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1. Multi-scale Modeling of Ca2+-induced Ca2+ release in the cardiac myocyteJoseph L. GreensteinInstitute for Computational MedicineCenter for Cardiovascular Bioinformatics and Modeling The Whitaker Biomedical Engineering InstituteThe Johns Hopkins University School of Medicine andWhiting School of Engineering Institute Website http://www.icm.jhu.edu Center Website http://www.ccbm.jhu.edu

2. Outline • 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. 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

4. 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

5. 10 nm Model Failure:Ca2+-Induced Ca2+ Release (CICR) CICR T-Tubule System Soeller & Cannell (1999). Circ. Res. 84: 266 Bers (2002) Nature 415: 198-205

6. 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

7. Since common pool models can reconstruct whole-cell level responses, is the inability to capture properties of CICR a critical failure? Question The incorporation of new experimental data suggests: YES

8. Isolated Myocytes Unstable APs (Alternans) Linz & Meyer (1998) J. Physiol. 513: 425-442 Incorporation of L-type Ca2+ Channel Inactivation 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

9. 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

10. 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

11. The detailed biophysical properties of the stochastic local-control CICR model are achieved at the cost of increased model complexity and computational load. Can we simplify this model without sacrificing its biophysical detail? Question

12. 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 press

13. 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

14. 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 • Coupled LCC-RyR reproduces characteristic features of EC coupling • Steep rise in gain at negative potentials is prominent for larger dyad configurations

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

16. 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

17. Work in Progress • 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.

18. Acknowledgements Modeling & Analysis Experiments Marban Lab O’Rourke Lab Tomaselli Lab Yue Lab Raimond Winslow Robert Hinch Antti Tanskanen Vivek Iyer Saleet Jafri Reza Mazhari Jeremy Rice 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