Lotte Ramekers

Modelling the Effects of Dofetilideon IKr Channel Activation

using a Markov Model Approach

Research questionsIntroductionModelsMethodsExperiments and resultsConclusionsQuestions

Outline

How can the effects of the drug dofetilide on the electrical activation of the IKr channel in a rabbit ventricular myocyte be modelled?

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Main Research Question

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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?

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Subquestions

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Introduction

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

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 channelTransports potassium (K+) ions

through the heart cell membraneHas 3 distinct states:

Open, closed and incativated

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Ion Channels

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Open

Closed Inactivated

How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled?

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Ion Flow

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chemical gradient chemical gradient

electrical gradient

chemical gradient

electrical gradient

+ - - + - + - + + -

+ - - - + + - + + -

+ - - - + + - + - +

Equilibrium

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 electrical gradientaffect all ion types

This results in a constant flow ofions in and out of the heart cells

Establishing the action potential (AP)Deficiencies in IKr channel: decreased repolarisation

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Action Potential

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How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled?

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

Ion Channel Deficiencies

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Regular IKr channel deficiency LQT2

How can the effects of the drug dofetilide on the electrical activation ofthe IKr channel in a rabbit ventricular myocyte be modelled?

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

Ion Channel Deficiencies

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Torsades de Pointes Ventricular Fibrillation

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

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

Based on the model by C. Clancy and Y. RudyExtend to incorporate block

Based on approach of C. Clancy, Z. Zhu and Y. Rudy

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Markov Models

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?

αb = γα [Dof]∙βb = γβ

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Markov Models: The Simple Model

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The possibility that a dofetilide molecule binds, depends on the physical shape of the ion channel

The shape is altered by drug binding

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Markov Models: Cooperative Binding

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αb = γα [Dof] ∙ δ

βb = γβ

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Markov Models: Cooperative Binding

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Suggested by E. Carmeliet

αbr = γαbr [Dof]∙βbr = γβbr

αbs = γαbs [Dof]∙βbs = γβbs

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Markov Models: The 2-Phase Model

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

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Experimental settingIsolate a ventricular cellAdd electrodes (voltage clamp)Apply voltages according to

a voltage clamp protocolAnalyse the effects

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Electrical Activation

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Given:The transition ratesThe voltage clamp protocol

We can calculate the fraction of ion channels per state

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Electrical Activation

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X: fraction of ion channels per stateR(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 ratesdX/dt = T(θ) X, with T(∙ θ) = RT(θ) – diag(R(θ) ∙ 1)

Voltage is clamped: T(θ) is constant for every voltage stepConservation of channels: 1T T(∙ θ) = 0Sum of fractions: ∑ Xi = 1

Steady state occupancy X is given by: T(θ) X = [ 0 0 1 ]∙ ∙ ∙ T

1 1∙ ∙ ∙

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Theoretical Analysis: Steady State

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Change in channel occupancy:dX/dt = T(θ) X∙

with T(θ) = RT(θ) – diag(R(θ) ∙ 1)

General solution:X(t) = eT(θ)t X∙ 0

Involves the matrix exponent

Using spectral decomposition:X(t) = ∑ αi ui eλit

No longer involves the matrix exponent

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Theoretical Analysis: Activation Curve

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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) G∙ Kr O∙V: membrane potentialEkr : equilibrium potentialGKr: cell conductanceO: fraction of ion channels in open state

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Theoretical Analysis: Tail Current

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Three Markov modelsThe Simple ModelThe Cooperative Binding ModelThe 2-Phase Model

The corresponding transition rates can be used to calculate the tail currentThe maximum tail current can be compared to experimental data to test the

model performance

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Recap

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

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Experiments performed by E. CarmelietOn a rabbit ventricular myocyteUsing the portrayed voltage protocolApplying different doses of dofetilide

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Experimental Data

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Activation Curve0 M Dof. at +10 mV scaled to 100%

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Experimental Data

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Concentration Response Curve0 M Dof. scaled to 100%, measured at 0 mV

Create an initial populationEvaluate the individual performancesPopulate the next generation

Determine individuals that are allowed to reproduce(using Tournament Selection)

Create offspring, based on parent’s parametersRandomly mutate parameter values

Repeat process…

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Genetic Algorithm

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Simple Model

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Model Fit

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Cooperative Binding Model 2-Phase Model

Two types of experimentsEffect of various noise functionsEffect of various number of affected parameters

General form for noise functionsPnew, i = (1 + r s) P∙ ∙ i

Pnew, i : new (altered) parameterPi : original parameterr: random value drawn from normal distribution (µ = 0, σ = 1)s: relative standard deviation

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Sensitivity Analysis

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Noise is added to all parametersAmount of noise is varied by varying sError without adding noise is scaled to 1

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Sensitivity Analysis:Various Noise Functions

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Noise function with s = 0.1Number of altered parameters is variedError without adding noise is scaled to 1

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Sensitivity Analysis:Various Number of affected Parameters

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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∙

Main Research Question

Model fit and sensitivity analysis: 2-Phase Model is bestCooperative Binding and 2-Phase Model produce similar output

Most importantly:The research provides a general approach for modelling the effects of drug induced blockage on the electrical activation of ion channels

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Conclusions

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Implement more IKr channel models

Incorporate the model into Puglisi and Bers’s rabbitventricular action potential model

Extend the theoretical analysis of Markov models forion channels

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Recommendations

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Questions ?