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Modelling the Effects of Dofetilide on I Kr Channel Activation using a Markov Model Approach

Modelling the Effects of Dofetilide on I Kr Channel Activation using a Markov Model Approach. Lotte Ramekers. Outline. Research questions Introduction Models Methods Experiments and results Conclusions Questions. Main Research Question.

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Modelling the Effects of Dofetilide on I Kr Channel Activation using a Markov Model Approach

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  1. Modelling the Effects of Dofetilideon IKr Channel Activationusing a Markov Model Approach Lotte Ramekers

  2. Outline • Research questions • Introduction • Models • Methods • Experiments and results • Conclusions • Questions

  3. Main Research Question • How can the effects of the drug dofetilide on the electrical activation of the IKr channel in a rabbit ventricular myocyte be modelled? Research Questions∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 2

  4. Subquestions • How can the behavioural kinetics and block of an IKr channel be modelled? • How can an IKr channel model be used to simulate the electrical activation? • What are the advantages and disadvantages of the different model structures? Research Questions∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 2

  5. Introduction Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions

  6. Ion Channels How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled? • The IKr channel… • Is an ion channel • Transports potassium (K+) ionsthrough the heart cell membrane • Has 3 distinct states:Open, closed and incativated • Open • Closed • Inactivated Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 3

  7. Ion Flow How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled? Equilibrium + - - + - + - + + - + - - - + + - + + - + - - - + + - + - + chemicalgradient electricalgradient chemicalgradient electricalgradient chemicalgradient Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 2

  8. ActionPotential How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled? • The chemical and electricalgradientaffect all ion types • Thisresults in a constant flow ofions in and out of the heartcells • Establishing the actionpotential (AP) • Deficiencies in IKr channel: decreasedrepolarisation Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 5

  9. Ion Channel Deficiencies How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled? • Regular • IKrchannel deficiencyLQT2 Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 5

  10. Ion Channel Deficiencies How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled? • Torsades de Pointes • VentricularFibrillation Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 5

  11. How can the behavioural kinetics and block of an IKr channel be modelled? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions

  12. Markov Models • Basedon the model by C. Clancy and Y. Rudy • Extend to incorporateblockBasedonapproach of C. Clancy, Z. Zhu and Y. Rudy ? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 9

  13. Markov Models: The Simple Model • αb = γα ∙ [Dof] • βb = γβ Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 11

  14. Markov Models: Cooperative Binding • The possibilitythat a dofetilide molecule binds, dependson the physicalshape of the ion channel • The shape is alteredby drug binding Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 11

  15. Markov Models: Cooperative Binding • αb = γα ∙ [Dof] δ • βb = γβ Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 11

  16. Markov Models: The 2-Phase Model • Suggested by E. Carmeliet • αbr = γαbr ∙ [Dof] • βbr = γβbr • αbs = γαbs ∙ [Dof] • βbs = γβbs Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 12

  17. How can an IKr channel model be used to simulate the electrical activation? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions

  18. ElectricalActivation • Experimental setting • Isolate a ventricular cell • Add electrodes (voltage clamp) • Apply voltages according toa voltage clamp protocol • Analyse the effects Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 12

  19. ElectricalActivation • Given: • The transition rates • The voltage clamp protocol • We can calculate the fraction of ion channels per state Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 12

  20. TheoreticalAnalysis: Steady State • X: fraction of ion channels per state • R(θ): matrix with transition rates • First order Markov property:Change in channel occupancy is determined solely bythe current state and the incoming and outgoing transition rates dX/dt = T(θ) ∙ X, with T(θ) = RT(θ) – diag(R(θ) ∙ 1) • Voltage is clamped: T(θ) is constant for every voltage step • Conservation of channels: 1T ∙ T(θ) = 0 • Sum of fractions: ∑ Xi = 1 • Steady state occupancy X is given by: T(θ) X = [ 0 ∙ ∙ ∙ 0 1 ] T 1 ∙ ∙ ∙1 Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 13

  21. TheoreticalAnalysis: Activation Curve • Change in channel occupancy: • dX/dt = T(θ) ∙ Xwith T(θ) = RT(θ) – diag(R(θ) ∙ 1) • General solution: • X(t) = eT(θ)t ∙ X0 • Involves the matrix exponent • Using spectral decomposition: • X(t) = ∑ αiui eλit • No longer involves the matrix exponent Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 14

  22. TheoreticalAnalysis: TailCurrent • Determine fraction of channels per state… • in the Steady State (corresponding with v1) • at the end of voltage step 2 (corresponding with v2) • in last voltage step (corresponding with v3) • Tail current is given by: • IKr = (V - EKr) ∙ GKr ∙ O • V: membrane potential • Ekr : equilibriumpotential • GKr: cellconductance • O: fraction of ion channels in open state Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 14

  23. Recap • Three Markov models • The Simple Model • The Cooperative Binding Model • The 2-Phase Model • The corresponding transition rates can be used to calculate the tail current • The maximum tail current can be compared to experimental data to test the model performance Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 14

  24. What are the advantages and disadvantages of the different model structures? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions

  25. Experimental Data • Experimentsperformedby E. Carmeliet • On a rabbitventricularmyocyte • Using the portrayed voltage protocol • Applying different doses of dofetilide Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 17

  26. Experimental Data • Concentration Response Curve0 M Dof. scaled to 100%, measured at 0 mV • Activation Curve0 M Dof. at +10 mV scaled to 100% Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 17

  27. GeneticAlgorithm • Createaninitialpopulation • Evaluate the individual performances • Populate the nextgeneration • Determineindividualsthat are allowed to reproduce(usingTournamentSelection) • Createoffspring, basedonparent’s parameters • Randomlymutate parameter values • Repeatprocess… Research QuestionsIntroduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 18

  28. Model Fit • Cooperative Binding Model • 2-Phase Model • Simple Model Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 24

  29. SensitivityAnalysis • Two types of experiments • Effect of variousnoisefunctions • Effect of variousnumber of affected parameters • General form for noise functions • Pnew, i = (1 + r ∙ s) ∙ Pi • Pnew, i : new (altered) parameter • Pi : original parameter • r: random value drawn from normal distribution (µ = 0, σ = 1) • s: relative standard deviation Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 25

  30. SensitivityAnalysis:VariousNoiseFunctions • Noise is added to all parameters • Amount of noise is varied by varying s • Error without adding noise is scaled to 1 Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 25

  31. SensitivityAnalysis:VariousNumber of affected Parameters • Noise function with s = 0.1 • Number of altered parameters is varied • Error without adding noise is scaled to 1 Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 26

  32. Main Research Question How can the effects of the drug dofetilide on the electrical activation of the IKr channel in a rabbit ventricular myocyte be modelled? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions

  33. Conclusions • Model fit and sensitivityanalysis: 2-Phase Model is best • Cooperative Binding and 2-Phase Model producesimilar output • Most importantly:The research provides a generalapproachformodelling the effects of drug inducedblockageon the electricalactivation of ion channels Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 29

  34. Recommendations • Implement more IKr channel models • Incorporate the model intoPuglisi and Bers’srabbitventricularactionpotential model • Extend the theoreticalanalysis of Markov models forion channels Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 31

  35. Questions ?

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