| HOME | HELP | FEEDBACK | SUBSCRIPTIONS | ARCHIVE | SEARCH | TABLE OF CONTENTS |
|
|
|
|||||||
|
|||||||||
1 Johannes-Müller-Institut für Physiologie, Humboldt-Universität Berlin, 10117 Berlin; 2 Institut für Theoretische Biologie, Humboldt-Universität Berlin, 10115 Berlin; 3 Physiologisches Institut der Universität Freiburg, 79104 Freiburg; 4 Institut für Physiologie und Pathophysiologie, Ruprecht-Karls-Universität Heidelberg, 69120 Heidelberg, Germany
Submitted 15 August 2003; accepted in final form 15 September 2003
 |
ABSTRACT |
|---|
 TOP ABSTRACT INTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
|
INTRODUCTION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
). In fact, the transmitter content of aminergic synapses is an important target of neuro- or psychoactive drugs, most prominently in the treatment of Parkinson's disease with L-DOPA. Similarly, drugs that increase the concentration of the inhibitory transmitter GABA (
-aminobutyric acid) at central inhibitory synapses yield anticonvulsant effects (Engel et al. 2000; Gram et al. 1988; Löscher et al. 1989; Taylor et al. 1992). Although these examples are based on therapeutic interventions, several recent studies indicate that changes in transmitter metabolism represent a genuine plasticity mechanism in the CNS. Synaptic inhibition seems to be regulated by changes in transmitter metabolism in a way supporting homeostasis of overall network activity: after epileptic seizures, inhibitory interneurons in the rat hippocampus increase the expression of glutamate decarboxylase (GAD), the key enzyme for the synthesis of GABA (Esclapez and Houser 1999; Feldblum et al. 1990). Conversely, GABA production is downregulated after deafferentation of cortical areas (Garraghty et al. 1991; Gierdalski et al. 1999; Hendry and Carder 1992). A direct role for GABA metabolism in synaptic plasticity is indicated by genetically modified mice that are devoid of GAD65, the most strongly regulated isoform of the GABA-producing enzyme. These animals show specific changes in the age-dependent forms of plasticity of ocular dominance columns in the visual cortex (Fagiolini and Hensch 2000; Hensch et al. 1998).
At the microphysiological level, experimental alterations of transmitter content have caused changes in quantal size and— more surprisingly—also in release rates at many different synapses. Incubation of midbrain dopaminergic neurons with the dopamine precursor L-dihydroxyphenylalanine (L-DOPA) increases the number of released dopamine molecules per vesicle (Pothos et al. 1998a). Conversely, suppression of the dopamine-synthetizing molecule tyrosine hydroxylase by activation of D2-autoreceptors reduces quantal size (Pothos et al. 1998b). At the same time, the frequency of quantal release was lowered and this effect could be reversed by application of L-DOPA, indicating that the filling state of vesicles is paralleled by changes in the readily releasable pool or in release probability. At the Xenopus neuromuscular junction, overexpression of the vesicular transporter for acetylcholine increases the quantal size as well as the frequency of miniature postsynaptic events, again pointing toward a relationship between variations in vesicle filling and vesicle dynamics (Song et al. 1997). Several acute biochemical manipulations of acetylcholine content or loading at frog neuromuscular junctions result in altered size of postsynaptic quantal events (Van der Kloot et al. 2000, 2002). However, these manipulations seem to affect neither the size of the readily releasable pool nor the size of individual vesicles. At GABAergic synapses, quantal size can be increased by blocking GABA degradation (Engel et al. 2001) or can be decreased by suppressing GABA synthesis (Golan and Grossman 1996; Murphy et al. 1998). Again, reduced GABA synthesis results in a decreased miniature inhibitory postsynaptic current (mIPSC) frequency (Murphy et al. 1998) or probability of release (Golan and Grossman 1996), whereas elevated presynaptic GABA levels are paralleled by an increased frequency of mIPSCs (Engel et al. 2001). The latter result contrasts, however, with recent observations by Overstreet and Westbrook (2001), who found a decrease in quantal size and in mIPSC frequency upon acute incubation of hippocampal slices with vigabatrin, an inhibitor of the GABA-degrading enzyme GABA-transaminase. Complex changes in synaptic efficacy have been observed after genetic ablation of the GABA-synthetizing enzyme GAD65: although basal synaptic function appears to be unchanged, sustained massive activation of presynaptic terminals results in a diminished GABA release, again indicating a relation between presynaptic transmitter concentration and supply of vesicles (Tian et al. 1999). Thus functional changes upon altered transmitter metabolism are diverse and may be confounded by additional effects of the experimental manipulations [e.g., increased tonic inhibition through nonvesicular release of GABA (Overstreet and Westbrook 2001; Wu et al. 2003; Yee et al. 1998)]. Nevertheless, multiple experimental findings indicate that vesicle filling and presynaptic vesicle dynamics can both be altered by changes in transmitter metabolism.
If transmitter metabolism is a genuine mechanism of synaptic plasticity, as we propose, there must be functional links between cytosolic transmitter content, vesicular loading, and the transition of vesicles between the different presynaptic compartments, including release. We have constructed a reduced compartmental model of the presynaptic terminal (Südhof 1995) and have analyzed the possibilities and constraints for such links. Using parsimonious assumptions, we find that changing the presynaptic cytosolic transmitter content will indeed profoundly alter the filling state of vesicles. The vesicle cycle could, in principle, be influenced by transmitter content at different stages and by different mechanisms. Our simulations show that different stages and mechanisms of links between transmitter metabolism and vesicle dynamics have unique, experimentally testable functional consequences. Such effects include states of sustained enhanced vesicular transmitter release upon elevation of presynaptic transmitter concentration, as experimentally observed.
|
METHODS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
We describe the distribution of vesicles in the presynaptic terminal with respect to their different transmitter content 
and, in the dynamic case, with respect to time. Presynaptic vesicles undergo a complex cycle between release, recovery, and maturation (Südhof 1995) that for the present purpose has been reduced to transitions between 3 functionally distinct vesicle pools: 1) the reserve pool (n, Eqs. a), 2) the readily releasable pool (nRRP, Eqs. b), and 3) the pool of empty, fused vesicles (nf, Eqs. c). The faster "kiss-and-run" pathway will be modeled as a case with infinitely small reserve pool [see Effects of transmitter concentration on directly recycling vesicles (shortcut pathway)]. In the full model, the vesicle cycle is given by transition from the reserve pool into the RRP (rate 
), subsequent synaptic release (rate r), and, finally, recovery of fused vesicles into the reserve pool (rate ; see Fig. 1 for illustration). Transitions between pools are described by the following set of ordinary differential equations
 | (1a) |
 | (1b) |
 | (1c) |
 | (2a) |
 | (2b) |
 | (2c) |
 | (3a) |
 | (3b) |
 | (3c) |
a denotes the fraction of vesicles in each pool).
|
Filling of vesicles
Neurotransmitters are transported into synaptic vesicles in exchange with protons that are previously accumulated by H+-ATPases (Masson et al. 1999). We assume that this process saturates with increasing vesicular transmitter concentration. This assumption is justified by 2 main reasons. First, transport energy increases with an increasing concentration gradient between axonal cytoplasm and vesicle interior. Thus the accumulation of transmitter molecules in vesicles is a self-limiting process. Second, nonsaturating vesicle loading should result in bigger quanta at low release rates and smaller quanta at high release rates. Such a release-dependent reduction of quantal size indeed occurs after massive repetitive stimulation of frog motor endplates (Naves and Van der Kloot 2001) and may contribute to the frequency-dependent fading of inhibitory and excitatory postsynaptic currents at central synapses (Galarreta and Hestrin 1998). At low to moderate release rates, however, many central synapses show quantal sizes for evoked or spontaneous (miniature) release that are independent from the frequency of release (e.g., Edwards et al. 1990; Kraszewski and Grantyn 1992; Ropert et al. 1990; Sahara and Takahashi 2001; Van der Kloot 1996) or that even increase upon increasing frequency (Behrends and ten Bruggencate 1998). Thus vesicular loading seems to be saturating and can limit vesicular transmitter content only at very fast release rates (see Fig. 2).
|
+) and out of (–) the vesicles, a cytosolic transmitter concentration c, and resulting vesicular transmitter concentration we get a net flux of
 | (4) |
max = (+/–)c.
In this equation, loading depends on the cytosolic transmitter concentration and leakage depends on intravesicular transmitter concentration (see Fig. 2A), which does not alter our qualitative results. Vesicles are still being filled until an equilibrium of influx and efflux is reached. Experimental observations show that the presynaptic cytosolic transmitter concentration can affect quantal size (Engel et al. 2001; Murphy et al. 1998; Pothos et al. 1998a). Our model reproduces this effect: an increase in c will increase the resulting amount of transmitter in the vesicle until equilibrium is reached (see RESULTS and Fig. 4). This qualitative result persists under the alternative assumption that leakage is independent of (Wang and Floor 1994).
|
To reproduce the experimentally observed dependency of synaptic function on transmitter metabolism, we then introduce the vesicular transmitter concentration as an additional variable into the description of vesicle distribution between the 3 pools. The total number of vesicles in the reserve pool and in the RRP, respectively, is now given by the integral of their distribution with respect to ; that is: 
and 
, where 
() is the integral of needed here to get the dimensions right (the pool of empty, fused vesicles nf is independent from ). Our model should account for experimental data, which suggest that presynaptic transmitter content affects vesicle dynamics. Therefore we will assume that the transition rates between different pools can, in principle, depend on [i.e., (), r()]. In principle, the rates could be modeled to depend on cytosolic transmitter concentration c rather than on . In this case, however, increases in cytosolic transmitter concentration would exert effects on incompletely filled vesicles and therefore mean quantal size would be reduced. Below, we will systematically examine how the dependency of rate constants on vesicular transmitter content influences the distribution of vesicles between the 3 compartments. In general terms, the presynaptic vesicle dynamics is now determined by the following set of partial differential equations [the recovery of empty vesicles () can, of course, not depend on the filling state]
 | (5a) |
 | (5b) |
 | (5c) |
 | (6) |
) and release (r)
 | (7) |
 | (8) |
Biological interpretation of variables and choice of parameters
We have modeled spontaneous release as a random process with a low probability in each time step. Fused vesicles (nf) are recycled with a constant rate . The number of recycled empty vesicles sets the boundary condition n(0, t) for the vesicular filling process in the reserve pool n(, t).
The system of Eqs. 1a–c contains 3 variables (the number of vesicles in each compartment n, nRRP, and nf) and 3 parameters (the transition rates , r, and ). The numerical values of parameters will differ between different types of synapses and situations but it should be noted that this will not influence the qualitative results (i.e., changes in synaptic function after changes in presynaptic transmitter concentration). As a typical case, we will consider 10 vesicles in the release-ready pool (Borges et al. 1995; Kirischuk and Grantyn 2000; Kraushaar and Jonas 2000; Murthy and Stevens 1999; Stevens and Tsujimoto 1995). The number of fused vesicles f will also be set to 10 and the vesicle content of the reserve pool is set to 80, based on data by Liu and Tsien (1995). Under steady-state conditions, the influx into each compartment equals the efflux into the next compartment. The spontaneous (action potential-independent) release rate of individual vesicles (r) in hippocampal slices is unknown (but see Murthy and Stevens 1999 for cultured hippocampal cells). We will assume a value of r = 0.01/s, translating into one vesicle per 10 s with 10 vesicles in the readily releasable pool. This is is below the rate of synaptic depression at inhibitory synapses (Galarreta and Hestrin 1998) and yields realistic values for the frequency of miniature postsynaptic currents (e.g., 5/s for 50 presynaptic terminals). With these assumptions, the parameters for the steady state in Eqs. 3 are: = 1.25 x 10–3/s; r = 1 x 10–2/s; = 1 x 10–2/s. Different assumptions for the absolute numbers of these parameters will not alter the qualitative conclusions in the RESULTS section (e.g., distribution of vesicles with respect to their transmitter content).
There is increasing evidence that vesicular recycling does not only occur on the classical timescale of 10s of seconds, but also on a faster timescale ("kiss-and-run"; Aravanis et al. 2003; Gandhi and Stevens 2003; Murthy and Stevens 1998; Sara et al. 2002; Stevens and Williams 2000; Valtorta et al. 2001). Fast cycling vesicles do not go through a reserve pool but seem to enter directly into a release-ready state after recovery from fusion. In the framework of our model, this faster pathway may have 2 important consequences: 1) cycling might become faster than the filling of vesicles, leading to the release of incompletely filled vesicles (Naves and Van der Kloot 2001; see Figs. 2B and 3B for illustration within our 3-compartment model); 2) the RRP cannot be refilled from a large reserve pool after losing vesicles (i.e., our presynaptic model is effectively reduced to 2 compartments). Within the present model, this direct pathway can be considered a limiting case for increased values of . Under these conditions, the number of vesicles in the reserve pool approaches zero and loses its rate-limiting function. The consequences of such an increase in are analyzed in detail below [see Effects of transmitter concentration on directly recycling vesicles (shortcut pathway)] and in Fig. 6. Alternatively, we also simulated the direct pathway in a 2-compartment model (containing only RRP and fused vesicles), which yielded similar results (data not shown).
|
|
. Experimental data on cytosolic transmitter concentrations in the presynaptic terminal are surprisingly scarce; recent evidence, however, suggests that it is in the order of 1–10 mmol (Ishikawa et al. 2002; Yamashita et al. 2003). Therefore, we will assume transmitter concentrations in the order of magnitude of the vesicular transporter affinity constant Km (
5 mmol for GABA; see Kish et al. 1989; McIntire et al. 1997). The cytosolic transmitter concentration c cannot be chosen too low as compared to Km because net transport of transmitter into vesicles must be fast enough to guarantee filling within the presynaptic cycling time of vesicles (20 s). Otherwise, vesicular transmitter concentration would strongly depend on release rate. As mentioned above, this seems to be the case only during very high cycling rates (Naves and Van der Kloot 2001). On the other hand, if c was much higher than Km, vesicular transmitter transporters would be permanently saturated and changes in cytosolic transmitter concentration would not translate into changes in vesicular transmitter content, in contrast to experimental observations (Engel et al. 2001; Pothos et al. 1998a).
What is the maximal vesicular transmitter concentration that can be reached? Experimental and modeling studies have suggested that vesicular transmitter concentration can reach values of at least 100 mmol (Burger et al. 1989; Busch and Sakmann 1990). It is generally assumed that vesicular transmitter transporters do not build up very steep gradients between the inner and outer vesicular compartment (see, e.g., Fonnum et al. 1998), consistent with recent data from the calyx of Held, which suggest a cytosolic transmitter concentration around 1 mM (Yamashita et al. 2003). We tested various sets of parameters for vesicle loading until vesicular filling was saturating within about 20 s, and filling was dependent on c. Parameters used are: + = 10/s, – = 0.1/s, c from 1 to 10 mM, resulting in max ranging from 100 to 1000 mM. Using Eq. 4, these assumptions yield a mean value of = 5 mmol/s for c = 1 mmol.
The system of partial differential equations (Eqs. 5) was implemented by Monte Carlo simulations using Matlab (The Mathworks, Natick, MA) and was executed on Intel Pentium II–powered computers running under the Linux operating system.
|
RESULTS |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
(), or r(), respectively]. Under these conditions, the filling state of released vesicles depends on the cytosolic transmitter supply. We first compute the steady-state situation and afterward dynamic changes in presynaptic transmitter content. Together, the results show how synaptic efficacy changes with presynaptic transmitter metabolism. Distribution of vesicular transmitter content
As a first step, we model a single, homogeneous population of vesicles
 |
(c, ) = +c – – (see Fig. 2A). For the steady-state situation, this equation can be solved analytically and results in a distribution of vesicles that peaks at max, such that most vesicles are almost maximally full (Fig. 2B). The depicted number of vesicles in each filling state is proportional to the probability of being in this filling state. (Note that even if no vesicles are released, i.e., in the situation of r = 0, several vesicles are incompletely filled, reflecting the equilibrium of influx and efflux.) Increasing the release rate up to 5/min (corresponding to a cycling time of 12 s) results in reduced transmitter content of released vesicles but leaves the distribution qualitatively unchanged. At central synapses the shortest possible cycling time of single vesicles has been reported to be about 15 s (Klingauf et al. 1998; Liu and Tsien 1995; Ryan and Smith 1995; Ryan et al. 1993) except in special situations that are likely to involve kiss-and-run release (Aravanis et al. 2003; Burgoyne et al. 2001; Gandhi and Stevens 2003; Graham et al. 2002; Machado et al. 2000, 2001; Palfrey and Artalejo 1998; Sara et al. 2002). Thus for normal release processes vesicular transmitter content is high and relatively stable. If the release rate increases further, however, it reaches the filling time of vesicles that has been set to 6 s; at this point, the distribution flattens (Fig. 2B). An even higher release rate results in a monotonically decreasing distribution of vesicles because an increasing number of vesicles is incompletely filled (cf. Naves and Van der Kloot 2001).
For modest release rates, the distribution of presynaptic vesicles in Fig. 2B shows a very sharp peak at maximal values of (Fig. 2B). Miniature postsynaptic currents, however, usually show a skewed distribution with a large coefficient of variance of up to about 0.5 (e.g., Frerking et al. 1995; Sahara and Takahashi 2001). There is good indication that this variance is at least partially attributed to the release of differentially filled vesicles (Frerking et al. 1995), although different postsynaptic receptor numbers at different synaptic sites may contribute to the variance (Nusser et al. 1997). Recent evidence suggests that at some synapses variance of vesicular volume V (rather than of vesicular transmitter concentration) may underlie the variable transmitter content (Bruns et al. 2000; Colliver et al. 2000), although such a correlation has not been found at the neuromuscular junction (van der Kloot et al. 2002).
In our model, we introduced variance by convoluting the distribution of concentrations (Fig. 2B) with the distribution of vesicular volumes in presynaptic endings. The latter was based on analyses of vesicle diameters in cerebellar and hippocampal neurons (Bekkers et al. 1990; Palay and Chan-Palay 1974), yielding a coefficient of variance of about 0.12. This Gaussian distribution of diameters was transformed into the 3rd-order Gaussian describing vesicular volume (Frerking et al. 1995). From hereon, the distribution of vesicles in the readily releasable pool (RRP) and in the reserve pool will be plotted as n( x V) (i.e., with respect to transmitter content), rather than concentration. Figure 3A illustrates the influence of vesicular size variance on the distribution of differentially filled vesicles for a case of low release rate (r = 1/min). Obviously, at zero variance the distribution peaks at maximal transmitter content (yielding a distribution similar to Fig. 2B for r = 1/min). If such a distribution of vesicular transmitter content would underlie the experimentally observed amplitude distribution of miniature postsynaptic currents, variance would almost exclusively be attributed to postsynaptic factors, contrary to experimental evidence (e.g., Frerking et al. 1995; Sahara and Takahashi 2001). At higher values of CV the distribution becomes smoother, consistent with a role for differentially filled vesicles. Finally, we modeled the distribution of vesicles n( x V) at different release rates (diameter variance was set to 0.12 for this simulation; Fig. 3B). For modest release rates, this distribution is less sensitive to release rate than the data shown in Fig. 2B, and it yields a clear peak for highly, but not maximally, filled vesicles. Consequently, postsynaptic current amplitudes are largely independent of release rate within some range, consistent with experiments (Edwards et al. 1990; Kraszewski and Grantyn 1992; Ropert et al. 1990; Sahara and Takahashi 2001; Van der Kloot 1996). Only at high sustained release rates, filling becomes incomplete (Naves and Van der Kloot 2001; see Fig. 3B for release rates above 5/s).
Dependency of release rate r on transmitter content
There is experimental evidence that an increase in presynaptic transmitter concentration can increase the frequency or probability of vesicle release (Engel et al. 2001; Golan and Grossman 1996; Murphy et al. 1998; Pothos et al. 1998b; Song et al. 1997). To establish mechanisms for these observations within our model, we will now consider transition rates that depend on transmitter concentration. In contrast to the previous section, we will now use the full presynaptic model as introduced in Eqs. 5; that is, vesicles are distributed between a reserve pool (80% of vesicles in equilibrium), RRP (10% of vesicles), and fused vesicles waiting for recovery from the presynaptic membrane (10% of vesicles; numbers chosen to illustrate a typical case; see METHODS). Our model allows for concentration-dependent modulation of release rate r as well as of the transition rate (flow into the readily releasable pool). We start with the case where the release rate r depends on vesicular transmitter concentration: r = r() = r0[1 – exp(–/0)]. Afterward we will consider the alternative scenario where the supply of vesicles from the reserve pool to the RRP depends on [i.e., = ()].
For r() = r0[1 – exp(–/0)], the distribution of vesicles in the RRP becomes smoother and is shifted toward larger values when the cytosolic transmitter concentration is raised (Fig. 4B). Because in this scenario vesicles with higher transmitter content are released at higher rates than those with low transmitter content, the distribution of released vesicles maintains a relatively sharp peak at high transmitter content (Fig. 4C). Whereas Fig. 4 focuses on distributions of vesicles with respect to transmitter content, Fig. 5 shows the number of vesicles in the RRP and the number of vesicles per time undergoing exocytosis. An increase in cytosolic transmitter concentration c results in a drastic reduction of the number of vesicles in the RRP (Fig. 5A). The number of released vesicles per time remains relatively constant, however, because the reduced number of releasable vesicles is compensated by the increased release rate of these (fuller) vesicles (Fig. 5B). Thus in a model with distinct pools, a filling-dependent release rate cannot reproduce a strong influence of cytosolic transmitter concentration on the frequency of vesicular release.
|
for the transition of vesicles from the reserve pool into the RRP is much smaller than r and . Therefore the total flux of vesicles in our scenario depends mainly on the slowest transition rate . The number of vesicles in each pool, on the other hand, changes reciprocally with changes in the transition rates out of the respective pool. For example, an x-fold increase in the release rate r will lead to an x-fold decrease in the number of vesicles in the RRP. The analytic approximations match the numerical simulations quite well. The small mismatches between both approaches reside in the fact that the analytical solution uses direct changes in rates, whereas the numerical simulations are based on alterations in c, which are first translated into vesicular transmitter content and subsequently processed by Eqs. 5.
Dependency of vesicle supply on transmitter content
We will now consider the alternative scenario = (), where the transmitter content of a vesicle determines the rate of transition from the reserve pool into the RRP. In a broad sense, this scenario can be understood as "vesicle maturation": filling is a precondition for efficient translocation into the RRP. The distribution of vesicles in the reserve pool and in the RRP are shown in Fig. 4, D and E, respectively. Increasing cytosolic transmitter concentration results in a broadening of the distribution of differentially filled vesicles in the RRP. In contrast to Fig. 4B [r = r()], the total number of vesicles in the RRP increases with higher values of c. The distribution of released vesicles is largely similar to the distribution resulting from r() but is slightly broader and reaches a larger integral when cytosolic transmitter concentration is increased (Fig. 4E). Figure 5B shows how many vesicles reside in the RRP and Fig. 5D illustrates how many vesicles are being released per unit time when the supply of vesicles from the reserve pool depends on their filling state: the size of the RRP will now increase with increasing cytosolic transmitter concentration and the release rate also sharply increases, in parallel to the size of the RRP. Similar to the numerical data, the analytical approximation yields a drastic increase in release number/time with increasing c, as indicated by the continuous line superimposed on the numerical data in Fig. 5D.
The above simulations show that changes in vesicular filling state as well as changes in vesicle dynamics can be caused by changes in presynaptic transmitter concentration. We found that effects of c on the frequency of vesicular release can be best explained if the supply of vesicles into the RRP depends on vesicular filling, rather than the release rate itself (see also Brager et al. 2002).
Effects of transmitter concentration on directly recycling vesicles (shortcut pathway)
As mentioned in METHODS, there is increasing evidence that vesicles are recycled not only on the classical path involving the reserve pool, but also directly ("kiss-and-run"). We introduced such an alternative pathway into our model by increasing the rate 0, thereby diminishing the size of the reserve pool. As 0 approaches infinity, the reserve pool is effectively eliminated. The lifetime of an individual vesicle on this shortcut pathway may be as short as 1 s (Gandhi and Stevens 2003). Although the transmitter content of fast cycling vesicles has not directly been measured, it is possible that filling equilibrium cannot be reached in such vesicles (Naves and Van der Kloot 2001). In our model, this situation corresponds to very fast release rates in Figs. 2B and 3B, where the sharp peak in vesicle distribution broadens. Figure 6A shows the number of vesicles in each compartment as a function of increasing values of 0 according to Eqs. 3. The size of the reserve pool is reciprocally proportional to the velocity of "maturation" and the pool vanishes at high values of 0. Conversely, the pools of releasable and of fused vesicles, respectively, increase. What happens now in this system if the presynaptic transmitter concentration c is increased? Again, we must distinguish between effects of c on vesicle maturation (Fig. 6B) and effects on release rate r (Fig. 3C). When 0 is increased, the steep correspondence between transmitter concentration and release (see Fig. 5D and case 0 = 1 in Fig. 6B) is lost, and the number of released vesicles per time becomes largely independent from c. This is also illustrated in Fig. 6D. At low values of (0 = 1), vesicular release is strongly increased after a 10-fold increase in c. Increasing 0 reduces the rate-limiting role of and thereby abolishes any effects of transmitter concentration on the frequency of vesicle release. At high values of 0, one might assume that effects of c on the release rate r [implemented as r(); see above] become more pronounced. However, Fig. 6C shows that the weak effect of c on release is lost when 0 is increased. This is caused by a reciprocal compensation of 2 effects: at increased values of c, vesicles are being filled more rapidly and are released with higher probability, if r increases with . On the other hand, this will reduce the number of vesicles available in the RRP. Therefore, the product rnRRP is roughly constant.
In summary, the simulations within our parameter regime show that any effects of transmitter concentration on presynaptic vesicular dynamics requires the existence of a reserve pool. Simulations within a 2-compartment model (consisting of only the RRP and a pool of fused vesicles) yielded equivalent results, that is, that the synaptic release is always independent of transmitter concentration in the absence of the reserve pool.
Dynamic alterations of vesicle cycling
To further demonstrate the differences between alterations of vesicular release rate r() and vesicle recruitment (), we subsequently computed dynamic changes of vesicular release for a stepwise increase in c. Although such a sudden increase in cytosolic transmitter content will not happen in natural neurons, the data can still be interpreted in a biologically realistic manner. For the scenario with r = r(), a stepwise increase in c corresponds to a stepwise change in the rate of release (e.g., by a high-frequency stimulus train). This experimental paradigm is being used by many authors to induce processes of synaptic plasticity (for a review, see Zucker and Regehr 2002) or to probe the size of the RRP (e.g., Kirischuk and Grantyn 2000; Rosenmund and Stevens 1996). For the alternative scenario [ = ()], the change in c translates into a situation of increased flow of vesicles into the RRP. Experimental data suggest that the supply of vesicles can indeed be varied by different mechanisms, including increased presynaptic Ca2+ influx and activation of protein kinase C (PKC) (Gillis et al. 1996; Smith et al. 1998; Stevens and Sullivan 1998; Stevens and Wesseling 1998; Wang and Kaczmarek 1998).
Figure 7 shows the results of the stepwise increase in c for the 2 different scenarios: in the case of an isolated increase in r, the release rate will briefly increase and then decrease to reach a new plateau of release that is only about 10% above the prestimulus level (Fig. 7A). This small increase in release rate in equilibrium has already been demonstrated in Figs. 4 and 5. After returning to normal transmitter content c, the terminal shows a decreased release of vesicles until the RRP is filled again. Such a transient decrease in vesicular release is regularly observed upon depletion of the RRP by high-frequency stimuli (short-term depression; Brager et al. 2002; Dobrunz and Stevens 1997). In the other case, where = (), an increase in c will be followed, with some delay, by a proportional and sustained increase in vesicular release because of the increasing number of vesicles flowing into the RRP (Fig. 7B). This situation would allow for a stable increase in synaptic transmission without fatigue.
|
) or = ()
What could be the underlying causes for the dependency of vesicle processing on vesicular transmitter concentration? How can we experimentally distinguish between these possibilities? We can imagine two principally different links between vesicle transitions and vesicular transmitter content: first, an intrinsic detection mechanism that selects highly filled vesicles for further processing. This would correspond to "vesicle maturation" as a precondition for transition into the RRP or for release. Second, the released transmitter may exert feedback effects on r or by presynaptic autoreceptors. Each vesicle could then, by virtue of its released transmitter content, influence the fate of subsequent vesicles, but not its own dynamics. In the DISCUSSION we will give examples for such positive feedback mechanisms and contrast them to the better-known negative presynaptic feedback mechanisms. In total, these considerations allow for four different scenarios: () or r(); both either mediated by a detection mechanism or by autoreceptors. The following experiments may help to distinguish between the scenarios.
1) If r was increased by transmitter released from previous vesicles (feedback), then vesicular release would tend to occur in bursts. Results of a simulation of this mechanism are plotted in Fig. 8. Notably, release of vesicles in brief bursts, similar to the results from our simulation, has been observed at hippocampal GABAergic synapses with increased transmitter content (Engel et al. 2001). This observation is thus compatible with presynaptic GABAergic autoreceptors that are positively coupled to vesicular release.
|
; Liu and Tsien 1995; for modeling, see Brager et al. 2002; Matveev and Wang 2000; and our Fig. 7B). If presynaptic transmitter content affects the transition of vesicles into the RRP [()], increasing c will increase the number of vesicles in the RRP and the synapse should become more resistant toward fatigue. Conversely, if r = r(), the time constant for depletion should become faster when c is increased. A recent experimental and theoretical study on the modulation of short-term synaptic plasticity by PKC has revealed a very similar distinction between changes in vesicle supply versus changes in release probability (Brager et al. 2002). The effects of transmitter concentration on vesicle supply and depletion do, of course, reverse when either r or decreases with (i.e., in the case of a negative presynaptic feedback mechanism).
3) Refilling of the RRP after high-frequency stimulation is a process that depends essentially on and has time constants in the range of seconds to minutes (Pyott and Rosenmund 2002; Stevens and Tsujimoto 1995). After depletion, the rate of release of vesicles from the RRP is very small; therefore, any feedback mechanism acting by presynaptic autoreceptors is very ineffective in this situation. Thus if an increased presynaptic transmitter concentration leads to a faster recovery from depletion, it is likely that the rate of transition into the RRP depends directly on vesicular transmitter concentration (detection and faster processing of full vesicles). The different scenarios are summarized in Table 1.
|
|
DISCUSSION |
|---|
|
TOPABSTRACTINTRODUCTIONMETHODSRESULTSDISCUSSIONREFERENCES |
|---|
Filling of vesicles and transmitter content
At present, we lack information on many parameters of vesicular loading, the most important of which are the number of transmitter transport molecules per vesicle and the local cytosolic transmitter concentration. We therefore used the most parsimonious model, which takes into account the following experimental findings: 1) an increased cytosolic transmitter concentration enhances vesicular transmitter content (Engel et al. 2001; Pothos et al. 1998a); 2) transmitter can flow in and out of the vesicles; 3) changes in transport rate change the resulting vesicular transmitter content (Colliver et al. 2000; Song et al. 1997; Van der Kloot et al. 2000); and 4) transmitter content is equal at low and modest release rates (Behrends and ten Bruggencate 1998; Edwards et al. 1990; Kraszewski and Grantyn 1992; Ropert et al. 1990; Sahara and Takahashi, 2001; Van der Kloot 1996). We chose an equilibrium model that reaches a balance between inflow and outflow at a time defined by the relative weight of the rate constants, + and –. In this model, filling of vesicles depends on presynaptic transmitter concentration and there is no fixed value for maximal transmitter content (see Williams 1997). Although equilibrium models have been challenged by observations at the neuromuscular junction (Naves and Van der Kloot 1996; Van der Kloot et al. 2000), our model does account for the main observations at central synapses with varying transmitter concentration.
Any equilibrium model requires some minimal time until equilibrium is reached. After fusion and endocytosis, vesicles at central synapses need at least 20 s to reenter the readily releasable pool (Ryan and Smith 1995; Ryan et al. 1993; Stevens and Tsujimoto 1995; von Gersdorff and Matthews 1997). An alternative, very fast recycling track for vesicles (Sara et al. 2002) seems to follow partial release and therefore does not require complete refilling (Graham et al. 2002; Machado et al. 2000, 2001). Thus, 20 s is sufficient to guarantee complete filling of recycled vesicles at central synapses (Dobrunz and Stevens 1997). Consistent with experimental observations, our model yields stable vesicular filling states over a wide range of release frequencies (Edwards et al. 1990; Kraszewski and Grantyn 1992; Ropert et al. 1990; Sahara and Takahashi, 2001; Van der Kloot 1996). At higher rates, quantal size may decrease, as has been observed upon continuous stimulation of the neuromuscular junction (Naves and Van der Kloot 2001).
Our model produced a surprisingly uniform population of equally and almost completely filled vesicles. To reproduce the observed variance of postsynaptic responses we introduced some variability of vesicle size, consistent with experimental and theoretical work on the variance of mIPSCs (Bekkers et al. 1990; Frerking et al. 1995; Palay and Chan-Palay 1974). Recently variations in vesicular dopamine content of pheochromocytoma cells have been shown to cause parallel changes in the volume of large dense core vesicles (Colliver et al. 2000). It should be noted, however, that vesicles at the neuromuscular junction do not change their size with changing acetylcholine content (Van der Kloot et al. 2002). Variance between vesicles can certainly result from alternative mechanisms. For example, the rate constants + and – may differ between vesicles, possibly attributable to variable numbers of H+-ATPase or VGAT molecules (see Song et al. 1997). In any case, the introduction of an intrinsic variability of vesicles led to a distribution of vesicular transmitter content consistent with the experimentally observed variability of postsynaptic miniature currents.
Relationship between vesicular transmitter content, pool sizes, and vesicular release
Effects of vesicular filling state on synaptic function were modeled by assuming that one of the rate constants of the presynaptic vesicle cycle depends on transmitter content. The presynaptic vesicle cycle consists of multiple steps (Südhof 1995, 2000) that, for the present purpose, have been condensed to transitions between 3 major groups of vesicles: the readily releasable pool (RRP), the reserve pool, and empty vesicles after fusion. The RRP (Rosenmund and Stevens 1996) at central synapses is generally considered to contain 5–10 vesicles. Recent evidence indicates that the size of the RRP can be reduced after extensive activation of the synapse, possibly because of the disruption of release sites by fused vesicles or because of the depletion of certain molecule(s) needed for fusion (Stevens and Wesseling 1999; see capacity restrictions). This mechanism would tend to limit the capacity for increased vesicular release and thus is not likely to account for the observed increase in frequency of miniature postsynaptic current frequency upon increased transmitter loading of vesicles (Engel et al. 2001; Song et al. 1997). Our "reserve pool" contains all vesicles inside the terminal that might become available for release after going through additional steps of activation. At central synapses this pool is far greater than the RRP (Südhof 2000) and constitutes 80% of all vesicles in our model. The transition of these vesicles into the RRP has been condensed into one rate constant , which also includes the equilibrium between forward and backward reactions (e.g., the undocking of vesicles) (Murthy and Stevens 1999; Oheim et al. 1999). In reality, multiple different transitions may occur between various subpools, including more remote reserve pools (Wang and Zucker 1998), an alternative route through the endosome (Südhof 2000), or a fast track for individual vesicles (Murthy and Stevens 1998; Sara et al. 2002; Stevens and Williams 2000; Valtorta et al. 2001). However, our 3-pool model is a parsimonious approach to distinguish between effects of vesicular transmitter content at 2 principally different stages: 1) direct effects on the probability of release, modeled as r(), or 2) effects on the rate of recruitment into the RRP, modeled as () (see below for a discussion of fast recycling).
Figure 5 illustrates the main difference between these two possibilities. If the probability of release is directly affected by the filling state of vesicles [r()], the effects of transmitter content on release rate will be rather mild and may escape detection. If, on the other hand, the supply of vesicles into the RRP is affected by thei
