With increasing stimulus strength in terms of [Ca2+]i, increasing amounts of fast release at the expense of the slow component were observed in experiments (submaximal release in Fig.
23; chapter 3.4). This indicates that the fast and the slow release component are not mutually independent. Vesicles with an initially high release probability, and thus fast release rates, might convert into slow ones, and this process might directly or indirectly depend on [Ca2+]i. This was implemented in a novel single pool model with intrinsic heterogeneity in release kinetics (Fig. 24D), having tested several distinct models to describe both the experimentally observed appearance of two release components and the effect of submaximal release.
The basic concept of this model (Fig. 24D, E) is as follows. There are two states of the vesicle fusion machinery, which includes the Ca2+ sensor (denoted X, or X´ in Fig. 24E).
Release can occur from both states, X and X´, but with a lower rate constant from X´. With appropriate kinetic parameters, at resting [Ca2+]i (about 100 nM) almost all vesicles will be in state X with no Ca2+ bound (X 0Ca in Fig. 24E), before a stimulus is applied. When [Ca2+]i rises, the Ca2+ sensor will be more occupied with Ca2+ (states X 1Ca, X 2Ca, …). At the same time, if the rate of [Ca2+]i rise is slow enough, a sizeable fraction of vesicles might convert into the parallel states X´1Ca, X´2Ca, etc. (Fig. 24E, brown part), from which the vesicles will be released more ‘reluctantly’. Thus the conformational transition from X to X´ (Fig. 24E, from black to brown, respectively) might be seen analogous to the entry into a ‘desensitized’ state for ligand-activated ion channels. Moreover, this model assumes that release can occur also from the non-fully Ca2+ bound states (X 0Ca – X 4Ca and X´0Ca – X´4Ca), similar as described recently (Lou et al., 2005), but differing from the 5-site Ca2+ binding model described above (chapter 4.1; Fig. 24C; Schneggenburger and Neher, 2000). Conversion between the states X and X´ could occur from every state of Ca2+ binding (Fig. 24E, conversion between X nCa
and X´nCa with n = {1; 2; 3; 4; 5}), but not from the Ca2+ unbound states (X 0Ca and X´0Ca).
The reaction rates of the model (Fig. 24E) underlie certain theoretical constraints. The range of reasonable transition rates from the fast releasing state X to the slower releasing state X´
(cs in Fig. 24E) is limited towards the low end by the extent of submaximal release at relatively low stimulus intensities. Only if the transition rate cs from fast to slow (X to X´) is faster than the release rate from state X at low stimulus intensities, vesicles will be able to
‘desensitize’ to state X´ before they fuse from state X. This behavior is necessary to create a slow release component. On the other hand, the high end of possible transition rates from X to X´ is limited by release rates from state X at high stimulus intensities, because submaximal release showed the tendency to be overcome by very fast release kinetics at
high [Ca2+]i (Figs. 21 and 22, black traces). Thus, at high stimulus intensities release must be faster than the assumed transition from the fast releasing state X to the ’desensitized’ state X´, giving an upper limit for ‘desensitization’ rates. Also the impact of transition rates at basal [Ca2+]i is of importance. Without stimulation, the majority of the vesicles should be in the fast releasing state X, because if vesicles were initially in the state X´, fast release rates would be influenced by a necessary transition from X´ to X. Simulations of this scenario, with vesicles accumulated in the ‘desensitized’ state X´, did not predict fast release rates (not shown) like those which could be observed experimentally. Thus, to keep vesicles in the fast releasing state X at rest, convertibility between the states X and X´ was omitted for Ca2+ sensors not bound to Ca2+ (X 0Ca and X´0Ca). With this restriction, the fraction of vesicles being in the fast releasing state at rest depends mainly on the ratio between forward-reaction rates and backward-reaction rates from state X 0Ca to state X´1Ca. Instead of omitting convertibility between Ca2+ unbound states, also an alternative attempt to keep vesicles in state X at low [Ca2+]i was tried. The ratio of the conversion rates cs and cf for transitions between X 0Ca and X´0Ca was changed, while leaving the conversion rates between the Ca2+ bound states (X nCa and X´nCa with n = {1; 2; 3; 4; 5}) unchanged. This approach did not succeed, because microscopic reversibility necessitated concomitant changes in the rates of Ca2+ binding or unbinding, so that simulated release could not predict experimental findings anymore (not shown).
Indeed, the empirically obtained kinetic parameters of the model met the criteria mentioned above. The desensitization rate cs was 20-times faster than the resensitization rate cf. Moreover, the omission of convertibility between Ca2+ unbound states (X 0Ca and X´0Ca) prevented massive ‘desensitization’ at steady-state conditions with basal [Ca2+]i of less than 200 nM (not shown). Fusion rates from the ‘desensitized’ states (X´) were 100-times smaller as compared to the fast releasing states (X). To test for the impact of vesicle recruitment, simulations were run either without refilling, or with a refilling rate of 10 ves/ms (Fig. 28B1 and B2, respectively). Parameters were: kon = 1 · 10-8 M-1 s-1, koff = 4000 s-1, a = 1, b = 0.5, L
= 2 · 10-4 s-1, L´ = 2 · 10-6 s-1, f = 40, cf = 10 s-1, cs = 200 s-1, pool size = 4000 ves.
The predicted time course of release (Fig. 28B) showed a biphasic behavior very similar to that observed in experiments (Figs. 12, 16, 17, 21, 22). The separation between the fast and the slow release component was not as pronounced as compared to predictions from the two pool model with intrinsic heterogeneity (Fig. 27B; chapter 4.3), but predicted time courses of release more similar to experimental findings (compare Fig. 28B and 27B with Figs. 12, 16, 17, 21, 22).
The predicted [Ca2+]i dependence of release time constants, peak release rates, and amounts of vesicles released agreed well with experimental results (Fig. 28C - E), even the shallower dependence of peak release rates of the slow component at [Ca2+]i above 15 µM could be reproduced (Fig. 28D). Furthermore, the effect of submaximal release (Fig. 28E) was as pronounced as for the experiments (chapter 3.4; Fig. 23), the contribution of the fast component strongly increased at the expense of slow release (Fig. 28B3, compare to Fig. 21 – 22; Fig. 28E, compare open and closed triangles). However, times-to-peak release rate predicted by this model differed more from experimental results as compared to those predicted by the two pool model with intrinsic heterogeneity (Figs. 28F and 27F, respectively).
The single pool model with intrinsic heterogeneity showed times-to-peak release rate being less dependent on [Ca2+]i than expected.
Simulations without or with refilling (Fig. 28, red and blue data respectively) did not show any significant differences in the kinetic parameters estimated (Fig. 28C - D), thus the analysis method applied could filter refilling from simulated traces satisfyingly.
The same concept was also implemented using the 5-site Ca2+ binding model with fusion only from the fully Ca2+ bound state (X 5Ca in Fig. 24C), instead of the model with fusion from every state of Ca2+ binding (X 0Ca – X 5Ca and X´0Ca – X´5Ca in Fig. 24E). Results from both concepts were similar (not shown), but the latter (Fig. 24E) predicted peak release rates of the slow component, and submaximal release of the fast component more convincingly (not shown). Furthermore, the kinetic scheme shown in Fig. 24E was able to reproduce experimentally obtained low release rates at [Ca2+]i below 1 µM (not shown), whereas the other model (Fig. 24C) could not (Lou et al., 2005).
Fig. 28 Simulated release: The single pool model with intrinsic heterogeneity
Same display as in Fig. 25, but release was simulated using a single pool model with states of intrinsically different rates of vesicle fusion (A, also in Fig. 24D), as shown in the kinetic scheme in Fig. 24E. Parameters were: kon = 1 · 10-8 M-1 s-1, koff = 4000 s-1, a = 1, b = 0.5, L = 2 · 10-4 s-1, L´ = 2 · 10-6 s-1, f = 40, cf = 10 s-1, cs = 200 s-1, pool size = 4000 ves. Refilling was either omitted (B1, and red data), or accounted for with a rate of 10 ves/ms (B2, and blue data). B3 Selected release time courses (continuous traces) as in B1 are plotted together with the corresponding fast release components (dotted traces), as obtained from fits (shown in B1, red traces).
0.1
time to peak release rate (ms)
1 2 4 6 810 2 4 6 8100