Supervised learning for network topology reconstruction

To analyze fusome topology and intercellular volume distribution during cyst formation in females, we implemented a supervised learning algorithm to identify the location of fluorescently-labeled fusome and ring canals within the developing cyst (Fig 2)—as previously described [44, 45]. Briefly, for each cyst, the fusome (fluorescently-labeled through tagging of α-Spectrin in females and adducin in males) and the ring canals (through endogenously-tagged Pavarotti, a key component of ring canals in Drosophila) were identified using the supervised learning program ilastik [45, 46], which has been used in several other settings for volumetric reconstructions of cells and subcellular structures [44, 47–49]. Although the marker for fusome between the males and females was different, both of these have been demonstrated to be reliable markers of fusome size and shape [31, 36]. The fusome in females was taken as a single, simply-connected component within the developing germline cyst. Ring canals did not have this constraint, and based on the sample under consideration, either 1, 3, 7, or 15 rings were required to complete the fusome segmentation and reconstruction upon using skeletonization to identify objects which were closed loops within each image stack (corresponding to 2-, 4-, 8-, and 16-cell cysts, respectively). Each ring canal, which necessarily surrounds the fusome at cell junctions, was used as a marker to splice the fusome into multiple sections. A recursive function was then built so that for each distinct ring canal, the fusome was split into two fragments on either side.

At the first iteration, the fusome was split into two fragments. The algorithm then iteratively split the fusome at each ring canal, generating fragments that corresponded to the volumes present within each cell of the cyst. After generating these fragments, the function then logged information about their volumes and positions within the stack and moved to a different branch of the recursive loop. The final output of this algorithm was a three-dimensional stack of separated fusome fragments, whose sum amassed the entirety of the original fusome. These objects were then exported for further identification based on mutual adjacencies to assign a unique label to each piece of fusome based on its number of neighbors and distance from the presumed founder cell (in females). The volume of each fragment was calculated based on the number of voxels within each object, multiplied by the known voxel size.

We found that our pipeline reconstructed the correct maximally branched cyst structure in females (Fig 2A). Because the topology of the network at each division is symmetric during oogenesis, the cell with the larger fusome fragment and four ring canals was labeled cell 1. Each cell thereafter was uniquely identified based on its number of neighbors and proximity (number of intervening ring canals) to cell 1.

From here, the volumes of fusome within each cell in the cyst were also recorded to enable intercellular comparisons in the dividing cyst. Manual validation of ilastik volumes was performed on a subset of randomly selected samples. For each sample, manual thresholding was performed in FIJI to identify fusome area at each slice. All slices were summed and the total was multiplied was the voxel size to yield a fusome volume estimate. Across all samples, the difference between manual and automated fusome volumes was ∼ 8% on average (S1 Data).

To further test and extend the applicability of the developed algorithm, we turned our attention to the male, where we analyzed the 3D structure and topology of fusomes at successive stages of cyst formation (Fig 2B) [44, 45]. In contrast to the female cyst, where cells were tightly packed and the fusome compact, male germline cysts appeared more elongated, with thread-like fusomal materials connecting otherwise seemingly disjoint fusome fragments, as highlighted previously [19, 38, 43, 50].

Quantifying fusome growth dynamics during oogenesis

Intercellular asymmetry in fusome distribution is thought to mediate oocyte fate specification and polarity, which in Drosophila ultimately establish the embryo’s main body axes [17, 25, 26]. According to this ‘predetermination’ model for oocyte selection, the cell that contains the greatest amount of fusome becomes the oocyte, and that cell is always one of the two cells with four ring canals—the pro-oocytes (Fig 1C). This model builds on the fact that asymmetry in fusome content arises during the very first cell division, and that this asymmetry between the first cell and remaining cyst cells, including the other pro-oocyte, is maintained during subsequent divisions [27, 36, 51]. As microtubules associate with the fusome, its asymmetry is proposed to predetermine oocyte identity by directing the microtubule network towards one cell, along which dynein transports oocyte fate determinants [25, 30, 52, 53]. Formation of a polarized microtubule network is indeed key for oocyte specification [23, 53]. For example, egalitarian, in concert with Bicaudal-D, promotes the microtubule-dependent transport of factors to the presumptive oocyte; its mutants form cysts with 16 nurse cells despite forming normal fusomes that appear asymmetrically distributed [54–57]. The alternative model for oocyte selection postulates that fusome asymmetry is insufficient for determining oocyte fate; instead, the pro-oocytes are considered equivalent, with both having an equal chance of becoming the oocyte [25, 58]. According to this model, one of the pro-oocytes becomes the oocyte ‘stochastically’, through competition for some limiting oocyte determining factor(s) at the 16-cell stage (Fig 1C).

Quantification of fusome growth, inheritance, and relative fusome volumes within connected cells is key for distinguishing between models; however, these measurements are technically challenging. A further complication is the fact that oocyte identity only becomes clear once the 16-cell cyst of Drosophila is formed—a point at which several fusome components have begun to disintegrate [25, 30, 58, 59]. Here we take steps to address this gap using the supervised learning approach described above, limiting the analysis to cysts lying within the germarium and with fully intact fusomes. Flies heterozygous for an orb null mutation (orb is a known oocyte-specifying factor) were dissected for this analysis. Previous work did not identify any abnormalities in fusome formation, cyst formation, or cyst progression through the germarium in these samples [60]; our own analysis confirmed that these early stages of oogenesis were not affected.

Our data revealed a strong bias in fusome volumes between the pro-oocytes starting at the 2-cell stage. Specifically, our results showed that, for 2-cell cysts, the larger of the two fusome fragments comprised, on average, 70% of the total fusome volume. Subsequent divisions, however, decreased the asymmetry between the two most central cells, with the ratio of volumes between cells 1 and 2 decreasing from 2.4 ± 0.3 in the 2-cell cyst (n = 12) to 1.2 ± 0.2 in the 16-cell cyst (n = 11) (Fig 3). Nonetheless, at each stage, there was a persistent fusome volume bias toward these two central cells compared to the other 14: upon successive divisions to form a 4-, 8-, and finally 16-cell cyst, the volume fraction of these two cells was 78 ± 7% (n = 12), 58 ± 6% (n = 6), and 37 ± 3% (n = 11), respectively, dwarfing the fusome portions in each other cell at every stage of division.

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Fig 3. A model for fusome growth and inheritance during oogenesis.

A) Starting with a spectrosome of volume v₀ and fusome plug at the first division of volume v₁, the volume fraction f_1,2 of the 2-cell female cyst can be represented as shown in Eq 1, where the volume fraction in cell 1 at this stage is α and the asymmetry in sharing of the newly formed fusome component between mother and daughter cell is β. B) At the 2-to-4-cell transition, two new fusome plugs are added in the same manner as in A, with each contributing volume v₂. C) Divisions occur again to form 8- and 16-cell cysts, where the total fusome volume can be tracked throughout cyst formation, and expressions for volume fractions of fusome within each cell at each cyst size to be derived. D) Error calculations for ranges of the model parameters α and β. For each set of parameters, model volume fractions for each cyst size were calculated and compared with measured data by summing over the squared residuals between measured and derived volume fractions over each cell at all cyst sizes. The minimum error using this metric was found at the value α = 0.700, β = 0.515, corresponding to a scenario where fusome plugs are added evenly between the mother and daughter cells at each successive division. Explanation of model assumptions and equations can be found in the Materials and Methods. Comparison with measured data can be found in S1 Fig.

https://doi.org/10.1371/journal.pcbi.1010875.g003

We also found that aggregating the volume fractions based on ring canal number provided a meaningful metric with respect to when each cell is formed in the successive divisions. In particular, we found that cells with 4, 3, 2, and 1 ring canals comprised 37 ± 3%, 21 ± 3%, 22 ± 2% and 20 ± 3% of the total fusome volume (n = 11), respectively. Note that the two cells with 4 ring canals are the pro-oocytes. Within the measurement error of each group and for comparison with theory, these groupwise fractions at the 16-cell stage are taken as the following ratio: 2 : 1 : 1 : 1.

To rationalize these experimental data, we developed a minimal theoretical framework to model how relative fusome volume fraction in each cell changes during cyst generation. This model was built on the fact that the fusome in Drosophila grows through successive rounds of accumulation and fusion of fusome fragments in the ring canals connecting mother and daughter cells [25, 51, 58, 59]. Here, we only assumed that at each division there was no additional change in the relative volume fractions of fusome in the cells between divisions, other than what was added from the fusome plug [25, 51]. This model therefore treated the fusome as an irreducible building block, where plugs chain together at each division to form a larger and branched structure.

Building on these assumptions, we wrote a series of equations with two parameters: α, the volume fraction of fusome in the founder cell at the 2-cell stage, and β, the fraction of the fusome plug added to the parent cell at each division (see Materials and Methods). Using the 2 : 1 : 1 : 1 heuristic for the groupwise fractions at the 16-cell stage and inserting the derived relationships into equations for the volume fractions for each cell in the 2-, 4-, 8-, and 16-cell cysts yielded volume fractions that enabled direct comparison of model predictions with experimental measurements over a range of values for α and β (Fig 3D). For the parameter range α ∈ [0.25, 0.75] and β ∈ [0.25, 0.75], we found α = 0.700 and β = 0.515 minimized the error with our measurements, yielding for a range of values for α and β. Considering the range of parameters that yielded errors within 5% of the minimum gave ranges of α ∈ (0.688, 0.705) and β ∈ (0.480, 0.559). Notably, this interval for β captured the value 0.5, suggesting that fusome fragments are shared equally upon division [25, 51].

Reconstructing fusome and cyst topology during spermatogenesis

In any interconnected cyst, two types of cells exist: terminal cells—the cells at the very ends of the cyst, connected to only one other cell—and internal cells. Upon division, terminal cells form one cell connected to two cells and another cell that now again has only one connection (Fig 1F). In other words, terminal cell divisions results in an internal cell and a terminal cell. On the other hand, internal cells can divide in two ways: they can form a new terminal cell or two internal cells. These division types affect CLT topology: maximally branched trees form when all internal cells divide to form terminal cells (Fig 1F); however, if in-line divisions occur, maximal branching is lost. By tracking cell-cell connections, the topology of the germline CLT can be extracted [61, 62]. With these division rules in mind, we set out to catalog the series of connections present in male germline cysts and to compare those to the known sequence of divisions during Drosophila oogenesis.

Reconstructions of fusomes in male cysts revealed significant fusome fragmentation (Fig 4A). Indeed, we found that in only (50%) of reconstructed samples was the number of fusome-connected cells 2ⁿ, in contrast to females, where in all samples the number of fusome-connected cell was 2ⁿ. This deviation in males is unlikely to be due to an atypical number of cells. Indeed, when we counted the spermatid tails per sperm tail bundle present across a number of post-meiotic cysts, we observed an average of 63.1 ± 1.3 (n = 61) spermatids per bundle, consistent with each cyst comprising 16 cells (S2 Data) [63, 64]. To explore the effects of fusome fragmentation, we analyzed the various topologies that could be recapitulated by tracing fusomal connections in males, assuming that fusome topology reflects that of the CLT. Starting from a single cell, there is only one path towards forming a four-cell cyst via synchronous divisions: a linear fusome fragment with three ICBs. Upon dividing synchronously again, multiple eight-cell cysts are possible, depending on whether the divisions occur in a maximally branched fashion; that is, whether or not each division forms a new terminal fusome fragment budded off from the parent (Fig 1F). For cells at the terminal ends of the cyst, the fusome can only elongate in one manner; however, for the inner cells, the fusome either adds a branch or continues growth in a linear manner. By symmetry, one is left with three possible configurations for the cyst; of these, only one configuration is maximally branched, whereby each division creates a new branch (Fig 1F). Of all fusome reconstructions encompassing 5–8 cells (n = 21), we found none that were inconsistent with the maximally branched connections of an 8-cell cyst (Fig 4A).

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Fig 4. Fusome fragmentation during spermatogenesis and loss of maximal branching.

A) Starting with n = 62 reconstructed fusomes, a range of cyst sizes can be inferred by identifying the largest connected portions of fusome within each sample. These fusome portions, and their corresponding ring canals, can be used to identify the number of cells connected by each fusome fragment (fusome-connected cells). In approximately half of these, the number of fusome-connected cells was a power of 2 (n = 31). B) Two examples of fusomes connecting 16 and 15 cells, respectively, whose topology cannot be embedded onto that of a maximally branched network. C) Projections of 3D images of dividing cysts with labeled fusome (Adducin, gray), ring canals (Pav, red), and mitotic chromosomes (Phosphohistone 3, cyan), showing examples of a 2-cell (left), 4-cell (middle), and 8-cell cyst (right) during mitosis. In at least one location in the 8-cell cyst, cells are dividing without forming a new branch; as such, the resulting 16-cell tree will not possess a maximally-branch topology. In all examples, yellow dotted lines denote the likely plane of division for actively dividing cells, while yellow arrows depict clear bundles of aggregated or migrating chromosomes. In addition, nodes representing the locations of existing cells, as well as the likely positions of newly-formed cell based on the plane of division are shown. Scale bars = 10 μm.

https://doi.org/10.1371/journal.pcbi.1010875.g004

Starting with maximally branched 8-cell cysts then, 36 possible configurations are obtainable through another division to form a 16-cell cyst, with only one resulting in a maximally branched network. We analyzed fusome reconstructions connecting 9–16 cells and, while we observed fusomes whose structure was consistent with a 16-cell maximally branched cyst, we uncovered fusomes whose connections could not be embedded onto a maximally branched topology. Even in cases where fusomes did not connect 16 cells, the topology of the largest fragment was sufficient to demonstrate that divisions had not occurred in a maximally branched manner (Fig 4B). We next analyzed the orientation of mitotic spindles in dividing cysts, focusing on the fourth division cycle, when the cyst increases in cell number from 8 to 16. In female cysts, mitotic spindles align such that newly-formed cells divide to create a maximally branched tree as opposed to ‘in-line’ (Fig 1B); the fusome follows cyst growth, leading to its branching throughout the cyst [17]. This division pattern was observed in all dividing 2- and 4- male cysts, but not in 8-cell cysts, where we found mitotic spindles that were parallel to two disjoint fusomal fragments (Fig 4C)—consistent with cell division elongating the fusome rather than giving rise to a new branch. These findings suggest that the stereotyped pattern of connections in female cysts are not strictly preserved during spermatogenesis and that deviations from maximally branched structures in male cysts arise at the fourth division during cyst formation.

Fly stocks and sample preparation

Pav-mCherry females heterozygous for the orb null mutation orb^F343 (gift from Schedl lab, Princeton University) were used in this study as a marker for ring canals and to allow for isolation of 16-cell cysts. Ovaries were dissected and fixed as previously described, taking care to isolate germaria from ovarioles [44, 82]. After blocking, the primary antibody mouse anti-α-Spectrin 3A9 (1:30, gift from Schedl lab, Princeton University) was added and rocked overnight at 4°C overnight. The secondary antibody rat anti-mouse Alexa-Fluor 488 (1:100, Invitrogen) was then added to mark the fusome within each 2-, 4-, 8-, and 16-cell cyst in the germaria. Dissected ovaries were mounted in a 75:25 mixture of RapiClear 1.47 (SUNJin Lab) and Aqua-Poly/Mount (Polysciences).

Ubi-Pavarotti-GFP male flies (gift from Glover lab, California Institute of Technology) were dissected according to standard protocols [46]. Immunofluorescence staining was performed as described previously [83]. Briefly, tissues were dissected in PBS, transferred to 4% formaldehyde in PBS and fixed for 30 minutes. Tissues were then washed at least three times for 10 minutes in PBS-T (PBS containing 0.1% Triton X-100), followed by incubation with primary antibody in 3% bovine serum albumin (BSA) in PBS-T at 4°C overnight. Samples were then washed three times for 20 minutes in PBS-T, incubated with secondary antibody in 3% BSA in PBS-T at 4°C overnight, washed as above, and mounted in Vectashield with DAPI (Vector Labs). The following primary antibodies were used: rabbit anti-Phospho H3 (Ser10) (1:200, Thermo Fisher) and mouse anti-Hts (1:20, 1B1, Developmental Studies Hybridoma Bank). Secondary antibodies used were anti-rabbit IgG Alexa Fluor 488 and anti-mouse IgG Alexa Fluor 647 (both 1:200). Fluorescent images were acquired using a Leica TCS SP5 confocal microscope with a 63x/1.3 NA oil objective.

Confocal imaging was performed on a Leica SP5 confocal microscope using a 63x/1.3 NA oil objective. Three dimensional stacks were acquired using 488 and 546 nm lasers in series over roughly 100 slices of 16-bit, 1024 x 1024 images. Voxel sizes of acquired images were roughly 70 nm in x and y, and 210 nm in z.

Spermatid tail preparation and imaging

Testes were fixed for 1 hour or overnight (at 4°C) with 2.5% glutaraldehyde in 0.1M Sorensen’s buffer, pH 7.4. Samples were rinsed twice for 5 minutes each with 0.1 M Sorensen’s buffer and post-fixed for 1 hour in 1% osmium tetroxide in 0.1 M Sorensen’s buffer. Next, testes were rinsed twice in double distilled water for 5 minutes each and en bloc stained with 2% uranyl acetate in double distilled water for 1 hour. The samples were then dehydrated in increasing concentrations of ethanol, rinsed with acetone, and embedded in epon epoxy resin. Thin sections were mounted on Formvar/carbon-coated slotted grids and post-stained with uranyl acetate and lead citrate. Samples were examined on a JEOL1400 transmission electron microscope and images captured using a sCMOS XR401 custom-engineered optic camera by AMT (Advanced Microscopy Techniques).

Image acquisition and processing

Raw image stacks were first pre-processed to isolate individual cysts. Within germaria, intact fusomes were taken at the 2-,4-,8-, or 16-cell stage, provided the fusome was still fully connected throughout the cyst. Because male cysts maintain their fusome until the formation of 64 cells, only samples near the apical tip of the testis containing up to 16-cells based on counting nuclei near fusome pieces were taken [19]. Stacks were uploaded into ilastik for Pixel Classification to identify the locations of fusome and ring canals for each sample, in a manner similar to previous work [44, 45]. For each type of data, training was performed by manually identifying pixels that belong to each class of interest. This positional information, a set of probabilities at each voxel for belonging to fusome, ring, or image background, were imported into MATLAB for object identification and volume measurement. Using the probabilities for each voxel to be part of the fusome and ring canals, simple thresholding was used to find the most likely positions for each class.

Due to the invariance of cyst structure in the Drosophila female germline, the adjacencies between cells in the female cyst were known up to the identification of one cell due to cyst symmetry. In this case, larger fusome fragment with the most ring canals were taken to be the founder cell (cell 1), making it possible to assign all other identities within each cyst. The adjacencies for each set of fusome fragments were identified and mapped to the known adjacency matrices at each cyst size, allowing for reassignment through the Hungarian algorithm as previously described [44, 84].

In males, fusome fragmentation required manual segmentation and validation to ensure proper cell-cell adjacencies were collected. Samples stained with Phospho H3 were additionally trained within ilastik and inserted into MATLAB for further analysis for positioning. 3D reconstructions allowed for the identification of cells dividing without the formation of new fusome branches.

Mathematical model for fusome assembly in females

In this section, we introduce a theoretical model for fusome formation during Drosophila oogenesis using known biological features of the process, accompanied by a small number of assumptions. This minimal model, in coordination with the measured fusome volumes across stages, seeks a more coarse-grained, less stochastic view of fusome formation during oogenesis.

It was previously shown that the cystoblast contains the spectrosome, a fusomal precursor [25, 36]. Therefore, if the volume of the spectrosome in the cystoblast after division to form the 2-cell cyst is given by v₀ and the fusome volume added at the first division is v₁, the volume fraction of cell 1 in the 2-cell cyst (f_1,2) is described by: (1) where α is defined as the volume fraction of fusome in cell 1 after the first division and β is defined as the fraction of the fusome volume added to the already existing cell at each division (Fig 3A). Extending this quantitative description to the next division, from a 2-cell to 4-cell cyst, we have two fusome plugs to add, each contributing v₂ to the total fusome volume (Fig 3B). Under the assumption that fusome plugs added at each division are the same (in this case, v₂), the volume fractions in the cells of the cyst, f_i,4, can be derived: (2) (3) (4)

These derivations can be repeated at each subsequent division, allowing for fusome volume fractions in each cell of any cyst size to be defined (Fig 3A–C).

Our experimental measurements revealed that the average volume fractions of cells 1 and 2, cells 3 and 4, cells 5 through 8, and cells 9 through 16 at the 16-cell stage are given in the ratio 2 : 1 : 1 : 1. One can therefore write the following equations for the volume fractions of these groups of cells and, along with Eq 1, solve for v₁, v₂, v₃, and v₄, the average volume of the fusome fragment being added between mother and daughter at each division, in terms of v₀: (5) (6) (7) (8)

Solving this system of equations, along with Eq 1, allows for one to solve for v₁, v₂, v₃, and v₄ in terms of v₀. Inserting the derived relationships into equations for the volume fractions for each cell in the 2-, 4-, 8-, and 16-cell cysts yields volume fractions that can be compared with experimental measurements at the parameter values α = 0.7 and β = 0.5 heuristic values close to the parameter values found to minimize the total error, as shown above (Fig 3D and S1 Fig).