Figure 1.
CCM procedure for generating connectivity maps.
(A) Basic principles of identification of dendritic branch intersections and their connections. Dendritic intersections (A1) are identified based on their greater width compared to the dendritic segments composing them (A2, labeled in A3). The intersections are marked (A4), centralized (arrow in A5) and connected by a line (A6, arrow in A7). (B) General description of CCM operation. (B1) Starting image – grayscale, inverted. (B2) Contrast optimization. (B3) Background whitening. (B4) A scanning box with centralized pixel (arrow). (B5) Identified junction area (red) with estimated “intersection center pixels” (black squires). (B6) Areas at and near intersections are removed (colored in blue). (B7) second iteration on an updated image (using varying threshold for intersections) reveals thinner intersections (arrows). (B8) A third iteration generated after removal of the B7 new intersections and using a new threshold revealed additional and even thinner intersections (arrows). (B9) Generation of lines connecting the intersections, according to the neuritic map. Scale: A - 3.5 µm; B - 12 µm.
Figure 2.
Neighboring dendrites preferentially generate contacts among their branches.
Pictures are inverted images of hippocampal neurons grown in culture for 5 days and labeled with anti-MAP2 antibody. (A) An isolated neuron with no physical contacts with other neurons made a single contact between its own branches (arrow). (B) Within a neuronal assembly, dendritic branches turn (arrows) to contact branches of neighboring dendrites (red spots). (C, D) A dense culture in which all neurons orient dendritic branches toward a major overlapping area (circled) where heavy crossing takes place (D, red spots). (E) Dendrite-dendrite contact density is significantly higher among grouped rather than isolated neurons. Shown is the mean ± SEM. Scale: 20 µm.
Figure 3.
Reconstruction of dendritic networks and sub-networks by CCM.
(A) An area in a relatively dense one week old hippocampal culture (A1, MAP2) has ordered (yellow ellipse in (A2)) and less ordered (red circle in (A2)) regions. (A3) Within the ordered area, an even more highly organized region was found (green square) and used for analysis in (B). (B) Dendritic network reconstruction using CCM. (B1) High magnification of the boxed area in (A3). (B2) Reconstruction of (B1). (B3) Connectivity map of (B2). (C) Reconstruction of a sub-network of >1 micron caliber branches. (C1) Reconstructed “thick” branches network. Few thick branches adjacent to the cell bodies were excluded due to deletion of their crossings (located within the blue rectangles). (C2) The connectivity map of the “thick” (red) and fine (green) branches. Yellow arrows show that a large portion of the thin dendrites are at the edges of growing branches. (C3) The “thick” branches sub-network’s connectivity. (D) Comparison between CCM (B3) and the manual reconstructions (D2). (D1) The efficiency of junction and connecting segments detection by CCM compared to that of manual analysis (100%). Shown is the mean ± SEM. Scale (in C3): A - 60 µm; B–D - 15 µm.
Figure 4.
Dendritic branches cross through preferable angles.
(A, B) The procedure for analyzing dendritic crossing angles. A mesh of crossing dendritic branches (A) is reconstructed in (B) based on the intersections location (red spots) and their connections (black lines). Acute and right angles between crossing and bifurcating branches are collected. (C, D) Analysis of the field shown in figure 3D. (C) Crossing angle distribution of combined fine/thick branches. (D) Distribution of angles among >1 micron caliber branches. (E, F) A dendritic network (E) with similar preference of crossing angles ranges among “thick” branches as in (D) but of higher incidence (F). (G) Length distribution of fine (blue bars) and “thick” (red bars) intersections from the field in figure 3D. (H) Frequency of crossing angle range selection among 15 dendritic networks. (I) An astrocytic network. (J) Intersection angle distribution of (I). Note the 40°–50° range preference, which is absent from the dendritic networks (H). Scale (under H): A –4 µm; F, I –20 µm.
Figure 5.
Orientation of axonal traverse near dendritic intersections is affected by the dendritic crossing angle.
Green = dendrites (MAP2); Red = axons (NFM). (A) Axons tend to grow toward the vicinity of dendro-dendritic intersections. Shown are single axons traversing multiple dendritic intersections at angles 80°–90° (blue arrows) and non-80°–90° (yellow arrows). (B) Definition of obtuse (red) and acute (gray) angles of a non-80°–90° crossing between dendritic branches (green). (C) Axons traversing a non-80°–90° dendritic branch crossing. Traverse orientation is restricted to the obtuse angles zones. Axo-dendritic contacts are indicated by arrows. (D) Quantification of the occurrence of axonal traverse of non-80°–90° crossing through the obtuse and acute angles. (E) 80°–90° dendritic crossing (green) traversed (red arrows) in various combinations of its four angle zones (black). (F) Axons traversing an 80°–90° angle dendritic branch crossing (yellow arrows) from 3 out of 4 angle zones (blue spots). (G) Quantification of the occurrence of axonal traverse of 80°–90° crossings through the 4 possible angle zones. Intersections which were not traversed were indicated on the X axes as “0”. (H) Quantification of the distances of the traversing contacts from the dendritic intersections. Scale: A-35 µm, B, C–5 µm.
Figure 6.
Axons traverse dendrites preferably near dendritic intersections.
(A–C): The same field seen as merge (A), dendrites (MAP2) (B) and axons (C). Axons traverse predominantly near dendritic intersections (blue arrows) and rarely at non-intersecting regions along dendrites (white arrowhead). Most non-intersecting shafts of dendritic branches are not traversed but rather fasciculated by axons (yellow arrows). (D) Higher magnification of the central region of (A) shows traverse events near (blue arrows) and at a distance (yellow arrow) from dendritic intersections. (E) Further magnification of the left region of (D): Blue scanning circles (4 µm diameter) used for quantification of traverse frequency. (F) Traverse frequency was considered as the number of axons located within the circles. Scale: A–C - 30 µm; D - 13 µm; E - 3 µm.
Figure 7.
Axons preferentially traverse heavily intersecting dendritic branches.
Green = dendrites (MAP2); Red = axons (NFM). (A) Axons tend to fasciculate (yellow arrow) with dendritic branches at areas of low dendritic branch-to-branch crossing frequency, but prefer to traverse (blue arrows) regions with high rates of dendritic crossing. (B) Two axons defsciculate (blue arrow) from a thick, rarely-crossing dendritic branch to traverse several highly intersected dendritic branches (arrow colors specific to individual axons). (C) Non-crossing dendritic branches (C1) and axons (C2) interact (C3), forming only few axon-dendrite contacts (arrow colors specific to individual axons). (D) When crossing dendritic branches (D1) and axons (D2) interact, the axons heavily traverse dendritic branches (D3), forming axo-dendritic contacts involving multiple axons (D4). (E) A dendritic hub-like organization. The center of the hub (white circle) is composed of heavily crossing branches whereas branches located at the hub’s periphery (blue and yellow marks) have fewer axonal crossing events. (F) Magnification of the yellow rectangle region in (E) shows alignment of axons with rarely crossing dendritic branches and low frequency of axo-dendritic contacts. (G) Magnification of the white circled hub’s center in (E) showing high frequency of dendro-dendritic and axo-dendritic contacts. Scale (black line underneath (E): B - 15 µm; C, D - 6 µm; E - 30 µm; F, G - 10 µm.
Figure 8.
Quantification of preferential axonal traverse of heavily crossing dendritic branches.
I. definition of high vs low frequency crossing regions: (A1–C2) A field which is part of a dendritic hub. (green = dendrites (MAP2), red = axons (NFM)). (A1) The field was divided into two regions: left (“center”) – frequently crossing branches; Right (“periphery”) – rarely crossing branches including dendritic stems (arrows). The crossing points are shown by red spots in (A2). (B1, B2) axons and their crossing points in green (B2). (C1, C2) merge of A1/B1 and A2/B2. Note the higher crossing frequency in the center region compared to the periphery in all cases. II. Nomenclature of the various crossing types (D, left): den-den = crossing points between two dendritic branches; axo-axo = crossing points between two axons; axo-axo on dendrite = axo-axo contacts aligned with den-den contacts; axo-den = contacts between axons and a dendritic branchs. Examples are shown in the middle panels. III. Defining the crossing connecting segment types (titled ‘segments’): den-den = between two den-den crossing points; axo-axo = between two axo-axo crossing points; axo+den = between all crossing points in a merge image. IV. Analysis: (E) Crossing density ratio (at hubs’ center vs periphery), normalized to dendritic length. (F) Ratio of the average length of neuritic segments connecting the crossing points. E and F are combined analysis of 4 hubs. Shown is the mean ± SEM. (G) Length distribution of the connecting segments of the field shown in panels A–C. (H) The segment length distribution in (G) was narrowed to two subgroups. Y axis presents the values of right/left ratio of [#segments (axo+den)/(axo-axo+den-den)]. Shown is the mean ± SEM. Scale: A1–C2 - 7 µm; D, middle panels - 3 µm.
Figure 9.
Axons cluster their synapses near dendro-dendritic crossings by converging predominantly onto these sites.
Green = dendrites (MAP2); red = active synapses (FM1-43). (A) A non-90° dendritic intersection contacted by 7 axons (yellow arrows), most of them traversing through the obtuse angles zones. The axons cluster their active terminals (blue arrow) near the intersection (white arrow). (B) A 90° dendritic intersection traversed by axons from three different zones (yellow arrows), associated with a cluster of active axonal terminals (blue arrow). (C) Size distribution of synaptic clusters located at dendritic intersection vicinities. (D) Synaptic clusters on two dendritic intersections linked by multiple axons (arrows). (E) Same regions as (D) showing an inverted image of dendritic clusters and connecting axons (arrows). (F) A network with active synapses localized to dendritic intersections (arrows). Most clusters are linked through bundles of multiple axons(examples are indicated by pink arrows). Scale: A, B - 10 µm; D - F20 µm.
Figure 10.
The influence of angle and position of dendritic branch crossings on network wiring topology and synaptic clustering.
Green = dendrites; Red = axons. Left panels – wiring through a 60° dendritic intersection: (A1) (left) Two axons reaching a dendritic branch crossing from the blunt and acute angles zones. (Middle) Only the axon in the blunt zone traverses near the crossing site, making two contacts, one on each branch (yellow spots). (Right) Additional axons traversing in the same way align in an array, producing multiple contacts at the dendritic intersection vicinity (yellow dots). (A2) Four 60° angle crossings are positioned against the four angle zones of the central crossing taken from (A1). From the central crossing towards the periphery, the configurations are: obtuse to obtuse (center to right), obtuse to acute (center to left), acute to obtuse (red line pointing down), and acute to acute (dashed arrow). Based on the axonal preference to traverse through obtuse angles, the obtuse to obtuse configuration will become linked by the axonal group. Other crossings will be weakly (obtuse to acute) or rarely (red arrows) linked. (A3) The (A2) configuration yields central and the right crossings that become wired and both bear synaptic clusters. Right panels – wiring through a 90° intersection: (B1) Axons approaching a 90° intersection can traverse through the four angle zones. (B2) Same configurations as (A2) but with a 90° crossing at the center. Due to the higher traverse freedom that axons have with the 90° intersection, they can link two crossings in this configuration. (B3) The outcome is three wired crossings, all bearing synaptic clusters.