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

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)

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

Marban LabO’Rourke LabTomaselli LabYue Lab