Synthesizing and simplifying biological networks from pathway level information

Transcription

1 Synthesizing and simplifying biological networks from pathway level information Bhaskar DasGupta Department of Computer Science University of Illinois at Chicago Chicago, IL 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 and IIS

2 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.

3 Reverse engineering issues Given 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)

4 Given Reverse engineering issues 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)

5 Reverse engineering Process of backward reasoning, requiring careful observation of inputs and outputs, to elucidate the structure of the system.

6 Ingredients for reverse engineering of biological networks Appropriate mathematical models Differential equation model Computational techniques (algorithms) Set multicover Biological experiments Perturbation experiments

7 Iterative process in systems biology

8 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

9 Differential Equation Model of Biological Systems state variables evolve by (unknown) partial differential equations ),,,,,,, ( ),,,,,,, ( ), ( m n n n m n p p p x x x f t x p p p x x x f t x t x f t x = = = x = (x 1 (t),...,x n (t)) state variables over time t measurable (e.g., activity levels of proteins) p = (p 1,...,p m ) parameters that can be manipulated f(x *,p * )=0 p * wild-type (i.e., normal) condition of p x * corresponding steady-state condition

10 Settings for modular response analysis method do not know f but, prior information of the following type is available parameter p j does or does not effect variables x i (i.e., f i / p j 0 or not) Kholodenko, Kiyatkin, Bruggeman, Sontag, Westerhoff and Hoek, PNAS, 2002

11 Experimental protocols (perturbation experiments) perturb one parameter, say p k for perturbed p, measure steady state vector x = ξ(p) let the system relax to steady state measure x i (western blots, microarrys etc.) estimate n sensitivities : b ij ξi * 1 * = ( p ) ( ξi ( p + p je j ) ξi ( p * p p p j j j * )) for i = 1,2,, n where e j is the j th canonical basis vector

12 Modeling Goal Modeling goal can be at different levels 1. Topology of connections only 2. Direction of the relationship 3. Information about stimulatory or inhibitory effects 4. Strength of relationship A C B D Stark et al., Trends Biotechnology 21, pp , 2003

13 Our very modest goal Obtain information about the sign of f i / x j (x,p ) e.g., if f i / x j > 0, then x j has a positive (catalytic) effect on the formation of x i

14 In a nutshell after 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, 2002 Bermen, DasGupta and Sontag, Discrete Applied Math, 2007 Berman, DasGupta and Sontag, Annals of NYAS, 2007

15 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...

16 After some effort, one can see that designing minimal sets of experiments leads to the set multi-cover problem

17 Modular Response Analysis for Differential Equations model Linear Algebraic formulation Combinatorial Algorithms (randomized) Combinatorial formulation Selection of appropriate perturbation experiments Overall high-level picture

18 In our biological application context, it means... we can provide a set of suggested experiments such that # of experiments minimum possible

19 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, (2007)

20 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

21 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

22 steady state profiles of perturbations of the network hitting set (set cover) set multicover Boolean network introduce redundancy expression data representing state transition measurement for wildtype and perturbation data hitting set (set cover) set multicover topology of interconnection network introduce redundancy

23 Synthesizing and Minimizing Signal Transduction Networks

24 Overall Goal direct interaction A B A B network additional information Method (algorithms, software) minimal complexity biologically relevant double-causal interaction A (B C) A (B C) FAST

25 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

26 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.

27 Direct interactions A promotes B A B A B A inhibits B A B A B Illustration of double-causal interaction C promotes the process of A promoting B A pseudo B C

28 Critical edge (known direct interaction, part of input)

29 Main computational step for network synthesis Pseudo-vertex collapse (PVC) not so hard Binary transitive reduction (BTR) hard need heuristics

30 Pseudo-vertex collapse (PVC) Intuitively, the PVC problem is useful for reducing the pseudovertex set to the the minimal set that maintains the graph consistent with all indirect experimental observations. u pseudo-vertices in(u)=in(v) v out(u)=out(v) new psuedo-vertex uv

31 Illustration of Binary Transitive Reduction (BTR) remove? remove? no, critical edge yes, alternate path Intuitively, the BTR problem is useful for determining the sparsest graph consistent with a set of experimental observations

32 High level description of the network synthesis process Synthesize direct interactions Interaction with biologists Optimize BTR Synthesize double-causal interactions PVC Optimize BTR

33 Biological validation of the network synthesis approach

34 Plant signal transduction network consistent guard cell signal transduction network for ABAinduced 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

35 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:

36 Regulatory interactions between ABA signal transduction pathway components

37 Regulatory interactions between ABA signal transduction pathway components (continued) ERA1 (ABA CalM) NO GC not critical and not enzymatic

38 Some nodes in the network GCR1 OST1 NO ABH1 RAC1 putative G protein coupled receptor protein Nitric Oxide RNA cap-binding protein small GTPase protein

39 (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]

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41 Summary of comparison of the two networks Li et al. has 54 vertices and 92 edges our 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

42 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.

43 Software is available at: 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 to the authors

44 Data sources Signal transduction pathway repositories such as TRANSPATH ( protein interaction databases such as the Search Tool for the Retrieval of Interacting Proteins ( 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

45 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

46 LGL leukemia disordered clonal expansion of LGL and their invasions in the marrow, spleen and liver

47 Ras: Background (continued) 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.

48 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

49 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

50 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 pseudovertices 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.

51 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

52 Thank you for your attention! Questions? 52