| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
| ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
1Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, New Jersey; 2Department of Mathematics and Programs in Neuroscience and Molecular Biophysics, Florida State University, Tallahassee, Florida; and 3Laboratory of Biological Modeling, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda, Maryland
Submitted 30 January 2006; accepted in final form 1 September 2006
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
; Magleby 1987; Zucker 1999; Zucker and Regehr 2002). Facilitation of the synaptic response may be caused for instance by the facilitation of action potential (AP)-evoked Ca2+ currents due to a depolarization-dependent relief of G-protein-mediated inhibition of Ca2+ channels (Bertram et al. 2003; Brody and Yue 2000). However, in many preparations, facilitation can be achieved even under conditions of constant pulse-to-pulse Ca2+ influx. This was suggested in the pioneering studies of amphibian neuromuscular junctions by Katz and Miledi (1968) and Rahamimoff (1968), who proposed that facilitation results from the accumulation of residual Ca2+ bound to Ca2+-dependent vesicle release sensors. This so-called bound residual Ca2+ hypothesis of synaptic facilitation was later explored in modeling studies (Bennett et al. 1997; Bertram et al. 1996; Delaney et al. 1994; Dittman et al. 2000; Yamada and Zucker 1992). However, interest in the bound Ca2+ hypothesis has been limited due to experimental evidence demonstrating the reduction of facilitation by exogenous Ca2+ buffers. Because the main effect of exogenous buffers is to absorb the free Ca2+ ions, with no effect on Ca2+ that is already bound, these results have been used to argue that the free and not bound residual Ca2+ underlies facilitation (see review by Zucker and Regehr 2002). Notably, experiments of Kamiya and Zucker (1994) on crayfish neuromuscular junctions showed that the synaptic response is reduced within milliseconds of a UV flash photolysis of a fast Ca2+-absorbing buffer diazo-2 in the presynaptic terminal, demonstrating the apparent role of residual free Ca2+ in facilitated neurotransmitter release.
Thus it is now widely accepted that synaptic facilitation is caused primarily by the gradual accumulation of free [Ca2+] during the conditioning train of stimuli (Zucker and Regehr 2002). One mechanism for this is the facilitation of AP-evoked Ca2+ transients caused by the gradual saturation of endogenous buffers during continued stimulation. Proposed on purely theoretical grounds (Klingauf and Neher 1997; Neher 1998), this buffer saturation mechanism was recently shown to underlie facilitation at calbindin-positive neocortical and hippocampal synapses (Blatow et al. 2003; see also Jackson and Redman 2003; Maeda et al. 1999; Rozov et al. 2001). Recent modeling results indicate that a dramatic increase in Ca2+ transients can be achieved if buffers saturate in the entire presynaptic terminal, which requires optimal concentrations of fast mobile buffers similar to calbindin (Matveev et al. 2004).
Alternatively, if endogenous buffers are primarily immobile and are present in sufficiently large concentrations, they will mostly saturate locally, within a Ca2+ channel nanodomain, trapping Ca2+ that enters during a stimulus and then slowly releasing it during interstimulus intervals (Neher 1998; Nowycky and Pinter 1993; Sala and Hernández-Cruz 1990). This would lead to accumulation in residual free Ca2+ after each action potential in addition to some increase in Ca2+ transients associated with the local buffer saturation. Recent modeling studies (Matveev et al. 2002; Tang et al. 2000; see also Bennett et al. 2004) have shown that such a free residual Ca2+ mechanism of facilitation incorporating two spatially segregated Ca2+ binding sites can explain the magnitude and the time course of facilitation growth observed at the crayfish neuromuscular junction (NMJ). However, this two-site free-Ca2+ model requires a number of assumptions to match the experimental data, such as high tortuosity of the intracellular space close to the Ca2+ channel, the immobilization of exogenous Ca2+ buffers by the cytoskeleton, and a significant spatial separation (>150 nm) between two distinct release-controlling Ca2+-binding sites (both of which must be occupied for release to occur).
Thus recent modeling studies focused on the role of free Ca2+ in facilitation, based on the conclusion that the contribution of bound Ca2+ to facilitation, is ruled out by the experimentally observed sensitivity of facilitation to exogenous Ca2+ buffers. However, as we show in the following text, this conclusion is unjustified. Further, it explicitly rules out the contribution of slow processes involving priming and/or docking of synaptic vesicles (see DISCUSSION) (see also Millar et al. 2005) because such processes cannot instantly reach equilibrium with the changing intracellular Ca2+ concentration and may not be described by a model that only takes into account free Ca2+. Therefore we revisit the bound residual Ca2+ hypothesis of facilitation and show that its biophysically realistic implementation that takes into account the diffusion and buffering of Ca2+ can also account for the properties of the synaptic response recorded in the crayfish inhibitor NMJ. Moreover, we find that this model requires fewer assumptions than the abovementioned two-site mechanism. We show that it can be easily reconciled with the observed effect of exogenous Ca2+ buffers on synaptic response. Importantly, the model we present can readily account for several additional experimentally observed features of synaptic facilitation. For example, the same experiments that revealed the sensitivity of facilitation to exogenous buffers also uncovered a component of release whose decay lagged behind the decay of free residual [Ca2+] (Atluri and Regehr 1996; Kamiya and Zucker 1994), suggesting that residual bound Ca2+ is one component of facilitation (see also Dittman et al. 2000; Regehr et al. 1994). Further, our model easily accounts for the super-linear facilitation accumulation and its biphasic decay observed in a variety of synapses, and at the crayfish NMJ in particular (Tang et al. 2000). Therefore we believe that current experimental evidence does not rule out the involvement in facilitation of processes characterized by slow Ca2+ unbinding with unbinding time scales of tens of milliseconds and above.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
Fig. 2F). We are interested in comparing our bound residual Ca2+ model results with those of the two-site free residual Ca2+ model; therefore our model shares some of its features, in particular the geometry of the active zone, with the model of Matveev et al. (2002), which in turn is based on the work of Tang et al. (2000). These models are adapted to a specific experimental system, the crayfish inhibitor NMJ, which exhibits very pronounced facilitation not occluded by concomitant synaptic depression, making it a perfect system for the study of synaptic facilitation.
|
|
We assume that the binding of Ca2+ to both the endogenous and the exogenous buffers is described by simple mass action kinetics with one-to-one stoichiometry
 | (1) |
 | (2) |
 | (3) |
 | (4) |
). Following standard convention, in Eqs. 2 and 3, we have assumed that the initial distribution of the buffer is spatially uniform and that the diffusion coefficient of the buffer is not affected by the binding of Ca2+. Under these assumptions, the sum of the bound and the unbound buffer concentrations is constant in space and time and is equal to the total buffer concentration, Bjtotal. Thus [CaBj] = Bjtotal –[Bj]. The last term in Eq. 2 represents the Ca2+ influx, where F is Faraday's constant, ICa(t) is the (inward) calcium current per channel (see following text), and 
(r – ri) is the Dirac delta function centered at the location of the ith channel.
Recent experiments of Lin et al. (2005) indicate that crayfish NMJ terminals contain two distinct endogenous buffer classes, one of which is characterized by slow Ca2+ unbinding kinetics (kslowoff = 0.1–1 s-1). Similar buffering systems are found in central mammalian synapses, for instance in rodent Purkinje cells, which contain a slow buffer parvalbumin along with the fast-binding calbindin (Schmidt et al. 2003). Therefore we assume that two endogenous buffer species are present, one of which is characterized by slow Ca2+ binding kinetics, with an unbinding rate of kslowoff = 0.4 s-1 and an affinity of KDslow = 5 µM. For simplicity, we assume that both buffers have the same mobility, DB, assumed to be a free quantity with respect to the parameter sensitivity analysis presented in Fig. 6. The Ca2+-binding characteristics and the binding ratio of the fast buffer, 
0fast, are considered to be free parameters, while the capacity of the slow buffer is constrained to yield a total resting Ca2+-binding ratio of 600, as estimated by Tank et al. (1995): 0slow = 600 – 0fast. The results are more sensitive to 0fast than to 0slow and are only slightly affected if the total binding ratio is varied between 300 and 800 given a fixed value of 0fast. The list of free parameters is summarized in Table 1. The reference set of values shown in bold is used in the simulations presented in Figs. 2–5. Exogenous buffers fura-2 and diazo-2 are assumed to be mobile (Dfura = 118 µm2ms-1, Ddiazo = 100 µm2ms-1); their parameters are given in the captions to Figs. 3 and 4.
|
|
|
|
|
and Matveev et al. (2002), each AP is modeled as a 1-ms-long constant Ca2+ current, ICaAP, followed by a 3.5-fold larger 0.2-ms-long tail current entering through each of the Ca2+ channels, ICatail = 3.5 ICaAP. Given the large uncertainty in the value of single-channel Ca2+ influx (Tang et al. 2000; Tank et al. 1995), we consider ICaAP to be a free model parameter, varying over the range 0.04–0.4 pA. This yields a total Ca2+ influx per channel per action potential in the range QCa= 0.065–0.65 pA · ms (see Table 1).
We impose reflective boundary conditions for Ca2+ and buffer(s) on the sides of the box, thereby assuming that the Ca2+ and buffer fluxes flowing into the enclosure from the neighboring AZ regions are balanced by the equal fluxes flowing out of the enclosure. The boundary condition for [Ca2+] on the top and bottom surfaces relates the flux to the local Ca2+ concentration, simulating extrusion by surface pumps
 | (5) |
/n 
n · 
denotes differentiation in the direction normal to the boundary; M is the maximal pump rate, KP is the pump dissociation constant, and fleak is the Ca2+ leak term that is tuned to yield zero pump rate at rest: fleak = (M/DCa) [Ca2+]bgr/([Ca2+]bgr +KP), where [Ca2+]bgr = 0.05 µM is the resting background [Ca2+]. We use values of KP = 0.4 µM (Carafoli 1987; Dipolo and Beauge 1983) and M = 0.04 µM µm ms-1. At low [Ca2+], this yields a Ca2+ clearance time constant of 
(1 + 0) V (KP+[Ca2+]bgr)2/(KP M S) 
4 s, where V and S are the volume and the surface area of the bouton (Fig. 1), and 0 = 600 is the resting total endogenous buffering capacity at the crayfish NMJ. This pump rate is consistent with the experimental estimates of Tank et al. (1995). Ca2+ binding and synaptic response
The understanding of the fast Ca2+-triggered vesicle fusion is still incomplete. A promising candidate mechanism is provided by the Ca2+-dependent interaction of synaptotagmin I with phospholipids and the SNARE complex (reviewed by Chapman 2002; Koh and Bellen 2003). The molecular identity of the putative facilitation sensor is also uncertain, although recent evidence suggests the involvement of the neuronal Ca2+ sensor class of proteins, namely NCS-1 (Sippy et al. 2003) and its crustacean and Drosophila homologue, frequenin (Jeromin et al. 1999). In both cases, the exact molecular steps involved and the physiological affinities of the corresponding Ca2+-binding sites are unknown. Therefore we follow earlier work in the field and model the Ca2+ dependence of synaptic response via a phenomenological model that is tuned to reproduce the dynamics of synaptic response to trains of action potentials. Our Ca2+ binding scheme is similar to the one used in Yamada and Zucker (1992), Tang et al. (2000), and Matveev et al. (2002). It assumes the existence of two types of Ca2+ binding sites, X and Y, characterized by fast and slow unbinding rates, respectively. Further, to reproduce the biphasic F1/F2 decay time course of synaptic facilitation (see Fig. 5), we follow the approach of Bertram et al. (1996), and assume the presence of two distinct Y-type Ca2+ binding sites, YF1 and YF2
 | (6) |
 | (7) |
and Vyshedskiy and Lin (1997), whereas the F2 decay rate is chosen to match the decay time course of synaptic response shown in Fig. 4A, as measured by Kamiya and Zucker (1994). The corresponding F2 time scale of 300 ms is somewhat shorter than the F2 time scale of 530 ± 200 ms measured by Tang et al. (2000) and Vyshedskiy and Lin (1997). The binding rates of X and Y sites are determined from their affinities, which we consider to be free model parameters (see Table 1).
Reactions 6 and 7 are converted to ordinary differential equations using the law of mass action. The binding of all three sites is necessary to trigger release, schematically described by
 | (8) |
 | (9) |
 |
; Tang et al. 2000), we assume that both the X and the Y sensors are colocalized in space, and therefore the same [Ca2+] signal determines the forward rates of binding described by Eqs. 6 and 7. Facilitation is defined as the ratio of the peak value of R achieved during the nth action potential, divided by the first peak response, and normalized to zero in the absence of synaptic enhancement: Fn = Rn/R1 –1 (Figs. 3, A and B, and 5, A and B). Results would not be significantly affected if postsynaptic response and facilitation were defined in terms of a time-filtered (integrated) value of R. We note that there may be alternative ways to implement the biphasic facilitation decay time course not involving two sites with distinct Ca2+-binding kinetics. For instance, it is conceivable that the two decay time scales may correspond to the kinetics of two sequential state transitions of the facilitation site, activated downstream of Ca2+ binding. However, the model given by Eqs. 6–9 is the simplest scheme that yields both a biphasic decay and a super-linear accumulation time course of synaptic facilitation.
Numerical simulations
All simulations were performed using the CalC ("calcium calculator") software developed by one of us (Matveev). CalC uses the alternating-direction implicit finite-difference method to solve the buffered diffusion equations (Eqs. 2–4) with second-order accuracy in spatial and temporal resolution. To preserve the accuracy of the method in the presence of the nonlinear buffering term, equations for [Ca2+] and [B] are solved on separate time grids, shifted with respect to each other by half a time step. CalC uses an adaptive time-step method with a nonuniform spatial grid that has greater density of points close to the Ca2+ channel array. Grid size is adjusted to limit the numerical error to 5% (grid of 34 x 34 x 40 points). CalC integrates the ordinary differential equations (Eqs. 6–9) using the fourth-order adaptive Runge-Kutta method. CalC is freely available from http://web.njit.edu/matveev/calc.html, and runs on all commonly used computational platforms (UNIX, including Mac OS X, and Windows/Intel). To ensure reproducibility of this work, the commented simulation script files generating the data reported here are available at the CalC web site.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
Figure 2 demonstrates the response of the synaptic model when it is driven by a train of five simulated action potentials (Ca2+ current pulses), delivered at 100 Hz. Facilitation of release shown in F results from accumulation of Ca2+ bound to the two Y sites (Eq. 7) throughout the train of action potentials (Fig. 2, C and D). This accumulation is caused by the slow unbinding of Ca2+ from the YF1 and YF2 sites so that binding that occurs during one stimulus is only partially removed before the next stimulus. Examination of the Ca2+ and buffer concentration time courses given in A and B also reveals a very slight increase in Ca2+ transients associated with the saturation of the Ca2+ buffer. It makes only a negligible contribution to facilitation, slightly increasing the pulse-to-pulse growth in Ca2+ binding to the X and Y sites (see DISCUSSION).
Importantly, both the magnitude and the super-linear, nonsaturating time course of facilitation are in good agreement with the experimental results of Tang et al. (2000), reproduced in Fig. 3A (control curve). This super linearity was achieved with no additional assumptions, contrary to the two-site mechanism (cf. Fig. 2 of Matveev et al. 2002). In particular, tortuosity (retardation of diffusion close to the membrane) was not included in the present model, and the two Ca2+ binding sites are not spatially segregated, but located at the same distance (55 nm) from the nearest Ca2+ channel.
Facilitation is reduced in the presence of exogenous Ca2+ buffers
One of our main goals is to explore the sensitivity of a model with slow Ca2+ unbinding steps to changes in intracellular buffering capacity. Experimental results of Tang et al. (2000) are shown in Fig. 3A and suggest that facilitation is reduced about twofold on injection of 400 µM of the Ca2+ indicator dye fura-2 into the crayfish NMJ. We mimic this experiment by repeating the simulations shown in Fig. 2 after including in our model (Eqs. 2 and 3) 400 µM of a fura-2-like buffer. Because the background [Ca2+] should remain unchanged after the newly introduced buffer equilibrates with the intracellular Ca2+ homeostasis processes, in our simulations, the fura-2 buffer is assumed to be partially Ca2+ bound at rest, so that the background [Ca2+] remains constant at 0.05 µM. Simulation results presented in Fig. 3B show a reduction of facilitation to a degree comparable to that observed experimentally. This reduction is caused by the decrease in the free [Ca2+] in the vicinity of the X and Y binding sites (Fig. 3C), leading to a reduction in the amount of binding achieved during each action potential (Fig. 3, E–G). Thus even though additional buffers cannot accelerate the unbinding of Ca2+ from the Y sites, the reduction in the free ambient [Ca2+] caused by the added Ca2+ buffers is sufficient to reduce the magnitude of synaptic facilitation, demonstrating the sensitivity of the model to free [Ca2+].
Although the variation of the two-site residual free Ca2+ model considered by Matveev et al. (2002) was also successful in reproducing the twofold reduction of facilitation shown in Fig. 3, such agreement required an assumption of almost complete immobilization of the indicator dye in the entire presynaptic terminal. This is because a fast mobile buffer is extremely efficient in reducing the residual Ca2+ at a remote facilitation site and would predict a much more dramatic effect of fura-2 on facilitation than seen experimentally. In contrast, the model we present here does not impose any constraints on the diffusion of the fura-2, which is assumed to have a diffusion coefficient of DF2 = 118 µm2/s (Gabso et al. 1997). Further, the two-site model also required an assumption of significant tortuosity retarding Ca2+ diffusion in a 200-nm side layer proximal to the membrane, to achieve a nonsaturating facilitation accumulation time course. Again, this assumption is not necessary in the present model, where the super-linearity is caused by the accumulation of bound Ca2+.
Ca2+ buffering rapidly reduces facilitated response
A crucial experiment testing the sensitivity of neurotransmitter release to free Ca2+ was performed by Kamiya and Zucker (1994), who measured the effect of a rapid increase in intracellular buffering capacity on facilitated synaptic response, using flash photolysis of the caged Ca2+ buffer diazo-2. The UV flash increases the Ca2+ affinity of diazo-2, resulting in a rapid sequestering of free Ca2+. When the UV flash was applied after a facilitating train of pulses, the synaptic response to a test pulse administered 10 ms after the flash was reduced dramatically as compared with the control no-flash condition (Fig. 4A). This has been interpreted to suggest that the facilitation of neurotransmitter release is rapidly reduced when the free Ca2+ is buffered. Figure 4B demonstrates that our model reproduces these experimental observations. As shown in Fig. 4, C–F, diazo-2 rapidly buffers the free Ca2+, reducing binding to both the X and the Y gates. The reduction in the binding of the YF1 site contributes the most to the overall reduction of response. Because the X site has even faster kinetics, it is partially saturated by the peak Ca2+ transient even with diazo-2 present, limiting its impact, as compared with the YF1 site. Binding of the YF2 site on the other hand is too slow to contribute significantly to the reduction of the first test response (Fig. 4E) and has more impact on later test responses (note the difference in time scales in C–E). The binding of the YF2 sensor is reduced by only 6% at the peak of the first test pulse, as compared with a 32% reduction in the binding of the YF1 site (Fig. 4D), and a 18% reduction in the binding of the X site (Fig. 4C).
Thus in our model diazo-2 has two effects: it reduces the unfacilitated, baseline synaptic response, which is primarily controlled by the X and the YF1 sites, and it also decreases facilitation by reducing the binding of the YF1 and the YF2 sites. Both in the experiment and in our model, diazo-2 does not completely eliminate facilitation during the 10-ms-long interval between the UV flash and the first test pulse. In the model, this is due to the slow unbinding of the Y gates. In fact, the decay of facilitation lags significantly behind the decay of residual free Ca2+ (cf. Fig. 4, F and D and E), in agreement with the results of Kamiya and Zucker (see Fig. 4 therein) and consistent with experiments of Atluri and Regehr (1996).
Note that the reduction in response caused by the photolyzed diazo-2 gradually dissipates within a second after the UV flash, contrary to the prediction of our model (cf. Fig. 4, A and B). We suggest that such experimentally observed reduction of the diazo-2 effect may be caused either by the leak of diazo-2 into the axon or a reduction in its Ca2+ affinity because under conditions of constant diazo-2 concentration, the response should not approach its value in the absence of the exogenous buffer.
Facilitation decay time course
Because facilitation is defined in terms of the relaxation time scale of the enhanced response back to its prestimulation level, it is important to examine the decay time course of the model facilitation. Figure 5A demonstrates the decrease of synaptic response to the last pulse in a five-pulse train as the interval between the last two pulses is increased under control conditions and in the presence of 400 µM of fura-2, measured by Tang et al. (2000). Figure 5B presents the corresponding simulation results. The first data point corresponds to an interpulse interval of 10 ms and therefore matches the five-pulse facilitation magnitude shown in Fig. 3. Note that the biphasic decay time course of facilitation is captured by the bound-Ca2+ model. In the simulation, the time scales of both phases are determined by the rate of Ca2+ unbinding from the two Y gates. The model decay is faster than the one seen in experiment because the kF2off binding rate was adjusted to fit the decay time course of facilitation shown in Fig. 4B, recorded in an independent set of experiments by Kamiya and Zucker (1994). The decay time scale of the two phases can be easily adjusted by varying kF1off and kF2off. At present no other biophysical facilitation model can readily explain the biphasic nature of facilitation decay.
Parameter sensitivity analysis
Because many of the model parameters are either unconstrained or poorly constrained by existing experimental data, it is instructive to analyze the parameter sensitivity of the fit between model and experiment. Given the large number of parameters, we employ a technique called dimensional stacking (Taylor et al. 2006). Results presented in Fig. 6 show the dependence of facilitation accumulation properties indicated in color code as explained in the following text as a function of the following quantities: 1) the Ca2+ affinities of the X and Y sites, KDXY. Because the variation of any of these affinities affects the results in a similar way, regulating the saturation level of the corresponding site, for the sake of simplicity these are set to be equal. 2) The Ca2+ influx per action potential per active zone, QCa. 3) The mobility of the endogenous buffers, DB. We assume that both buffers have equal diffusion coefficients. 4) The affinity of the fast buffer, KDfast. Because the buffering capacity of the buffer is varied independently (see next parameter), the total concentration of the fast buffer is proportional to KDfast: Bfasttotal = 0fast KDfast. 5) The buffering capacity of the fast buffer, 0fast. Because the total buffering capacity is assumed to be fixed at 600, the capacity of the slow buffer is equal to 600 – 0fast. And 6) the distance from the exocytosis sensors to the center of the active zone, dXY.
These parameters are summarized in Table 1. Dimensional stacking involves nesting simple two-dimensional parameter scans within each other with several parameters (in our case, 3) varied along each of the two axes. Each of the largest principal blocks, at the highest nesting level, is outlined with wider lines and corresponds to fixed values of the parameters labeled using the largest font-size (QCa and KDXY). Further, each of the major blocks consists of a grid of sub-blocks, corresponding to different values of parameters labeled with medium-sized font, DB and KDfast. Finally, each of the sub-blocks presents a scan over the values of two model parameters labeled with the smallest font, 0fast and dXY. Thus each square pixel in Fig. 6 corresponds to a particular choice of the values of six model parameters, which are given in Table 1. For each set of parameter values, a five-pulse simulation has been performed, and the point colored according to the following rule: 1) white (color-free) pixels correspond to parameters yielding five-pulse facilitation below the lower bound of R5/R1 = 14. 2) Pixel is colored gray if fura-2 reduces facilitation by <30%. 3) Pixel is colored green if fura-2 reduces facilitation by >60%. 4) Pixel is colored yellow if the reduction of facilitation by fura-2 is within the 30–60% range, consistent with experiment (Fig. 3A) but the delayed response 1 ms after the last pulse in the train is greater than the first control response. And 5) pixel is colored magenta if the delayed response is limited, the reduction of facilitation by fura-2 agrees with experiment, and the facilitation accumulation is super-linear. The corresponding parameter sets are deemed to satisfy the main experimental constraints. The parameter point corresponding to simulations in Figs. 2–5 lies within this region, and appears as a black pixel pointed to by a black arrow.
Note that facilitation is small (white regions) for small values of Ca2+ current and high buffer mobility because in this case, the endogenous buffers are able to absorb most of the Ca2+ influx before it reaches the facilitation sensor. Facilitation is also reduced due to the binding site saturation when the affinity of the Ca2+ binding gates is high (5 µM) and the buffer concentration is low (recall that low Bfasttotal corresponds to low KDfast because the buffer capacity is varied independently). The abundance of gray pixels at high values of Ca2+ influx is likewise easy to explain because for high QCa values fura-2 cannot absorb a sufficient amount of Ca2+ influx to reduce facilitation. Similarly, the dominant green color on the left of Fig. 6 indicates a strong reduction of facilitation by fura-2 at low values of QCa. The effect of other parameters on facilitation time course can be explained through similarly simple arguments.
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
. The model indicates that introducing a fast exogenous buffer into a presynaptic terminal should affect not only the Ca2+-dependent facilitation but also the baseline, unfacilitated neurotransmitter release. Our model captures both of these effects, predicting the reduction of binding of both the secretory X site as well as the slow-unbinding Y gates that are responsible for facilitation. This is because buffering will reduce the number of free Ca2+ ions reaching both of these sites, leading to reduced binding regardless of their kinetic properties. Therefore although experiments demonstrating a reduction in facilitation by exogenous buffers have been correctly interpreted to show the importance of free Ca2+ dynamics during the induction of facilitation, we do not think those experiments rule out a role for accumulation of bound Ca2+.
Thus we believe that facilitation due to slow Ca2+ unbinding is consistent with available data from the crayfish NMJ and may apply to other synapses as well. More specifically, the decay time course of facilitation may not be determined solely by the dynamics of intracellular Ca2+ diffusion and clearance but may depend on the intrinsic dynamics of the Ca2+-binding sites involved in neurotransmitter release. This in fact is suggested by the experimentally observed discrepancy between the time scales of the decay of facilitation and the time scale of the concomitant decrease in intracellular [Ca2+] (Atluri and Regehr 1996; Kamiya and Zucker 1994).
The present model, the previously proposed two-site mechanism (Matveev et al. 2002; Tang et al. 2000), and the buffer saturation model (Matveev et al. 2004; Neher 1998) can all successfully reproduce the magnitude and the time course of facilitation recorded in the crayfish inhibitor as well as the reduction of facilitation by fast Ca2+ buffers. However, the two-site model assumes that two spatially segregated Ca2+-sensitive release gates control synaptic response, separated by distances of 
150 nm. Further, to explain significant residual facilitation on application of Ca2+ indicator dye fura-2, the two-site model requires an assumption of strong immobilization of fura-2 by the cytoskeleton. In contrast, the bound-Ca2+ mechanism described here assumes that the facilitation gates are co-localized with the Ca2+ binding site controlling phasic release and that mobile exogenous buffers remain mobile on injection into the terminal. Finally, the bound-Ca2+ model is more successful than either of the two alternative mechanisms in reproducing the biphasic decay of facilitation.
Although we do not speculate on the physiological identity of the facilitation process, we note that the main feature of a model that includes a contribution of bound Ca2+ is that the underlying mechanism does not instantly re-equilibrate with the changing ambient Ca2+ concentration in contrast to any mechanism that is only sensitive to free Ca2+ accumulation. Therefore a bound Ca2+ model would arise naturally in describing processes characterized by nonnegligible time of reversal such as vesicle priming, which was recently proposed to underlie facilitation at the crayfish tonic synapses by Millar et al. (2005) (see also Bykhovskaia et al. 2004). In fact, the mechanism suggested by Millar et al. bears some similarity to our model but assumes that the fast secretory process and the facilitatory priming process characterized by slower kinetics operate sequentially rather than in parallel to each other and are spatially segregated as in the preceding-mentioned two-site model.
To conclude, we have demonstrated the viability of the residual bound Ca2+ hypothesis proposed by Katz and Miledi (1968) and Rahamimoff (1968). We have shown in particular that this model can account for facilitation at the crayfish NMJ. However, we do not exclude some contribution of free Ca2+ to facilitation in this preparation. In fact, the simulations in Figs. 2–5 would have revealed either free Ca2+ accumulation or Ca2+ transient growth due to buffer saturation had we chosen a somewhat different set of buffering parameters (within the optimal range shown in magenta in Fig. 6). Whereas free Ca2+ accumulation requires large concentrations of fixed buffers, facilitation of Ca2+ transients requires more mobile buffers (Matveev et al. 2004). Although we did not optimize model parameters to exclude these two effects, the parameter combination that provided the best fit to all three experimental measures in Figs. 3–5 did not exhibit either of these two forms of free Ca2+ accumulation. Further, it is also possible that only one of the F1/F2 facilitation components is determined by the slow Ca2+ unbinding explored in this work, whereas the other component results from the effect of diffusion, buffering and/or Ca2+ clearance mechanisms on the free residual Ca2+. Finally, we do not believe that accumulation of bound Ca2+ represents the primary mechanism of facilitation at all facilitatory synaptic terminals. Recent studies indicate that distinct cell types differentially express distinct facilitation mechanisms and that these may undergo differential regulation during development. For example, saturation of the endogenous buffer calbindin has been implicated in facilitation at calbindin-positive but not calbindin-negative mammalian central nerve terminals (Blatow et al. 2003), whereas the expression of calbindin is known to change during development (Alcantara et al. 1996). Furthermore, experimental evidence suggests that in some synapses facilitation involves a combination of mechanisms. For instance, both buffer saturation and accumulation of residual free Ca2+ were implicated in facilitation at the calyx of Held (Felmy et al. 2003) and at facilitatory calbindin-positive neocortical and hippocampal synapses (Blatow et al. 2003). We believe that at some synaptic terminals, such as the crayfish NMJ, residual bound Ca2+ provides an important contribution to synaptic facilitation.
Because all three mechanisms can account for the observed accumulation time course of synaptic facilitation, as well as its reduction by exogenous Ca2+ buffers, the question of the relative roles of free versus bound residual Ca2+ accumulation has to be addressed using more specific experimental protocols. One such method involves tracking the Ca2+ affinity of neurotransmitter release during induction of facilitation. If facilitation results solely from the build-up of free residual Ca2+, the Ca2+ affinity of release should remain unchanged during stimulation because the state of the release machinery is not affected by stimulation under this assumption. This is indeed the case at the calyx of Held nerve terminals, as was shown by Felmy et al. (2003). If on the other hand there is an accumulation of Ca2+-bound exocytosis gates during stimulation, the apparent Ca2+ affinity of exocytosis should increase as well because in this case, higher release probability is achieved despite the absence of a significant change in the Ca2+ concentration at the release site from one pulse to the next (cf. Fig. 3, B and C). Such a shift in the Ca2+ dependence of response would also manifest itself as an activity-dependent decrease in Ca2+ cooperativity (Stanley 1986). This is explained by the fact that less than four Ca2+ binding sites have to become bound to cause fusion on induction of facilitation because some of the Y sites will still be occupied by Ca2+ bound during the conditioning stimulation. Because such a shift in Ca2+ cooperativity was observed by Stanley (1986) at the squid giant synapse, there is a strong indication that bound Ca2+ is involved in facilitation in that preparation. We conclude that bound Ca2+ contributes to facilitation in some, but not all, synaptic terminals.
|
GRANTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
|
ACKNOWLEDGMENTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
|
FOOTNOTES |
|---|
Address for reprint requests and other correspondence: V. Matveev, New Jersey Institute of Technology, University Heights, Newark, NJ 07102 (E-mail: matveev{at}oak.njit.edu)
|
REFERENCES |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONGRANTSACKNOWLEDGMENTSREFERENCES |
|---|
Allbritton NL, Meyer T, and Stryer L. Range of messenger action of calcium ion and inositol 1,4,5-trisphosphate. Science 258: 1812–1815, 1992.
Atluri PP and Regehr WG. Determinants of the time course of facilitation at the granule cell to Purkinje cell synapse. J Neurosci 16: 5661–5671, 1996.
Bennett MR, Farnell L, and Gibson WG. The facilitated probability of quantal secretion within an array of calcium channels of an active zone at the amphibian neuromuscular junction. Biophys J 86: 2674–2690, 2004.
Bennett MR, Gibson WG, and Robinson J. Probabilistic secretion of quanta and the synaptosecretosome hypothesis: evoked release at active zones of varicosities, boutons, and endplates. Biophys J 73: 1815–1829, 1997.
Bertram R, Sherman A, and Stanley E. The single domain/bound calcium hypothesis of transmitter release and facilitation. J Neurophysiol 75: 1919–1931, 1996.
Bertram R, Swanson J, Yousef M, Feng ZP, and Zamponi GW. A minimal model for G protein-mediated synaptic facilitation and depression. J Neurophysiol 90: 1643–1653, 2003.
Blatow M, Caputi A, Burnashev N, Monyer H, and Rozov A. Ca2+ buffer saturation underlies paired pulse facilitation in calbindin-D28k-containing terminals. Neuron 38: 79–88, 2003.[CrossRef][ISI][Medline]
Brody DL and Yue DT. Relief of G-protein inhibition of calcium channels and short-term synaptic facilitation in cultured hippocampal neurons. J Neurosci 20: 889–898, 2000.
Bykhovskaia M, Polagaeva E, and Hacket JT. Mechanisms underlying different facilitation forms at the lobster neuromuscular synapse. Brain Res 1019: 10–21, 2004.[CrossRef][ISI][Medline]
Carafoli E. Intracellular calcium homeostasis. Annu Rev Biochem 56: 395–433, 1987.[CrossRef][ISI][Medline]
Chapman ER. Synaptotagmin: a Ca2+ sensor that triggers exocytosis? Nat Rev Mol Cell Biol 3: 498–508, 2002.[CrossRef][ISI][Medline]
Delaney KR and Tank DW. A quantitative measurement of the dependence of short-term synaptic enhancement on presynaptic residual calcium. J Neurosci 14: 5885–5902, 1994.[Abstract]
Dipolo R and Beauge L. The calcium pump and sodium-calcium exchange in squid axons. Annu Rev Physiol 45: 313–324, 1983.[CrossRef][ISI][Medline]
Dittman JS, Kreitzer AC, and Regehr WG. Interplay between facilitation, depression, and residual calcium at three presynaptic terminals. J Neurosci 20: 1374–1385, 2000.
Felmy FE, Neher E, and Schneggenburger R. Probing the intracellular calcium sensitivity of transmitter release during synaptic facilitation. Neuron 37: 801–811, 2003.[CrossRef][ISI][Medline]
Fisher SA, Fischer TM, and Carew TJ. Multiple overlapping processes underlying short-term synaptic enhancement. Trends Neurosci 20: 170–177, 1997.[CrossRef][ISI][Medline]
Gabso M, Neher E, and Spira ME. Low mobility of the Ca2+ buffers in axons of cultured Aplysia neurons. Neuron 18: 473–481, 1997.[CrossRef][ISI][Medline]
Jackson MB and Redman SJ. Calcium dynamics, buffering, and buffer saturation in the boutons of dentate granule-cell axons in the hilus. J Neurosci 23: 1612–1621, 2003.
Jeromin A, Shayan AJ, Msqhina M, Roder J, and Atwood HL. Crustacean frequenins: molecular cloning and differential localization at neuromuscular junctions. J Neurobiol 41: 165–175, 1999.[CrossRef][ISI][Medline]
Kamiya H and Zucker RS. Residual Ca2+ and short-term synaptic plasticity. Nature 371: 603–606, 1994.[CrossRef][Medline]
Katz B and Miledi R. The role of calcium in neuromuscular facilitation. J Physiol 195: 481–92, 1968.
Klingauf J and Neher E. Modeling buffered Ca2+ diffusion near the membrane: implications for secretion in neuroendocrine cells. Biophys J 72: 674–690, 1997.[ISI][Medline]
Koh TW and Bellen HJ. Synaptotagmin I, a Ca2+ sensor for neurotransmitter release. Trends Neurosci 26: 413–422, 2003.[CrossRef][ISI][Medline]
Lin JW, Fu Q, and Allana T. Probing the endogenous Ca2+ buffers at the presynaptic terminals of the crayfish neuromuscular junction. J Neurophysiol 94: 377–386, 2005.
Maeda H, Ellis-Davies GC, Ito K, Miyashita Y, and Kasai H. Supralinear Ca2+ signaling by cooperative and mobile Ca2+ buffering in Purkinje neurons. Neuron 24: 989–1002, 1999.[CrossRef][ISI][Medline]
Magleby KL. Short-term changes in synaptic efficacy. In: Synaptic Function, edited by Edelman G, Gall W, and Cowan W. New York: Wiley, 1987, p. 21–56.
Matveev V, Sherman A, and Zucker RS. New and corrected simulations of synaptic facilitation. Biophys J 83: 1368–1373, 2002.
Matveev V, Zucker RS, and Sherman A. Facilitation through buffer saturation: constraints on endogenous buffering properties. Biophys J 86: 2691–2709, 2004.
Millar AG, Zucker RS, Ellis-Davies GCR, Charlton MP, and Atwood HL. Calcium sensitivity of neurotransmitter release differs at phasic and tonic synapses. J Neurosci 25: 3113–3125, 2005.
Neher E. Vesicle pools and Ca2+ microdomains: new tools for understanding their roles in neurotransmitter release. Neuron 20: 389–399, 1998.[CrossRef]
, positions of Ca2+ channels (16 per active zone); 
, position of the X and Y Ca2+ binding sites for simulations shown in 
