Integrative Models of the Cardiac Ventricular Myocyte Current Status and Future Directions Joseph L. Greenstein and Raimond L. Winslow Center for Cardiovascular Bioinformatics and Modeling The Whitaker Biomedical Engineering Institute The Johns Hopkins University School of Medicine and Whiting School of Engineering Center Website http://www.ccbm.jhu.edu Models, Data, Presentations Course – BME 580.682 Computational Models of the Cardiac Myocyte
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Integrative Models of the Cardiac Ventricular Myocyte Current Status and Future Directions Joseph L. Greenstein and Raimond L. Winslow Center for Cardiovascular.
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Integrative Models of the Cardiac Ventricular MyocyteCurrent Status and Future Directions
Joseph L. Greensteinand
Raimond L. Winslow
Center for Cardiovascular Bioinformatics and Modeling
The Whitaker Biomedical Engineering InstituteThe Johns Hopkins University School of Medicine and
Whiting School of Engineering
Center Website http://www.ccbm.jhu.eduModels, Data, PresentationsCourse – BME 580.682 Computational Models of the Cardiac Myocyte
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)
Adapted from Tomaselli, G. F. and Marbán, E. (1999) Cardiovasc. Res. 42: 270
Currents Contributing to the Cardiac AP
Inward
Outward
Integrative Modeling of the Cardiac Ventricular MyocyteCommon Pool Models
Ion channels & membrane transportersINaK
IK1 IKr Ito1IKs
ICaL
INabINa
INaCa
Na+ Ca2+
IpCa
Ca2+
Troponin/myofilamentTroponin/myofilament
Isometric force generation
1-Adrenergic Responses
1-ARAC
PKA
Mitochondrial energetics– Coupling to ATPases– Regulation by Ca2+
Mito
ATP
Winslow et al Circ. Res. 84: 571-586Iyer et al Biophys. J. 87: 1507-1525Rice 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
Human and canine ventricular myocyte models
JSRSarcoplasmic reticulum
Ca 2+ Ca 2+
Ca 2+
RyR
serca2aCa2+ cycling & EC Coupling
NSR
High-dimensional coupled system of ODEs
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)
Models Reconstruct the Cellular Phenotype of Heart Failure
Models Reconstruct Normal (N)and Failing (F) Canine APs
100200300400500600700800900
0 200 400 600 800 1000
[Ca i ]
(nM
)
Time (mSec)
0
100
200
300
400
500
600
0 200 400 600 800 1000
Model
[Ca i ]
(nM
)
Time (mSec)
B
Models Reconstruct Normal (N) andFailing (F) Canine Ca2+ Transients
N
N
F
F
Experiment
Model
Experiment
Model
NF
F
N
Winslow et al (1999). Circ. Res. 84: 571
Wier and Yue (1986) J. Physiol. 376: 507
Model
PeriodicPulse Train
S1 S2S0
Experiment
Rice et al (2000). Am. J. Physiol. 278:H913
Models Reconstruct Ca2+ and Force Transients in Response to Complex Pacing Behavior
VariableS0 – S1
Fixed
S1 – S2
(3 Sec)
Model Failure:Ca2+-Induced Ca2+ Release (CICR)
Soeller & Cannell (1999). Circ. Res. 84: 266
T-Tubule System
Katz (1992) Physiology of the Heart
Bers (2002) Nature 415: 198-205
T-Tubules & SR
CICR
10 nm
Model Failure (Cont):Ca2+-Induced Ca2+ Release (CICR)
Data
Model
Model
Wier et al (1994) J. Physiol. 474(3): 463-471
40
4
RyR Flux
LCC Flux
RyR FluxLCC Flux
Experiment
Model exhibits “all-or-none” rather than graded release
Conclusions (1)
1. Common pool models reconstruct many cellular responses.
2. Common pool models cannot reconstruct critical properties of CICR, specifically, graded Ca2+ release from the JSR.
3. However, given Item 1 does Item 2 really matter?
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.
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)
Cardiac L-Type Ca2+ Channels (LCCs) Activation and Inactivation Mechanisms
Ca2+-DependentInactivation (CDI)
Voltage-DependentActivation
Voltage-Dependent Inactivation (VDI)
Greenstein and Winslow (2002). Biophys. J. 83:2918Jafri et al (1998). Biophys J. 74: 1149Imredy and Yue (1994). Neuron. 12: 1301
22 22 mSS om
2 m
[Ca ] 0.341[Ca ]4CaL open CaL 1
2m SS
open 6 12
( ) [ ( ), ( ),[Ca ] ( )]
0,1
V F RT
V F RT
eV FRT e
I p P
dt t V t t
dtp x x y
x F x
Recombinant Channels
Peterson et al (1999) Neuron 22: 549
Linz & Meyer (1998) J. Physiol.513: 425-442
Isolated MyocytesWinslow et al (2001). Phil. Trans. Roy. Soc. Lond. A. 359: 1187
ModelsWRJ Canine JRW Guinea Pig LR-II Guinea Pig
Experiments: CDI VDIModels: VDI CDI
LCC Inactivation: Balance Between CDI and VDI
Incorporation of These Data Into Common Pool Models Leads to Instability
Ca2+L-Type Ca2+
Channel
Ca2+ ReleaseChannels (RyR)
10 nm
Unstable APs (Alternans)
When JSR Ca2+ release is all-or-none
and inactivation of ICa,L is almost totally controlled by JSR Ca2+ release
ICa,L is either “on” or “off”
and APs become unstable
Linz & Meyer (1998) J. Physiol.513: 425-442
Isolated Myocytes
The Local-Control Myocyte ModelGreenstein, J. L. and Winslow, R. L. (2002) Biophys. J. 83: 2918-2945
Ca2+ Release Unit
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
Jxfer,i,4
Jxfer,i,2
Jxfer,i,3
Jiss,i,1,4 Jiss,i,2,3
Jiss,i,3,4
Jiss,i,1,2
Jxfer,i,1
Ca2+ Flux from NSR
(Jtr)
Ca2+ Flux to Cytosol
(Jxfer)RyRs(Jrel)
JSR
LCC
(ICaL)ClCh
(Ito2)
Dyad Cross-section
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
12,500 CaRU
Ry
R O
pe
n F
rac
tio
n
Stochastic Integration Algorithm
Local Control Myocyte Model ExhibitsHigh Gain, Graded CICR & Stable APs
40
4
Experiment
Wier et al (1994) J. Physiol.474(3): 463-471
Model
-100
-80
-60
-40
-20
0
20
40
0 0.1 0.2 0.3 0.4 0.5-100
-80
-60
-40
-20
0
20
40
0 100 200 300 400 5000 0.1 0.2 0.3 0.4 0.5
Model Experiment
Action Potentials
Ca2+- vs V- Inactivation
VDI
CDI
Greenstein and Winslow (2002). Biophys. J. 83:2918
Ca2+-Mediated Inactivation of ICaL is a Major Factor Regulating AP Duration: Effects of Ablation
Model
Experiment
Alseikhan et al (2002). PNAS. 90(26): 17185
Mutant CaM1234
disables Ca Sensor for CDI
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
0 0 100
7.5 2 100
15 5 100
% Mode 2 # EADs # APs
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
Initiation of Stochastic EADs by Increased Mode-2 Gating
Mode 2 Current
Mode 1 Current
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
Conclusions (2)
1. 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.
2. The stochastic local-control CICR model reconstructs many experimentally-observed properties of CICR and predicts stable APs.
3. The stochastic model yields insight into the mechanism of EAD formation and the role of LCC modal gating.
4. This is achieved at the cost of increased model complexity and computational load.
5. How can we simplify the stochastic local-control model?
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)
Simplified L-Type Ca2+ Channel ModelSimplified RyR Model
Critical Assumption 1:
Identify and coalesce states in rapid equilibrium in order to minimize number of states
Simplifying the Stochastic Local-Control Model
Hinch et al (2004). Biophys. J. 87:3723Greenstein et al (2005). Biophys. J. In revision
The Coupled LCC-RyR Gating 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.
Timescale of [Ca2+]ss changes (~ 1s)
is fast wrt channel kinetics (~ 100’s s) [Ca2+]ss is in rapid equilibrium
[Ca2+]ss is an algebraic function of Vm, [Ca2+]cytosol, [Ca2+]jsr, and LCC/RyR state
Ca2+ Release Unit (CaRU) Model1 LCC, 1 RyR and the Dyadic Space
Critical Assumption 2:
Single Coupled Markov Model
Results
Local Control Model
Reduced Model
ExperimentalData
ReducedModel
EC-Coupling GainLCC & RyR Fluxes
LCC
RyRLCC:RyR
3:152:101:5
Role of unitary iCa vs. Npo
Integration into the Myocyte Model
Greenstein et al (2005). Biophys. J. In revision
Runtime < Real Time on desktop PC
Summary
Local Control Model
Reduced Model
ExperimentalData
ReducedModel
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
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.
Acknowledgements
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
Modeling & Analysis Experiments
Robert HinchVivek IyerSaleet JafriReza MazhariJeremy RiceAntti Tanskanen