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 Ca 2+ release results in emergence of local Ca 2+ 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 membrane potential 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 Ca 2+ Releases (LCRs) in SANC is The Calcium Clock Ca clock Membrane voltage clock 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 1.5 m 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– 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 Ca 2+ spark current (I spark ) on LCR rate and rhythm. Aim : 1 2 What controls the rhythmicity and period of the LCRs?

A recent study by Zhou et al. (PNAS 2009) showed that I spark 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 Ca 2+ dynamics 2. Complex systems numerical modeling of Ca 2+ clock fixed the restitution varied I spark 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 period Autocorrelation function Power spectrum

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 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 = ± 0.019, n= 29 cells, Mean±SEM Varied from 0.03 to Hardly rhythmic LCRs Almost rhythmic LCRs Autocorrelation function 1 s Fluorescence (Arbitrary Units) 1 s Fluorescence (Arbitrary Units) 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 Number of events Inter-spike interval, ms Number of events Restitution time Hardly rhythmic local Ca oscillator Almost rhythmic local Ca oscillator RI =0.04 RI=0.21 1,8001,5001, ,8001,5001,

,500 2,000 1,500 1, Cell#1 Cell#2 Inter-spike interval, ms Number of events Inter-spike interval, ms Number of events Restitution time Results:Our model reproduced experimental inter-event time distributions Hardly rhythmic local Ca oscillator Almost rhythmic local Ca oscillator RI =0.04 RI=0.21 I spark =1 pA I spark =1.125 pA Inter-spike interval, ms Experimental data Model prediction 1,8001,5001, Number of events 1,8001,5001, Restitution time 4,0003,6003,2002,8002,4002,0001,6001, Number of events

Results: SANC model development Sub-membrane space LCRspark 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 Ca 2+ release units (CRUs). Each CRU has a fixed I spark and restitution time. Ca 2+ 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

I spark =0.75 pA Sparks Small Wavelets Global multi- focal waves Larger Wavelets I spark =1 pA I spark =1.035 pA I spark =1.25 pA 300 ms No 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 synchronization Results: s s s s s 0 100% 0 26 s 0 100% 0 26 s 0 100% 0 26 s 0 100% 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 Ispark=1.125 pA; Average= % I spark=1 pA; Average= % Ispark=0.5 pA Average= % I spark (pA) Average of the largest LCR (% cell area) Release Size: phase transition sparks global waves wavelets time 1 sec

Autocorrelation at different I spark Lag Period (ms) Autocorrelation Function Estimate As I spark increases from 0.5 to 1.5 pA in the model, the CRUs interaction increases via diffusion and Ca 2+ induced Ca 2+ release (CICR). This results in a higher LCR Rhythmicity Index, and smaller LCR period, approaching the restitution time. LCR Rhythmicity Index LCR Period Simulation Results Restitution time 300 ms Restitution time 300 ms I spark (pA) 1.5pA 1.25pA 1 pA 0.5pA pA pA 1,2001,1001, pA I spark (pA) Rhythmicity Index LCR Period Release Periodicity sparks global waves wavelets sparks global waves wavelets

Model utility LCR Period Restitution time 300 ms I spark (pA) sparks global waves wavelets sparks global waves wavelets LCR Rhythmicity Index 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: Based on our model prediction, these effects could be explained a variability in the amount CRU synchronization. CAMP- dependent phosphorylation of Ca 2+ clock proteins increases CRU current, as in model.

The same spot in the presence of ISO *P<0.025; n=7 (Paired t-test) ISO Control * * Rhythmicity Index ISO Control 2,6002,4002,2002,0001,8001,6001,4001,2001, Autocorrelation Function Estimate Lag Period (ms) Results: Experimental Effect of ISO on LCRs in depolarized SANC: Rhythmicity Index increased Time (s) Signal (Arb.Units) Time (s) Signal (Arb.Units)

1.5pA 1.125pA 1pA I spark =0.875pA Restitution time 300 ms Integrated LCR period Reset (All CRU are synchronized to begin restitution) LCR Vinogradova et al. Circ Res. 2002;90: A B C LCR period A shorter LCR period LCRs Simulations of LCR emergence in transition from global restitution (as in spontaneously beating SANC) M 2.7 M 0.13 M 6.4 M 1.1 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 Ca 2+ 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 I spark. 3) LCR period = restitution time + recruitment time. As I spark 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 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!

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