Research ArticlesNeuroscience

Self-organized Notch dynamics generate stereotyped sensory organ patterns in Drosophila

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Science  05 May 2017:
Vol. 356, Issue 6337, eaai7407
DOI: 10.1126/science.aai7407

Self-organization for sensory brushes

Sensory hairs on the back of a fruit fly are lined up in neat rows. The orderliness of this arrangement has encouraged models based on organized specification of the hairs. Corson et al. now show that development is both less precise and more effective than that. They used mathematical modeling to recapitulate genetic effects as the developing epidermis becomes organized into enough rows and single lines of hairs. Their work suggests that the sensory field develops through self-organizing patterning that can adjust to the size of the epidermis.

Science, this issue p. eaai7407

Structured Abstract

INTRODUCTION

Spatial patterning in developing multicellular organisms relies on positional cues and cell-cell interactions. Stereotyped sensory organ arrangements in Drosophila are commonly attributed to a prepattern that defines regions of neural competence. Notch-mediated interactions then isolate sensory organ precursor (SOP) cells from among the competent cells. In support of this view, prepattern factors direct the expression of proneural factors in discrete clusters and determine the location of large bristles on the dorsal thorax. However, no such prepattern is known to establish the proneural stripes that give rise to finer-bristle rows.

RATIONALE

By analogy with reaction-diffusion systems, we wondered whether Notch-mediated cell-cell interactions might organize a pattern of proneural stripes. To explore a possible role for Notch in proneural patterning, we generated fluorescent reporters for the proneural factors Achaete and Scute, the ligand Delta, and the Notch early-response factor E(spl)m3-HLH, which antagonizes proneural activity. We observed expression of these reporters in live and fixed samples throughout early pupal development. In parallel, we developed a mathematical model for Notch-mediated patterning. In this abstract model, the dynamics of a cell is expressed in terms of just two variables, for the state of the cell and the level of signal it receives. The model incorporates a series of plausible assumptions that govern its patterning behavior: Cells, which adopt the SOP fate in the absence of signal and the alternative, epidermal fate under high enough signal, exhibit a bistable response under intermediate signal levels. Inhibitory signaling from a cell varies nonlinearly with cell state and reaches beyond immediate neighbors.

RESULTS

Before the onset of proneural gene expression, a bimodal gradient of Delta expression drove Notch activity; as a result of cis-inhibition, Notch was activated only in regions of intermediate Delta levels. This defined an inhibitory template for a first series of three proneural stripes. The spatial pattern of Notch activity dynamically changed as these first proneural stripes emerged, forming a negative template for a second group of intercalating stripes. Eventually, each stripe resolved into a row of isolated SOPs through Notch signaling. Thus, Notch mediated both proneural stripe patterning and SOP selection via a self-organized process. Simulations of the model, with a time-dependent inhibitory gradient describing the proneural-independent signaling seen in vivo, recapitulated the sequential emergence and resolution of proneural stripes. In both model and experiments, mutual inhibition drove a gradual refinement of the proneural group, concomitant with the buildup of proneural activity. Cells on the sides of the stripes were excluded first, such that stripes narrowed before isolated SOPs emerged. In terms of the model, cell-intrinsic bistability allowed cells with higher proneural activity, at the center of the stripes, to evade levels of inhibition that were sufficient to exclude cells on the sides. Nonlinear signaling allowed a smooth transition from weak mutual inhibition within an extended proneural group to strong lateral inhibition from emerging SOPs, ensuring that attrition of the proneural group proceeds until only isolated cells remain. Finally, the model correctly predicted the outcome of perturbation experiments affecting the pattern of Notch activity, the level and activity of Delta, and the range of signaling.

CONCLUSION

Our results show that self-organized Notch signaling can establish stripe and dot patterns on a tissue-wide scale. A transient spatial bias, mediated by an initial gradient of Delta, is transduced by cell-cell interactions to produce a finer pattern of proneural stripes and bristle rows. Input from extrinsic positional cues and self-organization, sometimes considered competing paradigms for fate patterning, combine during bristle development and operate through the same signal. Self-organized Notch dynamics may provide a flexible substrate to generate diverse patterns in response to varying inputs.

Self-organized bristle patterning.

(Top) Input from a prepattern (green, Delta) and cell-cell interactions [red, Achaete; blue, Senseless; green, E(spl)m3-HLH] combine to establish a regular pattern of bristle rows on the Drosophila thorax. (Bottom) A mathematical model incorporating cell-intrinsic bistability (magenta, SOP; green, epidermis) recapitulates proneural stripe patterning and the singling out of SOPs (red and magenta, cell state; green, signal).

Abstract

The emergence of spatial patterns in developing multicellular organisms relies on positional cues and cell-cell communication. Drosophila sensory organs have informed a paradigm in which these operate in two distinct steps: Prepattern factors drive localized proneural activity, then Notch-mediated lateral inhibition singles out neural precursors. Here we show that self-organization through Notch signaling also establishes the proneural stripes that resolve into rows of sensory bristles on the fly thorax. Patterning, initiated by a gradient of Delta ligand expression, progresses through inhibitory signaling between and within stripes. Thus, Notch signaling can support self-organized tissue patterning as a prepattern is transduced by cell-cell interactions into a refined arrangement of cellular fates.

Developmental patterning relies on morphogens (1) and cell-cell interactions (2) to define pattern formation. Sensory bristles on the Drosophila epidermis (36) derive from precursor cells [sensory organ precursors (SOPs)] that themselves emerge from groups of cells expressing proneural genes of the achaete-scute complex (AS-C). SOPs are selected through Notch-mediated lateral inhibition. Bristle patterns reflect the regulation of cell potential by prepattern factors (7): The pattern of large bristles (macrochaetae) depends on prepattern factors acting on individual enhancers in the AS-C, which drive expression in the corresponding proneural clusters (8). In contrast, patterning of the finer bristles (microchaetae) (fig. S1, A and B) does not seem to involve stripe-specific enhancers (fig. S1C). We asked whether Notch—in addition to its role in SOP selection within proneural stripes—might also organize the sequential emergence of the stripes themselves.

Patterning dynamics

To study the dynamics of Notch signaling and fate specification in the notum, we developed functional fluorescently tagged versions of the proneural proteins Achaete (Ac) and Scute (Sc), the Notch ligand Delta (Dl), and E(spl)m3-HLH, a direct transcriptional target of Notch, using bacterial artificial chromosome (BAC) transgenes and CRISPR-mediated homologous recombination (HR). We used these reporters, as well as antibodies against endogenous Dl and Senseless [(Sens), a SOP marker], to study their expression patterns at successive time points during pupal development (Fig. 1 and figs. S2 and S3).

Fig. 1 Notch dynamics and sensory organ precursor (SOP) patterning.

(A) Notch signaling couples proneural activity in neighboring cells. Cells with high proneural activity [red; Achaete (Ac) and Scute (Sc) synergize with Senseless (Sens)] inhibit proneural activity in their neighbors (green) via Delta (Dl)–Notch (N) signaling and its downstream target, the E(spl) repressor. (B to G) Dynamics of Notch activity (GFP-m3) and proneural expression (Ac, Sc, Sens; Sens also labels row-five macrochaetae) as proneural stripes emerge and resolve into SOPs (labeled by Sens). (H) Dl cis-inhibits Notch in stripe five (arrowhead): Notch (GFP-m3) is activated in Dl mutant cells (RFP-negative) along the clone border (inset). Asterisks indicate background signals. Numbering refers to the location of the proneural stripes. APF, after puparium formation. Scale bar, 50 μm. See table S1 for a full list of fly genotypes.

Analysis of early pupae identified two phases in the development of the pattern as the two hemi-notum epithelia fuse and move dorsally after head eversion. Up to 5 or 6 hours after puparium formation (APF), the pattern of signaling activity was essentially stationary, and proneural proteins were confined to macrochaeta positions. In the next 6 to 7 hours, the microchaeta pattern was established. Throughout these two phases, notum cells are blocked in G2 and do not divide.

Before 5 to 6 hours APF, expression of Dl exhibited a smoothly varying pattern, peaking at locations of future proneural stripes one and five, with minimal levels where proneural stripe three will emerge. We observed Notch activity [expression of E(spl)m3-HLH, as monitored by green fluorescent protein (GFP)–m3] only where Dl activity was intermediate, on the sides of the two Dl stripes. Thus, Notch activity formed a negative template for stripes one, three, and five (Fig. 1B).

After 5 to 6 hours APF, Ac and Sc expression emerged in stripes one, three, and five (Fig. 1, C and D), accompanied by Dl expression in stripe three (fig. S3). By 7 hours APF, these first three proneural stripes were being refined, with a subset of cells expressing Ac, Sc, and/or Sens, whereas the remaining cells expressed E(spl)m3-HLH (Fig. 1E and fig. S2). Concomitantly, the Dl stripes became narrower (fig. S3), and the range of Notch activity along stripes one and five decreased, giving rise to two bands of low Notch activity in the region of stripes two and four (Fig. 1E and fig. S2, B and C). By 8 hours APF, expression of proneural genes, as well as Dl, had emerged in these gaps, completing the pattern of proneural stripes (Fig. 1F and fig. S3). Subsequently, the stripes resolved into SOPs; by 12 hours APF, expression of Sens was restricted to regularly spaced cells in each row, with high levels of E(spl)m3-HLH in the remainder of the tissue (Fig. 1G). Further refinement of the pattern through addition or loss of SOPs and cell movements (911) is limited (fig. S4), and we concentrate on the period up to 12 hours APF.

Live imaging of pupae ~6 to 10 hours APF confirmed the dynamics reconstructed from fixed samples. Although we were not able to follow patterning to its completion because the pupa moves at head eversion, we could observe the sequential emergence of proneural stripes and part of their resolution using GFP-Ac and GFP-Sc (movies S1 and S2). Imaging of Dl-GFP and GPF-m3 showed the narrowing range of Dl expression and Notch activity in and along stripes one and five, accompanied by the onset of signaling in stripe three (movies S3 and S4). At later stages, emerging SOPs were visible as isolated cells with low GFP-m3 levels within the stripes (movie S4).

These observations suggested the following patterning mechanism: A transient prepattern of Dl expression (independent of proneural gene expression) drives early Notch activity, providing a template for stripes one, three, and five. Then the pattern self-organizes, with signaling from the first-formed stripes providing a template for stripes two and four and signaling within stripes driving their resolution into SOP rows.

This model carries two implications. First, Dl and proneural gene expression must receive temporal inputs that delimit the two phases of patterning and control when the initial Dl gradient recedes and when the proneural genes are switched on. At 6 hours APF, Sc expression was stronger in stripe five than in stripes one and three, and fewer cells expressed Ac than Sc in stripe three (fig. S2A), suggesting slight differences in the timing of activation between Ac and Sc and across the tissue. Second, cells in the middle of the initial Dl stripes must be irresponsive to the high levels of Dl exposed by their neighbors to yield the observed pattern of Notch activity (Fig. 1B). Hypothesizing that this could result from cis-inhibition of the Notch receptor by Dl (12, 13), we generated mosaic pupae carrying Dl mutant clones. Ectopic Notch activation in mutant cells along clone borders (Fig. 1H) indicated that Notch is cis-inhibited by Dl in the region of stripes one and five.

A mathematical model

To further explore a self-organized patterning mechanism, we formulated a mathematical model of Notch signaling and fate specification (Fig. 2). The state of each cell is described by a single variable u, which takes values between 0 (low proneural activity, or epidermal fate) and 1 (high proneural activity, or SOP fate). A cell produces an inhibitory signal D*(u), representing its level of active Delta ligand, and receives a signal s that sums contributions from neighboring cellsEmbedded Image(1)where cij describes the distance-dependent coupling between cells i and j. In these terms, a generic model for signal-dependent fate specification (14) takes the form of a differential equation for the evolution of cell stateEmbedded Image(2)where τ is the time scale of cell dynamics, f describes the response to signaling, and the stochastic term η(t) allows for fluctuations in signaling and gene expression. The dynamics of a cell can be represented as downhill motion in a one-dimensional (1D) landscape that shifts in response to signaling and can be summarized in a bifurcation diagram (steady states versus signal level) (Fig. 2A).

Fig. 2 A mathematical model.

(A) Cells exhibit a bistable response to intermediate signal levels. (Top) 1D landscapes depicting the dynamics of a cell for s = 0, ½, and 1 (Eqs. 2 and 3). epi, epidermis. (Bottom) steady states as a function of s. Solid lines represent stable states (valleys); the dashed line indicates an unstable state (hill). (B) Bistability depends on the nonlinear response function f, which goes from 0 to 1 with f(0) = ½ and f′(0) = 2. (C and D) Signaling from a cell increases nonlinearly with cell state (C) and reaches beyond immediate neighbors (D) (green, signal produced by the magenta cell with u = 1). (E) With a receding gradient of inhibition at the boundaries, the model recapitulates patterning of rows two to four (green, signal; red and magenta, cell state).

Based on a qualitative analysis of patterning dynamics, the model satisfied the following constraints (Fig. 2, A, C, and D): (i) Inhibitory signaling from a cell increases faster than linearly as it progresses toward the SOP fate; (ii) the range of signaling exceeds immediate neighbors; (iii) in the absence of signal, a cell adopts the SOP fate; (iv) under high enough signal, it adopts the epidermal fate; and (v) under intermediate signal levels, cells exhibit a bistable response—both fates are accessible. Our choice ofEmbedded Image(3)with f going from 0 to 1 as a sigmoid (Fig. 2B), balances inhibition and positive feedback on u, required for bistability. Although the variable u is not intended to represent the level of an individual protein, Eqs. 2 and 3 are formally equivalent to a phenomenological model for gene regulation (15), with a linear regulatory input (us), a saturating response (f), and a linear degradation term (–u).

To simulate patterning, we prescribed a time-dependent gradient of inhibitory signal that mimicked Notch activity around stripes one and five. As the gradient narrowed, the model recapitulated the sequential emergence of stripes two to four and their resolution into SOP rows (Fig. 2E). To also describe the emergence of stripes one and five, we incorporated cis-inhibition in the model (supplementary text S1). With cis-inhibition, specifying a transient gradient of Dl expression recapitulated the full sequence of five proneural stripes and SOP rows (fig. S5). However, because cis-inhibition is not essential for patterning, we concentrate on the simpler model.

Attrition of the proneural group and cell-intrinsic bistability

Expression patterns in fixed samples implied a progressive refinement of proneural stripes, extending over several hours. Stripe three, formed by 6 hours APF and already being refined at 7 hours APF, was not fully resolved at 8 hours APF (Fig. 1, D to G, and figs. S2, A and B, and S6A). Likewise, Sens was expressed in continuous bands of cells in emerging stripes two and four at 8 hours APF (Fig. 3A); adjacent Sens-expressing cells remained at 10 hours APF (Fig. 3A) but not 12 hours APF (Fig. 1G and fig. S4). At intermediate stages of stripe resolution, cells expressing Ac, Sc, and/or Sens were often arranged in nearly continuous rows, suggesting that resolving stripes initially narrow down. Live imaging of GFP-Sc supported these observations (Fig. 3B and movie S2).

Fig. 3 Attrition of the proneural group.

Sens expression patterns in fixed samples (A) and live imaging of GFP-Sc (green) (B) show a gradual refinement of proneural stripes. Histone 2A–RFP (H2A) is shown in red. Sens expression in stripes two and four, emerging around 8 hours APF, is sparser at 10 hours but not fully resolved. Sc expression, which is faintly detected in a broad stripe three at t0 + 0.8 hours (t0 = 5 to 6 hours APF), is restricted to a subset of cells at later stages, yet adjacent Sc-expressing cells remain at t0 + 3.6 hours.

In spite of qualitative similarities, Ac, Sc, and Sens exhibited different expression patterns, hinting to differences in their dynamics. At 8 hours APF, Ac was expressed broadly in emerging stripes, whereas Sc and Sens were restricted to cells with high Ac (figs. S2A and S6). Sc and Sens, but not Ac, reached higher levels in resolving stripes versus emerging stripes. This suggested that Ac plateaus in a broad proneural group, whereas Sc and Sens levels increase in cells progressing toward the SOP fate (thus, Sc provides a better readout of SOP selection dynamics than Ac; compare movies S1 and S2). Fewer cells expressed Sens than Sc in resolving stripes, which suggests that Sens is down-regulated more rapidly in cells that are excluded from the proneural group.

Our observations indicated that proneural stripes are initially refined through exclusion of lateral cells. Though a persistent spatial bias extrinsic to the stripe could favor more central cells, the pattern of Notch activity argued against this possibility. At 7 hours APF, Notch was activated on the sides of stripe three, whereas signaling activity had receded in the regions of stripes two and four (Fig. 1E and fig. S2, B and C). Thus, exclusion of cells on the sides of stripe three must result from mutual inhibition within this stripe, implying that stripe three narrows autonomously. However, cells on the sides are likely exposed to lower Dl levels than cells at the center of the stripe. This apparent paradox is resolved if cells exhibit a bistable response, as required in our model: Central cells, which are more advanced toward the SOP fate, can keep progressing under signal levels that are sufficient to inhibit lateral cells.

Specifically, the model suggests the following scenario for stripe resolution (Fig. 4, A to C). The onset of proneural activity in an extended group of cells is accompanied by weak mutual inhibition. Idealizing the proneural group as equivalent cells in a state u, each cell receives a signal s = C0D*(u), where C0 is the effective number of neighbors of a cell (C0 ≈ 18 with our parameters for signaling). Under mutual inhibition, perfectly equivalent cells would tend to a uniform steady state with low u. However, this steady state has each cell poised at the tipping point between the two fates, making it unstable regardless of the strength of mutual inhibition (supplementary text S3). Thus, cells are necessarily removed from the proneural group, allowing further progression of the remaining cells. Idealizing an intermediate state of stripe resolution as a file of equivalent cells, mutual inhibition with fewer effective neighbors (C1 ≈ 3) leads to a steady state with a higher value of u, which again is unstable. Finally, a pair of adjacent cells with high u is unstable, guaranteeing that only isolated SOPs remain in the final pattern. Thus, the qualitative structure of the model ensures a gradual attrition of the proneural group. In the absence of spatial bias, the cells that are excluded first depend on noise, resulting in a disordered pattern. However, because emerging proneural stripes are delimited by a gradient of inhibitory signaling, lateral cells are biased for early exclusion (Fig. 4D), and stripes narrow down before resolving.

Fig. 4 Cell-intrinsic bistability.

(A to B) Intermediates in pattern formation, idealized as groups of equivalent cells [(A), (A′), and (A′′)], tend to steady states (colors indicate u levels, as in Fig. 2) that lie on the unstable branch of the bifurcation diagram (B) (green, signaling activity; see text). (C) In a schematic time course of SOP selection (dashed lines), cells are excluded from the proneural group at each step, allowing further progression of cells in the group (divergent arrows). (D) Actual cell trajectories from the model (color coded by position within stripe three; inset) show a continuous branching off of excluded cells (trajectories reverting to low u) until SOPs remain. Cells on the sides (blue), receiving a higher initial signal, are biased for early exclusion.

Because the model introduces no extrinsic bias along the anterior-posterior axis, symmetry breaking in that direction depends on the amplification of random differences. With a broad range of unstable modes (supplementary text S3), intermediates states are variable in structure, and pairs of cells with high u can persist for some time (Fig. 2E, t = 2, and movie S5). As attrition proceeds, however, a regular spacing emerges: SOPs must be distant enough to evade each other’s inhibition, yet not too distant or intervening cells would not be inhibited.

Our experimental observations—including early exclusion of lateral cells (Fig. 1E), restriction of proneural activity to central cells (Fig. 3), and persistent expression of Sens in cell pairs [e.g., in stripes two and four at 10 hours APF (Fig. 3A)]—supported this scenario. As a signature, time courses of cell state in the model showed a gradual progression of cells toward the SOP fate, accompanied by a continuous branching off of cells that reverted to low u (Fig. 5, A and B). When we quantified Sc levels in individual cells in vivo, we observed a similar structure (Fig. 5, C and D). In both model and experiments, cells at intermediate positions between two SOPs could progress for an extended period of time and reach high levels of u or Sc before eventually being inhibited.

Fig. 5 Time courses of cell state.

(A and B) The gradual resolution of stripes in the model (A) is reflected in time courses of u as cells progress to different levels before they revert to low u (B) (a subset of stripe-three cells are represented). (C and D) Time courses of Sc expression in vivo show the same structure (C). GFP-Sc levels were quantified in a subset of stripe-three cells from (D). Colors in (B) and (C) highlight different outcomes: red and magenta, SOP; green, early exclusion; blue, late exclusion [arrowheads in (A) and (D)].

As a counterpoint, we considered a model lacking cell-intrinsic feedback: i.e., f(u,s) ≡ f(s) in Eq. 2 (supplementary text S2). Compared with the bistable case, patterning in a monostable model required stronger nonlinearities—for example, a sharp step in the signal-sending curve D*(u) (figs. S7 and S8). Although simulations showed that a monostable model could produce a pattern of SOP rows, these did not emerge through a gradual narrowing of the proneural group. Instead, cells within a stripe first plateaued at intermediate values of u, then isolated SOPs emerged while the remaining cells reverted to low u (fig. S8, B and C). A monostable response also allowed cells to remain at intermediate levels of u at steady state (fig. S8, B and C), when bistability enforces a clear segregation between cells with high and low u. Based on a linear stability analysis (supplementary text S3), a bistable model supports the emergence of a large-scale structure (on the scale of the signaling range, like proneural stripes). In a monostable model, this is suppressed and instability is driven by small-scale fluctuations (fig. S9).

Perturbation analysis

Patterning in the model depends on defined boundary conditions and signaling dynamics and is predicted to break down in different ways when these are affected. Self-organized proneural stripes should be displaced when Notch activity is perturbed in the neighboring tissue. Indeed, ectopic Notch mutant SOPs created gaps in the proneural stripes in the surrounding wild-type tissue (Fig. 6, A and A′).

Fig. 6 Perturbation studies.

(Top) Model predictions. (Bottom) Experiments. (A) Cells lacking Notch become SOPs (magenta) and displace neighboring stripes (t = 2). (A′) Wild-type cells (RFP-positive) around a Notch mutant clone (dashed outline) do not express Ac (imaged live), creating a gap in stripe two. (B) With signal levels reduced by a half, stripe three fails to narrow to a central row (t = 2; compare with Fig. 2E). (B′) In Dl heterozygous pupae, a disordered pattern of Ac-positive and -negative cells is observed in the region of stripe three at 8 hours APF (compare with Fig. 1F). (C) With a reduced signaling range, stripes two and four split as lateral cells progress to high u and central cells are inhibited (t = 2.5). (C′) Live imaging of GFP-Ac in a scabrous (sca) mutant shows a splitting proneural stripe (arrowheads). (D) Without enhancement of Dl activity in SOPs, continuous bands of SOPs are formed. (D′) Denser SOP rows (labeled by Sens) are observed inside a large neuralized (neur) mutant clone (RFP-negative cells; dashed outline).

Proneural stripes must be narrow enough, relative to the range of inhibition, to resolve into a central SOP row. Reduced Dl levels, affecting early Notch activity, should result in a broader stripe three and should also weaken lateral inhibition within the stripes. In the model, reducing Dl levels by a half was sufficient to disrupt patterning. As predicted, a disordered pattern developed in the interval between rows one and five in Dl heterozygous pupae (Fig. 6, B and B′).

By contrast, mutations affecting scabrous (sca) reduce the range of lateral inhibition (16) but should leave early patterns unaffected because sca is only expressed in proneural cells (17). With a moderate reduction in signaling range, the model predicted a normal stripe three, but stripes two and four split to form supernumerary rows (Fig. 6C and fig. S10B). In sca mutant pupae, we observed expression patterns that were hardly distinguishable from wild-type patterns up to 8 hours APF but were more densely packed SOPs at later stages (fig. S10A); the arrangement of these SOPs suggested supernumerary rows. When we monitored Sc expression in vivo in sca mutants, we could observe the splitting of proneural stripes, as predicted (Fig. 6C′).

Our model requires a nonlinear increase in signaling from emerging SOPs. If D*(u) varies linearly with u, either the stripes fail to emerge, because mutual inhibition is too strong, or they fail to resolve, because inhibition is too weak (fig. S11). Dl is broadly expressed within emerging proneural stripes (fig. S3), arguing against a sharp up-regulation of its expression in SOPs. Instead, differences in Dl activity levels may rely on posttranslational regulation. The E3 ubiquitin ligase Neuralized (Neur) is a key regulator of Dl activity that is specifically expressed in emerging SOPs (1820). In our model, this is represented as D*(u) = a(u)D(u), where the Delta level D(u) = u varies linearly as a default, and the ligand activity a(u) increases from a basal level Embedded Image to a(1) = 1 upon full activation. When we simulated patterning with reduced or no activity enhancement, stripes formed normally but failed to resolve (Fig. 6D and fig. S12). Such a phenotype is observed within neur mutant clones (21) (Fig. 6D′) and in gain-of-function mutants of Bearded (22), an inhibitor of Neur (23). In terms of our model, increased SOP density in stripes one, three, and five maintains an inhibitory template for stripes two and four.

The model can also account for the loss or gain of bristle rows in flies that are smaller or larger than average (fig. S13), an observation that hinted at a dynamic origin of proneural stripes (24). Together, these perturbation experiments provide strong support for the model.

Discussion

Proneural patterning is classically viewed as an output of positional information that is interpreted by specific cis-regulatory enhancers at proneural loci (4) or relayed via proneural inhibitors (25). Proneural patterning has also been proposed to depend on Notch. In the inner ear of vertebrates, Notch relays positional information to maintain undifferentiated progenitor cells (26). However, whether Notch specifies, rather than maintains, prosensory domains continues to be controversial (2628). Similarly, Notch has previously been proposed to pattern proneural stripes (29), yet the origin of the Notch activity pattern was not addressed. Here, time-resolved analysis of patterning dynamics establishes that both positional cues (setting up the initial pattern of Dl) and downstream cell-cell interactions contribute to pattern Notch activity, which in turn acts as a negative template for proneural gene expression. Thus, prepattern and self-organization, operating through the same Notch signal, combine during bristle development. Although stripes one and five play equivalent roles in our model, we observed minor differences. For instance, stripe one resolves later, and SOPs emerge along the distal side of stripe one. Thus, other regulatory inputs (e.g., signals produced by midline cells) may impinge on patterning.

Though the relevant cellular and molecular interactions are well characterized, the mechanism by which neural precursors are selected among proneural cells has remained controversial (3). In many accounts, proneural clusters either comprise a small number of cells, such that competition between contacting cells is sufficient to select isolated precursors (30), or a subgroup of more competent cells is delimited by an inhibitory template (31). In our model, the restriction of competence is dynamic and driven by mutual inhibition: Cells are continuously excluded as the level of inhibition increases. Signaling modulators (e.g., Neur) likely drive the gradual transition from weak mutual inhibition within an extended proneural group to strong lateral inhibition from emerging neural precursors.

Patterning occurs in a 2D field of nondividing cells before the first wave of cell division (32). Three or four epidermal cells are often present between SOPs within rows, and a comparable or larger interval is seen between rows, whereas Notch is activated in all non-SOP cells. As noted previously (11, 16, 33), this implies that the range of signaling must exceed immediate neighbors. Because Notch signaling requires direct cell-cell contact, it could be mediated via basal filopodia that connect distant cells (11, 16, 33).

Our model represents proneural activity by a single variable u that subsumes the dynamics of multiple genes (e.g., Ac, Sc, and Sens). Likewise, Dl activity is an instantaneous function of cell state. These simplifying assumptions, which allow a systematic analysis, could be rationalized by a model where different genes act as different readouts of a common regulatory input, integrating positive feedback and inhibition. In these terms, broad expression of Ac in an extended proneural group hints at a more threshold-like response than Sc and Sens patterns, which are more graded in space and time. Earlier resolution of Sens patterns, compared with those of Ac and Sc, is consistent with Sens acting as a switch in SOP selection (34, 35); proneural activity may gradually recede following Sens down-regulation.

Most previous models of lateral inhibition have focused on the dynamics of Dl and Notch (36), in the absence of cell-intrinsic feedback. Provided that mutual interactions are sufficiently strong, adjacent cells with high Dl levels cannot coexist, and initially equivalent cells resolve into a salt-and-pepper pattern (36). On the other hand, several recent models (37, 38) have incorporated cell-intrinsic bistability, which allows emergent neural precursors to evade inhibition from their neighbors; in the presence of an extrinsic bias, this makes it possible for cells at the center of a proneural cluster to be selected (38). Contingent on particular parameter choices, these studies (37, 38) focused on a regime where cells crossing a threshold in the progression to the neural fate become refractory to inhibition. In this regime, adjacent neural precursors can coexist, and the selection of isolated cells depends on isolated cells crossing the threshold. Both studies (37, 38) suggested a requirement for a sharp onset of inhibitory signaling. Consequently, signaling is mostly in the form of lateral inhibition from committed neural precursors, and all neighboring cells are excluded within a short time interval, as compared with the time needed to approach the threshold (i.e., an order of magnitude shorter) (38). In that limit, precursor selection can be described as a “race for the neural fate” (38). The model introduced here, with different choices of the response function f, can recover these two limiting behaviors in a compact form (one variable per cell) and allowed us to explore an intermediate regime, where cells are intrinsically bistable yet remain responsive to inhibition. This regime combines the desirable features of neural precursor emergence from the center of the proneural group and the exclusion of adjacent precursors. In addition, precursors emerge through a gradual narrowing of the proneural group, with central cells first inhibiting more lateral cells and then competing among themselves to become SOPs. These properties mesh well with our observations in the notum, showing an early onset of mutual inhibition within stripes, well before SOPs emerge, along with progressive refinement of the proneural group throughout the progression of the eventual SOPs.

Mechanistically, bistability could result from positive feedback on proneural activity (38, 39) and/or cis-inhibition of Notch (37, 40). Although our main model abstracts the consequences of bistability from its molecular basis, we also considered a model that explicitly incorporates cis-inhibition. In this model, we prescribed Dl levels that were sufficient to titrate Notch within stripes one and five but not in SOPs, which remained responsive to inhibition. The extent to which Dl cis-inhibits Notch in SOPs remains to be experimentally tested.

Notch mediates patterning in other epithelia in flies, as well as in other species (4146). In the Drosophila eye, expression of the proneural gene atonal begins as a broad stripe and becomes restricted to isolated R8 photoreceptors (41). Stripes of Dl expression also pattern bristle rows in the Drosophila leg (42). The interplay between cell-intrinsic bistability and cell-cell interactions may provide a simple framework to explain how distinct patterns are produced by varying boundary conditions.

Materials and methods

Flies

The N55e11, scaBP2, sca1, DlRev10, SerRx82, neurIF65 mutations were used. FLP/FRT clones were detected using loss of nuclear red fluorescent protein (RFP). GFP-Moe was expressed using neur-Gal4 (11).

The DeltaGFP and scuteGFP lines were generated using CRISPR-mediated HR. For each locus, two gRNA oligonucleotides were cloned into pU6-BbsI-chiRNA (Addgene 45946) as described in addgene.org/crispr/OConnor-Giles/. Donor templates for HR were first produced by BAC recombineering in E. coli and then transferred into multicopy vectors as described in (47). BACs encoding Dl (48) and scute (BAC CH321-32O15) were used to introduce sfGFP flanked by GVG linkers, at the KGAS//GGPG position (Dl-PA) and at the N terminus (Sc). The 3xP3-RFP selection marker flanked by loxP sites was produced by gene synthesis. Left and right homology arms flanking the target sites were 1.5 kb long. Proper HR was verified by genomic PCR. DeltaGFP and scuteGFP flies were viable with no phenotype.

GFP-m3 was generated using recombineering mediated gap-repair (47) from the E(spl)-C BAC (49) and was integrated at the M{3xP3-RFP.attP}ZH-51D site. The GFP-Ac and Cherry-6xMyc-Ac BACs were generated from the CH321-32O15 BAC that fully rescues the sc10-1 mutation. BACs were integrated at the PB{y+-attP3B}VK00033 (65B) landing site. Cloning details will be provided upon request.

Immunostainings

Staged pupae were dissected and stained following standard procedures. Primary antibodies were: rabbit and goat anti-GFP, rabbit anti-DsRed (Clonetech), guinea pig anti-Senseless (1:3000, gift from H. Bellen), rat anti-Delta (rat anti-DeltaICD, mAb 10D5, 1:1000, from M. Rand).

Live imaging

Staged pupae were mounted on a custom-made support and imaged through the pupal case. Movies were acquired using continuous imaging (Δt = 5 to 15 min) with Δz = 1.5 μm using z-stacks with 25 to 50 sections. A 63× (PL APO, N.A. 1.4 DIC M27) objective on a Zeiss LSM780 microscope was used. The Histone2Av-mRFP1 marker was used to detect all nuclei. All times are equivalent hours at the reference temperature of 25°C.

Image processing

Images were processed using custom Java software built on the ImageJ API.

Projections of live images were generated after subtraction of signal from the cuticle. The location of the cuticle, which produced a stronger signal than nuclei, was determined by thresholding a smoothed image. To allow for spread in the z direction, the cuticle signal was extrapolated below the cuticle, assuming an exponential decay with z. After subtraction, a smooth surface was fit to the tissue, by minimizing a cost function that draws the surface toward areas of strong signal while penalizing sharp variations in its profile. Projections were obtained by summing pixel intensities in a small z range around the surface.

Single-cell quantification

Cell nuclei were identified using a variation on the watershed algorithm. To prevent oversegmentation due to inhomogeneous signal intensity, a binary mask was generated by thresholding a filtered image, then the watershed algorithm was applied to the distance transform of the mask. In the case of live images, individual z slices were segmented separately, then nuclei in consecutive slices were matched by proximity; together with a manual correction step, this allowed identification of nuclei when the pupa had moved between two slices. The level of signal in a nucleus was defined as the average intensity of its pixels. To compensate for variations in imaging conditions across the tissue, the GFP-Sc level obtained from live images was divided by the level of the nuclear marker, corrected for bleaching. Time courses were obtained by manual tracking of the nuclei.

Mathematical model

The dynamics of cell i is described by a stochastic differential equation of the formEmbedded Image(4)with a characteristic time scale τ and uncorrelated fluctuationsEmbedded Image(5)Our main model is obtained withEmbedded Image(6)where σ is the sigmoidal functionEmbedded Image(7)which goes from 0 to 1 with σ(0) = 1/2 and σ′(0) = 1.

The signal si received by a cell integrates a time-dependent gradient and signaling from neighboring cellsEmbedded Image(8)where xi is the position of the cell along the medial-distal axis andEmbedded Image(9)describes the coupling between cells i and j according to their distance dij, with the convention that cii = 0.

The signal produced by a cell as a function of its state isEmbedded Image(10)where the ligand level D(u) = u is taken to vary linearly as a default, and the ligand activityEmbedded Image(11)increases from a basal level a(0) = a0 to a(1) = 1.

Simulations of patterning

Simulations were run on a fixed array of cells, occupying a unit square with periodic boundary conditions, such that stripes one and five are equivalent (as an exception, a larger box was used for fig. S6A). Disordered cell arrangements were generated using a vertex model of epithelial tissue dynamics (50), with a random Voronoi tessellation as initial condition and a noise level z = 30% as per (50). The resulting cell arrangements had a majority of cells with six neighbors and a standard deviation of cell-cell distances of ~10% the average.

The signaling gradientEmbedded Image(12)interpolated over a time scale τg between a Gaussian profile with peak level S0 and width L, and a narrower profile representing signaling from SOPs in rows one and five, with range l.

Model parameters

Parameter values (table S2) were chosen to reproduce wild-type patterning dynamics. A bistable response requires a slope f ′ > 1, and Eq. 6 was chosen to yield a slope of 2 as a default. The resulting model is bistable in a relatively narrow range of signal levels; with different choices of f that yielded a broader bistable range, the emergence of stripes and/or their resolution were affected. The number N of cells in simulations was chosen based on a typical cell-cell distance ≈5 μm and distance between rows one and five ≈75 to 100 μm in experiments. The range L of the initial gradient was adjusted to yield a stripe three that is a few cells wide. The signaling range l had to be large enough for resolution of stripes into a central row of SOPs [l = 1.25λ yields supernumerary rows (fig. S10B)], but not too large or stripes two and four were suppressed (e.g., with l = 2.5λ). Relative to the time scale of cell dynamics (τ), the decay of the initial gradient (parameterized by τg) was chosen to be slow enough to pattern stripe three, but fast enough for stripes two and four to emerge before complete resolution of stripe three, as observed in experiments (Fig. 1F). The shape of the activity curve a(u) was chosen such that the steady states in Fig. 4B lie on and are spread across the unstable branch of the bifurcation diagram; this implied a basal activity a0 of the order of 1/C0. The noise level D was large enough that different simulations with the same cell arrangement yielded different patterns (i.e., fluctuations primed over the frozen disorder in the cell arrangement), but small enough for orderly resolution of the pattern.

Supplementary Materials

www.sciencemag.org/content/356/6337/eaai7407/suppl/DC1

Supplementary Text

Figs. S1 to S13

Tables S1 and S2

References (5153)

Movies S1 to S5

References and Notes

  1. Acknowledgments: We thank B. Baum, H. Bellen, V. Courtier-Orgogozo, H. Jafar-Nejad, and M. Rand for reagents; V. Roca for embryo injection; and V. Hakim, B. Hassan, and E. Siggia for discussion and critical reading. This work was supported by grants ANR-16-CE13-0003 and ARC-PGA120140200771. The supplementary materials contain additional data.
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