Mechanisms of calcium sequestration during facilitation at active zones of an amphibian neuromuscular junction

ARTICLE IN PRESS

Journal of Theoretical Biology 247 (2007) 230–241 www.elsevier.com/locate/yjtbi

Mechanisms of calcium sequestration during facilitation at active zones of an amphibian neuromuscular junction M.R. Bennetta,, L. Farnellb, W.G. Gibsonb, P. Dickensa a

The Neurobiology Laboratory, Department of Physiology, The Institute for Biomedical Research, University of Sydney, New South Wales 2006, Australia b The School of Mathematics and Statistics, University of Sydney, New South Wales 2006, Australia Received 11 May 2006; received in revised form 16 March 2007; accepted 18 March 2007 Available online 24 March 2007

Abstract The calcium transients ðD½Ca2þ i Þ at active zones of amphibian (Bufo marinus) motor-nerve terminals that accompany impulses, visualized using a low-affinity calcium indicator injected into the terminal, are described and the pathways of subsequent sequestration of the residual calcium determined, allowing development of a quantitative model of the sequestering processes. Blocking the endoplasmic reticulum calcium pump with thapsigargin did not affect D½Ca2þ i for a single impulse but increased its amplitude during short trains. Blocking the uptake of calcium by mitochondria with CCCP had little effect on D½Ca2þ i of a single impulse but greatly increased its amplitude during short trains. This present compartmental model is compatible with our previous Monte Carlo diffusion model of Ca2þ sequestration during facilitation [Bennett, M.R., Farnell, L., Gibson, W.G., 2004. The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction. Biophys. J. 86(5), 2674–2690], with the single plasmalemma pump in that model now replaced by separate pumps for the plasmalemma and endoplasmic reticulum, as well as the introduction of a mitochondrial uniporter. r 2007 Published by Elsevier Ltd. Keywords: Calcium; Facilitation; Low-affinity calcium indicator; Sequestration; Mitochondria; Endoplasmic reticulum

1. Introduction The different phases of increased efficacy of transmitter release at synapses were first clearly delineated at the amphibian (frog) neuromuscular junction by Magleby and Zengel (1975, 1976). They consist of four components: the first (F1) and second (F2) components of facilitation which decay with time constants of 60 and 400 ms, respectively, augmentation, which decays with a time constant of about 7 s; and potentiation, which decays with a time constant that ranges from tens of seconds to minutes (Zengel and Magleby, 1982). The residual Ca2þ hypothesis for the increased efficacy of transmitter release (Katz and Miledi, 1968) suggests that the temporal aspects of cytosolic Ca2þ sequestration after nerve-terminal impulses should likewise follow these four different phases. Attempts to determine this possibility rely mostly on exposing Corresponding author. Tel.: +61 2 9351 2034; fax: +61 2 9351 3910.

E-mail address: [email protected] (M.R. Bennett). 0022-5193/$ - see front matter r 2007 Published by Elsevier Ltd. doi:10.1016/j.jtbi.2007.03.022

the junction to different methyl ester forms of either the fast calcium buffer BAPTA or the relatively slower acting buffer EGTA. BAPTA does not affect the size of the endplate potential at the amphibian neuromuscular junction (Tanabe and Kijima, 1992). This suggests that exocytosis is triggered by Ca2þ entry at the vesicle docking sites in the microdomains rather than by the net calcium in the submembraneous zone within 30 nm from the presynaptic membrane, arising from calcium entry that would be chelated by BAPTA (Bennett et al., 2000a). However, BAPTA does remove the F1 phase of facilitation (completely, according to Tanabe and Kijima, 1992; by 60% according to Suzuki et al., 2000), suggesting that the decline of Ca2þ in the submembraneous zone, due to this ion diffusing into the rest of the terminal and being removed by the mitochondrial uniporter and to a lesser extent by the endoplasmic reticulum calcium pump, provides the residual Ca2þ that drives the F1 phase of facilitation. Presumably, the buffer is primarily responsible for removing Ca2þ from the submembraneous region, and

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that as it releases this, the mitochondria/endoplasmic reticulum come into play. Clearly, the Ca2þ that collects in the submembraneous zone does not act effectively on the exocytotic protein for times greater than about 10 ms (Bennett et al., 2000b), since this protein has too low an affinity to be affected at longer times by those relatively low concentrations of Ca2þ (K d of about 10225 mM)—see Schneggenburger and Neher (2000) as well as Bollmann et al. (2000). This necessitates the action of separate facilitation molecules with relatively high affinities (Zucker, 1999) that act in synergy with the exocytosis molecule. Such a modified residual Ca2þ hypothesis states that the Ca2þ still present some tens of milliseconds after an impulse acts on different molecules than the exocytotic molecule to facilitate release by the latter (Tang et al., 2000). Such a model has recently been shown to give a quantitative account of F1 and F2 facilitation (Bennett et al., 2004). In the present work, we have further developed this model of Ca2þ sequestration and applied it to experimental observations on the Ca2þ transients observed in toad motor-nerve terminals during different protocols of stimulation and following interruption of different Ca2þ sequestering pathways. 2. Methods 2.1. Experimental methods 2.1.1. Preparation and solutions Experiments were performed on the lumbricalis digiti V muscle (Ecker, 1889) of the cane toad Bufo marinus. The toads were collected from their natural environment in northeastern Australia and experimented on within 6 weeks of collection. Animals were between 40 and 70 mm in length and killed by double-pithing. Muscles were dissected from the hind limb with up to 1 cm of nerve attached and pinned on a silicone elastomer (SYLGARD; Dow Corning, Midland, MI) bed in an organ bath. Ringer’s solution containing (in mM): NaCl 111.2, KCl 2.5, NaH2 PO4 1.5, NaHCO3 16.3, glucose 7.8, MgCl2 1.2, and CaCl2 1.8 mM, bubbled with a gas mixture of 95% O2 and 5% CO2 , constantly perfused the organ bath at a rate of 3 ml/min. The motor nerve was stimulated by applying brief (0.08 ms) suprathreshold depolarizing pulses through a suction electrode. To prevent muscle contraction during motor nerve impalements or electrical stimulation, d-tubocurarine chloride (o10 mg l1 ; Sigma, St. Louis, MO) was added to the bath. The temperature was maintained at 18  C. 2.1.2. Calcium imaging of nerve terminals Motor nerves were filled with the calcium-sensitive dye Oregon Green 488 BAPTA-5N (OG-5N) by ionophoretic injection as described previously (Macleod et al., 2001). Briefly, the tapered portion of a microelectrode was filled with a 3 mM solution of the dye in 130–150 mM KCl and the barrel of the microelectrode was filled with 150 mM

231

KCl. The final electrode resistance was between 200 and 350 MO. The microelectrodes were used to impale motor nerves within 100 mm of the last node of Ranvier of the terminal to be examined, and current ðo0:6 nAÞ was applied for periods of o15 min. The resting membrane potential of the axon was required to be stable and more polarized than 60 mV at the end of the injection. OG-5N fluorescence was imaged using a Leica TCS 4D confocal microscope (Wetzlar, Germany) with a 40 water-dipping objective (0.80 numerical aperture; Leica). The dye was excited with the 488 nm line from an argon–krypton laser and emitted fluorescence was filtered with a 515 nm longpass filter. The line scan mode of the confocal microscope was used to record Ca2þ responses to motor nerve stimulation. The temporal resolution of the line scan was between 0.5 and 2 ms (depending on the particular confocal settings). A light emitting diode connected to the stimulator and positioned near the microscope condenser reported the exact timing of a stimulus as a bright line on the scan. For recording of single pulses, up to 120 scans were collected and the motor nerve was stimulated during each scan (Fig. 1b). The interval between each pulse was 2 s. Single pulse frames were collected in groups of 30 and the preparation was rested for 45 min and refocussed between each group. A bleach control group of 30 scans was collected without stimulation for each experiment. In experiments involving trains of pulses up to five consecutive frames were used to record the transient. The second and third linescan frames were timed to coincide, respectively, with the first and last pulses in a train. In this way, the first few pulses of a train and the fluorescence

Fig. 1. Calcium concentration in a motor-nerve terminal branch following a single impulse. Images of Oregon-Green 488 BAPTA-5N (OG-5N) fluorescence in a section of a terminal branch as shown in both frame scan (a) and line scan (b) modes. (a) Shows the fluorescence along this portion of the terminal branch, with the transverse scan line position indicated by the line ending in arrow heads. (b) Shows the average fluorescence change over scans plotted against time. The vertical line indicates the moment of stimulation.

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decay after stimulation were recorded with high temporal resolution, and the excitation shutter was closed for most of the stimulus train, thereby minimizing bleaching and phototoxicity. Up to 20 individual recordings (separated by at least 2 min) were taken, along with four or five bleach controls. Although the low affinity of OG-5N is such as to introduce noise into the recordings, this was preferred to the distortions introduced into the changes in Ca2þ using low-noise high-affinity calcium indicators (see Section 4). 2.1.3. Data analysis Linescan data were analysed using NIH Image software. Pixel intensity was summed along a line encompassing the terminal fluorescence for each line in a scan. The average background value was determined from a region of the scan containing no terminal. The appropriate background value was then subtracted from the measured terminal fluorescence. Each scan was corrected for bleach as determined by the control scans, and normalized to their prestimulation level of fluorescence. Scans were then averaged and are presented as DF =F , where F is the prestimulation level of fluorescence and DF is the change in the level of fluorescence. The conversion from fluorescence ratio DF =F to calcium transient D½Ca2þ i can be found starting from the standard relation (Grynkiewicz et al., 1985): F i  F min ½Ca2þ i ¼ K d , F max  F i

ðDF =F rest Þ þ 1  ð1=bÞ , ðF max =F rest Þ  ðDF =F rest Þ  1

where a is a constant given by a ¼ Kd

ðF max =F rest Þ  ð1=bÞ , ½ðF max =F rest Þ  12

(7)

showing that D½Ca2þ i is directly proportional to the fluorescence change. David et al. (1997) give the K d range as 30270 mM and the F max =F min range as 30–70, leading to an a in the range 0:5422:52 mM. The value a ¼ 2 mM has been used for the conversions in the present work. D½Ca2þ i transients were fitted with exponential curves using the Igor Pro software least-squares curve fitting function. The Ca2þ decay following a single stimulus was fitted with an equation of the form D½Ca2þ i ¼ C expðt=tÞ,

(8)

where C and t are constants and the decay following short trains of pulses was fitted with the equation D½Ca2þ i ¼ C 1 expðt=t1 Þ þ C 2 expðt=t2 Þ þ C 3 ,

(9)

where C i and ti , i ¼ 1; 2; 3, are constants.

(1)

where F i , F min and F max are the measured fluorescence at Ca2þ concentrations ½Ca2þ i , zero, and saturation, respectively, and K d is the dissociation constant for indicator binding. It follows by straightforward manipulation that (David et al., 1997) ½Ca2þ i ¼ K d

Provided DF 5F max , which is certainly the case for the results reported here, this can be approximated by   DF D½Ca2þ i ¼ a , (6) F rest

2.1.4. Reagents The hexapotassium salt form of OG-5N was purchased from Molecular Probes (Eugene, OR). Sodium orthovanadate, CCCP (carbonyl cyanide m-chlorophenylhydrozone) and thapsigargin were purchased from Sigma. Thapsigargin and CCCP were both bath applied from 1 mM stock solutions in DMSO and EtOH, respectively.

(2) 2.2. Mathematical model

where b

F rest K d þ ðF max =F min Þ½Ca2þ rest ¼ . F min K d þ ½Ca2þ rest

(3)

DF =F rest ( DF =F ) is the measured fluorescence and the equilibrium ½Ca2þ i , ½Ca2þ rest is related to F rest by ½Ca2þ rest ¼ K d

1  ð1=bÞ . ðF max =F rest Þ  1

(4)

The change in ½Ca2þ i , D½Ca2þ i ¼ ½Ca2þ i  ½Ca2þ rest is then found to be D½Ca2þ i ¼ Kd

ðDF =F rest Þ½ðF max =F rest Þ  ð1=bÞ . ½ðF max =F rest Þ  ðDF =F rest Þ  1½ðF max =F rest Þ  1 ð5Þ

The terminal is modelled as 4 volumetric compartments, representing the external medium, the cytosol, the endoplasmic reticulum and the mitochondria (Fig. 2). The free calcium concentration in each of these compartments is, respectively, x0 ¼ ½Ca2þ ext , x1 ¼ ½Ca2þ cyt , x2 ¼ ½Ca2þ mito and x3 ¼ ½Ca2þ retic . The various Ca2þ fluxes occurring between these compartments are shown in Fig. 2; in addition, there are Ca2þ buffers in the cytosol and in the endoplasmic reticulum. On the time scale considered here, diffusion can be neglected and each compartment is treated as being spatially homogeneous. Previous modelling of similar systems includes Sala and Hernandez-Cruz (1990), Kargacin and Fay (1991), Nowycky and Pinter (1993), Friel and Tsien (1994), Friel (1995), Gunter and Gunter (1994) and David (1999). The rate of change of free Ca2þ in the cytosol can be written as a sum of contributions from the Ca2þ fluxes in

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There are two buffers in the model: B1 in the cytosol and B2 in the reticulum. They each obey first-order kinetics: kþ i

CaBi ; Bi þ Ca $  ki

i ¼ 1; 2,

(14)

where k i are forward and reverse rate constants. Defining þ T F b;i ðwi ; xj Þ  k i wi  k i ð½Bi   wi Þxj ,

(15)

½BTi 

is the total concentration of where wi is the ½CaBi  and buffer Bi , the contribution of B1 to the rate of Ca2þ change in the cytosol is   dx1 ¼ F b;1 ðw1 ; x1 Þ. (16) dt buffer The concentration change of bound buffer in the cytosol is governed by Fig. 2. Schematic diagram of the terminal showing the four compartments: external medium, cytosol, endoplasmic reticulum and mitochondria. The various Ca2þ fluxes between these compartments are represented by arrows. The cytosol and the endoplasmic reticulum each contain endogenous buffers, B1 and B2 , respectively.

and out of each compartment, plus a buffering term:       dx1 dx1 dx1 dx1 ¼ þ þ dt dt plasmalemma dt mitochondria dt reticulum   dx1 þ . ð10Þ dt buffer The plasmalemma contribution is   dx1 A1 x1 ¼ F p ðx1 Þ   dt plasmalemma K 1 þ x1 þ A2 ðx0  x1 Þ þ A3 HðtÞ,

ð11Þ

where the first term is due to the outward pump and the second to the inward leak (Kargacin and Fay, 1991); the third is the contribution from the Ca2þ influx due to stimulation of the cell, HðtÞ being equal to 1 during Ca2þ influx and zero otherwise. The mitochondrial contribution is   dx1 A4 x2 A5 x2 ¼ F m ðx1 ; x2 Þ   2 1 2 þ , dt mitochondria K 4 þ x1 K 5 þ x 2 (12) 2þ

where the first term is due to the uniporter taking Ca into the mitochondria and the second term to the Na/Ca exchanger taking Ca2þ out (Gunter and Gunter, 1994). The reticulum contribution is   dx1 A6 x2 ¼ F r ðx1 ; x3 Þ   2 1 2 þ A7 ðx3  x1 Þ, dt reticulum K 6 þ x1 (13) where the first term is due to the pump into the reticulum and the second to the outward leak (Kargacin and Fay, 1991).

dw1 ¼ F b;1 ðw1 ; x1 Þ. (17) dt It follows from the above that the change in free Ca2þ in the mitochondria is governed by dx2 1 ¼  F m ðx1 ; x2 Þ, n2 dt

(18)

where n2 is the ratio of the volume of the mitochondria to that of the cytosol and in the reticulum it is governed by dx3 1 ¼  F r ðx1 ; x3 Þ þ F b;2 ðw2 ; x3 Þ, n1 dt

(19)

where n1 is the ratio of the volume of the reticulum to that of the cytosol. The bound buffer concentration in the reticulum satisfies dw2 ¼ F b;2 ðw2 ; x1 Þ. (20) dt The concentration of Ca2þ in the cytosol, x1 ¼ ½Ca2þ cyt , is now found by solving simultaneously the differential equations (10)–(13) and (16)–(20), subject to the initial conditions xi ¼ xei , i ¼ 1; 2; 3, where xei are the resting levels of Ca2þ in each compartment before stimulation commences. Although the above 4-compartment model is the most complete representation of the system, it is more illuminating to build up to it gradually by considering a sequence of models, starting from the simplest 2-compartment one. Thus, we define three models



Model A. 2 compartments: cytosol and exterior; Model B. 3 compartments: mitochondria, cytosol and exterior; Model C. 4 compartments: endoplasmic reticulum, mitochondria, cytosol and exterior.

Model C is described by the full set of equations; reducing these by removing all variables and equations referring to the reticulum then describes Model B and further reduction by removing all reference to the mitochondria leaves a description of Model A.

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2.2.1. Parameter choice The parameter values used in the calculation are given in Tables 1–3. The values for Model A (Table 1) are essentially those used in Bennett et al. (2004), except that the fixed and mobile buffers have been combined and the plasmalemma pump rate and Ca2þ influx rate have been adjusted to fit the experimental data. The volume of the

Table 1 Values of the parameters used in the numerical calculations for the case of Model A where there are two compartments (external medium and cytosol) separated by the plasmalemma Quantity

Symbol

Value

External ½Ca2þ  Cytosol Terminal volume Equilibrium ½Ca2þ 

x0

2 mM 3

xe1

3:5 mm 0:1 mM

A1 K1

3000 mMs1 0:2 mM

A2 A3 t2  t1

ðmM ms1 Þ 3.5 ms

Bt1

5100 mM

On rate

kþ 1

500 mM1 s1

Off rate

k 1

5000 s1

Dissociation constant

þ k 1 =k 1

10 mM

See text Nowycky and Pinter (1993) Adjusted Kargacin and Fay (1991) (Balanced) Varied—see text See text

Bennett (2004) Bennett (2004) Bennett (2004) Bennett (2004)

et al. et al. et al.

Cytosol Pump rate Mitochondria Uniporter rate Na/Ca exchange rate Endoplasmic reticulum Volume fraction

Equilibrium ½Ca2þ  Pump rate Pump dissociation constant Leak rate Buffer Total concentration On rate Off rate Dissociation constant

Symbol

Value

Notes

A1

800 mM s1

Adjusted

A4 A5

3:64  105 mM s1 114 mM s1

Adjusted Adjusted

n1

0.06

xe3 A6 K6

250 mM 1800 mM s1 0:66 mM

Kargacin and Fay (1991) See text Adjusted See text

A7

(Balanced)

Bt2

7500 mM

See text

kþ 2 k 2 þ k 2 =k 2

10 mM1 s1 5000 s1 500 mM

See text See text See text

For the cytosol, only the pump rate has changed—the remaining parameter values are as for Model A (Table 1). For the Mitochondria, the Uniporter rate and the Na/Ca exchange rate have been changed—the remaining parameter values are as for Model B (Table 2). A value for A7 was obtained by balancing the leak rate and the pump rate at equilibrium.

et al.

A value for A2 was obtained by balancing the leak rate and the pump rate at equilibrium. Table 2 Values of the parameters used in the numerical calculations for the case of Model B where there are three compartments (external medium, cytosol and mitochondria)

Cytosol Pump rate Mitochondria Density Equilibrium ½Ca2þ  Uniporter rate Uniporter dissociation constant Na/Ca exchange rate Na/Ca exchange dissociation constant

Quantity

Notes

Pump rate Pump dissociation constant Leak rate Ca2þ influx rate Ca2þ influx time per pulse Buffer Total concentration

Quantity

Table 3 Values of the parameters used in the numerical calculations for the case of Model C where there are four compartments (external medium, cytosol, mitochondria and endoplasmic reticulum)

Symbol

Value

Notes

A1

1200 mM s1

Adjusted

n2 xe2

0:1 pg mm3 0

See text

A4 K4

5:45  105 mM s1 15 mM

A5

228 mM s1

Adjusted Gunter and Gunter (1994) Adjusted

K5

8:1 nmol mg1

Gunter and Gunter (1994)

For the cytosol, only the pump rate has changed—the remaining parameter values are as for Model A (Table 1).

terminal is that of a cylinder of diameter 1:5 mm and length 2 mm, this approximating the appropriate region of the nerve terminal. The addition of the mitochondrial compartment (Model B, Table 2) means that the cytosolic Ca2þ is now being removed both by the plasmalemma pump and the uniporter, and this necessitates an adjustment of these rates, as well as that of the Na/Ca exchanger. The further addition of the endoplasmic reticulum (Model C, Table 3) means that further adjustment is necessary in order to incorporate this new source of cytosolic Ca2þ removal. The parameter values for the mitochondria are from Gunter and Gunter (1994), with the uniporter and pump (Na/Ca exchanger) rates increased to agree with the present experimental data. The density corresponds to the mitochondrial mass forming 10% of the terminal mass, which is within the experimental range (Ishihara et al., 1997; Hirai et al., 2001). Parameter values for the endoplasmic reticulum are not well established. Bygrave and Benedetti (1996) cite the literature as giving a range 1022000 mM for the free Ca2þ concentration, though later this is narrowed to 1002500 mM (Laude et al., 2005); we have used an intermediate value of 250 mM. The pump dissociation constant, K 6 , was given as 0:22 mM by Kargacin and Fay (1991), but Lytton et al. (1992) give 1:1 mM for SERCA3

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which is the most likely form of ATPase in non-muscle cells; again, we have chosen an intermediate value ð0:66 mMÞ. The dissociation constant for Ca2þ binding to the ER buffer could range from 250 to 1000 mM (Milner et al., 1992) and the value 500 mM has been used, with k 2 being chosen to agree with this value. Using an intermediate value for the concentration of Ca2þ bound to the buffer of 2500 mM (range 100025000 mM: Bygrave and Benedetti, 1996) gives 7500 mM as the estimate of buffer concentration. Because of the uncertainty in some of the ER parameter values we did a number of runs, using values over the maximum ranges given above, to check parameter sensitivity. Changing the buffer dissociation constant or the equilibrium ½Ca2þ  level had only a small effect; increasing the total buffer concentration also had a small effect, but decreasing it too much reduced agreement, particularly in those experiments where the mitochondrial uptake was blocked. Reducing the pumping rate into the ER did not give the desired change when the pump was blocked; on the other hand, increasing it substantially gave the wrong time dependence to the rising phase of the Ca2þ transient. Other parameters listed as ‘‘adjusted’’ in the tables were essentially chosen to give the correct amplitude changes when the mitochondria and/or the ER contributions to cytosolic ½Ca2þ  were blocked. Ca2þ input, either as a single impulse or as a train of impulses, is approximated by a rectangular step function of duration 3.5 ms, this being the approximate duration of an action potential. The standard input is 50,000 ions per impulse, corresponding to a concentration increase of 6:78 mM ms1 . This input has been varied to allow for the differences in experimental preparations as stated in the figure captions. 3. Results 3.1. D½Ca2þ i following an impulse or short trains of impulses Calcium concentration changes at a site along the length of a terminal branch following a single impulse were determined using a low affinity indicator (OG-5N) and line scans (Fig. 1a). The ½Ca2þ i transient, D½Ca2þ i , declined exponentially with a time constant of 119  16 ms (SEM; n ¼ 7; Fig. 1b). In order to determine if the size and temporal characteristics of this transient were dependent on the position on the terminal branch where the recording was made, measurements were made of D½Ca2þ i at several different positions (up to 50 mm apart) along a terminal branch and found to be very similar. D½Ca2þ i for different protocols of stimulation was examined, with both the peak amplitude reached during the trains and the rate of recovery at the ends of the trains being determined. Fig. 3 shows the changes during stimulation of a terminal with long trains of 100 impulses at 20 Hz (Fig. 3a) or 100 impulses at 50 Hz (Fig. 3c) or shorter trains of either 6 impulses at 50 Hz (Fig. 3b) or 30

235

Fig. 3. Observed D½Ca2þ i during different trains of impulses: (a) 100 impulses at 20 Hz; (b) 6 impulses at 50 Hz; (c) 100 impulses at 50 Hz; (d) 30 impulses at 50 Hz. The vertical scale bar gives D½Ca2þ i ; the conversion from fluorescence used Eq. (6) with a ¼ 2 mM. The horizontal lines give the period of stimulation; in (a) and (c) the lines are broken indicating that the middle period of stimulation has been omitted in order to display the individual D½Ca2þ i for each pulse on an appropriate time base. The breaks in the recordings are a result of experimental procedure—a limited number of frames (4 or 5) had to cover the whole timecourse, so the data for the longer trains are less complete.

impulses at 50 Hz (Fig. 3d). Eq. (9) was fitted to the decaying portion of the experimental data of Fig. 3, resulting in values for t1 of 60 ms and for t2 of 310 ms. The Ca2þ sequestration models were then used to calculate the theoretical D½Ca2þ i for each of these stimulation protocols and the results are shown in Fig. 4, with panels a–d in each case corresponding to panels a–d in Fig. 3. The lines are the theoretical results and the open circles are experimental values taken from Fig. 3. The calculations were performed for each of the three models, A, B and C, as defined in the Section 2, using parameters from Tables 1–3, respectively. All three models are in reasonable agreement with the experimental data, though the 2-compartment model (Model A) does not always fit the tail of D½Ca2þ i (Fig. 4a). The poorer fit of Model C can be attributed to its having to fit a wider range of data than the other two models; that is, it has to also fit data coming from experiments in which the mitochondrial uniporter is blocked and in which the endoplasmic pump is blocked. 3.2. Calcium sequestration by mitochondria The possibility that the mitochondrial uniporter removed Ca2þ from the cytosol during the stimulation protocols used was examined by depolarizing the mitochondria with CCCP (1–2 mM) in four different preparations.

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[Ca2+]/µM

Model A

0.4

0.4

0.2

0.2

0.2

[Ca2+]/µM

5000

5500

6000

0

5000

5500

6000

0

0.5

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

[Ca2+]/µM

Model C

0.4

0

0

200

400

600

0

0

200

400

600

0

0.6

0.6

0.6

0.4

0.4

0.4

0.2

0.2

0.2

0

[Ca2+]/µM

Model B

2000

2500

3000

0

2000

2500

3000

0.5

0.5

0.4

0.4

0.4

0.3

0.3

0.3

0.2

0.2

0.2

0.1

0.1

0.1

0

500 1000 time/ms

1500

0

0

500 1000 time/ms

1500

0

0

0.5

0

5000

0

200

2000

0

5500

400

2500

500 1000 time/ms

6000

600

3000

1500

Fig. 4. Comparison between theoretical and observed ½Ca2þ i during different trains of impulses. In each case, panels (a–d) are for the corresponding experimental results in Fig. 3, with the open circles showing experimental points and the solid lines giving the theoretical results. The first column uses the two-compartment model (Model A), the second column uses the three-compartment model (Model B) and the third column uses the full fourcompartment model (Model C). In the theoretical curves the background ½Ca2þ  has been subtracted. In panels (a) and (b) the basic Ca2þ input rate of 50,000 ions per impulse has been multiplied by 2.5, 2 and 1.8 for Models A, B and C, respectively. In panels (c) and (d) the corresponding multiplicative factors are 2.5, 1.1 and 0.9. The RMS deviations between the experimental and theoretical results for Model A are 0.0825, 0.0237, 0.0672 and 0.0477 for panels (a), (b), (c) and (d), respectively; for Model B the corresponding numbers are 0.0566, 0.0193, 0.0745 and 0.0356; for Model C they are 0.0602, 0.0185, 0.1276 and 0.0378. Note that the time scales in (a–d) are different.

This depolarization had a small effect in increasing the time constant of decline of D½Ca2þ i due to a single impulse, but did not change the peak (compare Fig. 5a with Fig. 5c). However, depolarizing the mitochondria had a very significant effect on increasing the size of D½Ca2þ i reached during a train of 50 impulses at 20 Hz in three preparations (compare Fig. 5b with Fig. 5d).

The theoretical models (Model B and Model C), both of which contain a mitochondrial compartment, were able to account for the effects of mitochondrial depolarization, as can be seen in Fig. 6, where now the left and right columns are for the two models and again panels a–d correspond to those in Fig. 5. Note that for a single impulse the decay rate is reduced. With the uniporter operating, Ca2þ continues to

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Model B

[Ca2+]/µM

0.25

0.2

0.15

0.15

0.1

0.1

0.05

0.05

[Ca2+]/µM

3.3. Endoplasmic reticulum calcium pump Next the Ca2þ -ATPase pump of the endoplasmic reticulum was blocked with thapsigargin (2 mM; Fig. 7). There was no detectable difference in the size or temporal characteristics of D½Ca2þ i to single pulses (Fig. 7c) compared with the control (Fig. 7a) in each of three preparations. In one preparation, the peak DF =F was 7.5% compared with 6% in the control and the time constant of decline 106 ms compared with 118 ms in control. However, there was a considerable increase in D½Ca2þ i following a short train of 10 impulses at 50 Hz (Fig. 7d) compared with the control (Fig. 7b) in each of the three injected terminals. Theoretical Model C, containing both mitochondrial and endoplasmic reticulum compartments, was then used to test the effect of blocking the endoplasmic reticulum

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Fig. 6. Comparison between theoretical and observed D½Ca2þ i following a single impulse or a short train of impulses and the effects of blocking mitochondrial uptake of Ca2þ on this D½Ca2þ i . In each case, panels (a–d) are for the corresponding experimental results in Fig. 5, with the open circles showing experimental points and the solid lines giving the theoretical results; thus (a) and (b) are the controls and in (c) and (d) the mitochondrial uptake has been blocked by setting A4 ¼ 0 in Eq. (12). The first column uses the three-compartment model (Model B) and the second column uses the full four-compartment model (Model C). In the theoretical curves the background ½Ca2þ  has been subtracted. The basic Ca2þ input rate of 50,000 ions per impulse has been multiplied by 4 for Model A and 4.5 for Model B. The RMS deviations between the experimental and theoretical results for Model B are 0.00149, 0.0074, 0.0083 and 0.0281 for panels (a), (b), (c) and (d), respectively; for Model C the corresponding numbers are 0.0202, 0.0248, 0.0062 and 0.0410.

pump (Fig. 8) and again the theoretical results are quantitatively similar to those observed for trains of impulses (Figs. 8b and d) but in this case are poor for

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4.1.2. Endoplasmic reticulum Blocking the Ca2þ pump in the endoplasmic reticulum of frog motor-nerve terminals has been reported to have a major effect in slowing cytosolic Ca2þ sequestration during a short train of impulses by some (Castonguay and Robitaille, 2001) but not by others (Suzuki et al., 2002). In our work, blocking the reticulum pump with thapsigargin had a considerable effect on cytosolic Ca2þ accumulation during the first few impulses in a train, as was also reported by Castonguay and Robitaille (2001) for the frog terminal. We were, however, unable to detect any changes in Ca2þ sequestration following a single impulse after blocking the endoplasmic reticulum pump, although Castonguay and Robitaille (2001) detected a small slowing in sequestration at the frog terminal, which our theoretical work predicted (see Figs. 8a and c).

Fig. 7. Observed D½Ca2þ i following a single impulse or a short train of impulses and the effects of blocking the endoplasmic reticulum CaATPase on this D½Ca2þ i . D½Ca2þ i is shown for a single impulse in (a) and for 10 impulses at 50 Hz in a different terminal in (b). Following these recordings, the terminals were exposed to the endoplasmic reticulum CaATPase blocker thapsigargin (2 mM) and the terminals again stimulated with a single impulse (c) or the train of impulses (d). No significant changes in D½Ca2þ i due to a single impulse are observed following treatment with thapsigargin but there is a significant increase in D½Ca2þ i due to the train of impulses. The dot ð Þ in C gives the moment of stimulation in (a) and (c) and the horizontal line in (d) the period of stimulation in (b) and (d). The vertical scale bar gives D½Ca2þ i ; the conversion from fluorescence used Eq. (6) with a ¼ 2 mM.

the time course of a single impulse block (Figs. 8a and c). This might arise as a consequence of the relatively poor signal to noise ratio of D½Ca2þ i for single impulses as a result of using a low-affinity calcium indicator such as OG-5N. 4. Discussions 4.1. Calcium sequestration 4.1.1. Mitochondria We found that depolarizing with CCCP had the greatest effect in potentiating Ca2þ levels in the toad motor terminals during trains of pulses. Mitochondria plays an important role in sequestering cytosolic Ca2þ at motor terminals following short trains ð430Þ during highfrequency stimulation ð450 HzÞ at neuromuscular junctions in invertebrates (Ohnuma et al., 1999), reptiles (David et al., 1998), amphibia (Suzuki et al., 2002), and mammals (David and Barrett, 2000). On the other hand, we observed that Ca2þ sequestration from the cytosol in toad, following a single impulse, was not significantly affected by block of the mitochondrial uniporter with CCCP, as is the case at the reptilian terminals (David et al., 1998).

4.1.3. Plasmalemma Blocking the plasmalemma Ca2þ pump by raising the pH (Milanick, 1990) does not affect cytosolic Ca2þ sequestration following short trains of impulses at high-frequency (50 Hz) at the reptilian motor-nerve terminal (David, 1999) or the frog motor-nerve terminal (Suzuki et al., 2002) or the crayfish neuromuscular junction (Lin et al., 2005). The present model predicts very little contribution to Ca2þ sequestration by the plasmalemma Ca2þ pump. 4.1.4. Buffer One possible mechanism of sequestration of Ca2þ is an endogenous buffer with slow kinetics (Lee et al., 2000). High concentrations of endogenous buffers can modify transmitter release at synapses (Caillard et al., 2000; Matveev et al., 2004). If the present model of Ca2þ removal is correct, then these terminals should possess an endogenous buffer or buffers with slow kinetics (Lee et al., 2000). It is known that high concentrations of such buffers, up to 1 mM, occur in synaptic terminals formed by Purkinje cells (Kosaka et al., 1993) and that such high concentrations can modify transmitter release at synapses (Caillard et al., 2000). Furthermore, there is now evidence that such slow buffers determine the early decay of Ca2þ transients after an action potential in crayfish neuromuscular terminals (Lin et al., 2005). 4.2. Time course of sequestration following impulses at nerve terminals Three phases of cytosolic Ca2þ sequestration following medium length trains (20–100 impulses) at high frequencies (10–100 Hz) have been observed using high-affinity Ca2þ indicators at the amphibian motor-nerve terminal (Wells et al., 1998: Oregon Green 488 BAPTA-1, i.e., OGBI; Suzuki et al., 2000: OGBI and Indo 1). At 20–30 Hz the two dominant phases had decay time constants reported as variously 370 ms and 2.6 s (Wells et al., 1998) or as 280 ms and 4.1 s (Fig. 4 in Suzuki et al., 2000). Following short trains of 10 impulses at 100 Hz, time constants were 76 ms

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and 4 s (Fig. 4 in Suzuki et al., 2000). However, low-affinity indicators as used in the present study, namely Oregon Green 488 BAPTA-5N (i.e., OG5N), at 20–30 Hz and 100 impulses gave values of 60 and 310 ms. For a single impulse, a single dominant time constant of about 80 ms was obtained with the low-affinity indicator. This value may be compared with that found in the following synapses using low-affinity indicators (mostly calcium green): 80 ms, granule cell to stellate cell synapse (Chen and Regehr, 1997); 50 ms, granule cell to Purkinje cell synapse (Atluri and Regehr, 1996); 60 ms, single boutons on pyramidal neurons (Koester and Sakmann, 2000); 47 ms, the calyx of Held (Helmchen et al., 1997). We suggest that the highaffinity indicators (Wells et al., 1998; Suzuki et al., 2000) do not give a correct estimate of the phases of Ca2þ sequestration following impulses (see also Sinha et al., 1997; Sala and Hernandez-Cruz, 1990). This suggestion has recently been confirmed for the crayfish neuromuscular junction where it has been shown that high affinity indicators distort the temporal aspects of Ca2þ transients due to single impulses (Fig. 1 in Lin et al., 2005). In some cases where attempts have been made to measure the Ca2þ dynamics within the microdomains of Ca2þ at the presynaptic membrane (Naraghi and Neher, 1997), much shorter phases of Ca2þ transients following an impulse have been detected preceding the dominant time constant of about 80 ms; such components of the Ca2þ transients at cultured neuromuscular junctions have time

constants of about 16 ms (DiGregorio et al., 1999). It is very likely that such fast components are due to Ca2þ redistributing itself from the submembraneous region adjacent to the presynaptic membrane into the rest of the terminal (Bennett et al., 2000a,b). 4.3. Relation between calcium sequestration and the different components of increased efficacy of transmission In Bennett et al. (2004) (see also Tang et al., 2000; Matveev et al., 2002) we provided a quantitative model of facilitation of quantal release in which exocytosis is triggered by the combined action of a low-affinity Ca2þ binding molecule (X) at the site of exocytosis and a highaffinity Ca2þ -binding molecule (Y) 100 nm away. We arrived at theoretical changes in Ca2þ in the terminal that occur during a test impulse followed at different intervals after a conditioning impulse (see Fig. 3 in Bennett et al., 2004) or the changes in Ca2þ in the terminal during short trains of impulses (see their Fig. 8) that accompany the facilitated release of transmitter. In the present work, we have used a low-affinity Ca2þ indicator to measure changes in bulk ½Ca2þ i in the terminal. The time course of ½Ca2þ i , following a single impulse, is shown in Fig. 9 (dashed line). Also shown (light thick trace) is the bulk ½Ca2þ i , averaged over the whole terminal, that results from the Monte Carlo diffusion model of Bennett et al. (2004). It is seen that they have identical time courses. (The small difference in the two

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time constant of decay, corresponding to F2 facilitation. A shorter time constant, related to F1 facilitation, only becomes apparent in the bulk ½Ca2þ i when a train of impulses leads to a higher peak (as is the case in Fig. 3). Thus, the current model complements, but does not replace, our facilitation model. To account for facilitation, it is necessary to compute the spatial dependence of ½Ca2þ  within the terminal and the Y molecule is still necessary to give the observed amplitudes of F1 and F2 facilitation.

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Fig. 9. Comparison between the changes in bulk ½Ca2þ i averaged over the terminal following an impulse according to our Monte Carlo model that uses a single Ca2þ sequestration pump (light thick trace; Bennett et al., 2004) and the present model in which Ca2þ sequestration occurs via pumps in the plasmalemma and endoplasmic reticulum and the mitochondrial uniporter (dashed line). The dashed line has been scaled to the same mean amplitude as the Monte Carlo bulk ½Ca2þ i , since it is the time course of decline that is relevant here. Also shown is the Ca2þ transient at the site of the Y facilitation molecule, 100 nm above the plasmalemma (dark thick trace). This was calculated using the Monte Carlo scheme and is the average concentration in a box of dimension 60 nm  1 mm  60 nm centered on the Y-molecule site. This ½Ca2þ i transient decreases to about 6% of its peak value in about 80 ms, after which time it is comparable to the bulk ½Ca2þ i .

lower curves for times less than about 3 ms is due to the slightly different initial conditions used in the two calculations: the Monte Carlo simulation in Bennett et al. (2004) used an approximation to an action potential to determine the Ca2þ influx, whereas the present calculation uses a rectangular step. This difference has no implications for facilitation.) In addition, Fig. 9 shows (dark thick trace) the time course of ½Ca2þ i in the vicinity of the facilitating (Y) molecule; here, the concentration is considerably elevated above that of the bulk ½Ca2þ i for about the first 80 ms, but thereafter declines with an amplitude very similar to that of the bulk ½Ca2þ i . (A similar calculation shows that the ½Ca2þ i at the exocytotic (X) site peaks even higher that at the Y-site, but declines more rapidly and after about 10 ms the two traces are almost the same.) This means that at times greater than about 80 ms we would expect facilitation to decline with a time constant similar to that of the bulk ½Ca2þ i , which indeed is the case (namely 310 ms here compared with experimental values for the time constant of F2 facilitation of 300–475 ms (Mallart and Martin, 1967; Magleby, 1973; Tanabe and Kijima, 1992)). At times earlier than about 80 ms the ½Ca2þ i at the X and Y molecule sites is in excess of the bulk ½Ca2þ i (Fig. 9) and according to our facilitation model (Bennett et al., 2004) is responsible for the F1 phase of facilitation (Mallart and Martin, 1967; Magleby, 1973; Bennett and Fisher, 1977). For a single impulse, the bulk ½Ca2þ i exhibits only a single

This work was supported by ARC (Australia Research Council) Grant DP0345968. References Atluri, P.P., Regehr, W.G., 1996. Determinants of the time course of facilitation at the granule cell to Purkinje cell synapse. J. Neurosci. 16, 5661–5671. Bennett, M.R., Fisher, C., 1977. The effect of calcium ions on the binomial parameters that control acetylcholine release during trains of nerve impulses at amphibian neuromuscular synapses. J. Physiol. 271, 673–698. Bennett, M.R., Farnell, L., Gibson, W.G., 2000a. The probability of quantal secretion near a single calcium channel of an active zone. Biophys. J. 78 (5), 2201–2221. Bennett, M.R., Farnell, L., Gibson, W.G., 2000b. The probability of quantal secretion within an array of calcium channels of an active zone. Biophys. J. 78 (5), 2222–2240. Bennett, M.R., Farnell, L., Gibson, W.G., 2004. The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction. Biophys. J. 86 (5), 2674–2690. Bollmann, J.H., Sakmann, B., Borst, J.G., 2000. Calcium sensitivity of glutamate release in a calyx-type terminal. Science 289 (5481), 953–957. Bygrave, F., Benedetti, A., 1996. What is the concentration of calcium ions in the endoplasmic reticulum? Cell Calcium 19 (6), 547–551. Caillard, O., Moreno, H., Schwaller, B., Llano, I., Celio, M.R., Marty, A., 2000. Role of the calcium-binding protein parvalbumin in short-term synaptic plasticity. Proc. Natl Acad. Sci. USA 97 (24), 13372–13377. Castonguay, A., Robitaille, R., 2001. Differential regulation of transmitter release by presynaptic and glial Ca2þ internal stores at the neuromuscular synapse. J. Neurosci. 21 (6), 1911–1922. Chen, C., Regehr, W.G., 1997. The mechanism of cAMP-mediated enhancement at a cerebellar synapse. J. Neurosci. 17 (22), 8687–8694. David, G., 1999. Mitochondrial clearance of cytosolic Cað2þÞ in stimulated lizard motor nerve terminals proceeds without progressive elevation of mitochondrial matrix ½Cað2þÞ. J. Neurosci. 19 (17), 7495–7506. David, G., Barrett, E.F., 2000. Stimulation-evoked increases in cytosolic ½Cað2þÞ in mouse motor nerve terminals are limited by mitochondrial uptake and are temperature-dependent. J. Neurosci. 20 (19), 7290–7296. David, G., Barrett, J.N., Barrett, E.F., 1997. Stimulation-induced changes in ½Ca2þ  in lizard motor-nerve terminals. J. Physiol. 504, 83–96. David, G., Barrett, J.N., Barrett, E.F., 1998. Evidence that mitochondria buffer physiological Cað2þÞ loads in lizard motor nerve terminals. J. Physiol. 509 (Part 1), 59–65. DiGregorio, D.A., Peskoff, A., Vergara, J.L., 1999. Measurement of action potential-induced presynaptic calcium domains at a cultured neuromuscular junction. J. Neurosci. 19 (18), 7846–7859. Ecker, A., 1889. The Anatomy of the Frog. Asher, Amsterdam.

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