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Lotte Ramekers
Modelling the Effects of Dofetilideon IKr Channel Activation
using a Markov Model Approach
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
2
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∙ ∙ ∙ ∙ ∙ ∙
Subquestions
2
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
Research Questions ∙ Introduction Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙ ∙
Ion Channels
3
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?
Research Questions ∙ Introduction Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙ ∙
Ion Flow
2
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
Research Questions ∙ Introduction Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙ ∙
Action Potential
5
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
5
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
5
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
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Markov Models
9
?
αb = γα [Dof]∙
βb = γβ
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Markov Models: The Simple Model
11
The possibility that a dofetilide molecule binds, depends on the physical shape of the ion channel
The shape is altered by drug binding
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Markov Models: Cooperative Binding
11
αb = γα [Dof] ∙ δ
βb = γβ
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Markov Models: Cooperative Binding
11
Suggested by E. Carmeliet
αbr = γαbr [Dof]∙
βbr = γβbr
αbs = γαbs [Dof]∙
βbs = γβbs
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Markov Models: The 2-Phase Model
12
How can an IKr channel model be used to simulate the electrical activation?
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Experimental settingIsolate a ventricular cellAdd electrodes (voltage clamp)Apply voltages according to
a voltage clamp protocolAnalyse the effects
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Electrical Activation
12
Given:The transition ratesThe voltage clamp protocol
We can calculate the fraction of ion channels per state
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Electrical Activation
12
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∙ ∙ ∙Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Theoretical Analysis: Steady State
13
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 exponentResearch Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Theoretical Analysis: Activation Curve
14
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
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Theoretical Analysis: Tail Current
14
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
Research Questions Introduction ∙ ∙ Models Methods Experiments Conclusions Questions∙ ∙ ∙ ∙
Recap
14
What are the advantages and disadvantages of the different model structures?
Research Questions Introduction Models ∙ ∙ ∙ Methods Experiments Conclusions Questions∙ ∙ ∙
Experiments performed by E. CarmelietOn a rabbit ventricular myocyteUsing the portrayed voltage protocolApplying different doses of dofetilide
Research Questions Introduction Models ∙ ∙ ∙ Methods Experiments Conclusions Questions∙ ∙ ∙
Experimental Data
17
Activation Curve0 M Dof. at +10 mV scaled to 100%
Research Questions Introduction Models ∙ ∙ ∙ Methods Experiments Conclusions Questions∙ ∙ ∙
Experimental Data
17
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…
Research Questions Introduction Models ∙ ∙ Methods Experiments Conclusions Questions∙ ∙ ∙
Genetic Algorithm
18
Simple Model
Research Questions Introduction Models Methods ∙ ∙ ∙ ∙ Experiments Conclusions Questions∙ ∙
Model Fit
24
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
Research Questions Introduction Models Methods ∙ ∙ ∙ ∙ Experiments Conclusions Questions∙ ∙
Sensitivity Analysis
25
Noise is added to all parametersAmount of noise is varied by varying sError without adding noise is scaled to 1
Research Questions Introduction Models Methods ∙ ∙ ∙ ∙ Experiments Conclusions Questions∙ ∙
Sensitivity Analysis:Various Noise Functions
25
Noise function with s = 0.1Number of altered parameters is variedError without adding noise is scaled to 1
Research Questions Introduction Models Methods ∙ ∙ ∙ ∙ Experiments Conclusions Questions∙ ∙
Sensitivity Analysis:Various Number of affected Parameters
26
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
Research Questions Introduction Models Methods Experiments ∙ ∙ ∙ ∙ ∙ Conclusions Questions∙
Conclusions
29
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
Research Questions Introduction Models Methods Experiments ∙ ∙ ∙ ∙ ∙ Conclusions Questions∙
Recommendations
31