complex (biological) networks - borenstein...
TRANSCRIPT
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Elhanan Borenstein
Spring 2011
Complex (Biological) Networks
Some slides are based on slides from courses given by Roded Sharan and Tomer Shlomi
Analyzing Metabolic Networks
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Metabolism
“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”
Schilling et al. 2000
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Why study metabolism? (II)
� It’s the essence of life (and maybe its origins)
� Tremendous importance in Medicine
� Inborn errors of metabolism cause acute symptoms
� Metabolic diseases (obesity, diabetes) are on the rise
(and are major sources of morbidity and mortality)
� Metabolic enzymes becoming viable drug targets
� Bioengineering applications
� Design strains for production of biological products
� Generation of bio-fuels
� The best understood of all cellular networks
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Metabolites & Biochemical Reactions
� Metabolite: an organic substance� Sugars (e.g., glucose, galactose, lactose)
� Carbohydrates (e.g., glycogen, glucan)
� Amino-acids (e.g., histidine, proline, methionine)
� Nucleotides (e.g., cytosine, guanine)
� Lipids
� Chemical energy carriers (e.g., ATP, NADH)
� Atoms (e.g., oxygen, hydrogen)
� Biochemical reaction: the process in which
one or more substrate molecules are
converted (usually with the help of an
enzyme) to produce
molecules
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Pathways
Ouzonis, Karp, Genome Res. 10, 568 (2000)
� EcoCyc describes 131 pathways
� Pathways vary in length from a
single step to 16 steps (ave 5.4)
� But ... no precise biological definition and
partitioning of the metabolic network
into pathways is somehow arbitrary
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From Pathways to a Network
http://www.genome.jp/kegg/pathway/map/map01100.html
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Models
of
Metabolism
(and Metabolic Networks)
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Metabolic Network Modelsrequired data/accuracy /complexity
abstraction/scale
Topological analysis� Degree distribution
� Motifs
� Modularity
� Reverse ecology
Conventional models� Boolean models
� Discrete models
� Bayesian models Kinetic models� Dynamic system
(differential eq’s)
� Requires unknown
data constants and
concentrations
Constraint-based� CB-Models
� Flux Balance Analysis
� Extreme Pathways
� Growth/KO effects
Approximate
Kinetic models
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Reverse Ecology
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Reconstructing Metabolic Networks
Fructose + Glucose => Sucrose
A
B
C D
E× Incomplete data
× Noise
� Large-scale
� Simple directed
graphs
Simple Representation
� Nodes=compounds
� Edges=reactions
� Topology based
� Static
SucroseGlucose
Fructose
Describing the chemical reactions in the cell and the
compounds being consumed and produced
atgaaaaccgtcgttt
ttgcctaccacgatat
gggatgcctcggtatg
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Metabolic Network (E.Coli)
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Environment
& Ecology
System Topology
& Structure
Environments from NetworksCan the structure/topology of metabolic networks be used to
obtain insights into the ecology in which species evolved/prevail?
inference
(Borenstein, et al.PNAS, 2008)
Reverse Ecology of
Metabolic Environments
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Seed Sets
& Metabolic Environments
3
4
8
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2
1
3
0
5
En
vir
on
men
t
set of exogenously
acquired compounds
(seed set)
proxy for the environment(operational definition)
Seed set: a minimal subset of the compounds that cannot be synthesized from
other compounds and whose existence permits the synthesis of all other
compounds in the network.
(Borenstein, et al.PNAS, 2008)
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1310
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Identifying Seed Compounds:
A Simple Synthetic Example
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Identifying Seed Compounds:
Strongly Connected Components (SCC)
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13105
Kosaraju’s algorithm
for SCC Decomposition
� Given a graph G:
1. Run a Depth-First Search (DFS) on G to compute finishing
times f[v] for each node v
2. Calculate the transposed network G (the network G with
the direction of every edge reversed)
3. Run DFS on G, traversing the nodes in decreasing order
of f[v]
� Each tree in the DFS forest created
by the second DFS run forms a
separate SCC
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Identifying Seed Compounds:
Strongly Connected Components (SCC)
� SCCs are equivalent sets
(“seed”-wise)
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Identifying Seed Compounds:
Strongly Connected Components (SCC)
� Directed Acyclic Graph (DAG)
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Identifying Seed Compounds:
Source Components
� Candidate seeds are members of
source components
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Identifying Seed Compounds:
Candidate Seeds
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Identifying Seed Compounds:
Seed Confidence Level
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Metabolic Network with Seeds
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Multi-Species Large-Scale Seed Dataset
Oxygen
L-Glutam
ate
Sulfate
Leucine
Sucrose
Glycerol
Methanol
Thym
idine
B. aphidicola - ���� ���� � � - - �
S. pneumoniae ���� � - � � - - ����
R. typhi ���� � � � ���� - - ����
S. aureus ���� ���� � � � - - ����
M. genitalium � � ���� ���� � � � ����
2264 compounds4
78
sp
eci
es
accuracy 79%
precision 95%
recall 67%
� 478 species (networks); >2200 compounds
� Seed compounds for each species
� Large-scale dataset
of predicted metabolic
environments
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Applications of Reverse Ecology
� Reconstructing ecology-based phylogeny
� Predicting ancestral environments
� Identifying evolutionary dynamics of networks
� Predicting species interaction
� Analyzing genetic vs. environmental robustness
� Quantifying ecological strategies
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Constraint-Based Modeling
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Available CBM Metabolic Models
Bernhard Palsson
UCSD
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Constraint-Based Modeling
� Living systems obey physical and chemical laws
� These can be used to constrain the space of
possible behaviors of the network
How often have I said to you that when you
have eliminated the impossible, whatever
remains, however improbable, must be the
truth?– Sherlock Holmes (A Study of Scarlet)
Space of all solutions
Space of feasible
solution
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Evolution Under Constraints
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Evolution Under Constraints
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1 Glucose + 1 ATP 1 Glucose-6-Phosphate + 1 ADP
Reaction Stoichiometry
� Stoichiometry - the quantitative relationships
of reactants and products in reactions
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Stoichiometric Matrix
S
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Stoichiometric Matrix
S
.RHex1
RPGI
RPFK
RFBA
RTPI
RGAPD
RGPK
RPGM
RENO
RPYK
V. =?
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Stoichiometric Matrix
S
.RHex1
RPGI
RPFK
RFBA
RTPI
RGAPD
RGPK
RPGM
RENO
RPYK
V.dt
md=
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Stoichiometric Matrix and Fluxes
vSdt
md⋅=
� m: metabolite concentrations vector (mol/mg)
� S: stoichiometric matrix
� v: reaction rates vector
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Kinetic parameters
),( kmfSvSdt
md⋅=⋅=
Reaction rate equation
Requires knowledge of m, f and k!
A set of Ordinary Differential Equations (ODE)
A Full Model? Not Really
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Constraint-Based Modeling
� Assumes a quasi steady-state!
� No changes in metabolite concentrations
� Metabolite production and consumption rates are equal
� No need for info on metabolite concentrations,
reaction rate functions, or kinetic parameters
0=⋅= vSdt
md
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Constraint-Based Modeling
� In most cases, S is underdetermined:� a subspace of Rn (possible flux distributions)
0
0
0
S∙v=0
� Thermodynamic constraints:� a convex cone vi > 0
� Capacity constraints:� a bounded convex cone vi < vmax
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Flux Balance Analysis
� But this still leaves a space of solutions
� How can we identify plausible solutions within
this space?
� Optimize for maximum growth rate !!
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Flux Balance Analysis
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Flux Balance Analysis
How do we
solve this?
Linear Programming
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Linear Programming (LP)
� Assume the following constraints:
� 0<A<60
� 0<B<50
� A+2B<120
� Optimize:
� Z=20A+30B
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Application of CBM & FBA
� Predict metabolic fluxes on various media
� Predict growth rate
� Predict gene knockout lethality
� Characterize solution space
� Many more …
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