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 I Kr channel in a rabbit ventricular myocyte be modelled? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 2

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

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

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

How can the effects of the drug dofetilide on the electrical activation of the I Kr channel in a rabbit ventricular myocyte be modelled? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 2 chemical gradient electrical gradient chemical gradient electrical gradient Equilibrium

How can the effects of the drug dofetilide on the electrical activation of the I Kr 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 I Kr channel: decreased repolarisation Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 5

How can the effects of the drug dofetilide on the electrical activation of the I Kr channel in a rabbit ventricular myocyte be modelled? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 5 Regular I Kr channel deficiency LQT2

How can the effects of the drug dofetilide on the electrical activation of the I Kr channel in a rabbit ventricular myocyte be modelled? Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 5 Torsades de Pointes Ventricular Fibrillation

How can the behavioural kinetics and block of an I Kr 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 9

α b = γ α ∙ [Dof] β b = γ β Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 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 11

α b = γ α ∙ [Dof] δ β b = γ β Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 11

Suggested by E. Carmeliet α br = γ αbr ∙ [Dof] β br = γ βbr α bs = γ αbs ∙ [Dof] β bs = γ βbs Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 12

How can an I Kr 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 12

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

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) = R T (θ) – diag(R(θ) ∙ 1) Voltage is clamped: T(θ) is constant for every voltage step Conservation of channels: 1 T ∙ T(θ) = 0 Sum of fractions: ∑ X i = 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

Change in channel occupancy: dX/dt = T(θ) ∙ X with T(θ) = R T (θ) – diag(R(θ) ∙ 1) General solution: X(t) = e T(θ)t ∙ X 0 Involves the matrix exponent Using spectral decomposition: X(t) = ∑ α i u i e λ i t No longer involves the matrix exponent Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 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: I Kr = (V - E Kr ) ∙ G Kr ∙ O V: membrane potential E kr : equilibrium potential G Kr : cell conductance O: fraction of ion channels in open state Research Questions ∙ Introduction ∙ Models ∙ Methods ∙ Experiments ∙ Conclusions ∙ Questions 14

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

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 17

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

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 18

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

Two types of experiments Effect of various noise functions Effect of various number of affected parameters General form for noise functions P new, i = (1 + r ∙ s) ∙ P i P new, i : new (altered) parameter P i : 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

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

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

How can the effects of the drug dofetilide on the electrical activation of the I Kr 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 29

Implement more I Kr 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 31