Caffeine-induced Ca²⁺ oscillations in type I horizontal cell of carp retina: A mathematical model

Abstract

Oscillations in intracellular free Ca²⁺ concentration ([Ca²⁺]_i) have been observed in a variety of cell types. In the present study, we constructed a mathematical model to simulate the caffeine-induced [Ca²⁺]_i oscillations based on experimental data obtained from isolated type I horizontal cell of carp retina. The results of model analysis confirm the notion that the caffeine-induced [Ca²⁺]_i oscillations involve a number of cytoplasmic and endoplasmic Ca²⁺ processes that interact with each other. Using this model, we evaluated the importance of store-operated channel (SOC) in caffeine-induced [Ca²⁺]_i oscillations. The model suggests that store-operated Ca²⁺ entry (SOCE) is elicited upon depletion of the endoplasmic reticulum (ER). When the SOC conductance is set to 0, caffeine-induced [Ca²⁺]_i oscillations are abolished, which agrees with the experimental observation that [Ca²⁺]_i oscillations were abolished when SOC was blocked pharmacologically, verifying that SOC is necessary for sustained [Ca²⁺]_i oscillations.

Abbreviations

2-APB

2-Aminoethoxydiphenyl borate

[Ca²⁺]_ER

Free Ca²⁺ concentration inside the lumen of the ER

[Ca²⁺]_i

Intracellular free Ca²⁺ concentration

ANOVA

Analysis of variance

CICR

Ca²⁺-induced Ca²⁺ release

ER

Endoplasmic reticulum

H1 HC

Type I horizontal cell

HC

Horizontal cell

L-VGCC

Ca²⁺channel

NCX

Na⁺/Ca²⁺ exchanger

PM

Plasma membrane

PMCA

Plasma membrane Ca²⁺-ATPase

RyR

Ryanodine receptor

SERCA

Sarco/endoplasmic reticulum Ca²⁺-ATPase

SNK

Student-Newman-Keuls

SOC

Store-operated channel

SOCE

Store-operated Ca²⁺ entry

STIM

Stromal interaction molecule

TRP

Transient receptor potential

Introduction

[Ca²⁺]_i oscillations have been observed in a variety of cell types.¹ The present study is focused on caffeine-induced [Ca²⁺]_i oscillations in type I horizontal cell (H1 HC) of carp retina. Horizontal cells are interneurons in vertebrate retinas, which receive glutamate input from photoreceptors. In carp H1 HC, [Ca²⁺]_i increase is caused primarily by Ca²⁺ release from intracellular Ca²⁺ store (basically the endoplasmic reticulum, ER) via ryanodine receptor (RyR) activation^2,3 and Ca²⁺ influx from the extracellular environment, while Ca²⁺ removal depends on the activities of the sarco/endoplasmic reticulum Ca²⁺-ATPase (SERCA),^2-4 Na⁺/Ca²⁺ exchanger (NCX)⁵ and plasma membrane Ca²⁺-ATPase (PMCA).⁵

Ca²⁺ imaging study with carp H1 HC revealed that [Ca²⁺]_i oscillations could be induced when caffeine was applied at various concentrations.⁶ The application of caffeine activates RyR, leading to ER Ca²⁺ release and ER depletion. Subsequent ER refilling, which should be required for the maintenance of [Ca²⁺]_i oscillations, is dependent on Ca²⁺ entry via store-operated channel (SOC). Hence RyR and SOC, together with the Ca²⁺ removal processes are the major components for caffeine-induced [Ca²⁺]_i oscillations. However, how these components interact with each other to give rise to [Ca²⁺]_i oscillations observed in H1 HC is unclear.

In the present study, a computational model based on biophysical properties of H1 HC was constructed to explore the underlying mechanism(s) of caffeine-induced [Ca²⁺]_i oscillations observed in H1 HC of carp retina. Using this model, caffeine-induced [Ca²⁺]_i oscillations were simulated. The concentration-dependent caffeine effect on the pattern of [Ca²⁺]_i oscillations was explored, relevant contributions of RyR, SOC, L-type voltage-gated Ca²⁺ channel (L-VGCC), NCX, PMCA and SERCA for caffeine-induced [Ca²⁺]_i oscillations were suggested, and the importance of SOC in caffeine-induced [Ca²⁺]_i oscillations was evaluated.

Results

Simulating caffeine-induced [Ca²⁺]_i oscillations in isolated H1 HC

Figure 1A–C shows the experimental observations of caffeine-induced [Ca²⁺]_i oscillations of 3 representative H1 HCs in response to 3, 6, 10 mM caffeine (with identical caffeine application time of 90 s), respectively.⁶ Statistical results of the experimental data show that, when the concentration of caffeine was increased from 3 to 10 mM, the time interval between the first and the second Ca²⁺ transients (ΔT_1-2; Fig. 1D) was decreased from 46.08 ± 3.41 s to 28.37 ± 2.30 s (P < 0.05, ANOVA, post hoc SNK test; Fig. 1E). The amplitude decrement during the Ca²⁺ oscillations was also concentration dependent. To quantify such amplitude decrement, the amplitude of the second transient was normalized against that of the first one (A₂/A₁; Fig. 1D). When caffeine concentration was increased from 3 to 10 mM, the normalized amplitude of the second transient (A₂/A₁) was decreased from 0.82 ± 0.05 to 0.58 ± 0.03 (P < 0.05, ANOVA, post hoc SNK test; Fig. 1F).⁶

Figure 1.

Concentration-dependent caffeine effects on the caffeine-induced [Ca²⁺]_i oscillations. (A–C) [Ca²⁺]_i oscillations induced by the application of 3, 6, and 10 mM caffeine (90 s), respectively. Horizontal bars bellow the traces indicate the periods of caffeine applications. (D) Definition of time interval between the first and the second Ca²⁺ transients (ΔT_1-2) and the amplitude of the first and the second Ca²⁺ transients. (E) ΔT_1-2 was decreased with caffeine concentration. (F) A₂/A₁ ratio was decreased with caffeine concentration. Data are presented as mean ± SEM (with sample size in parentheses). *denotes statistical significance of P < 0.05 by one-way ANOVA followed by post hoc SNK test, NS: not significant.⁶

Caffeine-induced [Ca²⁺]_i oscillations can be attributed to a number of factors (Fig. 6). Using the model cell, [Ca²⁺]_i oscillations induced by 3, 6, 10 mM caffeine were simulated (Fig. 2A–C) with parameter values listed in Table 3 and 4. The positive currents reflect Ca²⁺ efflux from cytoplasm to external environment or Ca²⁺ entering the ER.

Figure 6.

Schematic illustration of Ca²⁺ pathways relevant to caffeine-induced [Ca²⁺]_i oscillations in carp retinal HC. L-VGCC: L-type voltage-gated Ca²⁺ channel; NCX: Na⁺/Ca²⁺ exchanger; PMCA: plasma membrane Ca²⁺-ATPase; RyR: ryanodine receptor; leak: passive Ca²⁺ leak; SERCA: sarco/endoplasmic reticulum Ca²⁺-ATPase; ER: endoplasmic reticulum; SOC: store-operated channels; PM: plasma membrane.

Figure 2.

Simulation of caffeine-induced [Ca²⁺]_i oscillations using the biophysical model of H1 HC. (A–C) [Ca²⁺]_i oscillations induced by 3, 6, 10 mM caffeine (90 s), respectively. Traces shown are the model output of [Ca²⁺]_i, [Ca²⁺]_ER and Ca²⁺ currents mediated by RyR, PMCA, NCX, SERCA, SOC, and L-VGCC, respectively. θ_th indicates the [Ca²⁺]_ER threshold at which ER Ca²⁺ release occurs. The insets show dynamic changes of I_NCX and I_PMCA during the first [Ca²⁺]_i transient induced by caffeine.

Table 3.

Parameter values used in the model

Component parameter	Symbol	Value	Unit	Reference
L-VGCC
				4
Half inactivation parameter	KCa	0.30	μM
Time constant	τCa	2.86	s
Maximum conductance	${\displaystyle {\overline{g}}_{Ca}}$	120.0	μS/ cm2
PMCA				4
Maximum pumping rate	APMCA	0.052	pM/cm2/ms
Dissociation constant	KPMCA	7.00e−4	mM
Na+/Ca2+ exchanger				4
Scaling coefficient	KNCX	0.97	nA/mmol4/cm2
	r	0.59
RyR				35-37
Rate constant	KRyR	3.50e−3	/ms
Activation constant	Kd,ca	1.00	μM
ER Ca2+ leak				2
Rate constant	Vleak	5.00e−5	/ms
SERCA				2,37
Maximum SERCA flux	VSERCA	1.18e−5	mM/ms
Activation constant	KSERCA1	1.00e−4	mM
Inactivation constant	KSERCA2	0.10	mM
SOC				38
Maximum SOCE flux	VSOC	5.60e−5	mM/ms
STIM [Ca2+]ER affinity	KSOC	0.05	mM
SOCE timescale	τSOC	20.0	s
ER Ca2+ equation				39
ER Ca2+ buffering coefficient	fER	0.01
ER volume/cell volume (excluding ER)	volER / volcyt	0.15
[Ca2+]i equation				39
Ca2+ buffering coefficient of cytoplasm	fcyt	0.01
Na+ and K+ channels				39
	${\displaystyle {\overline{g}}_{\mathrm{Na}}}$	120.0	nS
	${\displaystyle {\overline{g}}_{\mathrm{Kd}}}$	0.25	nS
	${\displaystyle {\overline{g}}_{\mathrm{Kt}}}$	2.0	nS
	${\displaystyle {\overline{g}}_{\mathrm{Ka}}}$	50.0	nS

Table 4.

The initial conditions and geometric parameters of the model cell

Component parameter	Symbol	Value	Unit	Reference
Non-zero initial conditions for the model				39
	[Ca2+]o	2.0	mM
	[Ca2+]i (t = 0)	30.0	nM
	[Ca2+]ER (t = 0)	100.0	μM
	Vm (t = 0)	−55.0	mV
	ENa	70.0	mV
	[Na+]i	7.0	mM
	[Na+]o	135.0	mM
	EK	−55.0	mV
	[K+]i	54.4	mM
	[K+]o	2.5	mM
Geometric parameters				39
Diameter of the model neuron		20.0	μm
Length of the model neuron		22.5	μm

Caffeine induces ER Ca²⁺ release by increasing the open probability of RyR (P_RyR), and P_RyR is increased when the concentration of caffeine is increased.^7,8 To simulate the caffeine effect on [Ca²⁺]_i, the RyR activation constant (K_d,Ca in Eq. 10), which reflects the RyR's sensitivity to Ca²⁺, was adjusted. [Ca²⁺]_i responses induced by 3, 6, 10 mM caffeine were simulated with K_d,Ca of 0.16, 0.14, 0.13 μM, respectively. The simulated [Ca²⁺]_i curves closely resemble the experimental observations (Fig. 2A–C).

Model output simulating [Ca²⁺]_i oscillations induced by 3 mM caffeine is shown in Figure 2A. Upon caffeine (3 mM) application, RyR current is increased immediately, leading to an increase in [Ca²⁺]_i and a decrease in free Ca²⁺ concentration inside the lumen of the ER ([Ca²⁺]_ER). Currents carried by PMCA, NCX, and SERCA are increased accordingly, which bring [Ca²⁺]_i back to the basal level, forming the first [Ca²⁺]_i transient (the relative contributions of PMCA and NCX are illustrated in the insets of Fig. 2A). Meanwhile, SOC current is increased slowly upon ER depletion, which leads to a gradual ER refilling. RyR current is increased slowly with the increasing [Ca²⁺]_ER, results in an increase in [Ca²⁺]_i, which further potentiates the RyR current. Once sufficient amount of RyRs are activated, Ca²⁺ recycled by ER is again released, forming the subsequent [Ca²⁺]_i transient. During caffeine application, periodical changes in [Ca²⁺]_i is concomitant with the periodical activities of the RyR, PMCA, NCX, SERCA, SOC, and L-VGCC. After caffeine removal, each Ca²⁺ process returns to the resting state.

Figure 2B and C show model output induced by 6 and 10 mM caffeine, respectively. During 6 mM and 10 mM caffeine applications, the overall patterns of dynamic changes in [Ca²⁺]_i, [Ca²⁺]_ER and Ca²⁺ currents are similar to that during 3 mM caffeine application.

By comparing simulated [Ca²⁺]_i curves with 3, 6, and 10 mM caffeine, it is shown that [Ca²⁺]_i signal is caffeine concentration dependent. We also calculated the values of ΔT_1-2 and A₂/A₁ with each caffeine concentration (Table 1). Results show that when the concentration of caffeine is increased from 3 mM to 10 mM, the ΔT_1-2 interval is decreased from 56.72 s to 38.46 s, and the A₂/A₁ ratio is decreased from 0.81 to 0.54, both in accordance with the experimental observations.

Table 1.

The effect of caffeine concentration on caffeine-induced [Ca²⁺]_i oscillations

	ΔT1–2 (s)		A1 (μM)	A2 (μM)	A2/A1		θth (μM)
Caffeine (mM)	E	M	M	M	E	M	M
3 mM	46.08 ± 3.41	56.72	1.79	1.45	0.82 ± 0.05	0.81	85.43
6 mM	35.40 ± 1.68	43.41	1.81	1.14	0.65 ± 0.04	0.63	73.34
10 mM	28.37 ± 2.30	38.46	1.82	0.98	0.58 ± 0.03	0.54	66.74

E: experimental results, data are presented as mean ± SEM; M: model simulation results.

By examining the simulated [Ca²⁺]_ER curves, it is found that following the initial ER Ca²⁺ release, ER Ca²⁺ release occurs again after [Ca²⁺]_ER reaches a certain level. The [Ca²⁺]_ER value at which the Ca²⁺ release is initiated is denoted by θ_th, indicating the [Ca²⁺]_ER threshold at which ER Ca²⁺ release occurs (Fig. 2). By comparing [Ca²⁺]_ER curves in Figure 2A–C, it can be noticed that θ_th is decreased from 85.43 μM to 66.74 μM when caffeine concentration is increased from 3 mM to 10 mM (Table 1).

Caffeine effect at different concentrations is represented by using different K_d,Ca values, which results in RyR current modulation by influencing P_RyR (Eq. 10). To further explore the effect of caffeine concentration on caffeine-induced [Ca²⁺]_i oscillations, dynamic changes of P_RyR during caffeine application are plotted together with the corresponding [Ca²⁺]_i curves (Fig. 3A–C). It can be observed that after the first [Ca²⁺]_i transient, P_RyR is decreased to a trough (P_trough) when [Ca²⁺]_i returns to the basal level, and a high caffeine concentration corresponds to a large P_trough value and a quick P_RyR increase (Fig. 3D). With a large P_RyR, the second [Ca²⁺]_i transient can be induce quickly. Therefore, when the concentration of caffeine is increased, the ΔT_1-2 interval is decreased (Table 1). After the initial release, [Ca²⁺]_ER is increased gradually with time, and a fast second [Ca²⁺]_i transient is related to a small corresponding θ_th value, while a small θ_th indicates that only a small amount of ER Ca²⁺ can be released, which results in a small A₂. Hence the value of A₂ is decreased when the caffeine concentration is increased. Simulation results show that A₂ is decreased from 1.45 μM to 0.98 μM as the concentration of caffeine is increased from 3 mM to 10 mM, while the values of A₁ is kept around 1.80 μM. Therefore, the A₂/A₁ ratio is decreased when caffeine concentration is increased (Table 1). The above results explain the caffeine concentration dependency of [Ca²⁺]_i oscillations.

Figure 3.

Dynamic changes of RyR open probability (P_RyR) during caffeine application. (A–C) Simulation output of P_RyR (black line, left y-axis) and [Ca²⁺]_i (blue line, right y-axis) induced by 3, 6, and 10 mM caffeine (90 s), respectively. (D) Dynamic changes of P_RyR during the application of 3 (blue line), 6 (green line), and 10 mM (red line) caffeine (90 s). P_RyR reaches a trough (P_trough) after the initial [Ca²⁺]_i transient. The value of P_trough is increased when the concentration of caffeine is increased.

Effect of SOC inhibition on caffeine-induced [Ca²⁺]_i oscillations

Experimental data from isolated H1 HCs showed that prolonged application of 3 mM caffeine (7 min) induced sustained [Ca²⁺]_i oscillations in H1 HCs (Fig. 4A),⁶ and such [Ca²⁺]_i oscillations were abolished when 2-APB (SOC inhibitor) was co-applied (Fig. 4B),⁶ suggesting that SOCE is necessary for ER refilling.

Figure 4.

The 2-APB effect on caffeine-induced [Ca²⁺]_i oscillations. (A) [Ca²⁺]_i oscillations induced by prolonged application of caffeine (3 mM, 7 min). (B) After [Ca²⁺]_i oscillations were induced by caffeine (3 mM), co-application of 2-APB (100 μM) abolished the oscillations immediately.⁶

Using our model, the above experimental results (Fig. 4) are simulated. The effect of 3 mM caffeine is simulated with K_d,Ca = 0.16 μM, the effect of 2-APB was simulated by setting V_SOC (the maximum SOC flux, Eq. 13) to 0. As shown in Figure 5A, prolonged application of caffeine (3 mM, 7 min) induces sustained [Ca²⁺]_i oscillations in the model cell, and the oscillation in [Ca²⁺]_i is concomitant with the periodical release and uptake of ER Ca²⁺, and SOC current follows the fluctuations of [Ca²⁺]_ER. A [Ca²⁺]_i transient is induced whenever [Ca²⁺]_ER reaches θ_th.

Figure 5.

Model output simulating the 2-APB effect on caffeine-induced [Ca²⁺]_i oscillations. (A) Sustained [Ca²⁺]_i oscillations induced by prolonged caffeine (3 mM, 7 min) application. (B) Caffeine (3 mM, 7 min)-induced [Ca²⁺]_i oscillations are abolished when 2-APB (100 μM) is applied. Traces shown are simulation output of [Ca²⁺]_i, [Ca²⁺]_ER and Ca²⁺ currents mediated by RyR and SOC, respectively. &theta;_th indicates the [Ca²⁺]_ER threshold at which ER Ca²⁺ release occurs.

Although [Ca²⁺]_i oscillations can be induced by caffeine (3 mM), [Ca²⁺]_ER increase can be immediately stopped when 2-APB is applied. In the presence of 2-APB, SOC is constantly blocked, which abolishes the SOC current (Fig. 5B). Without SOCE, [Ca²⁺]_ER is gradually decreased, unable to reach θ_th, hence no further Ca²⁺-induced Ca²⁺ release (CICR) is induced and no [Ca²⁺]_i transient is generated. This result verifies that SOCE is the main Ca²⁺ source for ER refilling, and the activation of SOC is required for the maintenance of sustained [Ca²⁺]_i oscillations.

Discussion

In the present study, we constructed a mathematical model to simulate the caffeine-induced [Ca²⁺]_i oscillations observed in type I horizontal cell of carp retina. Simulated [Ca²⁺]_i changes closely resemble the experimental observations, the concentration dependence of ΔT_1-2 and A₂/A₁ of the caffeine-induced [Ca²⁺]_i oscillations can be reproduced. Relevant contributions of RyR, SOC, L-VGCC, NCX, PMCA and SERCA for the caffeine-induced [Ca²⁺]_i oscillations are suggested. The oscillations in [Ca²⁺]_i are concomitant with the periodical changes of RyR, PMCA, NCX, SERCA, SOC, and L-VGCC activities.

Simulated [Ca²⁺]_ER curves in Figures 2 and 5A show that, continuous application of caffeine leads to repeated release/uptake of ER Ca²⁺. After each ER Ca²⁺ release, ER is gradually refilled, and subsequent Ca²⁺ release can be induced only when the [Ca²⁺]_ER level is recovered and reaches a certain threshold θ_th. When the concentration of caffeine is increased, the value of θ_th is decreased (Fig. 2, Table 1). The concentration-dependent caffeine effect on θ_th is consistent with the experimental results reported by Kong et al.⁹ In their study, by recording [Ca²⁺]_ER of HEK-293 cells expressing RyR, it was found that the threshold for Ca²⁺ release (θ_th) was decreased when the concentration of caffeine was increased.

In carp retinal horizontal cell, Ca²⁺ entering the cytoplasmic is extruded into the extracellular space by both PMCA and NCX.⁵ From the simulation output (Fig. 2, insets), it can be observed that during caffeine-induced [Ca²⁺]_i oscillations, Ca²⁺ is extruded mainly by PMCA when [Ca²⁺]_i is at lower levels; while at higher [Ca²⁺]_i levels, NCX-mediated Ca²⁺ current is larger than the PMCA Ca²⁺ current. These results confirm the previously reported basic characteristics of PMCA and NCX, i.e., PMCA has higher affinity for Ca²⁺ than NCX, while NCX has higher turnover rate,^10,11 suggesting that PMCA and NCX cooperate to regulate Ca²⁺ signals over a wide [Ca²⁺]_i range in H1 HC.

In addition to regulating the dynamic changes in [Ca²⁺]_i, PMCA has also been shown to participate in the regulation of resting Ca²⁺ homeostasis. It was reported that in rod-driven bipolar cell of mouse retina, PMCA was involved in the maintenance of the resting [Ca²⁺]_i levels.^12,13 For our model cell, after the extracellular stimulus is removed, [Ca²⁺]_i and [Ca²⁺]_ER gradually return to their resting levels, which is independent on the intensity of the previously given stimulation. The levels of [Ca²⁺]_i and [Ca²⁺]_ER, as well as currents carried by different Ca²⁺ components in the resting state are kept within limited ranges (Table 2) until a subsequent stimulus is applied. The model output shows that NCX is inactive at rest (${\displaystyle {\text{I}}_{\text{NCX}}^{\text{REST}}}$ ≈ 0.0 μA/cm², Table 2) and Ca²⁺ extrusion occurs through PMCA (${\displaystyle {\text{I}}_{\text{PMCA}}^{\text{REST}}}$ ≈ 0.4 μA/cm², Table 2). The simulation results suggest that in the resting state, extrusion of cytoplasmic Ca²⁺ depends mainly on PMCA in H1 HC.

Table 2.

Model output in the resting state

Symbol	Value	Unit
${\displaystyle {\text{I}}_{\text{NCX}}^{\text{REST}}}$	0.0	μA/cm2
${\displaystyle {\text{I}}_{\text{PMCA}}^{\text{REST}}}$	0.4	μA/cm2
${\displaystyle {\mathrm{I}}_{\text{SOC}}^{\text{REST}}}$	0.4	μA/cm2
${\displaystyle {\mathrm{I}}_{\text{leak}}^{\text{REST}}}$	−0.5	μA/cm2
${\displaystyle {\text{I}}_{\text{SERCA}}^{\text{REST}}}$	0.1	μA/cm2
${\displaystyle {\text{I}}_{\text{RyR}}^{\text{REST}}}$	0.0	μA/cm2
${\displaystyle {\mathrm{I}}_{\text{VGCC}}^{\text{REST}}}$	0.0	μA/cm2
${\displaystyle {[{\text{Ca}}^{2+}]}_{\text{i}}^{\text{REST}}}$	28	nM
${\displaystyle {[{\text{Ca}}^{2+}]}_{\text{ER}}^{\text{REST}}}$	94	μM

It can also be noticed that the SOCE complex is activated at rest (${\text{I}}_{\text{SOC}}^{\text{REST}}$ ≈ 0.4 μA/cm², Table 2). On the plasma membrane, Ca²⁺ extruded from the cell via PMCA is counterbalanced by Ca²⁺ entering the cell through SOC. On the ER membrane, the passive leakage of Ca²⁺ from the ER (${\text{I}}_{\text{leak}}^{\text{REST}}$ ≈ −0.5 μA/cm², Table 2) is compensated by SERCA (${\text{I}}_{\text{SERCA}}^{\text{REST}}$ ≈ 0.1 μA/cm²s, Table 2) and SOCE complex-mediated Ca²⁺ uptake. Ca²⁺ homeostasis of the model cell is maintained by the activities of PMCA, SOCE complex, ER passive leak, and SERCA, keeping resting [Ca²⁺]_i and [Ca²⁺]_ER levels at 28 nM and 94 μM, respectively (Table 2). The involvement of the SOCE complex in resting Ca²⁺ homeostasis has been reported in cells such as rat primary cortical neurons, mouse mammary epithelial cells, and HEK293 cells.^14-17 In these cells, 2 types of STIM proteins, i.e., STIM1 and STIM2, are expressed on the ER membrane. STIM1 triggers SOCE in response to store-depletion, while STIM2 activates Orai1 upon small fluctuations in [Ca²⁺]_ER, keeping resting [Ca²⁺]_i and [Ca²⁺]_ER stable. Therefore, our simulation results suggest that in addition to ER refilling upon stimuli-induced store depletion (Fig. 5), SOC activation in response to minor [Ca²⁺]_ER fluctuation may play a crucial role in maintaining [Ca²⁺]_i and [Ca²⁺]_ER levels in H1 HC at the resting state.

Experimental results from carp H1 HC show that, L-VGCC was activated during caffeine-induced [Ca²⁺]_i oscillations.⁶ The involvement of L-VGCC suggests that V_m of H1 HC should be depolarized upon caffeine application. Our simulation results show that changes in V_m are concomitant with changes in [Ca²⁺]_i, and L-VGCC current is activated periodically by membrane depolarization. When the L-VGCC current is blocked by setting ${\displaystyle {\overline{g}}_{\text{C}\text{a}}}$ to zero, [Ca²⁺]_i oscillations can still be induced by caffeine (10 mM, 60 s), at the meantime, the A₂/A₁ ratio and ΔT_1-2 interval are slightly increased as compared with control, showing good agreement with experimental data (data not show). Both the simulation and experimental results show that L-VGCC is involved in the caffeine-induced [Ca²⁺]_i oscillations. However, L-VGCC is not the major source of Ca²⁺ influx during caffeine-induced [Ca²⁺]_i oscillations, [Ca²⁺]_i oscillations can be induced when L-VGCC is completely blocked.

Our present study provides fundamental insight into the mechanisms of caffeine-induced [Ca²⁺]_i oscillations in carp H1 HC, and reveals possible roles of SOC in H1 HC [Ca²⁺]_i signaling. Further studies are needed to elucidate the molecular identities and functions of SOC in H1 HC physiology.

Methods

Ca²⁺ imaging data

Experimental data were obtained from isolated type I horizontal cell of carp retina using fluo-3-based Ca²⁺ imaging technique. All the materials and methods have been previously reported.⁶

Model description

All simulations were carried out using NEURON software.¹⁸ A cylindrical neuron was constructed, with the [Ca²⁺]_i dynamics being modeled at the whole-cell level.

The model system is schematically presented in Figure 6, which includes Ca²⁺ processes on the plasma membrane (PM), the ER, and the store-operated Ca²⁺ entry (SOCE) complex. Biophysical properties of the neuron membrane are spatially uniform.

The PM processes include the L-VGCC, NCX, and PMCA. L-VGCC mediates Ca²⁺ entry during membrane depolarization, while NCX and PMCA extrude Ca²⁺ from the cytosol into the extracellular space.

The ER processes involve 3 parallel components: Ca²⁺ release from the ER into the cytosol mediated by RyR, passive Ca²⁺ leakage from the ER into the cytosol, and Ca²⁺ uptake from the cytosol into the ER through SERCA.

SOCE is a process in which plasma membrane Ca²⁺ channel (SOC) is activated upon Ca²⁺ store depletion.¹⁹ The SOCE complex is composed of proteins including STIM, SOC, and SERCA. STIM which resides on the ER membrane senses the ER Ca²⁺ content,^20,21 while Orai channels^22-24 and/or TRP channels^25,26 form the SOC on the PM. Upon store depletion, STIM and SOC translocate and cluster at the ER-PM junctions, leading to the formation of the STIM-SOC complexes and SOC activation.^23,27,28 Activated SOC mediates Ca²⁺ influx, and SERCA in the ER-PM junctions uptakes these Ca²⁺ to refill the depleted ER.^29-33

Besides, voltage-gated K⁺ and Na⁺ channel conductance also contribute to the regulation of [Ca²⁺]_i by affecting the neuronal membrane potential, therefore, these processes are also included in our model.

Hence, in our model, Ca²⁺ dynamics can be described as:

$${\displaystyle \begin{array}{l}\frac{d{[\text{C}{\text{a}}^{2+}]}_{\text{i}}}{dt}=f_{cyt}·\frac{I_{\text{C}\text{a}}^{All}}{2·F·vo{l}_{cyt}}+J_{RyR}+J_{le\text{a}k}-J_{SER\text{C}A}\\ \frac{d{[\text{C}{\text{a}}^{2+}]}_{\text{ER}}}{dt}=f_{ER}·(vo{l}_{cyt}/vo{l}_{ER})·(J_{SO\text{C}}+J_{SER\text{C}A}-J_{RyR}-J_{le\text{a}k})\end{array}}$$ (1)

where [Ca²⁺]_i is the free intracellular Ca²⁺ concentration, [Ca²⁺]_ER is the free Ca²⁺ concentration inside the ER lumen; f_cyt and f_ER are Ca²⁺ buffering coefficients for cytoplasm and ER, respectively; vol_cyt and vol_ER are the volumes of the cell (excluding ER) and the ER, respectively; F is the Faraday constant; I^All_Ca represents the total Ca²⁺ currents across the cell membrane; J_RyR represents ER Ca²⁺ release via RyR; J_leak represents the passive Ca²⁺ leakage from the ER into the cytosol; J_SERCA represents the Ca²⁺ uptake from the cytosol into the ER through SERCA; J_SOC represents Ca²⁺ entering the ER through the SOCE complex.

The total Ca²⁺ currents across the plasma membrane are given by:

$${\displaystyle I_{\text{C}\text{a}}^{All}=I_{VG\text{C}\text{C}}+I_{\text{N}\text{C}X}+I_{PM\text{C}A}}$$ (2)

where I_VGCC, I_NCX, and I_PMCA denote the Ca²⁺ currents mediated by L-VGCC, NCX, and PMCA respectively.

Ca²⁺ current through L-VGCC (I_VGCC) can be described as:⁴

$${\displaystyle I_{VG\text{C}\text{C}}={\overline{g}}_{\text{C}\text{a}}·m_{\text{C}\text{a}}·h_{\text{C}\text{a}}·(V_m-E_{\text{C}\text{a}})\frac{d{m}_{\text{C}\text{a}}}{dt}={\alpha }_{m_{\text{C}\text{a}}}·(1-m_{\text{C}\text{a}})-{\beta }_{m_{\text{C}\text{a}}}·m_{\text{C}\text{a}}{\alpha }_{m_{\text{C}\text{a}}}=33·\frac{92.7-V_m}{\exp ((92.7-V_m)/9.6)-1}{\beta }_{m_{\text{C}\text{a}}}=3.3·\exp ((-65.2-V_m)/11.5)h_{\text{C}\text{a}}+{\tau }_{\text{C}\text{a}}\frac{d{h}_{\text{C}\text{a}}}{dt}=K_{\text{C}\text{a}}^n/(K_{\text{C}\text{a}}^n+{[\text{C}{\text{a}}^{2+}]}_i^n)E_{\text{C}\text{a}}=12.5·\text{log}({[\text{C}{\text{a}}^{2+}]}_o/{[\text{C}{\text{a}}^{2+}]}_i)}$$ (3)

where ${\displaystyle \overline{g}}$_Ca is the maximum conductance of L-VGCC; m_Ca and h_Ca are the activation and inactivation variables, respectively; V_m denotes the membrane potential; E_Ca stands for the reversal potential of Ca²⁺ current; K_Ca is the half-inactivation parameter; n is the Hill coefficient; α and β are forward and backward rate coefficients, respectively; τ_Ca represents the inactivation time constant.

Equation 3 shows that the Ca²⁺ dynamics are regulated by V_m, while Ca²⁺ currents together with Na⁺ and K⁺ currents across the plasma membrane all contribute to the V_m changes. Hence voltage-gated Na⁺ conductance and 3 types of K⁺ conductance (i.e., delay time rectifying K⁺ current, outward rectifying K⁺ current, and anomalous rectifying K⁺ current), which are expressed in carp retinal HC, are also included in our model.³⁴

Current carried by voltage-gated Na⁺ channel (I_Nav) can be described as:³⁴

$${\displaystyle \begin{array}{l}{I}_{\text{N}\text{a}v}={\overline{g}}_{\text{N}\text{a}}·m_{\text{N}\text{a}}^3·h_{\text{N}\text{a}}·(V_m-E_{\text{N}\text{a}})\\ \frac{d{m}_{\text{N}\text{a}}}{dt}={\alpha }_{m_{\text{N}\text{a}}}·(1-m_{\text{N}\text{a}})-{\beta }_{m_{\text{N}\text{a}}}·m_{\text{N}\text{a}}\\ {\alpha }_{m_{\text{N}\text{a}}}\text{= 40}·\frac{\text{80}-V_m}{\exp ((\text{80}-V_m)/\text{15})-1}\\ {\beta }_{m_{\text{N}\text{a}}}\text{= 10}·\exp (-V_m/\text{20})\\ \frac{d{h}_{\text{N}\text{a}}}{dt}={\alpha }_{h_{\text{N}\text{a}}}·(1-h_{\text{N}\text{a}})-{\beta }_{h_{\text{N}\text{a}}}·h_{\text{N}\text{a}}\\ {\alpha }_{h_{\text{N}\text{a}}}\text{= 0.01}·\exp (-V_m/\text{30})\\ {\beta }_{h_{\text{N}\text{a}}}\text{=}\frac{\text{2}}{\exp ((\text{70}-V_m)/\text{10})+1}\end{array}}$$ (4)

where ${\displaystyle \overline{g}}$_Na is the maximum conductance of the voltage-gated Na⁺ channel; m_Na and h_Na are the activation and inactivation variables, respectively; E_Na is the reversal potential of Na⁺ current.

Current carried by delay time rectifying K⁺ channel (I_kd) can be described as:³⁴

$${\displaystyle \begin{array}{l}{I}_{Kd}={\overline{g}}_{Kd}·m_{Kd}^4·V_K\\ V_K=V_m-E_K\\ \frac{d{m}_{Kd}}{dt}={\alpha }_{m_{Kd}}·(1-m_{Kd})-{\beta }_{m_{Kd}}·m_{Kd}\\ {\alpha }_{m_{Kd}}\text{=10}·\frac{\text{120}-V_K}{\exp ((12\text{0}-V_K)/20)-1}\\ {\beta }_{m_{Kd}}\text{= 5}·\exp (-V_K/\text{20})\end{array}}$$ (5)

where ${\displaystyle \overline{g}}$ _Kd is the maximum conductance of the delay time rectifying K⁺ channel; m_Kd represents the activation variable; E_K is the reversal potential of K⁺ current.

Current carried by outward rectifying K⁺ channel (I_Kt) can be described as:³⁴

$${\displaystyle \begin{array}{l}{I}_{Kt}={\overline{g}}_{Kt}·m_{Kt}^3·h_{Kt}·V_K\\ V_K=V_m-E_K\\ m_{Kt}=\frac{{\alpha }_{m_{Kt}}}{{\alpha }_{m_{Kt}}+{\beta }_{m_{Kt}}}\\ {\alpha }_{m_{Kt}}=4\text{0}·\frac{\text{140}-V_K}{\exp ((14\text{0}-V_K)/15)-1}\\ {\beta }_{m_{Kt}}=\text{8}·\exp (-V_K/\text{20})\\ \frac{d{h}_{Kt}}{dt}={\alpha }_{h_{Kt}}·(1-h_{Kt})-{\beta }_{h_{Kt}}·h_{Kt}\\ {\alpha }_{h_{Kt}}=0.01·\exp (-V_K/\text{20})\\ {\beta }_{h_{Kt}}=\frac{2}{\exp ((3\text{0}-V_K)/10)+1}\end{array}}$$ (6)

where ${\displaystyle \overline{g}}$_Kt is the maximum conductance of the outward rectifying K⁺ channel; m_Kt and h_Kt are the activation and inactivation variables, respectively.

Current carried by anomalous rectifying K⁺ channel (I_Ka) can be described as:³⁴

$${\displaystyle \begin{array}{l}{I}_{K\text{a}}={\overline{g}}_{K\text{a}}·m_{K\text{a}}^4·(V_m-E_K)\\ m_{K\text{a}}=\frac{1}{1+\exp \left(\frac{V_m-E_K}{30}\right)}\end{array}}$$ (7)

where ${\displaystyle \overline{g}}$ _Ka is the maximum conductance of the anomalous rectifying K⁺ channel; m_Ka represents the activation variable.

On the plasma membrane, Ca²⁺ extrusion is mediated by NCX and PMCA. Current carried by NCX (${\text{I}}_{\text{NCX}}^{\text{All}}$) can be described as:⁴

$${\displaystyle I_{\text{N}\text{C}X}^{All}=K_{\text{N}\text{C}X}·{[\text{N}{\text{a}}^{+}]}_i^3·{[\text{C}{\text{a}}^{2+}]}_o·\exp \left(r·V_m·\frac{F}{RT}\right)-{[\text{N}{\text{a}}^{+}]}_o^3·{[\text{C}{\text{a}}^{2+}]}_i·\exp [-(1-r)·V_m·\frac{F}{RT}]}$$ (8)

where K_NCX is a scaling coefficient; [Na⁺]_i, [Na⁺]_o and [Ca²⁺]_o are intracellular Na⁺ concentration, extracellular Na⁺ concentration and extracellular Ca²⁺ concentration, respectively; R and T are the gas constant and the absolute temperature, respectively. The ion exchange ratio is Na⁺:Ca²⁺ = 3:1, therefore the currents carried by Na⁺ and Ca²⁺ are equal to 3 × ${\text{I}}_{\text{NCX}}^{\text{All}}$ and −2 × ${\text{I}}_{\text{NCX}}^{\text{All}}$, respectively.

Ca²⁺ extrusion mediated by PMCA can be described as:⁴

$${\displaystyle J_{PM\text{C}A}=A_{PM\text{C}A}·\frac{{[\text{C}{\text{a}}^{2+}]}_i}{K_{PM\text{C}A}+{[\text{C}{\text{a}}^{2+}]}_i}}$$ (9)

where J_PMCA represents the amount of Ca²⁺ efflux; A_PMCA is the maximal pumping rate; K_PMCA is the dissociation constant.

RyR, passive ER Ca²⁺ leakage, and SERCA are involved in Ca²⁺ exchange between the cytoplasm and the ER. RyR-mediated Ca²⁺ flux from the ER into the cytosol is described as:^35-37

$${\displaystyle J_{RyR}=K_{RyR}·P_{RyR}·({[\text{C}{\text{a}}^{2+}]}_{ER}-{[\text{C}{\text{a}}^{2+}]}_i)P_{RyR}=\frac{{[\text{C}{\text{a}}^{2+}]}_i^3}{{[\text{C}{\text{a}}^{2+}]}_i^3+K_{d,\text{C}\text{a}}^3}}$$ (10)

where K_RyR is the rate constant; P_RyR is the open probability of RyR; K_d,Ca is the activation constant which reflects the [Ca²⁺]_i sensitivity of CICR.

Passive Ca²⁺ leakage from the ER into the cytosol is described as:²

$${\displaystyle J_{le\text{a}k}=K_{le\text{a}k}·({[\text{C}{\text{a}}^{2+}]}_{ER}-{[\text{C}{\text{a}}^{2+}]}_i)}$$ (11)

where K_leak is the rate constant.

ER Ca²⁺ uptake mediated by SERCA can be described as:^2,37

$${\displaystyle J_{SER\text{C}A}=V_{SER\text{C}A}·\frac{{[\text{C}{\text{a}}^{2+}]}_i}{{[\text{C}{\text{a}}^{2+}]}_i+K_{SER\text{C}A1}}·\frac{K_{SER\text{C}A2}^6}{{[\text{C}{\text{a}}^{2+}]}_{ER}^6+K_{SER\text{C}A2}^6}}$$ (12)

where V_SERCA is the maximum SERCA flux; K_SERCA1 and K_SERCA2 are the activation and inactivation constants, respectively.

Upon store depletion, SOCE complex can be formed in the ER-PM junctions. Due to the tight coupling between the SOC and SERCA, the majority of Ca²⁺ entering the cytoplasm via SOC is pumped into the ER by SERCA.^29-31 Ca²⁺ entering the ER through the SOCE complex can thus be described as:³⁸

$${\displaystyle \begin{array}{l}{J}_{SO\text{C}}=V_{SO\text{C}}·P_{SO\text{C}}\\ \frac{d{P}_{SO\text{C}}}{dt}=\frac{P_{SO\text{C}}^{\infty }-P_{SO\text{C}}}{{\tau }_{SO\text{C}}}\\ P_{SO\text{C}}^{\infty }=\frac{K_{SO\text{C}}^4}{K_{SO\text{C}}^4+{[\text{C}{\text{a}}^{2+}]}_{ER}^4}\end{array}}$$ (13)

where V_SOC is the maximum value of the SOC flux, and P_SOC represents the fraction of STIM proteins bound to SOC, i.e., the fraction of activated SOC. ${\text{P}}_{\text{SOC}}^{\text{∞}}$ is the fraction of STIM proteins dissociated from the ER Ca²⁺. K_SOC is the affinity of STIM for [Ca²⁺]_ER. τ_SOC represents the time constant for the adaptation of STIM to [Ca²⁺]_ER changes.

Parameter values for the above equations used in our model are listed in Table 3. The initial conditions (e.g., V_m at t = 0) and geometric parameters of the model cell are listed in Table 4.

Disclosure of Potential Conflicts of Interest

No potential conflicts of interest were disclosed.

Funding

This work was supported by National Nature Science Foundation of China (grant no. 61375114). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Funder's website: http://www.nsfc.gov.cn.