Serial synapse formation through filopodial competition for synaptic seeding factors

Summary

Following axon pathfinding, growth cones transition from stochastic filopodial exploration to the formation of a limited number of synapses. How the interplay of filopodia and synapse assembly ensures robust connectivity in the brain has remained a challenging problem. Here, we developed a new 4D analysis method for filopodial dynamics and a data-driven computational model of synapse formation for R7 photoreceptor axons in developing Drosophila brains. Our live data support a ‘serial synapse formation’ model, where at any time point only 1-2 ‘synaptogenic’ filopodia suppress the synaptic competence of other filopodia through competition for synaptic seeding factors. Loss of the synaptic seeding factors Syd-1 and Liprin-α leads to a loss of this suppression, filopodial destabilization and reduced synapse formation. The failure to form synapses can cause the destabilization and secondary retraction of axon terminals. Our model provides a filopodial ‘winner-takes-all’ mechanism that ensures the formation of an appropriate number of synapses.

Graphical Abstract

eTOC Blurb

How random axon filopodia dynamics lead to precise numbers of synaptic contacts during development is unknown. Özel et al. show through live imaging and computational modeling that a ‘winner takes all’ distribution of synaptic seeding factors renders one filopodium at a time synaptogenic, thereby pacing development and ensuring robust connectivity.

Introduction

After pathfinding, axon growth cones transition to become terminal structures with presynaptic active zones. How axon terminals form a defined number of synaptic contacts with a specific subset of partners is a daunting problem in dense brain regions (Sanes and Yamagata, 2009; Yogev and Shen, 2014). Stochastically extending and retracting filopodial extensions occur during both pathfinding (Chien et al., 1993; Mason and Erskine, 2000) and synapse formation (Ozel et al., 2015) and are thought to facilitate interactions between synaptic partners (Cohen-Cory, 2002; Vaughn et al., 1974; Ziv and Smith, 1996). However, little is known about the role of stochastic filopodial dynamics for robust synapse formation.

Presynaptic active zone assembly is a key step in synapse formation and regulated by a conserved set of proteins (Owald and Sigrist, 2009; Schoch and Gundelfinger, 2006). An early active zone ‘seeding’ step has been defined through the functions of the multidomain scaffold proteins Syd-1 and Liprin-α in C. elegans and Drosophila NMJ (Dai et al., 2006; Owald et al., 2010). Syd-1 is a RhoGAP-domain containing protein (Hallam et al., 2002) that recruits Liprin-α to the active zone (Owald et al., 2010). Liprin-α is an adaptor protein named after its direct interaction with the receptor tyrosine phosphatase LAR (Leukocyte common antigen-related) (Serra-Pagès et al., 1995; Zhen and Jin, 1999). The Liprin-α/LAR interaction has been directly implicated in active zone assembly across species (Dunah et al., 2005; Kaufmann et al., 2002). Downstream, Liprin-α and Syd-1 recruit core active zone components and ELKS/CAST family protein Brp (Dai et al., 2006; Fouquet et al., 2009; Wang et al., 2002). Finally, the RhoGEF Trio has been proposed to function downstream of the Lar/Liprin-α/Syd-1 (Astigarraga et al., 2010; Debant et al., 1996; Holbrook et al., 2012) and has recently been suggested to regulate active zone size (Spinner et al., 2017).

Remarkably, the proposed Lar/Liprin-α/Syd-1/Trio pathway has been characterized in parallel for its role in axon guidance, independent of active zone assembly (Bateman et al., 2000; Wills et al., 1999; Xu et al., 2015). In the Drosophila visual system, mutants in all four genes have been implicated in the layer-specific targeting of photoreceptor R7 axons in the medulla neuropil (Choe et al., 2006; Clandinin et al., 2001; Hofmeyer et al., 2006; Holbrook et al., 2012; Maurel-Zaffran et al., 2001; Newsome et al., 2000). It is unclear, whether any of the four mutants affect active zone assembly in R7 neurons. Dual roles in axon pathfinding and synapse formation have been shown or proposed for all four genes (Astigarraga et al., 2010; Hakeda-Suzuki et al., 2017; Holbrook et al., 2012; Maurel-Zaffran et al., 2001; Weng et al., 2011). Independent implications in active zone assembly and axon pathfinding raise the question what functions are primary or secondary.

In this study, we investigated the relationship between filopodial dynamics and synapse assembly in the presynaptic R7 terminal. The early synaptic seeding factors Liprin-α/Syd-1 accumulate in only a single filopodium per terminal at any given point in time. Consequently, only 1-2 filopodia per terminal are stabilized, suggesting that only 1-2 filopodia are synaptogenic at any time. A data-driven computational model shows that this ‘serial synapse formation model’ is supported by the measured dynamics and could be tested in mutants for liprin-α, syd-1, lar and trio. Specific defects in filopodial dynamics precede all other defects, including axon terminal retractions. We present a quantitative ‘winner takes all’ model, from stochastic filopodial dynamics to the formation of a limited number of synapses, as well as a model for axon terminal stabilization based on filopodia and synapses.

Results

In each optic lobe, ~800 R7 axon terminals reach their adult morphology as column-restricted, smooth, and bouton-like structures that contain around 20-25 presynaptic release sites (Fig. 1A–B) (Chen et al., 2014; Takemura et al., 2013). By contrast, during synapse formation these axon terminals exhibit highly dynamic filopodial extensions (Fig. 1A). The role of R7 filopodial dynamics in the second half of pupal development (P+50-100%) is unknown.

Figure 1: 4D filopodia tracking reveals stochastic dynamics prior to synapse formation and rare ‘bulbous’ filopodia that stabilize one at a time during synapse formation.

(A, B) Drosophila R7 photoreceptor axon terminals transition from a growth cone-like structure with multiple filopodia just prior to synapse formation at 50% pupal development (P50) to a smooth, adult terminal with 20-25 synapses (magenta: CD4-tdTomato, green: BrpD3-GFP). (C-D) A semi-automatic method for 4D filopodia tracking is based on the Amira filament editor. (E) Imaging protocol for >20 hour continuous time lapse and fast imaging at P40 and P60 for the same axon terminals. (F) R7 filopodia fall into short-lived and long-lived classes that both fit Poisson (stochastic) distributions at both P40 and P60. (G) Representative snapshots of an R7 axon terminal in the brain at P60 with a continuous stable bulb (yellow arrowhead). (H) Number of bulbous filopodia at P60. Separation into stable (middle) and transient (right) bulbs reveals that most time points contain 1-2 stable bulbs. The distributions can be fit with negative feedback (sold black lines), but not with Poisson product distributions (dotted lines). Scale bar: 2μm.

4D filopodia tracking reveals stochastic dynamics prior to synapse formation and rare ‘bulbous’ filopodia during synapse formation

The characterization of axon filopodia dynamics during synapse formation in the intact brain required a method to obtain quantitative high-resolution, long-term 4D data throughout the second half of fly brain development. We had previously developed long-term culture of intact developing brains in an imaging chamber (Ozel et al., 2015), but the challenge of tracking fast dynamics for thousands of filopodia in a developing brain have so far precluded large-scale analyses. We therefore devised a semi-automatic method for quantitative filopodia tracking based on a previously developed ‘filament editor’ (Fig. S1A–B) (Dercksen et al., 2014). In short, the algorithm predicts the growth cone centers for all time points by similarity-based propagation from the initial time point and thereby streamlines the segmentation of individual terminals (Fig. 1C). Next, filopodia are traced at each time point, sequentially propagated, and automatically matched to the corresponding filopodia at other time points based on the vicinity of their starting points (Fig. 1D). Using this method, we tracked 27,390 individual filopodia through time and space across 38 growth cones (Methods, Fig. S1A–B).

We first analyzed wild-type R7 axon development from just before synapse formation (P+40%, P40) until after 20-22h in culture, during synapse formation (P+60%, P60) for the same growth cones (1 minute time lapse for 1 hour periods; Fig. 1E). 4D tracking of several thousand filopodia revealed two distinct classes with separate exponential lifetime distributions: transient filopodia with a maximum lifetime of 8 minutes (short-lived), and stable filopodia with lifetimes of more than 8 minutes (long-lived) (Fig. S1C) with similar length and velocity distributions (Fig. S1D). At any time point at P40 each R7 terminal has twice as many long-lived (>8 min) compared to short-lived (<8 min) filopodia (Fig. 1F). The numbers of both classes reduce significantly by P60 (Fig. 1F), and by P100 all filopodia disappear (Fig. 1B). The measured filopodia exhibit linear stochastic dynamics, since all four distributions (long- and short-lived filopodia at P40 and P60) almost perfectly fit Poisson distributions (Gadgil et al., 2005) (red traces in Fig. 1F; STAR Methods, Mathematical Modeling).

In addition to the great majority of transient filopodia, we also consistently observed rare, long-lived filopodia that develop characteristic ‘bulbous tips’ around the time of synapse formation (Ozel et al., 2015). Quantitative analyses revealed no bulbous tips prior to synapse formation at P40. In contrast, at P60 there are 1-2 stabilized filopodia with bulbous tips present at any time point, most of which have a lifetime of >40 minutes(Fig. 1G–H; Movie 1). Because many of these bulbous filopodia existed before and after the 1-hour imaging window, the lifetime estimate is certainly an underestimation, and we observed bulbous tips that existed for hours in long-term time lapse. Notably, we counted almost no time instances with 0 bulbs (Fig. 1G–H; Movie 1). This heavily right-skewed distribution is indicative of a regulatory mechanism: While the absence of regulatory mechanisms would give rise to a Poisson product distribution (dotted lines in Fig. 1H), the inclusion of an inhibitory feedback, whereby existing bulbs suppress new bulbs, reveals an excellent fit of the observed distribution (solid lines in Fig. 1H). This skewed distribution causes a bulbous tip to be present at almost every time point, while a Poisson product distribution (= no feedback) would result in many time points without bulbs. Correspondingly, almost 100% of time points have at least one bulb, but rarely more than two. Hence, at the time of synapse formation, R7 growth cones continuously stabilize only 1-2 filopodia at any time point, while the overall number of filopodia decreases continuously from P40 till adulthood.

Only 1-2 filopodia at any time point accumulate synaptic seeding factors

Competitive stabilization of only 1-2 filopodia could be achieved through a ‘winner takes all’ mechanism of filopodial competition. We asked whether synaptic building proteins would exhibit such a competitive distribution at filopodial tips. First, we tested whether the active zone protein Bruchpilot (Brp) is associated with filopodia. Fluorescently tagged BrpD3 (or Brp^short) is a reliable marker for mature synapses and localizes specifically to sites of intrinsic Brp without affecting synapse function or causing overexpression artefacts (Berger-Muller et al., 2013; Schmid et al., 2008; Sugie et al., 2015). We never found BrpD3-marked mature active zones in filopodia, similar to recent findings in developing adult motoneurons (Constance et al., 2018) (Fig. 2A–B, G). To measure the dynamics of synapse formation, we performed live imaging of BrpD3 at 10 min resolution over several hours around P+70% (Movie 2). BrpD3 is strikingly excluded from filopodia; puncta never move into or form in filopodial tips, and instead form by gradual accumulation on the axon terminal main body. Tracking individual puncta for over 5 hours revealed that the vast majority of BrpD3-positive synapses are stable once formed (Fig. 2H, Movie 2). We conclude that mature synapses marked by BrpD3 are not associated with filopodia, but only form on the axonal trunk where they are stable once formed.

Figure 2: One filopodium at a time accumulates synaptic seeding factors.

(A-F) Localization in R7 photoreceptor terminals and filopodia for BrpD3-GFP (A, B), GFP-Syd-1 (C, D) and Liprin-α-GFP (E, F). Shown are two time points: P50 (A, C, E) and P70 (B, D, F). Yellow circles indicate filopodia with no measurable GFP signal, green circles weak signal, and blue circles clear accumulations. (A’-F’) show the single channel for the GFP-tagged proteins (green), and (A”-F”) show the single channel for the membrane tag CD4-tdTomato (magenta). Scale bar: 2 μm. (G) Quantification of filopodial accumulation of the three proteins. (H) Number of BrpD3 punctae per R7 terminal binned according to their lifetimes. R7 terminals were live imaged at 10 min resolution starting at P+50% + 22h in culture. Individual punctae were tracked for 5,5h to determine lifetimes (n = 5 terminals). Error bars denote SEM.

At the Drosophila neuromuscular junction, Brp is recruited late to nascent synapses by the early seeding factors Syd-1 and Liprin-α (Owald et al., 2010). We overexpressed GFP-tagged variants of each protein and asked to what extent they localize to filopodia. Unlike BrpD3-GFP, GFP-tagged Liprin-α and Syd-1 occur in bulbous filopodia tips (Fig. 2C–G). Remarkably, clearly discernable accumulations of Liprin-α and Syd-1 are only apparent in one or sometimes two bulbous filopodia, while the majority of filopodia contain no signal (Fig. 2C–G). In contrast to other filopodia, the number of filopodia tips containing Syd-1 or Liprin-α does not decrease between P50 and P70 but remains constant at 1-2 per axon terminal. Note that most filopodia do not contain any detectable Syd-1 or Liprin-α, despite large amounts of overexpressed proteins in the axon terminal trunks. The 1-2 positive filopodia could not be predicted based on size or length of the filopodia (compare c’-f’ to c”-f”). Antibody labeling of Syd-1 in wild type compared to syd-1 mutant R7 axon terminals confirmed the same sparse distribution to bulbous filopodia for the endogenous protein (Fig. S2A–C). Our findings support the idea that Syd-1 and Liprin-α match the criteria for a ‘winner takes all’ distribution: both localize sparsely and non-randomly to 1-2 filopodia per axon terminus.

Live imaging revealed the localization of Liprin-α-GFP only to stable filopodia with bulbous tips, while dynamically moving in and out of filopodia (Movie 3); GFP-Syd1 puncta were too dense for reliable tracking, but similar to Liprin-α, only exhibit clear accumulations in 1-2 bulbous filopodia per axon terminal at all times. These observations suggest that synapse assembly may start in filopodia. The data are further consistent with reversible molecular ‘seeding’ events (Owald et al., 2010) and filopodia stabilization through nascent synapses, as previously observed (Constance et al., 2018; Meyer and Smith, 2006). The findings suggest a model whereby only 1-2 filopodia at a time may be synaptogenic, i.e. competent to form a synapse.

A data-driven computational model predicts ‘serial synapse formation’ based on competition and negative feedback of bulbous filopodia

We tested a series of Markov models of filopodia dynamics based on the measured data at P40 and P60 before arriving at a model consistent with all observations (Fig. 3A; see also STAR Methods, Mathematical Modeling). We first modeled suppression of filopodia by synapses, such that the increasing number of synapses over time would lead to a decreased production of filopodia, until all filopodia are gone by P100 and a specific number of synapses has been generated. However, this model did not explain the non-Poisson distribution of bulbous filopodia seen in Fig. 1H (see Mathematical Modeling in STAR Methods). By contrast, suppression of new bulb generation through feedback by the bulbous filopodia themselves provided a minimal model that explains the non-Poisson distribution of bulbous filopodia as well as the slow progression of synapse formation (Fig. 3A). The model recapitulates the birth of filopodia, their transitions between short-lived and long-lived filopodia, transitions to bulbous filopodia, and finally transitions to synapses (Fig. 3A, C, E, G).

Figure 3: A data-driven computational model predicts ‘serial synapse formation’ based on competition and negative feedback of bulbous filopodia.

(A) Summary of the data-driven Markov state model from filopodial birth to synapse formation. All rates in blue are measured from live imaging data. Rates r₁ and r₂ denote the generation and retraction of filopodia, r₃ and r₄ denote the formation- and degeneration of a bulbous tip; r₅ denotes the stabilization of the bulbous tip and r₆ the formation of a synapse. (B) Estimation of time-dependent function required for the modeling from P40-P100 (40%-100% of pupal development). The reduction of filopodia was based on measured filopodial counts from fixed preparations (blue disks = average, error bars = standard deviation) and modelled by a time-dependent function f_F(t) (dashed red line) as outlined in the Methods section. The increased propensity to form bulbs on these filopodia (black dashed line) was estimated based on bulb measurements shown in panel (D) and as explained in the Methods section. (C) Output of Markov state model for filopodial dynamics based on measured rates according to the model in (A). Solid red lines indicate the median number of bulbs from the stochastic simulations, whereas dark grey areas denote the interquartile range (50% of the data) and light grey the 95% confidence range from the simulations. (D) Measured number of bulbous tips (disks = average, error bars = standard deviation). (E) Output of Markov state model for the development of bulbous tips. Black dotted lines: average number of bulbs; solid red line: median number of bulbs; grey confidence ranges as in (C). (F) Measured numbers of synapses between P40 and P100 (disks = average, error bars = standard deviation). (G) Output of Markov state model for synapse formation. Black dotted lines: average number of bulbs; solid red line: median number of bulbs; grey confidence ranges as in (C).

The live imaging data provides direct measurements of the filopodial birth and death rates (r1 and r2) and the observed rates of bulb disappearance (r4) (all measured data are labeled in blue in Fig. 3). Because of the introduction of inhibitory feedback on bulb formation, the average rate of bulb initiation (r3) at P60 is the product of a propensity to form bulbs (r2B) and the average inhibitory feedback f1, such that absence of feedback (f1=1) represents no inhibition of r3 and maximal negative feedback (f1=0) represents complete inhibition of r3. Based on the measurement of bulb appearances and the observed right-skewed distribution of bulbs (Fig. 1H) we determined the exclusive set of r2B and f1 that fit the observations for time point P60 (Table S1). Negative feedback f1 in WT is close to maximal, which ensures the measured sharp distribution of only 1-2 bulbs per time instance with almost no time instance of zero bulbs. As shown in Fig. 1H, almost every transient bulb stabilizes (r5). Lastly, we estimated the rate of synapse formation (r6) from the maximal slope in Fig. 3F. The number of mature synapses matched previous measurements (Chen et al., 2014; Takemura et al., 2013).

In addition to the live dynamics measurements at P60, we counted total numbers of filopodia, bulbous tips and synapses (BrpD3) in fixed preparations for the time points P40, P50, P60, P70, P80, P90 and P100 (blue data points in Fig. 3B, D, F). The live P60 data matches the fixed counts at P60 well. Based on these data, we determined a function for the filopodial decline (red dotted line in Fig. 3B) and the propensity to form bulbs (black dotted line in Fig. 3B; see STAR Methods, Mathematical Modeling). Based on the measured data and these two rates, we modeled the changes to types (Filopodia and Bulbs) and numbers of filopodia over time in 3600 time steps, equivalent to 3600 minutes from P40 to P100. The resulting model reproduces a minute-by-minute simulation of the number of filopodia (Fig. 3C), bulbs (Fig. 3E) and synapses (Fig. 3G). For model building and parameter estimation based on the measured data, see Methods section on Mathematical Modeling.

The appearance of only 1-2 bulbous tips at any time point between P55 and P85 leads to a continuous, limited generation of mature synapses that matches well with measured BrpD3 data (Fig. 3F, G). Furthermore, the model predicts variability of synapse numbers similar to the measured variability. We conclude that our serial synapse formation model, based on measurements of filopodia and competitive feedback between bulbs, can in principle explain the kinetics and distribution of synapse development observed in wild type.

Competition could either be the result of an active communication mechanism between filopodia, or, alternatively, passively arise from the uneven distribution of a limiting amount of synaptic seeding factors. We considered the restrictive distribution of seeding factors as a basis to model them as a resource with limited access to filopodia. In this model, a competitive advantage occurs if accumulation of seeding factors is associated with increased filopodial lifetime, which in turn provides more time for further accumulation of seeding factors, which further increase lifetime. Our modeling shows that, for a limited amount of synaptic seeding factors available to filopodia, such a ‘runaway’ positive feedback loop can lead to the accumulation of the majority of available seeding factors in just 1-2 bulbous filopodia (STAR Methods, Figs. S3–4). A passive mechanism can thereby effectively prevent other filopodia from accumulating enough seeding factors to stabilize. Hence, ‘winner takes all’ dynamics can arise from the dynamic distribution of a limited resource that confers a competitive advantage without the need for active filopodial communication or additional competitive mechanisms.

Loss of synaptic seeding factors Syd-1 and Liprin-α causes a loss of inhibitory feedback during filopodial bulb formation

Since our model predicts a role for synapse formation molecules in bulb stabilization, we tested the model experimentally in mutants. First, we tested the consequences of a loss of brp during R7 axonal development with a previously tested combination of two RNAi constructs (Wagh et al., 2006) and confirmed the known defect in neurotransmission (Fig. S5A–B). The knock-down of brp has no effect on the transition of R7 terminal morphology from filopodial to smooth bouton-like structures (Fig. S5C). These findings indicate no role for Brp in axon terminal development and are consistent with the absence of Brp from filopodia (Fig. 2). These findings further resemble previous observations in motoneurons (Constance et al., 2018), and are consistent with the observation of normal development in the absence of neurotransmission (Hiesinger et al., 2006).

To perturb early stages of synapse formation, we investigated mutants for liprin-α and syd-1. The analysis of filopodial dynamics is complicated by previous observations of R7 axon targeting defects for both mutants (Choe et al., 2006; Hofmeyer et al., 2006; Holbrook et al., 2012). To characterize the timeline and origin of these defects, we performed long-term live imaging from P+30%-P+70% for single mutant, positively labeled R7 cells in an otherwise heterozygous background (MARCM) (Lee and Luo, 1999). Our analyses of both mutants (liprin-α^E (Choe et al., 2006), syd-1^w46 (Holbrook et al., 2012)) revealed that all mutant R7 axons initially target correctly. Axon terminal dynamics of both liprin-α and syd-1 mutant axons are indistinguishable from wild type until P40 (Fig. S6A–C). Starting around P50, i.e. during the time period of synapse formation, individual terminals retract. At P60, the majority of liprin-α or syd-1 mutant R7 axon terminals continue to remain in their correct target layer. We therefore first performed a quantitative analysis of filopodial dynamics at P40 and P60 for those terminals that remained stable in their correct target layer. We provide a detailed analysis of retraction events in the last section (Fig. 6).

Figure 6: A computational model predicts axon retractions in lar, syd-1, and liprin-α, but not in trio.

(A) Schematic of timeline during synapse formation, including continuous decline of transient filopodia, the first appearance of bulbs and the continuous increase in synapse numbers. (B) Measured R7 axon retraction rates. (C) Probability of R7 axon terminal retractions at P100 based on computational modeling of stabilization through a combination of transient filopodia and synapses. (D-G) Representative time-lapse snapshots from long-term live imaging of R7 axon stabilization and retraction in the four mutants. Dashed lines mark the wild-type R7 target layer (M6). Scale bars: 3 μm. (H-K) Computational modeling of predicted probabilistic axon retractions between P40-P100 for all four mutants (comp. to measured data in panel B).

Quantitative 4D tracking of filopodia of both liprin-α or syd-1 mutant R7 axon terminals at P40 and P60 revealed distributions of numbers, lifetimes, lengths and velocities that are largely indistinguishable from wild type (Fig. S6A–O). syd-1 mutant axon terminals exhibit individual, unusually elongated filopodia during synapse formation, but their low number does not affect the statistics significantly (Fig. S6M). In contrast to other filopodia, the dynamics of bulbs were significantly altered. The lifetimes of bulbs in both syd-1 and liprin-α were reduced by 70-80% (Fig. 4A). Bulb destabilization is also reflected in a similar ~70% decrease of the number of stable (>40 minute) bulbous filopodia in both mutants. Correspondingly, the number of short-lived, destabilized bulbs is dramatically increased by ten to twenty-fold (Fig. 4B, Movie 4). The reduced lifetimes and increased numbers are a result of increased rates for both bulb appearance (r3) and bulb disappearance (r4) as measured at P60 (Table S1). A remarkable consequence of corresponding increases in both bulb generation and destabilization is that the average number of bulbs observed per time instance, i.e. the average appearance of what a fixed image would look like, is not significantly different from wild type (Fig. 4C). These findings suggest that the absence of synaptic seeding factors leads to a defect in bulb stabilization, resulting in continuous attempts to form new bulbs. Bulb stabilization by synaptic seeding factors is consistent with a competitive, non-random distribution of Liprin-α and Syd-1 proteins to filopodia. We conclude that synaptic seeding factors are required for bulb stabilization, but not for bulb initiation.

Figure 4: Loss of synaptic seeding factors Syd-1 and Liprin-α causes a loss of inhibitory feedback and filopodial bulb destabilization.

Analyses of filopodial dynamics and synapse formation for syd-1 (green), liprin-α (red) and control (blue). (A) Lifetime of bulbous filopodia. (B) Total number of bulbous filopodia per terminal per hour. (C) Average number of bulbous filopodia per time instance. (D) Number of concurrently existing bulbous filopodia per axon terminal per time instance observed in the data, simulated after inclusion of a feedback (+f1) and without a feedback (−f1). (E, F) Representative snapshots of syd-1 (E) and liprin-α (F) revealing only transient bulbs. (G-N) Markov state model simulation for syd-1 (G-J) and liprin-α (K-N) for the numbers of filopodia (G, K), transient bulbs (H, L), stable bulbs (I, M) and synapses (J, N). In all cases control traces from Fig. 3 are shown in yellow. Black dotted lines: mean number of bulbs; solid red line: median number of bulbs; dark grey denotes the interquartile range (50% of the data) and light grey the 95% confidence range. (O-R) Measurement of BrpD3 punctae in mutant axon terminals. (O’-R’) BrpD3 single channel. Scale bar: 2 μm. (S, T) Quantification of BrpD3 synapse numbers per terminal relative to control. n=18 and 16 (p = 0.0007). (T) Number of BrpD3 punctae per terminal with lifetimes greater than 3h in R7 axons live imaged for 4h at P+70% in wild-type (n=5) and liprin-α^E mutants (n=5). (U) Quantification of synapse numbers in syd-1^ΔRhoGAP flies. n = 45, 18 and 32 (p < 0.0001). Error bars denote SEM.

Next, we analyzed the distribution of bulbs present at any given time point over a one hour period at P60. In contrast to wild type, both syd-1 and liprin-α exhibit 20-30% of all time points without any bulbs (Fig. 4D). In wild type, the bulb distribution (blue boxes, data as in Fig. 1H) does not match a Poisson distribution without feedback (−f0), but can be simulated with inhibitory feedback (+f1) as described for Fig. 1H. By contrast, both syd-1 and liprin-α (green and red boxes, respectively) resemble Poisson product distributions (−f0) and are not better matched by applying the inhibitory feedback (+f1) (Fig. 4D, note that smaller f1 values indicates stronger feedback in Table S1). As with the wild type data, the observed rate of bulb appearance (r3) could be fitted with a single product of the average propensity to form a bulb (r2B) and the average inhibitory feedback (f1) at P60 (Fig. 3A). In both mutants the feedback is mostly lost (f1 >10-fold increased, Table S1). Together with a reduced bulb stabilization rate r5 in both mutants, the loss of feedback results in a high frequency of transient bulbs for both syd-1 (Fig. 4E; Movie 4) and liprin-α (Fig 4F; Movie 4).

We next simulated the entire time course from P40-P100, from filopodial dynamics to synapse formation as established for wild type (Fig. 3), using the measured live data at P60 for each mutant. For syd-1, overall filopodia numbers are slightly below wild type (Fig. 4G). However, in contrast to wild type, the simulation recapitulates the formation of large numbers of transient bulbs (Fig. 4H), but very few stabilized bulbs (Fig. 4I). In contrast, wild type forms almost no transient bulbs, because all bulbs stabilize (compare black trace for mean in syd-1 to yellow traces of the mean for control in Fig. 4H–I). The liprin-α simulation revealed a similar increase of transient bulbs combined with a further reduced number of stable bulbs (Fig. 4K–M). As a result of this altered distribution, the simulation predicts a reduction of adult synapses in syd-1 and liprin-α to 35% and 20% of the wild-type levels, respectively (Fig. 4J, N). These simulated reductions occur without changes to the synapse formation rate r6 and are purely because of the observed defect in bulb stabilization; an additional direct effect of syd-1 or liprin-α on synapse formation itself, as has been argued based on their molecular function as synaptic seeding factors (Owald et al., 2010), would reduce the number of synapses further.

To assess the number of synapses in vivo we performed BrpD3 counts at P70 in R7 axon terminals in their correct target layer. The number of BrpD3-positive synapses is significantly reduced in liprin-α (Fig. 4O–P, S) and almost completely abolished when a 3 hour stability criterion is applied (Movie 5, Fig. 4T). Similarly, syd-1 mutants exhibit almost no BrpD3-positive synapses (Fig. 4Q–R). We also generated a precise CRISPR-mediated knock-in of a mutant version of syd-1 lacking putative RhoGAP activity, which was previously predicted to play a role in active zone assembly (Wentzel et al., 2013) (Spinner et al., 2017). This gene-edited allele fully replaces the wild type gene locus (Fig. S5D–E). However, in contrast to loss of syd-1, the syd-1^ΔRhoGAP mutant flies are viable, fertile and exhibit no obvious defects other than a relatively mild reduction of BrpD3-positive synapse numbers (Fig. 4U, Fig. S5F–H) and are not further analyzed here. Consistent with studies in other systems, these findings indicate that syd-1 and liprin-α are required for normal synapse formation also in R7. In sum, our findings support the hypothesis that both proteins function as a limiting resource for synaptic ‘seeding’, which is in turn required for the stabilization of synaptogenic filopodia.

Analyses of additional pathway components reveal a role for Lar, but not Trio in bulb initiation

The membrane receptor LAR and the RhoGEF Trio have been proposed to function in a pathway with Liprin-α and Syd-1 in the contexts of axon pathfinding and synapse formation (Astigarraga et al., 2010; Holbrook et al., 2012; Maurel-Zaffran et al., 2001; Weng et al., 2011). We therefore performed live imaging, filopodia tracking, and computational modeling for lar and trio mutant R7 axons analogous to WT, syd-1 and liprin-α.

Long-term live imaging of single mutant R7 axons showed that, similar to liprin-α and syd-1, both lar and trio axon terminals initially target correctly and exhibit no significant alterations of their filopodial dynamics prior to P40 (Fig. S7A–C). However, individual lar mutant axon terminals exhibit the first probabilistic retractions shortly thereafter, resulting in retraction of nearly all terminals by P70, as previously reported (Clandinin et al., 2001; Maurel-Zaffran et al., 2001). In contrast, we did not observe any retractions of trio mutant axons. As with other mutants, we analyzed filopodial dynamics at P40 and P60 exclusively for axon terminals that remained stable in their correct target layer. We provide the detailed analysis of retractions in the last section (Fig. 6).

Similar to liprin-α and syd-1, the dynamics of lar mutant R7 growth cones exhibit no significant differences of filopodia numbers, lifetimes and lengths until P40 (Fig. S7A–C), except for a mildly increased birth rate r1 in trio (see model parameters in the Methods section). Similarly, both short-lived and long-lived filopodia exhibit distributions for numbers and lengths that are similar to wild type in both mutants at P40 and P60 (Fig. S7D–O). Remarkably, bulb dynamics are the only significantly affected variable in both mutants. Similar to syd-1 and liprin-α, both lar and trio mutants exhibit bulbs of significantly reduced lifetimes (Fig. 5A, Movie 6). Additionally, bulbs are destabilized in lar (Fig. 5B). However, in contrast to syd-1 and liprin-α, lar mutants form overall significantly less bulbs, suggesting a defect in bulb formation (Fig. 5D) and a specific role for lar in the initiation of synaptogenic filopodia.

Figure 5: Analysis of the Syd-1/Liprin-α pathway components reveal a role for Lar, but not Trio in bulb initiation.

Analyses of filopodial dynamics and synapse formation for lar (orange), trio (magenta) and control (blue). (A) Lifetime of bulbous filopodia. (B) Total number of bulbous filopodia per terminal per hour. (C) Average number of bulbous filopodia per time instance. (D) Number of concurrently existing bulbous filopodia per axon terminal per time instance observed in the data, simulated after inclusion of a feedback (+f1) and without a feedback (−f1). (E, F) Representative snapshots of lar (E) and trio (F) revealing only transient bulbs. (G-N) Markov state model simulation for lar (G-J) and trio (K-N) for the numbers of filopodia (G, K), transient bulbs (H, L), stable bulbs (I, M) and synapses (J, N). In all cases control traces from Fig. 3 are shown in yellow. Black dotted lines: mean number of bulbs; solid red line: median number of bulbs; dark grey denotes the interquartile range (50% of the data) and light grey the 95% confidence range. (O-R) Measurement of BrpD3 punctae in mutant axon terminals. (O’-R’) BrpD3 single channel. Scale bar: 2 μm. (O-Q) Measurement of BrpD3 punctae in trio and control axon terminals. (O’-P’) BrpD3 single channel. (Q) Quantification of BrpD3-marked synapse numbers relative to control at P90. n=87 and 61, p= 0.67 (R) Schematic summary of protein functions during synapse formation.

In contrast to lar, R7 axon terminals mutant for trio exhibit a strong increase of transient bulbs without significant loss of stable bulbs and a normal average number of bulbs per time instance (Fig. 5B, C). These observations suggest that trio axon terminals can initiate and stabilize bulbous filopodia, but form many additional unstable ones. Correspondingly, analysis of the bulb distribution at any given time point over a one hour period at P60 separates lar and trio further from syd-1 and liprin-α: In lar, the distribution is best matched with inhibitory feedback (+f1, orange boxes), suggesting partially intact feedback (Fig. 5D, Table S1). In contrast, trio (magenta boxes) resembles the wild type distribution (blue boxes, same control as Fig. 4D) suggesting that, in contrast to the other three mutants, one bulbous tip at any time point can still be stabilized (Fig. 5D). This finding was further corroborated by live imaging (Movie 6). Taken together, our mutant analyses suggest that lar is defective in bulb initiation (Fig. 5E), lar, syd-1 and liprin-α fail to stabilize bulbs, and trio exhibits 1-2 stable bulbs plus supernumerary unstable bulbs (Fig. 5F).

We next used our complete time course simulation from filopodial dynamics to synapse formation using the measured P60 data for lar and trio. As shown in Fig. 5G, simulated lar mutant terminals form normal numbers of filopodia. In contrast to syd-1 and liprin-α, very few transient or stable bulbs form in lar mutants (Fig. 5H–I). Consequently, the lar simulation produces only very few synapses (Fig. 5J). In contrast, trio exhibits continuously elevated levels of filopodia, and increased number of transient bulbs (similar to syd-1 and liprin-α), but also close to wild type levels of stabilized bulbs (Fig. 5M), which leads to close to wild type levels of synapses (Fig. 5N). Correspondingly, BrpD3-labeling reveals normal numbers of synapses in trio (Fig. 5O–P). We could not reliably measure BrpD3-positive synapses in lar, because most axons are retracted by P70 and none retained a normal morphology. However, at P50, prior to Brp recruitment, Syd-1 still localizes to bulbous tips in lar mutant terminals, while Liprin-α is almost completely lost (Fig. S2D–K. These findings suggest that the recruitment of Liprin-α, i.e. the Lar interacting protein α, depends on Lar. In contrast, in trio mutant terminals, both Syd-1 and Liprin-α exhibit unaltered localization to 1-2 bulbous tips at any time (Fig. S2D–K. We conclude that the increased number of (unstable) bulbous filopodia in the trio mutant does not lead to increased numbers of synaptogenic filopodia, consistent with the measured numbers of synapses and the limiting resource model.

In summary, our data reveal largely normal axon targeting and filopodial dynamics until P40 for all mutants. lar exhibits defective bulb initiation and lar, syd-1 and liprin-α all fail to stabilize bulbs, leading to significant reductions in synapse formation. In contrast, in trio ‘winner takes all’ stabilization of 1-2 filopodia is intact, but selective negative feedback on further bulb initiation is defective. Hence, all four mutants fit distinct roles of the ‘winner-takes-all’ mechanism and support the serial synapse formation model (Fig. 5R, Fig. 7).

Figure 7: Serial Synapse Formation Model.

The measured live dynamics and computational modeling suggest the following model: (1) stochastic filopodial exploration leads to synaptic capture via a cell surface receptor, e.g. Lar (2) early synaptic seeding factors (Syd-1 and Liprin-α) are recruited to the captured filopodium in an enlarged bulb; (3) secondary simultaneously forming bulbs are destabilized via the function of the RhoGEF Trio, thereby ensuring one synaptogenic filopodium at any given time; recruitment of the active zone protein Brp and synapse maturation occur after filopodial retraction back in the main axon terminal, allowing a new cycle of bulb formation and stabilization.

A computational model predicts axon retractions in mutants for lar, syd-1, and liprin-α, but not trio

We have so far performed all analyses on normally targeted axon terminals that remained stable in the correct target layers, thereby isolating defects in filopodial dynamics and synapse formation independent of axon retraction. We therefore set out to test the idea that defective synapse formation might contribute to axonal destabilization. In contrast to cadN (Ozel et al., 2015), none of the mutants analyzed here exhibited altered filopodial dynamics or retractions prior to P40, after which time synaptic partner identification is likely to start. The first stable bulbous filopodia can be observed around P45 and synapse formation increases thereafter (Fig. 6A). Similar to filopodial adhesion, synapses may contribute to the stabilization of axon terminals. We therefore hypothesized that axon terminal stabilization may be a function of both filopodia and synapses (Fig. 6A).

First, we measured the retraction rates between P40-P70 (Fig. 6B). lar and liprin-α exhibit similar retraction rates with a 5-hour delay for liprin-α after lar. The dynamics of these retractions appears similar in long-term live imaging of axon behaviors (Fig. 6E–F, Movie 7). In both cases, individual terminals probabilistically collapse to a smooth structure within 2 hours and are not recognizably different just one hour prior to collapse. A filopodial protrusion often remains for several hours and the terminals retain the remarkable ability to re-extend to M6, but do not stabilize there. In contrast, apparent retraction of syd-1 mutant axons plateau after P50 (Fig. 6B); syd-1 axons initiate retractions very similar to liprin-α and lar, but exhibit many more re-extensions back to M6 and even beyond (Fig. 6D, Movie 7). This behavior contributes to the appearance of less retracted syd-1 axons after P50 in fixed preparations (Fig. 6B). trio mutant axons exhibit increased filopodial extensions that are somewhat similar to syd-1, explaining the earlier observations of an additional overextension phenotype in fixed preparations (Holbrook et al., 2012). We did not observe any retractions of trio mutant axons. However, careful analysis of trio mutant strains with the same genotypes as those used by Holbrook et al., 2012 revealed rare, misplaced R7 axons only in the original stocks from that study, but not in different genetic backgrounds. Hence, trio may have a mildly increased probability to retract depending on the genetic background.

We next modeled retraction probabilities as a function of the number of filopodia and synapses. If only filopodia stabilize axon terminals, but not synapses, the model predicts similar retraction rates for wild type and all mutants (Fig. S8). In contrast, if synapses contribute to axon stabilization, the different synapse formation rates of the four mutants differentially affect retractions. We tested the retraction probability as a function of an equally weighted sum of filopodia and synapses based on the measured filopodia and simulated synapse formation data for all four mutants. If very few filopodia or synapses are required to retain the axon, none of the mutants should exhibit axon retractions before P100 (Fig. 6C). If we increase the ‘minimal stabilization’ number, i.e. the number of filopodia plus synapses, WT and all mutants exhibit an increasing probability to retract. WT and trio exhibit the same low probability to retract only if high numbers of filopodia and synapses are required for stabilization (Fig. 6C). In contrast, lar, liprin-α and syd-1 all exhibit significantly increased probabilities to retract. Notably, the regime where only lar, liprin-α and syd-1 exhibit retractions is robust over a wide range of the ‘minimal stabilization factor’ (Fig. 6C). Figures 6H–K show simulated retraction dynamics of all mutants for the ‘minimal stabilization’ number marked by an arrow in Fig. 6C. Remarkably, all mutants exhibited simulated retraction kinetics that closely resembled the observed retractions. In particular, liprin-α exhibits slowly decreasing retraction rates, while syd-1 appears significantly more dampened after P60 (comp. Fig. 6B and 6I, J). The least good match is lar, where the data show earlier retractions with higher rates than in the model. This suggests that retractions in lar are not sufficiently explained by synapse loss, but may occur earlier due to an additional adhesion role, as previously suggested (Hakeda-Suzuki et al., 2017; Weng et al., 2011). In sum, our combined live dynamics measurements and data-driven modeling suggest that the serial synapse formation model is sufficient to predict the number and distribution of synapses and their role in stabilizing axon terminals in wild type, liprin-α, syd-1 and trio. Our data further suggest that Lar plays a role in the same process as Liprin-α and Syd-1, but early retractions may be caused by an additional, earlier function.

Discussion

In this study we characterized the role of filopodial dynamics during synapse formation using the Drosophila R7 photoreceptor terminal as a model. We present a serial synapse formation model based on competitive distribution of synaptic building materials between synaptogenic filopodia (Fig. 7).

Serial Synapse Formation through filopodial competition for synaptic seeding factors

Our data link bulbous filopodia to synapse formation based on three findings: (1) In wild type, these are the only filopodia that specifically occur during the time window of synapse formation and do not exhibit stochastic dynamics; wild type R7 photoreceptor axons stabilize 1-2 bulbous filopodia at a time. (2) The synaptic seeding factors Liprin-α and Syd-1 non-randomly localize to 1-2 bulbous filopodia at a time. (3) Loss of liprin-α or syd-1 selectively affects the stabilization of bulbous filopodia. Loss of the upstream receptor lar similarly selectively affects bulbous filopodia, but, in addition to bulb destabilization, also strongly affects bulb initiation. Together, these findings support a model whereby stochastic filopodial exploration leads to bulb stabilization and synapse formation one at a time. In this model restrictive synaptogenic filopodia formation ‘paces’ the formation of ~25 synapses over 50 hours, effectively controlling synapse numbers within the available developmental time window.

The key mechanism of this model is inhibitory feedback of synaptogenic filopodium formation. In contrast to all other filopodia, the dynamics of bulbous filopodia are not independent events. How are synaptic seeding factors competitively distributed between these filopodia? Our live imaging data suggest that Liprin-α or Syd-1 can traffic in and out of filopodia but overexpressed proteins accumulate in the axon terminal trunk and do not enter to more than 1-2 filopodia, indicating that trafficking into filopodia is restricted. Morphologically, filopodia are very thin structures that may not provide much space for freely diffusing proteins or organelles. On the other hand, the bulbous tip provides a much larger volume that may be required for sufficient amounts of synaptic seeding factors and other building material to initiate synapse formation. Furthermore, our computational tests show that ‘winner takes all’ dynamics can arise from the dynamic distribution of a limited resource that confers a competitive advantage (longer lifetime, which leads to further accumulation) without the need for active filopodial communication (Figs. S3 and S4).

Since Syd-1 and Liprin-α are not required for bulb initiation, we speculate that filopodial contact with a synaptic partner may initiate the bulb and precede active zone formation. Our data suggest that Lar is a good candidate for a presynaptic receptor with such a role, but it is unlikely to be the sole upstream receptor. Neurexin (Owald et al., 2012) and PTP69D (Garrity et al., 1999; Hofmeyer and Treisman, 2009), for example, are other known candidates. In the absence of an upstream receptor or the seeding factors themselves, synapse assembly fails and bulbs destabilize. New bulb generation following loss of bulbs in the absence of seeding factors can also be explained with seeding factors as a limiting resource with a competitive advantage (Figs. S3, S4). This is reminiscent of other competitive processes that shape neuronal morphology, e.g. the restricting role of building material in the competitive development of dendritic branches in a motorneuron (Ryglewski et al., 2017). Our mutant analyses suggest that stable bulbs are linked to negative feedback on other bulbs via the function of the RhoGEF Trio. While the exact mechanism is unclear, it is tempting to speculate about a role of actin-dependent signaling downstream of synaptic seeding.

Our current model only considers the presynaptic axon terminal. The main postsynaptic partner of R7 are amacrine-like Dm8 cells, whose elaborate dendritic processes are present in direct vicinity to the R7 filopodia throughout the developmental period of synapse formation (Karuppudurai et al., 2014). We currently do not know the dynamics of the postsynaptic processes and whether they restrict availability or are ‘easily found’ as postsynaptic partners. Our presynaptic model could explain the observed slow, serial synapse formation even in the presence of abundant postsynaptic partner processes.

Cause and Effect: The Challenge to Identify Primary Defects in Circuit Assembly

Mutations in the proposed pathway components Lar, Liprin-α, Syd1 and Trio have been independently characterized for their roles in active zone assembly (mostly at the larval neuromuscular junction) and axon targeting, in large part in the visual system (Astigarraga et al., 2010; Hakeda-Suzuki et al., 2017; Holbrook et al., 2012; Maurel-Zaffran et al., 2001; Weng et al., 2011). It is likely that all four genes exert more than one function in different contexts. Defects in synapse formation and retraction are captured by the measured parameters and our model. However, some differences in overall morphology, including overextensions in the syd-1 mutant, may be described by parameters not considered in the model, e.g. filopodial length, and due to some differences in their molecular function (Astigarraga et al., 2010; Holbrook et al., 2012). Similarly, for Lar, independent context-dependent function have been characterized based on different downstream adaptors (Weng et al., 2011).

We asked to what extent a primary role for lar, trio, syd-1 and liprin-α in synapse formation could explain previously observed phenotypes. All filopodial defects in the four mutants occur independently and prior to possible retraction events. Our combined live imaging and computational modeling suggests that defects in the syd-1 and liprin-α mutants are consistent with a primary defect in bulb stabilization and synapse formation. These defects may in turn lead to axon destabilization or represent independent functions; lar may have an additional earlier adhesion function and trio does not play a critical role in the formation of the correct number of synapses, while its effect on general filopodial dynamics may sensitize mutant axons to other changes.

We base our conclusion that Lar, Liprin-α and Syd-1 have a primary function in synapse formation on three pieces of evidence: (1) all mutants initially target correctly and exhibit normal filopodial dynamics prior to synapse formation. (2) The mutants start retracting only when synaptic contacts initiate, in the order and severity from the receptor to the downstream elements. (3) All three mutants exhibit the loss of competitive bulb stabilization. Taken together, these observations support a direct role in synapse formation following bulb stabilization but we cannot exclude other molecular functions. For example, in both C. elegans and Drosophila Lar has been shown to function independently in axon guidance and synapse formation (Ackley et al., 2005; Weng et al., 2011). We found that syd-1^ΔRhoGAP mutants have normal terminal morphology and only a mild decrease in the number of BrpD3-puncta. This is consistent with recent findings that a RhoGAP-deficient Syd-1 fragment is sufficient to rescue early active zone seeding events at the Drosophila neuromuscular junction but not the recruitment of Brp as the active zones mature (Spinner et al., 2017). However, since homozygous syd-1^ΔRhoGAP flies have no obvious connectivity defects, synapse numbers are apparently sufficient for axon terminal stabilization.

Finally, our observations suggest that loss of the primary functions of these proteins in filopodial dynamics and synapse formation are sufficient to cause axon retractions. The phenotypes observed here for lar, liprin-α and syd-1 are somewhat similar, but in contrast to cadN only occur at or after the time of synaptic partner identification. While filopodia continuously decrease, synapses continuously increase (Fig. 6A), thereby allowing a take-over of the axon terminal stabilization function. The modelling fits wild type, liprin-α, syd-1 and trio remarkably well. On the other hand, retractions in the lar mutant are qualitatively predicted, but the model fails to explain retractions quantitatively. A partial explanation may be that we parameterized our model only based on the lar mutant axon terminals that are still unretracted at P60. These are only 30% of terminals by that time, and we have effectively selected for terminals with dynamics that prevented retractions thus far. It is likely that earlier retractions are caused by defects in filopodial adhesion or synaptic contacts. In sum, our data and modeling support a role for synapses in the stabilization of R7 axon terminals, which can lead to probabilistic axon retractions in mutants affecting synapse formation.

STAR Methods

Lead Contact And Materials Availability

Reagents generated in this study are available for distribution. Requests for resources and reagents should be directed to Robin Hiesinger (robin.hiesinger@fu-berlin.de).

Experimental Model and Subject Details

All experiments were performed with Drosophila pupae collected at P+0% (white pupae) and aged in 25°C unless otherwise specified. We did not select for gender in any of the imaging experiments. Source details for all fly lines are specified in the Key Resources Table.

Key Resources Table

REAGENT or RESOURCE	SOURCE	IDENTIFIER
Chemicals, Peptides, and Recombinant Proteins
Vectashield	Vector Laboratories	H-1000
PBS	Gibco	70011-36
Formaldehyde	Merck KGaA	1.03999.1000
Triton X-100	Sigma-Aldrich	T8787
Schneider’s Drosophila Medium [+] L-Glutamine	Gibco	21720-024
Agarose, low gelling temperature	Sigma-Aldrich	A9045-10G
Human insulin recombinant zinc	Gibco	12585014
Penicillin/Streptomycin	Gibco	15140122
ES Cell FBS	Gibco	16141-061
20-Hydroxyecdysone	Sigma-Aldrich	5289-74-7
SilGard and Silicone Elastomer Kit	Dow Corning	184
Experimental Model: Organisms/Strains
Drosophila, GMR-FLP (X)	Chang et al. (1995)	N/A
Drosophila, hs-FLP (X)	Bloomington Drosophila Stock Center (BDSC)	8862
Drosophila, GMR-Gal4 (II)	(BDSC)	1104
Drosophila, GMR-Gal4 (III)	BDSC	29967
Drosophila, GMR-FRT-stop-FRT-Gal4 (II)	Chen et al., 2014	N/A
Drosophila, FRT80B, tub-Gal80	BDSC	5191
Drosophila, FRT82B, tub-Gal80	BDSC	5135
Drosophila, FRT42D, GMR-Gal80	This paper. GMR-Gal80: Gift from Thomas Clandinin.	N/A
Drosophila, FRT40A, tub-Gal80	BDSC	5192
Drosophila, FRT2A, tub-Gal80	BDSC	5190
Drosophila, FRT40A	BDSC	8212
Drosophila, FRT42D	BDSC	1802
Drosophila, FRT80B	BDSC	8214
Drosophila, FRT82B	BDSC	5619
Drosophila, FRT2A	BDSC	1997
Drosophila, FRT82B, syd-1w46	Holbrook et al. (2012)	N/A
Drosophila, FRT82B, syd-1dRhoGAP	This paper.	N/A
Drosophila, FRT40A, liprin-αE	Choe et al. (2006)	N/A
Drosophila, FRT40A, lar2127	Maurel-Zaffran et al. (2001)	N/A
Drosophila, UAS-lar RNAi	Vienna Drosophila Research Center (VDRC)	36269
Drosophila, FRT2A, trio3	Newsome et al. (2010)	9130
Drosophila, / UAS-Brp-RNAiB3, UAS-Brp-RNAiC8	Wagh et al. (2006)	N/A
Drosophila, UAS-CD4-tdGFP (II)	BDSC	35839
Drosophila, UAS-CD4-tdGFP (III)	BDSC	35836
Drosophila, UAS-CD4-tdTomato (III)	BDSC	35837
Drosophila, UAS-BrpD3-GFP	Schmid et al. (2008)	N/A
Drosophila, UAS-BrpD3-mKate2 (II and III)	This paper.	N/A
Drosophila, UAS-Liprinα-GFP	Fouquet et al. (2009)	N/A
Drosophila, UAS-myc-Liprin	BDSC	63809
Drosophila, UAS-GFP-Syd1 (II).	Owald et al. (2010)	N/A
Drosophila, UAS-GFP-Syd1 (III).	Stephan Sigrist (unpublished)	N/A
Drosophila, GMR-myr-tdTomato (II and III)	Gift from S.Lawrence Zipursky	N/A
Antibodies
Mouse anti-Chaoptin	Developmental Studies Hybridoma Bank (DSHB)	24B10
Mouse anti-lar	DSHB	9D82B3
Mouse anti-Trio	DSHB	9.4A anti-Trio
Myc-Tag (71D10) Rabbit mAb	Cell Signaling Technology	2278T
Cy™3 AffiniPure Goat Anti-Mouse IgG (H+L)	Jackson Laboratories	115-165-166
Cy™5 AffiniPure Goat Anti-Mouse IgG (H+L)	Jackson Laboratories	115-175-166
Goat anti-Mouse IgG (H+L) Alexa Fluor 647	Thermofisher Scientific	A28181
Recombinant DNA
pTW BrpD3-GFP	Schmid et al. (2008)	N/A
pmKate2-C	Evrogen	FP181
Software and Algorithms
ImageJ	National Institutes of Health (NIH)	N/A
Imaris	Bitplane, Switzerland	N/A
GraphPad Prism	GraphPad Software, La Jolla, USA	N/A
Microvolution Plug-in	Microvolution	N/A
Clampfit	Axon Instruments	N/A
Clampex	Axon Instruments	N/A
MATLAB	Mathworks	N/A
Amira ZIB Edition	Zuse Institut Berlin	N/A

Following final genotypes were used for each experiment: For wild-type membrane and synapse imaging: (GMR-FLP/+; GMR-Gal4/GMR-myr-tdTomato; FRT80B, UAS-CD4-tdGFP/FRT80B, tub-Gal80) and (GMR-FLP/+; FRT42D, GMR-Gal80/FRT42D; GMR-Gal4, UAS-CD4-tdTomato/UAS-BrpD3-GFP). Membrane imaging with mutants: (GMR-FLP/+; FRT40A, tub-Gal80/FRT40A, liprin-α^E (or dlar²¹²⁷); GMR-Gal4, UAS-CD4-tdGFP, GMR-myr-tdTomato/+), (GMR-FLP/+; GMR-Gal4, UAS-CD4-tdGFP/GMR-myr-tdTomato; FRT82B, tub-Gal80/FRT82B, syd-1^w46 (or syd-1^dRhoGAP)), (GMR-FLP/+; GMR-Gal4, UAS-CD4-tdGFP/GMR-myr-tdTomato; FRT2A, tub-Gal80/FRT2A, trio³). Synaptic imaging with mutants and corresponding controls: (GMR-FLP/+; FRT40A, tub-Gal80/FRT40A, liprin-α^E (or dlar²¹²¹ or FRT40A only); GMR-Gal4, UAS-CD4-tdTomato/UAS-BrpD3-GFP), (GMR-FLP/+; GMR-Gal4, UAS-CD4-tdGFP/UAS-BrpD3-mKate2; FRT82B, tub-Gal80/FRT82B, syd-1^w46 (or syd-1^dRhoGAP or FRT82B only)), (GMR-FLP/+; GMR-Gal4, UAS-CD4-tdGFP/UAS-BrpD3-mKate2; FRT2A, tub-Gal80/FRT2A, trio³ (or FRT2A only)). For imaging of early synaptic markers: (hs-FLP/+; GMR-FRT-w⁺-FRT-Gal4/UAS-Liprin-α-GFP (or UAS-GFP-Syd1), UAS-CD4-tdTomato). For visualizing early synaptic markers in trio mutant axons (GMR-FLP/+; LGMR-Gal4; FRT2A (or FRT2A trio³)/ UAS-Liprin-α-GFP (or UAS-GFP-Syd1), UAS-CD4-tdTomato/FRT2A, tub-Gal80). For visualizing early synaptic markers in lar mutant axons (GMR-FLP/+; FRT40A, dlar²¹²⁷/ FRT40A, Tub-Gal80; GMR-Gal4, UAS-CD4tdTomato/+, and ;UAS-lar RNAi, UAS-Liprin-α-GFP/+; GMR-Gal4/+). For imaging with Brp RNAi: (GMR-FLP/+; FRT42D, GMR-Gal80/FRT42D; GMR-Gal4, UAS-CD4-tdGFP, GMR-myr-tdTomato/UAS-Brp-RNAi^B3, UAS-Brp-RNAi^C8). For ERG recordings: (; GMR-Gal4/FRT42D ;) and (; GMR-Gal4/FRT42D; UAS-Brp-RNAi^B3, UAS-Brp-RNAi^C8/+).

Molecular Biology

To build the UAS-BrpD3-mKate2 construct, EGFP sequence was removed from the pTW BrpD3-GFP plasmid (gift from S. Sigrist) using Xba1 and Age1 sites. mKate2 sequence was amplified from the pmKate2-C plasmid (Evrogen) using the following forward and reverse primers (respectively):gggTCTAGACggtggaggaggtATGGTGAGCGAGCTGATTAA and cccACCGGTTTATCTGTGCCCCAGTTTGCTAG. The products were digested with Xba1 and Age1 and ligated into the above-mentioned pTW BrpD3 plasmid. Injections were done by Rainbow Transgenics (USA) for P-element insertion and candidate lines were isolated and tested according to standard procedures.

syd-1^dRhoGAP allele was generated by Well Genetics (Taiwan) using CRISPR/Cas9 Scarless (DsRed) system (Fig. S5D). 2 gRNAs were used against the following target sites (PAM): CGGGAGTCTAAGAATGCTCC[CGG]; AGATACTTAAGCACCGCGAT[CGG]. Upon PBac-mediated excision, a specific and complete deletion of the RhoGAP domain was achieved with only a TTAA motif left embedded in the exogenous sequence GTTAAA (Fig. S5E). Insertion and excisions were verified by genomic PCR and sequencing. Full design details and sequencing results are available upon request.

Histology and Fixed Imaging

Eye-brain complexes were dissected in PBS, fixed in 3.7% paraformaldehyde (PFA) in PBS for 40 minutes, washed in PBST (0.4% Triton-X) and mounted in Vectashield (Vector Laboratories, CA). Images were collected using a Leica TCS SP8-X white laser confocal microscope with a 63X glycerol objective (NA=1.3).

Following antibodies were used for fixed imaging: Primary antibodies: anti-Trio (mouse, 1:50, DSHB), 24B10 (1:200, DSHB), anti-myc (1:200, Cell signaling), anti-Lar (mouse, 1:50, DSHB), anti-Syd-1 (rabbit, 1:500, gift from Stephan Sigrist).

Secondary antibodies: anti-mouse Alexa 647 (1:500, Life technologies), anti-mouse Cy5 (1:500, Jackson laboratories), anti-mouse-Cy3 (1:500, Jackson Laboratories), anti-Rabbit Alexa 647 (1:500, Life Technologies), anti-Rabbit Cy5 (1:500, Jackson Laboratories).

Brain Culture and Live Imaging

Ex vivo eye-brain complexes were prepared as described before (Ozel et al., 2015). For filopodial imaging, brains were dissected at P+40% and 1 μg/ml 20-Hydroxyecdysone was included in the culture media. For synaptic imaging, brains were dissected at P+50% and no ecdysone was included.

Live imaging was performed using a Leica SP8 MP microscope with a 40X IRAPO water objective (NA=1.1) with a Chameleon Ti:Sapphire laser and Optical Parametric Oscillator (Coherent). We used a single excitation laser at 950 nm for two-color GFP/Tomato imaging. For GFP/mKate2 imaging lasers were set to 890 nm (pump) and 1150 nm (OPO).

GFP-Syd-1 and Liprin-alpha-GFP overexpression did not obviously affect filopodial dynamics (Movie 3).

Electroretinogram (ERG) Recordings

1-5 day-old adult flies were reversibly glued on slides using nontoxic school glue. Flies were exposed to 1s pulses of light stimulus provided by computer-controlled white light-emitting diode system (MC1500; Schott) as previously reported (Williamson et al., 2010). ERGs were recorded using Clampex (Axon Instruments) and measured using Clampfit (Axon Instruments).

Quantification and Statistical Analysis

Data Analysis.

All live imaging data as well as all data involving synaptic markers were deconvolved (10 iterations with the theoretical PSF) using Microvolution Fiji Extension. Imaging data were analyzed and presented with Imaris (Bitplane). For synaptic counts, Spot objects were created from the BrpD3 channel and Surfaces were generated from the CD4 channel using identical parameters between experimental conditions and the corresponding control. Spots were then filtered for their localization on the positive clones by the Imaris 9 MATLAB extension ‘XTSpotsCloseToSurface’.

Further analysis regarding the quantified data and generation of corresponding graphs were done using Prism 7 (GraphPad). Where needed statistical differences were calculated with unpaired, parametric t-tests.

Filopodia Tracing and Tracking.

We developed an extension to the Amira Filament Editor (Dercksen et al., 2014) for tracing and tracking of individual filopodia in 4D datasets. Growth cones are represented by an annotated skeleton tree, in which each branch corresponds to a filopodium (Fig. S1B). This tree is traced for each time step and matched to the tree in the previous time step in a semi-automatic process.

First, the user interactively marks the growth cone (GC) centers in the first time step. The GC centers are automatically detected in the remaining time steps using template matching (Brunelli, 2009). Then, the GCs are processed one at a time. To this end, the images are cropped such that they contain only the current GC. The user interactively specifies the filopodia tips in the first time step. The filopodia are traced automatically from the tip to the GC center using an intensity-weighted Dijkstra shortest path algorithm based on (Sato et al., 2000). The onset of a filopodium is determined by identifying the point on the path where the 2D intensity profile orthogonal to the tracing changes from Gaussian (for the filopodium) to non-Gaussian (inside the GC body). The user visually verifies the tracing and, if necessary, interactively corrects it using dedicated tools provided by the Filament Editor. After tracing all filopodia in the first time step, they are automatically propagated to the next time step by template matching of tips and onsets, and tracing paths from tip to center through the onset. Propagated filopodia obtain the same track ID as the original. After each time step the user verifies the generated tracings, and adds newly emerging filopodia. This process is continued until all time steps have been processed (Fig. S1A).

Statistical quantities including length, angle, extension/retraction events, and lifetime are extracted from the filopodia geometry and stored in spreadsheets.

Mathematical Modeling

Stochastic filopodial dynamics were modelled by a Poisson process formalism motivated by the observed stochastic dynamics of filopodia (Fig. 1F). A model based on suppression of filopodia by synapses did not explain the non-Poisson distribution of bulbous filopodia seen in Fig. 1H (see Mathematical Modeling in STAR Methods for details). In addition, mutants that block synapse formation should maintain high levels of filopodia throughout development due to loss of feedback, which is not consistent with the mutant data shown below. Hence, a model in which synapses suppress filopodia could not be reconciled with the measured data. We therefore developed a data-driven minimal model capturing the dynamics of filopodia, bulbous tips and synapse formation. We first identified the systems variables, followed by parallel model selection and parameter estimation, testing higher complexity models whenever the best fit of a simpler model could not sufficiently explain the data. All data used for model inference and parameterization, as well as the parameter inference procedure are outlined below. All codes were written in MATLAB 2018a (Mathworks, Nattick). Parameter inference was performed using the MATLAB 2018a function ‘fminsearch’ and simulations were performed using the stochastic simulation algorithm.

Identification of state variables.

Besides synapses (S), which denote the endpoint of the modelling pipeline, bulbous tips were directly identified in the time-lapse data based on their altered morphology. Analysis of the bulbous lifetime data in wild type and mutants identified two populations: short-lived, unstable bulbous tips (sB) that appeared and disappeared within the 60 minutes imaging interval vs. stable bulbous tips that persisted for more than 40 minutes, termed ‘synaptogenic bulbous tips’ (synB) (Fig. S9A–E). Finally, we identified two types of filopodia, which are distinguished by their lifetime and which will henceforth be denoted short-lived- (sF) and long-lived (F) filopodia, as described below (Fig. S9F–G).

Short-lived vs. long-lived filopodia.

Our 4D filopodia tracking of 27,390 individual filopodia at P40 and P60 provided the trajectory data for statistical analyses of filopodia lifetimes (Fig. S1). We first tested whether the measured dynamics could be represented as a single population or two distinct sub-populations. Fig. S9F–G shows the respective fits with exponential lifetime distributions, which strongly support the existence of two populations based on the lifetime data (AIC_2cmp = 260 (three parameters) versus AIC_lcmp = 827 (one parameter)). The respective rate constants for retraction are c_2,sF = 0.69 (min⁻¹) and c_2,ℓF= 0.12 (min⁻¹) for short- and long-lived filopodia. The optimal cut-off to differentiate these two populations based on their lifetimes is 8 minutes (Fig. S9G, inset).

Transient vs. stable (synaptogenic) bulbous tip filopodia.

Analysis of the bulbous filopodia lifetime data in the mutants identified two populations: short-lived bulbous tips (sB) and stable bulbous tips that persisted once they appeared (synB) (Fig. S9A–E). In the wild type almost all bulbous tips were of the synB type. For the mutants, the lifetime distribution of the short-lived bulbous tips (left bars in Fig. S9B–E) appeared exponentially distributed with mean lifetimes as follows: lar = 3.3 min, liprin-alpha = 9 min, syd-1 = 5.9 min and trio = 7.6 min.

Model selection.

We first built a reference model for wild type and then adapted the model parameters to the mutants syd-1, liprin-alpha, lar and trio in a data-driven fashion. We tested several structural models and eliminated those that were inconsistent with measured data. For example, we initially tested a model in which synapse formation downregulates the number of filopodia. While this model could explain the wild type data, it failed to explain the downregulation of filopodia in mutants with compromised synapse formation capabilities (syd-1, liprin-alpha, lar). Consequently, this model, and all models in which synapse formation downregulates filopodia, were excluded.

Final model.

The final model is depicted in Fig. 3A and its reaction stoichiometries are determined by the following reaction schemes:

$$\begin{array}{c}{R}_{1,sF}:\varnothing \to sF,R_{2,sF}:sF\to \varnothing ,R_{1,\ell F}:\varnothing \to \ell F,R_{2,\ell F}:\ell F\to \varnothing \\ R_3:F\to sB,R_4:sB\to \varnothing ,R_5:sB\to synB,R_6:synB\to S\end{array}$$

Note that in R₃ we denote by F any filopodium (short-lived and long-lived) and in R₄ we have ignored the flux back into the filopodia compartment sF + ℓF as it insignificantly affects the number number of filopodia (small B, small rate r₄). In the following, we will guide through the model building and parameterization process.

Model parameterization: Retraction and generation of filopodia, r₁, r₂.

The exponential lifetimes of both short-lived and long-lived filopodia populations indicate a first-order decay with the respective rate constants c_2,sF = 0.69 (min⁻¹) and c_2,ℓF = 0.12 (min⁻¹). In addition, the number of filopodia per time instance is Poisson distributed (Fig. 1F), i.e. $sF~\mathcal{P}({\lambda }_{sF})$ and $\ell F~\mathcal{P}({\lambda }_{\ell F})$, where λ denotes the average number of filopodia per time instance. Given the first-order retraction of filopodia, the Poisson distribution can be explained by a zero-order input with rate c_1,sF and c_1,ℓF and λ_sF = c_1,sF/c_2,sF and λ_ℓF = c_1,ℓF/c_2,ℓF respectively. The latter is a well-established result for the stationary distribution of a birth-death process (Allen, 2003). The average number of filopodia decreased significantly over the 20 hours window from P40 to P60 (Fig. 1F, see Table below).

	short-lived		long-lived
Mutant	P40	P60	P40	P60
wt	5.6(3.9)	3.4(1.8)	10(3.5)	4.9(2)
dlar	3.8(2.3)	2.2(1.7)	13(2.3)	5.2(1.6)
lirin-α	4.5(2.7)	2.6(1.5)	8.6(2.1)	6.5(1.9)
syd-1	4.1(2)	1.6(1.3)	9.3(3.3)	3.8(1.7)
trio	6.8(2.8)	4.5(2.2)	14(3.7)	10(2.7)

Average (standard deviation) numbers of short-lived and long-lived filopodia per time instance.

This prompted us to introduce a time-dependent function f_F(t) that down-regulates the generation of new filopodia at a slow time scale. The time-dependent function f_F(t) was then fitted to normalized filopodia counts at P40–P100, as shown in Fig 3B. In summary, the propensity functions for reactions R_1,sF, R_2,sF ,R_1,tF , R_2,tF are given as follows.

$$\begin{array}{ll}{r}_{1,sF}(t)=f_F(t)\cdot c_{1,sF},& r_{2,sF}(sF)=sF\cdot c_{2,sF}\\ r_{1,\ell F}(t)=f_F(t)\cdot c_{1,\ell F},& r_{2,s\ell }(sF)=\ell F\cdot c_{2,\ell F}\end{array}$$

where $f_F(t)=\text{max}(0,{\sum }_{i=0}^5{p}_i\cdot t^i)$ is a fifth-order polynome with coefficients p₅ = −2.97 · 10⁻¹⁴, p₄ = 3.31 · 10⁻¹³, p₃ = −1.29 · 10⁻⁹, p₂ = 2.06 · 10⁻⁶, p₁ = −1.45 · 10⁻³ and p₀ = 1. Note, that t denotes the time in (min) after P40 (e.g. t_P40 = 0). Consequently, we have f_F(t_P40) = 1 and we can determine the input rate constant directly from the average number of filopodia at P40, i.e. c_1,sF = λ_sF,P40 · c_2,sF and c_1,ℓF = λ_ℓF,P40 · c_2,ℓF respectively.

Model parameterization: Bulbous dynamics, r3, r4 and r5.

Under the assumption that short-lived unstable bulbous tips retracted by first order kinetics (reaction r₄), the rate constant of retraction is equal to the inverse of the expected lifetimes of bulbous tips. We then wanted to investigate whether the bulbous tip number distributions in Fig. 1H, Fig. 4D and Fig. 5D can be explained by simple input-output relations or whether regulatory/feedback mechanisms are involved. The number distribution of short-lived bulbous tips sB and synaptogenic (stabilized) bulbous tips synB is given by:

$$\ast \underset{r_4}{\overset{r_3}{\rightleftharpoons }}sB\stackrel{r_5}{\to }synB\stackrel{r_6}{\to }\ast$$

Model I: No Feedback.

In the absence of any regulatory mechanisms (feedbacks), all reaction rates are of first order, e.g. r₄ = sB · c₄, r₅ = sB · c₅ and r₆ = synB · c₆. The net influx r₃ at t = P60 is r₃(t) = c₃(sF(t) + ℓF(t)) · f_FB(t), where we assume that sF(t), ℓF(t) and f_FB(t) are approximately constant over the time scale of interest. Parameters c₄ can be approximated by (the inverse of) the bulbous tip life times and c₆ = 1/120 (min⁻¹) can be approximated from the maximum slope of synapse generation presented in Fig. 3F–G. The two parameters c₅ and r₃(t) remain to be estimated for t = P60.

To perform this task we set up a generator matrix G that has entries (transition rates):

$$\begin{array}{ll}G([i,j],[i-1,j])=i\cdot c_{4,}& G([i,j],[i,j-1])=j\cdot c_6\\ G([i,j],[i+1,j])=r_3(t),& G([i,j],[i,j+1])=j\cdot c_5\end{array}$$

and diagonal elements such that the row sum equals 0. In the notation above, the tupel [i, j] denotes the state where i short-lived bulbous tips sB and j synaptogenic bulbous tips synB are present. The generator above has a reflecting boundary at sufficiently large N (maximum number of bulbous tips). The stationary distribution of this model is derived by solving the eigenvalue problem

$$G^T\cdot \upsilon =\upsilon \cdot \lambda$$

and finding the eigenvector corresponding to eigenvalue λ₀ = 0. From this stationary distribution, we compute the marginal densities of sB and synB (e.g. summing over all states where i = 0, 1, … for sB) and fit them to the experimentally derived frequencies (Fig. 1H, Fig. 4D and Fig. 5D) by minimizing the Kullback-Leibler divergence between the experimental and model-predicted distributions. The resulting best fit for the wild type is shown in Fig. 1H (dashed lines). Lastly, parameter c₃ is derived by calculating

$$c_3=\frac{r_3(t)}{(sF(t)+\ell F(t))\cdot f_{FB}(t,t_{1/2})}$$ (1)

where sF(t) = f_F(t) · sF(t_P40) and where we assumed that f_FB(t) is a tanh function with

$$f_{FB}(t,t_{1/2})=\frac{1}{2}\left(1+\tanh \left[\frac{3}{t_{1/2}}(t-t_{1/2})\right]\right)$$

that models a time-dependent increase in the propensity to form bulbous tips. We had set t_1/2 = 1000 (min), such that the rate of bulbous formation peaks at P60–P80. Note that for this particular (linear) model, one can also fit r3(t) and c5 to the marginal distributions of sB, synB, such that $sB~\mathcal{P}({\lambda }_1)$ and $synB~\mathcal{P}({\lambda }_2)$ with λ₁=r₃/(c₄+c₅) and λ₂ = λ · c₅/c₄.

Model II: Feedback on bulb generation.

We followed the analogous procedure as for model I, except that we incorporated a feedback mechanisms into the generator matrix

$$\begin{array}{ll}G([i,j],[i-1,j])=i\cdot c_4,& G([i,j],[i,j-1])=j\cdot c_6\\ G([i,j],[i+1,j])=r_3(t)\cdot f_1(j,B_{50}),& G([i,j],[i,j+1])=j\cdot c_5\end{array}$$

where r₃(t) is auto-inhibited by the total number of bulbous tips through the feedback function f₁(j,B₅₀) = B₅₀/(j + B₅₀). The resulting fit for the wild type is shown in Fig. 1H (solid lines), showing that this model can capture the observed bulbous tip dynamics much better than model I. Essentially, model II results in few non-synaptogenic bulbous tips and guarantees that at least one stabilized (synaptogenic) bulbous tip is present at all times, as observed for wild type. The biological mechanism behind this feedback could be a general resource limitation for factors stabilizing bulbous tips in combination with an allocation of this stabilizing resource to particular bulbous tips, which, in turn, prevents further bulbous tips to be stabilized, as described in the Results section and the computational test below.

Computational test whether resource limitation and a competitive advantage can give rise to “winner-takes-all”-dynamics.

We set up a simple mechanistic model of seeding factor uptake and stabilization of bulbous tips (Fig. S3) that allows to test the effects of (i) “resource”/seeding factor limitation and (ii) competitive advantage (seeding factor dependent stabilization of bulbous tips). First, we tested under what conditions the resource accumulated in bulbous tips in the model as experimentally observed (Fig. 2). Our simulation results (Fig. S4, left panels) indicate that “resource”/seeding factor limitation is a pre-requisite for the accumulation of seeding factors in bulbous tips. We then tested for all parameter configurations that passed this first test, whether the number of bulbous tips present per time instance agrees with the experimental data (Fig. S4, right panels). This second test revealed that only in the case of “resource”/seeding factor limitation plus competitive advantage the model predictions agree with the experimental data. In sum, these computational experiments show that resource limitation and competitive advantage are sufficient to explain competitive ‘winner-takes-all’ dynamics without an additional active filopodial communication mechanism.

Model parameterization: Synapse generation, r₆.

As mentioned earlier we assumed first-order kinetics and in line with the serial synapse formation model assumed that only one bulbous can generate a synapse at a time, deriving

$$r_6=c_6\cdot \min (synB,1)$$

Parameter c₆ = 1/120 (min⁻¹) was then approximated from the maximum slope of synapse generation presented in Fig. 3F.

Wild type model and parameters.

The reactions rate/propensities of the stochastic model are given by

$$\begin{array}{ll}{r}_{1,sF}(t)=f_F(t)\cdot C_{1,sF},& r_{2,sF}(sF)=sF\cdot C_{2,sF}\\ r_{1,\ell F}(t)=f_F(t)\cdot C_{1,\ell F},& r_{2,\ell F}(sF)=\ell F\cdot C_{2,\ell F}\\ r_3(t,sF,\ell F,B)=c_3(sF+\ell F)\cdot f_1(B,B_{50})\cdot f_{FB}(t,t_{\frac{1}{2}}),& r_4(sB)=c_4\cdot sB\\ r_5(sB)=c_5\cdot sB,& r_6(synB)=c_6\cdot \min (1,synB)\end{array}$$

Using the methods explained in the previous sections, we derived the parameters depicted in the table below for the wild type. We first estimated c_2,sF, c_2,ℓF from the filopodial lifetime data (Fig. S9G). Using the mean number of sF, ℓF at P40 (Fig. 1F, Fig. S6D–E, J–K and Fig. S7D–E, J–K), we then estimated c_1,sF, c_1,ℓF. Using these parameters and the measured slow-scale dynamics (Fig. 3B), we fit the fifth-order polynomial f_F(t). From the lifetimes of bulbous tips we estimated c₄, which we used together with the number distribution of short-lived and synaptogenic bulbous tips to estimate B₅₀, c₅ and r₃(t) in the auto-inhibition model (model II, Fig. 1H). Using all parameter estimates derived so far and setting t_1/2 = 1000 (min) in function f_FB(t, t_1/2), we estimated parameter c₃. All model parameters below are in units (min)⁻¹, except for t_1/2 (min) an B50 (unit less).

	C1,sF	C2,sF	C1, ℓF	C2, ℓF	C3	C4	C5	C6	B50	t1/2
wt	3.88	0.69	1.15	0.11	0.022	1/120	0.1133	1/120	0.0282	1000
dlar	2.63	0.69	1.49	0.11	0.00	0.3	0.0228	1/120	10−4	1000
liprin-α	3.12	0.69	0.99	0.11	0.0152	0.111	0.0028	1/120	0.363	1000
syd-1	2.84	0.69	1.07	0.11	0.0321	0.169	0.0048	1/120	1.084	1000
trio	4.71	0.69	1.61	0.11	0.0139	0.1311	0.1865	1/120	0.0231	1000

The fifth-order polynome $f_F(t)=\text{max}(0,{\sum }_{i=0}^5{p}_i\cdot t^i)$ has coefficients p₅ = −2.97 · 10⁻¹⁴, p₄ = 3.31 · 10⁻¹³, p₃ = −1.29 · 10⁻⁹ p₂ = 2.06 · 10⁻⁶ p₁ = −1.45 · 10⁻³ and p₀ = 1. Parameter C₆ could not be determined from data and was set to 1/120 minutes (almost all wild type bulbous tips eventually become synaptogenic). Note that the trio feedback mechanisms was modelled slightly different as outlined in the methods section.

Mutant models and parameters.

The lifetimes of short and long-lived filopodia were not markedly different between the mutants as shown below,

	short-lived			long-lived
Mutant	P40	P60	P40 and P60	P40	P60	P40 and P60
wt	2.4(1.7)	1.9(1.4)	2.2(1.6)	18(13)	23(18)	20(15)
dlar	2.7(1.7)	2.3(1.5)	2.5(1.6)	23(17)	19(15)	22(16)
liprin-α	2.6(1.9)	2.3(1.6)	2.5(1.8)	18(13)	20(15)	19(14)
syd-1	2.3(1.6)	2.2(1.7)	2.3(1.7)	18(13)	23(16)	20(14)
trio	2.3(1.7)	2.6(1.8)	2.5(1.8)	19(12)	20(15)	20(14)

where we depict the average (standard deviation) lifetime of filopodia (min) that were classified as short-lived vs. long-lived based on the 8min criterium. Hence, rates c_2,sF, c_2,tF were set equal for all mutants and wild type. By contrast, the number of short- and long-lived filopodia were different between wild type and mutants as shown below.

	short-lived		long-lived
Mutant	P40	P60	P40	P60
wt	5.6(3.9)	3.4(1.8)	10(3.5)	4.9(2)
dlar	3.8(2.3)	2.2(1.7)	13(2.3)	5.2(1.6)
liprin-α	4.5(2.7)	2.6(1.5)	8.6(2.1)	6.5(1.9)
syd-1	4.1(2)	1.6(1.3)	9.3(3.3)	3.8(1.7)
trio	6.8(2.8)	4.5(2.2)	14(3.7)	10(2.7)

Average (standard deviation) numbers of short-lived and long-lived filopodia per time instance.

We modelled these differences by estimating mutant-specific rates c_1,sF, c_1,tF. We observed distinct populations of transient and stable bulbous tips in all mutants (Fig. S9A–E). Consequently, parameters c₄ were set to the inverse of the mutant-specific bulbous tip life times (average (standard deviation) life time of transient bulbous tips sB in min; dlar: 3.3 (3), lirin-α: 9 (9.6), syd-1: 5.9 (6.4), trio: 7.6 (6.6) and wt: set to 120 min as it could not be determined from the data), trio, unlike the other mutants, exhibited at least one stabilized (synaptogenic) bulbous tip at all time points. The data measured suggest that trio may be a negative regulator of bulb initiation, such that bulbous initiation is more frequent in the trio mutant, while stabilization is essentially unaffected by trio. This observation prompted us to assume a strong auto-inhibitory feedback mechanisms of synaptogenic bulbous tips on their own production. The generator for this model is as follows:

$$\begin{array}{cc}G([i,j],[i-1,j])=i\cdot c_{4,}& G([i,j],[i,j-1])=j\cdot c_6\\ G([i,j],[i+1,j])=r_3(t),& G([i,j],[i,j+1])=j\cdot c_5\cdot f_1(j,B_{50})\end{array}$$

with parameters stated in the table in the section Wild type model and parameters above.

Simulation of growth cone retraction.

Fig. 6 shows the simulated probability of growth cone retractions up to time T, P_retract(T) based on the idea that both filopodia and synapses contribute to axon terminal stabilization. The probability of growth cone retraction was computed as

$${\text{P}}_{\text{retract}}(T)=1-\prod _{i=0}{P}_{\text{no-retract}}(i)$$

where P_no–retract(i) denotes the probability not to retract in the i-th time interval which is computed by P_no–retract(i) = e^{−Δt·r₀·f_retract(F(i),B(i),S(i),w,n_stab)}, where r₀ is the basal rate of retraction, Δt is the duration of the i-th time interval and F(i), B(i), S(i) are the simulated 979 number of filopodia, bulbous tips and synapses during that time interval. n_stab is the ‘minimal stabilization number’ and w are the user-defined weights such that

$$f_{\mathrm{retract}}(F(i),B(i),S(i),w,n_{stab})=0.5\left(1+\tanh \left[\frac{3}{n_{stab}}(n(i)-n_{stab})\right]\right)$$

with n(i) = w_f(sF + ℓF) + w_B(sB + synB) + w_s · S being the weighted sum of filopodia, bulbous tips and synapses affecting (preventing) retraction.

Data and Code Availability

Raw (.lif format) and processed (.ims and .am format) imaging datasets are available on request.

The filopodia tracking software is an extension of the commercial software Amira, which is available from Thermo Fisher Scientific. The filopodia tracking software is available from the corresponding author upon request in source code and binary form. Executing the binary requires a commercial license for Amira.

Matlab codes for model parameter inference and for model simulation are available through https://github.com/vkleist/Filo along with tracked filopodia data used for parameter inference.

Supplementary Material

1

Movie 1: Fast filopodial dynamics during synapse formation. Related to Figure 1.

2

Movie 2: Stability of BrpD3-positive presynaptic puncta on wild-type R7 terminals. Related to Figure 2.

3

Movie 3: Liprin-α transiently localizes to filopodia and Overexpression of GFP-Syd-1 or Liprin-α-GFP does not alter R7 filopodial dynamics. Related to Figure 2.

4

Movie 4: Fast filopodial dynamics during synapse formation in liprin-α and syd-1 mutants. Related to Figure 4.

5

Movie 5: Remaining BrpD3 puncta on liprin-α R7 terminals are unstable. Related to Figure 4.

6

Movie 6: Fast filopodial dynamics during synapse formation in lar and trio mutants. Related to Figure 5.

7

Movie 7: Loss of synaptic seeding factors results in late-stage destabilization of R7 axons. Related to Figure 6.

Highlights.

• stochastic filopodia dynamics are required for robust synapse formation in fly brains

• only 1-2 filopodia at a time contain synaptic seeding factors and are synaptogenic

• 4D tracking and computational modeling support a serial synapse formation model

• Synapse formation prevents axonal retraction