Article Figures & Data
Figures
- Fig. 1.
Model for a dynamic pool of primed vesicles at a release site. A, Schematic of a model release site at the first (left) and at the second (right) stimuli during a paired-pulse protocol. Within the release site, there are docking sites (four in the illustrated example) at which vesicles are in equilibrium between a primed (immediately releasable) and a nonprimed state. When an action potential arrives, at most one of the primed vesicles can be released. The probability of releasing a primed vesicle isPves,Pves1 at the first stimulus, andPves2 at the second stimulus. ThePr of the release site is given by Equation 1 (see Materials and Methods). It is assumed that the recruitment of nonprimed vesicles to a primed state is negligible between the two stimuli (20 msec) (Hanse and Gustafsson, 2001a). B, Distribution of the number of primed vesicles among trials before the first stimulus (preprimed vesicles, left) and before the second stimulus (right). The distribution is calculated from four docking sites and a probability of the primed state of 0.3.
- Fig. 2.
Lack of release dependence during paired-pulse activation. A, Pr in response to the second stimulus (P2) when release occurred in response to the first stimulus (P2rel) is divided by that obtained when there was a release failure to the first stimulus (P2fail). ThisP2rel/P2failratio is plotted against Pr in response to the first stimulus (P1). In the modeled example, the preprimed pool was 1.2, and bothPves1 and Pves2were 0.4. Ratio values obtained from 100 runs, each consisting of 100 trials, are shown. TheP2rel/P2failratio averaged 0.96 ± 0.35 (SD), andP1 averaged 0.40 ± 0.05. These average values are indicated by the dotted lines. Insets show the distribution of primed vesicles (compare Fig.1B) before the second stimulus when the first stimulus resulted in a release (top histogram,filled bars) and when the first stimulus resulted in a failure (bottom histogram, open bars). B, Variation inP2rel/P2failratio as a function of the number of trials and of the size of the preprimed pool. The number of trials per run was varied between 50 and 10,000, and 100 runs were made for each trial length. Filled circles represent a pool of 1.2 and open circlesrepresent a pool of 3.6.
- Fig. 3.
Influence of Pr on the release dependence during paired-pulse activation. A, TheP2rel/P2failratio is computed over a range of P1 values obtained by varying Pves1 between 0.1 and 0.9 (in steps of 0.1) and the average preprimed pool between 0.6 and 1.8 (in steps of 0.3). Pves2 was kept constant at 0.4. The dashed line indicates release independence (i.e., aP2rel/P2failratio equal to 1). Each measurement was obtained from 10,000 trials.B, TheP2rel/P2failratio is determined by Pves1 and the size of the preprimed pool. TheP2rel/P2failratio is plotted against P1 obtained using three different preprimed pool sizes: 0.6 (open triangles), 1.8 (open circles), and 3.6 (open squares). For each pool size,Pves1 was varied from 0.1 to 0.9 in steps of 0.1, and theP2rel/P2failratios obtained for the various Pves1 values using a given pool size are joined together. The dashed line indicatesP2rel/P2fail = 1.C, TheP2rel/P2failratio depends on the number of docked vesicles and their probability of occupancy of the primed state. TheP2rel/P2failratio is plotted against P1, varyingPves1 from 0.1 to 0.9 in steps of 0.1. This is done for three different preprimed pool configurations, all producing an average preprimed pool of 1.2 vesicles. These configurations are 12 (filled triangles), 4 (open circles), and 2 (filled squares) docked vesicles combined with priming probabilities of 0.1, 0.3, and 0.6, respectively. The dashed lineindicatesP2rel/P2fail = 1.
- Fig. 4.
Influence of Pvesheterogeneity on the release dependence during paired-pulse activation.A, Effect of a stochastic variation inPves1 and Pves2on the release dependence of P2. TheP2rel/P2failratio is plotted against P1 for two different situations. Open circles represent the release dependence of P2 in a control situation using four different values of Pves1 (0.2, 0.4, 0.6, and 0.8), and Pves2 was kept constant at 0.4. Filled circles represent the release dependence of P2 whenPves1 and Pves2were allowed to vary stochastically around these values, as described in Results. The dashed line indicatesP2rel/P2fail = 1.B, Different docking sites are associated with different Pves values. Open circles represent a control situation withPves1 and Pves2values of 0.4 at all the docking sites. Filled squaresrepresent a situation in which one of the two to six docking sites was associated with a Pves1 of 0.9, whereas the other docking sites were associated with aPves1 of 0.2.Pves2 was kept constant at 0.4 for all docking sites. Open squares represent a situation in which one of the two to six docking sites was associated with aPves1 and Pves2of 0.9, whereas the others were associated with aPves1 and Pves2of 0.2. The dashed line indicatesP2rel/P2fail = 1.
- Fig. 5.
Influence of activation failure and multivesicular release on the release dependence during paired-pulse activation.A, TheP2rel/P2failratio is plotted against P1 for two different situations of activation failure. Open circlesrepresent the release dependence of P2 in a control situation with no activation failure (i.e., a “probabilistic release”). Pves1 is varied from 0.1 to 0.9, and the preprimed pool and Pves2 are kept constant at 1.2 and 0.4, respectively (compare Fig.3C, open circles). Filled circles represent a situation in which 50% of the trials were associated with an activation failure (no release is allowed) in response to the first stimulus; in other words, activation failures occur on top of a probabilistic release.Pves1,Pves2, and pool were the same as in the control situation. Filled squares represent a situation in which P1 is determined by activation failures only. In this situation,Pves1 was (per definition) equal to 1, andPves2 (used only when there was activation and hence release in response to stimulus 1) was equal to 0.4. The pool size was 1.2. The dashed line indicatesP2rel/P2fail = 1.B, The effect of allowing multiple release of vesicles on theP2rel/P2failratio. Open symbols represent the control situation, in which at most one vesicle per stimulus is released.Pves1 is varied from 0.1 to 0.9 for three different sizes of the preprimed pool (0.6, 1.2, and 3.6 as indicated).Pves2 is kept constant at 0.4. Filled symbols represent the corresponding results when there is no restriction on the number of vesicles that can be released per stimulus. The dashed line indicatesP2rel/P2fail = 1.
- Fig. 6.
Comparison between experimentally observed and simulated release dependence during paired-pulse activation.A, TheP2rel/P2failratio is plotted against P1 for experimental (open circles) and simulated (filled circles) data. Because the experimental data do not include synapses exhibiting the smallest and largestP1 values, simulations were performed over a slightly smaller range of Pves1 values than used in the other simulations. The exclusion of those synapses depended on the fact that under conditions of very small and largeP1 values and with a limited number of trials, the number of release successes and failures, respectively, becomes too small to produce reliable results.Pves1 was varied between 0.2 and 0.8 (in steps of 0.1), the average preprimed pool was varied between 0.6 and 1.8 (in steps of 0.3), and Pves2 was kept constant at 0.4 (10,000 trials per measurement). The dashed line indicates release independence (i.e., aP2rel/P2failratio equal to 1). A linear regression line is shown both for the experimental (dotted line; y = 0.39 + 1.13x; n = 33;r = 0.43; tn − 2 = 2.65; p < 0.01) and simulated (solid line; y = 0.29 + 1.85x; n = 35) data.B, Same as A, but the simulated data were generated with a more experimentally realistic number of trials (100).
