Diffusion dynamics of CSL in Notch-Off conditions

We first set out to characterize the properties and analyse the kinetic dynamics of CSL in nuclei without endogenous Notch pathway activity using SMLM. We generated a Halo-tagged CSL (Halo::CSL), expressed at endogenous levels from a genomic rescue construct (Gomez-Lamarca et al, 2018) and tracked its behaviour in Drosophila larval salivary glands, whose large nuclei and polytene chromosome make them amenable for live imaging of transcription factors (Lis, 2007). To resolve single molecules of CSL, salivary glands were incubated with a limiting concentration of the Halo ligand TMR and imaged with 10 and 50 ms exposure times for 3–6 min (Video 1). For comparison, we also carried out SMLM of Halo-labelled Histone H2AV in the same tissue (Video 2).

Following SMLM movie acquisition, we performed single molecule localisation using a Gaussian fitting-based approach (Ovesný et al, 2014). Consecutive frame localisations likely to represent the same molecule were then linked into trajectories, by employing a Multiple Hypotheses Tracking Icy-plugin (Chenouard et al, 2013) (Fig 1A). As the molecules are likely to transition through a range of behaviours reflecting their interactions with the chromatin, the trajectories were then analysed to distinguish their properties using two different methods, which ultimately yielded similar conclusions. The first approach deployed a variational Bayesian treatment of Hidden Markov models (vbSPT) (Persson et al, 2013), where the diffusion constants of a particle trajectory can switch randomly according to a Markov process. The analysis uses a specified number of diffusive states and having set a ceiling, the number of coefficients/populations is chosen via model selection. The second approach, DDMap, assumes that trajectories (or subtrajectories) undergo diffusion, subdiffusion or superdiffusion movements (Saxton, 1993; Briane et al, 2018; Salomon et al, 2020). The software assigns a different diffusion coefficient to each trajectory and the value of the diffusion coefficients is not constrained in any way. For more information on the trajectory analysis see the Materials and Methods section.

As a starting point, we compared the behaviour of CSL in Notch-Off conditions to the histone H2AV. Because the majority of histones are integrated into nucleosomes and expected to display bound behaviour we first limited the population number for vbSPT analysis to two, which yielded a slow and a fast state. With 10 ms exposure times, the slow-moving population accounted for 34% of CSL trajectories in comparison to 62% of H2AV trajectories, indicating that a relatively smaller proportion of CSL are retained on the chromatin. With the 50 ms exposure time, a proportion of the fastest moving molecules would not be detected as they become blurred. As expected, the average diffusion coefficient of the fastest molecules population was concomitantly reduced from 1.192 to 0.367 μm²/s for CSL (Fig 1B and Video 3), indicating that the longer exposure times will give more scope for teasing apart different properties among the molecules whose motions are slowed by their interactions with the chromatin.

In order to probe into possible exploratory behaviours manifest by CSL in Notch-Off conditions, a more fine-grained vbSPT analysis of trajectories from the 50 ms exposure times was carried out using four diffusion states, D1–D4, from slowest to fastest diffusion constant. The four states were selected considering the likelihood estimation from the model selection in vbSPT, which indicated that fewer states were less likely. Trajectories were assigned in these four populations, according to their percentage time in each state and their position then mapped onto the nuclei (Fig 1C and D). Some regions were more strongly enriched for D4 fast-moving molecules and likely correspond to regions with lower density of chromatin (Fig 1C). Others were biased towards slower moving molecules although these were widely distributed in clusters throughout. To further characterize the four populations, we analysed displacement (Fig 1F) and angle distributions (Fig 1G). Displacement distributions inform about the range of motion, with small displacements indicating a restricted behaviour, as was the case for the slowest populations, D1 and D2 (Fig 1F). The distribution of angles indicates the extent to which the movement differs from the uniform distribution expected for regular Brownian motion. For example, an accumulation of angles around 180°, known as backwards anisotropy, occurs when molecules are more likely to move backwards than forwards. This compact behaviour suggests constraint or “trapping” of the molecules and was more enriched in the D1 and D2 populations (Ben-Avraham & Havlin, 2000; Liao et al, 2012; Burov et al, 2013; Izeddin et al, 2014).

By combining all these parameters together (diffusion coefficients, displacement, and angle analyses) we identified behaviours characteristic of each population. Those with the smallest diffusion coefficients, D1 and D2, have properties of bound/trapped molecules, with a high degree of anisotropy and little spatial displacement (Fig 1D–G). They accounted for 6% and 19% of the total CSL molecules respectively (Fig 1H). The slightly longer displacements exhibited by D2 molecules (Fig 1F) likely reflect an association with more mobile chromatin and/or local exchange on and off the DNA. The fastest population, D4, accounting for 48% of trajectories, showed properties of more freely diffusing molecules, with less backwards angular anisotropy and large spatial displacements (Fig 1D–G). As noted above, many freely/fast moving molecules in the nucleus will not have been captured with the 50 ms regime. Nevertheless, we refer to the D4 population as “free” as their movements are not demonstrably constrained (Fig 1D–G). Finally, molecules in the D3 population have intermediate characteristics, with less backwards anisotropy and more displacement than the bound populations (Fig 1D–G). These account for 27% and their characteristics suggest an exploratory behaviour, with a mixture of binding/trapping and freer movements (Fig 1E and H).

For comparison we utilised DDMap analysis which assigned a different diffusion coefficient to each trajectory (Fig 1J) and, using a nonparametric three-decision statistical test, classified them as Brownian, sub-diffusive or super-diffusive (Fig 1I). Only 6% of CSL trajectories were classified as sub-diffusive, a proportion close to those classified as “bound” D1 by the vbSPT analysis. The majority of CSL molecules (94%) were identified as Brownian, suggesting that all other CSL molecules have some element of Brownian motion associated with their trajectories (Fig 1K). Not unexpectedly, a negligible number of trajectories were classified as super-diffusive.

Together the results demonstrate that a relatively small proportion of CSL is stably associated with chromatin in the absence of Notch activity. The majority of CSL molecules are more transiently associated with chromatin and/or freely moving.

Notch activity leads to increased binding and exploratory behaviour of CSL

To investigate the effect of Notch activity on CSL we acquired SMLM movies at 50 ms exposure in Notch-On conditions (Video 4), achieved by expressing a constitutively active form of Notch in salivary gland cells. This gives rise to tissues with a steady state “Notch-On,” in which known target genes are transcriptionally active (Gomez-Lamarca et al, 2018; DeHaro-Arbona et al, 2023), that can be compared with the Notch-Off tissues where those are silent. When the trajectories from the Notch-On nuclei were partitioned into four states by vbSPT, the resulting populations had similar diffusions constants to those in Notch-Off conditions (Fig S1A, Table S1A), demonstrating that the overall properties were not substantially altered. However, the proportions mapping to each state differed. First, Notch activation led to a significant drop in the proportion of “free” CSL molecules (from 48% to 32%). Second there was an increase across the other populations, with the proportion of bound molecules (D1 + D2 increasing from 25% to 31%, Fig 2A) and the proportion of exploratory, D3 molecules increasing (from 27.5% to 37%) (Fig 2A, Table S2A).

The increase in CSL binding and exploration was also reflected in the results from DDMap analysis, which yielded a larger proportion of sub-diffusive trajectories in Notch-On (Fig S1C). More striking were the changes in mean diffusion coefficients which decreased significantly in Notch-On conditions (Fig 2B). These changes are consistent with CSL becoming less freely diffusing and instead exhibiting more stable binding behaviour and more exploration of chromatin in Notch-On conditions.

CSL participates in two types of protein complexes. In Notch-Off conditions, CSL partners with Hairless to form a corepressor complex (Morel et al, 2001; Barolo et al, 2002; Yuan et al, 2016). In Notch-On conditions, a fraction of CSL molecules are recruited into a tripartite complex with NICD and the co-activator Mastermind (Petcherski & Kimble, 2000; Nam et al, 2006; Wilson & Kovall, 2006). It is likely that the change in CSL behaviours is related to the nature of the complexes present in the two conditions. We therefore set out to investigate whether the dynamics of Mastermind and Hairless in Notch-On conditions correlated with the different behaviours detected for CSL, by generating endogenously expressed Halo-tagged variants of the two proteins and tracking them with SMLM (Video 5 and Video 6). The trajectories were partitioned into four states using vbSPT, and in all cases the resulting populations had similar diffusions constants consistent with them participating in the same complexes (Fig S1A and B, Table S1A). The diffusion characteristics of Hairless were very similar in both Notch-Off and Notch-On conditions and resembled those of CSL in Notch-Off conditions, (Fig 2A and Table S2), with a relatively large proportion of D4-freely diffusing molecules (48%). Conversely, diffusion characteristics of Mastermind were more closely aligned with those of CSL in Notch-On conditions, with lower proportion of D4 molecules (25%) and a higher proportion of bound molecules (44%). Similar proportions of Mam also exhibited D3, “exploratory,” behaviour (32% Mam versus 37% CSL). Thus, the Notch-induced changes in CSL behaviour are compatible with it being in a complex with Mam, albeit the proportions of Mam with “bound” D1/D2 behaviours (44%) were even greater than for Notch-On CSL (31%) suggesting some of the CSL remains in complexes with its other partner.

To investigate further the change in CSL behaviour in Notch-On conditions, we focused on the more dynamic molecules in the D3 and D4 states and measured their anisotropy to ascertain whether, on average, their movement becomes more compact, which would indicate that some undergo a change in searching behaviour (Fig 2C). Indeed, there was an overall increase in the backwards anisotropy of CSL trajectories in Notch-On conditions, effectively reducing the size of the spaces explored. As with the overall dynamics, these properties were more similar to those of Mam than of Hairless—the latter exhibiting little backwards anisotropy.

These comparisons show that the behaviours of CSL correlate with those of its partners and shift from having more freely-diffusing characteristics in Notch-Off conditions, similar to Hairless behaviour, to having more bound and compact properties in Notch-On conditions, similar to Mastermind.

Notch-On conditions promote recruitment and exploration at a target locus

The global changes in the properties of CSL could in theory increase the rate at which it binds to target sites. To investigate its movement and recruitment in relation to a specific genomic locus that it regulates, we focused on the Enhancer of Split Complex (E(spl)-C) a highly responsive locus containing 11 Notch-regulated genes (Delidakis & Artavanis-Tsakonas, 1992; Knust et al, 1992; Jennings et al, 1994; Bailey & Posakony, 1995; Lecourtois & Schweisguth, 1995; Lai et al, 2000). We have previously generated strains for live imaging E(spl)-C, introducing INT sequences into the 3′ end of the complex and combining this with fluorescently tagged ParB which recognizes INT, enabling us to visualise the locus as a clear “band” in salivary gland nuclei (Fig 3A and B) (Gomez-Lamarca et al, 2018).

Taking a snap-shot of the E(spl)-C at the start and end of each movie, we compared the behaviour of CSL around this locus against behaviour elsewhere in the nucleus (Fig 3). From the density and trajectory maps of CSL, it was already evident that there was a significant enrichment of trajectories around E(spl)-C in Notch-On nuclei (Figs 3A, B, and D and S2A and B). To quantify the locus associated trajectories relative to those elsewhere in the nucleus, we set a distance threshold of 550 nm around E(spl)-C and every trajectory falling within that region was designated as “near” while all other trajectories were designated as “away” (Fig 3B). Firstly, we measured the molecule density (number of trajectories per unit area) near the locus and calculated its ratio to the nuclear density. The ratio was significantly higher in Notch-On conditions (Fig 3C), confirming that Notch activity promoted recruitment of CSL molecules to the target locus. As expected, Mam also became enriched near E(spl)-C in Notch-On condition, indeed to an even greater extent than CSL (Fig 3A and C). Conversely, no enrichment was detected for the co-repressor Hairless for which there was a relatively small number of trajectories present near the locus (Fig 3A and C).

To investigate which type of CSL behaviour was affected, we calculated the enrichment in proportion for each diffusive population near the locus in Notch-On conditions. Of the four populations only the CSL D1 “bound” population showed a robust enrichment in proportion, a pattern that was replicated by the Mam populations. This was accompanied by a relative decrease in the proportion of faster moving D4 molecules (Fig 3E and F). Despite not becoming substantially enriched at the locus (Fig 3A and C), Hairless also exhibited proportionately more bound-like behaviour, evidenced by increased proportions of D1, D2 molecules and reduced proportion of D4. The increase in binding near the locus for all three molecules was also captured by DDMap analysis, both through a slight enrichment of the sub-diffusive population and through a significant decrease in the diffusion coefficients of Brownian trajectories near this region (Figs 3G and S2B and C).

The increase in bound CSL molecules at E(spl)-C in Notch-On conditions is consistent with previous imaging and ChIP data (Krejčí & Bray, 2007; Castel et al, 2013; Wang et al, 2014; Gomez-Lamarca et al, 2018). The fact that there is proportionately more binding for all three molecules, including the corepressor Hairless, suggests that there is a change in the chromatin environment that facilitates the binding or trapping of CSL complexes in that region (Gomez-Lamarca et al, 2018; DeHaro-Arbona et al, 2023).

Notch activity promotes local searching by CSL complexes

The increase in binding of CSL at E(spl)-C in Notch-On conditions led us to question whether there was a change in its local behaviour to favour its recruitment in the vicinity. For example, an increase in the anisotropy of trajectories, would reflect more compact diffusion around the locus that could aid recruitment. We therefore analysed the anisotropy of D3 and D4 trajectories near E(spl)-C in comparison to elsewhere in the nucleus. Based on the anisotropy metric f(180/0), there was a large increase in CSL backwards anisotropy near E(spl)-C (2.75 versus 1.85, Fig 4A). This demonstrates that the anisotropy is not uniform across the nucleus and suggests it is associated with specific regions of the genome that are regulated by Notch activity such as E(spl)-C.

The anisotropy indicates there is extensive “back-tracking” and implies that the effective size of the space CSL explores is reduced, by local trapping or transient binding, which would favour its on-rate at the target locus (Slutsky & Mirny, 2004; Kapanidis et al, 2018; Woringer & Darzacq, 2018; Hansen et al, 2020; Darzacq & Tjian, 2022). If this model is correct, the anisotropy should peak for displacement lengths corresponding to the size of regions where the motion of the molecules is constrained. We therefore asked how anisotropy changed with displacement length, keeping our analysis within a displacement range of 50–350 nm. This provided accuracy by excluding displacements close to/lower than our localisation error (20 nm) (see the Materials and Methods section) and by ensuring sufficient numbers of angles for the longest displacements in the range. First it was evident that the pattern of CSL anisotropy differed near the locus compared to away. Notably, near the locus CSL, acquired a peak of anisotropy between 100–150 nm, suggesting that there is a tendency for CSL molecules to become trapped in zones of that size (Fig 4D). Combined with the fact that anisotropy dropped for longer displacements, it implies a form of local exploration near the locus (Slutsky & Mirny, 2004; Kapanidis et al, 2018; Woringer & Darzacq, 2018; Hansen et al, 2020; Darzacq & Tjian, 2022). A similar behaviour was observed for the co-activator Mam, whose anisotropy also displayed a peak at the 100–150 nm range (Fig 4B and E). In contrast, Hairless showed no similar peak in anisotropy near the locus for any specific displacements (Fig 4C and F) arguing that the corepressor complex lacks the features that favour local searching.

Overall, our results show that Notch activity brings about changes in the behaviour of CSL at target loci. The properties it acquires, of increased binding and a more restricted compact diffusion, resemble those of Mam, consistent with the two forming a complex. Their anisotropic diffusion close to the target locus implies that they engage in local exploration (Izeddin et al, 2014; Hansen et al, 2020; Mazzocca et al, 2021) that could aid their recruitment.

Clustering analysis reveals higher backwards anisotropy near clusters of bound CSL

To investigate whether the searching behaviour observed at E(spl)-C is a more general feature of Notch-On conditions, we asked whether similar anisotropy was present at other genomic locations where CSL exhibits “bound” behaviours. First, we identified clusters of bound CSL (D1 and D2) molecules in each of our datasets (excluding those at E(spl)-C) and then analysed the anisotropy of the more motile populations in relation to those clusters.

A method to detect features, regions of high point densities, in spatial data that has a high degree of “clutter” (Byers & Raftery 1998, see the Materials and Methods section) was used to find clusters of slow trajectories. The bound (D1 and D2) trajectories were described by their average position (barycentre) and then these positions were modelled as a superposition of two spatial Poisson processes: a high intensity Poisson process describing clustered trajectories and a low intensity process describing non-clustered trajectories, (“clutter”). The trajectories belonging to these two classes were distinguished based on their kth nearest neighbour distance to other trajectories. Thus, the distance to the nearest neighbour was calculated for all molecules and they were then divided into two groups: one which had small distance to its kth nearest neighbour (clustered) and one which had large distance to kth nearest neighbour (non-clustered). The analysis remained robust over a range of k values and we focused on k = 11, which identified large and dense clusters, making these regions plausible candidates for other target enhancers (Figs 5 and S3A).

Based on this analysis, clustering of CSL bound molecules was significantly more common in Notch-On nuclei (Fig 5A, C, and E), where the proportion of clustered bound molecules was 1.7-fold higher than in Notch-Off. To analyse the behaviour of molecules close to the clusters we set a 550 nm search radius and captured all D3 and D4 localisations falling within that region (Fig 5B and D). These constituted what we defined as “near-cluster” jumps, while all other jumps were “away-cluster,” and we calculated what proportion of “near” jumps were anisotropic (see the Materials and Methods section). As a control we randomly shifted the position of the clusters and repeated the anisotropy analysis for localisations near the “fake” clusters (see the Materials and Methods section). Our results showed a significantly higher anisotropy in the diffusion properties of molecules near the bone fide CSL clusters compared to those located away from clusters in Notch-On conditions (Fig 5F). Unexpectedly, this difference was also detected in Notch-Off conditions, albeit there were many fewer CSL clusters (Figs 5E and S3B). These results suggest that the change in anisotropy is linked to the clustering of bound complexes rather than to a specific property of the activation complexes themselves. One likely explanation is that the bound clusters are associated with regions of more accessible chromatin, which would provide an environment that favoured searching, giving rise to more anisotropic behaviours. While increased anisotropy was observed near bound clusters regardless of Notch activity status, when comparing the proportion of anisotropic displacements that were located near bound clusters, we found this to be much higher in Notch-On conditions (42.8% versus 13.2%) (Fig 5G). If our bound cluster/open chromatin correlation hypothesis is correct, the accumulation of anisotropic behaviour near these clusters in Notch-On could indicate a mechanism through which local searching in regions of open chromatin enables these activation complexes to efficiently find their target sites.

Experimental animals

Drosophila melanogaster flies, as indicated, were maintained at room temperature (∼20°C) using standard cornmeal food (Glucose 76 g/liter, Cornmeal flour 69 g/liter, Methylparaben 2.5 ml/liter, Agar 4.5 g/liter and Yeast 15 g/liter.) Experimental crosses, from which larvae were collected for dissections, were kept at 25°C.

Generating Halo-tagged protein lines

To generate lines expressing endogenous levels of Su(H)::Halo and Hairless::Halo, we modified the AttB plasmids containing genomic rescue constructs Su(H)-eGFP and Hairless:eGFP, (Gomez-Lamarca et al, 2018). Briefly, eGFP coding sequence was replaced by HaloTag (pFN23K-Halo plasmid, given by St Jonhston lab, G2861; Promega), amplified using primers CACCTAGGATGGCAGAAATCGGTACTGGCTTTCCATTCGACC and CTACGCGTTGCCGGAAATCTCGAGCGTGG for Su(H)::Halo, and primers TTACAGATCTCTGAAATCGGTACTGGCTTTCC and TTTCTAGAGACAGCCGGAAATCTCGAGCGTGG for Hairless::Halo. Plasmids and HaloTag PCR products were digested using AvrII (R0174S; New England Biolabs) and MluI (R0198S; NEB) for Su(H)::Halo, or BglII (R0144L; NEB) and XbaI (R0145S; NEB) for Hairless::Halo. The resulting AttB plasmids were injected into a strain containing phiC31 integrase and AttP site in position 86F8 in chromosome 3 (Bloomington 24749; Su(H)) or position 51D in chromosome 2 (Bloomington stock 24483; Hairless) to generate transgenic Su(H)::Halo or Hairless::Halo flies.

Mam::Halo flies were generated using CRISPR/Cas9 genome engineering (flycrispr.org) to insert the coding sequence of HaloTag into the endogenous Mam gene. Briefly, a plasmid containing homology arms flanking the starting codon of Mam, HaloTag, SV40 and the PiggyBac 3xPax3-dsRED cassette from pHD-ScarlessDsRed (flycrispr.org) was synthesized by NBS Biologicals. Transformants were obtained by co-injecting this plasmid with a pCFD3-dU6:3gRNA plasmid (#49410; Addgene) expressing the gRNA GACGCATTTATGGATGCGGG and screening for 3xPax3dsRED. The 3xPax3-dsRED cassette was excised by crossing with αTub84B-PiggyBac flies (#32070; BDSC). Maps of the homology and gRNA plasmids and final genomic sequence can be found at https://benchling.com/bray_lab/f_/bRaeXvzx-mamhalo-endogenous-tag/.

Salivary gland cultures and Halo ligand treatments

Salivary glands were isolated from third instar larvae grown at 25°. Dissections and mounting in observation chambers were performed as described (Gomez-Lamarca et al, 2018) except for the additional following steps to sparse label with Halo ligand. Glands were incubated for 15 min in TMR Halo ligand (G825A; Promega) diluted in Dissecting medium (Gomez-Lamarca et al, 2018). Concentration of ligand was first adjusted in each case by serial dilutions to reach single molecule resolution which corresponded to a concentration of 10 nM for CSL-Halo and Hairless-Halo, of 50 nM for Mam-Halo and of 0.01–0.02 nM for H2AV-Halo. After incubation the glands were washed 3 × 10 min in Dissecting medium and briefly rinsed in PBS(1X) (#70011044; Thermo Fisher Scientific) before mounting.

SMLM

The custom build microscope and localisation errors were as described in Gomez-Lamarca et al (2018). Samples were continuously illuminated during imaging with a 561 nm excitation wavelength laser to excite the Halo ligand emitting at 585 and a 488 nm excitation wavelength laser to excite the GFP-labelled Locus Tag emitting at 510 nm. Laser power used for imaging with these lasers was ∼500 and 30 W/cm² respectively. For each data set, the region imaged was focused around the nucleus and consisted of a square of ∼40 µm × 40 µm dimensions. The pixel size of acquired movies was 110 nm. Between 4–13 nuclei were imaged for each condition each with 50 ms exposure time for 3.3–6.7 min. For the experiments with 10 ms exposure time, three nuclei were imaged for 2.8–3.3 min.

Trajectory analysis basic pipeline

Following movie acquisition, single molecules were localised with a Gaussian fitting-based approach (Ovesný et al, 2014) which allowed the enhancement of localisation precision to subpixel resolutions of ∼20 nm (Gomez-Lamarca et al, 2018). A multiple hypothesis tracking algorithm was employed for tracking of the molecules, allowing no detection gaps within tracks, using an Icy-plugin based on Chenouard et al (2013). Trajectories consisting of at least four time points were then analysed using two different methods. The first method was used to partition trajectories into distinct diffusive states and was based on variational Bayes analysis (vbSPT) (Persson et al, 2013), where the trajectories were divided in subtrajectories characterised by a Brownian diffusion coefficient. Setting a ceiling of four populations (with the exception of control analysis with H2AV where the ceiling was set to two), the finite number of diffusion coefficients allowed per experiment was chosen via Bayesian model selection, by maximising the score F = lnp(x|N) where p(x|N) is the probability of the data conditioned on the number of states (Persson et al, 2013). For all experiments, the model selected was that of four states. To account for the bias towards slow jumps due to defocalisation (fast molecules leaving the focal plane much quicker than slow ones, Kues & Kubitscheck, 2002; Mazza et al, 2012; Hansen et al, 2018), any analysis involving population proportions was carried out using the whole trajectories, assigning to each trajectory the mode state of its jumps.

The second analysis method was used to examine a wider class of motion types and was based on a Dense Mapping approach (DDMap) (Salomon et al, 2020). As this method uses Langevin equations (Lemons & Gythiel, 1997) and therefore takes into account both diffusion and drift, it enabled us to consider Brownian, sub-diffusion and directed motion (Saxton, 1993). Each trajectory was classified as one of these motion types using a nonparametric three-decision statistical test and a unique diffusion coefficient was calculated for it. DDMap scripts were adapted so that non-spatially averaged diffusion coefficients were calculated. For both trajectory analysis methods, the target locus in each nucleus was detected using image thresholding with Otsu’s method and a 2-D Gaussian smoothing kernel was used for filtering.

Angle and anisotropy analyses

Standard MATLAB procedures were used for angle calculation, as shown in Fig 1G. Angular statistics, including the calculation of the resultant vector, R, were carried out using the MATLAB package CircStat (Berens, 2009). For anisotropy analyses, the fold anisotropy metric f(180/0) was defined and calculated as how many-fold more likely a molecule is to make a step backwards compared to a step forward,f180/0=P180°±30°0°±30°

This definition, and scripts required for this analysis were adapted from Hansen et al (2020). Using only D3 and D4 jumps (as identified by vbSPT analysis) for anisotropy analyses guaranteed the displacements considered to be well above our localisation error (Gomez-Lamarca et al, 2018), ensuring the accuracy of angle calculations. Calculations of f(180/0) against mean displacement were carried out for 50 subsamples using 50% of the data (with replacement). Error bars on Fig 4D–F show SD from these sub-samplings.

Molecule density analysis

Molecule density maps showing the spatial distribution of molecule trajectories were generated using kernel smoothing in MATLAB, with 4 pixel (440 nm) bandwidth (Bowman et al, 1997). The units for all density maps are number of trajectories per 0.0001 μm². The design of the maps was carried out using the MATLAB package ColorBrewer (Stephen23, 2023). Values shown in Fig 3C as “Locus enrichment ratio” represent a fold increase of near-locus density compared to nuclear density and were calculated as follows:No. of trajectories near locusTotal no. of trajectories in nucleus×Nucleus areaLocus area

Locus and nucleus areas were calculated with standard MATLAB procedures, using the convex hull of localisations and masking.

Clustering

Clustering of bound molecules, described by their barycentre (average position), was performed in R using nnclean. It is based on a superposition of random (Poisson) processes model (Byers & Raftery, 1998) and uses the distance of each point to its kth nearest neighbour to distinguish molecules belonging to two Poisson processes: a high intensity (λ₁) Poisson process for clustered trajectories and a low intensity (λ₂) Poisson process describing non-clustered trajectories (Fig S3A shows the histogram of the kNN distances for one data set). The analytical expression of the kth NN distance distribution of a random Poisson process is known to be a transformed gamma distribution,Dk2∼Γ(k,λπ)and the analytical expression of the mixture of two kNN distance distributions becomes:Dk∼pΓ1/2(k,λ1π)+(1−p)Γ1/2(k,λ2π)

Through an expectation-maximisation algorithm, the parameters of the mixture distribution are estimated together with the “missing” data—the indicator if a point belongs to a cluster or not. Results of the clustering are visualised in Fig 5A and C (clutter is shown in dark blue, and clusters in orange). The analysis remained robust over a range of k values.

For anisotropy proportions shown in Figs 5F and G and S3B, a jump of a D3 or D4 trajectory was regarded as anisotropic if the angle it formed with its successive jump was within the range 180° ± 30°.

For each experiment, control analysis was performed in MATLAB by first identifying a region of interest using the convex hull of diffusive (D3 and D4) jumps. The localisation of bound molecules identified as “clustered” was randomly shifted to a different place in the nucleus, in this way the same “cluster shape” was retained for the control analysis and all bound clusters were translated by the same vector. If more than 80% of these molecules remained inside the region of interest after translation, anisotropy analysis was carried out for the diffusive molecules near and away the shifted clusters. The process was repeated 100 times for each movie and mean values were calculated.

Boxplots and statistical tests

For all boxplots, lines across represent the median, crosses represent the mean, boxes 5–95 percentiles and whiskers upper and lower extrema.

For statistical tests involving only one sample, one sample t tests (for normal samples) and Wilcoxon rank-sum tests (for not normal samples) were performed. For statistical tests involving two samples, two sample t tests (if samples were normal) and Mann-Whitney U tests (if samples were not normal) were performed. For paired data (clustering analysis in Fig 5), paired t tests (if samples were normal) and Wilcoxon signed rank tests (if samples were not normal) were performed. Normality of the samples was assessed using Q-Q plots and Shapiro-Wilk tests. Where two samples were compared, equality of variance was also assessed with Bartlett’s test (if samples were normal) and Levene’s test (if samples were not normal). In all cases significance was presented as follows: * for P < 0.05, ** for P < 0.01, *** for P < 0.001. All statistical tests were performed in R.