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
sinoatrial node cells
(SANC)
time
Ventricular
myocytes
An example of Ca signals (Fluo4) in
spontaneously beating rabbit SA node cells.
Hamamatsu camera recording.
Ca clock
Membrane voltage clock
A modern concept of cardiac pacemaker function:
Diastolic local Ca2+ Releases (LCRs) in SANC is
“The Calcium Clock”
From Lakatta et al. Circ Res (in press)



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
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
CRUs
RyRs are expressed and operate in clusters, Ca Release Units (CRUs)
A CRU generates Ca sparks of about 1.5 mm in size
CRUs are localized under cell surface membrane in SANC
10 mm
An example of Ca spark (Zhou et al. PNAS 2009)
Distribution of RyR2 in SANC (assayed by antibodies).
Rigg et al., 2000; Cardiovasc Res 48:254–264
What controls the rhythmicity and period of the LCRs?
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)
2
1
Aim :
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.
What controls the rhythmicity and period of the LCRs?
Ispark can vary in the cell.
A recent study by Zhou et al. (PNAS 2009) showed that Ispark can be increased via adrenergic receptor stimulation (ISO)
Our methods:
1. 2D imaging of Ca2+ dynamics
2. 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
Rhythms of cultured Drosophila antennae
From:
Signal analysis of behavioral and molecular cycles.
Levine JD, Funes P, Dowse HB, Hall JC.
BMC Neurosci. 2002;3:1-25.
The Rhythmicity Index is superior (vs. Fourier analysis) in assessing the degree of signal rhythm and period
Autocorrelation function
Power spectrum
Almost rhythmic signal
(T=250ms, SD=25ms)
A roughly rhythmic signal
(T=250ms, SD=50ms)
A hardly rhythmic signal
(T=250ms, SD=75ms)
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
Results:
Rhythmicity Index of LCRs greatly varied from cell-to cell: try to capture all in our model
Rhythmicity Index = 0.158 ± 0.019, n= 29 cells, Mean±SEM
Varied from 0.03 to 0.464
1s
A low RI =0.04
“Almost rhythmic” LCRs
Time series for average fluorescence in a spot
Fluorescence
(Arbitrary Units)
Fluorescence
(Arbitrary Units)
Time series for average fluorescence in a spot
Autocorrelation function
Cell#2
“Hardly rhythmic” LCRs
Autocorrelation function
Cell#1
1s
A high RI=0.21
Inter-event time distribution of “rhyhmic” local Ca oscillators reveals the restitution time
Cell#1
Cell#2
“Hardly rhythmic” local Ca oscillator
12
16
Number of events
Number of events
RI =0.04
8
4
0
0
300
600
900
1,200
1,500
Inter-spike interval, ms
1,800
“Almost rhythmic” local Ca oscillator
RI=0.21
12
8
Restitution
time
4
0
0
300
600
900
1,200
1,500
1,800
Inter-spike interval, ms
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
Our model of CRU is based on experimental finding of the restitution time
Results:
Our model reproduced experimental inter-event time distributions
Experimental data
Cell#1
Cell#2
“Hardly rhythmic” local Ca oscillator
12
16
Number of events
Number of events
RI =0.04
8
4
0
0
300
600
900
1,200
1,500
“Almost rhythmic” local Ca oscillator
RI=0.21
12
8
Restitution
time
4
0
1,800
0
300
600
Inter-spike interval, ms
900
1,200
1,500
1,800
Inter-spike interval, ms
Model prediction
2,500
Ispark=1 pA
Number of events
Number of events
200
100
0
400
800
1,200
1,600
2,000
2,400
2,800
Inter-spike interval, ms
3,200
3,600
4,000
Restitution
time
1,500
1,000
500
0
0
Ispark=1.125 pA
2,000
0
300
600
Inter-spike interval, ms
900
SANC model development
Results:

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
LCR
spark
[Ca] is coded by red shades
Sub-membrane space
CRUs
CRU in restitution (blue)
CRU ready to fire (gray)
Firing CRU (yellow)
Results:
Our model reproduces wavelet-like persistent LCRs in depolarized rabbit SANC
Spontaneous LCRs in KCl-depolarized SANC
Simulated LCRs in depolarized SANC
Results: Changes in Ispark give different levels of synchronization
Autocorr. function of [Ca]
in spot
Scanline images
0.8
Sparks
Ispark=0.75 pA
100%
300 ms
No periodicity
0
0
0
1.2 s
0
0
26 s
100%
0.8
Small
Wavelets
Max release size
(% cell area) vs time
Hardly periodic
Ispark=1 pA
0
0
Larger
Wavelets
Ispark=1.035 pA
1.2 s
0.8
0
0
26 s
100%
Roughly periodic
0
0
Global
multifocal
waves
Ispark=1.25 pA
1.2 s
0
0
26 s
100%
0.8
Almost periodic
0
0
1.2 s
0
0
26 s
Simulation Results
Release Size: phase transition
The largest LCR (% total submembrane space area) vs. time
Average of the largest LCR (% cell area)
As release pattern change from sparks to waves, the release size increases
25
20
global
waves
15
10
5
wavelets
sparks
0
0
0.5
1
1.5
Ispark (pA)
Ispark=1.125 pA;
Average=14.1001%
I spark=1 pA;
Average= 2.98613%
Ispark=0.5 pA
Average=0.248564%
1 sec
time
2
Simulation Results
LCR Rhythmicity Index
Release Periodicity
480
LCR Period
460
sparks
wavelets
440
420
400
380
global
waves
360
340
320
Restitution time
300 ms
300
280
0.8
1
1.2
1.4
1.6
0.7
0.6
0.5
global
waves
0.4
0.3
0.2
0.1
wavelets
sparks
0
0.8
Ispark (pA)
1
LCR Period
1.2
1.4
1.6
Ispark (pA)
Autocorrelation at different Ispark
1
Autocorrelation Function Estimate
0.8
1.5pA
Restitution time
300 ms
Rhythmicity Index
1.25pA
1.125 pA
1.065 pA
1.035 pA
1 pA
0.5pA
0
0
100
200
300
400
500
600
700
800
900
1,000
1,100
Lag Period (ms)
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.
1,200
480
LCR Period
460
sparks
wavelets
440
420
400
380
global
waves
360
340
320
Restitution time
300 ms
300
280
0.8
1
1.2
1.4
1.6
Ispark (pA)
LCR Rhythmicity Index
Model utility
0.8
0.7
0.6
0.5
global
waves
0.4
0.3
0.2
0.1
wavelets
sparks
0
0.8
1
1.2
1.4
1.6
Ispark (pA)
In skinned rabbit SANC:

cAMP increases rate and rhythmicity of LCRs

inhibition of PKA signaling by PKI decreases
LCR frequency and size
Based on our model prediction,
these effects could be explained
a variability in the amount CRU
synchronization. CAMPdependent phosphorylation of
Ca2+ clock proteins increases
CRU current, as in model.
Vinogradova et al. Circ Res. 2006;98:505-514.
Results:
Experimental Effect of ISO on LCRs in depolarized SANC: Rhythmicity Index increased
1
ISO
4800
4600
3800
3600
3400
4
6
8
Time (s) 10
12
14
The same spot in the presence of ISO
Signal (Arb.Units)
6000
5500
5000
0
*P<0.025; n=7
(Paired t-test)
4500
4000
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
*
*
ISO
4000
Control
Control
4200
Rhythmicity Index
4400
Autocorrelation Function Estimate
Signal (Arb.Units)
5000
0
-1 0
3500
6
8
10
12
Time (s)
14
16
18
200
400
600
800
1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600
Lag Period (ms)
Simulations of LCR emergence in transition from global restitution (as in spontaneously beating SANC)
Reset (All CRU are synchronized to begin restitution)
A
C
Restitution time
300 ms
Ispark=0.875pA
0.18 mM
178
176
174
172
170
168
166
134
132
162
160
158
156
154
152
0.13164
mM
150
148
146
144
142
140
138
136
1pA
1.1 mM
B
Integrated LCR period
LCR
0.13 mM
LCR period
1.125pA
2.7 mM
LCRs
LCR
0.13 mM
1.5pA
A shorter
LCR
period
Vinogradova et al. Circ Res. 2002;90:73-79.
6.4 mM
0.13 mM
Results:
The result summary of simulations of LCR emergence in transition from global restitution
Conclusions
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.
Possible extensions:
1. Check dependence of rhythmicity on size of the cell, since it is the smaller
ones 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!
Contributions and acknowledgements
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