Identifying Neuronal Lineages of Drosophila by Sequence Analysis of Axon Tracts

Tracing SATs

The first step in the identification of a SAT is its representation as a sequence of points in space. For this purpose, we have created a simple manual method: using semi-3D Bézier curves (Bézier curves whose points have a linearly interpolated z coordinate), a human operator can segment a SAT in well under a minute, approximating the skeleton of the SAT (Fig. 2). As an alternative and as part of an effort toward automation, we also use a semiautomated tracing method (Simple Neurite Tracer by Mark Longair) that automatically generates the most likely 3D path between user-defined starting and ending points as a sequence of sampled points in space.

Using these methods, we manually traced all neurotactin-labeled SATs from 5 Drosophila third instar brain hemispheres, building a reference database of annotated SAT traces.

Registering query and reference SAT traces into a common coordinate space

Each brain differs in its orientation relative to the volume defined by the confocal image stack that contains it. To compare SAT traces between brains, the latter must be registered with each other; otherwise, shape and position differences lack meaning. For this purpose, we use internal brain reference points to estimate a 3D transformation. The most obvious reference points to the Drosophila neuroanatomist are the mushroom body lobes, particularly the tips of the dorsal lobe, medial lobe, and peduncle, and the peduncle's branching point into dorsal and medial lobes (Fig. 3). These four reference points are easily identifiable across a variety of labelings, including no labeling (just differential background intensities).

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Figure 3.

Reference points in the brain for 3D registration. Top six panels show confocal sections illustrating the position of the eight reference points used in 3D registration. Medial to the left, dorsal to the top. dl indicates dorsal lobe tip; ml, medial lobe tip; bp, mushroom body branch point; pj, mushroom body lineages junction point, or tip of the peduncle; BLD6, sharp turn of the SAT of lineage BLD6 into the great commissure where it reaches the optic lobe (OL; dotted line indicates the SAT trace); BAla, point of divergence of the four BAla SATs (grouped as 1–2 and 3–4, their common nearby paths indicated as dashed lines; this point lies very close to the ventral nerve cord VNC); DPMm, entry point of the SAT of DPMm1 into the dorsoposterior brain commissure (DPC); BLVa, point of convergence of the three BLVa SATs, ventral to the entry of the great commissure (GC) into the optic lobe (OL). Lower four panels, 3D views of the eight reference points relative to the mushroom body lobes (magenta) and its four lineage SATs (magenta), and the SATs used as reference (gray).

The mushroom body constitutes an acceptable reference system for the following reasons. First, all lobes reasonably approximate a straight line and present clear boundaries. Second, their span is that of a large proportion of the neuropile volume, en par with the dimensions of the SATs to analyze. Third, each brain hemisphere contains a unique mushroom body. The mushroom bodies of the two hemispheres of a brain are mirror images of each other. Fourth, the fact that a mushroom body has three approximately perpendicular lobes naturally suggest a well posed 3D coordinate system. And fifth, the mushroom body is generally conspicuous even in the absence of a specific label, as background. Anti-neurotactin antibody, our molecular marker of choice for SATs, specifically labels the axons of newly born Kenyon cells in the mushroom body.

Our initial results suggested that the four reference points provided by the mushroom body allow for a good registration of lineages close to the mushroom body (posterodorsal, dorsal, dorsomedial, and dorsoanterior lineages), but that they are not sufficient for the lineages which are relatively far from it (the lateral, basal, and posteromedial lineages). We therefore searched for four additional reference points that are evenly spread out throughout the rest of the brain, and that are also easily recognizable in neurotactin-labeled brains. We have defined the basolateral dorsal (BLD) 6 elbow point, the basoanterior anterior-lateral (BAla) split point, the ventral basolateral (BLV) junction point, and the DPM entry point into the neuropile (Fig. 3). With all eight reference points, we estimate a nonlinear transformation using the moving least squares (MLS) method (Schaefer et al., 2006) for 3D affine transformations that provide an appropriate registration for all protocerebral and deuterocerebral SATs. By this method, the brain of interest is smoothly warped onto a reference brain, preserving the relative position of internal brain components.

With the eight-point 3D MLS transformation, any query SAT can be brought with a very good approximation into the coordinate space of the reference SATs with a very fast operation. The transformation corrects for global orientation, shear, scale including mirroring (hemispheric chirality), and to a sufficient degree for local deformation (Fig. 4). We have designed our system to provide the option to constrict the desired transformation to a linear transformation [translation, rigid body, similarity (isometric scaling), and affine] or nonlinear transformation through MLS, for minimal to maximal warping, as desired.

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Figure 4.

The neurite search algorithm. Schematic diagram of all steps in the neurite alignment and similarity quantification algorithm. The algorithm is fed with a query SAT trace and a database of reference annotated SAT traces (top left). SAT traces (red) are schematized in the context of their third instar brain hemisphere (optic lobe in gray). Each trace is resampled to a common point interdistance d and then transformed into a sequence of direction vectors. Then the query sequence is aligned to each reference one by dynamic programming, using the subtraction of two vectors as cost function. From the resulting matrix of cumulative vector length differences, we extract three main parameters that describe the similarity of the two compared sequences (bottom). The Levenshtein distance is the value contained in the bottom-right cell of the matrix. The sequence of editions is extracted backtracing the matrix and is the basis for the measurement of the mean Euclidean distance between the corresponding points of two SAT traces (bottom left, in red and gray).

The availability of pixel-accurate 3D registration methods (Jefferis et al., 2007) would necessarily increase the accuracy of our SAT recognition system if constrained to the invariant parts of the brain. Relying on manually selected fiduciary points has the practical advantages of (1) avoiding the computationally very time-consuming process of pixel-accurate brain registration, with the inevitable loss of pixel resolution, at the cost of accepting small very local inaccuracies in the registration process (we register not the brain but the traced SATs only, being a very fast computation); (2) to transition nicely into fewer fiduciary points and thus less accurate brain registration (but still valuable registration), if fewer fiduciary points are available due to lack of neurotactin or equivalent labeling; and (3) to improve with the availability of more fiduciary points, such as obtained by automatic 3D feature extraction.

Comparing SAT traces

A SAT trace is a sequence of ordered points, where origin and point order matter. Jiang et al. (2002) conceived a method to generate any number of intermediate lines between any pair of lines on the plane, by applying dynamic programming to an arbitrary point sequence representation of the lines. Their method is robust as long as lines do not present loops. SAT traces are ideally suited for the application of Jiang et al. (2002) method, with modifications, for the purpose of quantifying the similarity of any pair of SAT traces. The core concept is the transformation of lines into sequences of comparable elements and then defining a cost function for the comparison of any two elements.

Both the manual and the semiautomatic tracing of a SAT in a confocal stack generates a sequence of points which, because of the nature of Bézier curves (or rather, their de Casteljau approximation) and the integer accuracy of pixel coordinates, respectively, present uneven consecutive point interdistances. To generate sequences of comparable elements necessary for dynamic programming comparisons, we homogenize point interdistances by resampling SAT traces with an arbitrary point interdistance d, common to all SAT traces to compare. Then, we convert the sequences of points into their corresponding sequences of direction vectors between consecutive points (Fig. 4). For any given pair of traces to compare, the number of vectors thus generated may be unequal, but the resampling to a common point interdistance d imposed an homogeneous equal vector length (Fig. 4).

The choice of the resampling point interdistance d will affect the final number of points in the sequence: when d is small, sequences will have more points and represent more accurately the original SAT trace. In the presence of various sources of noise, increasing d will smooth 3D traces (by eliminating high frequencies) and thereby potentially increase the overall accuracy of the recognition. The number of points, in turn, affects quadratically the number of pairwise operations to compute. The choice of an adequate d for resampling is thus critical for the optimal performance of our algorithm. The calibrated pixel size sets a lower bound (the length of the diagonal of a voxel); the diameter of the volume enclosing a trace (i.e., the brain surface) sets the upper bound. We have explored numerically a range of values for d and found an optimal range between 1 and 6 μm for our Drosophila third instar brain confocal stacks (supplemental Fig. 2, available at www.jneurosci.org as supplemental material).

After resampling SAT traces, these sequences of direction vectors constitute sequences of comparable elements: a vector from a query sequence may be compared to a vector of the reference sequence simply by subtraction (the cost function), as shown by (Jiang et al., 2002) for the two-dimensional case. When equal, the length of the resulting vector is zero; when maximally unequal, the length is 2d. With this simple cost function for correspondences, we can apply dynamic programming techniques to compare the shape of any two SAT traces (Fig. 4) (dynamic programming is a mathematical optimization method, where complex problems—such as sequence alignment—are simplified by breaking them down into simpler subproblems such as the alignment of short subsequences, recursively, so that ultimately individual elements are compared). Dynamic programming requires two more costs: that of deleting and that of inserting a vector in the sequence. The trivial choice taken in the study by Jiang et al. (2002) assigns a cost of 1d to both; our numerical parameter exploration suggests that a cost of 1.1d is a better choice empirically (Fig. 2).

Scoring two SAT traces for similarity: Levenshtein distance, ratio of correspondences, and mean Euclidean distance between correspondences

Once both query and reference SAT traces have been transformed into a common reference space, resampled to an arbitrary and equal point interdistance d, and reformulated as sequences of direction vectors, we perform global sequence alignment using dynamic programming. Sequence alignment algorithms have been used previously for the alignment of sequences of discrete variables, such as for suggesting correct word spellings (Wagner and Fischer, 1974) and for nucleotide sequence alignment (Smith and Waterman, 1981; Altschul et al., 1990), as well as for alignment of sequences of continuous variables, such as for curve morphing (Jiang et al., 2002) and for recognition of Drosophila flight trajectory motifs (Grover and Tavaré, 2009). Inspired by Jiang et al. (2002), we formulated an alignment algorithm that provides the basis for the quantification of SAT trace similarity (Fig. 4; supplemental text, available at www.jneurosci.org).

The global alignment matrix delivers the Levenshtein distance and the sequence of editions (the correspondences) between the elements of the direction vector sequences representing the SAT traces (Fig. 4). The Levenshtein distance measures shape similarity. However, shape information is not enough to confer identity: two SAT traces of very similar shape but far apart in the brain would score as very similar. A good parameter describing SAT trace similarity would incorporate not just shape but also Euclidean distance. Measuring Euclidean distances between two sequences of points in space is not possible without a strategy to select which points to measure against which. The sequence of editions is one such strategy, which provides point correspondences between the query and the reference sequence based on shape similarity around any given point. Thus by combining the sequence of editions, which describes point correspondences between two SAT traces, and the sequences of points in space describing each SAT trace, we compute the mean Euclidean distance between corresponding points, synthesizing information on both shape and position in the brain (Fig. 4; supplemental text, available at www.jneurosci.org).

We measure a total of 11 parameters from the global sequence alignment of two SAT traces (supplemental text, available at www.jneurosci.org). The implementation of a successful SAT trace comparison algorithm revealed a number of strengths and limitations of these 11 parameters. Of note is the sensitivity of many parameters to uneven SAT trace lengths and to large insertions or deletions, as well as their value in handling branching events; on all of these we have elaborated further in the supplemental text (available at www.jneurosci.org as supplemental material).

The revised secondary neuronal lineage nomenclature

The secondary neuronal lineage nomenclature described by Pereanu and Hartenstein (2006) provided individual names for most lineages. Several lineages (e.g., DALcl1/2) were described as pairs of adjacent sister lineages whose SATs were so similar and close to each other that they could not be resolved. Finally, the diversity within lineages was not further considered. Numerous lineages are composed of smaller units [sublineages (Bello et al., 2008); hemilineages (Cornbrooks et al., 2007)] which, even though initially they project in a common SAT, they may later split into two or more branches. With the help of GFP-labeled clones, we have resolved as many as possible of the sister lineages into individual lineages and specified several SATs as sublineages.

Furthermore, we had to extend the nomenclature to distinguish individual axon tracts (SATs) formed by hemilineages or sublineages. Each SAT takes the name of the enclosing lineage plus a numerical postfix. For example, lineage CM3 has multiple prominent sublineages termed CM3:1, CM3:2, CM3:3, etc. In general, numbers are lower the more medial and dorsal the SAT trace lies.

The nomenclature described by Pereanu and Hartenstein (2006) defined a few lineages in groups consisting of adjacent or sister lineages (such as DPMpl1/2; and numerous others). We have resolved as many as possible into individual lineages, with the help of flip-out clones and by comparing multiple dense-labeled neurotactin brains.

Six new lineages were added to the map published by Pereanu and Hartenstein (2006). Five of the six newly described lineages (BLD6, BLP6, DALl2, BAlp4, DPMpl4) could be identified in all five reference brains. BLD7 was identified in two brains only.

Four of the previously identified lineages (CM2, BAlc2, DPLc5, BLVp2) turned out to be sub/hemilineages and have been removed. An updated list of all SATs is provided, which details the transition between the old and the new nomenclature (supplemental Table 1, available at www.jneurosci.org as supplemental material).

The large majority of SATs could be identified in all five brains. However, a few SATs do not have homologs across all brains (see supplemental Table 2, available at www.jneurosci.org as supplemental material), indicating either differential labeling by the antineurotactin antibody marker BP106, our inability to resolve the SAT trace in a dense neurotactin labeling (likely the case for the type II secondary lineages of the CM group; Bello et al., 2008) or variability of SATs (only two of five: BLD7, DPLc4; only three of five: BLAd3, BLD4, BLP1:1, DPMl2, DPMpm2:2; only four of five: BAmv1:1, BLAd4, CM3:2, CM3:8, CM4:1, CM5, CP1:2, DALl3, DPLl2:2, DPLpv:2, DPMpm1:1, DPMpm1:2, DPMpm2:1, DPMpm2:3).

Analysis of the stereotypy of SATs

Insect brains and Drosophila brains in particular have been described as highly stereotypical (Hartenstein and Campos Ortega, 1997; Jenett et al., 2006; Technau, 2008). Individual cells are recognizable across brains of different individuals [for neuroblasts, see the study by Urbach and Technau (2004); for late embryo ventral nerve cord neurons, see the studies by Bossing et al. (1996) and Schmidt et al. (1997)] and in the first instar larva (personal observation). We used the most discriminative parameter of NIT, the mean Euclidean distance, to measure the interbrain variability of SATs.

We use the tree of clustered lineages introduced above (Fig. 5). The tree illustrates that approximately half of the lineage traces are most similar to their homonymous partners across brains and thus cluster together (for instance, DAMd1) (Fig. 5A). Only three pairs are more similar intrabrain with their sister lineages than interbrain (BAmas 1 and 2, and to a lesser degree CP2/3:2 and :3; DAMv 1 and 2; DALd and DALcm2:2) (Fig. 5B). A few sets of lineages appear unresolved. The least well resolved set consists of the BLAd and the BLD 1-4, which are all closely apposed in space, and all project into the dorsal half of the compact transverse superior fascicle (Pereanu and Hartenstein, 2006). A second unresolved set includes the CM1 and CM3:1 and :2 traces, and the DPMpm1 and 2, DPMpl2 and CM4 traces.

For the lineage BAlv, all five instances (one per brain) cluster together in the same clade but present substantial distance from each other (Fig. 5C). The location of BAlv, as its name indicates, is baso-anterior lateral ventral, furthest away from the eight 3D landmarks used for estimating a 3D transformation for volume registration (Fig. 3). All tritocerebral lineages are likewise affected and have thus been used as outgroups for neighbor joining.

Only 3 of 634 traces are outliers in the sense that they do not get resolved well and appear as sister branches to entire groups, near their homonymous traces in the other brains. These are e-BAlc:2:2, e-CM5, and d-DPLpv:1 (where the prefix “a” to “e” indicates one of the five brains). Their idiosyncratic position in the tree despite their spatial position in the brain next to nonidiosyncratic traces suggests true variability in the projection pattern of these SATs.

Variability along the SAT trace: minimum enclosing envelope and standard deviation

We created a consensus trace for each SAT by condensing up to five SAT traces into a single one. We measured the mean Euclidean distance for all possible pairwise combinations, and then, using an unweighted pair group method with arithmetic mean (UPGMA) (Dubes and Jain, 1988) strategy, iteratively merged the closest pair until only one trace remained. Merging was performed in a weighted manner (Jiang et al., 2002), where the weight represents the proportion of the number of original traces that each trace in the pair contributes. (E.g., in merging two original SAT traces, each contributes itself only with a weight of 1/2. In merging an original trace with a trace resulting of merging two traces, the weights are 1/3 and 2/3, respectively).

We used the consensus trace as the ideal trace of each SAT. We then measured the deviation of the real SAT traces from the ideal, in two ways: (1) by determining the minimum envelope that encloses all original SAT traces; and (2) by plotting the standard deviation at each point in the consensus SAT trace sequence. We generated the lists of points of the source traces which were used to generate each point of the consensus trace. We measured the maximum distance between the consensus point and its corresponding source points and calculated the standard deviation. As a visual representation of SAT stereotypy, we built the minimum enclosing envelope by generating a tube centered on the consensus trace and has the maximum distance as its radius at any given point. The stereotypy of a SAT is correlated to the radius of its minimum enclosing envelope.

When plotting the standard deviation of radii along the trace, we observed a pattern common to most SATs. The initial segment of the envelope (corresponding to the trajectory of the SAT as it crosses the brain cortex) has a conical shape, with the base of the cone at the brain surface. For most of the trajectory of a SAT within the neuropile, the minimum envelope is cylindrical and of relatively small diameter. Distally, toward the ending of the SAT in its target area, we typically observed another smaller widening of the envelope (Fig. 6).

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Figure 6.

SAT minimal enclosing envelopes and variability plots. Dorsal, anterior, and medial 3D views of three lineages, BLD5, DALd, and DPLal3. Each panel shows the SAT traces of the homonymous lineages from the five reference brains, wrapped by a semitransparent minimal enclosing envelope (for detail on how the envelope is derived, see text). The mushroom body is provided as reference in gray. Red arrowhead indicates the proximal end. Plots to the right show the standard deviation of corresponding points across the five SAT traces relative to the consensus trace. The standard deviation, which correlates with the thickness of the minimal enclosing envelope, is highest at the proximal end of each SAT; it drops sharply where the SAT enters the neuropile and then typically rises slowly toward the distal end of the SAT. Supplemental Figures 4–15 (available at www.jneurosci.org as supplemental material) contain a row for each SAT in the third instar brain hemisphere, grouped by lineage families.

Reliability of SAT identification

The NIT measures 11 parameters that describe the degree of (dis) similarity between any two 3D SAT traces. We test the discriminative power of each parameter by comparing each annotated SAT of any of the five brains against the annotated SATs in each of the other four brains. For each comparison, we sorted the four sets of results and extracted from each the index of the homonymous SAT; ideally the top one. For the few combinations in which a brain did not contain the homonymous SAT, such were not considered.

The results of the parameter analysis indicate that the mean Euclidean distance between the substitution correspondences has the highest discriminative power: 82.0% of homonymous top matches, 93.8% for an homonymous match within the top 2, and saturates after top 5 with 99.0% (Table 1). By the same parameter, the recognition of the lineage group is 97.1% (where lineage group is one of BA, BLV, etc.). All other parameters present lower discriminative power. The accuracy in the classification varies among lineage groups. Some lineage groups score better than others, ranging from 100% accuracy for SATs in groups BA and DAM to 90.4% for group BLA (Table 2).

A multiparametric classifier

The combination of multiple parameters allows for more reliable SAT identification. We use a machine learning method known as Random Forest (Breiman, 2001), which combines many decision trees (70 in our case) (supplemental Fig. 3, available at www.jneurosci.org as supplemental material), to learn the best way of separating the samples between two different classes: correct or incorrect. The decision trees are simple binary trees in which each node divides the set of samples based on the most differentiating feature at the given tree level. In this fashion, the deeper we go in the tree, the better samples are differentiated.

We trained the algorithm with the results of comparing, on the expert-classified data, each SAT trace in one brain to all SAT traces in every other brain (five brains total, hence four lists of results for each trace). The number of expected incorrect matches is much higher than the expected correct matches; hence, to avoid overfitting for incorrect matches, we trained with only the top eight results of each test, as sorted by the most discriminative parameter (mean physical distance, which by itself never scores in our data a correct match lower than at position 8). We used an open source implementation of the Random Forest approach (WEKA library) (Witten and Frank, 2005) and stored the trained model for practical application to SAT classification.

The Random Forest approach results in 99.7% (2358 of 2368) correct good matches and 99.98% correct bad matches (292,745 of 292,753), with only eight false positives and 10 false negatives (Table 3). All eight false positives involve matches between DAMd2 and DAMd3, two extremely similar and closely overlapping SATs.

We tested the reliability of the classifier in identifying SATs of a brain not belonging to the training set. We traced 80 SATs, including the hardest lineage groups, BLA and BLD, in full. The classifier presented a high number of false positives (Table 4), but these were nonhomogeneously distributed: 42 of 80 traces had zero false positives, and another 20 had three or fewer false positives. In 75 of 80 SAT traces, the classifier found at least one true positive (true positives: 3.30 ± 1.66; false positives: 1.71 ± 2.31; false negatives: 1.89 ± 1.61). The five SATs without a true positive were relatively short SATs (BAlp3, BAlp4, BLD1:2, BLD7, and DPLm1). When sorting results by the mean Euclidean distance, the top result was correct in 68/80 cases, and the top two results contained a homonymous SAT in 76/80 cases. An example of comparing an unknown SAT to all traced SATS in the database is show in Figure 7.

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Figure 7.

Query of a SAT trace and visualization of matching results. An unknown query SAT traced in an antineurotactin-labeled third instar brain is compared to all SAT traces in the reference database. Results are sorted by mean Euclidean distance (MED) and classified as positive (true) or negative (false) matches. Of the five positive matches (highlighted in green), four are DALv2 and one is DALv3:1 (magenta), the latter likely a false positive. A DALv2 in the seventh row is classified as false, likely a false negative. The facts that the top two matches are DALv2, and four of five positive matches are DALv2, suggest that DALv2 is the correct annotation. In the top panels, 3D visualization of the matches with corresponding colored dots in the table. For clarity, only a true positive (red), a false positive (magenta), and a true negative (blue) are shown. The mushroom body lobes (dl, dorsal lobe; med, medial lobe; ped, peduncle) are shown for spatial reference.

Robustness: lineage identification in a glia-less mutant brain

The ablation of glial cells results in severely deformed brains, affecting the growth and pathfinding of SATs (Spindler et al., 2009). To test the robustness of our SAT identification algorithm, we traced and annotated 20, 25, 30, and 42 SATs in four glia-less third instar brain hemispheres (UAS-hid, UAS-rpr; Nirvana2-GAL4,UAS-GFP; tubGAL80[ts], confocal image stacks kindly provided by Shana Spindler, University of California, Los Angeles, CA), including the subset of lineages analyzed for fasciculation and growth defects in (Spindler et al., 2009) (Fig. 8). Despite SAT defects in the absence of neuropile glia, all SATs were classified correctly except in 1–4 lineages per brain, corresponding to lineages with a very high glia-association score (BAmas, DALcm1, DALcl1, and CP1). The BLD1–4 lineages, whose SAT is short and overlapping, and for which the classifier has a higher error rate in wild type (Table 2), were identified only at the lineage group level. The correct identification of a lineage like CP1 in three brains but not in the fourth may be explained by the incomplete penetrance of the heat-shock-induced glia-less phenotype.

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Figure 8.

SAT identification in a glia-less mutant brain. A–D, Confocal sections. A, Wild-type third instar brain hemisphere labeled with antineurotactin. B, Third instar brain hemisphere in which neuropile glia were ablated by targeted expression of a hid-reaper construct. Observe a reduced optic lobe (OL) and neuropile (np). BLV indicates cells of the BLV lineages. C, D, DAMv1 and DAMv2 lineages in (C) wild type and (D) glia-less. Note that the cells of the sister lineages are fused into a single cluster in the glia-less brain. Fusion of neighboring lineages (which are normally separated by glial sheaths) is a typical phenomenon observed in glia-less brain. E, Wild-type DAMv1 and DAMv2 lineages (in red and blue) are compared to the glia-less fused pair (in yellow); anterior view. Despite the fusion, DAMv1 and DAMv2 lineages are recognized as DAMv 1 or 2. F, SAT traces of CP1 lineage in wild-type and glia-less brain. Four glia-less brains were registered with one of the wild-type brains that formed part of our reference data base. The wild-type CP1 SAT trace is shown in blue; CP1 traces of glia-less brains are in white, yellow, magenta, and red. Mushroom body is shown as reference in gray. In three of four brains, CP1 SATs are unperturbed; in the fourth brain (in red), CP1 shows severe pathfinding errors. Our lineage recognition method conclusively classified all as CP1 lineage, except for the one with pathfinding errors (in red). The lack of positive matches and the elevated median Euclidean distance values of the top-scoring results suggests its condition as mutant. Its identity as CP1 was determined by elimination: all neighboring lineages have a positive match other than CP1. G, SAT traces of BAmas1/2 lineages wild-type (blue) and glia-less brains. Traces in three of four brains are unperturbed or slightly shorter than the wild type; in the fourth brain (red), the SAT is considerably shorter (red arrow indicates its terminal end). All BAmas1/2 SATs were identified as such using a substring global alignment approach (see supplemental text, available at www.jneurosci.org). The shortened terminal end was identified as a long sequence of deletions at the end of the sequence of editions resulting from the alignment. In E–G, the mushroom body skeletonized lobes [dorsal lobe (dl), medial lobe (ml), peduncle (ped)] are shown for spatial reference.

In accordance with the findings of Spindler et al. (2009), we observe three types of pathfinding errors: fusion of the proximal segment of the SAT in sister lineages (the four mushroom body lineages, DPLal1-3, DAMv1/2, and BLD1-4) (Fig. 8C–E), shorter terminal projection (BAmas, DALcm1 and DALcl1) (Fig. 8F), and complete misrouting (CP1) (Fig. 8G) [see Spindler et al. (2009), their Table 1]. Only complete misrouting prevented the classifier from suggesting appropriate SAT annotations. Of note, the absence of glial cells severely disrupted the formation of the optic lobe, which lays immediately adjacent to the BLV, BLD, and BLA groups; yet, SATs of the BLV and BLA group were identified correctly.

The success in identifying nearly all SATs in a severely disrupted third instar brain suggests that the combination of a simple eight-landmark-based registration approach and the parameters used by NIT are robust enough for reliable SAT identification.

Flexibility: SAT identification with incomplete traces

Secondary axon tracts show a temporally and spatially dynamic expression of molecular markers. Some proteins, at a given stage, may be only found in part of the neuron. As a result, an SAT traced for identification may appear labeled over a much shorter length than that of its correspondent in the database. The example we present here is a larval brain labeled with an antibody against DE-cadherin (Fig. 9). This adhesion protein is transiently expressed in newly born secondary neurons and therefore visualizes SATs; it is also expressed on glial processes, which prevents one from following SATs in the neuropile.

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Figure 9.

Identifying incomplete SAT traces. A, Confocal section of a wild-type third instar brain hemisphere labeled with anti-DE-cadherin. Medial to the left, dorsal is up. The proximal segments of SATs are visible as thick white lines; distal segments in the neuropile are for the most part invisible due to the fact that DE-cadherin is also expressed by the surrounding neuropile glia, which masks the SATs. B, Identifying SATs from small fragments is difficult when the fragment is part of a common tract shared by multiple SATs. For example, in the diagram shown here, BLD6, BLD5, and DPMpl3 overlap at different positions (dotted circles). We perform global sequence alignment of the short trace (red) over all possible continuous subsequences of the longer trace (gray). Hence, the two sequences being compared have the same length, avoiding sequence length-derived issues at the cost of an increased rate of false positives, while still optimizing for the best gap-less fit (see supplemental text, available at www.jneurosci.org). C–H, Three-dimensional models of SAT traces illustrating the problem of identifying incomplete fragments. Small fragments are depicted in yellow, positive matches in red, negative but nearby matches in blue. In C and D, the small fragment is conclusively identified. In F and G, the correct SAT is assigned, but numerous other positive (false) matches are nearby, barely discriminated. In E and H, the fragment is very small and close to the cell bodies; the classification for BLVp1:1 is correct only because of the lack of other potentially positive matches. In H, only the enclosing lineage name (i.e., CM1), but not the specific SAT, is identified.

On the other hand, SATs may be substantially longer than the traces by which they are represented in our database. This applies for the SATs of all lineages with a commissural projection. Because SATs of commissural lineages fasciculate with their contralateral counterparts, they cannot be traced beyond the midline in preparations that are globally labeled with antineurotactin. However, using clonal labeling techniques, these lineages may be visualized in their entirety.

The NIT would deliver inappropriate results in most cases when scoring a SAT trace considerably shorter or longer that its true correspondent in the database. Realizing that the true SAT trace correspondence must lack large sequences of insertions or deletions, we devised a strategy consisting in performing global sequence alignment of the shortest of either the query or the reference SAT trace over all possible continuous longer trace subsequences of the shorter length (Fig. 9B).

To test the reliability of the assignment for shorter SAT traces, we manually annotated SATs in an anti-DE-cadherin-labeled brain. For the 11 lineages analyzed in the test brain (Fig. 9), nine were conclusively identified. For the remaining two, only the lineage name but not the specific SAT was identified (Fig. 9H). The random forest classifier presented an increased number of false positives. These arise as a result of very good matches with multiple SATs, because the short fragment may be common to multiple SATs, when the latter join common brain tracts, or near the cell bodies before diverging significantly (Fig. 9H).

For longer SAT traces, we used the flip-out clones of secondary lineages which aided in the construction of the database and which cross the midline or are considerably longer than the span of the neurotactin-labeled fraction of the SAT. All 12 longer SAT traces tested were correctly identified by the classifier, with 0–6 false positives for each.

Flexibility: identifying primary neurons and adult brain SATs with third instar SATs as reference

Primary neurons project a PAT into the neuropile (Nassif et al., 1998; Younossi-Hartenstein et al., 2006) where they arborize profusely, forming the larval neuropile. Secondary neurons, which develop throughout larval stages, form a SAT that follows the PAT into the neuropile (Larsen et al., 2009). We traced the proximal segment of the PAT for four individual primary neurons and two clusters of three primary neurons labeled with antidopamine in third instar brains. Then we ran NIT on the traces to identify SATs that follow similar trajectories (Fig. 10). We found that the four individual primary neurons were followed by four distinct SATs (BLVa1, a2 and a3; and DPMm1:4) (Fig. 10A–E), and one cluster of three primary neurons was followed by one SAT (CP2/3:1) (Fig. 10A–C). The remaining dorsomedial cluster of three primary neurons was not followed by any SAT. While primary neuron identification results were not and cannot be conclusive when comparing with SATs, NIT cuts down search to approximately three SATs in each case, suggesting between two and six positive matches with repetitions (Fig. 10B,C).

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Figure 10.

Assigning primary neurons to SATs. Confocal z-projection (A) and confocal sections (D, E) of a larval brain labeled with antineurotactin (BP106; red) and anti-GFP (green), visualizing the set of dopaminergic neurons which expressed a UAS–GFP construct driven by tyrosine hydroxylase-specific promoter. In A, two clusters of dopaminergic neurons in the dorsomedial (p-DPM) and posterior (p-CP) brain; D shows an additional group (p-BLV) located further anteriorly and ventrally. All of these clusters represent primary neurons, as evidenced by the fact that their neurites have highly branched projections in the neuropile. As primary neurons, the dopaminergic cells project their axons adjacent or close to the SATs of secondary neurons, but not within the SATs themselves. Nevertheless, tracing and scoring the proximal unbranched segments of the primary neurons using NIT results in several positive matches. For the posterior neurons, the closest matches are DPLp2 and CP2/3:1 (B, C, and table). Each of the three individual BLV primary neurons (p-BLV in D) can be related by position and projection to one of the three BLVa SATs (E); the classifier suggests a collection of positive matches for BLVa SATs (data not shown). Only one cluster of dopaminergic primary neurons (labeled with a question mark) cannot be related to a SAT.

Secondary neurons arborize during pupal stages, forming the largest fraction of the adult fly brain. The low-order branch of the SAT remains recognizable for at least a subset of lineages with antineuroglian antibody or with genetically targeted GFP-labeling. We traced the two SATs of one of the two CP2/3 sister lineages (Fig. 11A) and ran NIT against the third instar SAT reference library. There were two true positives for one SAT (CP2/3:3) (Fig. 11C). While the classifier did not find any positives for the other SAT (CP2/3:1) (Fig. 11B), the top five results contained three instances of CP2/3:1. The 3D registration with only four fiduciary landmarks (the four mushroom body corners) proved sufficient for NIT to provide good annotation suggestions for the adult CP2/3 lineage SATs.

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Figure 11.

Identifying lineages in the adult brain using third instar annotated SATs. A, Confocal section of an adult Drosophila brain hemisphere, labeled with synaptotagmin (red). One lineage is labeled by the MARCM technique (in green); its two visible SATs were traced manually. Manual traces are indicated in blue (path above current slice), yellow (path within visible slice), and red (path below current slice). Dotted vertical line indicates midline; cc, central complex. B, C, Results of scoring the SATs of the adult brain against all SATs in the larval reference library. The tips and branch point of the mushroom body (dotted outline in A) provide four fiduciary points for registration of the traced SATs into the reference library coordinate space. The two tables show the top 14 results only, sorted by median Euclidean distance (Avg Dist column). Three-dimensional views show selected results from tables, indicated with corresponding colored dots. The Random Forest classifier labels the matches as true or false. The first GFP-labeled SAT (top table) results in zero true positives, one false positive, and five false negatives. The second GFP-labeled SAT (bottom table) results in two true positives, zero false positives, and three false negatives. In this case (C), the identity is clear: CP2/3:3. In the first case (B), without any true positives, the second and third results suggest CP2/3:1 over the first result, DPLp1:1. Visual inspection of the SAT traces in 3D offers further support for this decision. The possibility of annotating SATs in the adult brain using the third instar library of SATs as reference and only four fiduciary points suggests that the relative position of SATs lowest-order axonal branches do not change significantly from late larva to adult. dl indicates dorsal lobe; ml, medial lobe; ped, peduncle.

Effect of 3D registration on SAT identification

The algorithmic classification of an anatomical structure depends both on the recognition and quantification of its geometrical properties and on the correct elucidation of its relative spatial location to other potentially similar structures. We have approached the spatial positioning problem with a 3D registration strategy based on eight fiduciary points, which are easily recognizable and evenly distributed (Fig. 3). Each brain was mounted in a different orientation, and thus artifactual deformations were introduced in a nonsystematic way. However, SAT identification across brains is accurate in wild-type brains, in the four mutant glia-less brains, and in the DE-cadherin labeled brain (Tables 1⇑⇑–4).

We have observed the effect of insufficient brain-to-brain registration for some SATs as an increased distance between correspondent SATs across the five reference brains (e.g., BAlv) (Fig. 5C). The fact that no other lineage presents such large distances between its cognates (Fig. 5) suggests that volume registration with only eight landmarks is sufficient for the identification of protocerebral and deuterocerebral lineages. All tritocerebral lineages, which lay beyond the volume circumscribing the eight fiducial points, cannot be reliably identified.

The better the 3D brain registration, the more reliable the recognition of any brain structure will be. Our approach is flexible regarding the number of fiduciary points. For many lineages, using only the four corner points of the mushroom body is sufficient for accurate recognition. The additional four fiduciary points greatly enhance the fidelity for many other lineages, particularly the basal and lateral groups. If needed, further fiduciary points could be added. The strength of our approach is that it performs reliably even if “perfect” registration is not possible (e.g., across mutant brains) (Fig. 8).