Predicting local SR Ca(2+) dynamics during Ca(2+) wave propagation in ventricular myocytes

Abstract

Of the many ongoing controversies regarding the workings of the sarcoplasmic reticulum (SR) in cardiac myocytes, two unresolved and interconnected topics are 1), mechanisms of calcium (Ca(2+)) wave propagation, and 2), speed of Ca(2+) diffusion within the SR. Ca(2+) waves are initiated when a spontaneous local SR Ca(2+) release event triggers additional release from neighboring clusters of SR release channels (ryanodine receptors (RyRs)). A lack of consensus regarding the effective Ca(2+) diffusion constant in the SR (D(Ca,SR)) severely complicates our understanding of whether dynamic local changes in SR [Ca(2+)] can influence wave propagation. To address this problem, we have implemented a computational model of cytosolic and SR [Ca(2+)] during Ca(2+) waves. Simulations have investigated how dynamic local changes in SR [Ca(2+)] are influenced by 1), D(Ca,SR); 2), the distance between RyR clusters; 3), partial inhibition or stimulation of SR Ca(2+) pumps; 4), SR Ca(2+) pump dependence on cytosolic [Ca(2+)]; and 5), the rate of transfer between network and junctional SR. Of these factors, D(Ca,SR) is the primary determinant of how release from one RyR cluster alters SR [Ca(2+)] in nearby regions. Specifically, our results show that local increases in SR [Ca(2+)] ahead of the wave can potentially facilitate Ca(2+) wave propagation, but only if SR diffusion is relatively slow. These simulations help to delineate what changes in [Ca(2+)] are possible during SR Ca(2+)release, and they broaden our understanding of the regulatory role played by dynamic changes in [Ca(2+)](SR).

Figure 1

Ca²⁺ wave model schematic. Each release site is placed beside a transverse tubule and is located at a distance d from its neighbors. The default distance d between RyR clusters in the longitudinal direction, left to right in the figure, is 2 μm; results shown in Figs. 4, 6, and 7 also consider the case where d = 1 μm. A single cluster containing 56 RyRs is assumed to wrap completely around each T-tubule. For clarity of illustration, this is drawn as two clusters on either side of the T-tubule. NSR connects the regions of JSR associated with each release site. SERCA pumps are homogeneously distributed throughout the NSR.

Figure 2

(A) Space-time image of cytosolic [Ca²⁺] (on a logarithmic scale) during a Ca²⁺ wave (left), with the corresponding image of SR [Ca²⁺] (right). Transverse tubules are indicated by horizontal white lines. (B) Spatiotemporal changes in [Ca²⁺]_SR within two sarcomeres are displayed for three values of D_Ca,SR: 12 μm²/s (slow; left), 60 μm²/s (medium; middle), and 300 μm²/s (fast; right) Slow SR diffusion causes the most dramatic increases in [Ca²⁺]_SR above the baseline value (1500 μM) in unactivated regions. (C) Recovery of total JSR [Ca²⁺] after release at an individual site depends on D_Ca,SR. Time constants range from 54 ms (fast) to 84 ms (slow).

Figure 3

Logarithmic plots of [Ca²⁺]_i versus location (A) at different times during a Ca²⁺ wave for D_Ca,SR = 12 μm²/s (left), 60 μm²/s (middle), and 300 μm²/s (right), with the corresponding logarithmic plots of [Ca²⁺]_SR (B). The speed of SR Ca²⁺ diffusion can greatly influence [Ca²⁺]_SR but has little effect on [Ca²⁺]_i.

Figure 4

Effects of SERCA inhibition on [Ca²⁺]_i (A) and [Ca²⁺]_SR (B) at the target site. Bars show percentage changes in [Ca²⁺] with normal and partially blocked SERCA for different values of D_Ca,SR and different spacing between release sites.

Figure 5

Effects of SERCA stimulation on [Ca²⁺]_i and [Ca²⁺]_SR at the target site. Increasing SERCA activity leads to a decrease in [Ca²⁺]_i, and an increase in [Ca²⁺]_SR for all values of D_Ca,SR.

Figure 6

Effects of SERCA pump [Ca²⁺]_i dependence with cluster spacing of 1 μm (left) and 2 μm (right). In either case, the exponent in the equation describing SERCA activity (η) was set to either 3, the control value of 1.78, or 0.75. An increased exponent leads to greater increases in [Ca²⁺]_SR, and slow diffusion favors accumulation of [Ca²⁺]_SR, in all cases.

Figure 7

(A) Time course of JSR refilling for different values of NSR-to-JSR transfer rate v. (B) Percentage changes in target site [Ca²⁺]_SR for different values of v and D_Ca,SR.