a mechanism of heart rate regulation via synchronization of calcium release
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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
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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
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