biological network analysis: introduction to metabolic networks
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Biological Network Analysis: Introduction to Metabolic Networks. Tomer Shlomi Winter 2008. Lecture Outline. 1. Cellular metabolism 2. Metabolic network models 3. Constraint-based modeling 4. Optimization methods. 1. Cellular metabolism. - PowerPoint PPT PresentationTRANSCRIPT
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Biological Network Analysis:Introduction to Metabolic
Networks
Tomer ShlomiWinter 2008
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Lecture Outline
1. Cellular metabolism2. Metabolic network models3. Constraint-based modeling4. Optimization methods
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1. Cellular metabolism
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Metabolism (I)Metabolism is the totality of all the chemical reactions that operate in a living organism.
Catabolic reactionsBreakdown and produce energy
Anabolic reactionsUse energy and build up essential cell components
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Metabolism (II)“Metabolism is the process involved
in the maintenance of life. It is comprised of a vast repertoire of enzymatic reactions and transport processes used to convert thousands of organic compounds into the various molecules necessary to support cellular life” Kenneth et al. 2003
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Why study metabolism? (I)1. Basic science - it’s the essence of life..
2. Tremendous importance in Medicinea. In born errors of metabolism cause acute
symptoms and even death on early ageb. Metabolic diseases (obesity, diabetics) are
major sources of morbidity and mortality.c. Metabolic enzymes and their regulators
gradually becoming viable drug targets
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Why study metabolism? (II)
3. Bioengineering applicationsa. Design strains for production of biological
products of interestb. Generation of bio- fuels
4. Probably the best understood of all cellular networks: metabolic, PPI, regulatory, signaling
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Metabolites and Biochemical Reactions
• Metabolite - an organic substance:– Sugars – glucose, galactose, lactose, etc’– Carbonhydrates – glycogen, glucan, etc’– Amino-acids – histidine, proline, methionine, etc’– Nucleotides – cytosine, guanine, etc’– Lipids– Chemical energy carriers – ATP, NADH, etc’ – Atoms – oxygen, hydrogen
• Biochemical reaction: the process in which one or more substrate molecules are converted (usually with the help of an enzyme) to product molecules
Glucose + ATP
Glucokinase
Glucose-6-Phosphate + ADP
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Metabolic Networks• A set of reactions and the corresponding metabolites• A directed hyper-graph representation
– Nodes - represent metabolites– Edges - represent biochemical reactions
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18 .Lecture WS 2008/09
Metabolites (I)The 744 reactions of E.coli small-molecule metabolism involve a total of 791 different substrates.
On average, each reaction contains 4.0 substrates.
Number of reactions containing varying numbers of substrates (reactants plus products).
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18 .Lecture WS 2008/09
Bioinformatics III 11
Each distinct substrate occurs in an average of 2.1 reactions.Metabolites (II)
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Reactions Catalyzed by More Than one Enzyme
Diagram showing the number of reactions that are catalyzed by one or more enzymes. Most reactions are catalyzed by one enzyme, some by two, and very few by more than two enzymes.
For 84 reactions, the corresponding enzyme is not yet encoded in EcoCyc.What may be the reasons for isozyme redundancy?
(2) the reaction is easily „invented“; therefore, there is more than one protein family that is independently able to perform the catalysis (convergence).
(1) the enzymes that catalyze the same reaction are homologs and have duplicated (or were obtained by horizontal gene transfer),acquiring some specificity but retaining the same mechanism (divergence)
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Enzymes that catalyze more than one reactionGenome predictions usually assign a single enzymatic function.However, E.coli is known to contain many multifunctional enzymes.Of the 607 E.coli enzymes, 100 are multifunctional, either having the same active site and different substrate specificities or different active sites.
Number of enzymes that catalyze one or more reactions. Most enzymes catalyze one reaction; some are multifunctional.
The enzymes that catalyze 7 and 9 reactions are purine nucleoside phosphorylase and nucleoside diphosphate kinase.
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18 .Lecture WS 2008/09
Bioinformatics III 14
Pathways (I)EcoCyc describes 131 pathways:
energy metabolismnucleotide and amino acid biosynthesissecondary metabolism
Pathways vary in length from a single reaction step to 16 steps with an average of 5.4 steps.
Length distribution of EcoCyc pathways
Ouzonis, Karp, Genome Res. 10, 568 (2000)
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Pathways (II)However, there is no precise biological definition of a pathway.
The partitioning of the metabolic network into pathways (including the well-known examples of biochemical pathways) is somehow arbitrary.
These decisions of course also affect the distribution of pathway lengths.
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Pathway in the Context of a System
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Reactions participating in more than one pathway
The 99 reactions belonging to multiple pathways appear to be the intersectionpoints in the complex network of chemicalprocesses in the cell.
E.g. the reaction present in 6 pathways corresponds to the reaction catalyzed by malate dehydrogenase, a central enzyme in cellular metabolism.
The 99 reactions belonging to multiple pathways appear to be the intersectionpoints in the complex network of chemicalprocesses in the cell.
E.g. the reaction present in 6 pathways corresponds to the reaction catalyzed by malate dehydrogenase, a central enzyme in cellular metabolism.
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2. Metabolic Network Models
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Metabolic Network Models• The application of computational methods to
predict the network behavior usually requires additional data other than the network topology
• A ‘GS metabolic network model’ is a collection of such data:– Reaction stoichiometry – Reaction directionality– Cellular localization– Transport and exchange reactions– Gene-protein-reaction association
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Metabolic Network Model: Reaction Stoichiometry
• Stoichiometry - the quantitative relationships of the reactants and products in reactions
1 Glucose + 1 ATP <-> 1 Glucose-6-Phosphate + 1 ADP
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Metabolic Network Model: Reaction Directionality
• Biochemical studies may test the reversibility of enzymatic reactions
• But the directionality can differ between in vitro and in vivo due to different temperature, pH, ionic strength, and metabolite concentrations.
• A subset of the reactions in a model is uni-directional and the remaining reactions are bi-directional
1 Glucose + 1 ATP -> 1 Glucose-6-Phosphate + 1 ADP
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Metabolic Network Model: Cellular Localization (I)
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Metabolic Network Model: Cellular Localization (II)
• Algorithms: PSORT and SubLoc to predict the cellular localization of proteins based on nucleotide or amino acid sequences
• High-throughput experimental approaches such as immunofluorescence and GFP tagging of individual proteins.
Cytoplasm: 1 Glucose + 1 ATP -> 1 Glucose-6-Phosphate + 1 ADP
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Metabolic Network Model: Transport and Exchange
Reactions• An extra-cellular compartment is also included in the
model• Transport reaction move metabolites between
compartments (across membrane boundaries)– Glucose[c] <-> Glucose[e]
• Exchange reaction move metabolites across the model boundary– Glucose[e] <->
• Uptake = in• Secretion = out
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Gene-Protein-Reaction (GPR) Association (I)
• Formulated via Boolean logic• Sdh protein made up of 4 peptides, catalyzes 2
reactions
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Gene-Protein-Reaction (GPR) Association (II)
• A protein complex made up of 3 proteins catalyzes a single reaction
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Gene-Protein-Reaction (GPR) Association (III)
• Isozymes – alternative enzymes that catalyze the same reaction
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Metabolic Network Models• A ‘GS metabolic network model’ is a collection
of:– A metabolic network– Reaction stoichiometry – Reaction directionality– Cellular localization– Transport and exchange reactions– Gene-protein-reaction association
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Model Reconstruction Process (I)
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Model Reconstruction Process (II)
• Performed mainly in Bernhard Palsson’s lab in UCSD.
• Model naming convention:
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Reconstruction of E. coli models
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Available Metabolic Models
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3. Kinetic modeling
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Stoichiometric Matrix (I)• Stoichiometric matrix – network topology with
stoichiometry of biochemical reactions (denoted S)• A Metabolite that exists in multiple compartments is
represented with multiple rows in the matrix• How would transport and exchange reactions
represented?
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Stoichiometric Matrix (II)
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Kinetic Modeling: Definition
• Predict changes in metabolite concentrations • m – metabolite concentrations vector - mol/mg• S – stoichiometric matrix• v – reaction rates vector - mol/(mg*h)
),( kmfSvSdtmd
Reaction rate equation Kinetic parameter
s• Requires knowledge of m, f and k!
A set of Ordinary Differential Equations (ODE)
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Kinetic Modeling: Reaction Rate Equations (I)
• Consider the reaction: S->P• A simple rate equation (Michaelis-Menten) is:
• In this case, we have only 2 kinetic parameters – vmax and Km
][][
max sKsVv
M
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Kinetic Modeling: Reaction Rate Equations (II)
• Consider the reaction: S + E <-> P + E• A more complex Michaelis-Menten equation:
• In this case, we have only 4 kinetic parameters – vmax+, vmax-, KmS, and KmP,
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Kinetic Modeling: Reaction Rate Equations (III)
• Reaction rate equations also depends (via k) on:– Regulation: effectors, inhibitors– Enzyme concentration– Surrounding reactions and molecules– pH, ion-balance, molecule-gradients, energy
potentials
• Kinetics are problematic– Obtained from test tube tests of purified enzymes– Measurement doesn’t apply on cell environment• Most of these parameters are unknown!
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4. Constraint-based modeling
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Constraint-based modeling (CBM) (I)
0 vSdtmd
• Assumes a quasi steady-state– No changes in metabolite concentrations (within the system)– Metabolite production and consumption rates are equal
• Representing the ‘average’ flow in the network over a long enough period of time
• The reaction rate vector v is referred to as a ‘steady-state flux distribution’
• No need for information on metabolite concentrations, reaction rate equations, and kinetic parameters
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CBM (II)
Solution space
Correct solutions
0vS• In most cases, S is underdetermined, and there exist a space
of possible flux distributions v that satisfy: • The idea in CBM is to employ a set of constraints to limit the
space of possible solutions to those more likely/correct– Mass balance is enforced by the above equation– Thermodynamic: irreversibility of reactions– Enzymatic capacity: bounds on enzyme rates– Availability of nutrients
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CBM (III)• The solution space decreases with the addition of more
constraints
Mass balanceS·v = 0Subspace of R
Thermodynamicvi > 0Convex cone
Capacityvi < vmax
Bounded convex conen
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CBM Example (I)
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CBM Example (II)
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CBM Example (III)
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Determination of Likely Flux Distributions
• In most cases lack of constraints provide a space of solutions
• How to identify plausible solutions within this space?
• Optimization methods (next lesson)– Maximal biomass production rate – Minimal ATP production rate– Minimal nutrient uptake rate
• Exploring the solution space (the following lesson)– Extreme pathways– Elementary modes
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4. Optimization methods
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Flux Balance Analysis (I)• An optimization method for finding a feasible flux distribution
that enables maximal growth rate of the organism• Based on the assumption that evolution optimizes microbes
growth rate• To enable maximal growth rate the essential biomass
precursors (metabolites) should be synthesized in the maximal rate
• Add to the model a pseudo ‘growth reaction’ representing the metabolites required forproducing 1g of the organism’s biomass
• These precursors are removed from the metabolic network in the corresponding ratios:
41.1 ATP + 18.2 NADH + 0.2 G6P… -> biomass
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For example: Biomass reaction of E. coli
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Other Possible Objective Functions
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Flux Balance Analysis (II)
000
• Searches for a steady-state flux distribution v:
• Satisfying thermodynamic and capacity constraints:
S∙v=0
vmin≤v ≤vmax
• With maximal growth rateMax vbiomass
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Flux Balance Analysis (II)
000
• Searches for a steady-state flux distribution v:
• Satisfying thermodynamic and capacity constraints:
S∙v=0
vmin≤v ≤vmax
• With maximal growth rateMax vbiomass
How do we find this flux distribution v?
Linear Programming
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Linear Programming Basics (I)
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Linear Programming Basics (III)
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Linear Programming: Types of Solutions (I)
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Linear Programming: Types of Solutions (II)
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FBA and LP: Single solution
• Assume that b2 is the ‘biomass’ reaction which we maximize
• Let b1≤5 (i.e. the maximal uptake rate of A is bounded by 5)
• One optimal solution exist in which b2=5
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FBA and LP: Unbounded• Assume that b2 is the ‘biomass’ reaction which we
maximize• Let b1≤∞ (i.e. the maximal uptake rate of A is
unbounded)
• No optimal solution exist• B2 can be as high as we want
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FBA and LP: Solution space (I)
• Assume that b2 is the ‘biomass’ reaction which we maximize
• Let b1≤5
• There are many possible optimal solutions in which b2=5
• Different solutions reflect the activity of alternative pathways:v1+v2=b1≤5
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FBA and LP: Solution space (II)
• The LP solution space is convex! (bounded within the original feasible solution space)
vbiomass=c
S∙v=0vmin≤v ≤vmax
Max vbiomass =c
S∙v=0vmin≤v ≤vmax
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FBA and LP: Solution space (III)• The convex solution space can be further analyze• For example, finding the optimal growth solution with
minimal nutrient uptake
vbiomass=c
S∙v=0vmin≤v ≤vmax
Min vmet_uptake
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References:• Price ND, Papin JA, Schilling CH, Palsson BO. 2003.
Genome-scale microbial in silico models: the constraints-based approach. Trends Biotechnol 21(4):162-9.