📒 Li 2012

Mechanisms by which Cytoplasmic Calcium Wave Propagation and Alternans Are Generated in Cardiac Atrial Myocytes Lacking T-Tubules—Insights from a Simulation Study1



  • the mechanisms underlying Ca2+ wave propagation and [Ca2+]i alternans in cardiac myocytes lacking t-tubules (atrial cells in small mammals) are still unclear
  • Here: biophysically detailed computer model for Ca2+ release and Ca2+ wave propagation in cardiac myocytes lacking t-tubules


Mathematical model of Ca2+ wave propagation in atrial myocytes

  • Adapted from Tao et al. equations to simulate Ca2+-wave propagation in atrial myocytes that lack t-tubules
  • A cell divided into 13 elements with a spatial resolution of 2 μm

Stimulation protocol and simulated intracellular Ca2+-wave propagation

  • on each voltage-clamp pulse, Ca2+ influx via VOCCs triggered CICR at the peripheral units, resulting in large [Ca2+]i transients in these regions
  • localized [Ca2+]i transients diffused inward toward the central region, provoking successive CICR that led to Ca2+-wave propagation.
  • Ca2+ wave did not fully propagate to the center. the [Ca2+]i transients (Fig. 1 B ii) and the SR Ca2+ release (Fig. 1 B iii) were large in the periphery of the cell but small in the central region
  • These simulation results matched experimental observations in rat (15,19), guinea-pig (20), and cat (4) atrial myocytes that lack t-tubules.

Model validation

  • sustaining the intracellular Ca2+ waves through increasing Ca2+ influx by elevating the extracellular Ca2+ concentration
  • increasing the RyR sensitivity by decreasing the threshold of RyR for CICR
  • elevating the SR content by pausing pacing for 10 s while increasing SERCA Ca2+ uptake (Pup increased by 75%) to allow SR Ca2+ content accumulation
  • increases in the Ca2+ influx, the RyR sensitivity, or the SR content helped to sustain full Ca2+-wave propagation from the periphery to the center of the cell, producing a more homogeneous [Ca2+]i, similar to experimental results.


Effect of increasing Ca2+ influx

  • An increase in Ca2+ influx via elevating [Ca2+]o has been shown to help facilitate full Ca2+-wave propagation toward the center region and to reduce the [Ca2+]i spatial heterogeneity in atrial cells
  • Also in increasing the maximum channel conductance of the VOCCs (gCaL)

  • There is a time delay in the [Ca2+]i and [Ca2+]SR transients between the peripheral and central regions => propagation rather than synchronized

Effect of increasing RyR sensitivity

  • reducing the threshold of RyR for CICR (Krel)
  • When Krel was reduced by 10%, a complete Ca2+ wave spreading toward the interior region of the cell was established temporarily. But amplitude is smaller.
  • Due to the reduced SR content, propagation of the Ca2+ wave toward the center of the cell was unstable, leading to alternans

Effect of increased SR content

  • increased SR Ca2+ content (Fig. 4Bi, lower), leading to a period of complete Ca2+ wave propagation into the center of the cell; then Ca alternans
  • enhancing the SR Ca2+ uptake (ii): hindered the inward Ca2+ wave propagation at first. Then a stable complete Ca2+ wave was observed (Fig. 4 A ii) when the SR Ca2+ content was significantly elevated in both central and peripheral regions

Effect of partial inhibition of SERCA pump

  • SERCA pump rate (Pup) was decreased by 10%: alternans
  • increasing the threshold of SERCA Ca2+ uptake (Kup) by 20% + SERCA pump rate (Pup) was increased by 50% : enhanced Ca2+-wave propagation; the amplitude of [Ca2+]i transients was greatly enhanced in the interior region of the cell

Exploring the mechanisms for Ca2+ alternans

Ca2+ diffusion

  • increase of the time constant of the Ca2+ diffusion (τ) => [Ca2+]i alternans (bifurcation)
  • complicated pattern of alternans are possible
  • cancelling Ca diffusion (rapid equilibrium) eliminates Ca alternans
  • Ca diffusion dramatically increased the steepness of dependence on SR Ca content
  • Increasing Kup shifted the dependence curve leftward (smaller SR Ca2+ content region)

Ca2+ influx & RyR sensitivity & the SERCA pump

  • When gCaL was increased over the range 100%–500% of its control value, a cascade of bifurcations occurred
  • More dramatic in the central region than in the peripheral region
  • With decreasing Krel, a cascade of bifurcations occurred, leading to [Ca2+]i alternans with various patterns
  • When Kup was increased from 100% to 140% of its control value, a cascade of bifurcations was triggered, decreased SR uptake due to increased Kup resulted in a low level of SR Ca2+ content and, consequently, reduced [Ca2+]i transient amplitude

Spontaneous Ca2+ release

  • Overloading the SR Ca2+ content may produce spontaneous Ca2+ release from the SR
  • Increased Ca2+ influx (gCaL increased to 370%) and SERCA pump activity (Pup increased to 150%) => irregular pattern of [Ca2+]i transients



  • Model validated by its ability to reproduce typical Ca2+-wave propagation patterns of atrial myocytes without t-tubules
  • reproduce experimentally observed effects of modulations of various aspects of Ca2+ cycling, such as Ca2+ influx, SERCA pumps (SR Ca2+ uptake), and RyRs (SR Ca2+ release), on spatial distribution of Ca2+ transients
  • steep relationship between the SR Ca2+ content and the cytoplasmic Ca2+ concentration due to Ca transient propagation, more prone to Ca alternans
  • theoretical exploration of possible associations between the occurrence of Ca2+ alternans and parameters related to calcium handling
  • Spontaneous Ca2+ release observed

Mechanisms of incomplete Ca2+-wave propagation in cardiac cells without t-tubules

Mechanisms of Ca2+ alternans in cardiac cells devoid of t-tubules


  1. Li Q, O’Neill SC, Tao T, Li Y, Eisner D, Zhang H. Mechanisms by which cytoplasmic calcium wave propagation and alternans are generated in cardiac atrial myocytes lacking T-tubules-insights from a simulation study. Biophys J. 2012;102(7):1471-82. PMC3318133 ↩︎