Building Retinal Connectomes

Introduction

Though the broad outlines of retinal networks have been known for decades, no total subnetwork is known for any retinal neuron. New electron imaging technologies now have the potential to build complete networks: connectomes. This article addresses connectome completeness and advances in imaging, data management, data navigation and validation in connectomics.

The Motivation for Connectomics

Why can’t we infer networks from physiology or modeling? Graph theory [1, 2••] provides the answer. Retinal and brain networks are multi-edge digraphs (directed graphs): collections of vertices (cells or cell compartments) connected by directed (synaptic) edges. The number of possible graphs N_n constructed from n vertices is extremely large even with aggressive constraints (Fig. 1). Even the simplest 3-vertex labeled digraph admits N₃ = 64 networks. The human retina has ≈ 70 classes of cells [3], and the human brain has no fewer than 250 regions ( ≈ 200 for cortex alone [4]) and likely >1000 classes of neurons. Topologic complexities such as diverse cell copy numbers and coverages [5], molecular connection types, and synaptic weights exponentially expand this universe of possible networks. Inference based on inverse solutions for such high complexity systems is untenable as provable mappings of physiologic transfer functions onto unique graph topologies do not exist [6]. Graph theory also clarifies the limits of modeling since discovering network motifs is one of the most intractable of computational problems: the subgraph isomorphism or clique decision [7]. The solution space is likely not computable and computational proof of a motif’s biological role is impossible. The same problems afflict analyses of genomic, proteomic and metabolic networks [8]. The solution lies in network ground truth [9•], not inference. Despite heroic efforts, anatomy has built only small fragments of real networks [10, 11•,12, 13•, 14–17]. The way forward is connectomics, now feasible because (1) electron microscope platforms have been repurposed for high throughput data acquisition and (2) large-scale storage / imaging is affordable.

Fig. 1. Network Enumeration.

Graph enumeration for networks. A three vertex (n=3) network (ABC) can form different numbers of motifs if the connections are undirected U(n), directed D(n) (solid arrows), or directed with re-entrant loops R(n) (dotted arrows). Networks can be limited to vertex clusters of size k [C(n,k)]. Directed (D) and combinatoric (C) networks in retina (n=70), brain regions (n=250) and brain neurons (n=1000) were calculated using the Wolfram Alpha engine (www.wolframalpha.com).

Connectomics

A connectome is the complete graph (the adjacency matrix) of a neural volume that describes all partners and non-partners. Connectomics includes macroscopic analyses such as the Human Connectome Project [18] and other large-scale initiatives [19, 20] as well as microscopic analyses of synaptic networks in delimited structures like the vertebrate retina [21••,22•]. Molecular markers, synapse numbers and synapse sizes can also be used to weight the adjacency matrix and preselect candidate cells for analysis. Though only physiology can correctly parameterize the matrix, the key is creating the matrix. The stages of any synaptic connectome project are sample treatment, sectioning, electron imaging, tagging, tiling, navigation, annotation, analysis and data sharing.

Sample treatment and molecular tags

Connectomics samples are chemically derivatized for electron imaging, and often augmented with molecular or functional segmentations inserted by physical or optical methods. Anderson et al. [9,21] used excitation mapping with organic actions to embed small molecule light response histories into a retinal sample. Briggmann et al. [22] and Bock et al. [23••] used registration of optical calcium imaging onto ultra-structural datasets to pre-identify functional neuron classes. Glutaraldehyde-based fixation followed by metallization steps are ideal for visualization of neural connectivity by transmission electron microscope (TEM) imaging, and other marker strategies based on genetically modified organisms [24–26] are possible. The new “miniSOG” method, an electron-imaging analogue of GFP labeling, is particularly promising [27••]. In contrast, ablation imaging (see below) permits only en bloc staining to generate tissue contrast and currently has limited marker options. Molecular markers are essential for connectomics. Only TEM has proven capable of incorporating them into routine connectome datasets via small molecules and some proteins immunoprobed optically on intercalated ultrathin sections, with clustering to classify cells [9, 28–30]. Another variant of this is array tomography, which uses re-probing methods to build molecular data volumes into which ultrastructural data can be inserted [31••,32–33].

Sectioning

Ultrastructural connectome datasets are formed by ablation or slicing. Ablation includes in vacuo serial block-face (SBF) sectioning [34,35] or ion beam surface milling [36], followed by SEM or scanning TEM (STEM) imaging of surface-backscattered electrons. SEM/STEM systems only image surfaces. Slicing is dominated by manual ultramicrotomy [9,37] onto electron-transparent film supports followed by conventional staining and automated TEM (ATEM) imaging [9]. Primary electron transmission imaging generates projection images of the section thickness, optimally at 50–70 nm. Manual ultramicrotomy is fast, inexpensive, and compatible with an extensive repertoire of stains and molecular markers. Automated sectioning onto electron-opaque supports can also be used, followed by STEM imaging [38], but these platforms are not widely available. Though ablation methods benefit from coarse pre-registration of image fields, SEM/STEM imaging imposes limits in resolution, speed, and molecular tagging. Slicing requires additional computational registration of image tiles, but that is a solved problem [39].

Electron Imaging, Tiling and Registration

Connectomics requires tens to hundreds of terabytes of data depending on resolution and volume subtended [9,21]. In retina, TEM volumes are collections of slices imaged at >1000 overlapping tiles (Fig. 2). Robust detection of gap junctions and synapses requires ≈ 2 nm resolution, and validation requires re-imaging at finer resolutions with goniometric tilt, which is only possible with TEM [9, 21,37]. Typical SEM platforms usually cannot acquire data at better than 10 nm, suited to coarse-grained connectomics only, and cannot prove completeness. A recent review of connectome methods by Kleinfield et al. [38], inexplicably ignored any work with resolutions better than 10 nm, though 2 nm resolution is essential for completeness [9] and synaptic weighting [37]. As they are based on commercial electron-imaging cameras and automated acquisition [40••], ATEM platforms can be implemented by many existing TEM facilities. A more advanced TEM design uses reconfigured columns, custom phosphor plates, and custom camera arrays [23], producing the fastest connectome imaging architecture. This approach requires a dedicated TEM and skilled staff. Different schemes have been used to generate navigable ultrastructural data-sets. Preserving the slice as a 2D page simplifies data navigation, distribution and sharing [41•]. Fully automated precision mosaicking and slice-to-slice registrations developed by Tasdizen et al. [39] exploits image Fourier shift to compute net displacement vectors. Resampled slice-to-slice alignments, refined by nonrigid grid alignment, are then used to automatically build 2 nm resolution volumes. These strategies and their derivatives are also applicable to large scale optical atlases [42].

Fig. 2. Connectome RC1 slice 001.

Connectome RC1 slice 001 composed of >1000 high-resolution TEM tiles. The slice is augmented with a multispectral transparency mapping simultaneously displaying GABA (red), glycine (green, glutamate (blue), and a logical AND of glutamine and taurine signals as a dark gold alpha channel. GABA+ (red) neurons are amacrine cells, while glycine+ (green) neurons are either amacrine or an ON cone bipolar cell subset. Glutamate+ (blue) neurons are largely bipolar cells. Image width, 243 µm. From Anderson et al., 2011, Molecular Vision 17:355–379 by permission of the authors.

Navigation, Annotation & Analysis

Terabyte-scale imagery cannot be explored with conventional imaging tools and new tools are required [41, 43,44]. Several groups have successfully used image pyramids as a data delivery architecture [41,45]. The open-source Viking environment [41] allows multiuser remote visualization by converting datasets to web-optimized tiles and delivering volume transforms to client devices via conventional internet connections. Generation of 3D cell renderings and mapping of synaptic networks requires integrated annotation and database architectures. In Viking, disc markers are used to approximate convex hulls and linked to build 3D representations (Fig. 3) with accurate size scaling for modeling. Relational structures (presynaptic complexes, postsynaptic densities, gap junctions, adherens junctions) are located, sized and linked to build adjacency matrices. Annotations also store metadata and permits bookmarked web-tours of networks. Analysis requires rendering, graphing, network touring, and informatics. The open-source Viz web services for Viking allow cell renderings at higher resolutions than optical methods, automated network graphs, navigation between ultrastructural data and network motifs, and automated statistical summaries. While significant efforts have been made to achieve automated tracing [43, 46–48], all connectomes must presently be validated by human annotation [41] and none are currently practical for connectomics of complex neuropil. Correcting annotation errors has proved rather straightforward. Completeness ultimately purges errors and metadata parsing can detect early errors. Errors such as skipping between processes in tracing are flagged as forbidden switches in molecular signatures, associated synapse type, targets or inputs. One of the best methods is parsing network graphs for violations.

Fig. 3. Stereo pair rendering.

A stereo pair of 3D volumetric constructions. A_II amacrine cell 476 (dark red) is shown with all of the rod bipolar cells that drive it and an adjacent microglial cell (5016). Each of the bipolar cells is numbered with the total number of ribbon synapses it makes with cell 476 in parentheses. The cells were rendered using the Vikingplot application, calling the open-access RC1 database.

Sharing

Connectomics datasets must be shared [41, 43,49], but distributing raw datasets is impractical. The solution is open-access via web services. The Viking strategy involves open source tools and common file formats to accommodate other widely used applications, e.g. Blender (www.blender.org). Such open-access approaches minimize the overhead for journals as data gatekeepers, but poses problems of intellectual ownership. We have opted for full public sharing of our datasets and tools as proposed by Jeong et al. [43]. The next critical stage is integrating annotated datasets and summary networks with large informatics frameworks [50, 51].

Examples of Connectomics Discovery

Ultimately, hypotheses addressing retinal signal processing, network development, network evolution, and visual behavior will only yield to mapping at resolutions sufficient for completeness: 2nm or better. Validation involves several levels. First, do connectome datasets replicate previous reconstructions? An exceptional test case is the A_II amacrine cell (AC), a critical interneuron in mammalian scotopic vision, previously reconstructed by several different groups [11, 13,52,53]. Fig. 3 shows a stereo pair of A_II AC 476 from the RC1 rabbit retinal connectome and every rod bipolar cell (BC) associated with it. Connectomics extracts all previously reported features of this cell in over 30 instances, corrects prior errors and omissions, and extends the network [21] by characterizing previously undiscovered synaptic partners including wide-field ON cone BCs and unique sets of GABAergic ACs. A higher level of validation involves building navigable network graphs with synaptic weighting data such as postsynaptic density areas (http://connectomes.utah.edu/viz). Such graphs show that scotopic operations are, unexpectedly, a minor facet of the A_II connectome. This suggests that A_II cells are central elements in the evolution of photopic ON → OFF crossover networks later repurposed to serve rod vision. Fig. 4 displays a condensed 1-hop connectome for the A_II AC, showing the minimum partner set. There may be subclasses within some GABAergic groups. Such analyses can be applied to every retinal cell class, including glia, microglia and vascular elements, enabling accurate volumetric adjacency analyses in the retina of every species. Connectomics at 2 nm resolution also provides insights to important associations [21] such as heterocellular and homocellular gap junctions [54•,55], fasciculation and glomerular associations via adherens junctions, new architectures for intercellular contacts, nanoscale synaptic assemblies, synaptic and gap junction turnover by endocytosis, synaptic ribbon transport, postsynaptic density assembly, as well as glial and microglial intercalations by fins as thin as 20 nm, and more. At a coarser resolution, connectomics analysis supports the preferential association of starburst AC dendrites with the corresponding directional bias of ON directionally selective ganglion cells [22]. Whether high resolution connectomics of complete networks will affirm this remains to be seen.

Fig. 4. Summary network.

The complete connectome for class A_II glycinergic ACs in the mammalian retina. The connectome shows four modes of excitation (solid arrows), three modes of coupling (lines), five modes of GABA inhibitory input (open arrows), and four glycine inhibitory output modes (double arrows). CBa, OFF cone BCs; CBb, ON cone BCs; WF, wide field ON cone BCs; RB, rod BCs; TH1, class 1 dopaminergic axonal cells; α, alpha GCs; δ, delta GCs; pAC, peptidergic GABAergic AC; OFF AC1, dominant monostratified OFF cone AC population; OFF AC2, minor monostratified OFF cone AC population; ON AC, dominant monostratified ON cone AC population; ON SAC, ON starburst amacrine cell; AI-S2 subclass S2 class AI rod-dominated GABAergic AC. Some of the groups can be further weighted. For example, though ON cone BCs classes (there are at least five) are coupled to A_II cells via gap junctions, they differ in their gap junction areas and one class (WF ON cone BCs) is also pre-synaptic via ribbon synapses.

Towards completeness

Completeness requires mapping all contacts and contact patterns across multiple instances of a cell class. The variance of some metric should be minimized when sampling approaches completeness, but we are still discovering those metrics. For example, the mean rod BC ribbon synapse count for four adjacent A_II ACs in RC1 is 74 ± 5 (1 SD) with coefficient of variation (CV) 0.066. The same cells have a mean rod BC contact count of 11.5 ± 3.7 (CV = 0.32), suggesting that neurons normalize synapse number despite varying neurite overlap geometries. Completeness is also gauged by edge density in network graphs where submotifs can be extracted and quantitatively compared.

Conclusion

Completeness in connectomics involves three key issues. (1) Resolution at 2 nm or better to unambiguously mark synapses and gap junctions is absolutely critical for completely mapping any network [37, 54,55] and, at present, TEM is optimal for such investigations. (2) Molecular [21, 27] or optical [22, 23] tagging to pre-select cells of interest in complex neural populations is also essential as an independent test of identity and as a segmentation strategy. (3) Increasing the number of platforms available to investigators and sharing them is the only practical way forward for synaptic connectomics [9]. Building artisanal tools is an important strategy, but inexpensive, high resolution commercial systems must be developed, mirroring commercial fMRI systems that support macroscale connectomics. The next generation of tools should facilitate the emergence of comparative connectomics to explore the evolution and development of retinal networks and pathoconnectomics of retinal neurodegenerations [28, 29].

Highlights.

• Complete retinal networks must be mapped by connectomics and cannot be inferred

• Transmission electron microscope imaging provides optimal synaptic resolution

• Many existing electron microscopes can be converted to connectomics imaging

• Ultrastructurally compliant molecular tags are required for fast connectome assembly

• Retinal neurons thought to be well-understood are proving to be unexpectedly complex