The largescale Organization of Metabolic Networks

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The large-scale Organization of Metabolic
Networks

• H. Jeong, B. Tombor, R. Albert, Z.N. Oltvai,and
  A.-L. BarabásiNature 407, 651-654 (2000)

Presented by Padmavati Sridhar PhD CISE UFl
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Outline

• Introduction
• Modeling of Metabolic Networks
• Analysis Methodology
• Database Preparation
• Construction of Metabolic Network Matrices
• Connectivity Distribution
• Biochemical Pathway Lengths
• Substrate Ranking
• Analysis of Effect of Database Errors
• Conclusion

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Introduction

• Genome SequencingWhat Next?

• Essential Step in Post genomic Era
• the prediction of function from the metabolic
  networks reconstructed from the gene products

- Prediction of function
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Integrative Biology a paradigm shift in
molecular biology
Biological Sciences
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What is a Metabolic Network?

• Cellular Metabolism Complex Network of
• Reactions cluster in modules called Metabolic
  Maps
• Complete set of Metabolic Maps Metabolic Network

Reactants
Reactions
Products
Enzymes
METABOLISM
Bio-chemical reactions
Citrate Cycle
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Complexity in Metabolic Networks
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Complexity in Metabolic Networks

• Arises more from the Complexity of Interactions
  than from the quantity of genes
• Large-scale structure of Metabolic Networks is
  unknown
• The large-scale design principles that integrate
  the cellular constituents like DNA, RNA, Proteins
  into a complex system are poorly understood

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Recent Developments

• Large-scale Genome-Sequencing Projects
• Complete sequence information of gt 2 dozen
  Prokaryotes
• Allows the identification of known pathways in
  the annotated genome of an organism

Integrated Pathway- Genome Databases
Organism-specific Connectivity Maps of Metabolic
Networks

• Maps Complex, afford limited insight into
  Design principles governing the Network
  Organization
• Due to the large number and diversity of
  constituents and reactions forming the network

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Objective of this paper

• To Show

• Metabolic networks demonstrate
• striking similarities to
• the Inherent Organization of
• Complex Non-Biological Systems

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How?

• By the systematic comparative mathematical
  analysis of the metabolic networks of 43
  organisms representing all three domains of life.

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Universality Practical Interest

• When studying a given problem, one may pick the
  most tractable system to study and the results
  one obtains will hold for all systems in the same
  class
• Recent advances in understanding the Generic
  properties of complex Networks
• Enables us to quantitatively address the
  Structure of Cellular Network

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Classical Model for Complex Networks
Erdös-Rényi model (1960)
Random Network Theory
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Most real world networks have the same internal
structure
Scale-free networks
Why?
What does it mean?
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SCALE FREE NETWORKS

• The Number of Nodes (n) is not fixed
• Networks continuously expand by the addition of
  new nodes
• Examples
• WWW addition of new documents
• Citation publication of new papers
• The Attachment is not uniform
• A node is linked with higher probability to a
  node that already has a large number of links.
• Examples
• WWW new documents link to well known sites
• (CNN, YAHOO, NewYork Times, etc)
• Citation well cited papers are more likely to
  be cited again

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BA model
Scale-free model
(1) GROWTH
At every timestep we add
a new node with m edges (connected to the nodes
already present in the system). (2) PREFERENTIAL
ATTACHMENT The
probability ? that a new node will be connected
to node i depends on the connectivity ki of that
node
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PREFERENTIAL ATTACHMENT
Rich gets richer
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Airlines
What does it mean?
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Generic properties of complex Networks

• Robustness
• Error-tolerance
• Scale-free property

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Robustness
Robustness
Complex systems maintain their basic functions
even under errors and
failures
(cell ? mutations Internet ?
router breakdowns)
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Robust-SF
Robustness of scale-free networks
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S
0
1
f
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Achilles Heel
Achilles Heel of complex networks
failure
attack
Internet
R. Albert, H. Jeong, A.L. Barabasi, Nature 406
378 (2000)
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Objective of this paper

• To Show

• Metabolic networks demonstrate
• striking similarities to
• the Inherent Organization of
• Complex Non-Biological Systems

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I. Database construction

• The WIT database (ERGO Light)was utilized for
  analysis which divides the full cellular network
  of each organism into 6 subgroups
• 1. Intermediate metabolism and bioenergetics
• 2. Information pathway
• 3. Electron transport
• 4. Trans membrane transport
• 5. Signal transduction
• 6. Structure and function of cell

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Corrections applied to the WIT database

• Prior to analysis, the downloaded data was
  carefully examined for inconsistencies by the
  following steps.
• 1. Substrates that were represented by several
  different synonyms (e.g. uroporphyrinogen-III
  uroporphyrinogen III). were replaced with one
  unique name. (26 substrates out of 1316)
• 2. Substrates without defined chemical identity,
  such as "acceptor", were removed from the
  analysis.  

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A Typical Pathway
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Construction of the metabolic network

• Each Pathway Several Reactions (6 reactions,
  R1, R2,...,R6)
• Each Reaction composed by substrates and
  enzymes
• Nodes E-ducts and Products connected by
  directed links
• The nodes are connected to the temporary
  educt-educt complexes
• Unique Ids
• Nodes -gt S1, S2, S3,
• Temporary Complexes-gt M1, M2, ....
• To each temporary complex we associate an
  enzyme, denoted by E1, E2,...

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Construction of the metabolic network contd..

• Connectivity information
• S1 M1-E1, S2 M1-E1, M1-E1 S3, M1-E1
  S4.
• Bi-directional reactions (R1-R5) were considered
  as two separate reactions in each direction
• The same substrates can participate in multiple
  reactions, both as products and educts

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Data

• Cellular network data (for 43 organisms)
• ASCII file
• Each number represents substrate in cellular
  network of corresponding organism Data-format
  From -gt To (directed link) (number larger than
  1000000 corresponds to intermediate state)
• Metabolic Network data for E.Coli

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Matrix Representation

• For a given organism, that has
• N substrates,
• E enzymes and
• R intermediate complexes,
• The full stoichiometric interactions about the
  metabolic network can be compiled in an (NER)
  (NER) matrix

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Adjacency Matrix Example

• S1 M1-E1, S2 M1-E1, M1-E1 S3, M1-E1
  S4
• For example, should an organism possess only the
  reactions described, the adjacency matrix would
  have the form  

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Adjacency Matrix Example

• S1 M1-E1, S2 M1-E1, M1-E1 S3, M1-E1
  S4
• For example, should an organism possess only the
  reactions described, the adjacency matrix would
  have the form  

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Connectivity information

• The adjacency matrix, A, then contains the full
  connectivity information of the system, and from
  it one can reconstruct the full metabolic
  network.
• Such a matrix was generated for each of the 43
  organisms separately.  

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II. Database analysis

• Once A was obtained, several quantities, which
  are frequently used in graph theory, are measured
• 1. Connectivity distribution, P(k)
• P(kin) Connectivity distribution for incoming
  links
• P(kout) Connectivity distribution for outgoing
  links.
• 2. Histogram of biochemical pathway lengths, P
  (l)
• 3. Diameter, D
• 4. Average number of incoming (outgoing) links
  per node, L/N
• 5. Substrate ranking, r

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Numerical values

• N Total number of substrates that appear as an
  educt or product in a metabolic network for each
  organisms, determined from the adjacency matrix
  A.
• L(IN/OUT) Total number of (incoming/outgoing)
  links that exist in a network for each organisms,
  again determined from A.
• R Total number of individual reactions or
  temporary intermediate states (substrate-enzyme
  complex).
• E Total number of enzymes present in each
  organism
• gin(out) The connectivity exponent from the
  slope of P(kin(out)) on a log-log plot
• D Diameter of network
• Hub(IN/OUT) List of ten substrates with the
  largest number of (incoming/outgoing) links

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III. Analysis of the effect of database errors

• 2 major sources of possible errors in the
  database could potentially affect the analysis
• the erroneous annotation of enzymes and
  consequently, biochemical reactions for the
  organisms with completely sequenced genomes this
  is the likely source of error.
• reactions and pathways missing from the database

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Conclusion

• Metabolic Organization is not only identical for
  all living organisms, but complies with the
  design principles of Robust and Error-tolerant
  networks
• It may represent a common blueprint for the
  large-scale organization of interactions among
  all cellular constituents.

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Questions
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Thank You