Results

2.5. Results

In the previous sections the complete dynamics of release and recruitment of presynaptic vesicles, including facilitation of release due to repetitive stimulation has been formu-lated. Fitting the model to experiments requires setting the model parameters, which are summarized in Tab. 2.1. Some of these parameters can be identified directly with experimental observables. These are the two time constants of vesicle recruitment, τ_P1 and τ_P2 (Eqs. 2.4), which are known from studying the recovery of synaptic transmission after repetitive high-frequency stimulation (Schneggenburger, 1999) or application of a strong, depolarizing voltage-step pulse (Wu and Borst, 1999). Furthermore the analysis of EPSC-amplitude fluctuations indicates that the release-sites are occupied up to∼ 80 % (Meyer, 1999), which we use as an estimate for the ratio of filled sites at rest, R(Eq. 2.6).

Data concerning the Ca²⁺-influx, J_Ca,max and EC₅₀ (Eq. 2.11), have been measured by Schneggenburger et al. (1999). Although employed as fit parameters, the range of values for x₀ and τ_x (Eq. 2.15) to model the global Ca²⁺-dynamics is restricted and chosen close to the estimates given in by Helmchen et al. (1997).

The remaining model-parameters (see Tab. 2.1) are taken as free parameters to fit the model to three sets of experimental data. The first set is given by recordings of the depres-sion of EPSC-amplitudes following a 10 Hz-train of 30 stimuli (von Gersdorff et al., 1997;

Weis et al., 1999) (normalized by dividing by the first EPSC response). After approx-imately 10 stimuli the normalized current reaches a steady-state value (see Fig. 2.5B), which decreases for increasing frequency (von Gersdorff et al., 1997; Weis et al., 1999).

Its frequency-dependence is displayed in Fig. 2.5D. The recovery of release from high-frequency stimulation as studied by a test-AP after a time interval ∆t following the last depressing stimulus (Fig. 2.5A) provides a third set of experimental estimates (Schneggen-burger, 1999).

As shown in Figs. 2.5 and 2.6 and given by the values in Tab. 2.1 two sets of parameters have been found, which are able to comprise the experimentally observed depression of EPSC amplitudes, recovery from depression as well as the frequency-dependence of the steady-state depression current. Systematic deviations of theory and experiments are only seen for the response of the second stimulus in a 10 Hz stimulus train, where the theory fails to reproduce the strong decay in the amplitude of the second stimulus compared to initial amplitude.

It should be taken into account that the experimental data itself exhibit a large variability between individual cells: During a 10-Hz-stimulus train, steady-state level and relative amplitude of response to the second stimulus seem to correlate with absolute amplitude of the first response (von Gersdorff et al., 1997). Larger responses (white rectangles in Fig. 2.6) come along with a stronger relative decay in the second amplitude and reach a lower level of steady-state depression. This effect most probably reflects the abundant use of limited resources by a first strong release. Cross-correlations between subsequent stimuli are currently being studied by an extended theoretical and experimental analysis (Neher, 1999). In this context we want to point out that variations in the kinetic parameters of

0.0 0.5 1.0 1.5 2.0 2.5 3.0

recovered fraction test with AP, model

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A

B

C

D

Figure 2.5.: Synaptic depression and recovery from depression as recorded in experiments (black symbols) and calculated by the theoretical model (solid line, parame-ters from set 1 in Tab. 2.1). A: Recovery as tested by a subsequent AP at t = ∆t after high-frequency stimulation with 100 Hz. B: Normalized EPSC amplitude during stimulation with 10 Hz. C: Theoretically calculated re-covery from complete depletion, for the joint occupancy in both pools (solid line) and as tested by a subsequent APt = ∆tafter complete depletion (white circles). D: Frequency-dependence of the normalized steady-state depression current on the stimulus frequency.

2.5 Results 27

recovered fraction test with AP, model

joint occupancy, both pools

Figure 2.6.: Synaptic depression and recovery from depression as recorded in experiments (black and white symbols) and calculated by the theoretical model (solid line, parameters from set 2 in Tab. 2.1). A: Recovery as tested by a subsequent AP att = ∆tafter high-frequency stimulation with 100 Hz. B: Normalized EPSC amplitude during stimulation with 10 Hz. Cells with a first large response exhibit a lower steady-state depression current level (white rectangles) than those with a smaller first response (black circles). C: Theoretically calculated recovery from complete depletion, for the joint occupancy in both pools (solid line) and as tested by a subsequent APt = ∆tafter complete depletion (white circles). D: Frequency-dependence of the normalized steady-state depression current on the stimulus frequency.

our model (Tab. 2.1, set 2) also manage to cover the depression of EPSC-amplitudes for large first amplitudes, shown in Fig. 2.6B (white rectangles).

In Fig. 2.6C the theoretically predicted recovery after complete depletion of both pools is displayed. In accordance with the findings of Wu and Borst (1999) and with experimental results at the rat climbing fiber-Purkinje cell synapses (Silver et al., 1998) our calculations indicate that the joint occupancy of both pools recovers with a two-exponential time course (solid line in Fig. 2.6C). The initial rapid increase in the total number of occupied sites is due to the rapid replenishment of pool1with a fast time-constantτP1 ∼ 0.3 s, while the slow component in the time-course of recovery reflects the much slower shuffling of vesicles from pool1to pool2(time constant,τ_P2 ∼ 5.2 s; see also Fig. 2.7 and next section). The recovery from complete depletion as tested by a subsequent single test-AP occurs with a single exponential time course (time-constant τ ∼ 4.76 s), which is about three times faster than the time constant observed by Wu and Borst (1999), but in the same order of magnitude as the estimates by Silver et al. (1998) and the measured recovery from depletion by a 100 Hz-stimulus train (τ ∼ 4.92 s) displayed in Figs. 2.5 and 2.6. Finally notice, that the small bump in the early recovery from 100 Hz-stimulation is also seen in the model-calculations and, as demonstrated in the next section, arises as a combined effect of facilitation and “overshooting” of pool 1.