Modelling the effects of dofetilide on i kr channel activation using a markov model approach
This presentation is the property of its rightful owner.
Sponsored Links
1 / 35

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


  • 93 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

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

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


Modelling the effects of dofetilide on i kr channel activation using a markov model approach

Modelling the Effects of Dofetilideon IKr Channel Activationusing a Markov Model Approach

Lotte Ramekers


Outline

Outline

  • Research questions

  • Introduction

  • Models

  • Methods

  • Experiments and results

  • Conclusions

  • Questions


Main research question

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


Subquestions

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


Modelling the effects of dofetilide on i kr channel activation using a markov model approach

Introduction

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


Ion channels

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


Ion flow

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


Action potential

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


Ion channel deficiencies

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


Ion channel deficiencies1

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


Modelling the effects of dofetilide on i kr channel activation using a markov model approach

How can the behavioural kinetics and block of an IKr channel be modelled?

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


Markov models

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


Markov models the simple model

Markov Models: The Simple Model

  • αb = γα ∙ [Dof]

  • βb = γβ

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

11


Markov models cooperative binding

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


Markov models cooperative binding1

Markov Models: Cooperative Binding

  • αb = γα ∙ [Dof] δ

  • βb = γβ

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

11


Markov models the 2 phase model

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


Modelling the effects of dofetilide on i kr channel activation using a markov model approach

How can an IKr channel model be used to simulate the electrical activation?

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


Electrical activation

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


Electrical activation1

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


Theoretical analysis steady state

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


Theoretical analysis activation curve

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


Theoretical analysis tail current

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


Recap

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


Modelling the effects of dofetilide on i kr channel activation using a markov model approach

What are the advantages and disadvantages of the different model structures?

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


Experimental data

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


Experimental data1

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


Genetic algorithm

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


Model fit

Model Fit

  • Cooperative Binding Model

  • 2-Phase Model

  • Simple Model

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

24


Sensitivity analysis

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


Sensitivity analysis various noise functions

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


Sensitivity analysis various number of affected parameters

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


Main research question1

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


Conclusions

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


Recommendations

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


Questions

Questions ?


  • Login