Biological Network Analysis:Introduction to Metabolic

Networks

Tomer ShlomiWinter 2008

Lecture Outline

1. Cellular metabolism2. Metabolic network models3. Constraint-based modeling4. Optimization methods

1. Cellular metabolism

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

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

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

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

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

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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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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Each distinct substrate occurs in an average of 2.1 reactions.

Metabolites (II)

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)

Enzymes that catalyze more than one reaction

Genome 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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Pathways (I)EcoCyc describes 131 pathways:

energy metabolism

nucleotide and amino acid biosynthesis

secondary 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)

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.

Pathway in the Context of a System

Reactions participating in more than one pathway

The 99 reactions belonging to multiple

pathways appear to be the intersection

points in the complex network of chemical

processes 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 intersection

points in the complex network of chemical

processes 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.

2. Metabolic Network Models

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

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

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

Metabolic Network Model: Cellular Localization (I)

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

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

Gene-Protein-Reaction (GPR) Association (I)

• Formulated via Boolean logic• Sdh protein made up of 4 peptides, catalyzes 2

reactions

Gene-Protein-Reaction (GPR) Association (II)

• A protein complex made up of 3 proteins catalyzes a single reaction

Gene-Protein-Reaction (GPR) Association (III)

• Isozymes – alternative enzymes that catalyze the same reaction

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

Model Reconstruction Process (I)

Model Reconstruction Process (II)

• Performed mainly in Bernhard Palsson’s lab in UCSD.

• Model naming convention:

Reconstruction of E. coli models

Available Metabolic Models

3. Kinetic modeling

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?

Stoichiometric Matrix (II)

Kinetic Modeling: Definition

• Predict changes in metabolite concentrations • m – metabolite concentrations vector - mol/mg• S – stoichiometric matrix• v – reaction rates vector - mol/(mg*h)

),( kmfSvSdt

md

Reaction rate equation Kinetic parameter

s• Requires knowledge of m, f and k!

A set of Ordinary Differential Equations (ODE)

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 sK

sVv

M

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,

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!

4. Constraint-based modeling

Constraint-based modeling (CBM) (I)

0 vSdt

md

• 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

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

CBM (III)• The solution space decreases with the addition of more

constraints

Mass balance

S·v = 0

Subspace of R

Thermodynamicvi > 0Convex cone

Capacityvi < vmax

Bounded convex conen

CBM Example (I)

CBM Example (II)

CBM Example (III)

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

4. Optimization methods

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

For example: Biomass reaction of E. coli

Other Possible Objective Functions

Flux Balance Analysis (II)

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

Flux Balance Analysis (II)

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

How do we find this flux distribution v?

Linear Programming

Linear Programming Basics (I)

Linear Programming Basics (III)

Linear Programming: Types of Solutions (I)

Linear Programming: Types of Solutions (II)

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

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

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

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

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

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.