1. C3MIG Model-based analysis of ß-adrenergic modulation of I Ks in the guinea-pig ventricle Biomedical Engineering Laboratory DEIS, University of Bologna Cesena, Italy Dept of Biotechnology and Bioscience University of Milano Bicocca Milano, Italy Stefano Severi

2. C3MIG 2 Outline 1 Introduction –I Ks and its sympathetic modulation –I Ks rate dependency –Silva and Rudy I Ks model Methods –Experimental –Computational

3. C3MIG 3 Outline 2 Results & Discussion –Model identification on CTRL data –ISO effects –Model based analysis of the ISO effects Conclusions

4. C3MIG 4 Introduction: I Ks and its sympathetic modulation

5. C3MIG 5 Introduction: I Ks and its sympathetic modulation I Ks is strongly upregulated by ISO Volders, P.G.A. et al. Circulation 2003; 107:2753-2760

6. C3MIG 6 Introduction: I Ks and its sympathetic modulation Genetically determined loss of function of I Ks in humans is associated with QT prolongation (LQT1, Wang et al. 1996) Schwartz, P.J. et al. Circulation 2001; 103:89-95

7. C3MIG 7 Introduction: I Ks and its sympathetic modulation β-adrenergic modulation of I Ks arrhythmic consequences of LQT1 mutations  I Ks has a central role in the complex pattern of current changes required to maintain repolarization stability during sympathetic activation in humans

8. C3MIG 8  AR outward currents (I Ks ) heart rate +++ REPOLARIZATION Introduction: I Ks and its sympathetic modulation inward currents (I CaL, I NaCa )

9. C3MIG 9 Rocchetti, M. et al, J.Physiol 2001; 534:721- 732 CL 1 s CL 0.25 s Introduction: I Ks rate dependency

10. C3MIG 10 Introduction: Silva-Rudy I Ks model Silva, J. et al. Circulation 2005;112:1384- 1391

11. C3MIG 11 Introduction: Silva-Rudy I Ks model Copyright ©2005 American Heart Association Silva, J. et al. Circulation 2005;112:1384- 1391

12. C3MIG 12 Dynamic guinea pig IKs conductance during AP clamp Introduction: Silva-Rudy I Ks model Copyright ©2005 American Heart Association Silva, J. et al. Circulation 2005;112:1384- 1391

13. C3MIG 13 Introduction: Silva-Rudy I Ks model Copyright ©2005 American Heart Association Silva, J. et al. Circulation 2005; 112:1384-1391

14. C3MIG 14 Aim To test whether the complex interaction between direct and rate-dependent effects of β-adrenergic modulations of I Ks can be interpreted within the framework of the same kinetic model. –Experimental evaluation of I Ks kinetics in guinea-pig ventricular myocytes –Identification of the model parameters –Model-based analysis

15. C3MIG 15 Methods: Experimental Ventricular myocytes from Hartley guinea-pigs Whole-cell configuration (Axon Multiclamp 700A, Axon Instruments) at 36 °C Extracellular (mM): 154 NaCl, 4 KCl, 2 CaCl 2, 1 MgCl 2, 5Hepes-NaOH and 5.5 d-glucose, adjusted to pH 7.35 with NaOH Intracellular (mM): 110 potassium aspartate, 23 KCl, 0.4 CaCl 2 (calculated free Ca 2+ of 10 −7 M), 3 MgCl 2, 5 Hepes-KOH, 1 EGTA-KOH, 0.4 GTP-Na salt, 5 ATP-Na salt, and 5 creatine phosphate Na salt, adjusted to pH 7.3 with KOH Each voltage clamp protocol without (CTRL) and with (ISO) 0.1 μM isoprenaline

16. C3MIG 16 Methods: Experimental Voltage-clamp protocols: –Activation / I-V –Deactivation –Two activating steps (S1 and S2 to +20 mV) separated by a pause (at −80 mV) of variable duration. 20 -80 (mV) S1 S2

17. C3MIG 17 Methods: Computational P O : sum of the probabilities to be in (occupancies of) the open states O 1 and O 2 V: membrane potential E Ks : K + reversal potential (−72.4 mV) G Ks : maximum membrane conductance of I Ks (12 nS) To compute the current a system of 17 ODEs must be solved:

18. C3MIG 18 Methods: Computational Transition rates  = P 1  /(1+exp(-(V m -P 2  )/P 3   F/R/T))  = P 1  /(1+exp((V m -P 2  )/P 3   F/R/T))  = P 1  /(1+exp(-(V m -P 2  )/P 3   F/R/T))  = P 1  exp(P 2   V m  F/R/T)  = (P 1  -P 4  )/(1+exp((Vm-P 2  )/P 3   F/R/T))+ P 4   = P 1  exp(P 2   V m  F/R/T)  = P 1  exp(P 2   V m  F/R/T) 21 parameters (s -1 ) (mV)       

19. C3MIG 19 Methods: Computational Simulink / Matlab environment

20. C3MIG 20 Methods: Computational Simulink / Matlab environment

21. C3MIG 21 Methods: Computational Cost function Minimization procedure Parameters update “manual tuning” Nelder-Mead simplex direct algorithm

22. C3MIG 22 -40 20 (mV) EXP:  reactmax = 411 ms  rest = 69 ms Results: Experimental CTRL -40 50 (mV) EXP: I Ksmax = 215 pA V 0.5 = 26 mV 20 -80 (mV) S1 S2 -80 20 (mV)

23. C3MIG 23 Results: Simulations CTRL EXP: I Ksmax = 215 pA V 0.5 = 26 mV SIM: I Ksmax = 231 pA V 0.5 = 26 mV EXP:  reactmax = 411 ms  rest = 69 ms EXP:  reactmax = 406 ms  rest = 63 ms I CTRL exp CTRL sim

24. C3MIG 24 Results: ISO ISO exp CTRL exp ISO sim CTRL sim

25. C3MIG 25 Results: ISO ISO exp CTRL exp ISO sim CTRL sim

26. C3MIG 26 Results: Simulations ISO ISO exp CTRL exp ISO sim CTRL sim CTRL:  reactmax = 406 ms  rest = 63 ms ISO:  reactmax = 339 ms  rest = 132 ms

27. C3MIG 27 Results: Model-based analysis ISO CTR     15 7.5 0 60 30 -50050-100 0 -50050-100 0 (mV) (s -1 )