A mechanism of heart rate regulation via synchronization of Calcium release Anna V. Maltsev*#, Victor A. Maltsev*, Maxim Mikheev*, Larissa A. Maltseva.

A mechanism of heart rate regulation via synchronization of Calcium release

Anna V. Maltsev*#, Victor A. Maltsev*,Maxim Mikheev*,

Larissa A. Maltseva&, Syevda G. Sirenko&, Edward G. Lakatta*,

Michael D. Stern*

*Laboratory of Cardiovascular Sciences, NIA/NIH, Baltimore, MD, USA# California Institute of Technology, Department of Mathematics, Pasadena, CA, USA&MedStar Research Institute, Bethesda, MD, USA

Summary

• Synchronization of Ca2+ release results in emergence of local Ca2+ oscillators – Increasing size – Increasing rhythmicity– Decreasing period– Phase transition

• We achieve synchronization via -adrenergic receptor stimulation

• A stochastic agent-based model• 2D imaging

Sinoatrial node cells beat spontaneously and are different from ventricular myocytes

sinoatrial node

Ventricular myocytes

from F. Dobrzynski H

et al. Circulation

2005

me

mb r

an

e p

ote

nti a

lm

em

b ra

ne

po

ten

ti al

time

diastolic

depolarization

sinoatrial node cells (SANC)

An example of Ca signals (Fluo4) in spontaneously beating rabbit SA node cells.

Hamamatsu camera recording.

A modern concept of cardiac pacemaker function:Diastolic local Ca2+ Releases (LCRs) in SANC is

“The Calcium Clock”

Ca

cloc

kM

emb

rane

vol

tage

clo

ck

LCRs are Ca wavelets that precede action potential-induced Ca transients each cycle Those LCRs are spontaneous and have been referred as to “Ca clock” within SANC “Ca clock” interacts with membrane electrogenic molecules (“membrane clock” or “M clock”)

and control SANC beating rate via their period of occurrence

From Lakatta et al. Circ Res (in press)

Distribution of RyRs: Assumptions

Release elements: RyR, CRU, and sparks

Ca release is produced by Ca release channels, ryanodine receptors, (RyRs) from the Sarcoplasmic Reticulum (SR), the major Ca store in cardiac cells

RyRs are expressed and operate in clusters, Ca Release Units (CRUs) A CRU generates Ca sparks of about 1.5m in size CRUs are localized under cell surface membrane in SANC

An example of Ca spark (Zhou et al. PNAS 2009)

Rigg et al., 2000; Cardiovasc Res 48:254–264

10 m

Distribution of RyR2 in SANC (assayed by antibodies).

CRUs

Possibilities:1. SR load:

RyRs spontaneously open only when SR reaches sufficient load. Thus, the SR restitution time determines the LCR period

2. Synchronization of CRUs: the likelihood that one CRU firing will recruit a neighbor, accomplished via Ca-induced-Ca release (CICR)

We focus on the second factor:

The number of RyRs activated within a CRU to participate in Ca spark can vary. We examined the impact of variations in the Ca2+ spark current (Ispark) on LCR rate and rhythm.

Aim :

12

What controls the rhythmicity and period of the LCRs?

A recent study by Zhou et al. (PNAS 2009) showed that Ispark can be increased via -adrenergic receptor stimulation (ISO)

Ispark can vary in the cell.

What controls the rhythmicity and period of the LCRs?

Our methods:1. 2D imaging of Ca2+ dynamics2. Complex systems numerical modeling of Ca2+ clock

fixed the restitution varied Ispark

3. Autocorrelation data analysis

How to assess signal periodicity?

Definition: Rhythmicity index, RI

From: Signal analysis of behavioral and molecular cycles.

Levine JD, Funes P, Dowse HB, Hall JC.BMC Neurosci. 2002;3:1-25.

Rhythms of cultured Drosophila antennae

A hardly rhythmic signal (T=250ms, SD=75ms)

A roughly rhythmic signal (T=250ms, SD=50ms)

Almost rhythmic signal(T=250ms, SD=25ms)

The Rhythmicity Index is superior (vs. Fourier analysis) in assessing the degree of signal rhythm and periodA

utoc

orre

latio

n fu

nctio

nP

ower

spe

ctru

m

Methods:

In spontaneously beating SANC the phase of LCRs is not steady but interrupted by the Ca2+ transient. Ca clock function was explored in SANC, in which activation of voltage-gated currents was excluded by cell depolarization with high KCl. Persisting multiple LCRs were recorded (for 30-120 sec) in rabbit SANC.

An example of spontaneous LCRs in KCl-depolarized SANC

Ca clock without the membrane clock

Time series for average fluorescence in a spot

Cell#1 Cell#2

A low RI =0.04

A high RI=0.21

Rhythmicity Index of LCRs greatly varied from cell-to cell: try to capture all in our model Results:

Rhythmicity Index = 0.158 ± 0.019, n= 29 cells, Mean±SEM Varied from 0.03 to 0.464

“Hardly rhythmic” LCRs “Almost rhythmic” LCRs

Aut

ocor

rela

tion

func

tion

Aut

ocor

rela

tion

func

tion

1 s

Flu

ores

cenc

e (A

rbitr

ary

Uni

ts)

1 s

Flu

ores

cenc

e (A

rbitr

ary

Uni

ts)

Time series for average fluorescence in a spot

Our model of CRU is based on experimental finding of the restitution time

Inter-event time distribution of “rhyhmic” local Ca oscillators reveals the restitution time

Possible mechanisms contributing to the CRU restitution (not studied here):1) the gating transition of RyRs to return to a reactivated state (i.e. ready to open state) 2) the activation of a RyR is modulated by SR luminal [Ca] (e.g. via calsequestrin polymerization). 3) SR local and/or global depletion

Cell#1 Cell#2

Inter-spike interval, ms

Nu

mb

er

of

eve

nts

Inter-spike interval, ms

Nu

mb

er

of

eve

nts

Restitutiontime

“Hardly rhythmic” local Ca oscillator “Almost rhythmic” local Ca oscillatorRI =0.04 RI=0.21

1,8001,5001,2009006003000

16

12

8

4

01,8001,5001,2009006003000

12

8

4

0

9006003000

2,500

2,000

1,500

1,000

500

0

Cell#1 Cell#2

Inter-spike interval, ms

Nu

mb

er

of

eve

nts

Inter-spike interval, ms

Nu

mb

er

of

eve

nts

Restitutiontime

Results: Our model reproduced experimental inter-event time distributions

“Hardly rhythmic” local Ca oscillator “Almost rhythmic” local Ca oscillatorRI =0.04 RI=0.21

Ispark=1 pA Ispark=1.125 pA

Inter-spike interval, msInter-spike interval, ms

Experimental data

Model prediction

1,8001,5001,2009006003000

16

12

8

4

0

Nu

mb

er

of

eve

nts

1,8001,5001,2009006003000

12

8

4

0

Restitutiontime

4,0003,6003,2002,8002,4002,0001,6001,2008004000

200

100

0

Nu

mb

er

of

eve

nts

Results: SANC model development

Sub-membrane space

LCR spark

Firing CRU (yellow)CRU in restitution (blue) CRU ready to fire (gray)

CRUs

[Ca] is coded by red shades

The model uses a 2D array of stochastic, diffusively coupled Ca2+ release units (CRUs).

Each CRU has a fixed Ispark and restitution time.

Ca2+ is balanced: after its release, it diffuses within the subspace into cytosol and then pumped back into the SR

Results:

Spontaneous LCRs in KCl-depolarized SANC

Simulated LCRs in depolarized SANC

Our model reproduces wavelet-like persistent LCRs in depolarized rabbit SANC

Ispark=0.75 pASparks

Small Wavelets

Globalmulti-focal

waves

Larger Wavelets

Ispark=1 pA

Ispark=1.035 pA

Ispark=1.25 pA

300 msNo periodicity

Hardly periodic

Almost periodic

Roughly periodic

Autocorr. function of [Ca] in spot

Max release size (% cell area) vs time

Changes in Ispark give different levels of synchronizationResults:

0

0 1.2 s

0

0.8

0 1.2 s

0

0.8

0 1.2 s

0

0.8

0 1.2 s

0

0.8

0 26 s0

100%

0 26 s0

100%

0 26 s0

100%

0 26 s0

100%

Scanline images

As release pattern change from sparks to waves, the release size increases

Simulation Results

The largest LCR (% total submembrane space area) vs. time

25,00024,80024,60024,40024,20024,00023,80023,60023,40023,20023,00022,80022,60022,40022,20022,00021,80021,60021,40021,20021,00020,80020,60020,40020,20020,00019,80019,60019,40019,20019,000

100

98

96

94

92

90

88

86

84

82

80

78

76

74

72

70

68

66

64

62

60

58

56

54

52

50

48

46

44

42

40

38

36

34

32

30

28

26

24

22

20

18

16

14

12

10

8

6

4

2

0

-2

-4

Ispark=1.125 pA; Average=14.1001%

I spark=1 pA;Average= 2.98613%

Ispark=0.5 pAAverage=0.248564%

Ispark (pA)

Ave

rage

of

the

larg

est

LCR

(%

cel

l are

a)

0

5

10

15

20

25

0 0.5 1 1.5 2

Release Size: phase transition

sparks

globalwaves

wavelets

time

1 sec

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.8 1 1.2 1.4 1.6

280

300

320

340

360

380

400

420

440

460

480

0.8 1 1.2 1.4 1.6

Autocorrelation at different Ispark

Lag Period (ms)

Au

toco

rre

latio

n F

un

ctio

n E

stim

ate

As Ispark increases from 0.5 to 1.5 pA in the model, the CRUs interaction increases via diffusion and Ca2+ induced Ca2+ release (CICR). This results in a higher LCR Rhythmicity Index, and smaller LCR period, approaching the restitution time.

LCR

Rhy

thm

icity

Ind

ex

LCR

Per

iod

Simulation Results

Restitution time300 ms

Restitution time300 ms

Ispark (pA)

1.5pA

1.25pA

1 pA0.5pA

1.125 pA

1.035 pA

1,2001,1001,0009008007006005004003002001000

1

0

1.065 pA

Ispark (pA)

Rhythmicity Index

LCR Period

Release Periodicity

sparks

globalwaves

wavelets

sparks

globalwaves

wavelets

Model utility

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.8 1 1.2 1.4 1.6

280

300

320

340

360

380

400

420

440

460

480

0.8 1 1.2 1.4 1.6

LCR

Per

iod

Restitution time300 ms

Ispark (pA) Ispark (pA)

sparks

globalwaves

wavelets

sparks

globalwaves

wavelets

LCR

Rhy

thm

icity

Ind

ex

In skinned rabbit SANC:

cAMP increases rate and rhythmicity of LCRs

inhibition of PKA signaling by PKI decreases LCR frequency and size

Vinogradova et al. Circ Res. 2006;98:505-514.

Based on our model prediction, these effects could be explained a variability in the amount CRU synchronization. CAMP-dependent phosphorylation of Ca2+ clock proteins increases CRU current, as in model.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

The same spot in the presence of ISO

*P<0.025; n=7 (Paired t-test) IS

O

Con

trol

**

Rh

yth

mic

ity

Ind

ex

ISO

Control

2,6002,4002,2002,0001,8001,6001,4001,2001,0008006004002000

1

0

-1

Au

toco

rre

latio

n F

un

ctio

n E

stim

ate

Lag Period (ms)

Results:

Experimental Effect of ISO on LCRs in depolarized SANC: Rhythmicity Index increased

141210864 Time (s)

Sig

nal (

Arb

.Uni

ts)

3400

3600

3800

4000

4200

4400

4600

4800

5000

181614121086Time (s)

Sig

nal (

Arb

.Uni

ts)

3500

4000

4500

5000

5500

6000

1.5pA

1.125pA

1pA

Ispark=0.875pA

Restitution time300 ms

Integrated LCR period

Reset (All CRU are synchronized to begin restitution)

LCR

LCR

Vinogradova et al. Circ Res. 2002;90:73-79.

A

B

C

LCR period

A shorter LCR period

LCRs

Simulations of LCR emergence in transition from global restitution (as in spontaneously beating SANC)

178176174172170168166164162160158156154152150148146144142140138136134132

0.13 M

2.7 M

0.13 M

6.4 M

1.1 M

0.13 M

0.13 M

0.18 M

Results:

The result summary of simulations of LCR emergence in transition from global restitution

1) The emergence of the local Ca2+ oscillators is an inherent property of an ensemble of diffusively interacting, stochastic CRUs with fixed restitution time.

2) The documented reduction of LCR period, increased LCR rhythmicity, and

increased LCR size under -AR stimulation can be explained by local synchronization of CRU firing caused by increasing Ispark.

3) LCR period = restitution time + recruitment time. As Ispark increases, recruitment time decreases and the LCR period approaches

the restitution time.

Conclusions

Possible extensions:

1. Check dependence of rhythmicity on size of the cell, since it is the smallerones that actually set the heart beat.

2. Combine the model of the Ca clock with the model of the membrane clock

3. Simplify further to an interacting particle system, maybe the contact process, and see if experimental results are still reproduced.

Thank you!

Numerical Modeling:Anna V. Maltsev*

2D-imaging:Larissa A. Maltseva

Anna V. Maltsev

Cluster computing and parallel processing:Maxim Mikheev

Supervisors:Michael D. Stern Victor A. Maltsev

Edward G. Lakatta

Laboratory of Cardiovascular Sciences, NIA/NIH, Baltimore, MD, USA

Contributions and acknowledgements