1. Developing Models in Virtual Cell Susana Neves, Ph.D. 1

2. Part 1: Compartmental Models (ODE models) Compartments Components and Reactions Kinetics Applications Part 2: Spatial Models (PDE models) Geometries Diffusion Coefficients – Experimental approaches » FRAP » FCS – Estimation of Diffusion coefficents Reactions – FRET 2

3. Vcell Requirements Registration Java Version 1.5 or later Internet connection Vcell.org 3

4. Steps to Develop A Kinetic Model 4 Time courseDose response

5. Vcell Organization BioModel representation of the model: compartments, molecules, connectivity map, kinetics Applications initial conditions: initial concentrations, diffusion coefficients, actual morphologies, electrical protocols, etc. Simulations time length, time step, sampling rate, resolution, solvers to use, parameter overrides, etc. 5

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7. BioModels compartments molecules biomodelsApplications 7

8. Compartments 8

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10. Molecules 10

11. Molecules 11

12. Reactions reactions fluxes connectors Right click on compartment of interest and select reactions 12

13. Reactions Reactants connect to the left of the reaction icon, products to the right Enzymes connect to the center of the reaction icon 13

14. Reactions Kinetic Type: – General – Mass Action – Henri Michaelis-Menten (irreversible) – Henri Michaelis-Menten (reversible) 14

15. Mass Action Right click on reaction icon; select properties 15

16. Enzymatic 16

17. ODE application Right click on Biomodel icon in the application box; select create deterministic application 17

18. ODE application Input the volume and surface of your compartment. In this case we assume cytosol to be a sphere with a radius of 10 um 18

19. ODE application Select the “initial concentrations” tab. Input the initial concentrations of your molecules. Cytosolic molecules have units of uM. Membrane molecules have units of molecules/um2 Select “clamped” if the molecule of interest is supposed to be buffered (not limiting, endless supply). 19

20. ODE application For each application, it is possible to disable specific reactions under the “reaction mapping tab” 20

21. ODE application Select ”Simulation” tab and click on New, and then edit 21

22. ODE application Under the parameters tab, there will be a list of all the parameters in your application/biomodel (initial concentrations, kinetic parameters, etc). By selecting “scan” you can run several simulations simultaneously with different combinations of parameters. 22

23. ODE application Under the task tab, input the length of the simulation (in seconds), and the sampling rate (how many time samples you want to retrieve in your results) Under the advanced tab, select solver (either variable time step or fixed time step) 23

24. ODE application Upon completion, view graph results by selecting variable of interest; multiple variables can be selected by holding the ctrl key. Right clicking on graph will allow you to change the scale of the graph. 24

25. ODE application Results can also be viewed in a table format. To copy data, right click 25

26. ODE application To export multiple variables, click on export tab, and select time interval and variables of interest. You will get a zipped comma-delimited ASCII file that you can open in Excel. 26

27. Part 2 Part 2: Spatial Models (PDE models) Geometries Diffusion Coefficients – Experimental approaches » FRAP » FCS – Estimation of Diffusion coefficents Reactions – FRET 27

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30. PDE Application 30

31. Upload geometry File->New-> Geometry -> from image -> from file Image Tiff format Grayscale 8 bit Each compartment should have its own gray-scale coloring 31

32. Geometry 32

33. Geometry ((x*x+y*y)<100.0) File>New>Geometry>Analytic>2-D 33

34. Virtual Cell ΔV volume element ΔSsurface delineating the volume element 10 x 10 elements The more intricate the geometry, the smaller the mesh (more elements per unit area) 34

35. Spatial Models Assuming that the volume element ΔV, is small enough to ignore any spatial changes within it, net flux of the species X across the surface ΔS, delineating the volume element; j n,X is the flux density reaction term, sum of all the reaction rates v X that affect the species X. Slepchenko BM. et al., Trends in Cell Bio 13:570 (2003) 35

36. PDE Application Rate = (J_MEK_activates_MAPK - J_PP2A_MAPK - J_PTP - J_PTP_PKA) J_MEK_activates_MAPK = (Vmax_MEK_activates_MAPK * MAPK_cyto / (Km_MEK_activates_MAPK + MAPK_cyto) J_PTP = (Vmax_PTP * MAPK_active_cyto / (Km_PTP + MAPK_active_cyto) J_PTP_PKA = (Vmax_PTP_PKA * MAPK_active_cyto / (Km_PTP_PKA + MAPK_active_cyto) J_PP2A_MAPK = (Vmax_PP2A_MAPK * MAPK_active_cyto / (Km_PP2A_MAPK + MAPK_active_cyto) PdeEquation MAPK_active Rate (J_MEK_activates_MAPK - J_PPase_MAPK - J_PTP - J_PTP_PKA); Diffusion MAPK_active_cyto_diffusionRate; Initial MAPK_active_cyto_init; 36

37. Geometry reconstructed from serial stacks of purkinje neuron 37

38. PDE application 38

39. PDE Application 39

40. PDE Application 40

41. PDE Application 41

42. FRAP 42

43. http://vcell.org/vcell_software/user_materials.html FRAP tutorial 43

44. FCS 44

45. Diffusion coefficent 45 Where D GFP = 25  m 2 /s, and MW GFP = 27 kDa.

46. FRET 46

47. Comparing simulations to FRET imaging experiments 47

48. Modifiers 48

49. Modifiers 49

50. Modifiers 50

51. Modifiers 51

52. Parameter Estimation 52

53. Parameter Estimation 53

54. Parameter Estimation 54

55. PDE model of PIP2 in spines 55 Brown SA, et al.,. Analysis of phosphatidylinositol-4,5- bisphosphate signaling in cerebellar Purkinje spines. Biophys J. 2008 Aug;95(4):1795-812.

56. PDE model of Ca ++ in neuroblastoma cells 56 Fink CC, Slepchenko B, Moraru II, Watras J, Schaff JC, Loew LM. An image-based model of calcium waves in differentiated neuroblastoma cells. Biophys J. 2000 Jul;79(1):163-83.

57. PDE model of nuclear Ran transport 57 Smith AE, Slepchenko BM, Schaff JC, Loew LM, Macara IG. Systems analysis of Ran transport. Science. 2002 Jan 18;295(5554):488-91

58. PDE model of signaling microdomains 58 Neves SR, Tsokas P, Sarkar A, Grace EA, Rangamani P, Taubenfeld SM, Alberini CM, Schaff JC, Blitzer RD, Moraru II, Iyengar R. Cell shape and negative links in regulatory motifs together control spatial information flow in signaling networks. Cell. 2008 May 16;133(4):666-80

59. www.sciencesignaling.org Slides from a lecture in the course Systems Biology—Biomedical Modeling Citation: S. R. Neves, Developing models in Virtual Cell. Sci. Signal. 4, tr12 (2011).