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1 Extended Petri Nets for Systems Biology Selina Sommer LFE Practical Informatics and Bioinformatics Department Institut für Informatik

2 Outline Extended Petri nets for the simulation of network dynamics Introduction to fuzzy logic Petri nets with fuzzy logic Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 2

3 Petri net elements place transition place [token] [token] Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 3

4 Petri net execution Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 4

5 Extended Petri nets 4 2 Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 5

6 Extended Petri nets conditions x y Typed token values: Transition statements: integers real numbers strings Colored Petri nets functions / programs depending on token values of input places defining new token values of output places Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 6

7 Extended Petri nets - example x: string y: integer x string: hello y = length(x) integer: 5 Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 7

8 Petri nets in systems biology Metabolic networks Signal transduction networks Regulatory networks reaction/ compound compound interaction metabolite protein gene metabolic reaction activation inhibition binding Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 8

9 Petri nets in systems biology reaction/ compound compound interaction concentration ODE number of molecules discrete values stochastic simulation rules Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 9

10 Example for Petri nets in systems biology Cell Illustrator: Petri Net modeling system for biology (Nagasaki, Miyano, et al., Applied Bioinformatics, 2003) Example model: regulation of lacz gene (lac operon) encoding ß-galactosidase, which catalyzes lactose glucose Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 10

11 Example for Petri nets in systems biology Cell Illustrator: Petri Net modeling system for biology (by Nagasaki, Miyano et al., Applied Bioinformatics, 2003) Example model: regulation of lacz gene encoding ß-galactosidase, which catalyses lactose glucose Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 11

12 Extended Petri nets for the simulation of network dynamics Introduction to fuzzy logic Petri nets with fuzzy logic Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 13

13 Fuzzy logic - introduction Fuzzy set theory (L. Zadeh, Information and Control, 1965) A fuzzy set is defined by a membership function f: R [0;1] Unlike classical sets, fuzzy sets contain an element with a certain possibility (not probability!) cold warm hot example: fuzzy concept temperature temperature Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 14

14 Fuzzy logic - introduction Fuzzy set theory Elements belong to fuzzy sets with a possibility defined by the membership functions 1 cold warm hot temperature temp(12) = (1, 0, 0) temp(27) = (0, 0.5, 0.5) temp(17) = (0.2, 0.7, 0) Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 15

15 Fuzzy logic - introduction Fuzzification of a real number x: Apply membership function of each fuzzy set to x Fuzzy value = vector of membership values m = (m 1,, m n ) Defuzzification of a fuzzy value: Several methods, e.g. maximum method, center of gravity method 1 0 m = (0.1, 0.9, 0.4) Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 16

16 Fuzzy logic - introduction Fuzzy logic rules: if x is fuzzy set A then y is fuzzy set B 1 cold warm hot Example: fan regulation if temperature is cold then fan speed is zero if temperature is warm then fan speed is slow if temperature is hot then fan speed is fast Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 17

17 Fuzzy logic - introduction Fuzzy logic rules: if x is A then y is B : m B (y) = m A (x) x 1 AND x 2 : e.g. min(m(x 1 ), m(x 2 )) x 1 OR x 2 : e.g. max(m(x 1 ), m(x 2 )) outcomes of several rules can be OR combined Fields of application: washing machines, control systems, and systems biology Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 18

18 Fuzzy logic in systems biology In systems biology: Fuzzy sets describe e.g. the concentration of metabolites or the regulation of genes 1 0 concentration very low low medium high very high Fuzzy logic rules describe the reactions or interactions e.g. for reaction A B if concentration of A is high then concentration of B is high Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 19

19 Fuzzy logic - motivation Motivation for using fuzzy logic in systems biology Fuzzy aspects in (models of) biological systems: unknown parameters uncertain parameters fuzzy systems Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 20

20 Fuzzy logic - motivation unknown parameters Simulations based on ODEs or stochastic simulations require exact values for kinetic constants Often unknown must be guessed or estimated Fuzzy logic is a natural way of describing the dynamics of a network with unknown parameters Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 21

21 Fuzzy logic - motivation uncertain parameters: e.g. measurement errors Example: expression time series microarray data are inherently fuzzy Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 22

22 Fuzzy logic - motivation fuzzy systems e.g. gene regulation: quantitatively exact description of interactions often not adequate Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 23

23 Extended Petri nets for the simulation of network dynamics Introduction to fuzzy logic Petri nets with fuzzy logic Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 24

24 Fuzzy logic in Petri nets Tokens: Transition statements: type: fuzzy concept value: membership values for the fuzzy sets fuzzy logic rules token values of input places: rule premises new token values of output places: rule conclusions Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 25

25 Fuzzy logic in Petri nets Example 1: modeling of the signal transduction pathway induced by epidermal growth factor (EGF) (D.-Y. Lee, et al., Metabolic Engineering, 2006) Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 27

26 Example 1: EGF-induced signal transduction pathway Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 28

27 Example 1: EGF-induced signal transduction pathway Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 29

28 Example 1: EGF-induced signal transduction pathway Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 30

29 Example 1: EGF-induced signal transduction pathway Rules of the form if concentration of substrate(s) is low then change of concentration of product(s) is low if concentration of substrate(s) is high then change of concentration of product(s) is high Enzymatic reactions: E ES P S Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 31

30 Example 1: EGF-induced signal transduction pathway Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 32

31 Fuzzy logic in Petri nets Example 2: simulation of yeast cell cycle expression data (B. Sokhansanj, et al., BMC Bioinformatics, 2004) 12 core genes 18 time points rules restricted to 4 input genes 3 fuzzy sets: expression ratio = low, medium, high Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 33

Example 2: yeast cell cycle expression data Rules for B-type cyclin CLB5: if CDC20 is low then CLB5 is high if CDC20 is med then CLB5 is high if CDC20 is high then CLB5 is low if CLN2 is low then

32 Example 2: yeast cell cycle expression data Rules for B-type cyclin CLB5: if CDC20 is low then CLB5 is high if CDC20 is med then CLB5 is high if CDC20 is high then CLB5 is low if CLN2 is low then CLB5 is low if CLN2 is med then CLB5 is low if CLN2 is high then CLB5 is high if CLB6 is low then CLB5 is low if CLB6 is med then CLB5 is med if CLB6 is high then CLB5 is low if CDC6 is low then CLB5 is low if CDC6 is med then CLB5 is med if CDC6 is high then CLB5 is high Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 34

33 Conclusion Advantage of Petri nets: flexible tool for visualization and simulation of networks Fuzzy logic natural representation for models with imprecise knowledge or data well suited for modeling e.g. microarray expression data Required: techniques for learning fuzzy logic rules, especially for larger networks Selina Sommer, LMU Institut für Informatik, Lehrstuhl für Praktische Informatik und Bioinformatik 35

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