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Lotte Ramekers
 Research questions
 Introduction
 Models
 Methods
 Experiments and results
 Conclusions
 Questions
 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
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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?
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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 of
the IKr channel in a rabbit ventricular myocyte be modelled?
 Open
 The IKr channel…
 Is an ion channel
 Transports potassium (K+) ions
through the heart cell membrane
 Has 3 distinct states:
Open, closed and incativated
 Closed
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
 Inactivated
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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?
Equilibrium
+ -+
+ -
-
+
+ + chemical gradient
+ +
-
+
-
+
+
+
+ -
-
+
-
+
chemical gradient
chemical gradient
electrical gradient
electrical gradient
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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?
 The chemical and electrical gradient
affect all ion types
 This results in a constant flow of
ions 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
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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?
 Regular
 IKr channel deficiency LQT2
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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?
 Torsades de Pointes
 Ventricular Fibrillation
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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. Rudy
 Extend to incorporate block
Based on approach of C. Clancy, Z. Zhu and Y. Rudy
?
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 αb = γα ∙ [Dof]
 βb = γβ
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 αb = γα ∙ [Dof] δ
 βb = γβ
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 Suggested by E. Carmeliet
 αbr = γαbr ∙ [Dof]
 βbr = γβbr
 αbs = γαbs ∙ [Dof]
 βbs = γβbs
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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How can an IKr channel model be used to
simulate the electrical activation?
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
 Experimental setting
 Isolate a ventricular cell
 Add electrodes (voltage clamp)
 Apply voltages according to
a voltage clamp protocol
 Analyse the effects
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 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
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 X: fraction of ion channels per state
 R(θ): matrix with transition rates
 First order Markov property:
Change in channel occupancy is determined solely by
the 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)
1 ∙ ∙ ∙1
X = [ 0 ∙ ∙ ∙ 0 1 ]T
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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 ∙ X0
 Involves the matrix exponent
 Using spectral decomposition:
 X(t) = ∑ αi ui eλit
 No longer involves the matrix exponent
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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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) ∙ GKr ∙ O
V: membrane potential
Ekr : equilibrium potential
GKr: cell conductance
O: fraction of ion channels in open state
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 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
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What are the advantages and
disadvantages of the different model
structures?
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
 Experiments performed by E. Carmeliet
 On a rabbit ventricular myocyte
 Using the portrayed voltage protocol
 Applying different doses of dofetilide
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 Activation Curve
0 M Dof. at +10 mV scaled to 100%
 Concentration Response Curve
0 M Dof. scaled to 100%, measured at 0 mV
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 Create an initial population
 Evaluate the individual performances
 Populate the next generation
 Determine individuals that are allowed to reproduce
(using Tournament Selection)
 Create offspring, based on parent’s parameters
 Randomly mutate parameter values
 Repeat process…
Research Questions Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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 Simple Model
 Cooperative Binding Model
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
 2-Phase Model
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 Two types of experiments
 Effect of various noise functions
 Effect of various number 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
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 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
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 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
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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
 Model fit and sensitivity analysis: 2-Phase Model is best
 Cooperative 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
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 Implement more IKr channel models
 Incorporate the model into Puglisi and Bers’s rabbit
ventricular action potential model
 Extend the theoretical analysis of Markov models for
ion channels
Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions
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