1. A couple of approaches to modelling and analysis of biochemical networks ”Biomodelling” seminar, October 2006 Matúš Kalaš more an inspiration for a discussion than a talk...

2. 2 Contents 1.The variety of modelling paradigms 2.An example of systematic approach (M. Heiner & D. Gilbert) 3.Another example (GOALIE; B. Mishra, M. Antoniotti et al.)

3. 3 Models of biochemical networks How do various modelling paradigms differ? entities concentrations individuals qualitative continuous discrete AMOUNTS OF SPECIES PRESENCE/ABSENCE, HIGH/LOW/MEDIUM, ACTIVE/INACTIVE, HIGH-LEVEL STATES WITH ID, WITH INTERNAL STATE... WITH SHAPE

4. 4 space divided into homogeneous compartments continuous homogeneous WELL-STIRRED discrete space points containing non-reacting entities Models of biochemical networks (cnt.) ”unspaced” HIGH-LEVEL STATES AFFECTING MOVEMENT OF THE ENTITIES

5. 5 time timed hybrid untimed discrete continuous QUANTITATIVE TIME EVENTS, QUALITATIVE TIME TIMED EVOLUTION + EVENTS Models of biochemical networks (cnt.)

6. 6 progression non-deterministic stochastic deterministic synchronous asynchronous APPROXIMATION, MORE REACTIONS IN 1 STEP IDEAL CASE, AVERAGE CASE MORE CASES, ”ALL” CASES, ALL CASES INDIVIDUAL REACTIONS, CONCURRENT & COMPETITIVE Models of biochemical networks (cnt.)

7. 7 Example models ? entitiesconcentrations individuals qualitative continuous discrete space divided into homogeneous compartments continuous homogeneous discrete space points containing non-reacting entities timetimed hybrid untimed discrete continuous progression non-deterministic stochastic deterministic synchronous asynchronous unspaced

8. 8 Prevalent paradigms / buzz words : ODEs continuous concentrations homogeneous space or compartments continuous time deterministic Petri Nets qualitative, discrete or continuous concentrations homogeneous space (or compartments) untimed, discrete or continuous time non-determistic, deterministic, stochastic synch. or asych. Hybrid Automata continuous concentrations homogeneous space or compartments hybrid non-determistic, deterministic,... Gillespie’s Algorithm and alternatives discrete or continuous concentrations homogeneous space or compartments continuous time stochastic asynchronous or synchronous Process Algebras and Logics qualitative,... homogeneous, compartments,... untimed, timed,... non-deterministic or stochastic

9. 9 Now an instant introduction to Petri Nets...

10. 10 An example of systematic modelling: Step-wise modelling David Gilbert, Monika Heiner: From Petri Nets to Differential Equations – An Integrative Approach for Biochemical Network Analysis ICATPN 2006, TR 2005... a tutorial example of different useful features of different modelling paradigms step-wise modelling

11. 11 Step-wise modelling REACTIONS IDENTIFICATION QUALITATIVE MODEL QUALITATIVE ANALYSIS CONTINUOUS MODEL QUANTITATIVE ANALYSIS STRUCTURAL PROPERTIES DYNAMIC PROPERTIES (PREDICTION/SIMULATION, STEADY STATES...) ”debugging” qualitative model (i.e. model structure) validated adjusting constants

12. 12 REACTIONS IDENTIFICATION a simple signalling system: ERK/RKIP pathway Raf-1* + RKIP  Raf-1*_RKIP Raf-1*_RKIP + ERK-PP  Raf-1*_RKIP_ERK-PP Raf-1*_RKIP_ERK-PP  Raf-1* + ERK + RKIP-P MEK-PP + ERK  MEK-PP_ERK MEK-PP_ERK  MEK-PP + ERK-PP RKIP-P + RP  RKIP-P_RP RKIP-P_RP  RP + RKIP

13. 13 QUALITATIVE MODEL a standard place/transition Petri Net (discrete, untimed, non-deterministic)

14. 14 Static analysis of marking-independent properties QUALITATIVE ANALYSIS – automated tool-supported checking of properties - in the example there are 5 minimal P-invariants (Raf-1*, Raf-1*_RKIP, Raf-1*_RKIP_ERK-PP) (MEK-PP, MEK-PP_ERK) (RP, RKIP-P_RP) (ERK, ERK-PP, MEK-PP_ERK, Raf-1*_RKIP_ERK-PP) (RKIP, Raf-1*_RKIP, Raf-1*_RKIP_ERK-PP, RKIP-P_RP, RKIP-P) - these cover the whole net (thus, net is bounded) - Biological meaning: P-invariants correspond to several states of a given species P-invariants (sets of places, over which the weighted sum of tokens is constant during operation)

15. 15 - example net is covered by T-invariants - only 1 non-trivial minimal T-invariant:(k1; k3; k5; (k6; k8), (k9; k11)) QUALITATIVE ANALYSIS (cnt.) Static analysis of marking-independent properties (cnt.) T-invariants - can be also read as the relative firing rates of transitions (reactions/phases in sysbio) (this corresponds to the steady-state behaviour) - minimal T-invariants characterise minimal self-contained subnetworks with an enclosed biological meaning - useful to comprehend the network if it is very complex {not in this tutorial example}

16. 16 QUALITATIVE ANALYSIS (cnt.) Static analysis of marking-independent properties (cnt.) reasonable initial marking constructed with a help of identified invariants

17. 17 QUALITATIVE ANALYSIS (cnt.) Static analysis of marking-dependent properties example net is boolean / 1-bounded / safe the net is live Dynamic analysis of marking-dependent properties example net is reversible MODEL CHECKING of any interesting properties formulated in CTL (Computational Tree Logic) - e.g.:”the phosphorylation of ERK does not depend on a phosphorylated state of RKIP” EG [ERK  E (~(RKIP-P \/ RKIP-P_RP) U ERK-PP) ]

18. 18 QUALITATIVE ANALYSIS (cnt.) VALIDATION OF THE QUALITATIVE MODEL (i.e. structure of the system) all expected structural and general behavioural properties hold covered by P-invariants no minimal P-invariant without biological interpretation covered by T-invariants no minimal T-invariant without biological interpretation no known biological behaviour without corresponding T-invariant all expected logic-formulated properties hold a break?

19. 19 - within this step, all we need is to find suitable rate constants (e.g. to fit in-vivo or in-vitro quantitative experiments) CONTINUOUS QUANTITATIVE MODEL Continuous Petri Net - tokens: real numbers - transitions associated with a rate - semantics: a set of ODEs (e.g. reaction-rate equation) - thus a continuous, timed (continuously) and deterministic model - basically a set of ODEs enhanced with a graphical representation

20. 20 QUANTITATIVE ANALYSIS Prediction (easy) - both qualitative and quantitative Steady-state properties, oscillations, sensibility,... (hard) (... you know better...)

21. 21 Discussion before the next example?

22. 22 Marco Antoniotti, Naren Ramakrishnan, Bud Mishra: GOALIE, A Common Lisp Application to Discover Kripke Models: Redescribing Biological Processes from Time-Course Data ILC 2005 Another example: Automated modelling Samantha Kleinberg, Marco Antoniotti, Satish Tadepalli, Naren Ramakrishnan, Bud Mishra: Remembrance of Experiments Past: A redescription based tool for discovery in complex systems ICCS 2006... building a model in order to understand very complex processes...

23. 23 GOALIE approach / software system GENOMIC MICROARRAY TIME-COURSE DATASET SYSTEM MODEL EXPRESSED IN GENE ONTOLOGY TERMS SYSTEM MODEL ANALYSIS BY FORMAL REASONING GOALIE = Gene Ontology Algorithmic Logic for Invariant Extraction MODEL OF THE SYSTEM /PROCESS DYNAMIC QUALITATIVE PROPERTIES =

24. 24 - qualitative, high-level, untimed and non-deterministic model with clear biological meaning GOALIE approach / software system (cnt.) Model: Kripke Structure - called also ”Hidden Kripke Model” in GOALIE - annotated by Gene Ontology terms (propositional logic)

25. 25 Controlled vocabulary: Gene Ontology GOALIE approach / software system (cnt.)  8517 possible GO process ontology terms

26. 26 Example: yeast cell cycle GOALIE approach / software system (cnt.) (a small part of the whole model)

27. 27 Techniques used to automatically build a model: - time-windowed clustering (k-means) - data-to-GO association done by GoMiner software - Fisher exact test (p-values) - empirical Bayes approach (Benjamini-Hochberg test) - information bottleneck principle (generalised Shannon-Kolmogorov’s rate-distortion theory) - connecting annotated clusters (Jaccard’s coefficient) GOALIE approach / software system (cnt.) Analysis: - propositional temporal-logic reasoning (model checking of temporal invariants (CTL)) - graph rewriting rules for projection and collapsing, preserving ”bisimulation-like” relations  getting higher-level clusters - process / dataset alignment (similarity of cellular processes)

28. 28 A couple of diverse systematic approaches: C. Wiggins, I. Nemenman: Process Pathway Inference via Time Series Analysis, 2006 M. Calder, S. Gilmore, J. Hillston: Automatically deriving ODEs from process algebra models of signalling pathways, CMSB 2005 N. Chabrier-Rivier, M. Chiaverini, V. Danos, F. Fages, V. Schächter: Modeling and Querying Biomolecular Interaction Networks, TCS 2004 A. Arkin, P. Shen, J. Ross: A Test Case of Correlation Metric Construction of a Reaction Pathway from Measurements, Science 1997 M. Chen, R. Hofestädt: A medical bioinformatics approach for metabolic disorders: Biomedical data prediction, modeling, and systematic analysis, JBMI 2006

29. 29 ”Clearly, if the truth must be found, it will need formal methods that no amount of simulation can deliver.” DISCUSSION? THANK YOU! Carla Piazza & Bud Mishra in ’Stability of Hybrid Systems and Related Questions from Systems Biology’, 2005