Synthesizing and simplifying biological networks from pathway level information
Bhaskar DasGuptaDepartment of Computer ScienceUniversity of Illinois at Chicago
Chicago, IL [email protected]
Joint works with Reka Albert, Piotr Berman, German Enciso, Sema Kachalo, Paola Vera-Licona, Eduardo Sontag, Kelly Westbrooks, Alexander Zelikovsky and Ranran Zhang
Supported by NSF grants DBI-0543365 and IIS-0346973
Cellular Networks• A single cell by itself is complex
enough to understand its functions completely.
• Various technologies have facilitated the monitoring of expression of genes and activities of proteins.
• Difficult to find the causal relations and overall structure of the network.
http://www.nyas.org/ebriefreps/ebrief/000534/images/mendes2.gif
Reverse engineering issuesGiven
– partial knowledge about the process/network– access to suitable biological experiments
how to gain more knowledge about the process/network?– effective use of resources (time, cost)
Reverse engineering issuesGiven
– partial knowledge about the process/network– access to suitable biological experiments
how to gain more knowledge about the process/network?– effective use of resources (time, cost)
Reverse engineering
• Process of backward reasoning, requiring careful observation of inputs and outputs, to elucidate the structure of the system.
http://www.computerworld.com/computerworld/records/images/story/46Reverse-engineering.gif
Ingredients for reverse engineering of biological networks
• Appropriate mathematical models– Differential equation model
• Computational techniques (algorithms)– Set multicover
• Biological experiments– Perturbation experiments
Iterative process in systems biology
Difficulty with traditional perturbation experiments
• Perturbation given to any gene or part of network may quickly spread to whole network
• Measurement of only global changes is possible
http://www.cumc.columbia.edu/news/journal/journal-o/winter-2006/img/MAGNet-diagram.jpg
Differential Equation Model of Biological Systems
state variables evolve by (unknown) partial differential equations
),,,,,,,(
),,,,,,,(
),(
2121
212111
mnnn
mn
pppxxxft
x
pppxxxftx
txftx
=∂∂
=∂∂
≡=∂∂
x = (x1(t),...,xn(t)) state variables over time tmeasurable (e.g., activity levels of proteins)
p = (p1,...,pm) parameters that can be manipulated
f(x*,p*)=0p* “wild-type” (i.e., normal) condition of px* corresponding steady-state condition
Settings for modular response analysis method
– do not know f
– but, prior information of the following type is available• parameter pj does or does not effect variables xi
(i.e., ∂fi /∂pj ≡ 0 or not)
Kholodenko, Kiyatkin, Bruggeman, Sontag, Westerhoff and Hoek, PNAS, 2002
Experimental protocols(perturbation experiments)
• perturb one parameter, say pk
• for perturbed p, measure steady state vector x = ξ(p)– let the system relax to steady state– measure xi (western blots, microarrys etc.)
• estimate n “sensitivities”:
nipepppp
pp
b ijjijjj
ij ,,2,1for ))()((1)( ***
*i=−+
−≈
∂∂
= ξξξ
where ej is the jth canonical basis vector
Modeling Goal
A
DC
B1. Topology of
connections only
2. Direction of the relationship
3. Information about stimulatory or inhibitory effects
4. Strength of relationship
+
+ -+
-2.1
9.3 1.24.8
5.3
Modeling goal can be at different levels
Stark et al., Trends Biotechnology 21, pp.290-293, 2003
Our very modest goal
Obtain information about the sign of ∂fi/∂xj(x∗,p∗)
e.g., if ∂fi/∂xj> 0, then xj has a positive (catalytic) effect on the formation of xi
In a nutshellafter some combinatorics and linear algebra
one can quantify the additional prior knowledge necessary to reach the goal
Kholodenko, Kiyatkin, Bruggeman, Sontag, Westerhoff and Hoek, PNAS, 2002Bermen, DasGupta and Sontag, Discrete Applied Math, 2007Berman, DasGupta and Sontag, Annals of NYAS, 2007
But, assuming (near)-sufficient prior information
• how to determine a minimum or near-minimum number of perturbation experiments that will work?
This now becomes a algorithmic/complexity issue...
After some effort, one can see that
designing minimal sets of experimentsleads to
the set multi-cover problem
Modular Response Analysis for
Differential Equations modelLinear Algebraic
formulation
Combinatorialformulation
CombinatorialAlgorithms
(randomized)
Selection ofappropriate
perturbation experiments Overall high-level picture
In our biological application context, it means....
we can provide a set of suggested experiments such that
# of experiments ≈ minimum possible
Experimental validation of Modular Response Analysis (MRA) Method
Growth factor-induced MAPK network topology shapes Erk response determining PC-12 cell fate
by
Silvia D. M. Santos, Peter J. Verveer, Philippe I. H. Bastiaens
Nature Cell Biology 9, 324 - 330 (2007)
Experimental validation (continued)
• MAPK pathway involving proteins Raf, Mek and Erk is activated through receptor tyrosine kinases TrkA and epidermal growth factor receptor (EGFR) by two different stimuli, NGF (neuronal-) or EGF (epidermal growth factor)
• MRA method was applied to determine the MAPK network architecture in the context of NGF and EGF stimulations
Another ongoing work on reverse engineering (with Paola Vera-Licona (INRIA), Eduardo Sontag (Rutgers), Joe Dundas (UIC))
Comparison of reverse engineering methods to infer network topology from gene expression data
steady state profiles ofperturbations
of the network
Boolean network
hitting set (set cover)
introduceredundancy
set multicover
expression data representing state transition measurement
for wildtype and perturbation data
topology of interconnection
network
hitting set (set cover)
introduceredundancy
set multicover
http://sts.bioengr.uic.edu/causal/
Synthesizing and Minimizing Signal Transduction Networks
Overall Goal
direct interactionA → BA ┤B
double-causal interaction
A → (B → C)A → (B ┤C)
additionalinformation
Method(algorithms, software)
FAST
network
minimal complexitybiologically relevant
Nature of experimental evidence
• biochemical (e.g., enzymatic activity, protein-protein interaction)– direct interaction
• pharmacological evidence– double-causal interaction
• genetic evidence of differential responses to a stimulus– can be direct, but most often double-causal
We describe a method for synthesizing double-causal (path-level) information into a consistent network
Our method significantly expands the capability for incorporating indirect (pathway-level) information. Previous methods of synthesizing signal transduction networks only include direct biochemical interactions, and are therefore restricted by the incompleteness of the experimental knowledge on pairwise interactions.
Direct interactions
A promotes B A → B
A inhibits B A ┤ B
Illustration of double-causal interactionC promotes the process of A promoting B
A B
BA
C
BApseudo
“Critical” edge(known direct interaction, part of input)
Main computational step for network synthesis
• Pseudo-vertex collapse (PVC)– not so hard
• Binary transitive reduction (BTR)– hard– need heuristics
Pseudo-vertex collapse (PVC)
Intuitively, the PVC problem is useful for reducing the pseudo-vertex set to the the minimal set that maintains the graph consistent with all indirect experimental observations.
u
v
in(u)=in(v)out(u)=out(v)
uv
pseudo-vertices
new psuedo-vertex
Illustration of Binary Transitive Reduction (BTR)
remove?
yes,alternate path
remove?
no,critical edge
Intuitively, the BTR problem is useful for determining the sparsest graph consistent with a set of experimental observations
High level description of the network synthesis process
Synthesize direct interactions
Optimize
Synthesize double-causal interactions
Optimize
Interaction with
biologists
BTR
PVC
BTR
Biological validation of the network synthesis approach
Plant signal transduction network
consistent guard cell signal transduction network for ABA-induced stomatal closure– manually curated– described in S. Li, S. M. Assmann and R. Albert, Predicting Essential Components
of Signal Transduction Networks: A Dynamic Model of Guard Cell Abscisic Acid Signaling, PLoS Biology, 4(10), October 2006
– list of experimentally observed causal relationships collected by Li et al. and published as Table S1. This table contains
• around 140 interactions and causal inferences, both of type “A promotes B” and “C promotes process (A promotes B)”
– We augment this list with critical edges drawn from biophysical/biochemical knowledge on enzymatic reactions and ion flows and with simplifying hypotheses made by Li et al. both described in Text of S1
Arabidopsis thaliana is a small flowering plant that is widely used as a model organism in plant biology. Arabidopsis is a member of the mustard (Brassicaceae) family, which includes cultivated species such as cabbage and radish. Arabidopsis is not of major agronomic significance, but it offers important advantages for basic research in genetics and molecular biology
(source: http://www.arabidopsis.org/portals/education/aboutarabidopsis.jsp)
Regulatory interactions between ABA signal transduction pathway components
Regulatory interactions between ABA signal transduction pathway components (continued)
NO → GC not critical and not enzymatic
ERA1 ┤(ABA → CalM)
Some nodes in the network
GCR1 putative G protein coupled receptorOST1 proteinNO Nitric OxideABH1 RNA cap-binding proteinRAC1 small GTPase protein
…
(left) Guard cell signal transduction network for ABA-induced stomatal closure manually curated by Li, Assmann and Albert [source: PloS Biology, 10 (4), 2006].
( right) our developed automated network synthesis procedure produced a reduced (fewer edges) network while preserving all observed pathways [source: DasGupta’s group, Journal of Computational Biology and Bioinformatics]
Summary of comparison of the two networks
• Li et al. has 54 vertices and 92 edgesour network has 57 vertices but 84 edges
• Both networks have identical strongly connected component of vertices
• All the paths present in the Li et al.’s reconstruction are present in our network as well
• The two networks have 71 common edges• It took a few seconds to synthesize our network
Summary of comparison of the two networks (continued)
Thus the two networks are highly similar but diverge on a few edges,
All these discrepancies are not due to algorithmic deficiencies but to human decisions.
Software is available at:
http://www.cs.uic.edu/~dasgupta/network-synthesis/
• runs on any machine with MS Windows (Win32)– click, save the executable and run
• for linux/unix fans, source files for a non-graphic version of the program, that can be compiled and run from the console, can be obtained by sending an email to the authors
Data sourcesSignal transduction pathway repositories such as
• TRANSPATH (http://www.gene-regulation.com/pub/databases.html#transpath)
• protein interaction databases such as the Search Tool for the Retrieval of Interacting Proteins (http://string.embl.de)
contain up to thousands of interactions, a large number of which are not supported by direct physical evidence.
NET-SYNTHESIS can be used to filter redundant information while keeping all direct interactions
Other applications of the software Synthesizing a Network for T Cell Survival and Death in LGL Leukemia
Backgound• Large Granular Lymphocytes (LGL)
– medium to large size cells with eccentric nuclei and abundant cytoplasm– comprise 10%~15% of the total peripheral blood mononuclear cells– two major lineages
• CD3- natural-killer (NK) cell lineage: ~85% of LGL cells• CD3+ lineage: ~15% of LGL
LGL leukemia
disordered clonal expansion of LGL and their invasions in the marrow, spleen and liver
Background (continued)Ras:
– small GTPase essential for controlling multiple essential signaling pathways
– its deregulation is frequently seen in human cancers
Activation of H-Ras required its farnesylation, which can be blocked by Farnesyltransferase inhibitiors (FTIs)
This envisions FTIs as future drug target for anti-cancer therapies, and several FTIs have entered early phase clinical trials
This observation, together with the finding that Ras is constitutively activated in leukemic LGL cells, leads to the hypothesis that Ras plays an important role in LGL leukemia, and may functions through influencing Fas/FasL pathway.
To further understand the molecular mechanism(s) of the onset of LGL leukemia, we constructed the cell-survival/cell-death regulation-related signaling network, with special interest on the Ras’ effect on apoptosis response through Fas/FasL pathway
Goal: initiates the understanding of the interactions between Ras pathway and Fas/FasL pathways, two of the major pathways that regulate cell survival/death decision.
Currently, there is no standard therapy for LGL leukemia. Understanding the mechanism of this disease is crucial for drug/therapy development
Proteins that modulate the Ras-apoptosis response can potentially serve as future reference for drug design and therapeutic-target-molecule search, and this may not be restricted to LGL leukemia
Synthesizing a Network for T Cell Survival and Death in Large Granular Lymphocyte Leukemia
• Synthesized a cell-survival/cell-death regulation-related signaling network from the TRANSPATH 6.0 database, with additional information manually curated from literature search
• 359 vertices of this network represent proteins/protein families and mRNAs participating in pro-survival and Fas-induced apoptosis pathways
• 1295 edges represent regulatory relationships between nodes, including protein interactions, catalytic reactions, transcriptional regulation (no double-causal interactions were known)
• Performing BTR with NET-SYNTHESIS reduced the total edge-number to 873
To focus on pathways that involve the 33 known T-LGL deregulated proteins, we designated vertices that correspond to proteins with no evidence of being changed during T-LGL as pseudo-vertices and deleted the label “Y” for those edges whose both endpoints were pseudo-vertices
Recursively performing “Reduction (faster)” BTR and “Collapse degree-2 pseudonodes” of NET-SYNTHESIS until no edge/node could be further removed simplified the network to 267 nodes and 751 edges.
For further results, see
R. Zhang, M. V. Shah, J. Yang, S. B. Nyland, X. Liu, J. K. Yun, R. Albert, and T. P. Loughran,
Network Model of Survival Signaling in LGL Leukemia PNAS, 2008
Thank you for your attention!
Questions?
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