Center Website ccbm.jhu Models, Data, Presentations

1. Integrative Models of the Cardiac Ventricular MyocyteCurrent Status and Future DirectionsJoseph L. GreensteinandRaimond L. WinslowCenter for Cardiovascular Bioinformatics and Modeling The Whitaker Biomedical Engineering InstituteThe Johns Hopkins University School of Medicine andWhiting School of Engineering Center Website http://www.ccbm.jhu.eduModels, Data, Presentations Course – BME 580.682 Computational Models of the Cardiac Myocyte

2. Roadmap • Integrative Models of the Cardiac Ventricular Myocyte • Model Strengths and Weaknesses • Recent Data motivates The Local-Control Model of CICR • Simplification of the Local-Control CICR Model to Enable Multi-Scale Simulations (EC Coupling – Integrative Cell – Tissue)

3. Currents Contributing to the Cardiac AP Inward Outward Adapted from Tomaselli, G. F. and Marbán, E. (1999) Cardiovasc. Res. 42: 270

4. INaCa IpCa ICaL Na+ Ca2+ b1-AR AC Ca2+ PKA Ca 2+ • Ion channels & membrane transporters Troponin/myofilament INaK RyR serca2a • Ca2+ cycling & EC Coupling Mito Ca 2+ Ca 2+ • Isometric force generation ATP • Mitochondrial energetics • Coupling to ATPases • Regulation by Ca2+ JSR Sarcoplasmic reticulum • b1-Adrenergic Responses IK1 IKr INa IKs INab Ito1 NSR Integrative Modeling of the Cardiac Ventricular MyocyteCommon Pool Models • Human and canine ventricular myocyte models • High-dimensional coupled system of ODEs Winslow et al Circ. Res. 84: 571-586 Iyer et al Biophys. J. 87: 1507-1525 Rice et al. Am J Physiol., 276:H1734-H1754 Cortassa et al Biophys. J. 84: 2734-2755 Greenstein et al Ann. N.Y.Acad. Sci., 1015: 16-27

5. Roadmap • Integrative Models of the Cardiac Ventricular Myocyte • Model Strengths and Weaknesses • Recent Data motivates The Local-Control Model of CICR • Simplification of the Local-Control CICR Model to Enable Multi-Scale Simulations (EC Coupling – Integrative Cell – Tissue)

6. Models Reconstruct the Cellular Phenotype of Heart Failure Models Reconstruct Normal (N) and Failing (F) Canine Ca2+ Transients Models Reconstruct Normal (N) and Failing (F) Canine APs Experiment Experiment N N F F Model Model N N F F Winslow et al (1999). Circ. Res. 84: 571

7. Models Reconstruct Ca2+ and Force Transients in Response to Complex Pacing Behavior S0 S1 S2 Fixed S1 – S2 (3 Sec) Periodic Pulse Train Variable S0 – S1 Experiment Wier and Yue (1986) J. Physiol. 376: 507 Model Rice et al (2000). Am. J. Physiol. 278:H913

8. Katz (1992) Physiology of the Heart Model Failure:Ca2+-Induced Ca2+ Release (CICR) T-Tubules & SR CICR 10 nm T-Tubule System Bers (2002) Nature 415: 198-205 Soeller & Cannell (1999). Circ. Res. 84: 266

9. Model 4 RyR Flux Data LCC Flux Model RyR Flux LCC Flux 40 Wier et al (1994) J. Physiol. 474(3): 463-471 Model Failure (Cont):Ca2+-Induced Ca2+ Release (CICR) Experiment • Model exhibits “all-or-none” rather than graded release

10. Common pool models reconstruct many cellular responses. Common pool models cannot reconstruct critical properties of CICR, specifically, graded Ca2+ release from the JSR. However, given Item 1 does Item 2 really matter? Conclusions (1) 4.The answer is YES. The ability of a common pool model to reconstruct basic cellular responses (Item 1) will be diminished upon incorporation of new experimental data.

11. Roadmap • Integrative Models of the Cardiac Ventricular Myocyte • Model Strengths and Weaknesses • Recent Data motivates The Local-Control Model of CICR • Simplification of the Local-Control CICR Model to Enable Multi-Scale Simulations (EC Coupling – Integrative Cell – Tissue)

12. Cardiac L-Type Ca2+ Channels (LCCs)Activation and Inactivation Mechanisms Voltage-Dependent Activation Ca2+-Dependent Inactivation (CDI) Voltage-Dependent Inactivation (VDI) Greenstein and Winslow (2002). Biophys. J. 83:2918 Jafri et al (1998). Biophys J. 74: 1149 Imredy and Yue (1994). Neuron. 12: 1301

13. Isolated Myocytes Recombinant Channels Models WRJ Canine JRW Guinea Pig LR-II Guinea Pig Peterson et al (1999) Neuron 22: 549 Linz & Meyer (1998) J. Physiol. 513: 425-442 Winslow et al (2001). Phil. Trans. Roy. Soc. Lond. A. 359: 1187 LCC Inactivation: Balance Between CDI and VDI Experiments: CDI VDI Models:VDI  CDI

14. Isolated Myocytes Unstable APs (Alternans) Linz & Meyer (1998) J. Physiol. 513: 425-442 Incorporation of These Data Into Common Pool Models Leads to Instability When JSR Ca2+ release is all-or-none Ca2+ Release Channels (RyR) and inactivation of ICa,L is almost totally controlled by JSR Ca2+ release L-Type Ca2+ Channel Ca2+ ICa,L is either “on” or “off” and APs become unstable 10 nm

15. Ca2+ Flux from NSR (Jtr) Jxfer,i,1 Jxfer,i,2 Jiss,i,1,2 Jiss,i,1,4 Jiss,i,2,3 Ca2+ Flux to Cytosol JSR RyRs (Jxfer) Jxfer,i,4 (Jrel) Jxfer,i,3 Jiss,i,3,4 ClCh LCC (ICaL) (Ito2) The Local-Control Myocyte ModelGreenstein, J. L. and Winslow, R. L. (2002) Biophys. J. 83: 2918-2945 Ca2+ Release Unit Dyad Cross-section • 1 ICaL : 5 RyR per Functional Unit • 4 functional units coupled via Ca2+ diffusion per Calcium Release Unit (CaRU) • ~ 12,500 independent CaRUs per myocyte (=> ~ 50,000 LCCs per cell) • Model relates single LCC/RyR gating properties to macroscopic behavior of the myocyte

16. 12,500 CaRU RyR Open Fraction Stochastic Integration Algorithm • Improved pseudo-random number generator (MT19937) with longer period and improved performance • Dynamic allocation algorithm for controlling number of CaRUs • Parallel implementation, ~ linear scaling • ~1 minute per 1 Sec of activity

17. 4 Model 40 Local Control Myocyte Model ExhibitsHigh Gain, Graded CICR & Stable APs Action Potentials Experiment Model Experiment Ca2+- vs V- Inactivation VDI CDI Wier et al (1994) J. Physiol. 474(3): 463-471 Greenstein and Winslow (2002). Biophys. J. 83:2918

18. Ca2+-Mediated Inactivation of ICaL is a Major Factor Regulating AP Duration: Effects of Ablation Model Experiment Mutant CaM1234 disables Ca Sensor for CDI Alseikhan et al (2002). PNAS. 90(26): 17185

19. % Mode 2 #EADs # APs Early After-Depolarizations in Response to LCC Phosphorylation (Mode 2 Gating) • Early After-Depolarizations (EADs) are thought to trigger polymorphic ventricular tachycardia • Rate of occurrence of EADs is increased in myocytes isolated from failing hearts • No EADs in the absence of Mode 2 gating • => rate of EAD generation increases with increased Mode-2 gating • Identical initial conditions, but different random number seeds produce different LCC and RyR realizations • => stochastic gating of LCCs triggers EADs Tanskanen et al (2005). Biophys. J. 88:85

20. Mode 2 Current Mode 1 Current Initiation of Stochastic EADs by Increased Mode-2 Gating • Long Mode-2 open time increases likelihood of clustered random Mode-2 LCC openings • Spontaneous, near simultaneous openings of a sufficient number of LCCs gating in Mode 2 generates inward current • Resulting depolarization re-activates LCCs gating in Mode 1, producing an EAD • Novel hypothesis regarding generation of EADs

21. Common-pool CICR models of the ventricular myocyte incorporating strong negative feedback coupling between LCCs and RyRs are unstable due to the all-or-none nature of Ca2+ release. The stochastic local-control CICR model reconstructs many experimentally-observed properties of CICR and predicts stable APs. The stochastic model yields insight into the mechanism of EAD formation and the role of LCC modal gating. This is achieved at the cost of increased model complexity and computational load. How can we simplify the stochastic local-control model? Conclusions (2)

22. Roadmap • Integrative Models of the Cardiac Ventricular Myocyte • Model Strengths and Weaknesses • Recent Data motivates The Local-Control Model of CICR • Simplification of the Local-Control CICR Model to Enable Multi-Scale Simulations (EC Coupling  Integrative Cell  Tissue)

23. Critical Assumption 1: Identify and coalesce states in rapid equilibrium in order to minimize number of states Simplifying the Stochastic Local-Control Model Simplified L-Type Ca2+ Channel Model Simplified RyR Model Hinch et al (2004). Biophys. J. 87:3723 Greenstein et al (2005). Biophys. J. In revision

24. The Coupled LCC-RyR Gating Model Ca2+ Release Unit (CaRU) Model 1 LCC, 1 RyR and the Dyadic Space Single Coupled Markov Model • All transition rates are expressed mathematically as functions of parameters in the original model! • Model building is automated in software and can be accomplished for arbitrary LCC and/or RyR models and configurations. Critical Assumption 2: • Timescale of [Ca2+]ss changes (~ 1ms) • is fast wrt channel kinetics (~ 100’s ms) • [Ca2+]ss is in rapid equilibrium • [Ca2+]ss is an algebraic function of Vm, [Ca2+]cytosol, [Ca2+]jsr, and LCC/RyR state

25. Results LCC:RyR 3:15 2:10 1:5 RyR LCC LCC & RyR Fluxes EC-Coupling Gain Local Control Model Reduced Model Reduced Model Experimental Data Role of unitary iCa vs. Npo

26. Integration into the Myocyte Model • Runtime < Real Time on desktop PC Greenstein et al (2005). Biophys. J. In revision

27. Summary • Existing models of the cardiac myocyte fail when new data on strong feedback coupling between LCCs and RyRs is incorporated • A stochastic model based on local-control of CICR does exhibit graded release and stable APs under these conditions, but is computationally complex • By making use of separation of time-scales, a “coupled-gating” model of LCC-RyR interactions can be developed in which • all model parameters may all be derived from those of the underlying stochastic system • the coupled gating model consists of a low-dimensional system of ODEs and thus is suitable for multi-scale simulation of heart tissue Local Control Model Reduced Model Reduced Model Experimental Data

28. Next Steps • Modeling other sources of stochastic behavior • Estimated dyad volume, ~ 10-19 L • Few free Ca2+ ions, ~ 0 at rest! • Continuum models may not be valid • Dynamics of Ca2+ ions become important • Need approaches for moving between models of molecular dynamics in the dyad to cell and tissue.

29. Acknowledgements Modeling & Analysis Experiments Marban Lab O’Rourke Lab Tomaselli Lab Yue Lab Robert Hinch Vivek Iyer Saleet Jafri Reza Mazhari Jeremy Rice Antti Tanskanen Supported by the NIH (HL60133, HL70894, HL61711, HL72488, P50 HL52307, NO1-HV-28180, ), the Falk Medical Trust, the Whitaker Foundation, the D. W Reynolds Foundation and IBM Corporation