside the solution space polytope
Choose an arbitrary solution
Iteratively make a step in a random direction
Bounce off the walls of the polytope in random directions
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Alternative Optima: Uniform
Random Sampling
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Wiback, et. al, 2004
The problem of uniform sampling a high-dimensional polytope is
NP-Hard
Find a tight parallelepiped object that binds the polytope
Randomly sample solutions from the parallelepiped
Can be used to estimate the volume of the polytope
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Topological Methods
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Not biased by a statement of an objective
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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
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Extreme Pathways and
Elementary Flux Modes
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Unique set of vectors that spans a solution space
Consists of minimum number of reactions
Extreme Pathways are systematically independent
(convex basis vectors)
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Extreme Pathways and
Elementary Flux Modes
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Inherent redundancy in metabolic networks (Price, et. al.,
2002)
Robustness to gene deletion and changes in gene
expression (Stelling, et. al., 2002)
Enzyme subsets (correlated reaction sets) in yeast
(Papin, et. al., 2002)
Design strains (Carlson, et. al., 2002)
Assign functions to genes (Forster, et. al, 2002)
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Altering Phenotypic Potential:
Gene Knockouts
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Altering Phenotypic Potential:
Gene Knockouts
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Minimization Of Metabolic Adjustment (MOMA) (Segre
et. al, 2002)
 The flux distribution after a knockout is close to the
wild-type’s state under the Euclidian norm
Regulatory On/Off Minimization (ROOM) (Shlomi et. al,
2005)
 Minimize the number of Boolean flux changes from
the wild-type’s state
w
v
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Altering Phenotypic Potential
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Explaining gene dispensability (Papp, el. al., 2004)
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Only 32% of yeast genes contribute to biomass production in
rich media
Considered one arbitrary optimal growth solution
OptKnock – Identify gene deletions that generate desired
phenotype (Burgard, et. al., 2003)
OptStrain – Identify strains which can generate desired
phenotypes by adding/deleting genes (Pharkya, el., al.,
2004)
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Modeling Gene Knockouts
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Gene knockout
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Enzyme knockout
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Reaction knockout
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Cellular Adaptation to Genetic and
Environmental Perturbations
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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)
growth
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minutes
generations
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Regulatory On/Off Minimization (ROOM)
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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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w
v
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ROOM: Implementation
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Solved using Mixed Integer Linear Programming (MILP)
Boolean variable yi
yi = 1
Min yi
s.t
v – y ( vmax - w)  w
v – y ( vmin - w)  w
S∙v = 0,
vj = 0, jG
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Flux vi change from wild-type
- minimize changes
- distance constraints
- distance constraints
- mass balance constraints
- 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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ROOM’s Implicit Growth Rate
Maximization
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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
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Growth Reaction
Biomass
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Mn
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Intracellular Flux Measurements
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Intracellular fluxes measurements in E. coli
central carbon metabolism
Obtained using NMR spectroscopy in13 C
labeling 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
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
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ROOM
steady-state growth rate predictions are
significantly more accurate than MOMA
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ROOM vs. MOMA
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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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Additional Constraints
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Transcriptional regulatory constraints (Covert, et. al.,
2002)
 Boolean representation of regulatory network
 Used to predict growth, changes in expression levels,
simulate courses of batch cultures
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Energy balance analysis (Beard, et. al., 2002)
 Loops are not feasible according to thermodynamic
principles – resulting in a non-convex solution space
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Additional Constraints:
Slow Changes in the Environment
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Timescales of cellular process are shorter than those of
surrounding environment
Generate dynamic curves to simulate batch experiments
(Varma, et. al., 1994)
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 Thank
you for listening
 Questions