Computational Models in Systems Biology Karan Mangla 22 nd April, 2008

1. Computational Models in Systems BiologyKaran Mangla22nd April, 2008

2. References • Sachs, K., Perez, O., Pe'er, D., Lauffenburger, D. A. & Nolan, G. P. Causal protein-signaling networks derived from multiparameter single-cell data. Science308, 523-529 (2005) • Fisher, J. & Henzinger, T. A. Executable cell biology. Nat Biotech25, 1239-1249 (2007)

3. Overview • Introduction to Systems Biology • Review of Modeling Techniques • An Example of Systems Biology in action

4. Systems Biology • Goal of systems biology: How do the individual parts interact to yield system behavior? • Biology has focused on figuring out the pieces • But what happens when you fit them together? Slide courtesy of Prof. David Dill, Stanford University

5. Large Data sets in Biology • Protein Interaction Maps • Synthetic Lethality Tests • Genome Sequencing • DNA Microarray • Capture the relative quantities of a large number mRNA’s in the cell

6. Need for Systems Biology • Large data sets • Need to store, integrate and analyze this information into a coherent system • Simple diagrammatic representation schemes can no longer provide usable information

7. A Simple Kohn Map Source: http://discover.nci.nih.gov/kohnk/fig6b.html

8. Types of Models • Mathematical models are used to represent actual quantitative relations between the molecules in the system • Used widely in physics • Generally use a system of differential equations to represent the process • Can be simulated and, in some cases, analyzed • Require very detailed knowledge of the system

9. A Mathematical Model Souce: http://www.homepages.ucl.ac.uk/~ucbpdsb/Report/node21.html

10. Computational Models • Allow for abstract representations of biological processes • Have an inherent execution scheme attached to the model • Certain techniques create finite state machines which can be model checked

11. Model Checking • A technique to analyze finite state machines • Essentially can check for certain temporal properties along all possible executions of the machine • Properties are of two types • LTL : Only temporal properties • In the next state, eventually, always • CTL : Temporal and path properties • Does there exist a path, Along all paths

12. Criteria for Evaluating Models • Scalability of the modeling scheme • Completeness of representation • Ability to incorporate a variety of effects at different levels of abstraction • Ease and Intuitiveness of the modeling scheme • The scheme should be related to actual biology • Tools available for the analysis of the information encoded in the model

13. Types of Biological Processes • Gene Regulatory Networks Source: http://www.bioinfo.de/isb/2006/06/0010/fig4_small.jpg

14. Metabolic Pathways Source: http://pinguin.biologie.uni-jena.de/bioinformatik/Forschung/figs/Cglut_net3_color.png

15. Protein Interaction Pathways Source: http://jorde-lab.genetics.utah.edu/people/reha/4.gif

16. Computational Models • Boolean Network: • Each molecule is considered a node with states as active or inactive • Connections between molecules define activation or inhibition of one molecule by another • A molecule is considered to become active if the sum of its activation is smaller than the sum of its inhibitions

17. Robustness of the Yeast Cell Cycle • Built a boolean network for the yeast cell cycle • Identified one fixed point attracting 86% of the states • Found that the cell cycle steps are extremely stable Proc Natl Acad Sci U S A. 2004 Apr 6;101(14):4781-6. Epub 2004 Mar 22

18. Petri Net Modeling • Two types of nodes: places and transitions • Edges are either from places to transitions or transitions to places • State of the system is defined by the places holding tokens p2 p1 t3 t1 t2 p3

19. Petri Net Modeling • Any transition for which all incoming places have tokens is active • State of the system changes when an active transition fires shifting tokens from in-places to out-places t1 fires p2 p1 t3 t1 t2 p3

20. Petri Net Modeling • Any transition for which all incoming places have tokens is active • State of the system changes when an active transition fires shifting tokens from in-places to out-places t1 fires p2 p1 t3 t1 t2 p3

21. Petri Net Modeling • Any transition for which all incoming places have tokens is active • State of the system changes when an active transition fires shifting tokens from in-places to out-places t1 fires p2 p1 t3 t1 t2 p3

22. Petri Net Modeling • Any transition for which all incoming places have tokens is active • State of the system changes when an active transition fires shifting tokens from in-places to out-places t2 fires p2 p1 t3 t1 t2 p3

23. Petri Net Modeling • Any transition for which all incoming places have tokens is active • State of the system changes when an active transition fires shifting tokens from in-places to out-places t2 fires p2 p1 t3 t1 t2 p3

24. Petri Net Modeling • Any transition for which all incoming places have tokens is active • State of the system changes when an active transition fires shifting tokens from in-places to out-places t2 fires p2 p1 t3 t1 t2 p3

25. Pathalyzer • A place represents a molecule, a location and an activation state • Transitions represent reactions possible in the process Source: http://chicory.stanford.edu/PAPERS/pathalyzer.pdf

26. Interacting State Machines • Model biological systems as state machines • Allow multiple levels of hierarchy to capture different levels of detail in biological systems • Model concurrency through definition of parallel communicating state machines Source: “Statecharts: A Visual Formalism for Complex Systems”, Jeff Pang

27. Modeling C. Elegans Vulval Development using StateChart StateChart Model Actual Biology

28. Process-Calculus • Model molecules as communicating processes • Model reactions as communication between these processes • Try to capture the underlying constraints behind interactions Source: Phillips et. al, Bioconcur, 2004

29. Hybrid Models • Combine mathematical models with computational models • Have discrete variables controlled by discrete state changes • Have continuous variables with rate of change governed by discrete variable

30. Challenges for the Future

31. Discovering Signaling Pathways

32. Problem Definition • Cell Processes require numerous cellular signaling pathways • Information flow occurs through a cascade of molecules being modified chemically and physically • These transitions activate molecules allowing further propagation of the signal Source: http://jorde-lab.genetics.utah.edu/people/reha/4.gif

33. Traditional Means of Studying Pathways • Identify the phenotypic response generated by the pathway • Construct mutants to identify genes involved in the pathway • Perform double mutant experiments to discover relation between genes to understand causality in the pathway

34. Drawbacks • Cannot capture interactions between the different pathways • Cannot consider changes in behavior of the pathway under varied conditions

35. Algorithm for Discovering Signaling Pathways

36. Flow Cytometry • Cells are treated with antibodies which stain specific phosphorylated proteins in the cells • These cells are injected into a sheath flow to cross a laser one cell at a time • Light scatter and light excitation are used to identify quantity of stained molecules Source: http://biology.berkeley.edu/crl/flow_cytometry_basic.html

37. Sample Pathway

38. Modeling Scheme-Bayesian Networks • A Bayesian network over a set X is a representation of the joint probability distribution over X • The representation consists of a directed acyclic graph with variables as nodes and conditional distribution of each variable given its parent • Each variable is independent of its non-descendants, given its paren X1 X4 X2 X5 X3 Source: Peer et. al

39. Example- A Simple Garden • There are two events which could cause grass to be wet: either the sprinkler is on or it's raining • Also, suppose that the rain has a direct effect on the use of the sprinkler (namely that when it rains, the sprinkler is usually not turned on) Source: http://en.wikipedia.org/wiki/Bayesian_network

40. Modeling Signaling Pathways using Bayesian Networks • Model molecules in specific activation states as variables • Arcs represent dependencies between molecules • Direction of arc is decided using intervention data

41. Need for Bayesian Learning

42. Bayesian Inference Algorithm • Use standard scoring metrics that reward relatively simple models • Adapt model to incorporate interventions

43. Bayesian Inference Algorithm • Start with a random network • Explore the possible networks with steps of addition, deletion or reversal of single arc • Accept transition if score is increased

44. Choosing High-Confidence Edges • Process initialized 500 times with different random graphs • Choose only the high confidence networks • Select final edges present in >85% of the high confidence graphs

45. Results- A High Accuracy Map of the Signal Causality Pathway

46. Features of the Approach

47. Experimental Validation of Hypothesis • Tested reported edges experimentally • To test Erk1 on Akt causality used small interfering RNA to inhibit Erk1

48. Advantages of Flow Cytometry • Ability to observe molecular quantities in each cell separately preventing population averaging of results • Large amounts of data generated to enable accurate prediction of pathway structure • Possible to apply a variety of intervention reagents to further classify inter-pathway connections

49. Verification of importance of Flow Cytometry • Applied Bayesian Network Analysis on 3 different data sets • An observation only data set • A population averages data set • A truncated individual cell data set

50. Future Possibilities • Flow Cytometry will grow in power as more antibodies are discovered to allow measurement of different molecules • Handling shortcomings due to need for acyclic graphs enforced by Bayesian Networks • All three edges missed in this paper were due to the acyclic condition