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1. http://creativecommons.org/licenses/by-sa/2.0/

2. IntegrativeComputationalBiology Prof:Rui Alves ralves@cmb.udl.es 973702406 Dept Ciencies Mediques Basiques, 1st Floor, Room 1.08 Website:http://web.udl.es/usuaris/pg193845/testsite/ Course Website:http://web.udl.es/usuaris/pg193845/Bioinformatics_2009/

3. Recap: Hey, it’sraining!!! Whydon’twe try and figure outhowallthelittle molecular pieces in a cellworktogether and do stuff?!?!?! Look!! We now know how to use bioinformatics to reconstruct biological networks. What now?

4. The whys and hows of mathematical modeling of biological networks, with a view to pitfalls and limitations Prof:Rui Alves ralves@cmb.udl.es 0034973702406 Dept Ciencies Mediques Basiques, 1st Floor, Room 1.08 http://web.udl.es/usuaris/pg193845/testsite/index.htm Course Website:http://web.udl.es/usuaris/pg193845/Bioinformatics_2009/

5. Organization of thetalk • Fromnetworkstophysiologicalbehavior • Graphicalnetworkrepresentations • Mathematicalformalisms • Types of problems • Typicalbottlenecks and assumptions in modelbuilding

6. Have gene, wantnetwork • Youhave a gene orprocess of interest • Genes/Proteins do notworkalone • Howdoesyour gene work in itsphysiologicalenvironment? • Use differentmethods and reconstructthenetworkwherethe gene isworking

7. Lo and Behold, a network

8. Thatisnicedear, but can youtell me… • What do theinteractionsbetweennodes mean?

9. Lo and Behold, a network No

10. Thatisnicedear, but can youtell me… • What do theinteractionsbetweennodes mean? • No!!! • Whichproteins are importantregulatorypoints in thedynamic responses?

11. Lo and Behold, a network No No

12. Thatisnicedear, but can youtell me… • What do theinteractionsbetweennodes mean? • No!!! • Whichproteins are importantregulatorypoints in thedynamic responses? • No!!! • All genes that are fundamental forthefunction of thenetwork?

13. Lo and Behold, a network No No No, notreally, althoughyou can use somecombination of centralitymeasuresto figure out a few.

14. Ambiguous in silicofunctionalnetworks are limited as predictors of physiologicalbehavior

15. Howtopredictbehavior of networkorpathway? • Maybeifnetworkrepresentation has precise and unambiguousmeaningwe can do it!!!!

16. Organization of thetalk • Fromnetworkstophysiologicalbehavior • Graphicalnetworkrepresentations • Mathematicalformalisms • Types of problems • Typicalbottlenecks and assumptions in modelbuilding

17. A B A B A B A B B A B A Function Function Function Function Network representationis fundamental forclarity of analysis Whatdoesthis mean? Possibilities:

18. Defining network conventions A and B – Dependent Variables (Changeover time) C – Independent variable (constantvalue) C - + A B Full arrowrepresents a flux between A and B. Dashedarrowwith a plus signrepresents positive modulation of a flux. Dashedarrowwith a minussignrepresentsnegativemodulation of a flux. Dashedarrowrepresentsmodulation of a flux.

19. Defining network conventions C + 3 D+ A B 2 Reversible Reaction Stoichiometric informationneedstobeincluded. Dashedarrowrepresentsmodulation of a flux. Dashedarrowwith a plus signrepresents positive modulation of a flux. Dashedarrowwith a minussignrepresentsnegativemodulation of a flux.

20. Defining network conventions C + 2 A B 3 D Stoichiometric informationneedstobeincluded. Dashedarrowrepresentsmodulation of a flux. Dashedarrowwith a plus signrepresents positive modulation of a flux. Dashedarrowwith a minussignrepresentsnegativemodulation of a flux.

21. Renaming Conventions Havingtoomanynamesornamesthat are closelyrelatedmaycomplicateinterpretation and set up of themodel. Therefore, using a structurednomenclatureisimportantforbookkeeping. Letuscall Xi to variable i A X1 B X2 C X3 D X4

22. New Network Representation X3 + 2 X1 X2 3 X4 A X1 B X2 C X3 D X4

23. Production and sink reactions X0 X2 ProductionReaction SinkReaction

24. Cells have compartments X0 X2 Cell Organel Compartmentalmodels are important, bothbecausecompartmentsexist in thecell and becauseeven in theabsence of compartmentsreaction media are notalwayshomogeneous.

25. Consistency is important • Whateverrepresentationisused, besureyou are consistent and youknowexactlywhatthedifferentelements of a representation mean.

26. 1 – Metabolite 1 isproducedfrommetabolite 0 byenzyme 1 2 – Metabolite 2 isproducedfrommetabolite 1 byenzyme 2 3 – Metabolite 3 isproducedfrommetabolite 2 byenzyme 3 4 – Metabolite 4 isproducedfrommetabolite 3 byenzyme 4 5 – Metabolite 5 isproducedfrommetabolite 3 byenzyme5 6 – Metabolites 4 and 5 are consumedoutsidethesystem 7 – Metabolite 3 inhibitsaction of enzyme 1 8 – Metabolite 4 inhibitsenzyme 4 and activatesenzyme 5 9 – Metabolite 5 inhibitsenzyme 5 and activatesenzyme 4 Test Cases: Metabolic Pathway

27. 1 – mRNAissynthesizedfromnucleotides 2 – mRNAisdegraded 3 – Proteinisproducedfrom amino acids 4 – Proteinisdegraded 5 – DNA isneededformRNAsynthesis and ittransmitsinformationforthatsynthesis 6 – mRNAisneededforproteinsynthesisittransmitsinformationforthatsynthesis 7 – Proteinis a transcription factor thatnegativelyregulatesexpression of themRNA 7 – Lactosebindstheproteinreversibly, with a stoichiometry of 1 and creates a form of theproteinthatdoesnotbind DNA. Test Cases: Gene Circuit

28. 1 – 2 stepphosphorylationcascade 2 – Receptor protein can be in one of twoformsdependingon a signal S 3 – Receptor in active form can phosphorylate a MAPKKK. 4 – MAPKKK can bephosphorylated in twodifferentresidues; both can bephosphorylatedsimultaneously 5 – MAPKK can bephosphorylated in twodifferentresidues; both can bephosphorylatedsimultaneously 6 – Residue 1 of MAPKK can onlybephosphorylatedifbothresidues of MAPKKK are phosphorylated 7 – Residue 2 of MAPKKK can bephosphorylatedifone and onlyone of theresidues of MAPKKK are phosphorylated. Test Cases: Signal transduction pathway

29. Mayberesolvingambiguity in representationisenoughtopredictbehavior? X0 X1 X2 X3 E1 E2 E3 E4 t0 t1 t2 t3 X0 X1 X2 X3

30. X3 t Dynamicbehaviorunpredictable in non-linear systems X0 X1 X2 X3 Unambiguousnetworkrepresentationisnotenoughtopredictdynamicbehavior.

31. Unambiguousnetworkrepresentations are notenough • Unambiguousnetworkrepresentations are necessarybutnotsufficientforpropernetworkanalysis. • Why? • Non linear behavior of biologicalsystems!

32. Howtopredictbehavior of networkorpathway? • Buildmathematicalmodels!!!! Britton ChanceTHE KINETICS OF THE ENZYME-SUBSTRATE COMPOUND OF PEROXIDASEJ. Biol. Chem., Dec 1943; 151: 553 - 577 

33. Organization of thetalk • Fromnetworkstophysiologicalbehavior • Graphicalnetworkrepresentations • Mathematicalformalisms • Types of problems • Typicalbottlenecks and assumptions in modelbuilding

34. Representing the time behavior of your system C + A B

35. Flux Linear A or C Saturating Sigmoid What is the form of the function? C + A B

36. What if the form of the function is unknown? C + A B Taylor Theorem: f(A,C) can be written as a polynomial function of A and C using the function’s mathematical derivatives with respect to the variables (A,C)

37. Are all terms needed? C + A B f(A,C) can be approximated by considering only a few of its mathematical derivatives with respect to the variables (A,C)

38. Linear approximation C + A B Taylor Theorem: f(A,C) is approximated with a linear function by its first order derivatives with respect to the variables (A,C)

39. What if system is non-linear? • Use a firstorderapproximation in a non-linear space.

40. Logarithmic space is non-linear C + A B Use Taylor theorem in Log space PowerLawFormalism: g<0 inhibits flux g=0 no influence on flux g>0 activates flux

41. Why log space? • Intuitiveparameters • Simple, yet non-linear • Convexrepresentation in cartesianspace • Linearizesexponentialspace • Manybiologicalprocesses are closetoexponential→ Linearizesmathematics

42. Whyisformalismimportant? • Reproduction of observedbehavior • Tayloring of numericalmethodstospecificforms of mathematicalequations

43. Test Cases: Metabolic Pathway _ _ X3 + X0 X1 X2 + _ X4 _

44. Are thereotherapproximativeformalisms? • Yes: Linlog, Log-Lin, Inverseformalism, SC formalism, etc… • Linlog and log lin are equivalenttothepowerlawformalism • Whatdoestheinverseformalism looks like?

45. InverseFormalism • Xi Yi=1/Xi • Vi(X) Fi(Yi)=1/Vi This is what the inverse formalism looks like

46. Test Cases: Gene circuit _ X0 X1 + X2 X3 + + X6 X4 X5 +

47. Are thereotherapproximativeformalisms? • Yes: Linlog, Log-Lin, Inverseformalism, SaturatingCooperativeformalism, etc… • Linlog and log lin are equivalenttothepowerlawformalism • Whatdoestheinverseformalism looks like? • Whataboutthe SC formalism?

48. SaturatingCooperativeFormalism C • Xi Yi=1/X • Vi(X) Fi(Yi)=1/Vi May be very usefull when representing saturable and cooperative phenomena

49. Test Cases: Signaltransduction + + + X4 X4 X1 X3 X6 X6 X3 X0 + X5 X5 + X2 + + +

50. SaturatingCooperativeFormalism in a log space C • Xi Yi=1/X • Vi(X) Fi(Yi)=Log[1/Vi] May also be very usefull when representing saturable and cooperative phenomena