Desensitisation of Notch signalling through dynamic adaptation in the nucleus

Abstract During embryonic development, signalling pathways orchestrate organogenesis by controlling tissue‐specific gene expression programmes and differentiation. Although the molecular components of many common developmental signalling systems are known, our current understanding of how signalling inputs are translated into gene expression outputs in real‐time is limited. Here we employ optogenetics to control the activation of Notch signalling during Drosophila embryogenesis with minute accuracy and follow target gene expression by quantitative live imaging. Light‐induced nuclear translocation of the Notch Intracellular Domain (NICD) causes a rapid activation of target mRNA expression. However, target gene transcription gradually decays over time despite continuous photo‐activation and nuclear NICD accumulation, indicating dynamic adaptation to the signalling input. Using mathematical modelling and molecular perturbations, we show that this adaptive transcriptional response fits to known motifs capable of generating near‐perfect adaptation and can be best explained by state‐dependent inactivation at the target cis‐regulatory region. Taken together, our results reveal dynamic nuclear adaptation as a novel mechanism controlling Notch signalling output during tissue differentiation.


Introduction
Signalling dynamics have emerged as fundamental to cellular information processing in the context of tissue differentiation and organogenesis (Freeman & Gurdon, 2002;Sonnen & Aulehla, 2014). The cellular response to a signalling stimulus depends on the concentration, duration and frequency at which cells are exposed to it (Rogers & Schier, 2011;Mc Mahon, Sim et al, 2014;Johnson & Toettcher, 2019;Keenan et al, 2020). However, understanding how cells integrate and translate dynamic signalling information into specific gene expression outputs in vivo has proven challenging, as it requires methods for precise spatio-temporal control of the input and quantification of output levels in real time (Sako et al, 2016;Huang et al, 2017;Krueger et al, 2019;McDaniel et al, 2019;Hartmann et al, 2020;Johnson et al, 2020;Rogers & M€ uller, 2020). Towards this aim, we combined optogenetics with live imaging of nascent transcripts to study the input-output relationship linking Notch signalling activation and target gene expression during early Drosophila embryogenesis.
Notch signalling is a conserved pathway controlling cell fate decisions through direct cell-cell contacts (Artavanis-Tsakonas et al, 1999;Bray, 2016). Upon binding to one of its ligands (Delta or Serrate in Drosophila) presented on the surface of an adjacent signal-sending cell, the Notch receptor undergoes a series of intramembranous proteolytic cleavages culminating in the release of NICD, a soluble cytosolic fragment. Cleaved NICD translocates into the nucleus, where it activates target gene expression by interacting with the DNA-binding protein Suppressor of Hairless Su(H) (Bray & Furriols, 2001;Gomez-Lamarca et al, 2018). As such, Notch signalling does not involve any signal amplification step, and its strength is thought to be directly related to the level of NICD production.
Our findings reveal an unexpected dynamic input-output relationship between Notch signalling and target gene expression. Optogenetically induced nuclear translocation of NICD causes rapid induction of target mRNA expression followed by gradual inactivation over time, despite continuous photo-activation and nuclear NICD accumulation. Such desensitisation, where a system returns to basal or near-basal levels of activity despite continued stimulation, is known as perfect or near-perfect adaptation (Barkai & Leibler, 1997;Ma et al, 2009;Sorre et al, 2014;Ferrell, 2016). By combining mathematical modelling and molecular perturbations, we show that the adaptive transcriptional response to Notch signalling is best explained by a known fundamental regulatory motif that implements adaptation through state-dependent inactivation (Friedlander & Brenner, 2009).
Adaptation can serve different functions, including limiting the duration of a signalling response and allowing cells to detect changes in molecules over a broad range of concentration. Well-established examples of adaptation involve regulation of signal transduction components at the cell membrane or in the cytoplasm, as in the case of EGFR (Vieira et al, 1996) or chemokine receptor downregulation following ligand stimulation (Yuan et al, 2012). Our results demonstrate that even for a simple signal transduction system, where a cleaved surface receptor directly controls target gene expression, dynamic and context-sensitive input-output relationships can be implemented at the level of transcriptional regulation.

Optogenetic control of NICD nuclear translocation and target gene expression
To gain direct and time-resolved control over Notch signalling, we constructed an optogenetic system that allows reversible induction of NICD nuclear translocation by light (opto-Notch). To minimise dark state activity (i.e. NICD nuclear translocation in the dark), we designed a double-gated strategy by coupling NICD nuclear localisation signal (NLS) photo-tagging with dark state-specific mitochondrial trapping. We employed LANS (Niopek et al, 2014;Guntas et al, 2015) to cage the NLS of NICD with a photo-sensitive LOV domain and LOVTRAP (Wang et al, 2016) to anchor NICD-LOV to mitochondria through a Zdark tag, which recognises the dark conformation of the LOV domain and was itself localised to mitochondria by a TOM20 tag. Blue light illumination should cause simultaneous unbinding from mitochondria and uncaging of the NLS, resulting in NICD nuclear translocation (Fig 1A and B). Embryos co-expressing the opto-Notch module (with NICD tagged also with mCherry to follow its localisation) demonstrate that in the dark NICD is localised to particulate structures in the cytoplasm ( Fig 1C and Movie EV1) and upon blue light illumination (λ = 488 nm), it rapidly translocated into embryonic nuclei, reaching maximum accumulation after 10 min (Figs 1D and EV1A,and Movie EV1). To test whether NICD nuclear translocation was functional and could elicit a signalling response, we measured target gene expression by quantitative live imaging of sim nascent transcripts using the MS2-MCP system (Garcia et al, 2013). sim is a well-established Notch target that specifies the embryonic mesectoderm (Bardin & Schweisguth, 2006;De Renzis et al, 2006;Falo-Sanjuan et al, 2019;Viswanathan et al, 2019). In addition to Notch, its expression requires input from the maternal Dorsal gradient and zygotic expression of the transcription factor Twist (Kasai et al, 1998). In the mesoderm, sim expression is repressed by the transcription factor Snail (Cowden & Levine, 2002). As a result of this regulation, sim expression starts towards the end of cellularisation, before the onset of gastrulation in a single row of cells on either side of the mesoderm (Fig 1E). Optogenetic activation at the beginning of cellularisation caused a premature activation of sim transcription, appearing as a bright nuclear dot from˜5 min after NICD began translocating into the nucleus (Fig 1F and G, Movie EV2). Importantly, sim was not transcribed in the dark at this stage (Fig 1F), demonstrating the validity of our approach. Consistent with the regulatory network controlling sim expression, optogenetic activation did not cause sim expression in the mesoderm, but only in a region of the ectoderm where Dorsal and Twist are also present ( Fig 1G). Intriguingly, ectopic sim expression appeared to decrease after˜30 min of continued photo-activation (Fig 1H and Movie  EV2), approximating its wild-type pattern of expression in a single row of cells (Movie EV3). In summary, these results demonstrate that opto-Notch is a suitable tool to study Notch signalling inputoutput relationships and they suggest transcriptional adaptation to NICD stimulation over time.
Transcriptional activation in response to NICD nuclear translocation undergoes adaptation To quantify sim expression in response to NICD nuclear translocation, we developed an image analysis pipeline (see Materials and Methods) which confirmed that sim expression started a few minutes after photo-activation, reached a plateau at 10-15 min and then started decreasing at˜20 min to reach its lowest level of expression after˜35 min (Fig 2A). Quantification of NICD localisation demonstrated stable nuclear localisation after 10 min of photoactivation and throughout the remainder of the experiment ( Fig 2D, and Movie EV4). This reduction in sim expression despite stable NICD nuclear localisation could indicate either that nuclei were not competent to transcribe sim after˜20 min because some other required factor was not present anymore at that point, or alternatively that nuclei started to adapt to NICD. Late photo-activation after˜25 min from the beginning of cellularisation demonstrated that nuclei were still competent to transcribe sim ( Fig 2B, and Movies EV5 and EV6), thus suggesting that continuous photoactivation caused nuclear adaptation to NICD. If this was the case, one prediction is that discontinuous pulsatile light inputs should prevent adaptation as NICD would move out of the nuclei in the dark. To test this hypothesis, we administered 5 min pulses of photo-activation followed by a 10 min interval of darkness (Fig 2C and Movies EV7 and EV8). This protocol was established by considering several factors including the overall time window for performing this experiment before the onset of gastrulation (˜40 min), the kinetics of sim expression (Fig 2A), and the levels of NICD in the nucleus, which drop substantially after 10 min in the dark ( Fig  EV1A). Pulsatile optogenetic activation resulted in NICD cycling in and out of the nuclei (Fig 2E and Movie EV9) and in stable, non-adaptive sim expression (Fig 2C), supporting the conclusion that NICD nuclear accumulation causes transcriptional adaptation over time.
Mathematical modelling reveals that NICD adaptation fits to known circuits responsible for generating near-perfect adaptation These results reveal an unexpected dynamic input-output relationship linking Notch signalling and sim expression, suggesting that a linear pathway which directly transfers information from the plasma membrane to the nucleus can implement adaptation through transcriptional regulation. To elucidate the regulatory principles that mediate adaptation to NICD, we used mathematical modelling to fit the kinetics of sim transcription to motifs known to implement nearperfect or perfect adaptation. Although there are many potential circuits that can generate such adaptation, prior theoretical and experimental work has indicated that they can generally be reduced to three main elementary motifs: the negative feedback loop, A, B Illustration depicting the optogenetic system employed to control NICD nuclear translocation (opto-Notch). NICD (purple) with its endogenous NLS deleted was tagged with the AsLOV2 domain (turquoise) from Avena Sativa in such a way that its Jα helix masks an engineered NLS in the dark (A). To ensure maximal nuclear exclusion, Zdark (blue dashed line on the mitochondrion), a protein domain which binds specifically to the dark conformation of AsLOV2, was localised to mitochondria through a TOM20 targeting motif (not depicted). Blue light illumination triggers a conformational change in the LOV2 domain, which results in the simultaneous unbinding from mitochondria and exposure of the engineered NLS, thus allowing NICD nuclear translocation and target gene (sim) expression, appearing as a green dot in the nucleus (B). C, D Snapshots from confocal live imaging movies of a representative embryo (N = 7) during cellularisation co-expressing opto-Notch, Mito-Zdk, MCP::GFP and sim-MS2. Continuous photo-activation from the onset of cellularisation with a stack size of z = 25 μm (λ = 488 nm) was alternated with mCherry excitation (λ = 561 nm) at 1 min intervals. Single confocal z-slices of the mCherry channel are shown to record opto-Notch localisation before, and 10 min after sustained photo-activation. Magnified insets show opto-Notch bound to the mitochondrial anchor in the dark (C) and in the nucleus upon photo-activation (D). Scale bar, 10 μm. incoherent feedforward regulation and state-dependent inactivation (Barkai & Leibler, 1997;Mangan & Alon, 2003;Friedlander & Brenner, 2009;Ma et al, 2009;Ferrell, 2016) We began our analysis with the most parsimonious version of each of these motifs (Fig 3A-I) and hence did not consider more sophisticated configurations such as Antithetical Integral Control (Aoki et al, 2019). In negative feedback, an input activates a component (A) which in turn activates both the output and a negative regulator (B) of its own activity ( Fig 3A). In feedforward regulation, an input activates two components (A) and (B), of which (A) activates the output and (B) inhibits (A) (Fig 3B). In state-dependent inactivation, an input activates a component (A) that controls the output and can switch into an inhibited (IN) state without further signalling input. The IN state prevents renewed activation for the duration of some refractory period, after which (A) may return to the OFF state ( Fig 3C).
We began by simulating all three of these motifs using simple ordinary differential equations (ODEs) based on elementary mass action kinetics and performed automated parameter searches to look for regimes that fit the observed adaptive dynamics of sim expression. At this stage, we did not assign specific molecular identities to components (A) and (B) to avoid bias. In accordance with the relatively short time scales involved, we chose equations that best reflect an implementation of the motifs by protein-protein interactions rather than by gene regulatory networks. We considered nuclear NICD levels as the input to the motif and component (A) as a direct regulator of promoter activity, meaning the level of (A) is expected to be proportional to the rate of sim mRNA production as measured by the MS2-MCP system. To get an accurate time profile of nuclear NICD levels (i.e. the model input) under continuous and pulsatile optogenetic activation, we performed separate experiments to quantify import and export rates and built a simple 2-compartment model capturing NICD import-export dynamics ( Fig  EV1A and B, and Movies EV4 and EV9) (see Materials and Methods for more details). Since all nuclei in a sample receive a similar dose of NICD activation, we use bulk sim expression as the output measurement for model fitting, as this averages out inputindependent fluctuations exhibited by individual cells due to transcriptional bursting (Falo-Sanjuan et al, 2019). Our model thus captures the average input-output mapping across a population of activated nuclei.
We found that all three motifs were capable of reproducing sim expression dynamics under continuous optogenetic activation andwithout further parameter optimisation-also qualitatively reproduced the response to pulsatile activation ( Fig 3D-I), albeit at a slightly lower level than the average of experimentally measured time profiles. We also tested the effect of allowing more complex interactions, i.e. Hill coefficients greater or smaller than 1.0. Although the inclusion of these additional degrees of freedom enabled slightly better fits under continuous activation, the predictions for sim expression under pulsatile input were further reduced ( Fig EV2A-F). Taken together, these results indicate that all three basic adaptation motifs behave similarly and can in principle explain transcriptional adaptation to NICD.

NICD adaptation is best explained by state-dependent inactivation
To narrow down the most likely candidate motif at play during Notch signalling, we tested whether the three motifs would respond differently to various simulated perturbations (Fig 4A-C). Specifically, we checked the effects of removing negative regulators of sim expression, including the feedback and feedforward inhibitors (B) ◀ Figure 2. Transcriptional activation in response to NICD nuclear translocation undergoes near-perfect adaptation.

A-C The number of sim-expressing nuclei as counted by automated spot detection is shown over time for different optogenetic activation regimes (top blue bars). (A)
Continuous opto-Notch activation initially induces sim expression across a large number of nuclei. Over time, the majority of nuclei adapt to the input and terminate expression. (B) Inactivation is not due to developmental timing, as nuclei remain responsive when activation is delayed to a later time point. (C) Sustained nuclear localisation of NICD is required for adaptation to take place, as pulsatile activation can overcome adaptation. Note that sim expression could not be measured during dark phases of pulsatile photo-activation as its visualisation requires 488 λ nm excitation which causes photo-activation; dashed lines are a visual aid connecting data from the same embryo. D, E Quantification of nuclear localisation of mCherry::NICD during opto-Notch photo-activation. Raw data were bleaching-corrected with an exponential fit and shown is the nuclear/total ratio, which further normalises bleaching and embryo-to-embryo variability. NICD displays persistent nuclear enrichment during continuous activation (D) and shuttles back and forth between nucleus and cytoplasm under the pulsatile protocol (E).
▸ Figure 3. Modelling shows that target gene transcriptional dynamics fit motifs known to underlie near-perfect adaptation.
A-C Illustrations of the three simple and fundamental motifs that frequently reoccur in perfect or near-perfect adaptation (modified from Ferrell, 2016): negative feedback (A), incoherent feedforward (B) and state-dependent inactivation (C). Here, the input is the concentration of nuclear NICD and the output is target gene promoter activity, i.e. the rate of sim mRNA production (not to be confused with total levels of sim mRNA in the cell). The components (A) and (B) in these motifs are placeholders for single or compound molecular regulators; at this point, no specific assumptions are made in our models about their identity. Note that in (C), A in stands for the inhibited state of (A), which can no longer be activated. The dashed line back to A off indicates recovery at slow time scales relative to the motif's adaptation dynamics. D-I Results of elementary mass action ODE model fitting to sim adaptation dynamics. The input (NICD nuclear concentration; dashed blue line) is modelled based on separate experiments elucidating opto-Notch import-export dynamics (see Fig EV1 and Materials and Methods). Sim expression is total MCP::GFP spot intensity, linearly rescaled to match the non-dimensional scale of the ODE models (see Material and Methods for details). (D, F, H) Despite their simplicity, the models of all three motifs can readily be fitted to sim adaptation dynamics. (E, G, I) Without further fitting, the resulting models also approximate the loss of adaptation during pulsatile activation, although the model predictions are slightly lower and slightly less responsive to the second and third pulse than experimentally measured nuclei, which may be due to the simplifying assumptions made in the equations describing the motifs.   A-C Simulated predictions of sim expression dynamics during continuous opto-Notch activation under different molecular perturbations. Row 1 shows the wild-type model behaviours. Rows 2-3 show the response to a knock-out of a negative regulator of sim expression, which could be either the internal inhibitor (B) of the adaptation motifs (row 2) or an attenuator that in wild-type dampens the activation of (A) (row 3). Row 4 simulates the stabilisation of (A) in its active state by reduction of either the inhibitory action of (B) or the auto-inactivation of (A). Note that these perturbations generally lead to a loss of adaptive behaviour, with the exception of the attenuator knock-out on state-dependent inactivation (C; row 3). and a putative attenuator of the NICD input on (A). We also simulated the effect of increasing the stability of component (A), the direct controller of sim expression. Removal of the negative regulator (B) resulted in a loss of adaptation for the negative feedback and feedforward motifs (Fig 4A and B) and could not be tested for the state-dependent inactivation motif, as in this case (A) itself transits into an inhibited state. Removal of a putative attenuator also resulted in a lack of adaptation for the negative feedback and feedforward motifs, but caused faster activation and higher output levels without preventing adaptation for the state-dependent inactivation motif ( Fig 4C). All motifs responded similarly to the stabilisation of (A), namely by overcoming adaptation and increasing output levels compared to wild-type (Fig 4A-C). Equivalent simulations on the more complex Hill models produced similar results: a lack of adaptation when the inhibitor (B) was removed, while removal of the attenuator caused a substantial reduction in adaptation only in the incoherent feedforward motif (Fig EV3A-C). Stabilisation of component (A) reduced adaptation for all three motifs, but unlike in the elementary mass action models, output levels increased only for state-dependent inactivation (Fig EV3A-C). Thus, our model predicts that it is difficult to distinguish the feedback and feedforward motifs through perturbations, whereas state-dependent inactivation can be clearly separated from the two, primarily by the persistence of adaptation when negative regulators of sim are removed, as well as by an increased output when (A) is stabilised.
To test these predictions experimentally, we combined molecular perturbations with optogenetic control of Notch input. A wellestablished negative regulator of Notch signalling is Hairless (H), which competes with NICD to bind Su(H) and inhibits transcription of target genes (Barolo et al, 2002). In principle, Hairless could take the role of the inhibitor (B) in the negative feedback and feedforward motifs, as there is evidence that NICD increases, directly or indirectly, Hairless binding to Notch target genes (Gomez-Lamarca et al, 2018). Alternatively, Hairless might act as an attenuator on the input in any of the three motifs. The transcription factor Twist is a suitable molecular tool to test the consequences of stabilisation of (A), as mutations in its binding sites in the sim enhancer cause a loss of wild-type sim expression in the mesectoderm, yet on its own Twist is not capable of activating sim expression (Kasai et al, 1998;Falo-Sanjuan et al, 2019). We generated opto-Notch embryos either heterozygous for a hypomorphic allele of Hairless (H 2 ) (Bang & Posakony, 1992) or overexpressing Twist under Gal4-UAS and measured sim expression by live imaging upon optogenetic activation. Downregulation of Hairless activity did not alter sim expression in the dark (Fig EV4A and B), but caused a faster activation rate (59.4 AE 12.2 nuclei/min compared to 28.3 AE 8.6 nuclei/min in WT; all numbers are meanAEst.dev.) and an increase of˜1.5 fold in the number of nuclei actively transcribing sim in response to lightinduced NICD nuclear translocation, when compared to wild-type opto-Notch embryos (Fig 4D and Movie EV10). Crucially, Hairless downregulation did not overcome adaptation (Fig 4D). These results were further confirmed by testing an additional allele of Hairless (H LD ) carrying a point mutation which abolishes binding to Su(H) (Praxenthaler et al, 2015) (Fig EV5). Conversely, Twist overexpression overcame nuclear adaptation and caused a˜2-fold increase in peak mean sim expression in response to optogenetic activation ( Fig 4E, Movie EV11, and Fig EV4C) when compared to control embryos (Fig 2A). Both Hairless downregulation and Twist overexpression also appeared to cause an expansion of sim expression into a more dorsal region of the ectoderm.
Among the motifs we considered, the results of these combined molecular and optogenetic perturbations are most consistent with the predictions from the state-dependent inactivation model. In the elementary mass action models, the only motif that increased sim expression but retained adaptation upon removal of the attenuator is the state-dependent inactivation motif (Fig 4C). In the Hill models, both negative feedback and state-dependent inactivation still exhibited substantial adaptation when the attenuator was removed. However, stabilisation of the active state caused an increase in output levels only in the state-dependent inactivation regime, which matches what we observed experimentally upon Twist overexpression (Fig EV3C). Thus, we propose that the sim cis-regulatory region in complex with Su(H) and presumably other trans-acting factors undergoes state-dependent inactivation upon continuous NICD stimulation, switching first from an OFF to an ON state (in which sim is transcribed) and then transitioning into an inhibited refractory state (Fig 4F). Transition into the inactive state can be prevented by tissue-specific transcription factors such as Twist and more generally adaptation can be ameliorated if NICD input is discontinuous, preventing the IN state from saturating and ultimately allowing the system time to cycle back to the OFF state.

Discussion
Taken together, the results presented in this study led us to propose a model in which NICD nuclear accumulation triggers statedependent inactivation of sim transcription. This interpretation is supported by the responses to NICD optogenetic stimulation upon Hairless downregulation and Twist overexpression, which are consistent with the predictions of both elementary mass action and Hill-type simulations of the state-dependent inactivation motif. However, it must be kept in mind that our ODE model is a coarsegrained approximation of the true dynamics occurring in the nucleus and specifically at the enhancer-promoter complex. Although this approximation captures the overall adaptation dynamics and responses to perturbations, it does not do so perfectly. In particular, the elementary mass action version does not fully recapitulate the dynamics at the beginning of activation (Fig 3  H) and both model versions-especially the Hill-type version-fall short of producing the experimentally observed levels of sim expression under pulsatile activation (Figs 3I and EV2F). It is likely that some mechanism not included in our model, such as local transcription priming (Falo-Sanjuan et al, 2019), further modulates statedependent inactivation. Indeed, the true regulatory motif might be far more complex, with multiple additional components producing an input-output relationship that-although matching the predictions of state-dependent inactivation within the scope of the experiments we performed-in truth does not reduce to one of the three motifs tested here. Along similar lines, we cannot rule out that downregulation of as yet unknown negative regulators other than Hairless might yield an outcome favouring other motifs over statedependent inactivation. However, Hairless is a well-established negative regulator of Notch signalling (Bang & Posakony, 1992), and our results are fully consistent with a previous report demonstrating its role in repressing sim expression in the early embryo 8 of 14 The EMBO Journal 40: e107245 | 2021 ª 2021 The Authors (Morel et al, 2001). All of this considered, state-dependent inactivation is at the present stage of our knowledge the most parsimonious model explaining how NICD nuclear adaptation is implemented at the level of sim transcriptional regulation. Future studies should seek to elucidate the exact molecular mechanism, which will resolve the open questions discussed above. The adaptive response induced by continuous NICD stimulation ultimately results in one or two rows of cells expressing sim, partially resembling its normal pattern of expression (Fig 1E and H,  Movie EV2). In wild-type embryos, the transcription factor Snail represses sim expression in the mesoderm (ventral region of the embryo) and cell non-autonomously activates Notch signalling in the mesectoderm (Cowden & Levine, 2002;Bardin & Schweisguth, 2006;De Renzis et al, 2006). There, NICD activates sim transcription in concert with Dorsal and Twist (Kasai et al, 1998). Twist expression is restricted to the mesoderm and a few additional rows of cells immediately dorsally (Kosman et al, 1991), which explains why the stripe that resists adaptation under continuous activation is slightly wider than the single row of sim expression observed in wild-type embryos, consistent with the role of Twist in our model as a stabiliser of sim expression. The transcription factor Dorsal forms a gradient along the entire dorso-ventral axis of the embryo, with higher concentrations in ventral nuclei. Dorsal levels decrease over time in dorso-lateral regions (Reeves, Trisnadi et al, 2012), so a simple alternative explanation for the reduction in sim transcription during continuous NICD stimulation would be that over time Dorsal concentration drops below the levels needed to support sim transcription. However, this explanation is inconsistent with the demonstration that late and pulsatile optogenetic activation induce sim transcription in nuclei which would otherwise undergo adaptation (Fig 2B and C). Furthermore, both Twist overexpression and Hairless downregulation cause an expansion of sim expression more dorsally compared to NICD optogenetic stimulation alone. These two outcomes are likely due to the overexpression of the stabiliser Twist in cells that do not normally express it and due to the reduced level of Hairless activity which has been suggested to render the sim cis-regulatory region more sensitive to Dorsal (Ozdemir et al, 2014), respectively.
Dynamic nuclear adaptation might explain how Notch signalling, a relatively simple pathway operating through the cleaved cytoplasmic tail of a surface receptor which directly controls target gene expression (Bray & Furriols, 2001), can dynamically self-terminate or persist in a context-dependent fashion. On the one hand, the presence of factors such as Twist allows the continuous expression of target genes by counteracting adaptation. On the other hand, adaptation could translate a constant Notch signalling input into a pulsatile output by defining a refractory period during which cells are insensitive to the input. This might be particularly relevant during oscillatory developmental processes such as somitogenesis in vertebrates, which require Notch activity for the cyclic generation of new somites (Liao et al, 2016;Sonnen et al, 2018). In addition, discontinuous optogenetic activation also shows that pulsatile NICD inputs can counteract adaptation, demonstrating yet another layer of dynamic regulation through which the output of Notch signalling can be modified. While adaptation is an important property of many signalling systems, so is the ability to overcome it when necessary. For example, migrating cells moving along a chemokine gradient regulate receptor internalisation and recycling back to the plasma membrane to overcome signalling adaptation and move over long distances (Wong et al, 2020). Here our results suggest that a linear signal transduction system, which does not involve signal amplification or other forms of relay through cytoplasmic proteins, can implement dynamic adaptation in the nucleus at the most downstream level of developmental signalling regulation.

Live imaging and optogenetics
All imaging and optogenetic experiments were done as previously described . Briefly, Cages with flies expressing the opto-Notch module, the sim MS2 reporter and MCP:: GFP were kept in the dark in a box. Cycle 14 embryos were selected under halocarbon oil and mounted using a stereomicroscope equipped with a red-emitting LED as the transmission light source (Guglielmi & De Renzis, 2017). Embryos were dechorionated with 100% sodium hypochlorite for 2 min, rinsed with water and mounted immersed in PBS onto a 35 mm glass-bottom dish (MatTek corporation). Embryos were then positioned with their ventrolateral side facing the cover-slip. Photo-activation and acquisition of movies were done at 22°C with a Zeiss LSM 780 confocal microscope (Carl Zeiss) using a 40×/NA 1.1 water immersion objective (Carl Zeiss). Bright field illumination was filtered using a Deep Amber lighting filter (Cabledelight, Ltd.) in order to locate the embryos. The Microscope was controlled using Zen Black software (Carl Zeiss), and photo-activation protocols were carried out with the Pipeline Constructor Macro (Politi et al, 2018). For all experiments, an initial mCherry frame was acquired (λ = 561 nm) prior to photo-activation. Photo-activation was carried out by illumination with a 488 nm laser line (pixel dwell time = 0.79 microsec, laser power was set at 10% corresponding to an out of the objective power of 35.6 µW) with a stack size of z = 25 µm from the apical surface. Photo-activation was alternated with mCherry excitation (λ = 561 nm) to record NICD localisation at 1 min intervals as a single confocal z-slice. sim nuclear spots were simultaneously recorded also using a 488 nm laser at a time resolution of 30 s and a stack size of 25 µm (z-interval of 1 µm). Imaging and photoactivation were started either at the onset of cycle 14 (early) or when the cellularisation furrow reached the base of the nuclei (late) and photo-activation was continuous until the onset of ventral furrow formation. For pulsatile activation, each pulse lasted for a period of 5 min following which the embryo was kept in the dark for 10 min prior to the next activation round. For measuring NICD import and export kinetics, the same photo-activation protocol alternated with mCherry excitation (as mentioned in all the experiments above) was followed for a period of 10 min. After either 5 min or 10 in the dark, a final acquisition of both the His::GFP signal (λ = 488 nm) and mCherry signal (λ = 561 nm) was recorded.

Image analysis and modelling
Research software stack Image analysis, data analysis, numerical simulations and data visualisation were all performed using the Anaconda distribution (Anaconda, Inc., Austin, US-TX) of python 3.7 (64-bit) (Python Software ª 2021 The Authors The EMBO Journal 40: e107245 | 2021 Foundation, Beaverton, US-OR). The following scientific libraries and modules were used: numpy 1.16.4 (Harris et al, 2020) for numerical computation, scikit-image 0.13.0 (van der Walt et al, 2014) for image processing, sympy 1.4 for symbolic mathematics (Meurer et al, 2017), several scipy 1.2.1 modules  for image processing, numerical solving of differential equations and parameter fitting, and matplotlib 3.1.0 for plotting. Jupyter Notebooks (jupyter 1.0.0, notebook 6.0.0) were utilised to develop and run all code. Git 2.24.1.windows.2 (github.com/git/git) was employed for version control.

Sim MS2-MCP spot detection and quantification
We implemented a spot detection pipeline to identify, count and quantify sim expression. Image stacks were maximum z-projected and adaptive background subtraction was performed by smoothing the image with a Gaussian filter with σ = 10 and then subtracting this strongly blurred image from the original. Spots were then detected using the scikit-image blob_log spot detector. This pipeline was applied independently to every time point in each time course. The number of spots detected at each time point was counted and the median intensity of each spot was measured within a bounding box of edge length 3σ, where σ is an indicator of spot size returned by blob_log. The median intensity was chosen rather than the total or mean intensity to reduce the influence of bounding box size and of peripheral pixels in the bounding box, though the three measures do not behave in qualitatively different ways. Where possible we report spot counts as our primary measure of global sim expression, as it is largely independent of fluorescence intensity and thus slightly more robust.2

Quantification and modelling of NICD nuclear translocation
To quantify mCherry::NICD nuclear translocation during continuous and pulsatile opto-Notch activation experiments (Movies EV4 and EV9), nuclei were segmented based on the Histone::GFP channel by applying Gaussian smoothing (σ = 2) and subsequent thresholding using Otsu's method (Otsu, 1979). mCherry::NICD intensity was measured within segmented nuclei and in the surrounding cytoplasmic space, which was masked by dilating the binary nuclear mask with a disk-shaped structural element (radius = 10px). The lowest mean nuclear intensity per track was considered a proxy for background intensity and subtracted from all measurements of that track. Bleaching was captured by fitting an exponential decay function IðtÞ ¼ I 0 Á e Àbt to overall mean intensity (I) in the 10-20 min time window of the continuous activation experiment (i.e. in the opto-Notch on-state equilibrium). The fitted function was used for an approximate bleaching correction of both continuous and pulsatile mCherry::NICD time courses by adding the predicted bleached fraction of the signal back to the signal itself. Reported in Figs 2D and E, and EV1B is the ratio of nuclear to total signal. To obtain a quantitative description of NICD nuclear import and export kinetics with and without activating light, a simple twocompartment model was fit to data acquired specifically for this purpose, where 10min of continuous activation was followed by darkness for either 5 or 10 min before a final acquisition (see Fig  EV1A). Nuclei were segmented based on Histone::GFP, and mCherry::NICD nuclear and cytoplasmic intensities were measured and background-subtracted as described above. The 2-compartment model was expressed in the following system of ordinary differential equations (ODEs): where C and N are cytoplasmic and nuclear concentrations, F and B stand for fluorescent (unbleached) and bleached mCherry, k i and k e are the rate constants for import and export, and b is the rate of bleaching. This ODE system was integrated automatically using sympy.dsolve, and the integrated equations were fit to the data. Specifically, the model was first fit to the continuous activation data (i.e. the first 10min) to retrieve characteristic rate constants k i and k e during light exposure of opto-Notch. For this purpose, the initial values of N D and C D were set to zero, whereas those of N F and C F were considered free parameters alongside k i and k e . These free parameters were estimated by minimising the mean squared error between the observed nuclear/total mean intensity ratio and the model's prediction. This ratio was chosen for fitting both because it is non-dimensional and because it normalises for variations in the observed total intensity such as cells moving slightly relative to the plane of image acquisition. Following this first fit, the model was also fitted to export data in order to estimate characteristic rate constants k i and k e for opto-Notch in darkness. Specifically, the dataset used for fitting comprised the last time point of the 10 min of continuous activation and end point data from samples that were left either 5 or 10 min in the dark following the initial activation. Initial values for N F , N D , C F and C D were taken from the last time point of the on-state fit and bleaching factor b was set to zero, leaving only two free parameters. The same ratio-based metric was used for optimisation. The scipy.optimize.minimize function was employed for all minimisations, the results of which are shown in Fig EV1A.   The three fundamental adaptive motifs (see Fig 3) were modelled using Ordinary Differential Equations (ODEs). We started from a previously published formulation (Ferrell, 2016), which we simplified such that all interactions follow elementary mass action kinetics to study the simplest case possible. To test how greater interaction complexity changes modelling outcomes, we subsequently introduced additional degrees of freedom by allowing Hill exponents in the closed interval h∈ ½0:25, 4:0 for all interactions except firstorder decay terms.
The following ODEs were used for the elementary mass action models: Negative feedback motif The following ODEs were used for the more complex Hill models: Negative feedback motif State-dependent inactivation motif We used scipy.integrate.odeint to numerically solve these systems of equations and thereby produce simulations of the timedependent behaviour of the variables.
The time profiles of the Input, which represents nuclear NICD, were determined using the fitted import-export model described in the previous section (see eqns. 1-4), by computing NðtÞ ¼ N F ðtÞ þ N B ðtÞ. For simulations of continuous optogenetic activation, the fit to the "light" condition was used. For simulations of pulsatile activation, the "light-fitted" and "dark-fitted" importexport equations were used intermittently during/between light pulses, with the end point values of one step being forwarded as initial values to the next. The appropriateness of the resulting Input time profiles was confirmed by deriving nuclear/total ratios and comparing them to experimentally measured NICD nuclear/total ratio profiles, finding that they are largely consistent (see Fig  EV1B). Residual differences likely result from the approximate nature of bleaching correction on the experimental data as compared to the more precise treatment of bleaching in the importexport model.

Model fitting and prediction of perturbation outcomes
Models were fitted to total sim expression (the sum of spot intensities determined as described above) over time in continuous optogenetic activation experiments. We here used total sim expression rather than spot count, as the latter is a discrete measure and thus less suited for ODE fitting. Both spot count and total spot intensity are highly correlated and thus both represent robust measures of sim expression. As both data and model output are on arbitrary but different scales, they were linearly rescaled by multiplication with fixed factors (1/300 for data, 100 for model output) to bring them to into a comparable range, which was chosen to be neither very small nor very large to simplify numerical computations. This was done for computational convenience and does not affect model parameters or dynamics. The loss function minimised was the mean squared error between the thus rescaled model output and all data points. Rate constant initial values were based on (Ferrell, 2016), and rate constant ranges were constrained to 6 orders of magnitude (0.0001 to 100). Hill coefficient initial values were set to 1.0, and their range was constrained to 4 th -order (0.25 to 4). Minimisation was performed using scipy.optimize.basinhopping. The fitted parameter values for ODE models of adaptation are listed below. Note that the degradation of the inhibitors (and thus the recovery of the adaptive system) is being reduced to a minimum, which reflects that our experiments end when near-perfect adaptation is achieved, and hence, recovery must be slow compared to the relatively short time scale of the data.
To simulate dynamics under various perturbations, reaction rates were changed as follows: knock-out of the inhibitor (B) was represented by setting k 4 = 0.0 (only in feedback and feedforward), knock-out of a putative attenuator of (A) activation by setting k 1 ¼ 10 Ák 1 and stabilisation of active (A) by setting k 2 ¼ 0:1 Ák 2 , wherek represents the original fitted value.

Statistics and data visualisation details
Means in Figs 2 and 4D and E were computed as a running mean with a time window of 1min. 95% confidence intervals were determined using scipy.stats.norm.interval at each time point. Means are only shown if ≥ 9 data points were present within the 1min window and confidence intervals are only shown if ≥ 5 samples were present at a given time point. Activation rates were determined as the slope of the activation curve at its steepest point early on during activation (between 0 and 7 min), as calculated by numpy.gradient.

Data and code availability
All code and extracted numerical data are available freely under the MIT open source license on GitHub at github.com/WhoIsJack/optonotch-adaptation.
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