1. Volume 74, Issue 1, Pages 153-174 (January 1998)
Calcium Concentration and Movement in the Ventricular Cardiac Cell during an Excitation-Contraction Cycle 
A. Peskoff, G.A. Langer 
Biophysical Journal 
Volume 74, Issue 1, Pages (January 1998)
DOI: /S (98)
Copyright © 1998 The Biophysical Society Terms and Conditions

2. Figure 1
Geometry of the model, showing one-half of a sarcomere extending from a Z-line to an adjacent M-line. The position in the sarcomere is expressed in cylindrical coordinates (r, z), with the plane of the Z-line defined as z=0. The half-sarcomere is modeled as a circular cylinder of radius b=0.5μm and length l=1.0μm; the cleft is modeled as a coaxial circular disk of radius a=0.2μm and thickness h=12nm, with its center at (r, z)=(0, 0). The eight points shown in the z=0 plane at differing radial locations (four points inside the cleft, one point on the cleft boundary, and three points outside the cleft) and the five points shown at r=a=200nm at differing axial locations are points at which graphs of [Ca] versus time will be shown. The shaded plane is the surface over which 3-D snapshots of the spatial distribution of [Ca] in the sarcomere outside the cleft will be shown.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

3. Figure 2
[Ca] for an SR release of 2×10−19 moles. (A) [Ca] versus t at the eight points in the z=0 plane shown in Fig. 1. (B) The first 20ms of A on a 10-fold expanded time scale. (C) Three-dimensional picture of the same information as in A, shown at 41 uniformly spaced times (Δt=5ms) and at 21 uniformly spaced positions (Δr=25nm) along a radial line (0≤r≤500nm) in the z=0 plane. The shaded portion of the graphs represents the interior of the cleft; the unshaded portion represents the sarcomere outside the cleft.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

4. Figure 3
[Ca] for an SR release of 2×10−19 moles. (A) [Ca] versus t at the five axially spaced points at r=a=200nm shown in Fig. 1. The uppermost curve is of [Ca] at the boundary of the cleft, and is the same as the curve in Fig. 2 B for the same point. The dashed curve is the average of the [Ca] over the volume of the sarcomere outside the cleft. (B) The first 20ms in A on a 10-fold expanded time scale.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

5. Figure 4
[Ca] for an SR release of 2×10−19 moles. (A) Four snapshots of the free [Ca] in the sarcomere outside the cleft at t=5, 10, 20, and 50ms, as a function of radial and axial position in the shaded plane pictured in Fig. 1. Note that the portion of the curves at z=0 from r=0 to r=a=200nm are of [Ca] in the Z-line plane, outside the cleft, unlike the shaded portions of Figs. 2 A–C, which are of [Ca] inside the cleft (see text: Geometry of the Model). (B) The same as in A, but for total [Ca] (i.e., the sum of free Ca and Ca bound to troponin and calmodulin).
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

6. Figure 5
(A) The partition of Ca ions among the various possible states in or departed from the cleft: the fraction of the Ca ions released by the SR up to the time t that have left the cell via the Na-Ca exchanger, that have diffused radially out of the cleft and entered the sarcoplasm, or that are still within the cleft volume either free, or bound to low- or high-affinity sites. All amounts are normalized with respect to the total SR release and multiplied by 100%. Note that at t=200ms, 92% of the Ca has diffused to the general sarcoplasm and 8% has been transported out through the exchanger. (B) The fraction of Ca ions released from the SR up to the time t that are free in the sarcomere outside the cleft, that are bound to troponin or calmodulin, or that have diffused to the cylindrical boundary of the sarcoplasm, r=b=500nm, and have been taken up by the SR. At any instant the sum of the fractions equals the percentage of the total 10-ms-long SR release that has diffused out of the cleft up to that instant. Note that at t=200ms, ∼3% of the Ca is bound to troponin, 1% is bound to calmodulin, 88% has been taken up by the SR, and 0.016% is free in the sarcoplasm. The remaining 8% has exited from the cell via the Na-Ca exchanger (see A).
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

7. Figure 6
[Ca] for an SR release of 1×10−19 moles. (A) [Ca] versus t at the eight points in the z=0 plane shown in Fig. 1. Compare to Fig. 2 A. (B) [Ca] versus t at the five axially spaced points at r=a=200nm, shown in Fig. 1. The dashed curve is the average of the [Ca] over the volume of the sarcomere outside the cleft. Compare to Fig. 3 A. (C) Four snapshots of the free [Ca] in the sarcomere outside the cleft at t=5, 10, 20, and 50ms, as a function of radial and axial position in the shaded plane pictured in Fig. 1. Compare to Fig. 4 A for an SR release of 2×10−19 moles.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

8. Figure 7
The partition of Ca among the various states outside the cleft. Same as Fig. 5 B, but for an SR release of 1×10−19 moles. Note that at t=200ms, ∼4% of the Ca is bound to troponin, 1% is bound to calmodulin, 80% has been taken up by the SR, and 0.02% is free in the sarcoplasm. The remaining 15% has exited from the cell via the Na-Ca exchanger.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

9. Figure 8
[Ca] for an SR release of 2×10−19 moles, with 100μM fluo-3 added to the sarcoplasm. (A) [Ca] versus t at the five axially spaced points at r=a=200nm shown in Fig. 1. The dashed curve is the average of the [Ca] over the volume of the sarcomere outside the cleft. Compare to Fig. 3 A for the same conditions without the added fluo-3. (B) Same as in A, but for [Ca-fluo-3] and volume average of [Ca-fluo-3].
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

10. Figure 9
The partition of Ca among the various states outside the cleft. Same as Figs. 5 B and 7, but for an SR release of 2×10−19 moles, with 100μM fluo-3 added to the sarcoplasm. Note that at t=200ms, ∼3.1% of the Ca is bound to fluo-3, 4.3% is bound to troponin, 1.3% is bound to calmodulin, 83% has been taken up by the SR, and 0.03% is free in the sarcoplasm.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

11. Figure 10
Same as in Fig. 8, but for an SR release of 1×10−19 moles, with 100μM fluo-3 added to the sarcoplasm. (A) [Ca] versus t at the five axially spaced points at r=a=200nm, shown in Fig. 1. The dashed curve is the average of the [Ca] over the volume of the sarcomere outside the cleft. Compare to Fig. 6 B for the same conditions without the added fluo-3. (B) Same as in A, but for [Ca-fluo-3] and volume average of [Ca-fluo-3].
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

12. Figure 11
The partition of Ca among the various states outside the cleft. Same as in Figs. 5 B and 9, but for an SR release of 1×10−19 moles, with 100μM fluo-3 added to the sarcoplasm. Note that at t=200ms, ∼3.6% of the Ca is bound to fluo-3, 5.0% is bound to troponin, 1.6% is bound to calmodulin, 75% has been taken up by the SR, and 0.03% is free in the sarcoplasm. The remaining 15% has exited from the cell via the Na-Ca exchanger.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

13. Figure 12
Free [Ca] versus t at nine radial distances from the cleft center, r=0, to the cleft outer radius, r=a=200nm after 1ms of L-channel opening. The r=0 curve, which represents the mean concentration over a circle of 1.25nm radius, has a peak concentration of 0.94mM. The r=200nm curve rises only a small amount above 100 nM, is still rising at t=20ms, and reaches a peak of 111 nM at about t=30ms (not shown).
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

14. Figure 13
Snapshot of [Ca] on the shaded plane in Fig. 1. at t=30ms after channel opening, the time at which [Ca] at r=a=200nm reaches its maximum value. It indicates that the release from a single Ca channel at the center of the cleft has a trivial effect on [Ca] outside the cleft.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

15. Figure 14
[Ca] for an SR release of 4×10−20 moles in a 2-ms-duration pulse. A release of this magnitude simulates a Ca spark. (A) [Ca] versus t at the eight radially spaced points in the z=0 plane, shown in Fig. 1. (B) [Ca] versus t at the five axially spaced points at r=a=200nm, shown in Fig. 1. The dashed curve is the average of the [Ca] over the volume of the sarcomere outside the cleft. (C) Snapshot at t=8ms, the instant of peak [Ca] outside the cleft, on the shaded plane in Fig. 1. Thesuperimposed heavy curves are constant [Ca] contours: [Ca]=0.2, 0.5, 1.0, and 2.0μM (bottom to top). The rate of release in this example is 2×10−20 moles/ms/cleft, the same rate as for the maximum-force case considered above, but the duration is only one-fifth as long.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

16. Figure 15
Same SR release of 4×10−20 moles in a 2-ms-duration pulse, as in Fig. 14, but with the addition of 100μM fluo-3 to the sarcoplasm. (A) [Ca] versus t at the eight radially spaced points in the z=0 plane, shown in Fig. 1. (B) [Ca] versus t at the five axially spaced points at r=a=200nm, shown in Fig. 1. The dashed curves are the average of the [Ca] over the volume of the sarcomere outside the cleft. (C) Same as in B, but for [Ca-fluo-3] and volume average of [Ca-fluo-3]. (D) Snapshot at t=8ms, the instant of peak [Ca] outside the cleft, on the shaded plane in Fig. 1. The superimposed heavy curves are constant [Ca] contours. Comparing Figs. 14 A and B with 15 A and B, inside the cleft the effect of adding fluo-3 is negligible, but outside it is significant: the peak concentrations are lower and the peaks are delayed and broadened. Comparing Fig. 15 B ([Ca]) with Fig. 15 C ([Ca-fluo-3]) indicates an additional delay and broadening of the peaks for [Ca-fluo-3] transients compared to those for [Ca]. Comparing Figs. 15 D and 14 C indicates that the [Ca] transient is more localized spatially when 100μM fluo-3 is present.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

17. Figure 16
[Ca] versus t at the eight radially spaced points in the z=0 plane, shown in Fig. 1. 1×10−19 moles of Ca is released into the cleft from the JSR between t=0 and t=10ms, followed by an equal release into the sarcomere outside the cleft from the CSR between t=10 and t=20ms. The first 10ms are identical to the results shown in Fig. 6 A for a release of 1×10−19 moles inside the cleft. After 10ms there is an additional surge in [Ca] outside the cleft, but inside the cleft [Ca] is relatively unaffected. Comparing Fig. 16 with Fig. 2 A, where the same total of 2×10−19 moles was released during a 10-ms period, but entirely inside the cleft, indicates that dividing the release between JSR and CSR over a total 20ms duration yields somewhat lower peak values, but more sustained increases in [Ca].
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

18. Figure 17
Snapshots of [Ca] versus position in the shaded plane pictured in Fig. 1, at four instants after initiation of the CSR release: t=15, 20, 25, and 50ms. The snapshots before CSR release for t=5 and 10ms are shown in Fig. 6 C. The effect of the CSR release is to form a second peak at the CSR release ring, and a plateau region between this peak and the peak at the cleft exit during the period 10<t≤20ms. The CSR peak disappears rapidly but the cleft peak persists because the movement of Ca out of the cleft is slower than the 10ms duration of the Ca pulse entering from the CSR.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

19. Figure 18
[Ca] versus t at the eight radially spaced points in the z=0 plane shown in Fig. 1, for an SR release of 4×10−20 moles in a 2-ms-duration pulse. All conditions are identical to those in Fig. 14 B, except that the high- and low-affinity Ca binding sites have been deleted from the cleft. This deletion 1) increases [Ca] within the sarcomere at end-release by >10-fold; 2) causes average [Ca] to return to 200 nM within 2ms as compared to 20ms; 3) decreases the latency for spark appearance to ∼100μs from ∼5ms; 4) reduces the total spark duration to ∼5ms from >30ms.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions

20. Figure 19
[Ca] snapshots at 2, 4, 8, and 16ms for an SR release of 4×10−20 moles in a 2-ms-duration pulse. (A) With and (B) without binding sites in the cleft. Note that at t=4ms, in A the response is just beginning to appear, whereas in B it has already decreased by two orders of magnitude from its peak.
Biophysical Journal  , DOI: ( /S (98) )
Copyright © 1998 The Biophysical Society Terms and Conditions