Dendritic integration in olfactory bulb granule cells: Thresholds for lateral inhibition and role of active conductances upon simultaneous activation

The inhibitory axonless olfactory bulb granule cells (GCs) form reciprocal dendrodendritic synapses with mitral and tufted cells via large spines, mediating recurrent and lateral inhibition. Rat GC dendrites are excitable by local Na+ spine spikes and global Ca2+- and Na+-spikes. To investigate the transition from local to global signaling without Na+ channel inactivation we performed simultaneous holographic two-photon uncaging in acute brain slices, along with whole-cell recording and dendritic Ca2+ imaging. Less than 10 coactive reciprocal spines were sufficient to generate diverse regional and global signals that also included local dendritic Ca2+- and Na+-spikes (D-spikes). Individual spines could sense the respective signal transitions as increments in Ca2+ entry. Dendritic integration was mostly linear until a few spines below global Na+-spike threshold, where often D-spikes set in. NMDARs strongly contributed to active integration, whereas morphological parameters barely mattered. In summary, thresholds for GC-mediated bulbar lateral inhibition are low.


24
The classical role of dendrites is to receive synaptic or sensory inputs and to conduct the 25 ensuing electrical signals towards the site of action potential (AP) initiation at the axon hillock. 26 While this conduction is passive for smaller membrane depolarizations, recent decades have 27 revealed the presence of active dendritic conductances, most importantly voltage-gated Na + 28 and Ca 2+ channels (Na v s, Ca v s) and NMDA receptors (NMDARs), that can amplify locally 29 suprathreshold electrical signals and thus generate dendritic spikes in many neuron types; 30 dendritic Na v s also facilitate backpropagation of axonal APs into the dendritic tree (Stuart and 31 Spruston, 2015). 32 The dendritic integration of multiple excitatory inputs -as detected at the soma -is Conversely, sublinear integration is performed by e.g. GABAergic cerebellar stellate cell 45 dendrites, that is mainly determined by passive cable properties and reductions in driving force 46 for large dendritic depolarizations (Abrahamsson et al., 2012). In contrast to supralinear 47 integration, this type of integration will favor sparse and/or distributed inputs. 48 Aside from such computations that ultimately convert analogue signals into binary code 49 at the axon initial segment, another functional outcome of dendritic integration is the (possibly 50 graded) release of transmitter from the dendrites themselves. Dendritic transmitter release 51 occurs in many brain regions and is particularly well known from the retina and the olfactory 52 potential of -80 mV and median unitary EPSP amplitudes ≤ 2 mV (Egger et al., 2005;Bywalez et 81 al., 2015), we expected a similar outcome. 82 Another question is whether the local spine spikes contribute to dendritic integration in 83 GCs. Is it conceivable that activation of neighboring spines causes an invasion of the dendritic 84 segment associated with this spine cluster by the spine spike(s)? Could this scenario result in a 85 D-spike? Conventional sequential uncaging (that involves moving the 2D xy-scanner from one 86 uncaging spot to the next) would preclude any observations of such effects because of the 87 inactivation of Na v s during the stimulation sequence. Therefore, we implemented a holographic 88 stimulation system to simultaneously stimulate spines in 3D (Go et al., 2019). This paradigm is 89 also coherent with physiological activation, since the firing of MC/TCs within a glomerular 90 ensemble is precisely locked to the sniff phase and thus can be synchronized within 1 ms 91 (Shusterman et al., 2011). Holographic stimulation also enabled us to target sufficient numbers 92 of inputs, a problem in 2D because of the low GC spine density (1-2 spines per 10 µm, 93 Saghatelyan et al., 2005). 94

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To study synaptic integration within GC apical dendrites we mimicked simultaneous MC/TC 96 inputs to a defined number and arrangement of GC spines in the external plexiform layer by 2P 97 uncaging of DNI-caged glutamate (Palfi et al., 2018;Bywalez et al., 2015) at multiple sites in 3D 98 using a holographic projector (Go et al., 2019). GCs in juvenile rat acute brain slices were patch-99 clamped and filled with Ca 2+ -sensitive dye OGB-1 (100 µM) to record somatic V m and Ca 2+ influx 100 into a stimulated spine and several dendritic locations by 2P Ca 2+ imaging within a 2D plane (see 101

Methods). 102
Subthreshold dendritic integration 103 To characterize subthreshold dendritic integration in terms of somatic V m we first consecutively 104 stimulated single GC spines to obtain single synapse uEPSPs, followed by simultaneous 105 activation of the same spines, resulting in compound cuEPSP. The number of coactivated spines 106 was increased until either AP threshold or the available maximum were reached (10-12 spines, 107 see Methods). Under the given experimental conditions, we succeeded to elicit an AP in 35 out 108 of 111 GCs, 8 of which fired 2 or more APs (e.g. Fig 1a), with an average latency of 41 ± 40 ms 109 (average ± SD, also below). The average single spine uEPSP across all spiking GCs was 1.4 ± 0.8 110 mV. Integration was quantified by plotting the arithmetic sum of the respective single spine 111 uEPSP amplitudes versus the actually measured multi-spine cuEPSP amplitude for increasing 112 numbers of coactivated spines, yielding a sI/O relationship for each GC. (1) For low numbers of coactivated spines, the average sI/O relationship across GCs was linear. 117 (2) In most GCs the cuEPSP amplitude exceeded the arithmetic sum of the single spine uEPSPs 118 beyond a certain stimulation strength by an O/I ratio of at least 1.2 (n = 19 of 29 GCs). We 119 classified these sI/O patterns as supralinear (for further validation of the supralinearity criterion 120 see below and Methods). In this subset of cells, supralinearity was attained at an average of 6.7 121 ± 2.6 stimulated spines and maintained beyond this threshold until AP generation (except for 1 122 cell where the last added uEPSP was very large). 123 Across all GCs that could produce both Ca 2+ -and global APs under our experimental conditions, 155 stimulation of on average 5.5 ± 2.1 spines sufficed for Ca 2+ -spike generation (at an average 156 somatic threshold of -67.8 ± 7.6 mV), whereas activation of 9.0 ± 1.6 spines was required to 157 elicit an AP (at a somatic threshold of -60.2 ± 8.8 mV; both spine number and threshold: p < 158 0.001 Ca 2+ -vs Na + -spike, Fig 2c). We also investigated Ca 2+ -spike thresholds in 25 GCs that did 159 not yet fire a Na + -spike at the maximum number of stimulated spines, which showed no 160 significant difference to those in spiking GCs (5.3 ± 2.3 spines and -72.1 ± 4.3 mV, respectively). 161 Thus, Ca 2+ -spike generation required substantially lower numbers of coactive excitatory inputs 162 than global AP generation. However, when cuEPSPs were aligned to Ca 2+ -spike threshold spine 163 number before averaging (Fig 2d), there was no discontinuous increase in amplitude at 164 threshold (i.e. not significantly different from linear fit to subthreshold regime, see Methods), 165 and also no significant increase in O/I ratio. Thus, the onset of a Ca 2+ -spike as reported by 166 dendritic ∆F/F is not substantially involved in the generation of V m supralinearity. 167 The kinetics of the cuEPSP also did not change significantly at Ca 2+ -spike threshold (Fig  168   2e). Aside from the lack of EPSP boosting and broadening, there was another discrepancy 169 between the Ca 2+ -spike reported here and earlier observations, since the LTS generated by 170 glomerular or external electrical field stimulation (Pinato and Midtgaard, 2005) was an all-or-171 none event that spread evenly throughout the GC dendrite, whereas here dendritic Ca 2+ -spikes 172 attenuated substantially while propagating from the activated spine set along the dendrite 173 towards the soma (Fig 2b). Thus, the Ca 2+ -spike reported here is mostly a regional signal, which 174 also explains the lack of effects on somatic cuEPSP amplitude and kinetics. Beyond the Ca 2+ -175 spike threshold, higher numbers of activated spines resulted in larger dendritic ∆F/F signals 176 with increased extent (Fig 2a,  Transition to supralinear behavior due to dendritic Na + -spikes (D-spikes) 179 Since Ca 2+ -spike onset did not coincide with the transition to supralinear integration, we 180 investigated the transition between linear and supralinear regimes in more detail in the GCs 181 with supralinear sI/Os (n = 18). This transition happened at an average of 6.5 ± 2.7 spines, 182 significantly higher than the spine number required for Ca 2+ -spike onset and lower than the 183 spine numbers for Na + -spikes (Fig 3c). Arrangement of the data relative to the transition spine 184 number (Fig 3d) show a significant discontinuous increase in cuEPSP amplitudes at threshold 185 (i.e. significantly different from linear fit to subthreshold regime, see Methods), and a 186 concomitant increase in mean O/I ratios. The alignment of cuEPSP kinetics to the spine number 187 at the transition in amplitude also revealed highly significant increases of half duration τ_1/2, 188 maximal rate of rise and rise time (Fig 3a, b, e). 189 An increased rate of rise could indicate the occurrence of a dendritic D-spike (Losonczy 190 and Magee, 2006;Zelles et al., 2006). Indeed, in 7 GCs (out of 35 spiking cells) distinct spikelets 191 were detected at the soma, a hallmark of attenuated D-spikes (Fig 3a; Golding and Spruston, 192 1998;Stuart et al., 2007;Llinas and Nicholson, 1971;Smith et al., 2013;Epsztein et al., 2010). 193 However, how can such D-spikes be consistent with the observed increase in overall rise time? 194 Previously, we had observed that single spine uEPSP rise time increased upon blocking of Na v s 195 by wash-in of Tetrodotoxin (TTX; Bywalez et al., 2015). 196 This apparent discrepancy can be explained by a substantial latency of D-spikes. While 197 we could not determine the peak of the D-spike in most GCs, the latency between TPU onset 198 and the peak of spikelets was 21 ± 19 ms (median 10 ms; n = 7 GCs). The delayed occurrence of 199 the D-spike increases the total rise time of the ∆V m signal and also indicates that D-spikes are 200 unlikely to be globalized spine spikes (see Discussion). 201 Finally, we tested whether the observed changes in EPSP kinetics were indeed due to 202 the activation of dendritic Na v s. Application of TTX (0.5 -1 µM) to a set of 7 GCs with 203 supralinear sI/Os significantly reduced both the increases in cuEPSP rise time and maximal rate 204 of rise at supralinearity threshold (Fig 3f, g). Note that below threshold cuEPSP rise times were 205 slowed in TTX, as expected for spine spike-mediated signals (Bywalez et al., 2015). 206 Moreover, there was a significant increase in ∆Ca 2+ both in activated spines and in 207 nearby dendrites associated with the transition to the D-spike in these experiments (see Fig 4d,  208 f), which was also sensitive to Na v blockade (Fig 4g, h). This observation further proves the 209 presence of a Na v -mediated D-spike, since dendritic Na v activation will recruit both low-voltage-210 activated (LVA) and HVA Ca v s and thus can further contribute to Ca 2+ -spikes (Egger et al., 2003;211 Isaacson and Vitten, 2003). 212 In conclusion, the supralinearity observed in the sI/Os of most GCs is due to the onset of a D- threshold in both spine S1 and dendrite. Since for low numbers of coactivated spines (1-4, not 222 aligned to AP threshold, not shown) there was no significant difference in the S1 Ca 2+ signal, we 223 normalized S1 ∆F/F of each GC to its mean of S1 (1-4) to reduce variance (see Methods). 224 From 5 coactive spines below AP threshold onwards, S1 and dendritic ∆Ca 2+ increased in 225 a linear fashion up to AP threshold. This observation seems to imply that an individual GC spine 226 could 'know' about the number of coactive spines from 5 spines below AP threshold upwards, 227 based on the average amount of extra Ca 2+ entry. However, arrangement of the data relative to 228 Ca 2+ -spike threshold (as detected in the dendrite, Fig 4e) revealed that below threshold spine 229 (∆F/F) was by and large constant, whereas at threshold a highly significant increase in ∆Ca 2+ 230 occurred in S1 (by on average ± SD: 1.44 ± 0.80 [0] Ca2+-spike vs [-1/-2] Ca2+-spike , n = 25 spines, Fig  231   4c). Similarly, arrangement of the data relative to the D-spike threshold also revealed a highly 232 significant step-like increase in S1 ∆F/F (by 1. global AP generation lead to yet more substantial, highly significant additional Ca 2+ 4b). Compared to the local spine 237 spike, global APs increased spine Ca 2+ entry by 3.08 ± 1.32 (Fig 4b), thus coincident local inputs 238 and global APs are likely to summate highly supralinearly (see Discussion). 239 From all these observations, we infer that all three types of non-local signals, Ca 2+ -spike, 240 D-spike and global AP, can mediate substantial additional Ca 2+ influx into the spine on top of the 241 contribution of the local spine spike, and that the apparently linear mean increase in spine 242 ∆Ca 2+ (Fig 4b) is actually due to overlapping step-like increases due to Ca 2+ -spike and D-spike 243 onsets at different spine numbers in individual GCs. Thus, a GC spine 'knows' about the general 244 excitation level of the GC, but cannot resolve individual added coactive spines. Similar step-like 245 increases will occur in dendrites close to the activated spine set and also nearby silent spines 246 (not receiving direct inputs), since those were found previously to respond with similar 247 increases in ∆Ca 2+ to non-local spikes as dendrites (Egger et al., 2005;Egger et al., 2003;Egger, 248 2008  For all pharmacological interventions related to dendritic integration mechanisms below 258 the global Na + -spike threshold we stimulated 1, 2, 4, 6, 8, 10 spines before and after wash-in of 259 the drug (see Methods). We blocked Na v s by wash-in of 0.5 -1 µM TTX (n = 12 GCs, Fig 5 top). 260 Amplitudes of single and cuEPSPs were unaltered (Fig 5b). However, the significant increase of 261 average O/I ratios from 6 to 8 coactivated spines in control was blocked in the presence of TTX 262 (Fig 5c). 4 of the 12 GCs fired an AP upon stimulation of 10 spines, which was always abolished 263 by wash-in of TTX. 264 In 7 out of the 12 GCs summation was supralinear, and as shown above (Fig 3), supralinear 265 integration is associated with the occurrence of D-spikes. Indeed, the supralinear increase in V m 266 at threshold was significantly reduced in the presence of TTX (Fig S1c). 267 Across all 12 GCs the S1 spine Ca 2+ signal and dendritic Ca 2+ signals were significantly and 268 similarly reduced in TTX across all numbers of activated spines (Fig 5d; spine: 0.89 ± 0.54 of 269 control, p<0.001; dendrite: 0.75 ± 0.28 of control, p=0.014). Moreover, as shown above, the 270 stepwise increase in spine ∆Ca 2+ at D-spike threshold (Fig 4d) was abolished in TTX (Fig 4g, h). investigated their contribution to GC multi-spine signals in n = 11 GCs. Wash-in of 10 µM 305 mibefradil did not alter cuEPSPs upon activation of up to 8 spines. Only for 10 spines cuEPSPs 306 were slightly but significantly reduced by on average 0.8 ± 1.4 mV (p=0.01, Fig 6b). Under 307 control conditions activation of 10 spines also lead to supralinear V m summation (Fig 6c), which 308 was reduced by blockade of T-type Ca v s. CuEPSP kinetics were unaltered (data not shown). In 309 one experiment an AP was generated upon stimulation of 10 spines under control conditions, 310 which was abolished in the presence of mibefradil. 311 Ca 2+ signals in spine S1 and dendrite were significantly reduced for all spine numbers 312 (spine: average ± SD 0.74 ± 0.31 of control, p < 0.001; dendrite: 0.74 ± 0.38 of control, p=0.003, 313 Fig 6d). However, mibefradil did not entirely block dendritic ∆Ca 2+ upon stimulation of 4 spines 314 and beyond (remaining signal 16 ± 9 % ∆F/F at 10 coactivated spines). 315 To identify the source for the remaining dendritic ΔF/F TPU , we additionally washed in 316 100 µM Cd 2+ to block HVA Ca v s in 4 cells (Isaacson and Vitten, 2003). Cd 2+ effectively abolished 317 the dendritic Ca 2+ signal and substantially further reduced the S1 spine Ca 2+ signal to 0.52 ± 0.26 318 of mibefradil or 0.41 ± 0.22 of control (n = 8 spines), leaving the cuEPSP unaltered (Fig 6 e-g). 319 We conclude that T-type Ca v s substantially contribute to Ca 2+ entry into the spine and dendrite 320 during dendritic integration and mediate the onset of the Ca 2+ -spike, but that HVA Ca v s also 321 contribute, most likely involving additional Ca 2+ entry via L-type Ca v s or other channel types that 322 are activated by D-spikes. Both LVA and HVA Ca v s did not substantially influence somatic ∆V m in 323 our stimulation paradigm. 324 Limited influence of morphology on non-local spike generation 325 To determine whether the spacing of stimulated spines, the location of the stimulated spine set 326 on the dendrite relative to the MCL, the average spine neck length and other morphological 327 parameters influenced the efficacy of activated subsets of spines to elicit non-local spiking, we 328 analyzed the positions of the stimulated spines relative to the GCs' dendritic tree as 329 reconstructed in 3D (Fig 7, see Methods). Table S1 shows that only 2 out of 9 morphological 330 parameters correlated with Ca 2+ -spike threshold in terms of coactivated spine numbers, 331 whereas both D-spike and global Na + -spike initiation threshold spine numbers did not correlate 332 significantly with any morphological parameter, with a weak trend for a positive correlation 333 between spine distribution and global Na + -spike initiation (Fig 7c). Ca 2+ -spike generation was 334 facilitated by close packing of spines that were located on the same and/or a rather low # of 335 branches (Fig 7 c, d). 336 Within the experimentally accessible range of parameters, individual spine sets have 337 thus by and large an equal impact on local and global Na + -spike generation, independent from 338 GC morphology or their relative location on the dendritic tree, which indicates a highly compact 339 GC dendrite and strong isolation of the spines. For Ca 2+ -spike generation clustered spines are 340 more efficient than distributed inputs. 341

342
High excitability of GC apical dendrites 343 Upon holographic simultaneous multi-spine stimulation, GC dendrites can generate Ca 2+ -, D-344 and Na + -spikes already at rather low numbers of coactivated dendrodendritic inputs (Ca 2+ -spike 345 ~ 5 inputs, D-spike ~ 7 inputs, global Na + -spike ≥ 9 inputs). Thus, GC dendrites are highly 346 excitable, also in comparison to cortical PCs whose AP threshold required a similar number of 347 coactive spines using the very same holographic system (10 ± 1, n = 7 in 4 PCs, Go et al. The somatic AP threshold (∼ -60 mV) was substantially below Na v activation threshold, 361 indicating a distal AP initiation zone. The threshold spine number reported here is a lower limit, 362 since in ∼2/3 of GCs in our sample full-blown APs at the soma could not yet be elicited at the 363 maximal number of 10 -12 co-stimulated spines (with the available laser power as bottle neck). 364 Morphological parameters did not influence AP thresholds, indicating that the superficial GC's 365 dendritic tree is electrotonically compact (see also below). 366 The low threshold spine number seems to match previous observations that 367 uniglomerular stimulation can already fire GCs (Egger, 2008 Dendritic spiking: D-spike and localized Ca 2+ -spike 379 A substantial presence of dendritic Na v channels in GCs was already indicated by a 380 backpropagation study (Egger et al., 2003) and recently demonstrated more directly (Nunes 381 and Kuner, 2018). Na + spikelets have not been reported from juvenile rat OB GCs so far; they 382 probably emerged here due to clustered stimulation. In about 2/3 of GCs in our sample we 383 detected D-spikes correlated with the onset of supralinear integration at the soma either as 384 distinct spikelets or, if these were masked by electrotonic filtering, by characteristic step-like 385 increases in the cuEPSP rate of rise, rise time, decay and spine ΔF/F (Fig 3). under conditions of clustered spine activation, which is further supported by the lack of a 392 correlation between spatial clustering and D-spike or Na + -spike threshold spine numbers. 393 Rather, EPSPs are strongly attenuated and also temporally filtered across the spine neck, 394 resulting in slowed integration (Aghvami and Egger, unpublished simulations); moreover, A-395 type K + currents are known to delay GC firing (Schoppa and Westbrook, 1999) and thus also 396 possibly involved in the yet longer latency of global Na + -APs at threshold observed here (∼40 397 ms). Initiation of D-spikes most likely happens at dendritic Na v hot-spots (Nunes and Kuner,398 2018), whereas the existence of a dedicated global Na + -AP initiation zone in GC apical dendrites 399 seems probable, with its precise location a matter of speculation at this point (but see Pressler 400 and Strowbridge, 2019). 401 All GCs in our sample featured Ca 2+ -spikes (in terms of dendritic Ca 2+ entry), which at 402 threshold were rather regional, decreasing strongly towards the soma. Although Ca v densities 403 are apparently lower in the proximal apical dendrite (Egger et al., 2003), Ca 2+ -spikes evoked by 404 glomerular stimulation occurred in an all-or-none fashion throughout the entire dendritic tree 405 with a concomitant increase and broadening of somatic EPSPs that were not observed here 406 (Egger et al., 2005). We conclude that the main initiation zone for global Ca 2+ -spikes is probably 407 not located in the distal apical dendritic tree (see also Pressler and Strowbridge, 2019). Thus, in 408 contrast to the global Ca 2+ -spike upon glomerular activation, input to rather densely packed 409 spines might provide a substrate for more local lateral inhibition as suggested earlier (Woolf et  GCs, EPSP half durations were > 50 ms at higher numbers of coactive spines, thus dendritic 433 Ca 2+ -and Na + -spikes are closely intertwined with NMDA-spikes. 434 As a note of caution, holographic uncaging might overemphasize the role of NMDARs, 435 since (1) APV blocks TPU-evoked spine ∆F/F slightly more than synaptic ∆F/F (to 65% vs 50% of 436 control, Bywalez et al., 2015) and (2)                    Combined two-photon imaging and multi-site uncaging in 3D 707 Imaging and uncaging were performed on a Femto-2D-uncage microscope (Femtonics). The 708 microscope was equipped with a 60× water-immersion objective used for patching (NA 1.0 W, 709 NIR Apo, Nikon) and a 20× water-immersion objective used for two-photon (2P) imaging and 710 uncaging (NA 1.0, WPlan-Apo, Zeiss). Green fluorescence was collected in epifluorescence 711 mode. The microscope was controlled by MES v4.5.613 software (Femtonics). Two tunable, 712 verdi-pumped Ti:Sa lasers (Chameleon Ultra I and II, respectively, Coherent) were used in 713 parallel, set to 835 nm for excitation of OGB-1 and to 750 nm for uncaging of DNI-caged 714 glutamate (DNI, Femtonics; Chiovini et al., 2014). DNI was used in 0.6 mM concentration in a 715 closed perfusion circuit with a total volume of 12 ml and was washed in for at least 10 min 716 before starting measurements. To visualize the spines and for Ca 2+ imaging we waited at least 717 20 min for the dyes to diffuse into the dendrite before starting measurements. 718 Imaging and uncaging beam were decoupled before the entrance of the galvanometer-719 based 2D scanning microscope using a polarizing beam splitter to relay the uncaging beam to a 720 spatial light modulator (SLM X10468-03, Hamamatsu). Using our custom-written Matlab based 721 SLM software, we next positioned multiple uncaging spots/foci in 3D at a distance of 0.5 μm 722 from the spine heads. Our system allowed for a maximum number of 12 spots in a volume of 723 Imaging of uncaging-evoked Ca 2+ signals in selected spines and dendritic positions within one 734 2D plane (see below) was carried out as described earlier (Bywalez et al., 2015). During 735 simultaneous Ca 2+ imaging and photostimulation, imaging was started 700 ms before the 736 uncaging stimulus. During uncaging the scanning mirrors were fixed. 737 In each experiment, single spines were consecutively activated and somatic uncaging 738 EPSPs (uEPSPs) were recorded for each spine separately. Next, successively increasing # of 739 these spines were simultaneously activated and somatic compound uEPSPs (cuEPSPs) were 740 recorded until the GC fired an AP or, in the experiments with focus on subthreshold integration, 741 until a maximum # of 10 activated spines was reached. A subset of spines and dendritic 742 locations located within the same focal plane were chosen for 2P line-scanning to gather Ca 2+ 743 imaging data. At least one spine, termed S1 in the following, was always located in this imaging 744 plane to gather complete data from activation of a single spine to activation of n spines. Due to 745 the spine density being higher in distal regions and Ca 2+ imaging being restricted to one focal 746 plane, most dendritic measurements in a distance from the center of the stimulated spine set 747 (Fig 1b) were proximal to the stimulation site. The sequence of the successively more activated 748 spines with respect to their position on the dendritic tree was randomly chosen. However, the 749 low spine density (see Introduction) and the restriction to a volume of 70x70x70 µm 3 mostly 750 determined the choice of activated spines. Both single spine stimulations and the different 751 combinations of multi-site uncaging were, if possible, performed at least twice and recordings 752 were averaged for analysis. 753 Since such experiments were performed with up to 40 different stimulation conditions, we 754 decided to increase the spine # by increments of two for some experiments (in particular for 755 pharmacology) in order to limit the experiment duration and thus to ensure a good recording 756 quality. 757

Data analysis
758 Changes in Ca 2+ indicator fluorescence were measured relative to the resting fluorescence F 0 in 759 terms of ΔF/F as described previously (Egger et al., 2005). Electrophysiological and Ca 2+ imaging 760 data were analyzed using custom macros written in IGOR Pro (Wavemetrics). Traces 761 contaminated by spontaneous activity were discarded. As described above, multiple (2 or 762 more) recordings of the same stimulation type were averaged and smoothed (box smoothing) 763 for analysis. uEPSP and (ΔF/F) TPU rise times were analyzed in terms of the interval between 20% 764 and 80% of total uEPSP/(ΔF/F) TPU amplitude; uEPSPs and (ΔF/F) TPU half times of decay (τ_1/2) 765 were analyzed in terms of the interval between the peak and 50% of the total EPSP or (ΔF/F) TPU 766 amplitude. The uEPSP maximum rate of rise was determined by the peak of the first derivative 767 of the uEPSP rising phase. The AP threshold was detected via the zero point of the 2 nd 768 derivative of the AP rising phase. 769 Integration was quantified by plotting the arithmetic sum of the respective single spine uEPSP 770 amplitudes versus the actually measured multi-spine cuEPSP amplitude for increasing numbers 771 of coactivated spines, yielding a subthreshold input-output relationship (sI/O; Tran-Van-Minh et 772 spine ∆F/F amplitude for local, unitary activation. Because of the undersampling problem, we 802 tested for up to which spine number there was no significant increase in ∆F/F, which was 4 803 spines (Friedman repeated measures ANOVA on ranks: Χ 2 F (3)=4.802, p=0.187). Therefore, we 804 averaged S1 (∆F/F) for (co)stimulations of 1, 2, 3, 4 spines and used the mean as basal unitary 805 ∆F/F for normalization. Thus, undersampling could be compensated for by this means. 806 Since dendritic (ΔF/F) TPU was usually detectable only in stimulations above 4 spines in 807 most cases, (ΔF/F) TPU in the dendrite was normalized to the mean of all stimulations below 808 global Na + AP threshold, or the average size of the dendritic Ca 2+ -spike mediated Ca 2+ -signal. 809 Since each GC required its individual spine number to reach the threshold for the non-810 local events Ca 2+ -spike, D-spike and global Na + -spike (for the respective pattern of stimulation), 811 we aligned the data in relation to the onset of the non-local event (e.g. Fig 2d, e relative to Ca 2+ -812 spike). Such realignments allow to reveal effects across the sampled cells that otherwise would 813 be smeared out because of cell-specific thresholds, such as recruitment of active conductances 814 near thresholds (Losonczy and Magee, 2006). 815 Morphological analysis 816 GC apical dendrites were reconstructed from 2P fluorescence z-stacks gathered at the end of 817 each experiment, using Neurolucida (MBF Bioscience). Distances were measured along the 818 dendrite. Mean distances of a spine set were analyzed in terms of the average distance of all 819 stimulated spines from e.g. the MCL. The distribution of a stimulated spine set across the 820 dendrite was analyzed in terms of the mean distance of each spine from all other stimulated 821 spines along the dendrite. Spine neck lengths were estimated as described before (Bywalez et 822 al., 2015). 823

824
Statistical tests were performed in Sigmaplot 13.0 (Systat Software, Inc) or on vassarstats.net. 825 To assess statistical significance levels across spine numbers or threshold V m values for Ca 2+ -826 spike versus global Na + -spike (Fig 2c), data sets were compared using paired t-tests for 827 dependent data sets. Not normally distributed data sets (Shapiro-Wilk Normality Test) were 828 compared using Wilcoxon signed rank tests. To assess statistically significant differences from 829 linear summation in sI/O relation data sets, the distribution of ratios of the measured uEPSP 830 amplitudes/arithmetic sums (O/I ratio) was tested against a hypothesized population 831 mean/median of 1.0 (corresponding to linear summation), using one-sample t-tests or one-832 sample signed rank tests for not normally distributed data. To assess variation in repeated 833 measure data sets (Fig 3c) repeated measures ANOVA together with all pairwise multiple 834 comparison procedure (Holm-Sidak-method) was performed. For pharmacology experiments 835 (e.g. Fig 5) repeated measures two-way ANOVA together with all pairwise multiple comparison 836 procedure (Holm-Sidak-method) was performed. For statistical analysis of dendritic (ΔF/F) TPU 837 before and after pharmacological treatment just stimulations of ≥ 4 spines were taken into 838 account, since for lower numbers of spines usually no signal was detectable under control 839 conditions. 840 Due to the increase of spine numbers by increments of 2 in some experiments, averaged 841 data points for a given spine number do not contain the same n of individual measurements 842 across different spine numbers. Even more so when the data were aligned relative to individual 843 spike thresholds (e.g. alignment relative to Ca 2+ -spike threshold in Fig 2d, e), since not all 844 experiments contained data points for the more remote spine numbers +2 or -3. In addition, in 845 experiments with data gaps just before a global spike threshold at spine number x, it is not 846 possible to know whether the spike threshold could have already been reached at x-1 spines 847 (e.g. alignment relative to Ca 2+ -spike in Fig 2 d, e). We accounted for this uncertainty by 848 averaging the data in the continuous experiments for -2 and -1 and used these averaged data 849 for paired comparison of parameters below and at threshold (non-parametric Wilcoxon test).  To assess statistical significance for linear increase and decrease (Table S1) we performed a 856 linear regression analysis. Given r 2 values are adjusted r 2 values. 857