1. Introduction to COPASI (5 min) Exercise 1. Building and analyzing dynamic models in COPASI (20 min) Exercise 1.1. MAP kinase model Exercise 1.2. MAP Kinase/phosphatase model Exercise 2. Paradoxes in “ATP module” (30 min) Exercise 3. Design principle studies of ROS management Introduction (5 min) Exercise 3.1. Simplified ROS model (10 min) Exercise 3.2. Negative feed-back (keap1-nrf2). Homeostasis (10 min) Exercise 3.3. Amplifying homeostasis (NF  B and DJ-1) (10 min) Exercise 4. Detailed ROS model for personalized medicine Introduction (5 min) Exercise 4.1. Simulation of stress and distress in ROS model (15 min) Exercise 4.2. Coffee effect (15 min) Exercise 4.3. Parkinson’s Disease personalised medicine (20 min) Four tutorials (Dr. Alexey Kolodkin and Prof. Hans V. Westerhoff): Designing individualized therapies by using systems medicine

2. Exercise 1 MAP kinase/phosphatase model

3. Part 1. Building and analyzing dynamic models in COPASI Exercise 1.1. The MAP kinase pathway is not a MAP kinase pathway. reactionrateVmKmk1 1X1 -> X1P; RkinaseVm*Act*S/(Km+ S) 0.1 3X2 -> X2P; X1PkinaseVm*Act*S/(Km+ S) 0.1 1a. Build the model: equations, parameter values X1X1PRX2X2P 20020 1b. Build the model: Initial conditions R= Activated receptor X i =phosphorylate d kinases

4. Please install COPASI beforehand (for free) www.copasi.org Download free version

5. 1.Open COPASI 2.Create species

6. 3. Create reactions 4. Create rate laws (Functions)

7. 5. Create Output Specifications -> Plots

8. 6. Run Tasks Time Course, Steady State, Metabolic Control Analysis

9. Exercise 1.1 MAP kinase model COPASI model: Exercise1.1-ERK1-kinaseOnly.cps

10. Part 1. Building and analyzing dynamic models in COPASI Exercise 1.1. Map kinase (kinase cascade for signal transduction) model. R=0X1X1PX2X2P ???? totalX1+X1P=2X2+X2P=2 1. Find Steady State for R=0 and take these values as Initial Conditions R=1X1X1PX2X2P ???? totalX1+X1P=2X2+X2P=2 2. Fix R=1 and find new Steady State values 3. Simulate Time Course for all species Question to be addressed: What is wrong with the concept ‘a protein kinase pathway’?

11. Answers for Exercise 1.1. Kinases model R=0X1X1PX2X2P 2020 X1+X1P=2X2+X2P=2 1. Find Steady State for R=0 and take these values as new Initial Conditions R=1X1X1PX2X2P 0202 X1+X1P=2X2+X2P=2 2. Fix R=1 and find new Steady State values 3. Time Course for all species Both X1 and X2 become completely phosphorylated

12. R (growth factor)=0.01: More slowly but ultimately X 2 and X 1 are completely phosphorylated:  MAP kinase cascade always active, hence oncogenic? The MAP kinase cascade: R=1 and R=0.01 Question to be addressed: What is wrong with the concept ‘a protein kinase pathway’?

13. …………. ……………… …….. What is the remedy (cure)? ………… ………….. ………… Question to be addressed: What is wrong with the concept ‘a protein kinase pathway’? What is the answer?

14. Exercise 1.2 MAP kinase/phosphatase model COPASI model: Exercise1.2-ERK1-kinaseANDphosphatase.cps

15. Part 1. Building and analyzing dynamic models in COPASI Exercise 1.2. MAP kinase/phosphatase pathway: Add phosphatases. reactionrateVmKmk1 1X1 -> X1P; RkinaseVm*Act*S/(Km+S)0.1 2X1P -> X1phosphataseVm*S/(Km+S)0.1 3X2 -> X2P; X1PkinaseVm*Act*S/(Km+S)0.1 4X2P -> X2phosphataseVm*S/(Km+S)0.1 1a. Build the model: equations, parameter values X1X1PRX2X2P 11011 1b. Build the model: Initial conditions

16. Part 1. Building and analyzing dynamic models in COPASI Exercise 1.2. Kinase/phosphatase model. R=0X1X1PX2X2P ???? totalX1+X1P=2X2+X2P=2 1. Find Steady State for R=0 and take these values as new Initial Conditions R=1X1X1PX2X2P ???? totalX1+X1P=2X2+X2P=2 2. Fix R=1 and find new Steady State values 3. Simulate Time Course for all species

17. Answers for Exercise 1.2. Kinase/phosphatase model. R=0X1X1PX2X2P 2020 X1+X1P=2X2+X2P=2 1. Find Steady State for R=0 and take these values as new Initial Conditions R=1X1X1PX2X2P 1111 X1+X1P=2X2+X2P=2 2. Fix R=1 and find new Steady State values Time Course for all species With phosphatases phosphorylation level not complete in steady state

18. The MAPkinase+phosphatase cascade: R=1 and R=0.01 When R (growth factor)=0.01, X2 is almost completely unphosphorylated When R (growth factor)=1, X2 is phosphorylated

19. Conclusions (tell us whether you agree) The MAP kinase pathway should better not be a MAPkinase pathway –It would cause cancer One can figure things out with small models –General principles Amsterdam is the capital of Denmark –Denmark is more organized than that Phosphatases have negative but equal control –Yes, there is even a mathematical proof COPASI is doable –You showed it

20. Exercise 2 Paradoxes in “ATP module”

21. Part 2. Paradoxes of an “ATP” Module: Hierarchies in control: Mitochondria make ATP for the cell, but do they determine the ATP level? M (Mitochondria, cell, organism) S 2 substrate (Energy) S 1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 What are your expectations? 1.ATP is determined by balance between v 3 and v 4 2.Mitochondria is determined by balance between v 1 and v 3 This expectation may be wrong! Why?

22. Exercise 2 Paradoxes in “ATP module” COPASI model: Exercise2-only ATP reactions.cps

23. Part 2. Paradoxes of “ATP” Module: Mitochondria make ATP for the cell M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 Rate equations: v3=k3*S2*M v4=k4*ATP Balance equation: dATP/dt = v3-v4 1.Show that the mitochondria bring ATP to a steady state level (not to infinity) (on the back of an envelope and in COPASI) 2. Show that the ATP level depends on substrate, on concentration of mitochondria and on consumption rate constant. 3. Calculate the corresponding control coefficients.

24. Answers: Mitochondria make ATP for the cell M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 v3=k3*S2*M v4=k4*ATP dATP/dt = v3-v4 Steady state: 0=dATP/dt = v3-v4 =k3*S2*M-k4*ATP ATP ss =k3*S2*M/k4: ATP strongly dependent on both k3 and k4 But how do we quantify strongly dependent?

25. Answers: Mitochondria make ATP for the cell M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 v3=k3*S2*M v4=k4*ATP dATP/dt = v3-v4 Steady state: 0=dATP/dt = v3-v4 =k3*S2*M-k4*ATP ATP ss =k3*S2*M/k4: ATP strongly dependent on both k3 and k4

26. Exercise 2 Paradoxes in “ATP module” COPASI model: Exercise2-Only Mitochondrial reactions.cps

27. Part 2. Paradoxes of “ATP” Module: Making mitochondria costs ATP M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 v1= k1*S1*n ATP *ATP*M v2=k2*M dM/dt = v1-v2 dATP/dt = -v1 1.Find conditions when steady state is possible (on the back of an envelope and in COPASI)

28. Answers: Making mitochondria costs ATP M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 0=dM/dt = k1*S1*n ATP *ATP*M-k2*M ATP=k2/(k1*S1*n ATP ) 0=dATP/dt = -n ATP *k1*S1*n ATP *ATP*M= (n ATP ) *(k1)*(S1)*M*k2/(k1*S1*n ATP ) M*k2=0 Hence: M=0, i.e. mitochondria will disappear at steady state. How come? v1= k1*S1*n ATP *ATP*M v2=k2*M dM/dt = v1-v2 dATP/dt = -v1= -n ATP *v1

29. Exercise 2 Paradoxes in “ATP module” COPASI model: Exercise2-Complete-ATP-Paradoxes.cps

30. Part 2. Paradoxes of “ATP” Module The system combined M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulators) v1 v2 v3v4 v1= k1*S1*n ATP *ATP*M v2=k2*M v3=k3*S2*M v4=k4*ATP dM/dt = v1-v2 dATP/dt = v3-v4-n ATP *v1 1.Find conditions when steady state is possible (on the back of an envelope and in COPASI) 2. How is the Mitochondrial concentration affected by reaction 4 (k4)?

31. M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulator) v1 v2 v3v4 v1= k1*S1*n ATP *ATP*M v2=k2*M v3=k3*S2*M v4=k4*ATP k1*S1*ATP*M - k2*M =0 (M balance) k3*S2*M - n ATP *k1*S1*ATP*M - k4*ATP =0 (ATP balance) dM/dt = v1-v2 dATP/dt = v3-v4-n ATP *v1 Steady State: dM/dt = 0 dATP/dt = 0 M balance requires: ATP= k2/(S1*k1) k3*S2*M - n ATP *k1*S1*M*k2/(S1*k1) - k4*k2/(S1*k1) =0 k3*S2*M - n ATP *M*k2- k4*k2/(S1*k1) =0 M*(k3*S2 – k2) = k4*k2/(S1*k1) S1*k1*(k3*S2 – n ATP *k2) M= k4*k2 S2 > k2/k3 Paradox: k4 increases=> M increases S1 increases=> M decreases ATP independent of k3 and k4 Answers for part 2. Paradoxes of “ATP” Module

32. M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulator) v1 v2 v3v4 S1*k1*(k3*S2 – n ATP *k2) M= k4*k2 S2 > k2/k3 Paradox: k4 increases=> M increases S1 increases=> M decreases ATP independent of k3 and k4 Answers for part 2. Paradoxes of “ATP” Module ATP= k2/(S1*k1) Remember: In the absence of mitochondrial turnover (k2=0=k1): Steady state: 0=dATP/dt = v3-v4 =k3*S2*M-k4*ATP ATP=k3*S2*M/k4: ATP strongly dependent on k3 and k4

33. Answers for part 2. Paradoxes of “ATP” Module in COPASI Mitochondria vs S1 Indeed, this all works in COPASI

34. Exercise 2 Paradoxes in “ATP module” COPASI model: Exercise2-More realistic model.cps

35. More realistic model: ATP converts to ADP in reaction v1 (ATP is used for mitoch synthesis) but, at the same time, ADP activates v1 (Model ATP-ADP attached) Works at Steady State

36. ATP concentrationMitoch Concentration 1. Perfect adaptation to exercises (ATP consumption): Increase ATP consumption 100 fold (e.g. k4 increased from 0.1 to 10) This does not affect ATP concentration!!! (while Mitoch goes to new Steady State) ROBUST! Because this part is fragile! Perfect adaptation!!! Mitoch is fixed ATP collapses

37. 2a. Perfect adaptation to exercises has a limit: ATP consumption may be increased 500 fold (e.g. k4 increased from 0.1 to 50) Still perfect adaptation!!! But, if we increase k4 too much (e.g. k4=60), then systems collapses to a new ‘death’ steady state; please explain k4=60 k4=50 ROBUST! Collapse!

38. ATP consumption may be increased 500 fold (e.g. k4 increased from 0.1 to 50) Still perfect adaptation!!! But, if we increase k4 too much (e.g. k4=60), then systems collapses Indeed, collapse due to the loss of Mitochondria!!!

39. M (Mitochondria, cell, organism) S2 substrate (Energy) S1 substrate (“Building blocks”) ATP (Energy accumulator) v1 v2 v3v4 v1= k1*S1*n ATP *ATP*M v2=k2*M v3=k3*S2*M v4=k4*ATP k1*S1*ATP*M - k2*M =0 (M balance) k3*S2*M - n ATP *k1*S1*ATP*M - k4*ATP =0 (ATP balance) dM/dt = v1-v2 dATP/dt = v3-v4-n ATP *v1 Steady State: dM/dt = 0 dATP/dt = 0 M balance requires: ATP= k2/(S1*k1) or ATP=0; M=0: all v’s zero M= 0 The second, death steady state:M=ATP=0 Answers for part 2. Paradoxes of “ATP” Module: the death state once ATP=0

40. Initial Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Perturbation ATP decrease Around 40% Mitoch = 0.911774 ATP=0.6 ADP=0.4 Final Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 3a. Dynamics of the response to the decrease of ATP concentration ATP grows back Mitoch ROBUST! Perfect homeostasis Sensitivity provides robustness!

41. Initial Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Perturbation ATP increase Around 10% Mitoch = 0.911774 ATP=0.95 ADP=0.05 Final Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Mitoch 3b. Dynamics of the response to the increase of ATP concentration ROBUST! Perfect homeostasis Sensitivity provides robustness!

42. Initial Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Perturbation Mitoch increase Around 100% Mitoch = 1.4 ATP=0.887298 ADP=0.112702 Final Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Mitoch decreases back ATP robust! 3c. Dynamics of the response to the increase of Mitochondrial concentration

43. Initial Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Perturbation Mitoch decrease around 50% Mitoch = 0.35 ATP=0.887298 ADP=0.112702 Final Mitoch= 0.698569 ATP=0.887298 ADP=0.112702 ATPtot=1 Mitoch increases back ATP robust! 3d. Dynamics of the response to the decrease of Mitochondria concentration

44. The closer to the unstable state, the longer (higher area under the curve) it takes to come back to steady state under perturbation k4=0.1->10k4=0.1->0.2

45. Please summarize these findings If mitochondria are dynamic then ATP may be determined by their kinetics not by the kinetics of oxidative phosphorylation This should be valid for slow steady states Robustness in one part of network comes at the cost of high fragility (sensitivity) in other parts And, a second, ‘death state’ may appear!

46. Exercise 3 Design principle studies of ROS management

47. mitochondria, ER, cytoplasm ROS ROS regulatory network Cell differentiationImmune responseCell damage Reactive Oxygen Species (ROS) management ROS Part 3. Design principle studies of ROS management

48. Exercise 3 Design principle studies of ROS management. Simplified ROS model. COPASI model: Exercise3-ROSdesign-model1.cps

49. Part 3. Design principle studies of ROS management Exercise 3.1. Simplified ROS model (10 min) Simplified network diagram of ROS-management is shown in SBGN format. There is continued synthesis of Healthy Mitochondria. Healthy Mitochondria get older and are turned into Impaired Mitochondria. Impaired Mitochondria produce ROS. Mitochondrial aging is catalysed by ROS (positive feed-back). ROS are quenched by antioxidant machinery and Impaired Mitochondria are removed in mitophagy (mitoptosis) with the help of p62 and Parkin proteins: Open COPASI file ComoExercise2-ROSdesign-model1.cps and run Steady State. Then check how step increase of ROS generation affects concentration of other species. The increase of ROS generation is observed in many diseases (e.g. disruption of Electron Transport Chain by toxins or due to mutations). In order to activate ROS generation, increase kf for reaction 4 from 100 till 200 a.u. and run Time Course

50. Answers for exercise 3.1. Simplified ROS model An increase of ROS synthesis results in a proportional increase of ROS concentration (no homeostasis) Control coefficient of 1

51. Exercise 3 Design principle studies of ROS management. Negative feed-back (keap1-nrf2). Homeostasis COPASI model: Exercise3-ROSdesign-model2.cps

52. Part 3. Design principle studies of ROS management Exercise 3.2. Negative feed-back (keap1-nrf2). Homeostasis (10 min) We add nrf2-keap1 system (pink) that is activated by ROS and regulates p62 and antioxidants concentration (COPASI file ComoExercise2-ROSdesign-model2.cps): Open COPASI file ComoExercise2-ROSdesign-model2.cps. Plot the response to step increase of ROS generation (increase kf for reaction 4 from 100 till 300 a.u. and run Time Course)

53. Answers for exercise 3.2. Negative feed-back (keap1-nrf2). Homeostasis Homeostasis emerges: ROS activates Nrf2, Nrf2 induces Antioxidant response and p62. The later counteracts the increase of ROS concentration (negative feed-back loop) ROS Antioxidant Response:

54. Exercise 3 Design principle studies of ROS management. Amplifying homeostasis (NFkB and DJ-1) COPASI model: Exercise3-ROSdesign-model3.cps

55. Part 3. Design principle studies of ROS management Exercise 3.3. Amplifying homeostasis (NFkB and DJ-1) (10 min) We add NFkB signaling and DJ-1 (Park7). DJ-1 is activated by ROS and activates both Nrf2- keap1 system and NFkB signaling. Open ComoExercise1-ROSdesign-model3.cps. Increase ROS generation and check the response. (Increase ROSsynt from 100 to 300, then run Time Course)

56. Answers for exercise 3.3. Amplifying homeostasis (NFkB and DJ-1) System exhibits strong homeostasis and compensates the increase of ROS generation

57. Conclusions Loops for homeostasis and amplification

58. Exercise 4 Detailed ROS model for personalized medicine COPASI model: Exercise4-ROS-DetailedModel.cps

59. ROS-activated Regulatory Network ROS network on Parkinson's disease (PD) map

60. Detailed model of ROS management

61. distress (when stress is too high, stress accumulates and system collapses). Hans Selye (1907-1982): Stress and distress stressing factor (e.g. increased ROS) Response (e.g. ATP level) eustress (general adaptation syndrome) Hans Selye (1907-1982)

62. Stressing factor: increase of ROS generation Stress and distress in ROS model (Healthy) ROS ATP adaptation to stress (eustress) accumulation of stress (distress) Response: ATP concentration System allows to compensate stress (increased ROS generation) in the short term. However, in the long term, system collapses. Nrf2

63. Open COPASI file Exersise3-ROS-DetailedModel.cps. Assign “Oscillations” (transient values) to ROSsynt in “Global quantities”. Run Time Course in the time scale 100 min. Check the behaviour of ROS, Healthy Mitochondria and ATP and give your interpretation: In the long term, stress may accumulate (“distress” by Selye) and finally system collapses. Run Time Course in the time scale 10,000 min. Check the behaviour of ROS, Healthy Mitochondria, Damaged Mitochondria, ATP, p62 and cyt c in the long term and provide your interpretation. Part 4. Detailed ROS model for personalized medicine Exercise 3.1. Simulation of stress and distress in ROS model (15 min)

64. ROS first increases but then can be compensated (also noise damping): Healthy Mitochondria first decreases but then can be partially recovered (training, since new pulses of ROS do not cause further mitochondrial lost): In the short term Answers for Exercise 4.1. Simulation of stress and distress in ROS model Explain what is oscillated here? And why the ROS curve looks like this System is trained to maintain ATP concentration:

65. Healthy mitochondria is lost In the long term Answers for Exercise 4.1. Simulation of stress and distress in ROS model ROS grows up Due to the loss of Healthy Mitochondria, ATP also drops down System slowly collapses because p62 concentration slowly decreases (p62 does not have time to recover)

66. In the long term Answers for Exercise 4.1. Simulation of stress and distress in ROS model Due to the loss of p62, the efficiency of mitophagy (dark blue line) decreases and ROS accumulates The fraction of damaged mitochondria (blue line) grows and ROS concentration (yellow line) grows as well If we consider certain “crucial” level of Cyt C (green line below) starting apoptosis, then the cell might be eliminated just at the beginning of the regime of high ROS production

67. Exercise 4.2. Coffee effect. (10 min) Coffee activates Nrf2 synthesis. How does it affect the response to oxidative stress? Nrf2

68. Exercise 4.2. Coffee effect (15 min) Go to COPASI file and increase Nrf2 synthesis 6 fold. You can open “Slider” (the button is on the upper task bar, near button “Save”) or, alternatively, you can change values of NRf2synt in reaction 15. Run Time Course and check how activation of Nrf2 affects systemic behaviour of ATP.

69. Answers for Exercise 4.2. Coffee effect Treatment with Nrf2 activators might help to prolong the life time of neuron (indeed, there are statistical data that drinking coffee negatively correlates with PD) ATP Without treatment Nrf2 activated

70. Patient 1. Increased concentration of alfa- synuclein Patient 2. Several PD-related mutations are knockdown How does coffee affect Patient 1 and Patient 2? Exercise 4.3. PD ppersonalised medicine (15 min)

71. Patient 1 (increased alfa-synuclein) ROS Exercise 4.3. Personalised medicine

72. Patient 1 (increased alfa-synuclein) Exercise 4.3. Personalised medicine Go to initial COPASI file Exercise3-ROS-DetailedModel.cps and increase concentration of alfa- synuclein from 3 to 3.5 a.u. Run Steady State for the fixed value of ROS generation (ROSsynt=0.1). You can check that this perturbation has little effect on the Steady State, thus the mutation is hidden. Take the results of Steady State as initial conditions. Go to the value of ROSsynt in “Global quantities” and assign this to “Oscillations” (transient values). Run Time Course and study the dynamics of ATP and ROS. Increase Nrf2 synthesis 1000 times. Run Steady State for the fixed value of ROS generation (ROSsynt=0.1). Take the results of Steady State as initial conditions. Go to the value of ROSsynt in “Global quantities” and assign this to “Oscillations” (transient values). Run Time Course and study the dynamics of ATP and ROS.

73. Patient 2 (several mutations) Exercise 4.3. Personalised medicine

74. Patient 2 (several mutations) Exercise 4.3. Personalised medicine Run Steady State for the fixed value of ROS generation (ROSsynt=0.1). You can check that this perturbation has little effect on the Steady State, thus the mutation is hidden. Take the results of Steady State as initial conditions. Go to the value of ROSsynt in “Global quantities” and assign this to “Oscillations” (transient values). Run Time Course and study the dynamics of ATP and ROS. Increase Nrf2 synthesis 1000 times. Run Steady State for the fixed value of ROS generation (ROSsynt=0.1). Take the results of Steady State as initial conditions. Go to the value of ROSsynt in “Global quantities” and assign this to “Oscillations” (transient values). Run Time Course and study the dynamics of ATP and ROS. Go to initial COPASI file Exercise3-ROS-DetailedModel.cps and make the following changes: NormPD Alfa- Synuclein33.5 Keap1synt11.5 Pink14030 Park7 (Dj1)12080 VDAC19050

75. healthy PD (alfa-synuclein is increased twice) PD treated by Nrf2 activation (50 fold) ATP ROS Patient 1 (increased alfa-synuclein) => coffee helps! Answers for Exercise 4.3. Personalised medicine

76. healthy PD (several mutations) PD treated by Nrf2 activation (1000 times) ATP ROS ATP ROS ATP Patient 2 (several mutations) => Coffee does not help Answers for Exercise 4.3. Personalised medicine

77. Conclusions Apparently minor differences in persons’ genomes that do not affect function May affect function when challenged with ROS Mitochondria suffer as a buffer/battery, but can run out of charge Coffee time!