Comprehensive Estimates of Potential Synaptic Connections in Local

Research Articles: Systems/Circuits Comprehensive estimates of potential synaptic connections in local circuits of the rodent hippocampal formation by axonal-dendritic overlap https://doi.org/10.1523/JNEUROSCI.1193-20.2020

Cite as: J. Neurosci 2020; 10.1523/JNEUROSCI.1193-20.2020 Received: 14 May 2020 Revised: 19 October 2020 Accepted: 13 December 2020

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1 Comprehensive estimates of potential synaptic connections in local circuits of

2 the rodent hippocampal formation by axonal-dendritic overlap

3 Running title: Quantifying the hippocampus neuron connectivity

5 Carolina Tecuatl, Diek W. Wheeler, Nate Sutton, Giorgio A. Ascoli*

6 Center for Neural Informatics, Structures, & Plasticity, Krasnow Institute for Advanced

7 Study; and Bioengineering Department, Volgenau School of Engineering; George

8 Mason University, Fairfax, VA 22030-4444, USA.

9 *Correspondence: [email protected]

11 Keywords: CA1, CA3, dentate gyrus, entorhinal cortex, interneuron, network.

12 Number of pages: 74

13 Number of figures: 8

14 Number of tables: 1

15 Number of Extended Data files: 21

16 Number of words in the abstract: 250

17 Number of words in the introduction: 650

18 Number of words in the discussion: 1788

19 Conflict of interest: The authors declare no competing financial interests

21 Acknowledgments

22 The authors are grateful to Keivan Moradi, Siva Venkadesh, Jeffrey D. Kopsick, and

23 Nikhil Koneru for their help and feedback. Carolina Tecuatl thanks the Consejo Nacional

24 de Ciencia y Tecnología, México for providing fellowship 253060 allowing this project to

25 start during her PhD training. This work was supported in part by NIH grants

26 R01NS39600 and U01MH114829.

28 Abstract

29 A quantitative description of the hippocampal formation synaptic architecture is

30 essential for understanding the neural mechanisms of episodic memory. Yet the existing

31 knowledge of connectivity statistics between different neuron types in the rodent

32 hippocampus only captures a mere 5% of this circuitry. We present a systematic

33 pipeline to produce first-approximation estimates for most of the missing information.

34 Leveraging the Hippocampome.org knowledge base, we derive local connection

35 parameters between distinct pairs of morphologically identified neuron types based on

36 their axonal-dendritic overlap within every layer and subregion of the hippocampal

37 formation. Specifically, we adapt modern image analysis technology to determine the

38 parcel-specific neurite lengths of every neuron type from representative morphological

39 reconstructions obtained from either sex. We then compute the average number of

40 synapses per neuron pair using relevant anatomical volumes from the mouse brain

41 atlas and ultrastructurally established interaction distances. Hence, we estimate

42 connection probabilities and number of contacts for over 1,900 neuron type pairs,

43 increasing the available quantitative assessments more than 11-fold. Connectivity

44 statistics thus remain unknown for only a minority of potential synapses in the

45 hippocampal formation, including those involving long-range (23%) or perisomatic (6%)

46 connections and neuron types without morphological tracings (7%). The described

47 approach also yields approximate measurements of synaptic distances from the soma

48 along the dendritic and axonal paths, which may affect signal attenuation and delay.

49 Overall, this dataset fills a substantial gap in quantitatively describing hippocampal

50 circuits and provides useful model specifications for biologically realistic neural network

51 simulations, until further direct experimental data become available.

53 Significance statement

54 The hippocampal formation is a crucial functional substrate for episodic memory and

55 spatial representation. Characterizing the complex neuron type circuit of this brain

56 region is thus important to understand the cellular mechanisms of learning and

57 navigation. Here we present the first numerical estimates of connection probabilities,

58 numbers of contacts per connected pair, and synaptic distances from the soma along

59 the axonal and dendritic paths, for more than 1,900 distinct neuron type pairs

60 throughout the dentate gyrus, CA3, CA2, CA1, subiculum, and entorhinal cortex. This

61 comprehensive dataset, publicly released online at Hippocampome.org, constitutes an

62 unprecedented quantification of the majority of the local synaptic circuit for a prominent

63 mammalian neural system and provides an essential foundation for data-driven,

64 anatomically realistic neural network models.

66 Introduction

67 The hippocampal formation is a group of cytoarchitectonically distinct adjoining

68 subregions linked by a largely unidirectional neuronal pathway (Andersen et al. 1971):

69 the dentate gyrus (DG), cornu ammonis (CA3, CA2, and CA1), subiculum (Sub), and

70 entorhinal cortex (EC). Like other cortical areas, the hippocampus is characterized by a

71 high degree of neuronal interconnectivity and considerable cellular diversity. A single

72 neuron is typically targeted by thousands of afferents from multiple neuron types,

73 whereas the efferent output of an individual neuron contacts thousands of postsynaptic

74 neurons of multiple types (Ali et al. 1999; Halasy et al. 1996; van Strien et al. 2009).

75 Proper hippocampus functioning requires each subregion to integrate the received

76 information prior to propagating it to adjacent areas (Freund & Katona 2007; Nilssen et

77 al. 2018; Pelkey et al. 2017). The local circuits of all hippocampal subregions are

78 comprised of a glutamatergic principal neuron type and a wide range of largely

79 GABAergic interneurons, which regulate neural activity mainly by feedforward and

80 feedback inhibition (Quattrocolo & Maccaferri 2014; Schmidt-Hieber et al. 2017; Sohal

81 et al. 2009). Many interneurons can subserve both mechanisms, thus providing a

82 functional link between afferent input patterns and resulting outputs (Bartos et al. 2010;

83 Chamberland et al. 2010; Tyan et al. 2014). Neuron types exhibit distinct axonal and

84 dendritic laminar distributions, defining specific connectivity patterns (Booker & Vida

85 2018; Freund & Buzsáki 1996; Klausberger & Somogyi 2008). For example, CA1 O-LM

86 interneurons innervate only the apical tuft of pyramidal cells in stratum lacunosum-

87 moleculare (SLM) and receive inputs only in stratum oriens (SO) (Losonczy et al. 2002;

88 McBain et al. 1994; Zemankovics et al. 2010).

89 Local interneuron circuits can generate recurrent activity patterns and transmit these

90 rhythms onto principal cells for broader network propagation (Gulyás et al. 2010;

91 Quilichini et al. 2010; Tukker et al. 2007). These oscillations underlie mechanisms of

92 spatial navigation (Colgin 2016; Ekstrom et al. 2003) and memory (Bauer et al. 2007;

93 Jensen et al. 2007), implicating various interneuron types in different roles (Csicsvari et

94 al. 2003; Szabó et al. 2010). Several extrinsic afferent pathways from the brainstem and

95 forebrain nuclei also provide neuron type-selective modulation (Halasy & Somogyi

96 1993; Kinnavane et al. 2018; Witter et al. 2017), powerfully shaping any subsequent

97 output.

98 The online knowledge base Hippocampome.org identifies more than 120 neuron types

99 throughout the hippocampal formation (Wheeler et al. 2015) based on axonal and

100 dendritic morphology, intrinsic and synaptic electrophysiology (Komendantov et al.

101 2019; Venkadesh et al. 2019), and molecular expression (White et al. 2019). This public

102 resource links each property to available experimental evidence annotated from the

103 peer-reviewed literature (Hamilton et al. 2017).

104 Despite the wealth of knowledge regarding the rodent hippocampus, quantitative

105 estimates of connection probabilities among specific neuron types are extremely

106 sparse, only accounting for 5% of the estimated 3,120 pairs of potentially connected

107 neuron types (“potential connections”). Local circuits make up more than three-quarters

108 of all potential connections in the hippocampal formation (Rees et al. 2016). Although

109 much of these data can be derived in principle from electron microscopy, the

110 painstaking amount of time, effort, and resources required for that approach has so far

111 limited the connectivity quantification to a minor proportion of the circuit (Megıaś et al.

112 2001; Mishchenko et al. 2010; Schmidt et al. 2017).

113 Here we present a data-driven pipeline to estimate most local connection probabilities

114 among Hippocampome.org neuron types. Using a custom image processing approach,

115 we quantify the layer-specific distributions of axonal and dendritic lengths for over 200

116 representative neuron morphology reconstructions from all subregions of the

117 hippocampal formation. From these data, in conjunction with available volumes for each

118 anatomical parcel and ultrastructural reports of synaptic interaction distances, we

119 estimate the probability of spatial overlap between potential presynaptic axons and

120 postsynaptic dendrites. Hence, we calculate the average number of synapses for almost

121 2,000 pairs of neuron types (Figure 1) as well as their mean synaptic distances from the

122 soma along the axonal and dendritic paths.

123

124 Material and Methods

125 Data sources

126 We analyzed one to five reconstructed morphologies per identified neuron type in

127 Hippocampome.org (see Figure 2A for representative examples): 35 reconstructions for

128 18 neuron types in DG, 35 for 22 neuron types in CA3, 8 for 5 neuron types in CA2, 85

129 for 40 neuron types in CA1, 6 for 3 neuron types in Sub, and 56 for 27 neuron types in

130 EC. Each two-dimensional reconstruction corresponds to a published neuronal tracing

131 image in the peer-reviewed literature (detailed in Extended Data Figures 2-1 through 2-

132 6), with sometimes multiple reconstructions coming from the same publication. We

133 selected the reconstructions based on five inclusion criteria: (i) the neuron type was

134 present in Hippocampome.org v1.7 in order to obtain maximum coverage of the

135 knowledge base; (ii) the image contained a calibration scale bar and clear demarcations

136 of relevant layer and subregional boundaries; (iii) the traced dendritic and axonal

137 distributions as well as soma location corresponded to the textual description in the

138 source publication; (iv) the reconstruction included both axons and dendrites, except for

139 perisomatic-targeting neuron types (basket and axo-axonic cells), for which only

140 dendrites were considered; and (v) axons and dendrites could be unambiguously

141 discerned and ascribed to a single neuron type (for this reason we excluded

142 reconstructions from paired recordings).

143 It is important to note that the 225 utilized reconstructions come from 96 different

144 publications encompassing a broad variety of experimental preparations (Extended

145 Data Figure 2-7), including differences in animal species, strain, age, and sex (both

146 females and males were used), as well as histological details, such as slice orientation,

147 section thickness, recording technique, and labeling method. This heterogeneity of data

148 sources requires adequate data normalization strategies, described in the next section,

149 and extreme caution in interpreting the results (see Discussion).

150

151 Axonal and dendritic lengths

152 In order to extract parcel-specific neurite lengths, we isolated the axonal and dendritic

153 reconstructions of each neuron type according to the different layers of each subregion

154 (Figure 2B). Starting from the original unmodified image, we manually segregated the

155 axons and dendrites within each anatomical parcel using the GNU Image Manipulation

156 Program (GIMP 2.8; gimp.org), and separately saved the axonal and dendritic domains

157 in distinct files for every layer and subregion. Next, we dissected each image into

158 different channels for white (background) and non-white (neurites) pixels with a custom-

159 made MATLAB algorithm (github.com/Hippocampome-Org/QuantifyNeurites), which

160 returns the neurite pixel count. We carefully inspected each separate image channel to

161 confirm visually that the algorithm isolated the appropriate signals. The length in pixels

162 of the calibration scale bar was measured with the open-source program Plot Digitizer

163 (plotdigitizer.sourceforge.net).

164 The conversion from pixel numbers to parcel-specific length requires three logical steps.

165 The first accounts for the non-uniform tracing widths across images: often neuronal

166 arbors (especially dendrites) are reconstructed with variable branch thickness ranging

167 from single to multiple pixels. To solve this issue, we randomly selected three locations

168 for every neuron image, parcel, and neurite domain, measured the branch width in

169 pixels at each location, and averaged the three values. The second logical step requires

170 calculating the pixel length in physical units, which is simply the nominal calibration

171 scale-bar value (in μm) divided by the measured bar length in pixels. Consequently, the

172 parcel-specific neurite length is obtained by multiplying the pixel count for that neurite in

173 the given parcel by the physical pixel length and dividing the result by the average

174 branch width in pixels. The final step corrects for the artifactual flattening of three-

175 dimensional arbors into two-dimensional images by combining the parcel-specific

176 lengths p with the reported section thickness s using Pythagoras’ formula

177 = + , (1)

178 where represents the final corrected length.

179 The majority of the available reconstructions (78%) were from rat, and most of those

180 (56% of the rat data) came from adult (≥1 month old) animals. For several neuron types,

181 however, tracing data were only available for young adult (defined as 13 - 30 days old,

182 consistent with Hippocampome.org) rats (34%) or from mice (21%). Normalizing all

183 lengths to the adult rat setting requires two scaling factors: one for young to adult, and

184 another for mouse to rat. Seminal studies have measured the differences in arbor size

185 between adult and juvenile rats in the hippocampus and elsewhere: Bannister &

186 Larkman (1995) report a length ratio of 1.10 for CA1 pyramidal cells, but note that this

187 may be an underestimate due to non-uniform histological processing, and point to

188 parallel studies suggesting a ratio of 1.24 for the same neuron type (Ishizuka et al.

189 1995). Also investigating CA1 pyramidal cells, but solely focusing on the basal

190 dendrites, Juarez et al. (2008) provide lengths corresponding to a ratio of 1.30. The

191 same authors also include data for principal cells in the prefrontal cortex (adult/juvenile

192 ratio of 1.14) as well as GABAergic neurons from the nucleus accumbens (ratio of 1.20).

193 Taking this evidence into consideration, we chose to correct the length measurements

194 () from young animals by the multiplicative factor of 1.20. In order to normalize mouse

195 length values to rats, we used the cubic root of the parcel-specific volume scaling factor,

196 which is described at the end of the next section (see below and cf. Extended Data

197 Figure 2-8).

198

199 Average number of synapses per neuron pair

200 We calculate the average number of synapses per pair of presynaptic and postsynaptic

201 neurons, Ns, from their parcel-specific axonal and dendritic lengths by separately

202 estimating the numbers, Nsx, of axonal-dendritic overlaps in each parcel x (Amirikian

203 2005; DeFelipe 2015). For any x, the value Nsx can be derived as the product of three

204 factors: the probability that a presynaptic and postsynaptic elements occur within a

205 given interaction distance r, the number of presynaptic elements (axonal boutons) in the

206 given anatomical parcel, and the number of postsynaptic elements (dendritic spines or

207 shafts) in the same parcel. The first factor is given by the ratio between the volume of

208 the interaction sphere within which the two elements must be and the volume of the

209 entire parcel, Vx. The second factor is given by the presynaptic axonal length in parcel

210 x, Lax, divided by the average distance between consecutive presynaptic boutons, bd.

211 The third factor is given by the postsynaptic dendritic length in x, Ldx, divided by the

212 distance between postsynaptic elements, sd:

213 = ∗ ∗ . (2)

214 The total count of synapses per directed neuron pair, Ns, is just the sum of the numbers

215 per parcel, Nsx, over all parcels.

216 The above calculation requires a series of realistic assumptions regarding the needed

217 parameters. We obtained the average dendritic distance between postsynaptic

218 elements, sd, and axonal distance between presynaptic elements, bd, from available

219 ultrastructural measurements in the rodent hippocampus (1.09 μm and 6.2 μm,

220 respectively: Extended Data Figure 2-9 and 2-10). Moreover, we set the interaction

221 radius r (Figure 2C) to 2 μm, corresponding to a sphere with 4 μm diameter, according

222 to the sum of two components: a 2.5 μm assessment for bouton size and synaptic

223 spillover (Coddington et al. 2013) plus a 1.5 μm estimate similarly ascribed to dendritic

224 spine reach (Papa & Segal 1996) and aspiny dendrite thickness (Mishchenko et al.

225 2010; Stepanyants et al. 2004). For lack of more specific information, these parametric

226 estimates were applied equally to all pairings of neuron types evaluated.

227 Stereological investigations offer suitable estimates for a subset of the required

228 anatomical parcel volumes, Vx, for the adult rat, namely all layers of DG, CA3, and CA1

229 (Extended Data Figure 2-8). Overall volumes (though not laminar subdivisions) are also

230 available for CA2 and for the whole hippocampal-subicular complex, but data are

231 missing altogether for the subiculum proper and all layers of the entorhinal cortex

232 (Kamsu et al. 2013). To fill in the required missing values, we leverage the Allen

233 Reference Atlas, which provides volumes for each hippocampal parcel in the adult

234 mouse brain (Erö et al. 2018). Specifically, we calculate a rat/mouse ratio for the overall

235 CA2 volume and apply that to each CA2 layer; we then compute by subtraction the rat

236 subiculum volume and use it to calculate a rat/mouse subiculum ratio to derive rat

237 estimates for each subicular layer. Lastly, we utilize the rat/mouse volumetric ratio

238 computed over the entire hippocampal formation to estimate the volumes for all

239 entorhinal layers (Extended Data Figure 2-8).

240

241 Number of contacts per connected pair, convex hulls, and connection probabilities

242 The number Ns, defined above, can be also construed as the expected number of

243 contacts (in parcel x) per connected neuron pair, Ncx, multiplied by the connection

244 probability, px, between the presynaptic and postsynaptic neurons in parcel x. The first

245 of these values, Ncx, can be derived using a similar logic as harnessed in the

246 formulation of Nx, except that the relative position of the presynaptic and postsynaptic

247 elements is now constrained by the extant contact between their respective neurons. In

248 other words, the space available to form synapses between connected neurons is not

249 the entire volume of parcel x, but only the volume of intersection, or overlap, Vo,

250 between the presynaptic axons and postsynaptic dendrites in that parcel. Thus, if a

251 given pair of neurons forms at least a single synaptic contact, the expected number of

252 additional contacts for that pair is:

253 = ∗ ∗ , (3)

254 where the volumetric ratio between the sphere defined by the radius of interaction r and

255 Vo represents the chance of encounter for any given pair of axonal boutons and

256 dendritic spines or shafts, and Lax/bd and Ldx/sd correspond, respectively, to the number

257 of axonal boutons and dendritic spines or shafts in parcel x. The volume of intersection,

258 Vo, is given by:

259 = ( + ), (4)

260 where Vdx and Vax are the sub-volumes of parcel x invaded by the postsynaptic dendrite

261 and presynaptic axon, respectively, and is the overlap factor, which varies from at

262 complete overlap to zero at a single point of synaptic contact. On average, the volume

263 of overlap in parcel x is therefore given by:

264 = ( + ). (5)

265 To measure Vdx and Vax, we extract the convex hull areas in parcel x from the isolated

266 axonal and dendritic images for each reconstruction, utilizing the Shape Analysis plug-in

267 (Wagner & Lipinski 2013) of the open-source software Fiji. Then we convert the area

268 measurements from pixel units to μm2 and multiply the resultant values by the reported

269 slice thicknesses.

270 The overall number of contacts per connected pair is the sum of the contacts in each

271 parcel augmented by one, reflecting the initial assumption that the neuron pair is

272 connected:

273 = + ∑ , (6)

274 where the symbol Σx represents the sum over all parcels.

275 The connection probability for a pair of neuron types in parcel x is obtained by dividing

276 the average number of synapses per neuron pair by the number of contacts per

277 connected pair in the same parcel:

278 = = . (7)

279 The overall probability of connection for a pair of presynaptic and postsynaptic neurons

280 in any parcel is given by the sum of inclusive events:

281 = −(−), (8)

282 where the symbol x represents the product over all parcels.

283

284 Axonal and dendritic path distances

285 In order to estimate synaptic path distance from the soma along the axons and

286 dendrites, we used the Simple Neurite Tracer plug-in (Longair et al. 2011) of Fiji.

287 Starting from the soma, we traced up to 5 distinct dendritic and axonal paths for each

288 neuron and parcel. We then converted the length measurements from default pixel units

289 to microns using the pixel length extracted from the calibration scale bar as described

290 above. For a neurite ending in a parcel, the ending point constitutes the maximum path

291 distance for that parcel. For neurites crossing into a subsequent parcel, the crossing

292 point corresponds to the maximum path distance. Similarly, for neurites crossing from a

293 previous parcel, the crossing point constitutes the minimum path distance. For somatic

294 parcels, the minimum distance is zero. In all cases, the average path distance for a

295 neurite in a parcel was calculated as the average between minimum and maximum. The

296 mean and standard deviation of these averages were computed over different paths.

297

298 Experimental Design and Statistical Analysis

299 We calculated the connection probabilities, number of contacts per connected pairs,

300 and somatic distances along the presynaptic axon and postsynaptic dendrite from the

301 neurite lengths measured for every neuron type in each subregion and layer, as

302 described above. In order to validate the axonal and dendritic length measurements, we

303 used Pearson’s correlation analysis for comparing our results with independent reports

304 and, whenever available, with author-reported values for individual neuron

305 reconstructions. Similarly, we utilized Pearson’s correlation analysis to compare our

306 estimated number of contacts per connected pair with values previously reported for a

307 subset of CA1 neuron types (Bezaire & Soltesz 2013).

308 Once we pooled several neurite measurements to determine the means and standard

309 deviations of the neurite lengths and convex hull volumes, we utilized standard error-

310 propagation formulas for sums and differences,

311 = + − (9)

312 = (∆) +(∆) +(∆), (10)

313 and products and quotients,

⋅ 314 = (11)

315 = || + + , (12)

316 to calculate the final uncertainties for the average number of synapses per neuron pair,

317 for the number of contacts per connected pair, and for the connection probabilities.

318 Factors, such as the volume of interaction and the parcel volumes, were considered

319 constants. In instances where there was only a single example of a presynaptic neuron

320 type and only a single example of a postsynaptic neuron type, we assigned a value of

321 “N/A” to the associated uncertainties.

322

323 Resource sharing

324 All results and underlying experimental data are freely available through the

325 Hippocampome.org web portal. Specifically, the following values are available at

326 hippocampome.org/phpdev/synapse_probabilities.php [the password, “hippo”, will be

327 lifted upon acceptance for publication]: means and standard deviations of dendritic and

328 axonal lengths for all neuron types and parcels; means, standard deviations, minima,

329 and maxima of the synaptic distances from the soma along the axonal and dendritic

330 paths, for all potentially connected neuron-type pairs and parcels; and means and

331 standard deviations for the connection probabilities, average numbers of synapses per

332 neuron pair, and numbers of contacts per connected pair, for all pairs of potentially

333 connected neuron types. Each set of values is linked to the morphological

334 reconstruction images from which they were extracted. Additionally, we also provide an

335 online tool at hippocampome.org/phpdev/connprob.php to re-calculate the connection

336 probability and number of contacts per connected pair for any pair of neuron types upon

337 altering the assumptions regarding inter-bouton and inter-spine distances as well as

338 interaction radius.

339

340

341

342

343 Results

344 Potential connectivity

345 The 122 neuron types identified by Hippocampome.org v1.7, across the six subregions

346 of the rodent hippocampal formation (Figure 1A), give rise to 3,120 potential synaptic

347 connections based on spatial co-location of presynaptic and postsynaptic elements

348 (Moradi & Ascoli 2019). Over 71% (2,220) of these connections arise from dendritic-

349 targeting axons in local circuits, with the rest consisting mainly of projections between

350 different subregions (23%) and a minority of perisomatic contacts from basket and axo-

351 axonic cells (6%). Only for 167 potential connections (5%) has the synaptic interaction

352 been experimentally established (Rees et al. 2016): the remaining, including 2,120 local

353 dendritic connections, so far lack any quantitative assessment of synaptic connectivity

354 (Figure 1B). Our approach allows for estimating the synaptic connectivity parameters

355 (connection probability and number of contacts per connected pair) of 1,970 potential

356 synapses: 1,870 for which no data was previously reported and 100 for which at least

357 partial data exists in the literature. The last 250 local dendritic connections cannot be

358 estimated due to the unavailability of morphological reconstructions for the pre- or

359 postsynaptic neurons. Altogether, the present work fills nearly two-thirds of the missing

360 data in the hippocampal formation, increasing the available knowledge over 11-fold and

361 leaving only a minority (<35%) of the potential synaptic connections unknown. Notably,

362 prior information was mainly limited to dentate gyrus and area CA1, while residually

363 absent estimates are restricted to entorhinal cortex and CA3 (Figure 1C).

364

365

366 Axonal and dendritic length validation

367 We validated our pixel-count neurite-length-estimation pipeline (Figure 2) with two

368 independent approaches. First, we compared our estimations with independent reports

369 of axonal and dendritic length for the same neuron types (Table 1). The results show a

370 tight correspondence between our estimations and the original measurements (ratio =

371 0.96 ± 0.19; Pearson’s correlation = 0.99, p<0.001). Second, we identified a subset of

372 reconstructions for which the authors also directly reported neurite lengths (Extended

373 Data Table 1-1), again demonstrating a tight alignment (ratio = 0.89 ± 0.12; Pearson’s

374 correlation = 0.90, p<0.005). While these data are largely sourced from slice

375 preparations, we include for completeness a comparison with in vivo reconstructions,

376 when available (Extended Data Table 1-2). As expected, the traceable extent of axons

377 intracellularly labeled in vivo is substantially longer and more variable due to factors

378 such as the duration of current injections (Li et al. 1993).

379

380 Laminar distributions of axons and dendrites

381 The distribution of local axonal and dendritic lengths across layers of the hippocampal

382 formation varies by neuron type and subregion. Here we report the relative proportions

383 (Figure 3) as well as the means and standard deviations (Extended Data Figure 3-1

384 through 3-6) for a representative subset of neuron types in each subregion. The

385 comprehensive data for all neuron types are available at

386 hippocampome.org/phpdev/synapse_probabilities.php. For neuron types whose axon

387 invades different subregions, we only account for the local collaterals in this analysis.

388 For example, only 78.3 ± 8.3% of the DG Granule cells (GC) axons remain in the hilus

389 (H), while the remaining 21.6 ± 9.64% (not shown) cross over into CA3 stratum lucidum

390 (SL) and stratum pyramidale (SP). DG interneurons regulate GC activity by innervating

391 specific parcels (Figure 3A and Extended Data Figure 3-1). For instance, DG Basket

392 cells (BC) innervate stratum granulosum (SG), whereas HICAP neurons extend their

393 axons into the inner one-third of stratum moleculare (SMi). Both interneuron types

394 spread their dendrites across all four DG layers, though nearly half of the BC dendrites

395 (>48%) are found in the outer two-thirds of stratum moleculare (SMo), while the HICAP

396 distribution is more uniform (27% in SMo, 41% in H, and 32% between SG and SMi).

397 Other interneurons, such as HIPP and MOPP, restrict their axon terminals within SMo

398 and are differentiated by their dendrite localizations: HIPP in H and MOPP in SMo.

399 For the CA3 local circuit, we illustrate eight of twenty-two neuron types (Figure 3B and

400 Extended Data Figure 3-2), with the remaining data reported online. The CA3 principal

401 cells are the Pyramidal cells (PC), whose local axons form recurrent collaterals in

402 stratum radiatum (SR) and stratum oriens (SO) and dendrites invade in different

403 proportions all layers: stratum lacunosum-moleculare (SLM), SR, SL, SP, and SO. Our

404 estimations confirm previous reports indicating that basal dendrites account for ~42-

405 45% of the whole dendritic tree (Ishizuka et al. 1990). Whereas both CA3 Ivy and

406 Bistratified cells (BiC) have axons and dendrites extending from SR to SO, the present

407 analysis reveals that BiC are three-to-four-fold longer than Ivy in both axonal (55.6 mm

408 vs. 18.4 mm) and dendritic trees (14.3 mm vs 3.3 mm). Others CA3 interneurons, like

409 O-LM or IS Oriens, restrict their dendrites to SO, while CA3 Radiatum cells confine into

410 a single layer both their axons and dendrites.

411 In area CA2 (Figure 3C and Extended Data Figure 3-3), Pyramidal cells also distribute

412 their dendrites across all layers but concentrate their axons in SO (63.6 ± 24.0%), with

413 smaller proportions in SR and SP, again corroborating earlier reports (Ishizuka et al.

414 1995). CA2 Bistratified neurons display quantitatively similar axonal and dendritic

415 patterns from SR to SO, aligned with the arbor distributions of homologous cell types in

416 different hippocampal subregions (Mercer et al. 2007).

417 Hippocampome.org v1.7 identifies thirty-seven distinct interneuron types in subregion

418 CA1 (cf. Somogyi & Klausberger, 2005), eight of which were further investigated by

419 Bezaire & Soltesz (2013). CA1 Pyramidal cells have dendrites spanning all layers in

420 proportions comparable to previous reports (Bannister & Larkman 1995; Ishizuka et al.

421 1995), but axons restricted to SO (Figure 3D and Extended Data Figure 3-4). Axo-

422 axonic (AA), fast-spiking Basket, and Basket CCK+ (BC CCK+) types innervate only

423 SP, directly modulating CA1 PC somatic activity, similarly to previous reports (Fuchs et

424 al. 2007). Our analysis shows that among the dendritic-targeting interneurons,

425 Bistratified and Schaffer Collateral-Associated (SCA) axons mainly innervate SR,

426 whereas CA1 Ivy cells show a strong preference (~68%) for SO. Other neuron types

427 exclusively target SLM, like Neurogliaform and O-LM cells.

428 Hippocampome.org identifies three neuron types in the subiculum (Figure 3E and

429 Extended Data Figure 3-5). The EC-Projecting and CA1-Projecting Pyramidal cells

430 show qualitatively similar, but quantitatively distinct, dendritic and local axonal

431 distributions, while subicular Axo-Axonic cells have dendrites restricted to SM and

432 axons to SP. Interestingly, the local subicular circuit includes axons in the polymorphic

433 layer (PL), despite the dearth of identified postsynaptic elements in Hippocampome.org

434 v1.7. This underscores the prospect of discovering new neuron types in this subregion

435 to receive the transmitted signals (Kinnavane et al. 2018; see Discussion below).

436 The entorhinal cortex is traditionally divided into lateral (LEC) and medial (MEC)

437 components, respectively implicated by electrophysiological evidence in objects

438 representations and spatial tasks and underlying distinguishable connectivity patterns

439 (Masurkar et al. 2017). Despite this functional and architectural partition, several neuron

440 types are common to both areas (Canto et al. 2008), such as LI-II Multipolar-Pyramidal,

441 LI-II Pyramidal-Fan, and LIII Pyramidal, each with their own quantitatively distinct

442 axonal-dendritic distributions (Figure 3E and Extended Data Figure 3-6). Stellate cells

443 are the most numerous neuron type in MEC, with dendrites equally distributed across

444 layers I and II and axons spread across all six layers, according to our analysis. In

445 addition, our results indicate that two identified interneuron types have axonal

446 innervations restricted to the superficial layers of MEC: LII Basket and LIII Superficial

447 Multipolar Interneuron; however, the former preferentially target LII (>75%), while the

448 latter LIII (>83%). We report further quantitative data for all additional neuron types at

449 hippocampome.org/phpdev/synapse_probabilities.php.

450

451 Connection probability

452 Based on the dendritic and axonal length distributions, we estimated the connection

453 probability p (equation 8 in Methods), for each directional pair of neuron types in the

454 local circuit (Figure 4). This probability can be interpreted as the average fraction of

455 neurons of the postsynaptic type contacted by a given neuron of the presynaptic type

456 or, equivalently, the average fraction of neurons of the presynaptic type contacting a

457 given neuron of the postsynaptic type. Figure 4 illustrates the complete set of

458 probabilities by presynaptic sources and postsynaptic targets for the main hippocampal

459 subregions. Here we summarize the mean values and coefficients of variation (CV) for

460 each “connection category”: excitatory to excitatory (E-E), inhibitory to excitatory (I-E),

461 excitatory to inhibitory (E-I), and inhibitory to inhibitory (I-I). Specifically, within each

462 subregion, we average the individual connection probabilities for all pairs of neuron

463 types corresponding to each connection category; for example, the E-E category

464 includes all pairs of excitatory presynaptic neuron type and excitatory postsynaptic

465 neuron type as long as the presynaptic axons share at least one parcel with the

466 postsynaptic dendrites (defining a potential connection) and unless that connection has

467 not been refuted experimentally (Rees et al. 2016).

468 The local DG circuit (Figure 4A), which includes 5 different glutamatergic types,

469 including Granule cells (that do not have potential connections with each other), exhibits

470 a greater connection probability for E-E pairs (0.66 ± 0.10%, CV range = 0.18-1.60, n =

471 21 pairs of neuron types) than for I-E pairs (0.59 ± 0.08%, CV range = 0.15-2.45, n =

472 44), with intermediate values for E-I (0.61 ± 0.08%, CV range 0.11-2.09, n = 53) and I-I

473 (0.59 ± 0.06%, CV range 0.20-4.04, n = 110). In contrast, connectivity analysis in CA3

474 (Figure 4B) reveals a higher probability from inhibitory cells (I-E: 0.81 ± 0.11%, CV

475 range = 0.04-4.08, n = 38; I-I: 0.59 ± 0.04%, CV range = 0.07-3.54, n = 213) than from

476 the 3 types of excitatory cells (E-E: 0.40 ± 0.09%, CV range = 0.04-2.94, n = 8; E-I: 0.35

477 ± 0.05%, CV range = 0.04-2.98, n = 48). The probability of CA3 Pyramidal cells to CA3

478 Pyramidal cells, alone, is 1.0 ± 0.41% (well matching the 0.9% experimental value

479 measured by Guzman et al. 2016). This relative trend holds true for CA2 (not shown in

480 Figure 4 but included in the online data at Hippocampome.org) and CA1, too, though

481 with dramatic and opposite differences in absolute values: nearly an order of magnitude

482 greater in CA2 (I-I: 5.5 ± 1.5%, CV range = 0.36-0.80, n = 8; I-E: 5.3 ± 3.0%, CV range

483 = 0.43-0.70, n = 2; E-I: 3.6 ± 2.1%, CV range = 0.80-1.40, n = 4; and E-E: 3.1 ± 3.3%,

484 CV = 1.04, n = 1) and smaller in CA1 (I-I: 0.32 ± 0.02%, CV range = 0.02-4.99, n = 852;

485 I-E: 0.38 ± 0.09%, CV range = 0.02-4.01, n = 62; E-I: 0.09 ± 0.04%, CV range = 0.68-

486 6.23, n = 69; and E-E: 0.07 ± 0.13%, CV range = 1.19-5.30, n = 5). Due to the small

487 number of neuron types discovered in the subiculum to date, there are no characterized

488 local axonal-dendritic inhibitory synaptic connections, and the data are very sparse for

489 the excitatory connections (E-E: 1.4 ± 0.2%, CV range = 0.21-0.65, n = 4; E-I: 0.28 ±

490 0.09%, CV range = 0.35-1.06, n = 2). The entorhinal cortex displays a pattern of

491 synaptic-connection probabilities with greatest proportions for I-E (0.38 ± 0.22%, CV

492 range = 0.23-4.54, n = 32) and smallest for E-I (0.25 ± 0.19%, CV range = 0.32-5.72, n

493 = 61), with intermediate values for I-I (0.30 ± 0.26%, CV range = 0.73-4.54, n = 10) and

494 E-E (0.33 ± 0.07%, CV range = 0.22-5.72, n = 323), the latter of which excludes the

495 refuted MEC LII Stellate to MEC LII Stellate connections (Couey et al. 2013; Dhillon &

496 Jones 2000; Kelsch et al. 2014).

497 Across all local circuits of the hippocampal formation, this analysis reveals considerably

498 variable, but overall sparse, axonal-dendritic connection probabilities (mean ± standard

499 deviation: 0.55 ± 0.79%) exhibiting a long tail distribution (Figure 4E), well described by

500 a lognormal function (Figure 4F), with a range spanning four orders of magnitude

501 (0.0084% - 9.9%) and a median of 0.33%.

502 The (very sparse) estimates available in the experimental literature (Extended Data

503 Figure 4-1) generally fall within the estimated probability ranges derived by our analysis.

504 The remaining discrepancies may be explained by differences in preparation details.

505 Specifically, the probabilities previously reported for DG Mossy to DG Granule included

506 polysynaptic connections, whereas our analysis is specific for monosynaptic

507 connections, and the CA1 PC to CA1 PC connectivity may be highly sensitive to slice

508 orientation and inter-somatic distances, due to substantial cross-lamellar connectivity

509 along the longitudinal axis (Yang et al. 2014).

510

511 Number of contacts per connected neuron pair

512 The number of synaptic contacts, Nc, per pair of directionally connected neurons

513 estimated with our approach (equation 6 in Methods) differs broadly by presynaptic

514 neuron type and postsynaptic target, but remains within a biologically reasonable range

515 (1-15) for the vast majority (>95%) of neuron-type pairs (Figure 5). Over all 1,970 local

516 dendritic potential synapses examined, the number of contacts per connected pair had

517 a mean ± standard deviation of 5.7 ± 5.3, a median of 4.1, and a range of 1.1 - 62.8

518 (Figure 5A).

519 The relative patterns concerning the number of contacts was generally consistent

520 across all hippocampal subregions. The average number of contacts per connected pair

521 was systematically larger for inhibitory than for excitatory presynaptic types (DG: 6.7 ±

522 0.9, n = 154 pairs vs 3.5 ± 0.7, n = 74 pairs; CA3: 8.8 ± 0.7, n = 251 pairs vs 4.0 ± 0.7, n

523 = 56 pairs; CA2: 8.9 ± 2.9, n = 10 pairs vs 7.2 ± 4.3, n = 5 pairs; CA1: 5.8 ± 0.4, n = 914

524 pairs vs 2.5 ± 0.8, n = 74 pairs; EC: 11.6 ± 3.3, n = 42 pairs vs 3.6 ± 0.3, n = 384 pairs).

525 Moreover, in areas CA3, CA2, CA1, and subiculum, the number of contacts onto

526 excitatory cells was larger than onto inhibitory cells (9.5 ± 1.2, n = 120 pairs vs 5.8 ±

527 0.3, n = 1,196 pairs), consistent with other studies (Booker & Vida 2018; Deuchars &

528 Thomson 1996). The entorhinal cortex and dentate gyrus, however, displayed an

529 opposite and milder trend with an average of 4.3 ± 0.4 contacts onto excitatory cells (n =

530 420 pairs) and 5.7 ± 0.7 onto inhibitory cells (n = 234 pairs).

531 Next, we compared our data with a previous estimation of the CA1 circuit (Bezaire &

532 Soltesz 2013). This earlier study focused on seven dendritic-targeting neuron types:

533 Pyramidal, Bistratified, Ivy, Neurogliaform, O-LM, Perforant path-associated, and

534 Schaffer collateral-associated. For every presynaptic type, they reported the total

535 number of axonal boutons contacting two distinct postsynaptic targets: pyramidal cells

536 and interneurons. From these data, it is possible to calculate the average number of

537 synapses per neuron pair from each of the seven specified neuron types onto pyramidal

538 cells and interneurons. This calculation requires an estimate of the numbers of

539 pyramidal cells and interneurons. The aforementioned study assumes a count of

540 311,500 pyramidal cells and 38,500 interneurons in the adult rat CA1. While the former

541 value is consistent with contemporary literature (Herculano-Houzel et al. 2011;

542 Murakami et al. 2018), recent reports suggest a more than doubled abundance of

543 interneurons (Erö et al. 2018). We thus used a number of 77,000 interneurons and

544 compared the so-derived average number of synapses per neuron pair with the

545 corresponding quantities independently obtained in the present work (Extended Data

546 Figure 5-1). The two sets of values are significantly correlated (R = 0.73, p<0.0002),

547 and the best fitting line with zero intercept has a slope close to unity (0.91 with the data

548 derived from Bezaire & Soltesz 2013 as ordinate and the data from this work as

549 abscissa).

550 We had previously estimated the number of contacts per connected pair in selected

551 neuron types of the CA3 circuit based on in vivo morphological reconstructions

552 embedded in a 3D model of the hippocampal formation (Ropireddy & Ascoli 2011). That

553 earlier study had quantitatively differentiated two distinct components of the ‘recurrent

554 collateral’ connectivity between CA3 PCs. Specifically, postsynaptic pyramidal cells

555 were found to receive a higher number of contacts from presynaptic pyramidal cells

556 located in the distinct subfield CA3c (5.6 ± 0.2) than from CA3 PC in the rest of area

557 CA3 (3.4 ± 0.3). The approach presented in the present work confirms the same

558 qualitative difference, with the number of contacts from CA3c PCs exceeding those from

559 other CA3 PCs 1.49-1.97 fold in the range of interaction radius used in the two reports

560 (Ropireddy & Ascoli 2011: 1 μm; here: 2 μm). Altogether, our results are thus well

561 aligned with the very sparse existing literature estimates, while substantially extending

562 them to the majority of local connections throughout the hippocampal formation.

563

564 Quantification of tri-synaptic circuit

565 The connection probabilities and numbers of contacts per connected pair allow us to

566 derive a quantitative summary of synaptic connectivity by layer onto the principal cells of

567 the main subregions of the hippocampal formation (Figure 6). While this analysis is

568 limited to axonal-dendritic interactions in the local circuit (and the Fig. 6 schematic only

569 illustrates selected presynaptic neuron types), a full understanding of the hippocampal

570 network also requires similar data for projection and perisomatic presynaptic neuron

571 types. For completeness we thus collated the available experimental evidence for these

572 complementary cases (Extended Data Figure 6-1). Out of 60 pairs of neuron types with

573 available data, connection probabilities were reported or derivable in only 10 cases, and

574 numbers of contacts per connected pair in 16. In most other cases the synaptic

575 connections were confirmed to exist, but not quantified.

576 On the one hand, this compilation identifies a set of “unknown parameters” that are

577 important for computational simulations but have yet to be measured experimentally. On

578 the other, it may allow the community to extend, update, and complement the existing

579 quantitative knowledge of the hippocampal network. According to previous

580 measurements of the CA1 local circuit in vitro (Takács et al. 2012), 29.3% of CA1

581 Pyramidal cell boutons contact other CA1 Pyramidal cells, 65.9% contact interneurons,

582 and 4.9% of local synapses are made onto unknown targets. However, experimental

583 evidence from cells labeled in vivo yields different percentages (46.2% interneurons,

584 39.2% CA1 Pyramidal cells, 6.9% unknown targets) and more heterogeneous

585 distributions. In terms of extrinsic inputs, the same study shows that Schaffer collaterals

586 preferentially target CA1 Pyramidal cells (92.9%) over interneurons (7.1%), while EC

587 temporo-ammonic axons in CA1 SLM predominantly contact Pyramidal cell dendrites

588 (90.8%).

589

590 Laminar distributions of axonal and dendritic path distances from the soma

591 To determine the distance from the soma of potential synapses along the presynaptic

592 and postsynaptic neural arbors, we measured the layer-specific distributions of the

593 minimum, mean, and maximum axonal and dendritic paths distances from the somatic

594 origin for every neuron type. Here we illustrate the results for representative cells in DG,

595 CA3, CA2, CA1, and EC (Figure 7). The measurements for all analyzed neuron types

596 are available at hippocampome.org/phpdev/synapse_probabilities.php. As expected,

597 path distances tended to increase moving away from the somatic layer. However, the

598 range of distances within each layer was substantially broad and, in most cases, larger

599 than the difference between layers.

600 We then compared the estimated postsynaptic somatic distances of CA3 PC with the

601 distribution of potential synapses onto dendrites of the same neuron types previously

602 derived from embedding morphological reconstructions into a 3D hippocampal model

603 (Ropireddy & Ascoli, 2011; their Figures 5C & 6E). In SO, the synaptic distance from the

604 soma along the dendritic path of CA3 PCs obtained in the present work (128.5 ± 51.2

605 μm) tightly matched the distribution of potential synapses on CA3 PC basal dendrites

606 from the earlier study (110 - 160 μm). In SR, the dendritic distance from the present

607 work (256.4 ± 64.7 μm) also yielded an excellent correspondence with the Ropireddy &

608 Ascoli 2011 distribution of potential synapses on CA3 PC apical dendrites (200 - 320

609 μm). Lastly, in SLM the dendritic distance from the soma derived here (507.1 ± 130.1

610 μm) was consistent with the distribution of inhibitory synapses from GABAergic

611 interneurons on the apical tuft of CA3 PCs (500 - 750 μm).

612

613 Public digital resource and online data accessibility

614 All connection probabilities and numbers of contacts per connected pair, for each of the

615 1,970 pairs of neuron types analyzed here, as well as the (644) parcel-specific axonal

616 and dendritic lengths and (568) somatic path distances for every neuron type, are

617 publicly posted on Hippocampome.org, increasing the count of Pieces of Knowledge

618 (PoKs) of this resource by 5,152. The published evidence underlying all values,

619 including 1,181 neurite lengths, 3,663 path lengths, 1,091 convex hull volumes, 94 slice

620 thicknesses, and 26 parcel volumes are also directly accessible through the web portal,

621 amounting to a total of 6,055 additional Pieces of Evidence (PoE) in this public

622 knowledge base.

623 Specifically, the “Synapse Probability” option in the dropdown menu of the

624 Hippocampome.org ‘Browse’ tab provides a compendium of companion web pages

625 associated with this research that allow users to interactively explore the results (Figure

626 8). Users can find specific data related to their research interests, such as the distances

627 along dendrites and axons measured from the soma, by selecting a value associated

628 with the desired neuron type and parcel (Figure 8A). Each value is linked to an evidence

629 page, which displays the supporting quotes, figures, and measurements (in this specific

630 example, of somatic distances) found in each individual supporting article (Figure 8A1-

631 A1b). By selecting a presynaptic neuron type and a postsynaptic neuron type (Figure

632 8B), researchers can gain information about connection probabilities and numbers of

633 contacts per connected pair in each parcel (Figure 8B1) and inspect the evidence used

634 to generate the data (Figure 8B2), such as neurite lengths (Figure 8B2a-b) and convex

635 hull volumes. All the estimations are available to download in comma-separated value

636 files that contain matrix values and further statistics (Figure 8C). Finally, we provide a

637 tool allowing investigators to choose their own desired values for the ultrastructural

638 parameters (distance between axonal boutons, distance between dendritic spines or

639 postsynaptic locations, and interaction radius) and then obtain parcel-specific

640 connection probabilities and numbers of contacts per connected pair for any selection of

641 neuron types (Figure 8D-D1).

642

643 Discussion

644 Despite a continuous growth of information pertaining to the morphology,

645 electrophysiology, and gene expression of neurons in mammalian brains, direct

646 experimental evidence for quantifying neuron type-specific synaptic connectivity

647 remains exceedingly sparse, even in the most intensively investigated neural systems,

648 such as the rodent hippocampal formation. Here, we have introduced a novel pipeline to

649 produce a zeroth-order approximation of the connection probability, number of contacts

650 per connected pair, and presynaptic and postsynaptic somatic distances for most pairs

651 of potentially connected neuron types in the local circuits of the hippocampus and

652 entorhinal cortex. While this initial order-of-magnitude estimate of connectivity will

653 undoubtedly require successive quantification refinements, our results nonetheless

654 constitute a remarkably comprehensive characterization of nearly 2,000 neuron-type

655 connections. This dataset provides a useful placeholder for computational modeling and

656 network analyses until firmer empirical measurements are collected and released

657 (Ascoli & Atkeson 2005) . Notably, biologically realistic simulations of the hippocampal

658 circuit will also require a complete neuron census, that is, the count of neurons within

659 each type (Attili et al. 2020).

660

661 From morphology to function: synaptic count and implications for local circuits

662 The framework introduced in this study focuses on axonal-dendritic connections, thus

663 excluding perisomatic synapses that only constitute a minority (~6%) of the

664 hippocampal connectivity (Megıaś et al. 2001). Moreover, our approach is limited to the

665 local circuit, as captured by typical slice preparations from which most available

666 morphological data are derived. While recent technological advancements now allow

667 the systematic 3D reconstruction of long-range single-neuron axonal projections

668 (Winnubst et al. 2019), that process is still too slow to yield dense coverage of the

669 needed data, and currently only provides access to a small proportion (<4%) of neuron

670 types in the mouse hippocampal formation. In contrast, representative local two-

671 dimensional morphological tracings are available for 115 of the 122 distinct neuron

672 types identified by Hippocampome.org. The seven missing reconstructions (three in

673 CA3 and four in EC) account for 250 connections, representing only 11% of the 2,206

674 neuron type pairs potentially connected by local axonal-dendritic synapses. At the same

675 time, as additional neuron types are likely to be discovered in the future, continuous

676 screening of neuronal morphologies will be required to maintain this information up to

677 date.

678 Peters’ rule assumes that the overlap of presynaptic axons with postsynaptic dendrites

679 is equivalent to the probability of synaptic connectivity in the absence of targeting

680 preference (Peters & Feldman 1976). Experimental evidence in the neocortex indicates

681 that interneuron axons have smaller branch lengths and higher tortuosity compared to

682 pyramidal cells, suggesting greater specificity in their targeting of postsynaptic neurons

683 (Stepanyants et al. 2004). Furthermore, while the number of actual synapses made by

684 pyramidal cells is just a fraction (10 - 30%) of all axonal-dendritic overlaps (Stepanyants

685 et al. 2002), our estimated count of presynaptic and postsynaptic elements based on

686 inter-bouton and inter-spine distances, respectively, already corrects for this factor.

687 Importantly, axonal and dendritic morphology in the rodent hippocampal formation have

688 been proven to correctly predict circuit connectivity at the neuron-type level (Rees et al.

689 2017), at an accuracy of 99%, when exceptions are made for axo-axonic and

690 interneuron-specific connections. For example, the predominant local connections from

691 CA1 Pyramidal cells to CA1 O-LM cells and other interneurons with horizontal dendritic

692 arbors at the border of SO and the alveus (Maccaferri 2005) are a consequence of

693 Peters’ rule: CA1 O-LM cells and these other SO interneurons receive approximately

694 70% of their glutamatergic input from CA1 Pyramidal cells (Blasco-Ibáñez and Freund

695 1995). Still, proven synaptic specificity, such as that for axo-axonic and interneuron-

696 specific connections, takes precedence over Peters’ rule in our framework: in other

697 words, we excluded experimentally refuted connections from the calculations of

698 connection probability and number of contacts per connected pair.

699 Among all analyzed subregions, CA2 had the highest connection probability, by nearly

700 an order of magnitude (weighted average for CA2: 0.048, n = 15 neuron type pairs;

701 weighted average for the rest of the hippocampal formation: 0.0053, n = 1,955). This

702 may be due, at least in part, to the smaller total volume of CA2 compared to other areas

703 (CA2: 2.28 mm3; CA1: 30.13 mm3): we calculate connection probabilities based on

704 axonal-dendritic overlap density, thus resulting in higher values for CA2 given similar

705 axonal-dendritic extents. CA1 exhibits shorter axonal lengths within the local circuit on

706 top of the greater volume. The small number of known neuron types in CA2 nonetheless

707 urges interpretative caution. At the same time, connection probability is often correlated

708 to synaptic amplitude (Jiang et al. 2015), and amplitudes are indeed larger in CA2 than

709 in CA1 neurons (Kohara et al. 2013; Sun et al. 2014), suggesting that our finding is not

710 artifactual.

711 The neurite length analysis presented here also showed that the principal cells of the

712 subiculum, the CA1-Projecing Pyramidal cells, exhibit substantial axonal extensions in

713 the polymorphic layer (4,543.9 μm), even though there are no known neuron types

714 extending dendrites in that layer. This observation invites two alternative explanations.

715 One is the existence of yet undiscovered neuron types that can receive the mentioned

716 inputs. In general, the subiculum local circuit remains largely unexplored and there is

717 growing evidence supporting the idea of new cell types (Kinnavane et al. 2018;

718 Menendez de la Prida et al. 2003; Witter 2006). The other possibility is that this layer

719 might be a mere transition zone for axonal projections to reach other areas.

720 The involvement of gap junctions in the hippocampal formation are associated with

721 neuronal synchronization during oscillatory activity, mainly between GABAergic

722 parvalbumin-positive interneurons (Baude et al. 2007; Fukuda & Kosaka 2000; Ylinen et

723 al. 1995). Recent evidence showed that gap junctions are present in the adult

724 hippocampus between glutamatergic cells as mixed synapses, but remain mainly closed

725 under control conditions (<10%) and require acidic changes in intracellular pH to

726 increase the opening probability (Ixmatlahua et al. 2020). Additional experimental

727 evidence should be collected to address the role of gap junctions during non-rhythmic

728 activity and for inclusion in circuitry estimates.

729

730 Path tracing and synaptic attenuation

731 Temporal neuronal dynamics depend on axonal delays as well as on the attenuation of

732 evoked postsynaptic potentials across the dendritic tree. Because axonal spikes

733 propagate at approximately constant velocity (Rama et al. 2018), presynaptic signal

734 delay is essentially proportional to the somatic path distance to the release sites.

735 Dendrites are constantly receiving synaptic inputs and signals may be enhanced or

736 reduced according to their locations (Destexhe & Paré 1999; Ferrante et al. 2013;

737 Maccaferri et al. 2000). These effects are the result of multiple factors that change as a

738 function of the distance from the soma along the arbor path, such as internal resistivity,

739 resting membrane potential, and receptor expression, activation, conductance, and

740 modulation (Golding et al. 2005; Grillo et al. 2018; Magee 1998). We estimated the

741 mean axonal and dendritic distance from the soma across every layer. Another key

742 influence on signal attenuation is exerted by branch diameter, which can vary

743 substantially between layers (Megıaś et al. 2001), but has not been assessed yet for

744 many neuron types. The distal dendritic diameter of hippocampal neurons is often near

745 the resolution limit of traditional light microscopy, and its measurement is notoriously

746 unreliable (Scorcioni et al. 2004).

747

748 Limitations and confounds

749 Our approach to calculating linear-length estimations of axons and dendrites for all

750 Hippocampome.org neuron types is constrained by the relatively small number of

751 reconstructions available in the peer-reviewed literature. In order to circumvent this

752 limitation, we collated neuronal reconstructions from several different strains of both

753 mice and rats (Extended Data Figure 2-7). In the absence of comparative morphological

754 data for specific neuron types, we adopted a conversion factor equal to the cubic root of

755 the volume scaling parameter from mouse to rat (West et al. 1978). In contrast, we did

756 not perform any correction for the different strains used, as a comparison of different rat

757 atlases indicates that the hippocampal formation remains remarkably consistent across

758 strains (Kjonigsen et al. 2015). Another large effect on neurite length and anatomical

759 volume pertains to the age of the animals. To compensate for this known source of

760 variability, we applied a scaling factor to normalize the measurements from young to

761 adult animals (Juárez et al. 2008).

762 The variety of labeling methods are also likely to cause significant differences in

763 observed morphological features, even within the same neuron type (Farhoodi et al.

764 2019). New approaches to identify neuron populations, such as genetic barcoding, will

765 provide improved specificity to describe the properties and dynamics associated with

766 different neuron types and their functional role in neuronal circuits (Sugino et al. 2019).

767 Techniques like octuple patch-seq recordings, optogenetics and labeling, and serial-

768 block-face scanning electron microscopy will continue to fill the gaps in the experimental

769 acquisition of electrophysiology, connectivity, morphology, and transcriptomics for a

770 large set of different neuron types (Cadwell et al. 2015; Jiang et al. 2015). However, the

771 existing experimental toolsets still lack the scalability and specificity needed to classify

772 all identified neuron types at Hippocampome.org. More accurate and unbiased labeling

773 techniques are required to completely characterize neuron type populations and

774 morphologies.

775 Another issue to consider is the completeness of the reconstructions. Tracings from

776 slices are necessarily incomplete if the maximal span of the axonal or dendritic trees

777 exceeds the slice thickness (Parekh et al. 2015; Uylings et al. 1986). Unfortunately, the

778 depth from the slice surface to the recording neuron is seldom reported in peer

779 reviewed publications. Slicing orientation can also heavily affect the physical integrity of

780 neural arbors. Ideally, different sectioning angles should be utilized in order to obtain

781 optimal axonal reconstruction (Gloveli et al. 2005; Harris et al. 2001). For example,

782 hippocampal-entorhinal cortex slices preserve the fibers from the perforant path, mossy

783 fibers, and Schaffer collaterals (SC), whereas coronal slices only preserve SC fibers

784 (Xiong et al. 2017). Interestingly, while some authors showed in silico that the

785 completeness of axonal collaterals remain constant independent of slice orientation

786 (Guzman et al. 2016), other studies report that axonal collateral densities in 400 μm

787 coronal slices are discontinuous with the cell body (Li et al. 1993). In general, axonal

788 reconstructions can rarely be considered complete in any slice preparation. Therefore,

789 the data reported here, largely sourced from slices, are likely underestimates of in vivo

790 connectivity (Extended Data Table 1-2).

791

792 Concluding remarks

793 Detailed modeling of hippocampal circuits with biologically realistic neural network

794 simulations requires quantitative information related to identified neuron types. Our

795 estimations constitute the first attempt to fill in the gaps about the connection

796 probabilities and numbers of contacts per connected pair between different neuron

797 types in an approximate but comprehensive manner, until further direct experimental

798 data become available. We also measured the layer-specific axonal and dendritic

799 distances from the soma, which can be used to determine temporal integration of

800 signals during circuit-related activity in distinct neuron types by electrotonic propagation

801 and axonal delay along the neurites.

802

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1539

1540 Figure 1. Hippocampal circuitry. A Subregional delineation of the hippocampal

1541 formation with circles denoting neuron types and numbers in parentheses indicating

1542 their counts. The blue arrows illustrate the local outgoing connectivity of a

1543 representative neuron type for every major subregion: DG MOPP, CA3 Bistratified, CA1

1544 SO-SO, and EC LIII Pyramidal. B The connection probability is unknown for most

1545 (2,953) of the 3,120 hippocampal potential synapses. The continuous line marks the

1546 proportion of connection probabilities estimated by axonal-dendritic overlap. The dotted

1547 line represents the connections excluded from analysis. C Relative fractions and

1548 absolute numbers of local axonal-dendritic connections in each subregion, for which

1549 quantitative estimates were previously reported, were unknown and are estimated here,

1550 or remain unknown due to lack of morphological reconstructions.

1551

1552 Figure 2. Morphological reconstructions of hippocampal neuron types and their image

1553 processing. Details regarding the full dataset and sources are reported in Extended

1554 Data Figures 2-1 through 2-10. A Representative tracings of selected neuron types from

1555 different subregions of the hippocampal formation (glutamatergic: black; GABAergic:

1556 gray). A1 DG HIPP (Hosp et al. 2014), A2 CA3 Granule (Szabadics et al. 2010), A3 EC

1557 LII Basket Multipolar Interneuron (Tahvildari et al. 2012). B Exemplary cases of image

1558 processing for pixel count and neurite path tracing. B1 CA1 Basket cell reconstruction

1559 (Lee et al. 2011); axons are red and dendrites black. B2 Extraction of the stratum

1560 radiatum (SR; yellow frame) dendrites from the original image. B3 Estimation of mean

1561 distance from the soma along the dendritic path. We traced and averaged up to five

1562 dendrites per parcel. C Connection probability estimation. C1 CA1 LMR-Projecting

1564 Neuroscience). C2 CA1 Neurogliaform postsynaptic interneuron (Price et al. 2005:

1566 oriens with Bistratified axons in green and O-LM dendrites in blue. The orange sphere

1567 shows the zoomed-in volume of interaction (radius = 2 μm). Scale bar = 100 μm for A

1568 and C1-3 and 50 μm for B1-3. Images in B and C have been modified from the originals

1569 to enhance colors.

1570

1571 Figure 3. Relative laminar distributions of dendritic and axonal patterns across

1572 subregions (see Extended Data Figures 3-1 through 3-6 for absolute means and

1573 standard deviations). Heatmap distributions of dendrites (blue) and axons (red) for

1574 representative neuron types in dentate gyrus (DG; A), CA3 (B), CA2 (C), CA1 (D),

1575 subiculum (Sub; E), and entorhinal cortex (EC; F) (n = 8 for DG, CA3, CA1, and EC; n =

1576 3 for CA2 and Sub). Each row corresponds to the labeled neuron type (glutamatergic:

1577 black; GABAergic: gray), and each column represents a different subregion’s layer.

1578 Abbreviations: Granule cell, GC; Hilar Ectopic cell, HEGC; Semilunar Granule cell,

1579 SGC; Mossy cell, MC; Basket cell, BC; Hilar Commissural Associational Pathway

1580 related cell, HICAP; Total Molecular Layer cell with only MOlecular Layer AXons ,

1581 MOLAX; Neurogliaform cell, NGFC; Pyramidal cell, PC; CA3c Pyramidal cell, PC-c;

1582 Bistratified cell, BiC; Interneuron Specific Oriens, IS Oriens; Mossy Fiber Associated

1583 cell, MFA; Oriens-Lacunosum Moleculare cell, O-LM; Radiatum cell, R; Cajal-Retzius

1584 cell, C-R; Schaffer Collateral Associated cell, SCA; Stratum Oriens-Oriens cell SO-SO;

1585 Entorhinal Cortex Projection Pyramidal cell, EC-Proj-PC; CA1 Projection Pyramidal cell,

1586 CA1-Proj PC; Axo-axonic cell, AA; LI-II Multipolar-Pyramidal cell, LI-II MPC-PC; LI-II

1587 Pyramidal-Fan cell, LI-II PC-Fan; MEC LII Stellate cell, MEC LII Stellate; LIII Pyramidal

1588 cell, LIII PC; MEC LV Pyramidal cell, MEC LV PC; MEC LV Superficial Pyramidal cell,

1589 MEC LV Sup PC; MEC LII Basket cell, MEC LII BC; MEC LIII Superficial Multipolar

1590 Interneuron cell, MEC LIII Sup MPI.

1591

1592 Figure 4. Connection probability by pair of presynaptic and postsynaptic neuron types.

1593 Summary plot of connection probabilities in local circuits of DG (B), CA3 (C), CA1 (D),

1594 and EC (E). Presynaptic (left horizontal axis) and postsynaptic (right horizontal axis)

1595 neuron types are labeled with numbers (glutamatergic: black; dendritic-targeting

1596 GABAergic: gray; perisomatic GABAergic: blue) as coded in Extended Data Figures 2-1

1597 through 2-6 and Hippocampome.org. See Extended Data Figure 4-1 for comparison

1598 with sparse estimations available in the literature. F, G Distributions of axonal-dendritic

1599 connection probabilities from all 1,970 analyzed pairs of neuron types across all

1600 subregions. Mean and median values are indicated by blue and green vertical lines,

1601 respectively. Abbreviations: SMo, outer two-thirds of stratum moleculare; SMi, inner

1602 one-third of stratum moleculare; SG, stratum granulare; H, hilus.

1603

1604 Figure 5. Number of contacts per connected pair. (A) Distributions of the number of

1605 synaptic contacts per connected neuron pair from all 1970 analyzed axonal-dendritic

1606 overlaps, across all subregions. Mean and median values are indicated by blue and red

1607 vertical lines, respectively. Number of contacts per connected pair in local circuits of DG

1608 (B), CA3 (C), CA1 (D), and EC (E), with background colors reflecting the numerical

1609 values according to the heat map next to panel C. Presynaptic (vertical axis) and

1610 postsynaptic (horizontal axis) neuron types are labeled as in Figures 4A-D.

1611 Abbreviations: SMo, outer two-thirds of stratum moleculare; SMi, inner one-third of

1612 stratum moleculare; SG, stratum granulare; H, hilus.

1613

1614 Figure 6. Representative local axonal-dendritic connections onto selected principal cells

1615 of the hippocampal formation. Numbers of contacts per connected pair are shown in

1616 circles, connection probabilities ± standard deviations are shown for each layer and

1617 presynaptic neuron. Principal cells: black; other glutamatergic cells: gray shades;

1618 GABAergic interneurons: colors. A Synaptic connectivity from 7 different presynaptic

1619 neuron types onto DG Granule Cell. B Synaptic connectivity from 7 different presynaptic

1620 neuron types onto CA3 Pyramidal Cell. C Synaptic connectivity from 7 different

1621 presynaptic neuron types onto CA1 Pyramidal Cell. D Synaptic connectivity from 6

1622 different presynaptic neuron types onto EC LV Deep Pyramidal Cell. Abbreviations:

1623 Granule cell, GC; Semilunar Granule cell, SGC; Mossy cell, MC; Hilar Commissural

1624 Associational Pathway related cell, HICAP; hilar perforant path-associated cell, HIPP;

1625 Total Molecular Layer cell with only MOlecular Layer AXons, TML; Outer Molecular

1626 Layer cell, OML; Molecular layer perforant path-associated cell, MOPP; Pyramidal cell,

1627 PC; Mossy Fiber Associated cell, MFA; Quadrilaminar, QuadD; Radiatum cell, R;

1628 Bistratified cell, BiC; Oriens-Lacunosum Moleculare cell, O-LM; Neurogliaform cell,

1629 NGFC; Perforant Path Associated cell, PPA; Schaffer Collateral Associated cell, SCA;

1630 LIII-V Bipolar Pyramidal cell, LIII-V BPC; MEC LII Stellate cell, LII SC; LIII Pyramidal

1631 cell, LIII PC; MEC LIII Superficial Trilayered Interneuron, STI; MEC LIII Superficial

1632 Multipolar Interneuron cell, SMI; SMo, outer two-thirds of stratum moleculare; SMi, inner

1633 one-third of stratum moleculare; SG, stratum granulare; H, hilus, SLM, stratum

1634 lacunosum-moleculare; SR, stratum radiatum; SL, stratum lucidum; SP, stratum

1635 pyramidale; SO, stratum oriens.

1636

1637 Figure 7. Mean distances from the soma. A1 DG HICAP interneuron (Mott et al. 1997:

1639 in SMi and in blue for dendrites in SMo, starting from the soma, shown in black. A2

1640 Layer-specific axonal and dendritic distances from the soma for DG HICAP interneurons

1641 (n = 4). The central dot and box boundaries represent mean and standard deviation,

1642 respectively, while the whiskers indicate minimum and maximum values. Somatic layer

1643 is shaded in gray. B Layer-specific axonal and dendritic distances from the soma for

1644 CA3 Spiny Lucidum interneurons (n = 5). C Layer-specific axonal and dendritic

1645 distances from the soma for CA2 Bistratified interneurons (n = 6). D Layer-specific

1646 axonal and dendritic distances from the soma for CA1 Pyramidal cells (D: n = 15; A: n =

1647 8). E Layer-specific axonal and dendritic distances from the soma for EC LIII Pyramidal

1648 cells (n = 5). Glutamatergic neurons are shown in black; GABAergic: gray.

1649 Abbreviations: SLM, stratum lacunosum-moleculare; SR, stratum radiatum; SL, stratum

1650 lucidum; SP, stratum pyramidale; SO, stratum oriens; SMo, outer two-thirds of stratum

1651 moleculare; SMi, inner one-third of stratum moleculare; SG, stratum granulare; H, hilus.

1652

1653 Figure 8. Interactive browsing and downloading of data associated with the

1654 quantification of neurites and potential synaptic connectivity on Hippocampome.org. (A)

1655 Representative screenshot of a Hippocampome.org data matrix. The drop-down menu

1656 (light blue box) provides options to display dendritic and axonal lengths, somatic

1657 distances, average numbers of potential synapses, numbers of contacts per connected

1658 pair, and connection probabilities. The green-outlined box shows the Connection

1659 Probabilities tool, and the red box highlights the download section for the data. The

1660 representative entry in the brown box, enlarged in the dark blue box, corresponds to the

1661 somatic distances along the dendrite for a CA1 Radiatum Giant cell in SLM. (A1)

1662 Bibliographic evidence underlying the reported somatic distance. (A1a) Depiction of the

1663 dendrites measured to determine the above distance value. (A1b) Source figure from

1664 which A1a is derived. (B) Section of the ‘number of contacts’ matrix. The dark red box

1665 highlights the number of contacts between presynaptic Mossy MOLDEN and

1666 postsynaptic Basket CCK+, whose parcel-specific values are shown in (B1). (B2)

1667 Bibliographic evidence for the selected number of contacts per connected pair and

1668 illustration of the neurites isolated in computing the number of contacts for the selected

1669 parcel (B2a) and the corresponding source image (B2b). (C) Users can download all

1670 values from the matrix in comma-spaced-value format. (D) The Connection Probabilities

1671 tool is used to find connection probabilities and numbers of contacts from user-supplied

1672 ultrastructural parameter values for a given pair of neurons. (D1) The results are

1673 computed for all of the local layers involved in the connection between the two selected

1674 neuron types. Abbreviations: SLM, stratum lacunosum-moleculare.

1675

Table 1. Total length estimations of neurites compared to previous reports*

Area Neuron type Reported length Estimated length Reference D: 2,793 ± 74 μm Claiborne et al. 1986 Buckmaster et al. D: 3,337 ± 88 μm Granule D: 3,538.9 ± 328.4 μm 2012 Patton & D: 3,221 ± 78 μm McNaughton 1995

Mossy D: 5,392 ± 313 μm D: 4,792.9 ± 395.9 μm Kowalski et al. 2010

Bartos et al. 2001, Basket D: 9,800 μm D: 6,583.4 ± 4,277.1 μm 2002 DG D: 1,108 μm D: 1,258.3 μm Markwardt et al. MOCAP A: 15,750 μm A: 14,438.3 μm 2011

HICAP A: 9,700 ± 200 μm A: 7,745.2 ± 642.0 μm Mott et al. 1997

D: 2,500-3,200 μm D: 3,839.3 ± 7.3 μm Yuan et al. 2017 HIPP A: 22,500-26,800 μm A: 23,708.7 ± 1,683.5 μm A: 25,780 μm Sik et al. 1997 Total Molecular D: 2,500-3,200 μm D: 3,074.3 μm Mott et al. 1997 Layer A: 22,500-26,800 μm A: 21,136.4 μm D: 14,624.6 ± 4,604.0 Pyramidal D: 12,481 ± 2,998.9 μm Ishizuka et al. 1995 μm Mossy Fiber Vida & Frotscher CA3 A: 20.3-28.6mm A: 21,750.9 ± 1,714.2 μm Associated 2000 A: 67,180.4 ± 31,195.4 Trilaminar A: 99,770 μm Sik et al. 1997 μm D: 11,111.0 ± 4,237.0 Pyramidal D: 15,405.8 ± 949.7 μm Ishizuka et al. 1995 CA2 μm SP-SR D: 4,200 μm D: 4,152.9 μm Mercer et al. 2012 Bannister & Larkman D: 11,915 ± 1,030.0 μm D: 10,957.4 ± 1,669.4 1995 Pyramidal CA1 D: 13,424.2 ± 1,060.9 μm Ishizuka et al. 1995 μm Basket CCK+ D: 6,338 μm D: 7,372.6 ± 598.4 μm Mátyás et al. 2004

* See also Extended Data Table T1-1