A mechanism of heart rate regulation via synchronization of Calcium release

1. 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

2. 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

3. Sinoatrial node cells beat spontaneously and are different from ventricular myocytes membrane potential time membrane potential sinoatrial node sinoatrial node cells (SANC) diastolic depolarization Ventricular myocytes from F. Dobrzynski H et al. Circulation 2005

4. A modern concept of cardiac pacemaker function: Diastolic local Ca2+ Releases (LCRs) in SANC is “The Calcium Clock” Membrane voltage clock An example of Ca signals (Fluo4) in spontaneously beating rabbit SA node cells. Hamamatsu camera recording. Ca clock From Lakatta et al. Circ Res (in press) • LCRsare 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

5. 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 1.5 mm in size • CRUs are localized under cell surface membrane in SANC CRUs 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

6. 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.

7. 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)

8. 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

9. 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.

10. The Rhythmicity Index is superior (vs. Fourier analysis) in assessing the degree of signal rhythm and period Almost rhythmic signal (T=250ms, SD=25ms) A hardly rhythmic signal (T=250ms, SD=75ms) A roughly rhythmic signal (T=250ms, SD=50ms) Power spectrum Autocorrelation function

11. 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

12. 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 Cell#2 “Almost rhythmic” LCRs Cell#1 “Hardly rhythmic” LCRs Time series for average fluorescence in a spot Time series for average fluorescence in a spot Fluorescence (Arbitrary Units) Fluorescence (Arbitrary Units) 1 s 1 s A high RI=0.21 A low RI =0.04 Autocorrelation function Autocorrelation function

13. Inter-event time distribution of “rhyhmic” local Ca oscillators reveals the restitution time Cell#1 Cell#2 “Hardly rhythmic” local Ca oscillator “Almost rhythmic” local Ca oscillator 12 RI =0.04 16 RI=0.21 12 8 Restitution time Number of events Number of events 8 4 4 0 0 0 300 600 900 1,200 1,500 1,800 0 300 600 900 1,200 1,500 1,800 Inter-spike interval, ms Inter-spike interval, ms • Possible mechanisms contributing to the CRU restitution (not studied here): • the gating transition of RyRs to return to a reactivated state (i.e. ready to open state) • the activation of a RyR is modulated by SR luminal [Ca] (e.g. via calsequestrin polymerization). • SR local and/or global depletion Our model of CRU is based on experimental finding of the restitution time

14. Results: Our model reproduced experimental inter-event time distributions Experimental data Cell#1 Cell#2 “Hardly rhythmic” local Ca oscillator “Almost rhythmic” local Ca oscillator 12 RI =0.04 16 RI=0.21 12 8 Restitution time Number of events Number of events 8 4 4 0 0 0 300 600 900 1,200 1,500 1,800 0 300 600 900 1,200 1,500 1,800 Inter-spike interval, ms Inter-spike interval, ms Model prediction 2,500 200 Ispark=1.125 pA Ispark=1 pA 2,000 Restitution time 1,500 Number of events Number of events 100 1,000 500 0 0 0 300 600 900 0 400 800 1,200 1,600 2,000 2,400 2,800 3,200 3,600 4,000 Inter-spike interval, ms Inter-spike interval, ms

15. SANC model development Results: CRUs • 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 CRU in restitution (blue) CRU ready to fire (gray) Firing CRU (yellow)

16. Results: Our model reproduces wavelet-like persistent LCRs in depolarized rabbit SANC Spontaneous LCRs in KCl-depolarized SANC Simulated LCRs in depolarized SANC

17. Results: 0.8 0.8 0.8 0.8 100% 100% 100% 100% 0 0 0 0 1.2 s 1.2 s 1.2 s 1.2 s 0 0 0 0 0 0 0 0 0 0 0 0 26 s 26 s 26 s 26 s Changes in Ispark give different levels of synchronization Autocorr. function of [Ca] in spot Max release size (% cell area) vs time Scanline images 300 ms No periodicity Ispark=0.75 pA Sparks 0 Small Wavelets Hardly periodic Ispark=1 pA Ispark=1.035 pA Larger Wavelets Roughly periodic Ispark=1.25 pA Global multi-focal waves Almost periodic

18. Simulation Results Release Size: phase transition As release pattern change from sparks to waves, the release size increases The largest LCR (% total submembrane space area) vs. time global waves Average of the largest LCR (% cell area) wavelets sparks 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

19. Simulation Results Release Periodicity sparks wavelets global waves LCR Period LCR Rhythmicity Index global waves Restitution time 300 ms wavelets sparks Ispark (pA) Ispark (pA) Autocorrelation at different Ispark 1 LCR Period 1.5pA Rhythmicity Index Restitution time 300 ms 1.25pA 1.125 pA Autocorrelation Function Estimate 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 1,200 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.

20. Model utility sparks wavelets global waves LCR Period LCR Rhythmicity Index global waves Restitution time 300 ms wavelets sparks Ispark (pA) 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. CAMP-dependent phosphorylation of Ca2+ clock proteins increases CRU current, as in model. Vinogradova et al. Circ Res. 2006;98:505-514.

21. Results: 1 ISO Control 0 Autocorrelation Function Estimate -1 0 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 Lag Period (ms) Experimental Effect of ISO on LCRs in depolarized SANC: Rhythmicity Index increased 5000 4800 4600 Signal (Arb.Units) 4400 4200 4000 3800 3600 3400 4 6 8 10 12 14 Time (s) The same spot in the presence of ISO 6000 * 5500 * 5000 Signal (Arb.Units) Rhythmicity Index *P<0.025; n=7 (Paired t-test) ISO Control 4500 4000 3500 6 8 10 12 14 16 18 Time (s)

22. 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 178 176 174 172 170 168 166 164 162 160 158 156 154 152 150 0.13 mM 148 146 144 142 140 138 136 134 132 1pA 1.1 mM Integrated LCR period B LCR 0.13 mM LCR period 1.125pA 2.7 mM LCRs 0.13 mM LCR 1.5pA A shorter LCR period 6.4 mM Vinogradova et al. Circ Res. 2002;90:73-79. 0.13 mM

23. Results: The result summary of simulations of LCR emergence in transition from global restitution

24. Conclusions • 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.

25. Thank you!

26. 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