Cardiomyocyte Calcium Ion Oscillations—Lessons From Physics

Figure 1. Isolated RyR channel opening probability P0 as a function of cytoplasmic calcium concentration Ca2+. (A) When the cytoplasmic calcium concentration (top) was varied slowly (on a scale of ~10 s), the RyR opening probability (bottom) was shown to follow the instantaneous [Ca2+]. (B) When the calcium concentration (top) was increased rapidly (~1 μs) and kept roughly constant afterwards, the RyR opening probability (bottom) displayed a rapid increase (overshoot, denoted by β—orange arrow), followed by a slow relaxation (with typical rate of ~10 Hz, denoted by H—blue arrow) to a new steady-state determined by the long time calcium concentration (denoted by α—green arrow). Adapted from Valdivia et al. (1995). Reprinted with permission from AAAS.

Figure 2. A schematic representation of calcium cycling between the cytoplasm (CP) and the sarcoplasmic reticulum (SR), according to the model presented in Cohen and Safran (2019) and the main text. RyR channels (orange) embedded in the SR membrane stochastically switch between closed (right) and opened (middle) conformation—with rates R±[C] that depend on cytoplasmic calcium C. Opened RyR release calcium to the cytoplasm with a current that, in principle, also depends on cytoplasmic calcium Jp[C]. Calcium is restored to baseline concentrations via calcium pumps embedded in the SR (green, left), the mitochondria, and the cellular membrane (not shown) with a “lumped” rate K. RyR “adaptive” response to calcium (see Equation 1) is marked by a green arrow.

Figure 3. Experimental entrainment of cardiomyocyte beating by a mechanical probe. Isolated cardiomyocytes (n = 30) seeded on an elastic substrate were subject to mechanical pacing by an oscillating inert probe located ~100 μm away from the paced cell. The probe introduced periodic deformations of the underlying substrate with a frequency ωprobe. The cell beating frequency was measured before (ω0) and ~15 min after (ωcell) the pacing probe was activated. The scaled cellular beating frequency (ωcell/ω0) was plotted vs. the scaled probe frequency (ωprobe/ωo) since ω0 varies between cells. Red dots represent full entrainment by the probe, i.e., synchronization to the probe frequency (see top left figure, plotting the scaled fluorescent [Ca2+] signal F/F0 of a representative cell). Blue dots represent “bursting” behavior, where the cell alternates between beating with the frequency of the probe ωprobe and quiescence (see top right figure). The time between consecutive intervals of quiescence was comparable to ω0-1. Reprinted by permission from Springer: Springer Nature (Nitsan et al., 2016).

Figure 4. An example of the time evolution of the phase predicted by the theoretical Equation (6) (top row), the resulting scaled oscillation in c(t) (middle row), and the oscillations observed in experiments (bottom row). Here we fix the cell and probe frequency at Ωc = 2π, Ωp = 6π, respectively, and vary the amplitude of pacing to control the value of Q. (A) Q = 0.2, below threshold of entrainment (Q = 1), the cell beats with its spontaneous frequency Ωc as indicated by the quasi-linear increase in phase. Inset: comparison to linear slope (dashed) that shows large regions of slips and much smaller intervals of plateaus. (B) Q = 0.97 Intermittent periods of entrainment (plateaus) followed by fast “phase-slip” events. This corresponds to the “bursting” behavior observed in experiments (bottom row). (C) Q = 2, above the threshold of entrainment. The cell beats with the probe frequency Ωp. Top and middle rows adapted from Cohen and Safran (2018). Top and middle rows reprinted by permission from Springer: Springer Nature (Cohen and Safran, 2018). Bottom row reprinted by permission from Springer: Springer Nature (Nitsan et al., 2016).

Figure 5. Stationary probability density Ps(ϕc) as a function of the shifted phase (ϕc − β), for a fixed noise amplitude D* = 0.5 [s−1], spontaneous frequency Ωc=1 [rad·s-1] and pacing frequency Ωp=1.5 [rad·s-1]. Different colors show different pacing amplitudes with α* = 0 (blue) α* = 0.5 [s−1] (orange) and α* = 2[s−1] (green). Figure adapted by permission from Springer: Springer Nature (Cohen and Safran, 2018).