Volume 24, Issue 4, Pages 989-1002 (December 1999) Supralinear Ca2+ Signaling by Cooperative and Mobile Ca2+ Buffering in Purkinje Neurons  Hitoshi Maeda, Graham C.R. Ellis-Davies, Koichi Ito, Yasushi Miyashita, Haruo Kasai  Neuron  Volume 24, Issue 4, Pages 989-1002 (December 1999) DOI: 10.1016/S0896-6273(00)81045-4

Figure 1 Two-Phase Responses of [Ca2+]i Induced by a Prolonged Depolarization Command in Cultured Purkinje Neurons (A) Pseudocolor images of the increases in [Ca2+]i induced by a 500 ms depolarization command. The Ca2+ images were generated from the fluorescence ratio of BTC. The image denoted by 0 ms was acquired immediately before depolarization, and those denoted by 130, 210, 290, and 450 ms were obtained during depolarization. The black-and-white photograph is a fluorescence image of the cell excited at a wavelength of 480 nm. (B) Time courses of [Ca2+]i during depolarization that were obtained at the three different regions of the cell indicated in (A): the soma as well as proximal and distal dendrites. Open triangles indicate the time points at which the Ca2+ images shown in (A) were acquired. (C) Time courses of [Ca2+]i recovery during and after depolarization at the same three regions of the cell as those in (B). (D) Prevention of the depolarization-induced increase in [Ca2+]i by AgaIVa. A Purkinje cell different from that in (A) through (C) was pretreated with 100 nM AgaIVa for 2 min before depolarization. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 2 Supralinear Summation of [Ca2+]i Increases Induced by Repetitive, Short-Duration Pulses of Depolarization (A) Pseudocolor images of [Ca2+]i increases induced by a train of 50 ms depolarization commands at a frequency of 1 Hz. The Ca2+ images were generated from the fluorescence ratio of BTC and were obtained before depolarization (0 ms) and immediately after the 1st, 2nd, 6th, and 22nd depolarization commands. The black-and-white photograph is a fluorescence image of the cell. (B) Time courses of [Ca2+]i during repetitive depolarization obtained at the three different regions of the cell indicated in (A): soma, dendrite 1, and dendrite 2. (C) Time courses of [Ca2+]i increases induced by the first four depolarization commands. Open triangles in (B) and (C) indicate the time points at which the Ca2+ images shown in (A) were acquired. (D) Dependence of the increment in [Ca2+]i (Δ[Ca2+]i) on the initial [Ca2+]i ([Ca2+]i,0) at the time of depolarization. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 3 Two-Phase Responses of Fura-2 Fluorescence to Depolarization in Purkinje Cells (A) Increases in the fluorescence ratio (Rfura-2) of fura-2 in the soma and a dendrite of a Purkinje cell during a 500 ms depolarization command. (B) Time courses of [Ca2+]i recovery after the 500 ms depolarization pulse for the cell studied in (A). (C) Time courses of [Ca2+]i in the soma and a dendrite of a Purkinje cell during repetitive 50 ms depolarization pulses applied at a frequency of 1 Hz. (D) Time courses of the [Ca2+]i increases induced by the first three depolarization commands for the cell studied in (C). Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 9 Two-Phase Ca2+ Dynamics Predicted by a Nonlinear Cable Equation (A) Time courses of [Ca2+]i during repetitive depolarization in cylinders with diameters (d) of 2, 10, or 20 μm, assuming the Ca2+ current density as 1.2 pA/μm2 and the pump rate normalized to the surface-to-volume ratio (Pm) as 25 s−1 μm. The resting [Ca2+]i is 0.1 μM in all simulation experiments in this figure. (B) Time courses of the fluorescence ratio of fura-2 during the changes in [Ca2+]i shown in (A). The Kdβ for fura-2 is set at 0.8 μM. (C and D) Ca2+ dependence of the time constant of Ca2+ signaling (t) and the diffusion length of Ca2+ (λ), respectively, under conditions of the standard buffer parameters and a pump rate (P) of 50/s or 2000/s. (E) Ca2+ dependence of the apparent diffusion constant (Dapp) of Ca2+ at three different concentrations of the high-affinity buffer ([H]). (F) Time courses of [Ca2+]i when Ca2+ influx is applied to the middle compartment of a 19-compartment model with a unit length of 1 μm. Concentrations of the high-affinity Ca2+ buffer are 0, 400, 400, and 40 μM for (Fa) through (Fd), respectively. The diffusion constant of the high-affinity Ca2+ buffer (DH) is assumed to be 0 μm2/s for (Fb) and 80 μm2/s for (Fc) and (Fd). The duration of Ca2+ influx is 10 ms, and the total amount was adjusted to achieve a peak [Ca2+]i of 0.6 μM; the total amounts are 54, 590, 1000, and 155 μM for (Fa) through (Fd), respectively. The distances from the middle compartment are indicated (0 to 4 μm). (G) Ca2+ dependence of the supralinearity factor (S), representing the relative Ca2+-buffering capacity at a certain [Ca2+]i with respect to that at high [Ca2+]i (24). (H) Supralinear summation of local and global Ca2+ inputs applied at various time intervals (Δt) to a 19-compartment model. For the global input (by dendritic Ca2+ spike), a Ca2+ input of 0.9 mM is applied to all compartments, resulting in an increase in [Ca2+]i of 2.2 μM. For the local input (synaptic input), a Ca2+ input of 1 or 1.1 mM is applied to the middle compartment for a DH of 0 and 80 μm2/s, respectively. (I) Peak amplitudes of [Ca2+]i when local and global inputs are applied to the 19-compartment model at different time intervals (Δt). The shaded areas represent the time window during which the two successive inputs result in a peak [Ca2+]i greater than the sum of the individual peak values. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 4 Role of Ca2+ Influx and Ca2+ Release from Intracellular Stores in the Supralinear Ca2+ Responses of Purkinje Cells to Depolarization (A) Inward currents mediated by Na+ and Ca2+ channels during repetitive stimulation with 50 ms depolarization commands at a frequency of 1 Hz. Closed squares indicate the second peak of inward current, which was resistant to the Na+ channel blocker tetrodotoxin and corresponds to Ca2+ influx. (B) Peak amplitudes of the Ca2+ currents plotted against time. (C and D) Changes in [Ca2+]i (C) and Δ[Ca2+]i (D) measured from BTC fluorescence in the soma and a dendrite of the same cell as that in (A) and (B). (E and F) Inhibition of caffeine-induced Ca2+ release by CPA. A fura-2-loaded cell was stimulated with 100 mM KCl (closed squares) and 20 mM caffeine (open squares) in the absence (E) or presence (F) of 30 μM CPA. Fura-2 fluorescence was measured from a dendrite. (G and H) Supralinear Ca2+ response to repetitive depolarization (G) and dependence of Δ[Ca2+]i on [Ca2+]i,0 in the dendrite of a cell loaded with BTC and ruthenium red (20 μM) and exposed to 30 μM CPA. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 5 The Ca2+ Binding Ratio and Buffering Capacity for a Purkinje Cell Determined by Repetitive Photolysis of Caged Ca2+ or Repetitive Depolarization (A and E) Time courses of [Ca2+]i increases induced by either repetitive partial (6%) photolysis of the caged Ca2+ compound DMNPE-4 (A) or repetitive 50 ms pulses of depolarization (E) in the same BTC-loaded cell. Arrows indicate the timing of photolysis or depolarization. (B and F) Dependence of Δ[Ca2+]i (ΔC) on the [Ca2+]i,0 (C0) immediately before photolysis (B) or depolarization (F). The values for C and C0 were obtained as indicated in (A). (C and G) Ca2+ dependence of the Ca2+ binding ratio (κΔ) obtained with the use of 10 (see the Experimental Procedures) for repetitive photolysis (C) or depolarization (G). (D and H) Ca2+ dependence of the Ca2+-buffering capacity (βΔ) obtained from 11 for repetitive photolysis (D) or depolarization (H). The polygonal lines in (B) through (D) and (F) through (H) indicate analytical fits of the data with 18 and 19, assuming nH values of 1, 2, or 3. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 6 The Ca2+-Buffering Capacity of Purkinje Cells (A) Theoretical Ca2+ dependence of the buffering capacity of high-affinity (nH = 1, 2, or 4) and low-affinity Ca2+ buffers. The concentration of the high-affinity Ca2+ buffer, [H], is 0.8/nH mM, and the binding ratio of the low-affinity buffer is 100. (B) Actual buffering capacity obtained from data for DMNPE-4 photolysis in nine Purkinje cells. Plots were obtained by the slope method (11). Polygonal lines represent the best fit of the data with the analytical method (19). The data shown in Figure 5 are from the cell c1. (C and D) Ca2+ dependence of the buffering capacity in the soma (C) and in the dendrites (D) of Purkinje cells as determined from experiments based on repetitive depolarization. The data points were obtained by first estimating the constant Ca2+ influx by the analytical method to fulfill either the [H] acquired in the repetitive photolysis experiments (c1, c3, c4, c8) or βΔ = 200 μM at C = 1 μM (c10, c11, c12, c13); the plot of βΔ was then derived from 16 and 11 after determination of ΔCT. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 7 The Ca2+ Binding Ratio and Buffering Capacity for Adrenal Chromaffin Cells in the Absence (A–D) or Presence (E–H) of Internal 5,5′-Difluoro-BAPTA (A and E) Time courses of [Ca2+]i increases induced by repetitive partial (6%) photolysis of DMNPE-4 in BTC-loaded cells in the absence (A) or presence (E) of intracellular perfusion with 1 mM 5,5′-difluoro-BAPTA (dBAPTA). Arrows indicate the timing of photolysis. (B and F) Dependence of ΔC on the C0 immediately before photolysis. The values for ΔC and C0 were obtained as indicated in (A). (C and G) Ca2+ dependence of the Ca2+ binding ratio (κΔ) obtained from 10. Data from five different cells are plotted in (C). (D and H) Ca2+ dependence of the Ca2+-buffering capacity (βΔ) obtained from 11. The polygonal lines in (F) through (H) indicate analytical fits of the data with 18 and 19, assuming an nH of 1 or 2. Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)

Figure 8 Ca2+ Diffusion in the Soma of a Purkinje Cell after Depolarization Time courses of [Ca2+]i in the outermost (S0, thick solid line) and innermost (S6, closed circles) of seven compartments of the soma ([A], inset) from which averaged [Ca2+]i values were obtained after a depolarization command of 50 ms (A) or 500 ms (B). The data were obtained from the same cell. Thin lines indicate theoretical prediction of the data, assuming the indicated diffusion coefficients (D) of the Ca2+ buffers and the standard buffer parameters. Arrows denoted by S0,…, S6 indicate the initial values at the seven compartments. The process of equilibration was not markedly affected by DL in (A) or by DH in (B). Neuron 1999 24, 989-1002DOI: (10.1016/S0896-6273(00)81045-4)