Finite element modeling of sarcoplasmic reticular intraluminal Ca2+ diffusional fluxes during amphibian striated muscle excitation–contraction coupling

Figures

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  Figure 1. Basic modeling strategy and geometry of the sarcoplasmic reticular (SR) element forming the diffusion volume. (A) Summary of computational strategy. (B) Representation of the geometry of each modeled SR element as a cylinder joining the midpoint of the longitudinal SR (LSR) to the cisternal region (CSR) from which RyR-mediated Ca2+ release into the T–SR junction takes place. This structure is, in turn, (C) meshed into finite elements. In (B), face F1 represents the middle of the LSR element or the end of the half LSR element and is the closed end. F2 is the terminal cisterna forming the opposite CSR end. F3 is the lateral membrane of the SR element.

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  Figure 2. Time-dependent free and total Ca2+ diffusion concentration gradients along the length of the SR element through early times during SR Ca2+ efflux. Color maps summarizing computational results displaying SR free, [Ca2+]free, and total Ca2+ concentrations, [Ca2+]total, at different, equally spaced, longitudinal positions along the red line in the formalized SR geometry (inset) at different early times, t < 20 ms, following the onset of SR RyR1-mediated Ca2+ effluxes and SERCA-mediated influxes. These run from the center of the longitudinal SR, LSR at l = 0 nm, to the cisternal SR, CSR, l = 180 nm. Studies performed for modeled SR in the absence (I) and the presence (II, III) of previously reported SR calsequestrin concentrations uniformly distributed through the SR, [Casq], and its Ca2+ binding, Kd, properties. Results are shown for [Ca2+]free (I, II) and [Ca2+]total (III) under conditions where the RyR1-mediated SR efflux density Jefflux(t) remains constant through (A) or decays from its initial value Jefflux(0)with the consequent cisternal Ca2+ depletion (B, C) in the absence (A, B) and presence of SERCA-mediated Ca2+ influx JΔSR influx(t) (C).

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  Figure 3. Time-dependent free and total Ca2+ concentrations through the radius of each SR element at both the CSR and LSR during SR Ca2+ efflux. Color maps summarizing computational results showing SR free, [Ca2+]free, and total Ca2+ concentrations, [Ca2+]total, through the radius (vertical axis) of the cisternal, CSR (A) and center of the longitudinal, LSR, element (B) indicated by red lines in the formalized SR geometry (inset) at different early times, t < 20 ms (horizontal axis), following the onset of CSR Ca2+ effluxes and the presence of SERCA-mediated background Ca2+ influxes. The results shown are for [Ca2+]free (I, II) and [Ca2+]total (III) under conditions where Ca2+ efflux at the CSR Jefflux(t) decays from its initial value Jefflux(0) with the consequent cisternal Ca2+ depletion in the presence of SERCA-mediated Ca2+ influx JΔSR influx(t).

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  Figure 4. Quantification of the time courses of free and total Ca2+ concentration changes along the length of the SR element through early times during SR Ca2+ release. Time dependences of free [Ca2+]free (I, II) and total Ca2+ concentrations [Ca2+]total (III) in the absence (I) and the presence (II, III) of calsequestrin. These are shown under conditions where CSR Ca2+ efflux Jefflux(t) remains constant through (A) or decays from its initial value Jefflux(0) with the consequent cisternal Ca2+ depletion (B, C) in the absence (A, B) and presence of SERCA-mediated Ca2+ influx JΔSR influx(t) (C). The plots in each panel are color-coded to denote [Ca2+]free and [Ca2+]total at equally spaced axial positions along the red line in the formalized SR geometry (inset) at different early times, t < 20 ms following the onset of CSR Ca2+ efflux Jefflux(t) in the presence and absence of calsequestrin-mediated Ca2+ buffering and of background SERCA-mediated Ca2+ influxes JΔSR influx(t).

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  Figure 5. Quantification of the positional dependence of free and total Ca2+ concentrations along the length of the SR element at different early times during SR Ca2+ release. Spatial dependences of free, [Ca2+]free, (I, II), and total Ca2+ concentrations [Ca2+]total (III). These are shown under conditions of constant SR Ca2+ efflux Jefflux(t) (A) or one that decays from its initial value Jefflux(0) with the consequent cisternal Ca2+ depletion (B, C) in the absence (A, B) and presence of SERCA-mediated Ca2+ influx JΔSR influx(t) (C). The plots in each panel are color-coded to denote [Ca2+]free and [Ca2+]total at equally spaced longitudinal positions along the red line along the SR axis (inset) at different early times, t < 20 ms following the onset of CSR Ca2+ effluxes Jefflux(t) and SERCA-mediated influxes JΔSR influx(t).

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  Figure 6. Free and total Ca2+ time-dependent diffusion gradients along the SR axis through prolonged times during CSR Ca2+ efflux. Color maps of [Ca2+]free and [Ca2+]total along the SR axis indicated by the red line in the formalized SR geometry (inset) at late times, t < 2 s following the onset of the CSR Ca2+ efflux Jefflux(t). Studies in the absence (I) and presence of calsequestrin (II,III). Results shown are for [Ca2+]free (I, II) and [Ca2+]total (III) under conditions of constant CSR Ca2+ efflux Jefflux(t) = Jefflux(0) (A) and one that decays from its initial value Jinflux(0) with the consequent cisternal Ca2+ depletion (B, C) in the absence (A, B) and presence of SERCA-mediated Ca2+ influx JΔSR influx(t) (C).

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  Figure 7. Uniform free and total Ca2+ concentrations through the radius of each SR element during SR Ca2+ release through prolonged times during CSR Ca2+ efflux. Color maps of SR Ca2+ concentrations through the radius of the cisternal CSR (A) and center of the longitudinal LSR (B) indicated by red lines in the formalized SR geometry (inset) at late times, t < 2 s following the onset of the CSR Ca2+ efflux Jefflux(t). Studies in the absence (I) and presence of calsequestrin (II, III). Results shown are for free [Ca2+]free (I, II) and total Ca2+ concentrations [Ca2+]total (III) under conditions where the CSR efflux Jefflux(t) decays from its initial value Jefflux(0) with the consequent [Ca2+]free and [Ca2+]total depletion in the presence of SERCA-mediated Ca2+ influx JΔSR influx(t).

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  Figure 8. Free and total Ca2+ concentrations with time through prolonged intervals (<2 s) following SR Ca2+ release at different points along the length of the SR element. Studies in the absence (I) and presence of calsequestrin (II, III). Time dependences of free [Ca2+]free (I, II) and total Ca2+ concentrations [Ca2+]total (III) where CSR Ca2+ efflux remains constant Jefflux(t) = Jefflux(0) (A) or decays from its initial value Jefflux(0) with the consequent [Ca2+]free and [Ca2+]total (B, C) in the absence (A, B) and presence of SERCA-mediated Ca2+ influx JΔSR influx(t)(C). Note the overlapping decays at the different SR positions, suggesting diffusion equilibration through the SR axis.

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  Figure 9. Free and total Ca2+ concentrations along the length of the SR element at different late times during SR Ca2+ release. Studies in the absence (I) and presence of calsequestrin (II, III). Spatial dependences of free [Ca2+]free (I, II) and total Ca2+ concentrations [Ca2+]total (III) with a constant (A) or decaying (B, C) CSR Ca2+ efflux Jefflux(t) in the absence (A, B) and presence of SERCA-mediated Ca2+ influx JΔSR influx(t) (C). The plots in each panel were color-coded to denote SR Ca2+ concentrations at equally spaced axial positions along the red line in the formalized SR geometry (inset) at different late times, t < 2 s following the onset of CSR Ca2+ effluxes and SERCA-mediated influxes. Note the greater time spacing of the successive plots compared to Figure 5.

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  Figure 10. Consequences of the SR diffusion patterns for TSR rates of Ca2+ release, its driving CSR free Ca2+ concentrations, and axial heterogeneities in free Ca2+ concentrations. (A, D) Rates of release of free Ca2+ into the T–SR junction from the CSR, Jefflux(t) and (B, E) their driving cisternal [Ca2+]free ( [Ca2+]free(0,t)) and (C, F) the consequent differences between CSR and LSR [Ca2+]free ( [Ca2+]free(0,t)−[Ca2+]cyt(l/2,t)) with time following the onset of CSR Ca2+ efflux. Findings over (A–C) the shorter < 20 ms and (D–F) the longer < 2 s interval. The findings were compared for conditions of constant Ca2+ flux in the presence and absence of calsequestrin and of declining Ca2+ flux in the respective presence and absence of calsequestrin and of SERCA activity (color-coded). Note the overlapping lines obtained in the respective cases with and without SERCA activity.