The Developmental Rules of Neural Superposition in Drosophila

Abstract

Complicated neuronal circuits can be genetically encoded, but the underlying developmental algorithms remain largely unknown. Here, we describe a developmental algorithm for the specification of synaptic partner cells through axonal sorting in the Drosophila visual map. Our approach combines intravital imaging of growth cone dynamics in developing brains of intact pupae and data-driven computational modeling. These analyses suggest that three simple rules are sufficient to generate the seemingly complex neural superposition wiring of the fly visual map without an elaborate molecular matchmaking code. Our computational model explains robust and precise wiring in a crowded brain region despite extensive growth cone overlaps and provides a framework for matching molecular mechanisms with the rules they execute. Finally, ordered geometric axon terminal arrangements that are not required for neural superposition are a side product of the developmental algorithm, thus elucidating neural circuit connectivity that remained unexplained based on adult structure and function alone.

Figure 1. The Neural Superposition Sorting Problem

(A) The six outer photoreceptors R1–R6 from a single unit eye (ommatidium) receive input from six different points in the visual environment and project to six separate synaptic units (cartridges) in the brain. (B) The six R1–R6 photoreceptors from six different ommatidia that receive input from the same point in visual space connect to the same cartridge, in a pattern that is the reciprocal of that in (A). (C) Schematic view of a lamina section from dorsal (left) to ventral (right) across the equator. The color-coded R1–R6 axons from different ommatidia that receive input from points in the environment A–F are shown in their final cartridge arrangement on the left. The circular arrangement of axon terminals in the cartidges shows the precise rotational stereotypic arrangement of R1–R6.

Figure 2. Intravital imaging reveals the morphogenesis of the lamina and photoreceptor growth cones during brain development

(A) Imaging chamber for 2-photon live imaging through the intact, developing pupal eye. Right panel: side view of all photoreceptors labeled with membrane tagged CD4-tdGFP at 20h APF. (B–D) View of the same specimen as in (A) from inside the brain (B), with the axons viewed from a cut plane between eye and lamina (C) and after 20h hours of further development (D). (E–G) Side view of the same specimen as in (A–D) in 10h developmental intervals. See also Movie 01. (H–J) Side views of a specimen at the indicated time points with sparse photoreceptor labeling and individual identified growth cones marked in R1–R6-specific colors as defined in Figure 1. (K–L) Visualization of individually segmented growth cones from the specimen shown in (H–J) at 25h APF (K) and 40h APF (L).

Figure 3. The Scaffolding Rule: bipolar growth cones generate a stable framework that facilitates the sorting problem

(A–F) Movements of a cluster of 12 growth cones between 25h and 40h APF. Arrowheads denote heels, arrows mark growth cone fronts. (A′-F′) show the positions of the heels only. Note that the lower part of this cluster expands due to lamina unfolding between 25–34h APF, yet no heels shift relative to each other. Scale bar: 5μm. See Movies 02 and 03. (G–I) Cross-section through the lamina plexus at 40h APF for the same specimen as shown in (A–F). (G) Background labeling reveals a rhomboidal 80°/100° grid in the lamina plexus that overlaps all growth cone fronts (ovals). In contrast, all heels (arrows) are located outside the grid defined by R-cell fronts. Scale bar: 5μm. (H) Extrapolation of the position of all heels in the scaffold. (I) Vectors of R1–R6 growth cones at 40h APF based on measurements at 40h APF. (J) Updated schematic of growth cone sorting in the lamina plexus, viewed from the eye, based on the schematics shown in Figs. 1C,D. Note that the heels have a horseshoe-shaped arrangement within the circular ‘arrival units’ shown in Fig. 1C, whereas the target ovals form a intercalated grid. (K) Cartridge distances in the lamina plexus between 20h and 40h APF reveal scaffold stability throughout growth cone sorting. Measurements were taken from fixed preparations shown in Fig. S1. Data shown: mean +/− SD (n is ≥67 for each time point).

Figure 4. The Extension Rule: Quantitative analysis of growth cone dynamics reveals synchronized extension programs specific for each R1–R6 subtype

(A) Schematic of quantified heel, front and filopodial positions (same specimen as Fig. 3). (B) Heel-Front distance for R1–R6 between 25h–40h APF. Asterisks: denote the subtype-specific initiation of extension and black lines highlight periods of near-linear extension. (C) Heel-Front angles between 25h–40h APF reveals angle constancy for R1–R6 throughout the sorting process. (D) Angles between heel and longest front filopodium reveal average filopodial explorations at closely matching angles. (E–F) Angles of the longest front and heel filopodial exploration. (G–I) Extension dynamics are identical across the A–P axis, indicating synchronous movements across the entire lamina plexus. See also Fig. S2. (B–G) Data shown: mean +/− SD.

Figure 5. The Stop Rule - Part 1: How good a target is the target?

(A) Single frame at 28h APF from a 20h time-lapse movie of all target L-cells. Arrow: single representative heel bundle (arrival unit). The boxed area marks the heel scaffold and the blue line marks the equator. Scale bar: 5μm. (B) Enlarged region within the box in (A) with one heel bundle shown. The shape of a representative R3 originating from this heel bundle reveals overlap with at least two incorrect targets (black asterisks) in addition to the correct target (white asterisk). (C) Reference schematic for quantifications and the computational model; see text for details. (D–F) Analysis of target recognition with different sensing radii for an R-cell front in a schematic (D), a single representative R3 growth cone (E), and an overlay of all R3 growth cones analyzed for this study. (G–L) Overlap with any target throughout the simulated move of three R-cell sensing fronts of differing radii. Arrows indicate partial overlap, arrowheads indicate premature final stops. See also Fig. S3.

Figure 6. The Stop Rule - Part 2: R1–R6 growth cone front overlaps can increase the robustness of the stop rule

(A–F) R1–R6 outlines from intravital imaging data for 25h APF (A–C) and 35h APF (D–F). The outlines are shown in subtype pairs for R1+R3 (A, D), R2+R5 (B, E) and R4+R6) (C, F) to highlight the amount and increase in overlap in the target area (dark ovals) during these 10 hours of growth cone extension. (G) Representative growth cones at 40h APF. Shown are the ‘outgoing’ growth cones from one bundle, the ‘incoming’ growth cones to one target (arrow) and a pair or R1+R3 to highlight covering and overlap in the target area. (H) Computer simulations with a stop rule using coincidence detection of the target plus all other R fronts and the sensing radii 0.36 and 0.5. (I) R1–R6 front overlaps with other R-cell fronts or targets with the noted sensing radii. (J) Systematic parameter scan of all combinatorial stop rules and sensing areas from SR=0.2–0.5. (K–M) Systematic scans for sensing radii 0–0.5, sensing start time 20–40h and +/−10° randomly varied extension angles are shown for the ‘target only’ rule and two combinatorial stop rules without (L) and with target (M). Each data point was simulated 100 times for angles that were randomly offset +/−10° (Fig. S4).

Figure 7. The equator and rotational stereotypy validate the developmental algorithm and indicate a role for R1–R6 overlap sensing as part of the stop rule, but not the extension rule

(A–B) Schematic of all types of main and equator-type cartridges, their composition (top), the stereotypy of the arrangement of the varying types of R cells (A) and the result of a simulation of the developmental algorithm using the computational model (B). Simulation with SR=0.22 and a stop rule of ‘target+4R’ (C–G) Comparative analyses of R3 and R4 growth cone dynamics in the main lamina and across the equator. (H–M) Systematic parameter scans for the labeled stop rules and all sensing radii 0.2–0.5 across the main lamina and equator. The red bar indicates at what sensing radius correct superposition sorting fails. Note that all stop rules that include R front sensing exhibit reduced equator robustness at larger sensing radii. See also Figs. S5–6.