C3MIG

Model-based analysis of ß-adrenergic modulation

of IKs in the guinea-pig ventricle

Biomedical Engineering LaboratoryDEIS, University of BolognaCesena, Italy

Dept of Biotechnology and Bioscience University of Milano BicoccaMilano, Italy

2n

dvoltage

sensortransition

C7 C8

32

23

4

2 3 4

C9

1st voltage sensor transition

C10 C11

C13

2 22

3

32

C12

C14

23

4

4

4

23

23

32

C15

4

C54

2n

dvoltage

sensortransition

C7 C8

3232

2323

4

4

2 2 3 3 4 4

C9

1st voltage sensor transition

C10 C11

C13

2 2 22 22

3 3

32 32

C12

C14

23 23

4

4

4

4

4

4

2323

2323

3232

C15

4 4

C544

Stefano Severi

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Outline 1

• Introduction

– IKs and its sympathetic modulation

– IKs rate dependency

– Silva and Rudy IKs model

• Methods– Experimental– Computational

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Outline 2

• Results & Discussion– Model identification on CTRL data– ISO effects– Model based analysis of the ISO effects

• Conclusions

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Introduction: IKs and its sympathetic modulation

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Introduction: IKs and its sympathetic modulation

•IKs is strongly upregulated by ISO

Volders, P.G.A. et al.Circulation 2003; 107:2753-2760

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Introduction: IKs and its sympathetic modulation

• Genetically determined loss of function of IKs in humans is associated with QT prolongation (LQT1, Wang et al. 1996)

Schwartz, P.J. et al. Circulation 2001; 103:89-95

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Introduction: IKs and its sympathetic modulation

• β-adrenergic modulation of IKs

• arrhythmic consequences of LQT1 mutations

IKs has a central role in the complex pattern of current changes required to maintain repolarization stability during sympathetic activation in humans

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AR

outward currents

(IKs)

heart rate

+ ++

REPOLARIZATION

Introduction: IKs

and its sympathetic modulation

inward currents (ICaL, INaCa)

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Rocchetti, M. et al, J.Physiol 2001; 534:721-732

CL 1 s

CL 0.25 s

Introduction: IKs rate dependency

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Introduction: Silva-Rudy IKs model

Silva, J. et al.Circulation 2005;112:1384-1391

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Introduction: Silva-Rudy IKs model

Copyright ©2005 American Heart Association

Silva, J. et al.Circulation 2005;112:1384-1391

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Dynamic guinea pig IKs conductance during AP

clamp

Introduction: Silva-Rudy IKs model

Copyright ©2005 American Heart Association

Silva, J. et al.Circulation 2005;112:1384-1391

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Introduction: Silva-Rudy IKs model

Copyright ©2005 American Heart Association

Silva, J. et al.Circulation 2005;112:1384-1391

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Aim

• To test whether the complex interaction between direct and rate-dependent effects of β-adrenergic modulations of IKs can be interpreted within the framework of the same kinetic model.– Experimental evaluation of IKs kinetics in

guinea-pig ventricular myocytes – Identification of the model parameters– Model-based analysis

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Methods: Experimental

• Ventricular myocytes from Hartley guinea-pigs

• Whole-cell configuration (Axon Multiclamp 700A, Axon Instruments) at 36 °C

• Extracellular (mM): 154 NaCl, 4 KCl, 2 CaCl2, 1 MgCl2, 5Hepes-NaOH and 5.5

d-glucose, adjusted to pH 7.35 with NaOH

• Intracellular (mM): 110 potassium aspartate, 23 KCl, 0.4 CaCl2 (calculated free

Ca2+ of 10−7 M), 3 MgCl2, 5 Hepes-KOH, 1 EGTA-KOH, 0.4 GTP-Na salt, 5

ATP-Na salt, and 5 creatine phosphate Na salt, adjusted to pH 7.3 with KOH

• Each voltage clamp protocol without (CTRL) and with (ISO) 0.1 μM

isoprenaline

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Methods: Experimental

• Voltage-clamp protocols:

– Activation / I-V

– Deactivation

– Two activating steps (S1 and S2 to +20 mV) separated by a pause (at −80 mV) of variable duration.

0 1 2 3 4 5 6 7 8 9-0.05

0

0.05

-40

(mV)50

1 s-40

50(mV)

-40

20(mV)

0 2 4 6 8 10 12-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

0 1 2 3 4 5 6 7 8

-0.08

-0.03

0.02

2 3 4

-0.08

-0.03

0.02

20

-80

(mV)

S1 S2

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Methods: Computational

KsoKsKs EVPGI

PO: sum of the probabilities to bein (occupancies of) the open states O1 and O2

V: membrane potential

EKs: K+ reversal potential (−72.4 mV)

GKs: maximum membrane conductance of IKs (12 nS)

To compute the current a system of 17 ODEs must be solved:

QPP

)()(

tdt

td

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Methods: Computational

Transition rates

= P1/(1+exp(-(Vm-P2)/P3F/R/T))

= P1/(1+exp((Vm-P2)/P3F/R/T))

= P1/(1+exp(-(Vm-P2)/P3F/R/T))

= P1 exp(P2VmF/R/T)

= (P1-P4)/(1+exp((Vm-P2)/P3F/R/T))+ P4

= P1 exp(P2VmF/R/T)

= P1 exp(P2VmF/R/T)

• 21 parameters

(s-1)

(s-1)

(s-1)

(s-1)

(s-1)

(s-1)

(mV) (mV)

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Methods: Computational

Simulink / Matlab environment

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Methods: Computational

Simulink / Matlab environment

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Methods: Computational

Costfunction

Minimizationprocedure

Parameters update

• “manual tuning”• Nelder-Mead simplex direct algorithm

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0 2 4 6 8 10 12-0.05

-0.04

-0.03

-0.02

-0.01

0

0.01

0.02

-40

20(mV)

EXP:

reactmax= 411 ms

rest= 69 ms

Results: Experimental CTRL

0 1 2 3 4 5 6 7 8 9-0.05

0

0.05

-40

(mV)50

1 s

-40

50(mV)

EXP:

IKsmax= 215 pA

V0.5= 26 mV

0 1 2 3 4 5 6 7 8

-0.08

-0.03

0.02

2 3 4

-0.08

-0.03

0.02

20

-80

(mV)

S1 S2

2 3 4

-0.08

-0.03

0.02

-80

20

(mV)

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Results: Simulations CTRL

EXP:

IKsmax= 215 pA

V0.5= 26 mV

SIM:IKsmax= 231 pAV0.5= 26 mV

EXP:

reactmax= 411 ms

rest= 69 ms

EXP:reactmax= 406 msrest= 63 ms

ICTRL exp CTRL sim

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Results: ISO

ISO expCTRL exp

ISO simCTRL sim

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Results: ISO

ISO expCTRL exp

ISO simCTRL sim

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Results: Simulations ISO

ISO expCTRL exp

ISO simCTRL sim

CTRL:

reactmax= 406 ms

rest= 63 ms

ISO:reactmax= 339 msrest= 132 ms

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Results: Model-based analysis

-0.1 -0.05 0 0.050

7.5

15

-0.1 -0.05 0 0.050

30

60

ISOCTR

15

7.5

0

60

30

-50 0 50-100

0

-50 0 50-100

0

(mV)

(s-1) (s-1)