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Roadmap

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Roadmap

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  1. Ca2+- Induced Ca2+- Release in the Cardiac Myocyte:From Microscopic Channel Gating to Macroscopic Cell BehaviorRaimond L. WinslowCenter for Cardiovascular Bioinformatics and Modeling (http://www.ccbm.jhu.edu)The Johns Hopkins University School of Medicine andWhiting School of Engineering

  2. Roadmap • Review Properties of Ca2+ - Induced Ca2+ - Release (CICR) in Cardiac Ventricular Myocytes • Existing Models of CICR: Strengths and Weaknesses • The Local-Control Model of CICR • Simplifications of the Local-Control Model which Enable Multi-Scale Cell - Tissue Simulations

  3. Review of CICR Properties:The Cardiac Ventricular Myoycte ~ 100 x 25 mm Fozzard et al (1991). Ultrastructure of Cardiac Muscle. In: The Heart and Cardiovascular System: Scientific Foundations. Raven Press, NY.

  4. Katz (1992) Physiology of the Heart Structural Basis of CICR ~ 10 nm CICR T-Tubules & SR 10 nm T-Tubule System Bers (2002) Nature 415: 198-205 • ~50,000 active L-Type Ca2+ channels/cell (Rose et al, 1992) • Single channel opening triggers opening of ~ 4-6 RyRs (Wang et al 2001) • ~ 100 RyRs per cluster (Franzini-Armstrong et al, 1998) • ~ independent clusters Soeller & Cannell (1999). Circ. Res. 84: 266

  5. 4 40 CICR is Graded and Exhibits High(Voltage-Dependent) Gain Fabiato, A. (1985). J. Gen. Physiol. 85: 247-289 Wier et al (1994) J. Physiol. 474(3): 463-471

  6. Roadmap • Review Properties of Ca2+ - Induced Ca2+ - Release (CICR) in Cardiac Ventricular Myocytes • Existing Models of CICR: Strengths and Weaknesses • The Local-Control Model of CICR • Simplifications of the Local-Control Model which Enable Multi-Scale Cell - Tissue Simulations

  7. ICaL ICab Lack of Graded Ca2+ Release Common Pool Models Reconstruct the AP Experiment INaCa IpCa Data Ca 2+ Common Pool Na+ Ca2+ Ca2+ Troponin/myofilament RyR Model Ca 2+ Ca 2+ Model JSR NSR Sarcoplasmic reticulum Wier et al (1994) J. Physiol. 474(3): 463-471 IK1 IKr INa IKs Ito1 INab Common pool models cannot exhibit both high EC coupling gain and graded release (Stern, MD (1992). Biophys. J. 63: 497-517) Existing Models of CICR:The “Common Pool” Formulation

  8. Models Reconstruct Complicated Ca2+ Cycling 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

  9. 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

  10. Common pool models are able to reconstruct cellular responses including APs, Ca2+ transients and the dependence of their morphology on underlying sarcolemmal currents and transporters/exchangers Common pool models are not able to reconstruct critical properties of CICR, specifically, graded Ca2+ release from the JSR However, given Item 1 does Item 2 really matter? Conclusions 4.The answer is YES, it matters a great deal. Item 1 will turn out not to be true

  11. Roadmap • Review Properties of Ca2+ - Induced Ca2+ - Release (CICR) in Cardiac Ventricular Myocytes • Existing Models of CICR: Strengths and Weaknesses • The Local-Control Model of CICR • Simplifications of the Local-Control Model which Enable Multi-Scale Cell - Tissue Simulations

  12. Voltage-Dependent Activation The Local-Control Model of CICR:Properties of the L-Type Ca2+ Channel (LCC) Continuous Time Markov Chain Model Ca2+-Dependent Inactivation Voltage-Dependent Inactivation

  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(pt 2): 425-442 Winslow et al (2001). Phil. Trans. Roy. Soc. Lond. A. 359: 1187 Until Recently, Experiments Have not Been able to Reveal the True Balance Between Voltage- Versus Ca2+-Dependent Inactivation Models:Vinactivation Cainactivation Experiment: Cainactivation Vinactivation

  14. Isolated Myocytes Unstable APs (Alternans) Linz & Meyer (1998) J. Physiol. 513(pt 2): 425-442 Incorporation of These Data Into Common Pool Models Leads to Instability Ca2+ Release Channels (RyR) When JSR Ca2+ release is all-or-none 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” 10 nm and APs become unstable

  15. Ca2+ Release Unit Ca2+ Flux from NSR (Jtr) Jxfer,i,1 Jxfer,i,2 Jiss,i,1,2 Ca2+ Flux to Cytosol Jiss,i,1,4 Jiss,i,2,3 JSR RyRs (Jxfer) (Jrel) Jxfer,i,4 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 Functional Unit • 1 ICaL : 5 RyR per Functional Unit • 4 functional units coupled via Ca2+ diffusion per Calcium Release Unit (CaRU) • ~ 12,500 independent CaRU’s per myocyte (=> ~ 50,000 LCCs per cell) • Model relates single LCC/RyR gating properties to macroscopic behavior of the myocyte

  16. RyR Open Fraction Stochastic Integration Algorithm 12,500 CaRUs • 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 Exhibits Graded CICR & Stable APs Action Potentials Experiment Experiment Model Ca2+- vs V- Inactivation Not VI Not CaI Wier et al (1994) J. Physiol. 474(3): 463-471

  18. Ca2+-Mediated Inactivation of ICaL is a Major Factor Regulating AP Duration: Effects of Ablation Model Experiment Mutant CaM1234 disables Ca Sensor for Cainactivation Alseikhan et al (2002). Biophys J. 82:358a

  19. Common-pool CICR models of the ventricular myocyte incorporating strong negative feedback control of ICa,L by JSR Ca2+ release are unstable. This is due to lack of graded release. The stochastic local-control CICR model describes experimentally-observed properties of CICR including voltage-dependence of EC-coupling gain and graded release, and reconstructs stable APs This is achieved at the cost of model complexity and computational load Can the stochastic local-control model be simplified in a way that does not sacrifice the ability to describe important molecular detail? Conclusions

  20. Roadmap • Review Properties of Ca2+ - Induced Ca2+ - Release (CICR) in Cardiac Ventricular Myocytes • Existing Models of CICR: Strengths and Weaknesses • The Local-Control Model of CICR • Simplifications of the Local-Control Model which Enable Multi-Scale Cell - Tissue Simulations

  21. c1,2 are closed, non-conducting states I1,2 are Ca2+-inactivated, non-conducting states O is an open, conducting state a1,-1 are voltage-dependent rates k1,-1 are voltage-independent rates e1,-1 are rates dependent on [Ca2+]ss (diadic Ca2+) Critical Assumption 1: Identify and coalesce states in rapid equilibrium • 3-state model Simplifying the Stochastic Local-Control Model Simplified L-Type Ca2+ Channel Model Simplified RyR Model Based on Zahradnikova & Zahradnik (1996) Biophys. J. 71(6): 2996 k3 is dependent on diadic Ca2+

  22. Coupled Gating Model of LCC-RyR Interactions Ca2+ Release Unit (CaRU) Model Critical Assumption 2: 1 LCC, 1 RyR and the diadic space • Timescale of [Ca2+]ss changes (~ 1mSec) • is fast wrt channel kinetics ( 100’s mSecs) • [Ca2+]ss is in rapid equilibrium • [Ca2+]ss is an algebraic function of V(t), [Ca2+]cytosol, [Ca2+]jsr, and LCC/RyR state • This implies the 3-state LCC and RyR models can be combined to form a 9-state CaRU model • Yij are states, where • i denotes states {C,O,I} of the LCC • j denotes states {C,O,I} of the RyR • Further rapid equilibrium approximations to obtain a 4-state (3 ODE) model • All transition rates are expressed mathematically as functions of parameters in the original model!

  23. Results EC-Coupling Gain Ca2+-Mediated Inactivation of ICa,L Voltage-Dependence of ICa,L Local Control Model Reduced Model Reduced Model Experimental Data Normalized LCC & RyR Flux

  24. Summary • New experimental data show that negative feedback coupling between JSR Ca2+ release and LCC current dominates LCC inactivation • When this coupling is incorporated into CICR models that do not describe graded Ca2+ release (e.g., the common pool model), the models become unstable and can no longer reconstruct the cardiac AP • 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

  25. Acknowledgements Modeling & Analysis Experiments Marban Lab O’Rourke Lab Tomaselli Lab Yue Lab Joseph Greenstein Robert Hinch Vivek Iyer Saleet Jafri Reza Mazhari Jeremy Rice Antti Tanskanen Lei Xu 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

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