Complex (Biological) Networks · Metabolic diseases (obesity, diabetes) are on the rise (and are...
Transcript of Complex (Biological) Networks · Metabolic diseases (obesity, diabetes) are on the rise (and are...
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Elhanan Borenstein
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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79
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1
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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1310
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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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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)
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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 the reactants and products in reactions
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Stoichiometric Matrix
S
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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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Available CBM Metabolic Models
Bernhard Palsson
UCSD
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